Influence of Rock Boundary Conditions on Behaviour of Arched and ...

Influence of Rock Boundary Conditions on Behaviour ofArched and Flat Cemented Paste Backfill Barricade Walls

by

Andrew Cheung

A thesis submitted in conformity with the requirementsfor the degree of Master of Applied ScienceGraduate Department of Civil Engineering

University of Toronto

c© Copyright 2012 by Andrew Cheung

ii

Abstract

Influence of Rock Boundary Conditions on Behaviour of Arched and Flat Cemented

Paste Backfill Barricade Walls

Andrew Cheung

Master of Applied Science

Graduate Department of Civil Engineering

University of Toronto

2012

Current design of cemented paste backfill (CPB) barricades tends to be of unknown

conservativeness due to limited understanding of their behaviour. Previous work done

to characterize barricade response has not accounted for the effects of the surrounding

rock stiffness, which can have significant impact on the development of axial forces which

enhance capacity via compressive membrane action.

Parametric analyses were performed with the finite element analysis program Augustus-

2 to determine the effects of various material and geometric properties on barricade capacity.

Equations based on Timoshenko and Boussinesq solutions were developed to model rock

stiffness effects based on boundary material properties. An iterative simulation process

was used to account for secondary moment effects as a proof of concept.

It was found that, for a range of typical rock types, barricade capacity varied signif-

icantly. The commonly made design assumption of a fully rigid boundary resulted in

unconservative overpredictions of strength.

iii

Acknowledgements

Thanks!

No hour of life is lost that is spent in the saddle.

Winston Churchill

CONTENTS iv

Contents

1 Introduction 1

1.1 Motivation for Current Study . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Compressive Membrane Action and Secondary Moment Effects . . 1

1.1.2 Prior Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Current Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Relevant Research 6

2.1 Existing Bulkhead Modelling Efforts . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Ghazi (2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Revell and Sainsbury (2007) . . . . . . . . . . . . . . . . . . . . . 13

2.1.3 Helinski et al. (2011) . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Axially Restrained Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 Su et al. (2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Vecchio and Tang (1990) . . . . . . . . . . . . . . . . . . . . . . . 26

3 Finite Element Modelling 31

3.1 Augustus-2, Response-2012, and Membrane-2012 . . . . . . . . . . . . . . 31

3.2 Typical Augustus-2 Barricade Modelling . . . . . . . . . . . . . . . . . . 34

3.3 Secondary Moment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4 Rock Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5 Arch Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

CONTENTS v

4 Results and Discussion - FEM Validation 59

4.1 Comparison to Su et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Comparison to Vecchio and Tang . . . . . . . . . . . . . . . . . . . . . . 68

5 Results and Discussion - Parametric Modelling 73

5.0.1 Reference Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.1 Barricade Reinforcement Content, ρ . . . . . . . . . . . . . . . . . . . . . 79

5.2 Depth to Centroid of Reinforcement . . . . . . . . . . . . . . . . . . . . . 83

5.3 Barricade Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.4 Barricade Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.5 Concrete Compressive Strength, f ′c . . . . . . . . . . . . . . . . . . . . . 92

5.6 Young’s Modulus of Rock Wall, Erock . . . . . . . . . . . . . . . . . . . . 95

5.7 Arch Angle, α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6 Conclusions 102

7 Recommendations 103

Bibliography 105

Appendices 107

LIST OF TABLES vi

List of Tables

2.1 Specimen properties (a) and reinforcement properties (b) [14] . . . . . . . 22

2.2 Specimen material properties [17]. . . . . . . . . . . . . . . . . . . . . . . 26

4.1 Comparison of results for Su et al. beam A2 . . . . . . . . . . . . . . . . 62

4.2 Comparison of results for Su et al. beam B1 . . . . . . . . . . . . . . . . 64

4.3 Comparison of results for Su et al. beam C2 . . . . . . . . . . . . . . . . 66

5.1 Parameters and associated value ranges . . . . . . . . . . . . . . . . . . . 73

LIST OF FIGURES vii

List of Figures

1.1 Typical reinforced concrete CPB barricade [13] . . . . . . . . . . . . . . . 2

1.2 Net tensile strains at mid-depth of a typical gravity-loaded slab [17]. . . . 3

1.3 Components of compressive membrane action [17]. . . . . . . . . . . . . . 4

1.4 Member subject to eccentric load P over distance e from the centroid.

The internal moment Pe along the member is increased by an additional

moment P∆ as the member deflects by an amount ∆ at mid-height [6]. . 4

2.1 Typical element mesh and support conditions in Ghazi’s Augustus-2 models

[9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Vertical (a) and horizontal (b) reaction forces versus midspan deflection

for Augustus-2 models of beam A-1 [9] . . . . . . . . . . . . . . . . . . . 8


for Augustus-2 models of beam B-1 [9] . . . . . . . . . . . . . . . . . . . 8


for Augustus-2 models of beam C-1 [9]. . . . . . . . . . . . . . . . . . . . 8

2.5 Applied load versus midspan deflection for varying axial and rotational

stiffness values [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6 VecTor4 and Augustus-2 strength predictions versus slab strip aspect ratio

[9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.7 VecTor4 and Augustus-2 response predictions of applied pressure vs midspan

deflection for a test barricade . . . . . . . . . . . . . . . . . . . . . . . . 11

2.8 Applied pressure versus midspan deflection for varying material properties

and boundary conditions [9]. . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.9 Assumed yield line pattern for a simply supported square slab of side length

L with plastic moment mp [12]. . . . . . . . . . . . . . . . . . . . . . . . 13

LIST OF FIGURES viii

2.10 Barricade geometries modelled by FLAC3D [12]. . . . . . . . . . . . . . . 14

2.11 Ultimate loads for simply supported and fixed 5 x 5m square barricades with

barricade-rock interface models as compared to yield line and Australian

yield line solutions [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.12 Normalized barricade capacity vs unconfined compressive strength qucs (a)

and concrete friction angle φ (b) [10]. . . . . . . . . . . . . . . . . . . . . 17

2.13 Normalized barricade capacity vs ratio of modulus E to unconfined com-

pressive strength qucs [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.14 Normalized barricade capacity vs critical plastic strain in shear (a) and in

tension (b) [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.15 Normalized barricade capacity vs barricade arch angle α [10] . . . . . . . 19

2.16 Normalized barricade capacity vs barricade span (a) and height (b) [10]. 19

2.17 Normalized barricade capacity vs barricade height [10]. . . . . . . . . . . 20

2.18 Typical beam dimensions with reinforcement layout [14]. . . . . . . . . . 21

2.19 Schematic of test setup with horizontal and vertical struts at ends providing

axial and rotational restraint; applied load P is on center column stub [14]. 23

2.20 Vertical load and horizontal reaction force versus normalized midspan

deflection for series A beams showing yielding at supports and peak vertical

load [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.21 Normalized applied load, horizontal reaction force, and bending moments

at midspan and at supports versus normalized center deflection [14]. . . . 24

2.22 Geometric, support, and loading overview of specimens [17]. . . . . . . . 27

2.23 Specimen reinforcement details [17] . . . . . . . . . . . . . . . . . . . . . 28

2.24 Test setup for specimens TV2. Specimen TV1 has similar setup without

horizontal restraints [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.25 Load versus midspan deflection for specimens TV1 and TV2 [17]. . . . . 29

2.26 Applied load versus internal forces for specimens TV1 and TV2 [17]. . . . 30

2.27 Crack patterns in specimen TV1 at an applied load of 58kN [17]. . . . . . 30

2.28 Free-body diagram with internal and applied forces and moments used to

calculate secondary (P-∆) moment effects [17]. . . . . . . . . . . . . . . . 30

3.1 Typical program interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 32

LIST OF FIGURES ix

3.2 Modified concrete compressive stress-strain curve with increased post-peak

ductility in strong regions. . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3 Typical barricade model as rendered in Augustus-2 . . . . . . . . . . . . 34

3.4 Concrete material properties interface in Response-2012 . . . . . . . . . . 35

3.5 Augustus-2 model of vertical cantilever used in P-∆ calculations . . . . . 36

3.6 P-∆ geometry of vertical cantilever. . . . . . . . . . . . . . . . . . . . . . 37

3.7 Typical Augustus-2 cantilever element subject to force couple calculated

from P-∆ effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.8 Load versus displacement response of Augustus-2 models with and without

P-∆ effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.9 Curvature plot of example cantilever with horizontal applied load of 100 kN. 39

3.10 Loaded areas for displacement calculations [7]. . . . . . . . . . . . . . . . 42

3.11 Sample discretized displacement field for a rectangular loaded area with

weighting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.12 Given values and fit equation for coefficient C in eq. (3.5) versus aspect

ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.13 Correlation between displacement field and Jaeger methods for given aspect

ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.14 Point load profile used to represent a pure moment loading condition . . 46

3.15 Displacement profile of single point load applied on an infinite plate . . . 47

3.16 Displacement profiles for various discretizations of uniformly distributed

load. Loaded width is 400 mm, representative of a typical barricade . . . 48

3.17 Linearly varying point loads representative of a pure applied moment . . 49

3.18 Displacement profile of a series of eight linearly varying loads simulating

an applied moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.19 Effect of applied moment on slope of rock wall . . . . . . . . . . . . . . . 50

3.20 Effect of rock modulus of elasticity on slope of rock wall . . . . . . . . . 51

3.21 MErockt2

normalized by calculated slope versus barricade width. . . . . . . . 52

3.22 Slope of Timoshenko displacement profile divided by predicted slope for

various barricade widths . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.23 Typical geometry of rotational restraint in Augustus-2 model of barricade 54

LIST OF FIGURES x

3.24 Typical arch model (a) in Augustus-2 with small truss rods (in red) con-

necting rectangular beam elements along top edge (b) and arch angle

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.25 Augustus-2 models used to test use of truss rods in arched elements . . . 57

3.26 Applied load versus vertical tip displacement for normal and eccentric

cantilevers including longitudinal and transverse reinforcement . . . . . . 58

3.27 Applied load versus vertical tip displacement for normal and eccentric

cantilevers including only longitudinal reinforcement . . . . . . . . . . . . 58

4.1 Typical Augustus-2 model of specimen by Su et al . . . . . . . . . . . . . 60

4.2 Load-displacement comparison for Su et al. beam A2 . . . . . . . . . . . 63

4.3 Load-displacement comparison for Su et al. beam B1 . . . . . . . . . . . 65

4.4 Load-displacement comparison for Su et al. beam C2 . . . . . . . . . . . 67

4.5 Augustus-2 model of frame TV2 . . . . . . . . . . . . . . . . . . . . . . . 68

4.6 Load-displacement plot for experiment TV1 and Augustus-2 predictions . 69

4.7 Load-displacement plot for experiment TV2 and Augustus-2 predictions . 70

4.8 Load-axial elongation plot for specimen TV1 and Augustus-2 prediction . 70

4.9 Load-slab end reaction plot for specimen TV2 and Augustus-2 prediction 71

4.10 Load versus lateral column base reaction plot for specimens TV1 and TV2

and Augustus-2 predictions . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.1 Response of reference model . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2 Augustus-2 plots showing internal forces and stresses of critical midspan

element at failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.3 Reference barricade displaced shapes (magnified 10x) and average crack

directions in red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.4 Shear and bending moment diagrams at failure . . . . . . . . . . . . . . 78

5.5 Pressures causing first cracking, yielding, and failure versus reinforcement

content, ρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.6 Effect of varying reinforcement content, ρ . . . . . . . . . . . . . . . . . . 82

5.7 Pressures causing first cracking, yielding, and failure versus bottom clear

cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

LIST OF FIGURES xi

5.8 Effect of varying bottom clear cover . . . . . . . . . . . . . . . . . . . . . 85

5.9 Pressures causing first cracking, yielding, and failure versus barricade

thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.10 Effect of varying barricade thickness . . . . . . . . . . . . . . . . . . . . 88

5.11 Pressures causing first cracking, yielding, and failure versus barricade length 90

5.12 Effect of varying barricade length . . . . . . . . . . . . . . . . . . . . . . 91

5.13 Pressures causing first cracking, yielding, and failure versus concrete comp.

strength f ′c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.14 Effect of varying compressive concrete strength f ′c . . . . . . . . . . . . . 94

5.15 Pressures causing first cracking, yielding, and failure versus Young’s modu-

lus of rock wall, Erock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.16 Effect of varying the rock wall Young’s modulus, Erock . . . . . . . . . . 97

5.17 Arch angle, α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.18 Pressures causing first cracking, yielding, and failure versus arch angle, θ 99

5.19 Effect of varying barricade arch angle, θ . . . . . . . . . . . . . . . . . . 101

LIST OF FIGURES xii

Nomenclature

α Arch angle

m Jaeger coefficient based on aspect ratio of loaded area

λ Aspect ratio of loaded area

ν Poisson’s ratio

ρ Reinforcement content, measured in %

θ Surface rotation

a Horizontal distance from center of end support to rotational restraint rod in

Augustus-2

Aplate Area of loaded region

As,axial Area of axial stiffness rod in Augustus-2

As,rot Area of rotational stiffness rod in Augustus-2

C Axial stiffness coefficient

d Depth from surface of infinite half space where vertical displacement is zero

dv Effective shear depth of member

E Young’s modulus

Es Young’s modulus of steel

Erock Young’s modulus of surrounding rock

f ′c Concrete compressive strength

fy Steel yield strength

LIST OF FIGURES xiii

Frod,r Force in rotational stiffness rod in Augustus-2

G Shear modulus

Kaxial Axial stiffness, measured in N/mm

Krot Rotational stiffness, measured in Nmmmm·rad

Lrod,a Length of axial stiffness rod in Augustus-2

Lrod,r Length of rotational stiffness rod in Augustus-2

Lrod Length of restraint rod

M Applied moment

P Applied load

r Distance of point of interest on plate from applied point load

t Barricade thickness

v Vertical displacement profile

w Loaded width of plate

wp Point displacement in a uniformly loaded area

wavg Average displacement of a rectangular uniformly loaded area

1

Chapter 1

Introduction

1.1 Motivation for Current Study

In an effort to reduce the environmental impact and increase the efficiency of underground

mining operations, mine waste products (tailings) are often mixed with Portland cement

binders to create Cemented Paste Backfill (CPB) which is then pumped underground to

fill existing, open stopes. Reinforced concrete paste barricades (Figure 1.1) are constructed

in these stopes to isolate the poured CPB from neighbouring stopes which may still be

in use. This method of underground waste storage reduces the need for surface tailings

disposal and also provides a degree of support to surrounding stopes as the cement binder

hydrates and the CPB solidifies much like concrete. Prior to hardening, however, CPB

behaves hydrostatically due to its water content and exerts pressure on the surrounding

rock and barricades.

Existing industry design methods for barricades vary. Most barricades are designed

and built very conservatively to account for CPB pressures that may be higher than

assumed and make simplifying assumptions for barricade geometry [12]. Even so, there

are documented cases of barricade failure, making safety a genuine concern [13]. If the

structural behaviour and response of these barricades were well-understood, it would be

possible to make their design and construction more cost and time-efficient.

1.1.1 Compressive Membrane Action and Secondary Moment

Effects

A reinforced concrete member subject to loading will crack on the tension face while the

reinforcement elongates. Typically, strains on the tension face will be larger than those on

Motivation for Current Study 2

Figure 1.1: Typical reinforced concrete CPB barricade [13]

.

the compression face so the average strain at mid-depth will be tensile (Figure 1.2). This

net tensile strain causes the member to become longer as more load is applied. If this

expansion is sufficiently restrained, compressive axial forces will develop in the expanding

member (Figure 1.3a). These compressive forces produce an increase in flexural capacity

as shown by a typical axial load-flexure interaction diagram in Figure 1.3b. As loads

increase and concrete crushes, the only remaining capacity is the reinforcement acting in

tension as the main cable does in a suspension bridge: this is called catenary action.

In CPB barricades, the surrounding rock provides significant resistance to expansion

in the longitudinal or transverse directions. Because of this, the effects of compressive

membrane action are of interest to determine how they affect the strength and design of

barricades. Because the surrounding rock is not infinitely rigid, however, rock stiffness

must also be considered.

While compressive membrane action can increase the flexural strength of axially-

restrained members, increased deflections can give rise to secondary moment effects which

impose additional moment demand. Axial loads imposed over a distance from the member

centroid increase effective moments, causing the member to reach its moment capacity more

quickly [17]. This additional demand is called the P-∆ effect (Figure 1.4). As compressive

axial loads develop in a member subject to membrane action, any displacements will bring


Figure 1.2: Net tensile strains at mid-depth of a typical gravity-loaded slab [17].

about secondary moments which increase moment demand with increasing eccentricity

and axial load. The P-∆ effect is a consequence of the large axial forces in compressive

membrane action and thus must be included in analyses to avoid an overestimation of

member strength.

1.1.2 Prior Research

Barricades, commonly constructed with pumped concrete (shotcrete) around a mesh of

reinforcing steel, can be analyzed with similar techniques to those used for traditional

reinforced concrete structures due to similarities in material, geometry, and loading. In

an effort to characterize the behaviour of barricades to aid in efficient design, existing

research by Ghazi [9] performed at the University of Toronto used proprietary finite element

analysis tools which specifically accounted for the non-linear stress-strain behaviour of

reinforced concrete. Such non-linear behaviour is brought on by cracking which occurs in

virtually all reinforced concrete structures under serviceability loads. Because of this, the

accuracy of conventional linear plane sections remain plane Euler-type analyses cannot

fully characterize the post-cracking behaviour of concrete.

Ghazi’s research found that compressive membrane action and the rotational and axial

stiffness of the surrounding rock all had significant effects on barricade strength [9]. It was

also found that two-dimensional analyses which considered barricades as one-way slabs

yielded similar results to more complex and time-consuming three-dimensional analyses


(a) Restraint and compressive forces from resistanceto slab elongation.

(b) Axial load-moment interaction diagram showingincreased flexural capacity.

Figure 1.3: Components of compressive membrane action [17].

Figure 1.4: Member subject to eccentric load P over distance e from the centroid. The internal momentPe along the member is increased by an additional moment P∆ as the member deflects by an amount ∆

at mid-height [6].

which accounted for two-way slab behaviour. Secondary moment effects (such as the

P-∆ effect) were not considered due to software limitations. Also, more complex model

geometries such as arched fences (which are more common in industry [12]) were not

studied. While the effects of rotational and axial rock stiffness were simulated, their

significance merits further investigation.

Current Study 5

1.2 Current Study

The current study builds upon existing research performed by Ghazi [9] at the University

of Toronto through improved modelling of boundary stiffness as well as various arched

geometries. The proprietary software used by Ghazi, Augustus-2, has since been updated

to improve its accuracy. A parametric study of various geometric and material properties

will be carried out with the software. Its results will be validated through comparison to

existing experimental data and simulation results.

Because barricades are axially restrained, both compressive membrane action and

secondary moment effects should be considered by the simulations. Although Augustus-2

currently does not include secondary moment effects, a manual proof of concept analysis

will include these effects by the addition of applied moments to a simple cantilever model.

The object of this proof of concept is to demonstrate the method’s feasibility as well as

its effects on lowering barricade capacity.

6

Chapter 2

Relevant Research

2.1 Existing Bulkhead Modelling Efforts

2.1.1 Ghazi (2011)

In his Masters thesis, Ghazi investigated the behaviour of CPB barricades using both two

and three-dimensional finite element analyses [9]. Results were compared to measured

field data and laboratory experiments to gauge accuracy and then a parametric study

was carried out to determine the effects of material properties, boundary conditions,

reinforcement content, and geometry on barricade behaviour. Conclusions from the study

indicated that barricade strength was most influenced by the stiffness of the rock boundary

condition. The following is a summary of Ghazi’s research.

Comparison to Field and Experimental Data

Prior to the parametric study, results from the two-dimensional analysis program Augustus-

2 were compared to experimental results from Su et al [14]. These experiments were

conducted on reinforced concrete beams which were axially and rotationally restrained in

a manner similar to the boundary conditions for CPB barricades. Further details on the

experiments can be found in Section 2.2.1.

Comparisons were made between experimental results and Augustus-2 models of three

series of beams with differing geometry and reinforcement content. The Augustus-2

models were restrained in axial and rotational directions with a series of truss rods; axial

and rotational stiffnesses were controlled by changing the cross-sectional area of the rods

(Figure 2.1). Because the tested beams were symmetric about midspan, only half of the

Existing Bulkhead Modelling Efforts 7

beam was modelled. Support conditions at midspan allowed for vertical but not horizontal

displacements on the assumption that any horizontal expansion of the beam would occur

symmetrically outwards from midspan.

Figure 2.1: Typical element mesh and support conditions in Ghazi’s Augustus-2 models [9].

The simulations predicted vertical load-deflection behaviour well, with excellent pre-

dictions of initial stiffness and good accuracy from post-cracking through to failure. In

the models and as with the test data, flexural cracking occurred at midspan and at the

supports followed by first yielding at midspan and then at the supports. Crushing of

concrete at the support was correctly predicted to cause a drop in load capacity and

failure occurred at midspan as with the experiments. Typical load-deflection response for

each of the three series of beams is shown in Figures 2.2, 2.3, and 2.4.

While the vertical load-deflection response was well-modelled, issues were encountered

in predicting the horizontal reaction forces. The axial stiffness values of 1000 kN/mm

reported by Su et al [14] gave poor predictions when replicated in Augustus-2, so the author

adjusted the axial stiffness values by trial and error to obtain an accurate horizontal load-

deformation curve. The calibrated stiffness value which provided an accurate prediction

of load-deformation was similarly accurate for the development of axial force versus

deformation. This discrepancy was due to ambiguity in the original experimental setup:

it was not known whether the 1000 kN/mm value meant that the beam would elongate

by 1mm under a 1000 kN midspan load or if the supports themselves would displace

1mm when subject to a 1000 kN axial load. Axial stiffness values in Augustus-2 which

yielded accurate horizontal load predictions were typically ten to twenty times less than

the specified 1000 kN/mm value. Despite the axial stiffness issues, the Su et al specimens

[14] will again be used for comparison in this thesis due to a lack of relevant experimental

data from other sources.


(a) Vertical reaction force vs midspan deflection (b) Horizontal reaction force vs midspan deflection

Figure 2.2: Vertical (a) and horizontal (b) reaction forces versus midspan deflection for Augustus-2models of beam A-1 [9]


Figure 2.3: Vertical (a) and horizontal (b) reaction forces versus midspan deflection for Augustus-2models of beam B-1 [9]


Figure 2.4: Vertical (a) and horizontal (b) reaction forces versus midspan deflection for Augustus-2models of beam C-1 [9].


(a) Effect of changing axial stiffness values (b) Effect of changing rotational stiffness values

Figure 2.5: Applied load versus midspan deflection for varying axial and rotational stiffness values [9].

Because of the Augustus-2 models’ apparent sensitivity to axial stiffness, the value

was varied for a given model to determine its effect on load-deformation response. As

shown in Figure 2.5a, initial beam stiffness is similar between three varying axial stiffness

values, but lower values result in a drop in load capacity and more pronounced midspan

deflection. First cracking loads remained approximately equal, but first yield loads varied.

A similar analysis was carried out, varying rotational stiffness values. The model was

much less sensitive to changes in rotational stiffness, however at low values premature

beam failure occurred at the supports due to shear (Figure 2.5b).

Analytical Barricade Modelling

Programs Augustus-2 (two-dimensional) and VecTor4 (three-dimensional) were used to

create finite element models of flat test barricades installed in a mine in Turkey. Simulation

results were compared to test data from the barricade installations.

In an attempt to increase efficiency, simulations were performed in both two and three

dimensions to determine whether a simpler, faster two-dimensional analysis could be

performed for a given barricade in lieu of a more complex three-dimensional analysis.

One of the concerns was whether a barricade was governed by two-way slab behaviour,

which is characterized by bending moments of similar magnitude along both the width

and height of the barricade. Such behaviour would necessitate a more complex analysis.

However, since it was established that barricade behaviour in only one principal direction

yielded similar results to two-way slab simulations for many practical cases, a simpler

two-dimensional slab strip analysis was attempted which only considered one-way slab

behaviour. Figure 2.6 shows that as the aspect ratio increases, strength predictions of

a two-way slab analysis quickly approach the results of a one-way slab strip analysis

performed in VecTor4 and Augustus-2, respectively. Two-way predictions of strength


drop off sharply as the barricade aspect ratio approaches 2.0. The one-way results yield

the same strength predictions regardless of aspect ratio because they do not consider the

non-principal dimension of the barricade and its effect on behaviour.

Figure 2.6: VecTor4 and Augustus-2 strength predictions versus slab strip aspect ratio [9].

Figure 2.7 compares both two and three-dimensional model predictions to experimental

results from a test barricade with an aspect ratio (length to height) of 1.89. The test

barricade was loaded in a conventional manner with CPB, but testing was stopped before

failure occurred. Both VecTor4 and Augustus-2 predict a slight increase in strength

beyond the test’s ultimate stopping point as well as accurate behaviour modelling in both

pre and post-cracked states. It is important to note that rock stiffness values were not

provided, so all simulations were performed with calibrated stiffness values that provided

an accurate prediction. This was done in Augustus-2 by changing the cross-sectional

area of the axial and rotational truss rods and done in VecTor4 by assuming a different

compressive concrete strength.

Although the Augustus-2 result is more unconservative than the VecTor4 prediction, it

is expected that the implementation of secondary moment (P −∆) effects in Augustus-2

will result in lower strength predictions as such moments would increase demand on the

structure. The similarities between the Augustus-2 and VecTor4 simulations as well as

their accurate predictions of test data are a promising result. Because VecTor4 simulations

took considerably longer to prepare and execute than their Augustus-2 counterparts,

simulation work in this thesis will be performed with Augustus-2.

A sensitivity analysis was conducted in VecTor4, varying boundary conditions, concrete

strength, and reinforcement content. As seen in Figure 2.8a, barricade strength is very


Figure 2.7: VecTor4 and Augustus-2 response predictions of applied pressure vs midspan deflection for atest barricade

sensitive to boundary conditions, where full fixity grants over a three-fold increase in

ultimate pressure resistance and a two-fold increase in maximum deflection. Barricades

with a higher concrete compressive strength were both stiffer and stronger, while deflections

were relatively unaffected (Figure 2.8b). For the compressive strength analyses, the

boundaries were allowed to rotate. There was almost no difference in strength or stiffness

of a reinforced barricade compared to an unreinforced one (Figure 2.8c); it was concluded

that if the surrounding rocks were stiff enough to provide support to the barricade, the

reinforcement ratio had a small effect on behaviour. Although not explicitly mentioned

by Ghazi, it could be inferred that the boundary conditions for the reinforcement ratio

simulations were fully fixed based on his conclusions.


(a) Varying boundary conditions (b) Varying concrete strength

(c) Varying reinforcement content

Figure 2.8: Applied pressure versus midspan deflection for varying material properties and boundaryconditions [9].


2.1.2 Revell and Sainsbury (2007)

The following is a summary of a paper published by Revell and Sainsbury discussing

existing barricade design methods in industry as well as results from the authors’ numerical

barricade models [12].

American Concrete Institute (ACI) Code Design

Bulkhead design based on ACI structural requirements often idealizes the bulkhead

as a linear-elastic, simply supported beam for purposes of determining imposed loads.

Reinforcement is then detailed based on ACI code limits for standard reinforced concrete

structures. Because the actual rock wall boundary of the bulkhead in situ is partially

fixed as opposed to simply supported, the assumed loading is generally higher than in

reality which results in an overly conservative design.

Yield Line Theory

Traditional yield line theory for slabs assumes boundary conditions, hinge lines, and

a compatible flexural failure mechanism (Figure 2.9). As the slab reaches failure, it

is assumed to deflect plastically and the ultimate load is calculated using equilibrium

equations or the principal of virtual work. While yield line analysis is an acceptable and

established method for reinforced concrete slab design, the method does not account for

the increased strength brought on by compressive membrane action in barricades nor

does it cover all possible loading and support conditions. The theory also ignores the

possibility of shear failure. As such, barricade design based on yield line theory provides

conservative estimates of strength.

Figure 2.9: Assumed yield line pattern for a simply supported square slab of side length L with plasticmoment mp [12].


Australian Yield Line Design

Current barricade design methods for many Australian companies are based on a modified

form of yield line theory originally used to estimate the strength of masonry barricades.

However, the authors state that there is no theoretical basis for applying yield line theory

to unreinforced, orthotropic masonry walls. The basis for this modified theory is stated

by the authors as being of ambiguous origin.

Numerical Modelling and Results

The numerical modelling program FLAC3D was used to model barricades of varying

geometries (Figure 2.10). Results were compared to yield line theory with simply supports,

the modified Australian yield line method, and physical experiments on similar structures.

All models used the same material properties: concrete with an unconfined compressive

strength of 30 MPa using a Mohr-Coulomb strain-softening model to simulate post-peak

loss of strength. The simulated concrete was reinforced with fibers to increase ductility,

but traditional and wire mesh reinforcement was omitted. The interface between the

barricade and the surrounding rock surface was also modelled and studied.

Figure 2.10: Barricade geometries modelled by FLAC3D [12].

Simulation results of a variable thickness 5 x 5m barricade model matched yield line

theory exactly for the case of simply supported boundaries; both of these cases predicted

a much lower ultimate load than that predicted by the modified Australian yield line

method. Additional results for the same barricade with fully fixed boundary conditions


predicted ultimate failure loads significantly greater than those predicted by both yield

line and Australian methods (Figure 2.11). This was attributed to the contribution of

compressive membrane action to the strength of the barricade which yield line theory does

not consider. The barricade-rock interface model which allowed for both bending and

shear interaction was found to provide a more realistic failure mechanism when compared

to simple or fully fixed supports. Barricade models of a horseshoe shape or those that were

arched into the direction of the load were also found to be stronger than flat barricades.

Figure 2.11: Ultimate loads for simply supported and fixed 5 x 5m square barricades with barricade-rockinterface models as compared to yield line and Australian yield line solutions [12].

Program verification was done by modelling constructed experimental barricades and

comparing simulation results to experimental data gathered from mines. Two cases were

explored: a pair of bulkheads tested in 1990 and 1991 and an actual barricade failure

during a fill operation in 2006. In both cases, the FLAC3D simulations provided accurate

predictions of the failure mode (propagation of yielding from the rock-wall interface) and

failure pressure. However, the authors noted that there was a substantial amount of

uncertainty in the representation of material properties and loading conditions.


2.1.3 Helinski et al. (2011)

The following is a summary of a paper published by Helinski et al. which presents results

of a three-dimensional parametric study carried out on models of arched fiber-reinforced

concrete and waste rock barricades [10]. The work builds upon the previously summarized

paper by Revell and Sainsbury [12]. Because this thesis focuses on concrete barricades,

the waste rock barricade content of this paper is not summarized.

The numerical modelling program FLAC3D was once again used for the parametric

study. The fiber-reinforced concrete was simulated as a continuum with smeared reinforce-

ment using a Mohr-Coulomb model which also accounted for linear elastic strain-softening.

It should be noted that the simulations did not represent any form of traditional bar

reinforcement as is typically used in the construction of concrete barricades. Sliding

interfaces were used between the barricade and the surrounding rock wall. Pressures

imposed by the CPB were applied uniformly across the barricade surface. The parametric

study covered two main sensitivites: material and geometric. It was found that uncon-

fined concrete compressive strength, barricade arc radius, and barricade alignment were

important factors in barricade capacity.

Material Sensitivity

Several material properties of the fiber-reinforced concrete were varied to determine

their effects on strength: unconfined compressive strength, internal friction angle, elastic

modulus, strain-softening characteristics, and the barricade-rock wall interface.

Barricades with higher concrete compressive strengths were able to carry more load

before failure as could be expected (Figure 2.12a). The internal friction angle of the

concrete, which was found to increase as curing progressed in physical specimens, was

found to have little effect on barricade capacity due to unconfined compression being the

critical failure mode (Figure 2.12b). However, the capacity did decrease slightly as friction

angle increased; this was attributed to a decrease in the major and minor principle stress

capacities.

Changes in elastic modulus contributed little to barricade strength; values were

increased and decreased by 50% with minimal change in capacity (Figure 2.13). The

observed slight increase in capacity with increasing modulus was attributed to the reduction

in strain softening for a stiffer material after yielding.

The strain softening model used in the simulations linearly decreased the cohesive

(shear) and tensile strength of the fiber-reinforced concrete over a specified critical plastic


(a) Capacity vs qucs (b) Capacity vs φ

Figure 2.12: Normalized barricade capacity vs unconfined compressive strength qucs (a) and concretefriction angle φ (b) [10].

Figure 2.13: Normalized barricade capacity vs ratio of modulus E to unconfined compressive strengthqucs [10].

strain to represent the reduction in strength after yielding. A lower value of critical plastic

strain resulted in a faster decrease in strength after yielding, representative of a more

brittle material; a higher value provided increased ductility. The effects on both shear and

tensile due to changes in critical plastic strain were studied separately. It was found that

increased material shear ductility significantly increased barricade capacity; allowing for a

10% plastic shear strain after yield provided a threefold increase in strength (Figure 2.14a).

This ductility allowed for a more uniform redistribution of stresses after material yielding

along the barricade abutments which resulted in higher capacity. Varying the critical

plastic strain for tensile material strength had little impact on the ultimate capacity of

the barricade due to the arched geometry of the wall having a shearing failure mechanism

at the abutments (Figure 2.14b).


(a) Capacity vs εcrit−shear (b) Capacity vs εcrit−shear

Figure 2.14: Normalized barricade capacity vs critical plastic strain in shear (a) and in tension (b) [10].

Because the quality of the surrounding rock can vary from site to site, the strength of

the barricade-rock wall interface was varied in simulations. It was found that the strength

of the interface had little effect on ultimate barricade capacity, which suggested that

barricade strength was primarily a function of its material and not the condition of the

boundary.

The material sensitivity studies were conducted under the fundamental assumption

that the concrete was fiber-reinforced with no traditional reinforcing bars present. This

is not truly representative of actual constructed barricade walls which include cages of

reinforcing bars. Also, based on previous findings by Ghazi [9], boundary stiffness can

significantly affect barricade strength. This parametric study did not consider these

effects.

Geometric Sensitivity

Barricades with different curvatures, spans, heights, and alignments were tested to

determine their effects on capacity.

The curvature of the wall was varied as a function of the arc angle α as shown in

Figure 2.15. Strengths are normalized by the capacity of a straight barricade. For low

values of α, the barricade is relatively flat and is more prone to bending and tensile failure.

Thrust forces from the surrounding rock developed as α increased and the wall became

more arch-like, resulting in concrete compression failures. Large values of α resulted in

lower thrust forces and larger shearing forces which caused the barricades to fail in shear

and tension along the barricade-rock wall interface. The optimal range of arc angles α


was suggested to be approximately 60-80◦ to induce a preferred compression failure. This

would lessen the impact of the strength of the surrounding rock, which can vary between

locations.

Figure 2.15: Normalized barricade capacity vs barricade arch angle α [10]

.

The span of the barricade was varied between 4 to 6 m for a constant arc radius. For

a given radius, a longer span would result in a larger arc angle and vice versa. If an

appropriate arc radius is selected, barricade capacity varies by as little as -5% to 10%

(Figure 2.16a). Similarly, barricade height was found to have almost no effect on strength

(Figure 2.16b), as almost all of the stresses are transferred through the stiffer arch to the

surrounding rock instead of to the vertical connections.

(a) Capacity vs span (b) Capacity vs height

Figure 2.16: Normalized barricade capacity vs barricade span (a) and height (b) [10].

Due to inconsistencies in construction methods, barricades are sometimes built with

the arch direction not perfectly perpendicular to the direction of the applied pressure.


This misalignment was also studied and found to be a significant issue: a 25% offset (e.g.:

a 1 m offset over a 4 m span), for example, reduced the capacity of the barricade by

approximately 30% (Figure 2.17).

Figure 2.17: Normalized barricade capacity vs barricade height [10].

The study of geometric sensitivities presented is thorough, with many parameters

studied. However, the sample sizes of some analyses are small: only three different span

lengths were simulated for each of two different barricade radii for parameters such as

bulkhead span, height, and misalignment. As barricade strength did not vary much

between the three samples, though, this is a minor issue. Of more concern is the ability

of the FLAC3D software to model cracked fibre-reinforced concrete.

Axially Restrained Beams 21

2.2 Axially Restrained Beams

2.2.1 Su et al. (2009)

Su et al. tested twelve reinforced concrete beams representative of two-bay floor beams

after the removal of a center supporting column. Test results indicated that compressive

membrane action contributed significantly to the strength of axially restrained beams. A

parametric study of reinforcement ratio, span-to-depth ratio, and loading rate was also

conducted. The following is a summary of test results and discussion by the authors [14].

This same paper was also discussed by Ghazi [9]. The test results from this paper will be

used to validate the finite element analysis program Augustus-2 prior to the parametric

CPB barricade study.

Experimental Program

Twelve beams were constructed in three series: A, B, and C (Table 2.1). Each series

of beams had the same cross-sectional dimensions with varying reinforcement content.

Span lengths remained constant except with series B beams, which had varying span

lengths to study the effect of span-to-depth ratio on capacity. A sample beam with

reinforcement layout is shown in Figure 2.18. Closely spaced hooped bars were used for

shear reinforcement to avoid premature shear failure.

Figure 2.18: Typical beam dimensions with reinforcement layout [14].

To simulate the axial restraint provided by columns at each end of the beam, the column

stubs at both ends were secured with pinned steel sockets which were in turn connected

to vertical and horizontal struts to impose axial and rotational restraints. Roller bearings

were used on the side faces of the center column stub to prevent out-of-plane rotations


Table 2.1: Specimen properties (a) and reinforcement properties (b) [14]

(a) Specimen properties

(b) Reinforcement properties

during loading. Figure 2.19 shows a schematic of the test setup. Displacement-controlled

loads were imposed downwards onto the center column stub through a servo-controlled

actuator braced against a loading frame.

The horizontal and rotational stiffnesses of the supports were measured as 1000 kN/mm

and 17 500 kN-m/rad, respectively, but as shown by Ghazi [9] these quoted stiffness

values were ambiguously defined and needed to be changed to achieve similar results in

simulation models of the beams. As such, a separate set of experimental data by Vecchio

and Tang [17] will also be used to validate Augustus-2.


Figure 2.19: Schematic of test setup with horizontal and vertical struts at ends providing axial androtational restraint; applied load P is on center column stub [14].

Experimental Results and Discussion

Under loading, first flexural cracking occurred at the interface of the beam and center

column stub. As expected, cracking loads were lower for beams with longer spans. First

cracking was followed by cracking in the beam on top of the side supports. Horizontal

reaction forces, indicative of the onset of membrane action, began to increase after flexural

cracking.

First yielding of the reinforcement occurred at midspan due to positive bending;

yielding at the supports followed due to negative bending. Horizontal reaction forces

continued to increase past the peak imposed load until concrete crushing occurred

at midspan. As midspan deflections increased, axial forces began to transition from

compression to tension as compressive membrane action gave way to tensile catenary

action where the loads were being carried primarily by the reinforcement in tension. This

transition to catenary action resulted in a slight increase in the vertical load but only after

a large drop in capacity due to concrete crushing. Failure occurred due to rupturing of

the bottom reinforcement at midspan due to flexure. A sample plot showing both vertical

load and horizontal reaction forces versus midspan deflection is shown in Figure 2.20.

Beam load capacities were calculated using a classical plastic collapse mechanism

which assumed plastic hinges at midspan and at the supports without considering the

contributions of membrane action or shear. These capacities were then compared to

experimental results; a strength enhancement factor was calculated as the ratio of peak

experimental load to peak calculated load. This factor was found to range from 1.53 to

2.63, indicating a significant increase in flexural strength due to compressive membrane

action.

Contrary to Ghazi’s findings [9], the effects of axial stiffness were found to have little

effect on specimen strength when calculated using an analytical model based on plastic

analysis for longitudinally restrained one-way slabs. An 80% drop in support stiffness

yielded only a 10% drop in predicted ultimate load capacity.


Figure 2.20: Vertical load and horizontal reaction force versus normalized midspan deflection for series Abeams showing yielding at supports and peak vertical load [14].

The effects of axial restraint on internal beam forces was also investigated: axial forces

and moments in specimen B3 were measured and normalized by corresponding calculated

peak capacities for a plastically analyzed beam without membrane action. In Figure 2.21,

the internal midspan moment M , support moment M ′, and axial force N are normalized

by plastic midspan capacity M0, plastic support capacity M ′0, and maximum compressive

axial force Nmax. The applied load P was normalized by Pyu, the load at which the plastic

collapse mechanism formed without membrane action. Any of these normalized ratios

can be considered to be a strength enhancement effect if the values are greater than 1.0,

which would be indicative of the beam supporting more load or internal forces than a

traditional plastic analysis would allow.

Figure 2.21: Normalized applied load, horizontal reaction force, and bending moments at midspan and atsupports versus normalized center deflection [14].


Of note is the peak value of P/Pyu which is less than the peak values of M/M0 and

M ′/M ′0. This is representative of the P-∆ effect, which increases the effective moment

demand on the beam due to load path eccentricities. This led to the load P reaching its

maximum value before maximum bending moments were achieved as effective moments

were higher than those produced by the applied load.


2.2.2 Vecchio and Tang (1990)

To investigate the effects of compressive membrane action in reinforced concrete slabs,

two plane frame specimens representative of a collapsed warehouse structure were built

and tested at the University of Toronto. The following is a summary of the test results

and discussion by the authors [17]; the results will be used to validate the finite element

analysis program Augustus-2 prior to the parametric CPB barricade study. The authors’

simulation results, while representative of specimen behaviour, will not be discussed.

The warehouse that collapsed was a four-storey reinforced concrete structure with

slab floors supported by a series of columns. At the time of collapse, the estimated load

on several slab bays of the third floor was over 48 kN/m2 while the design load was only

10.8 kN/m2; this increase in strength was attributed to compressive membrane action and

studies were performed to determine its contributions to the strength of axially restrained

members. The authors also wanted to determine whether a two-way slab system such as

that in the warehouse could be modelled with a plane frame both physically and with

software simulations.

Experimental Program

Two half-scale models of the warehouse floor were constructed as shown in Figure 2.22a

with similar reinforcement percentages and layouts to the actual structure (Figure 2.23

and Table 2.2). Both models were identical, but one specimen (TV2) was fixed against

horizontal displacement while the other (TV1) remained free to expand longitudinally

under vertical loading. The slab ends of both specimens were fixed against vertical

deflection and the column bases were fixed against horizontal and vertical displacements

but free to rotate (Figure 2.22b).

Table 2.2: Specimen material properties [17].

The test setup is shown in Figure 2.24. The columns were supported on pin-roller

assemblies which were free to move horizontally while maintaining the same relative

distance from each other by way of displacement-controlled actuators. Two 25mm steel

rods were anchored to the slab ends and to a strong floor to prevent vertical displacement.


(a) Dimensions of slab strip specimens(b) Support and loading conditions

Figure 2.22: Geometric, support, and loading overview of specimens [17].

To ensure that slab TV2 did not displace horizontally, a displacement-controlled actuator

was used to maintain zero displacement of the slab end. The other end of the TV2 slab

was braced against a strong wall. Vertical loads were applied to the center of the frames

with two displacement-controlled actuators bearing on a spreader beam to simulate a

uniform line load across the width of the slab.

Experimental Results and Discussion

In both slabs, first flexural cracking was observed at midspan followed by transverse

flexural cracks at the supports. After yielding of the bottom reinforcement at midspan,

radial cracks began to form on the top slab surface near the columns. An actuator

malfunction resulted in premature failure of specimen TV1 after formation of radial

cracks near the columns, but TV2 was tested to failure. In slab TV1, decreases in slab

stiffness were evident upon first cracking as well as first yielding of the reinforcement at

midspan while the stiffness of TV2 did not drop until close to first yielding (Figure 2.25).

The stiffness of TV2 was similar to that of TV1 prior to first cracking, but was greater

afterwards owing to the effects of membrane action. Because TV1 failed prematurely due

to equipment malfunction, the difference between the full load-deformation response of

TV1 and TV2 could not be determined.

The lateral reaction forces in the column bases increased similarly throughout loading

for both specimens, indicating the small contribution of the columns to lateral slab

restraint (Figure 2.26b). The horizontal reaction force in TV2 (not present in TV1 as it

was free to move horizontally) increased more quickly after first cracking, showing the

onset of compressive membrane action and explaining the increase in stiffness seen in

Figure 2.25. Near ultimate loads, the axial compressive force in the slab reached almost 4.5


Figure 2.23: Specimen reinforcement details [17]

times the applied load (Figure 2.26a). Because horizontal restraint forces imposed by the

columns (Figure 2.26b) were similar between specimens, the majority of the compressive

membrane action was induced by the horizontal slab restraints in TV2.

For a given load, reinforcement strains at both midspan and at the supports in

specimen TV1 were higher than those in TV2. Cracking patterns in both specimens

were indicative of one-way behaviour: cracks on the top and bottom of the slabs formed

transversely across the entire width (Figure 2.27) with radial cracking near the columns

only occurring at advanced load stages.

Secondary moments due to load eccentricity increased along with axial load and

midspan displacement; their negative effects on strength were calculated using free-body


Figure 2.24: Test setup for specimens TV2. Specimen TV1 has similar setup without horizontalrestraints [17].

Figure 2.25: Load versus midspan deflection for specimens TV1 and TV2 [17].


(a) Load versus horizontal restraint force in TV2 (b) Load versus lateral column restraint force

Figure 2.26: Applied load versus internal forces for specimens TV1 and TV2 [17].

Figure 2.27: Crack patterns in specimen TV1 at an applied load of 58kN [17].

diagrams (Figure 2.28) and found to consume approximately 20% of flexural capacity. It

is important, therefore, to properly account for secondary (P-∆) effects in the simulation

of lightly reinforced structures subject to membrane action.

Figure 2.28: Free-body diagram with internal and applied forces and moments used to calculatesecondary (P-∆) moment effects [17].

31

Chapter 3

Finite Element Modelling

3.1 Augustus-2, Response-2012, and Membrane-2012

As with any useful model or simulation, accurate and precise results are essential. Prior to

cracking under load, reinforced concrete behaves in a fashion which is easy to predict with

linear relationships and is well-understood. However, after a reinforced concrete member

cracks, its behaviour can only be characterized by non-linear relationships which are

complex and difficult to model. One example of a finite element analysis program which

is able to model reinforced concrete structures is Augustus-2, developed by Professor

Evan Bentz at the University of Toronto. Augustus-2 is able to generate accurate results

for models ranging from individual reinforced concrete members to complex structures

[2]. In order to ensure accuracy, concrete members built for experiments were modeled in

Augustus-2 and the analysis results confirmed with experimental ones.

Augustus-2 directly models the behaviour of reinforced concrete accurately after crack-

ing when it transitions into the non-linear regime [5]. Elements use a fibre model for axial

loads and moments as well as the Modified Compression Field Theory (MCFT) for shear

response. The MCFT is a proven model [3] for predicting the shear response of reinforced

concrete sections and is the basis for shear design in the Canadian Standards Association

Standard A23.3 - Design of Concrete Structures as well as the American Association

of State Highway and Transportation Office Bridge (AASHTO) Load Resistance Factor

Design (LRFD) Bridge Design Specifications. More information regarding finite element

formulations in Augustus-2 can be found in the theses of Yeung [18] and Ganji [8].

Augustus-2 models are a combination of beam and column Response elements and

Membrane joint regions defined respectively in programs Response-2012 and Membrane-

2012. Additional truss rod elements can be used by creating a standard reinforced concrete

Augustus-2, Response-2012, and Membrane-2012 32

section in Response-2012 with the desired steel rod area and using the STEEL flag when

building the model to ignore the surrounding concrete. Typical program interfaces are

shown in Figure 3.1. All three programs were developed by Bentz for structural simulation

and analysis purposes. Models are defined in a text file using a series of nodes connected

by Response and Membrane elements. Each Response beam element is defined as a

two-dimensional cross section with configurable parameters including material properties

and reinforcement detailing. While Response-2012 is capable of performing sectional and

member analyses by itself, it is incapable of doing so with elements consisting of more

than one member.

(a) Membrane-2010 (b) Response-2012

(c) Augustus-2012

Figure 3.1: Typical program interfaces

Elements defined in Membrane-2012 are three-dimensional wall elements with rein-

forcement detailing in longitudinal and transverse directions. Membrane elements are

used at joint regions between beams and columns in order to model the intersection of

longitudinal reinforcement from perpendicular axes.

In order to prevent a physically unlikely shear failure in Augustus-2 models near sup-

ports, the corresponding strong beam sections in Augustus-2 were transversely reinforced

beyond their normal level. This was because the equations used in Augustus-2 to model

Augustus-2, Response-2012, and Membrane-2012 33

shear behaviour do not consider strut-and-tie style strength mechanisms (arch action)

that will be present near supports or concentrated loads. In addition, due to the confining

effect of the support or load application points, it is appropriate to increase the post-peak

ductility of the concrete in this region. In this thesis, approximately 0.5% of transverse

reinforcement was included in models areas dv from the face of the support or the location

of applied loads. Also, the default concrete stress-strain curve is changed to that shown

in 3.2. These strong sections extend an approximate distance dv from any support or

applied load.

Figure 3.2: Modified concrete compressive stress-strain curve with increased post-peak ductility in strongregions.

Typical Augustus-2 Barricade Modelling 34

3.2 Typical Augustus-2 Barricade Modelling

The typical Augustus-2 beam model used to simulate a two-dimensional strip of a CPB

barricade is shown in Figure 3.3. The beam height is representative of the thickness of

the barricade; applied pressures from the CPB act vertically in the model on the top

surface of the beam. All simulations are performed for a 1 metre section of barricade

height which corresponds to a beam width (in and out of the page) of 1 metre.

Figure 3.3: Typical barricade model as rendered in Augustus-2

The rock walls surrounding the barricade are modelled with strong end supports

connected to steel truss rods which act as rotational and axial restraints. The supports

are larger Response elements which have a significantly higher capacity (10 000 MPa

compressive and tensile strength) to prevent failure at the ends. The degree to which

the model is restrained is based on the cross-sectional area of the bars; this is further

discussed in Section 3.4.

The beam is composed of various Response elements, each with its own reinforcement

and concrete profile (Figure 3.4). The reinforcement can be laid out and varied to

approximate the reinforcement content of a series of typical barricades. As mentioned in

Section 3.1, strong Response-2012 elements are used up to an approximate distance dv

from the supports and point load to prevent premature shear failure which would not

occur in reality.

Typical Augustus-2 Barricade Modelling 35

Figure 3.4: Concrete material properties interface in Response-2012

Beam cross-sections and material properties of the concrete and reinforcing steel are

defined in Response-2012. While the software is capable of handling a variety of different

and more complex cross-sectional shapes (I-beams, T-beams, etc.) only rectangular (beam

elements) and circular sections (for truss rods) are used in these simulations.

Secondary Moment Effects 36

3.3 Secondary Moment Effects

As shown by Vecchio and Tang (Section 2.2.2), secondary moment effects (i.e. the P-∆

effect) have a significant weakening effect on capacity in axially restrained beams. This

effect is typically eclipsed by the benefits provided by compressive membrane action,

but should be included in analyses in order to prevent an overestimation of strength.

Augustus-2 does not currently account for secondary moment effects in its analyses. In

order to facilitate its inclusion in future versions of the software, a proof of concept analysis

is performed to show the likely method by which the P-∆ effect will be implemented.

A simple vertical cantilever model in Augustus-2 is the basis for this proof of concept

(Figure 3.5). It is fixed at its bottom while a constant vertical load is applied at the top,

in the middle of the element. A monotonically increasing horizontal load is then applied

to the cantilever which causes lateral displacement. Since the P-∆ effect is not currently

included in analyses, this model would not be subject to any additional moment demand

despite the applied axial force.

Figure 3.5: Augustus-2 model of vertical cantilever used in P-∆ calculations


To account for the increased moments in the beam due to this axial force, an iterative

process is used which, for a given applied load, imposes an additional moment on

each element equal to the axial force P multiplied by the distance ∆ for that element

(Figure 3.6). As each element is of a finite height, ∆ is taken as the distance from the

middle of the element to the line of action of the axial force P . The moment is imposed

in the Augustus-2 model by applying a force couple F on the top and bottom nodes of

each element (Figure 3.7). This couple acts across the element width h and thus applies

a moment P∆ = Fh to both the top and bottom of each element. For a given element,

these applied forces are self-equilibrating and thus will not result in an imbalanced sum

of forces.

Figure 3.6: P-∆ geometry of vertical cantilever.

Figure 3.7: Typical Augustus-2 cantilever element subject to force couple calculated from P-∆ effect.


Because the inclusion of the P-∆ moments would cause additional lateral displacements

to occur, the analysis must be run multiple times to determine the changed displacements

for each node in the model. Once the new lateral displacements are found, the force

couples on each element are updated and the model run again at the given horizontal

load. When the displacements no longer change between iterations, the process has

converged to a correct value of additional imposed moment due to the P-∆ effect. For

the example shown, between two to three iterations were required for each load stage to

reach convergence.

Figure 3.8 shows the load-displacement response of the test cantilever in Augustus-2

both with and without P-∆ effects. If P-Delta effects are considered, there is a loss of

beam capacity after first cracking through to failure. The approximate loss in capacity is

5%; this is considered to be low, as Vecchio and Tang calculated an approximate drop of

20% of flexural capacity in their experiments [17].

Figure 3.8: Load versus displacement response of Augustus-2 models with and without P-∆ effect.

As a confirmation of the results generated by Augustus-2 for the example cantilever,

the lateral displacement of its tip at a horizontal load of 100 kN is calculated with

the Moment-Area theorem. The curvature plot of the beam is shown in Figure 3.9

with simplified curvature shapes to simplify Moment-Area calculations. With these

simplifications, the displacement is calculated as:


Figure 3.9: Curvature plot of example cantilever with horizontal applied load of 100 kN.

Area A =0.273 · 4500

2= 614.3

Displacement A =614.3 · 4500 · 2

3= 1.843 mm

Area 2 = 0.273 · 5500 = 1502

Displacement 2 = 1502

(5500

24500

)= 10.89 mm

Area 3 =(3.625− 0.273)5500

2

Displacement 3 = 9218

(4500 +

2

35500

)

Total horizontal tip displacement = 1.843 + 10.89 + 75.28 = 88.0 mm


This tip displacement calculated with the Moment-Area theorem is within 1% of

the Augustus-2 result of 88.8 mm. Therefore, the simulation results can be considered

accurate.

Rock Stiffness 41

3.4 Rock Stiffness

As found by Ghazi [9], the stiffness of the rock into which the barricade is anchored has a

large influence on barricade strength. Ghazi’s simulations varying support stiffness showed

that barricade capacity could increase over three-fold between flexible and stiff boundary

conditions. More flexible boundary conditions also induced yielding of reinforcement at

lower midspan deflections. The research, however, did not determine actual rock stiffness

based on material properties, but rather assumed various values of stiffness in a parametric

study.

In order to better predict the effects of rock stiffness, equations are derived and then

used in Augustus-2 simulations. A combination of prior works by Timoshenko [16]; Jaeger

[11]; and Davis and Selvadurai [7] are used to derive the stiffness equations based on rock

material properties and barricade geometry. The rock walls are assumed to be linear

elastic semi-infinite homogeneous half-spaces, or infinitely large plates of infinite depth.

Two stiffness terms are considered: axial and rotational. In both cases, rock displacements

are found and then compared with deformations or rotations to determine a stiffness

term.

Axial Rock Stiffness

Davis and Selvadurai [7] present a series of equations to find the displacement at any

point in a loaded area on an infinite plate which is derived from an integration of the

classic Boussinesq solution. The derivation begins with the displacement w at a corner

A of a triangular area on a plate of dimensions a > b uniformly loaded under stress σ

(Figure 3.10a) given in eq. (3.1). The plate has shear modulus G and Poisson’s ratio ν.

wp =σ(1− ν)a

2πGsinh-1

(b

a

)(3.1)

Superimposing two triangles and reversing variables a and b gives the displacement

at the corner of a rectangular-shaped load (Figure 3.10b), which is more commonly

encountered:

wp =σ(1− ν)a

2πG

[sinh-1

(b

a

)+b

asinh-1

(ab

)](3.2)

Rock Stiffness 42

It is now possible to find the displacement at any point in a rectangular loaded area by

superimposing the displacements from four smaller sub-rectangles as shown in Figure 3.10c

using eq. (3.2) for the appropriate corner of each sub-rectangle.

(a) Triangular loaded area in equation(3.1)

(b) Rectangular loaded area in equation(3.2)

(c) Superimposed rectangles tofind displacement at any point.

Figure 3.10: Loaded areas for displacement calculations [7].

To determine a proper axial stiffness expression (Kaxial, measured in N/mm) for use

in Augustus-2 models, the displacement of a loaded area under a given load must be

determined. With eq. (3.2), it is possible to determine a displacement field under a

loaded area by discretizing the area into a number of evenly spaced points and finding

the displacement at each point (Figure 3.11).

A weighted average displacement under the entire plate can be found by accounting

for the fact that displacements at the four corners and sides of the loaded area have a

smaller effective ‘influence’ area: 14

at the corners and 12

along the sides. Thus, the average

displacement wavg for a loaded rectangular area is

Rock Stiffness 43

Figure 3.11: Sample discretized displacement field for a rectangular loaded area with weighting.

wavg =

14

4∑i=1

wi + 12

m∑j=1

wj +n∑

k=1

wk

4 +m+ n(3.3)

where m and n are the number of side nodes and interior nodes, respectively.

While this method is derived from the classical Boussinesq solution, it would be time-

consuming to set up the discretized displacement field determine the average displacement

for loaded areas of different dimensions and aspect ratios. A simpler equation by Jaeger

[11] gives the average deflection under a loaded rectangular plate of area Aplate on a

half-space as:

wavg =m(ΣP )(1− ν2)Erock

√Aplate

(3.4)

and can be rewritten in terms of the plate aspect ratio λ (longer to shorter dimension)

as

wavg = m√λ

(ΣP )(1− ν2)Erock

(3.5)

where m is a coefficient and ΣP is the total applied load. The coefficient m is given

by Jaeger [11] only for certain plate aspect ratios ranging from 1 to 100, but an equation

(Figure 3.12) can be fitted to the given values of m multiplied by√λ such that eq. (3.5)

can be used for any aspect ratio between the limits 1 to 100. Note that for a value of

λ = 1, the value of m is 0.95 [11].

Rock Stiffness 44

The fitted equation for C = m√λ as a function of plate aspect ratio λ is:

C = 0.6017 ln(λ) + 0.8941 (3.6)

which has a R2 value of 0.999 can be rewritten and simplified as:

C = 1.4logλ+ 0.9 (3.7)

while maintaining a R2 value of 0.950. Eq. (3.5) can then finally be rewritten in

stiffness form (Kaxial, units N/mm) as:

ΣP

wavg

= Kaxial =Erock

C(1− ν2)(3.8)

Figure 3.12: Given values and fit equation for coefficient C in eq. (3.5) versus aspect ratio.

While this solution proposed by Jaeger is convenient, it is presented in his book [11]

with no derivation. Also, the source of the coefficient m is not explained. To confirm that

eq. (3.5) gives accurate displacements, solutions were compared to those given through

the previously developed displacement field method (eq. (3.3)) for all aspect ratios with a

given coefficient of m by Jaeger. As shown in Figure 3.13, the correlation between answers

calculated with both methods is almost exact. Therefore, eq. (3.5) can be considered as

accurate.

To determine the cross-sectional area of the axial restraint rod, As,axial (Figure 3.3, in

Augustus-2 that would give an equivalent stiffness to eq. (3.8), eq. (3.8) is equated to the

traditional axial stiffness term for an elastic member AEL

:

Rock Stiffness 45

Figure 3.13: Correlation between displacement field and Jaeger methods for given aspect ratios.

As,axialEs

Lrod,a

=ΣP

wavg

=Erock

C(1− ν2)(3.9)

The first and third terms can be rearranged to obtain a term for the required amount

of steel As,axial:

As,axial =Erock

Es

Lrod,a

C(1− ν2)(3.10)

Rock Stiffness 46

Rotational Rock Stiffness

The rock wall’s rotational stiffness was determined through use of Timoshenko’s equations

for the vertical displacement profile of an infinitely large plate under a point force [16]. A

series of linearly varying point loads simulating a moment (Figure 3.14) is applied to a

semi-infinite surface and the resulting displacements from each point load are superimposed

to create a displacement profile. The slope of this profile is then compared to the imposed

moment to determine the rock’s rotational stiffness.

Figure 3.14: Point load profile used to represent a pure moment loading condition

The process begins with a general definition of the moment M per unit height of the

barricade (units Nmmmm

) applied to the rock wall:

M = Krotθ (3.11)

where Krot is the rotational stiffness term for the rock wall and θ is the amount of

rotation in the rock wall due to the imposed moment. This is analogous to the general

axial stiffness equation P = Kaxial∆.

If the rotation θ of the rock wall can be found for a given applied moment M , then

the rotational stiffness is

Krot =M

θ(3.12)

In order to find θ, Timoshenko’s equation for the vertical displacement profile v

(Figure 3.15) of an infinitely large plate under a single point load is used [16]:

v =2P

πElog

d

r− (1 + ν)P

πE(3.13)

where P is the magnitude of the point load; d is the depth from the surface at which

vertical displacement is arbitrarily assumed to be zero; and r is the distance of the point

of interest of the plate from the load. While with eq. (3.13) it is possible to determine the

Rock Stiffness 47

Figure 3.15: Displacement profile of single point load applied on an infinite plate

displacements of any point in the infinite plate, only the plate’s surface displacements are

of interest. Therefore, r is taken to be the distance from a point on the plate’s surface to

the point load.

The variable d introduces an arbitrary aspect to eq. (3.13) which can present problems

if absolute displacements are desired, as the choice of a zero-displacement depth causes

the value of v to vary significantly. This is why eq. (3.13) was not used to determine axial

stiffness in the previous section. However, since the only value of interest to the rotational

stiffness is the slope of the displacement profile, any chosen value of d will suffice. Since

the loads remain the same, the slope of the profile will remain the same regardless of the

chosen depth d.

The displacement calculated by eq. (3.13) is undefined directly underneath the point

load, as the distance r becomes zero. This problem is addressed by calculating the

displacement field with a sufficiently small increment of r to closely approximate the

displacement under the load.

In order to accurately represent a displacement profile of a uniformly distributed load

with a series of point loads, multiple profiles were plotted, each with the same total load

but a different number of loads over a constant width. As seen in Figure 3.16, fewer loads

result in a peaked profile which is not representative of an applied moment condition. A

larger number of loads yielded a smoother displacement profile; nine point loads provided

an acceptable balance of accuracy and calculation efficiency. In the case of the linearly

varying load profile, the middle load would have been zero by symmetry so eight equally

spaced loads were used instead to avoid redundancy.

Rock Stiffness 48

(a) Profile with three loads across width (b) Profile with five loads across width

(c) Profile with seven loads across width (d) Profile with nine loads across width

(e) Profile with eleven loads across width

Figure 3.16: Displacement profiles for various discretizations of uniformly distributed load. Loaded widthis 400 mm, representative of a typical barricade

A general set of equations was developed to determine the magnitude of each point

load in Figure 3.17 where P is the magnitude of the end loads and w is the loaded width

of the plate (equivalent to the thickness of a barricade).

The slope of the linear variation is 2Pw

and each load is an equal distance w7

apart. The

equation of the load variation is P − 2Pwx, where x is the distance along the width of the

loaded area. The total moment imposed by the loads in Figure 3.17 is:

M = Pw +

(P − 2P

w

)5w

7+

(P − 4P

7

)3w

7+

(P − 6P

7

)w

7(3.14)

Rock Stiffness 49

Figure 3.17: Linearly varying point loads representative of a pure applied moment

which simplifies to

P =49M

84w(3.15)

Eq. (3.15) gives the value of P in Figure 3.17 for a given moment M and loaded

width w with which the complete series of point loads can be calculated. Following this,

eq. (3.13) is used to calculate the displacement profile for each point load; these profiles

are then superimposed to generate a complete profile for a pure applied moment condition

(Figure 3.18). A linear fit of the resulting profile across the width of the loaded area

shows that the profile itself is approximately linear as would be expected; the slope of

this profile is thus the true rotation of interest, θ, in eq. (3.12). A barricade bearing on

the rock surface and applying a rotation would also be subject to large compressive forces

(from membrane action) which would maintain contact between the two. Thus, the two

surfaces should be expected to deform together prior to inelastic behaviour.

With the slope of the rock wall now calculated based on a linear fit to Timoshenko’s

theoretical displacement equations [16], the next step is to develop a general equation

for the slope of the rock wall based on applied moment, rock material properties, and

geometry of the barricade. The end goal is to determine the required rotational stiffness

of the Augustus-2 model to accurately represent the rock wall boundary based on the

aforementioned properties. The equation developed is compared to the theoretical

Timoshenko solution in order to determine accuracy.

The initial assumptions were that the slope of the rock wall was directly proportional

to the applied moment M (as before, per unit height) and inversely proportional to the

rock modulus of elasticity Erock; a higher moment would cause higher rotations while a

Rock Stiffness 50

Figure 3.18: Displacement profile of a series of eight linearly varying loads simulating an applied moment

higher modulus would stiffen the rock and reduce rotations. A larger barricade would

also decrease rotations because a given moment imposed by the barricade would be

spread over a larger area. Other factors investigated were the Poisson’s ratio of the rock,

second moment of area of the barricade, and barricade aspect ratio, but they showed no

meaningful correlation with the slope.

As shown in Figure 3.19, the slope of the displacement profile is directly proportional

to the applied moment M . For example, a doubling of moment doubles the slope of the

wall. In Figure 3.20, the slope of the rock wall is inversely proportional to the rock’s

modulus of elasticity Erock: a doubling of Erock halves the slope.

Figure 3.19: Effect of applied moment on slope of rock wall

Rock Stiffness 51

Figure 3.20: Effect of rock modulus of elasticity on slope of rock wall

Dimensionally, since the slope of the displacement profile is in radians (unitless), an

inverse squared distance would be required to satisfy this given the existing moment and

modulus relationship as such:

[θ] =moment/unit height

modulus× distance2=

[Nmmmm

Nmm2mm2

](3.16)

As the barricade comes under pressure and rotates against the rock wall, it does so

across its thickness. Therefore, it can be expected that the thicker the barricade, the more

resistant to rotation it will be. If a comparison is made between the term MEt2

, where t is

the thickness of the barricade, and the associated theoretical rotation from Timoshenko

using the same geometry and material properties, an approximately constant relationship

is found (Figure 3.21). This factor increases slightly with increasing thickness. According

to Helinski et al [10], typical bulkheads are usually built with a thickness between 200-400

mm. This corresponds to a dimensionless factor in Figure 3.21 between approximately

2.09 and 2.17. If this factor is simplified to 2.2 for all practical thicknesses, the following

relationship can be developed for the slope of the rock wall subject to applied moment

from an abutting barricade:

θ =2.2M

Erockt2(3.17)

or

Rock Stiffness 52

M =Erockt

2

2.2θ (3.18)

Figure 3.21: MErockt2

normalized by calculated slope versus barricade width.

The results of eq. (3.17) are compared to the actual slopes calculated from a linear fit

of the Timoshenko displacement profile in Figure 3.22 for a range of barricade thicknesses

from 100 to 800 mm. In all cases, the predicted slope is greater than the slope calculated

from the displacement profile. This would result in a lower predicted rock wall stiffness, a

conservative result.

With eq. (3.12), eq. (3.17) can be rewritten in stiffness form (Krot, units Nmmmm·rad) as:

Krot =Erockt

2

2.2(3.19)

To determine the cross-sectional area of the rotational restraint rods, As,rot (Figure 3.3,

eq. (3.12) is used with the following equations based on the geometry of the rotational

restraints in the Augustus-2 model (Figure 3.23)used to represent a barricade:

Frod,r = θaAs,rotEs

Lrod,r

(3.20)

M = Frod,r · 2a (3.21)

Equating eqs. (3.20) and (3.21) yields

Rock Stiffness 53

Figure 3.22: Slope of Timoshenko displacement profile divided by predicted slope for various barricadewidths

M = 2a2θAs,rotEs

Lrod,r

(3.22)

Substituting eq. (3.18) into eq. (3.22) yields

Erockt2

2.2θ = 2a2θ

As,rodEs

Lrod,r

(3.23)

Solving eq. (3.23) for As,rot and removing θ results in the following expression:

As,rot =Erock

Es

Lrod,rt2

4.4a2(3.24)

Rock Stiffness 54

Figure 3.23: Typical geometry of rotational restraint in Augustus-2 model of barricade

Arch Modelling 55

3.5 Arch Modelling

Previous work done by Ghazi [9] investigated the behaviour of flat bulkheads which were

simpler to model but more susceptible to tensile-related failures on the exterior bulkhead

face. In theory, a bulkhead arched towards the direction of the CPB pressure would be

stronger than a flat profile due to an arch’s ability to carry loads primarily in compression.

Since concrete is significantly stronger in compression than in tension, this arch effect

is desirable. This increase in strength, however, is balanced by the need for a strong

support at the base of the arch to resist its sideways thrusting action and sliding shear

along the rock wall. The level of restraint provided against these spreading forces by the

surrounding rock walls is therefore more important for arched barricades than for flat

ones. Bulkheads with arched profiles are commonly used in industry and the effects of

curvature on barricade strength were previously studied by Helinski [10].

A parametric study of the effects of arch geometry on barricade strength will be

carried out in this thesis. A limitation of the Augustus-2 modelling software is that it

can only employ rectangular, triangular, or rod elements. A program was written in

MATLAB to create an approximation of an arched structure out of a series of rectangular

and triangular elements based on user-defined parameters of horizontal arch length L,

barricade thickness t, and arch angle α (Figure 3.24). This program then outputs node

and element assignments in text format as required by Augustus-2 to create the arch

model.

The initial models used alternating rectangular Response beam elements and triangular

Membrane wall elements to form the arch (Figure 3.24). However, the aspect ratio of

the triangular Membrane elements was large, making the elements very narrow. This

yielded poor results in simulation, so truss rods connecting the outer nodes of the arch

model were used instead. A concern was that truss rods could transmit axial forces

but had no way of transmitting shear between elements. If an arch were shear-critical,

this may not be reflected in a model using truss rods. To verify that eccentric beam

elements connected by truss bars would provide similar results as a straight beam with no

special connections, a comparison was made between a standard cantilever and one that

was slightly askew but connected with truss bars and having the same effective length

(Figure 3.25). The eccentricity of the test cantilever was varied by changing the angle

between beam elements, ω, to determine its effect on behaviour. The same beam elements

were used in both models, so reinforcement layout was identical. Both cantilevers were

subject to point loading at their ends.

Arch Modelling 56

(a) Typical arch model

(b) Enlarged view of connecting truss bar elements

(c) Arch angle, α

Figure 3.24: Typical arch model (a) in Augustus-2 with small truss rods (in red) connecting rectangularbeam elements along top edge (b) and arch angle (c)

Two cases were tested: eccentric beams with typical longitudinal and transverse

reinforcement and eccentric beams which were shear-critical and had no transverse

reinforcement. In both cases, multiple element angles were tested. Figure 3.26 shows the

change in load-deformation response of eccentric cantilever models in Augustus-2 compared

Arch Modelling 57

(a) Reference cantilever model

(b) Eccentric cantilever model using truss rods (in red) to connect rectangular elements

Figure 3.25: Augustus-2 models used to test use of truss rods in arched elements

to a normal cantilever; all models had both longitudinal and transverse reinforcement

present. As the angle ω between beam elements increases, the response becomes somewhat

less accurate as can be expected. However, the difference is minimal even with an 8

degree angle between beam elements. As a typical arch model has element angles typically

between 1 to 4 degrees, using truss rods instead of actual triangular Membrane elements

would yield acceptably accurate results.

Figure 3.27 shows the load-deformation response for eccentric cantilevers which are

shear critical at the fixed end due to a lack of transverse reinforcement. This case

was tested to determine if truss rods provided an acceptable prediction of shear-critical

behaviour. Behaviour of the eccentric cantilever beams is almost indistinguishable from

the normal case until an element angle of 8 degrees. At this point, shear is no longer

fully transmitted from the support to the neighbouring element, resulting in continued

deformation in a fashion similar to that of the transversely reinforced beam previously

tested which failed in flexure. Based on these results, an arch with an angle between

beam elements of greater than 6 degrees may yield inaccurate results. However, as most

arches in the parametric study have element angles less than 4 degrees, simulation results

can still be considered acceptable.

Arch Modelling 58

Figure 3.26: Applied load versus vertical tip displacement for normal and eccentric cantilevers includinglongitudinal and transverse reinforcement

Figure 3.27: Applied load versus vertical tip displacement for normal and eccentric cantilevers includingonly longitudinal reinforcement

59

Chapter 4

Results and Discussion - FEM

Validation

Before a parametric study of CPB barricades can be performed with Augustus-2, the

program must first be validated through comparison to existing experimental results.

In this section, Augustus-2 models of specimens tested by Su et al. [14] and Vecchio

and Tang [17] will be compared to corresponding experimental data to gauge simulation

accuracy. Modelling details will be included in each section.

4.1 Comparison to Su et al.

Three series of beams were tested by Su et al. to investigate the effect of axially-restrained

beams. A summary of the experimental program and results can be found in Section 2.2.1.

The Augustus-2 models were meshed with Response-2012 elements with the same

reinforcement content as the specimens (Table 2.1)). The center column stub was removed,

as the larger cross-section at midspan would have resulted in stiffer simulation response

due to the neglect of yield penetration in the model. Because the test regions of interest

in the specimens were the clear spans between the column stubs, changing the height of

the midspan stub was deemed acceptable. The end column stubs were reinforced more

heavily in the model than in the specimen to ensure that they would not fail or crack

prematurely and affect simulation results.

Rotational and axial restraints were provided by truss rods with a cross-sectional area

corresponding to the desired stiffness. As opposed to determining a stiffness value based

on boundary properties as in Section 3.4, Su et al. published values of 1 000 kN/mm

Comparison to Su et al. 60

axial stiffness and 17 500 kNm/rad rotational stiffness. As mentioned in Section 2.2.1, it

is unclear how these stiffness values are defined; the assumption is that the given force

or moment was required to move the support by a unit displacement or rotation. The

expressions to determine the required truss rod cross-sectional area are simpler than those

derived in Section 3.4:

As,axial =KaxialLrod

Es

(4.1)

As,rot =KrotLrod

2a2Es

(4.2)

The geometry for eq. (4.2) is identical to that in Figure 3.23.

A typical Augustus-2 model is shown in Figure 4.1. The ends of the truss rods are

fixed against horizontal and vertical displacements, while the end supports are fixed

only against vertical displacements and are allowed to rotate about their centerline and

move longitudinally. The center of the beam is only permitted to displace vertically to

prevent any simulation instabilities. As the model is symmetric about its centerline, any

displacements will also be symmetric; the midspan restraints will not affect results. The

circular nodes shown in Figure 4.1 are Augustus-2 conditional nodes which allow elements

of different sizes to interface with each other. The conditional nodes distribute all their

forces to designated neighbouring nodes in proportion to their relative separation.

Figure 4.1: Typical Augustus-2 model of specimen by Su et al

The load-deflection results presented by Su et al. [14] compare favourably to those

from Augustus-2 simulations, but only after the axial stiffness values were significantly

reduced from those specified by the authors. As previously mentioned in Section 2.2.1

and as mentioned by Ghazi [9], the given stiffness values of 1000 kN/mm and 17 500

kN-m/rad were ambiguously defined and could also be difficult to measure in a laboratory

environment. In order to obtain accurate results with Augustus-2, the cross-sectional


area of the axial stiffness rod was reduced almost twenty-fold from 1000 mm2 to 60 mm2.

This corresponded to an axial stiffness reduction of 94 percent. Because this model was

not sensitive to changes in rotational stiffness, no adjustments in the rotational rods were

required. Comparisons between Augustus-2 and experimental results of one beam from

each of the series A through C are presented; simulation results and behaviour are typical

of all beams in each series. In all specimens, failure occurred due to flexure at midspan,

where the bottom reinforcement ruptured.


Specimen A2

Figure 4.2 compares results from beam A2 and includes Augustus-2 results using both

the author-specified axial stiffness values and the adjusted values which yield accurate

results. Augustus-2 accurately predicts both the load-displacement behaviour and the

development of horizontal restraint forces in the beam when the single axial stiffness value

has been calibrated. As shown, however, simulations performed with given stiffness values

result in an overly stiff and brittle beam with an over-prediction in capacity. Table 4.1

compares various experimental results to Augustus-2 predictions, which are generally

accurate. Of note is Augustus-2’s under-prediction of cracking load, which is inaccurate

but conservative.

The horizontal forces in the Augustus-2 prediction transition from net compression to

net tension at the second drop in load capacity, something that is not reflected in the

experimental data. In the simulation, the second drop in capacity occurs when the bottom

steel in the element adjacent to the supports ruptures under negative moment. This local

effect was an unintended by-product of joining the smaller beam element with the larger

support element. Because the longitudinal reinforcing steel was not contiguous between

the two elements, this caused a local stress concentration in the bottom reinforcement

which effectively terminated before it reached the support.

As with the experiment, failure of beam A2 in Augustus-2 was due to flexure when

the bottom steel at midspan ruptured.

Table 4.1: Comparison of results for Su et al. beam A2

Experiment Prediction exppred

Cracking load (kN) 30.0 13.3 2.26Load at support yielding (kN) 148.0 102.3 1.447Peak load (kN) 221.0 231.5 0.955Deflection at peak load (mm) 56.4 55.16 1.023Horizontal reaction at peak load (kN) 318 366.5 0.868Maximum horizontal reaction (kN) 324.0 358.7 0.903Deflection at max horiz reaction (mm) 59.3 55.5 1.069


0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reactio

n force (kN)

Midspan displacement / beam height

Test results

Given stiffness

Adjusted stiffness

(a) Vertical load versus normalized midspan displacement

‐750

‐650

‐550

‐450

‐350

‐250

‐150

‐50

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reactio

n force (kN)


Test results

Given stiffness

Adjusted stiffness

(b) Horizontal reaction force versus normalized midspan displacement

Figure 4.2: Load-displacement comparison for Su et al. beam A2


Specimen B1

Figure 4.3 compares results from beam B1 and includes Augustus-2 results using both the

author-specified axial stiffness values and the adjusted values which yield accurate results.

Augustus-2 accurately predicts the load-displacement behaviour and the development of

horizontal restraint forces in the beam when axial stiffness values have been adjusted. As

shown, however, simulations performed with given stiffness values result in an overly stiff

and brittle beam with an over-prediction in capacity. The inaccuracy is not as severe as

with beam A2, however.

The transition from net compression to tension after the second drop in capacity is

present again as with specimen A2 due to the discontinuous longitudinal steel between

cross-sections of different heights.

Table 4.2 compares various experimental results to Augustus-2 predictions, which are

generally accurate but again under-predict first cracking loads and over-predict both the

horizontal reaction at peak load and maximum horizontal reaction.

As with the experiment, failure of beam B1 in Augustus-2 was due to flexure when


Table 4.2: Comparison of results for Su et al. beam B1


Cracking load (kN) 13.0 7.90 1.646Load at support yielding (kN) 105.0 85.0 1.235Peak load (kN) 125.0 155.0 0.806Deflection at peak load (mm) 100.0 105.8 0.945Horizontal reaction at peak load (kN) 211 303 0.696Maximum horizontal reaction (kN) 225 326 0.690Deflection at max horiz reaction (mm) 146.0 148.1 0.986


0

20

40

60

80

100

120

140

160

180

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reactio

n force (kN)


Test results

Given stiffness

Adjusted stiffness


‐500

‐400

‐300

‐200

‐100

0

100

200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reactio

n force (kN)


Test results

Given stiffness

Adjusted stiffness


Figure 4.3: Load-displacement comparison for Su et al. beam B1


Specimen C2

Figure 4.3 compares results from beam C2 and includes Augustus-2 results using both the

author-specified axial stiffness values and the adjusted values which yield accurate results.

Augustus-2 accurately predicts the load-displacement behaviour and the development of

horizontal restraint forces in the beam when axial stiffness values have been adjusted. As

shown, however, simulations performed with given stiffness values result in an overly stiff

and brittle beam with an over-prediction in capacity. The inaccuracy is not as severe as

with beams A2 and B1, however.

As with specimen A2, the discontinuous longitudinal reinforcement between cross-

sections of different heights near the supports causes a local stress concentration in the

bottom reinforcement of the beam element, causing it to rupture prematurely.

According to the authors, the C series of specimens had varying loading rates which

affected the first cracking load. This could account for some of the inaccuracy in the

Augustus-2 prediction of cracking load in Table 4.3.

As with the experiment, failure of beam C2 in Augustus-2 was due to flexure when


Table 4.3: Comparison of results for Su et al. beam C2


Cracking load (kN) 9.1 3.8 2.4Load at support yielding (kN) N/A 40.4 N/APeak load (kN) 64.9 69.1 0.941Deflection at peak load (mm) 33.5 53.76 0.623Horizontal reaction at peak load (kN) 96.4 129.0 0.747Maximum horizontal reaction (kN) 117.0 116.5 1.004Deflection at max horiz reaction (mm) 65.4 59.8 1.094


0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reactio

n force (kN)


Test results

Given stiffness

Modified stiffness


‐200

‐150

‐100

‐50

0

50

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reactio

n force (kN)


Test results

Given stiffness

Modified stiffness


Figure 4.4: Load-displacement comparison for Su et al. beam C2

Comparison to Vecchio and Tang 68

4.2 Comparison to Vecchio and Tang

Two reinforced concrete frames were tested to investigate the membrane effect in axially-

restrained beams. Both frames were identical in geometry but had different restraint

conditions: frame TV1 was free to expand in the axial direction while frame TV2 was

axially restrained to induce compressive membrane forces. A summary of the experimental

program and results can be found in Section 2.2.2.

The Augustus-2 models were meshed with Response beam and column elements and

Membrane joint regions with the same reinforcement content as the specimens (Figure 2.23

and Table 2.2)). Both models were identical save for the restraint conditions (Figure 4.5),

as with the original experiments. Model TV1 was free to expand horizontally while TV2

was restrained in the same direction to prevent axial expansion. In both cases, however,

rigid truss rods were attached to the slab ends to restrain vertical end movement but

still allow for horizontal expansion. Another rigid truss rod connected the bases of the

two pin-ended columns to ensure zero relative displacement between them but still allow

for horizontal movement. Additional horizontal restraints were added at the midspan of

both models as a precaution to prevent any horizontal shifting. Since the models were

symmetric, these midspan restraints did not affect horizontal expansion. The frames were

point-loaded at midspan.

Figure 4.5: Augustus-2 model of frame TV2

Figure 4.6 shows the load-displacement response of frame TV1 as modelled in Augustus-

2 compared to the original experimental data. In the experiment, the specimen failed

prematurely due to an equipment malfunction. The Augustus-2 prediction is conservative

and over-predicts the frame stiffness both before and after cracking. As beam stiffness is

difficult to predict in software, the result can be considered acceptable. Because of the

TV1’s premature failure, no peak load comparisons could be made. If the displacements

from the Augustus-2 prediction are multiplied by a factor of 1.7 (Figure 4.6), the results

become far more accurate. A similar factor has also been found to work in other test

comparisons [1].


Figure 4.6: Load-displacement plot for experiment TV1 and Augustus-2 predictions

Figure 4.7 shows the load-displacement response of frame TV2 as modelled in Augustus-

2 compared to the original experimental data. As frame TV2 was restrained from axial

expansion, compressive membrane action as well as secondary moment effects (P-∆) were

present. Because Augustus-2 does not yet account for secondary moment effects which

would weaken response, the prediction is stronger and stiffer particularly as the peak

load is reached. If the same 1.7 factor is applied to the displacement predictions, the

results are again quite accurate, however the weakening due to the P-∆ effect has still

not been accounted for. This factor should be further examined in the future, as there

have been previous analyses performed by the author and others which exhibit the same

phenomenon.

Figure 4.8 shows the applied load versus total lateral slab end displacement for

specimen TV1 and the Augustus-2 prediction. The slab is predicted to not expand

axially until a load of approximately 20 kN which results in a stiffer prediction than

the experimental data. Because specimen TV1 failed prematurely, experimental data is

incomplete.

Figure 4.9 shows the applied load versus lateral slab end reaction force for specimen

TV2 and the Augustus-2 prediction. The prediction is acceptable but induces lower

axial loads in the slab for a given applied load. Because higher compressive membrane


Figure 4.7: Load-displacement plot for experiment TV2 and Augustus-2 predictions

Figure 4.8: Load-axial elongation plot for specimen TV1 and Augustus-2 prediction


forces would provide a larger increase in strength, it would be expected that the lower

simulated axial forces would result in a weaker slab. However, the prediction in Figure 4.7

shows that the Augustus-2 simulation is stronger than the experiment. This suggests that

secondary moment effects may play a significant role in strength reduction, as they were

not taken into account in simulations.

Figure 4.9: Load-slab end reaction plot for specimen TV2 and Augustus-2 prediction

Figure 4.10 shows the applied load versus lateral reaction at the column base for

specimens TV1 and TV2 and their associated Augustus-2 predictions. Both Augustus-2

predictions for TV1 and TV2 are accurate. This also illustrates the small contribution of

columns to providing axial restraint, as the lateral column reactions for both specimens

are almost identical. The predominant source of compressive membrane forces is the

restraint provided by the slab boundary conditions.


Figure 4.10: Load versus lateral column base reaction plot for specimens TV1 and TV2 and Augustus-2predictions

73

Chapter 5

Results and Discussion - Parametric

Modelling

To determine the sensitivity of a typical barricade to a variety of geometric and material

properties, a parametric analysis was carried out in Augustus-2. Reinforcement content;

clear cover; concrete compressive strength; barricade thickness and length; Young’s

modulus of the surrounding rock; and arched walls of various curvatures were tested.

The reference model was similar in geometry and reinforcement content to a previously

constructed barricade at the Cayeli Bakir mine in Turkey which was studied by Thompson

et al. [15]. In each test case, only one parameter was varied while the others remained

identical to the reference model. The parameter ranges are shown in Table 5.1.

Table 5.1: Parameters and associated value ranges

Parameter Unit Reference

Barricade thickness mm 100 200 300 400 500 600 700 800 900 1000Barricade length m 2 3 4 5 6 7 8Barricade reinforcement, ρ % 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 2.0Depth to centroid of reinforcement mm 50 100 150 200 250Concrete comp. strength, f′c MPa 5 10 15 20 25 30 35 45 55 65Young’s modulus of rock, Erock GPa 25 30 35 40 45 50 55 60 65 70Arch angle, α ◦ -20 0 20 40 60 80 120 140 160Steel yield strength, fy MPa 400

All simulations were performed on a 1 metre-wide strip taken along the shorter (and

weaker) dimension of the barricade. The applied pressure, therefore, can be calculated

as PL

where P is the total applied load and L is the length of the barricade. Loads

were uniformly distributed across the length of the model. Only reinforcement in the

74

longitudinal, or horizontal, direction could be included in the simulations, as Response-

2012 elements are only able to model longitudinal and transverse steel. The vertical

reinforcement was not modelled, but would have had little impact on behaviour, which is

predominantly similar to that of a one-way slab as shown by Ghazi [9].

5.0.1 Reference Model

The reference model for the parametric study is as described in Table 5.1. First cracking

occurred at an applied pressure of 12.25 kPa while first yielding occurred at midspan at

a pressure of 49.0 kPa. The reference rock stiffness value was not high enough to allow

for sufficient development of negative moment at the supports, so no yielding occurred

there prior to failure. Failure occurred due to concrete crushing at the midspan element.

Plots of applied pressure and the development of axial compression in the barricade

against midspan displacement are shown in Figure 5.1. Various plots from Augustus-2

showing the internal forces and stresses in the critical element at failure are shown in

Figure 5.2. Of note is the longitudinal concrete stress plot, which shows the top portion of

the cross-section having reached a concrete compressive strength of 35 MPa. As this limit

is reached, flexural crushing will occur which will bring about failure of the barricade.

The magnified displaced shapes and average crack directions are shown in Figure 5.3.

As applied pressure increases, cracks propagate from midspan towards the supports. First

cracking at the supports due to negative moment occured at approximately 73.5 kPa, well

after first yielding of the midspan reinforcement.

The shear force and bending moment diagrams at failure are shown in Figure 5.4. The

moment diagram is drawn on the tension side of the barricade.

75

(a) Applied pressure versus midspan displacement

(b) Barricade axial force versus midspan displacement

Figure 5.1: Response of reference model

76

Figure 5.2: Augustus-2 plots showing internal forces and stresses of critical midspan element at failure.

77

(a) First cracking, 12.25 kPa

(b) First yielding, 49 kPa

(c) Ultimate capacity, 80.9 kPa

Figure 5.3: Reference barricade displaced shapes (magnified 10x) and average crack directions in red

78

(a) Shear force diagram

(b) Bending moment diagram

Figure 5.4: Shear and bending moment diagrams at failure

Barricade Reinforcement Content, ρ 79

5.1 Barricade Reinforcement Content, ρ

The longitudinal reinforcement content of the barricade, ρ, was varied from zero to two

percent. The zero reinforcement case was analysed for completeness and should not be

used in practice. The required area of steel, As, in the cross-section was calculated using

the formula ρ = As

bwdwhere bw is the width of the section (1 metre in all cases) and d is

the effective depth of the member taken as the depth to the centroid of the layer of steel

(150 mm in all cases).

Figure 5.5 shows the predicted pressures for first cracking, yielding, and failure, in

all cases at midspan. The percentages shown on the figure are the change in ultimate

strength compared to the reference case. As ρ increases, the barricade is capable of

withstanding more pressure first yielding and failure. This result is expected, as a larger

area of reinforcement would require more force to reach yield and also increases flexural

capacity. First cracking occurred on the tensile face at the same pressure regardless of steel

content, as reinforcement content has no effect on the tensile strength of the concrete. In

the case of a barricade with no reinforcement, failure occurred at the onset of first cracking

because there was no steel to bear the tensile forces in the barricade. The ρ = 0.2% case

was below the minimum amount of reinforcement of 0.296% (specified by CSA A23.3 [4]

based on concrete compressive strength and steel yield strength), so simulations yielded

poor results. In all other cases, failure occurred due to flexural crushing at midspan.

There is a significant increase in strength between ρ = 0.2% and 0.4%: for ρ = 0.2%,

failure was considered to have occurred at yielding of the reinforcement when the crack

depth reached the rebar at mid-depth. The minimal area of steel was insufficient to resist

the tensile forces in the barricade. For poorly-reinforced barricades, a smaller amount of

steel results in higher steel stresses (and therefore, strains) for a given applied pressure.

These larger steel strains correspond to higher overall curvatures in the cross-section

which lead to an increased rate of crack formation after the first one develops. For this

reason, it is recommended that a minimum amount of reinforcement be required in the

construction of CPB barricades to avoid premature failure.

While a 2.0% reinforcement ratio gives almost a doubling in capacity compared to the

minimally reinforced 0.4% case, such amounts of reinforcement would not be recommended

due to potential construction issues, particularly with shotcrete penetration through the

rebar cage.

Figure 5.6 shows the applied pressure and axial force versus the midspan displacement

for each analysed case. Barricade capacity increases with higher values of ρ, while


Figure 5.5: Pressures causing first cracking, yielding, and failure versus reinforcement content, ρ

peak barricade displacement remains fairly similar until ρ = 1.0% then decreases with

increasing ρ. Larger amounts of steel also result in stiffer post-cracking barricade response,

with more pressure being required to cause the same amount of midspan displacement.

With the exception of minimally-reinforced barricades which failed at low pressures,

the development of axial forces in the barricade decreases with increasing amounts of

reinforcement. This is likely due to smaller net strains on account of higher ρ which result

in less axial elongation. The development of compressive axial forces in these barricades

is wholly dependent on a net tensile axial strain which is restrained by the boundary

conditions. More steel would result in less strain for a given tensile force, resulting in a

lower net strain distribution in the cross-section. Although this reduction in axial force

would correspond to a smaller strengthening contribution from compressive membrane

action, the increased amount of steel still raises flexural capacity and produces a stronger

barricade.

The lower peak midspan displacements at higher values of ρ are due to the larger steel

area, which induces correspondingly higher compression forces in the concrete. This causes

a drop in ductility despite an increase in capacity. Yielding occurs at larger displacements

with increasing ρ possibly due to the larger forces (and thus displacements) required to

yield a larger area of steel.


As an example, if a barricade of the simulated dimensions were designed for 60 kPa

capacity (without considering safety factors), the predicted peak midspan displacement

would vary from approximately 2 to 12 mm as ρ is varied.




Figure 5.6: Effect of varying reinforcement content, ρ

Depth to Centroid of Reinforcement 83

5.2 Depth to Centroid of Reinforcement

The depth of the reinforcement in the barricade was changed to address possible variability

in construction. Flexural capacity would likely decrease as the distance between the

barricade’s tension face and the reinforcement increases. For example, if concrete was to

be sprayed to such a thickness that the reinforcement was located further towards the CPB

face of the barricade (the flexural compression side at midspan), then its contributions to

strength would be lessened. To simulate these effects, the depth to the centroid of the

reinforcement in Response-2012 beam elements was varied from 50 mm (reinforcement

near the midspan tension face) to 250 mm (reinforcement near the midspan compression

face) over a constant barricade thickness of 300 mm.

Figure 5.7 shows the predicted pressures for first cracking, yielding, and failure,

in all cases at midspan. As cover increases and the steel moves from the tension to

the compression face, the barricade is capable of withstanding less pressure before the

reinforcement yields. First cracking occurred at similar pressures regardless of steel depth;

since cracking occurs on the tension face, steel height had no effect on the cracking

strength. In all cases, failure occurred due to flexural crushing at midspan. Because the

amount of reinforcement was constant, the change in applied pressure to cause yield and

failure was only a function of rebar height within the cross-section. If the steel were closer

to the flexural compression side, the moment arm between the concrete compressive zone

and the steel centroid would be smaller, resulting in higher steel and concrete stresses for

a given applied pressure and thus lower flexural capacity.

If the barricades were flexure-critical at the supports, where tension occurs on the

side facing the CPB, then steel placed close to the paste side would increase strength

considerably. This behaviour, however, did not arise in simulations because negative

moments at the supports were not high enough to cause failure (Figure 5.4). Nevertheless,

during construction it would be prudent to place steel on the tension face at all locations

in the barricade: towards the paste near the supports and away from the paste elsewhere.


for each analysed case. As the steel moves from the tension to the compression face,

barricade capacity decreases while the peak displacement is similar in all cases. This

is primarily due to the shorter lever arm between the steel in tension and the concrete

compressive zone which decreases moment capacity. The development of axial forces

remains similar as well with a slight increase as the steel moves further towards the

compression face. This increase can be considered minor enough to conclude that the


Figure 5.7: Pressures causing first cracking, yielding, and failure versus bottom clear cover

position of the steel within the barricade has a minimal effect on the development of axial

forces, and thus compressive membrane action.

A barricade of the simulated dimensions designed for 50 kPa capacity (without safety

factors) would have a peak midspan displacement between approximately 2 to 11 mm

depending on the location of reinforcement within the barricade depth.




Figure 5.8: Effect of varying bottom clear cover

Barricade Thickness 86

5.3 Barricade Thickness

Barricade thickness was varied from 100 to 1000 mm to determine the strengthening effect

of increasing concrete content. If it were possible to significantly strengthen a barricade by

adding slightly more concrete instead of more steel, construction costs could potentially

be lowered.

Figure 5.9 shows the predicted pressures for first cracking, yielding, and failure. The

percentages shown above the extreme values are the change in ultimate strength compared

to the reference case. Thicker barricades can support higher pressures before first cracking

and yielding. Cracking resistance increased on account of a larger area of concrete

supporting a given amount of tension when subject to flexure. However, at a thickness

of 900 mm and greater, shear failure at the supports occurs prior to the reinforcement

yielding. As the barricade grows thicker, so does the moment arm between the steel

and the compressive concrete zone. This larger moment arm reduces stresses in the

steel, resulting in shear failure in the concrete prior to yielding. Because the barricade

is uniformly loaded across its span and is partially fixed at both ends, maximum shear

would occur near the supports, where failures occurred in thicker models. All other cases

failed due to flexural crushing at midspan with the 700 and 800 mm thickness specimens

being close to shear failure.

Figure 5.9: Pressures causing first cracking, yielding, and failure versus barricade thickness



for each analysed case. As thickness increases, there is an increase in capacity but a

decrease in midspan deflection beyond 400 mm. This decrease in ductility is on account

of the increased cross-sectional area of concrete which requires a larger force to produce a

given curvature. As thickness increases, higher forces are needed to deflect the barricade

by the same amount.

The peak axial force increases until a thickness of 400 mm and then drops significantly

as thickness increases. Because the development of axial compression in the barricade is

dependent on strains caused by flexure, a stiffer model will develop smaller strains and

thus less axial force. Since flexural concerns are minimized with increasing thickness,

as the cross-section thickens, shear demand begins to dominate due again to higher

stiffnesses.

Based on these results, varying barricade thickness has a significant effect: doubling

the thickness can more than double the capacity. It is suggested, however, that barricade

thicknesses not exceed 400 mm to prevent brittle behaviour and to allow as much deflection

as possible to act as a warning prior to failure.




Figure 5.10: Effect of varying barricade thickness

Barricade Length 89

5.4 Barricade Length

The length of a barricade is dictated by the cross-sectional dimensions of the stope, and

so cannot be controlled. However, if it is determined that increased length dramatically

reduces capacity, additional measures can be taken to strengthen the barricade to avoid a

premature failure. For simulations varying barricade length, the reinforcement ratio ρ

was varied by a factor(

Lbarricade

Lreference

)2to account for the increasing moments (which, for a

uniformly loaded beam, vary by the square of the loaded length) for beams of a different

length. The reinforcement content varied from 0.03% for the 1 m long case to 3.1% for

the 10 m long case. It should be noted that both 1 m and 2 m lengths had a ρ value

below the minimum required by CSA standards.

Figure 5.11 shows the predicted pressures for first cracking, yielding, and failure.

Cracks occurred at lower pressures in longer barricades due to larger midspan moments,

while yielding of steel only occurred in test barricades of length 6 m or less. Because

longer barricades support significantly more moment, the concrete reached crushing at a

faster rate and failed prior to sufficient stress developing in the reinforcing steel. If the

steel were located closer to the tensile face of the barricade, it is possible that it would

have yielded prior to crushing even in the longer cases. For the shorter barricades in

which the reinforcement yielded, the scaling of reinforcement content ρ with the square of

the length resulted in a similar yield pressure independent of length. In all cases, failure

was due to flexural crushing at midspan despite the lack of yielding in barricades longer

than 6 m. Although the 1 m and 2 m long barricades had less than the minimum amount

of reinforcement required by CSA standards, they still developed significant strength.

This is possibly due to their short spans which reduced bending moments.


for each analysed case. Barricade capacity drops with increased length while peak axial

forces grow with decreasing length until a value of 3 m, after which axial forces decrease

dramatically. Longer barricades are slightly more ductile: in general, an increasing span to

depth ratio results in more ductile behaviour as flexure demand overtakes shear demand.

As length increases, the rate of development of axial forces decreases. This is due to

a lower curvature for a given displacement as barricade length increases. Longitudinal

strains are dependent on curvature, so there would be lower axial forces as a result.

Because there are significant decreases in capacity with increasing barricade length,

it is recommended that longer barricades be designed more conservatively, possibly by

Barricade Length 90

Figure 5.11: Pressures causing first cracking, yielding, and failure versus barricade length

increasing thickness and using more reinforcement and ensuring that it is placed near

tensile faces.

Barricade Length 91



Figure 5.12: Effect of varying barricade length

Concrete Compressive Strength, f ′c 92

5.5 Concrete Compressive Strength, f ′c

Concrete compressive strength, f ′c, was varied between 5 to 65 MPa while maintaining

constant geometry and boundary conditions.


Concretes with higher compressive strengths also have higher tensile strengths, so cracking

pressures increased with f ′c. Yielding pressures remained similar across different values of

f ′c, as concrete strength had no effect on steel behaviour. As expected, failure in all cases

was due to flexural crushing at midspan, with higher strength concretes failing at higher

pressures due to increased compressive capacity. Interestingly, however, there was little

increase in capacity for barricades using concrete with f ′c values between 35 to 65 MPa.

One possible explanation is that, prior to failure, the depth of concrete still capable of

carrying compression is so small that any increase in f ′c beyond a certain point provides a

negligible increase in the length of the lever arm between tensile forces in the steel and

net compressive forces in the concrete, thus maintaining compressive capacity.

Figure 5.13: Pressures causing first cracking, yielding, and failure versus concrete comp. strength f ′c


for each analysed case. As expected, lower concrete strengths result in a weaker barricade

with lower stiffness and peak midspan displacement. Values of f ′c above 35 MPa, however,

provide no appreciable increase in strength or stiffness as previously explained. Similar

behaviour is seen in the development of axial forces in the barricade: lower concrete


strengths result in less axial compression. Compression forces stop increasing at values

of f ′c higher than 35 MPa. Based on these simulation results, any reasonable concrete

compressive strength would have little strengthening effect in a barricade. However,

severely deficient concrete would result in a significant loss of strength and displacement

capacity.




Figure 5.14: Effect of varying compressive concrete strength f ′c

Young’s Modulus of Rock Wall, Erock 95

5.6 Young’s Modulus of Rock Wall, Erock

As determined by Ghazi [9], barricade strength is very sensitive to the stiffness of the

surrounding rock due to the onset of compressive membrane action. Because even a

slight increase in axial compressive force due to a stiffer boundary can cause a significant

increase in flexural capacity, it is important to properly account for these effects. Using

the methods discussed in Section 3.4, an equivalent axial and rotational stiffness value

was derived for a given value of Erock. Expressions were also developed to determine the

required area of steel As,axial and As,rot for the truss rods in the Augustus-2 model based

on the calculated stiffness values.

The values of Erock cover a range from 0 to 70 GPa. These results were also compared

to the case of a barricade with fully fixed boundaries and one which was free to expand

longitudinally (effectively simply supported).


Cracking pressure remains unchanged and yielding occurs at slightly higher pressures as

Erock increases. Any increase in yield strength would likely be brought on by a reduction

in curvature (and thus steel stresses) due to a more rigid boundary, but the effect is

minimal. The more pronounced, and valuable, result is the significant difference in

ultimate barricade capacity afforded by a stiffer boundary. A higher rock stiffness would

provide more resistance to axial expansion, resulting in the accelerated development of

compressive membrane forces which enhance strength. A barricade constructed in rock

with a modulus of 25 GPa has only half the capacity of the same barricade in rock with a

modulus of 70 GPa.

In the fully fixed case, the pressure to cause first cracking is doubled compared to

the simply supported and partially restrained cases. The simply supported barricade has

lowest yielding pressure and ultimate capacity of all simulations. Failure for all models

was by flexural crushing at midspan with the exception of the fully fixed case, which

failed in shear at the barricade supports. Figure 5.15 also shows the capacity of the

fully fixed case, which is at least 1.75 times stronger than any of the other simulated

barricades. This illustrates the danger in assuming fully rigid boundary conditions, which

could easily give a twofold overestimate of strength and a severe underestimate of ductility.

It should be noted that the response of the fully fixed case is unlike that modelled by

Ghazi (Figure 2.8a). Ghazi’s fully fixed model was able to deflect over 60 mm at midspan

prior to failure compared to a deflection of 6.3 mm in this parametric study. Despite this

difference, the ultimate pressures between both cases were similar.


Figure 5.15: Pressures causing first cracking, yielding, and failure versus Young’s modulus of rock wall,Erock


for each analysed case. Barricade capacity increases with boundary stiffness while peak

midspan displacement remains fairly constant prior to failure. This suggests that while

the rock wall modulus has a large effect on ultimate capacity, peak displacements would

remain similar for a given barricade design regardless of the boundary conditions. This

result would likely change with the inclusion of secondary moment effects in analysis which

would result larger displacements for the same applied pressure. Axial forces reached

a higher peak and developed more quickly with increasing rock stiffness. The simply

supported model reached a peak midspan deflection almost twice that of the other models,

while the fully fixed case deflected minimally before shear failure. The capacity of the

fully fixed barricade was approximately 4.5 times that of the simply supported case and

1.75 times that of the strongest partially restrained case.

In practice, situations may arise where the quality of the rock wall is poor and its

load-bearing capacity may not be as high as if it were intact. In this case, it may be

possible to apply a damage factor Df less than 1.0 to reduce the effective modulus

(Erock,eff = DfErock < Erock). Such application of a damage factor would be to the

discretion of the supervising engineer and should be used conservatively.




Figure 5.16: Effect of varying the rock wall Young’s modulus, Erock

Arch Angle, α 98

5.7 Arch Angle, α

The effect of arched geometry on barricade strength was studied by varying the arch

angle (Figure 5.17). An arched barricade should provide a significant increase in strength

over a flat one due to it carrying imposed loads primarily in compression. Rectangular

Response-2012 elements were laid out in a segment of a circle and connected with truss

rods to form an approximation of an arch for simulation. The span of the arch was kept

constant at 4 m while the arch angle was increased from 0 to 160 degrees. Because each

arch is laid out in a circular shape, it is expected that there will be more significant tensile

stresses than in arch shapes such as the parabola or the catenary, which are more efficient

because they carry more of the applied load in compression. To investigate the expected

loss in capacity for a reversed arch which thrusts away from the direction of loading, a -20

degree case was also simulated. Such a situation could arise with improper construction

techniques.

As discussed in Section 3.5, concerns about proper transfer of forces between eccen-

trically connected elements (such as those in an arch) arise when the angle between

neighbouring elements approaches six degrees as shear behaviour is not properly simulated

at the transition points. It should be noted that for an arch angle of 160◦, the angle

between elements reaches this six degree limit which could provide inaccurate results.

One potential inaccuracy would be the inability to predict a shear failure.

Figure 5.17: Arch angle, α


Cracking pressures remained fairly similar to the flat reference case for all arch angles;

first cracking always occurred at midspan for every model. As arch angle increased,

however, first yielding and failure pressures increased until an arch angle of 100◦, where

simultaneous yielding and crushing led to failure. At arch angles larger than 100◦, failure

Arch Angle, α 99

occurred due to concrete crushing before the reinforcement approached yielding due to

higher compressive forces. As the arch angle increases, more of the applied pressure is

carried in direct compression, which places higher demand on the concrete. After an

arch angle of 100◦, the compression stress in the concrete increases significantly, resulting

in crushing failure prior to yielding. Along with this, more shear demand was placed

on the area near the supports, but not enough to cause a shear failure at that location.

Because it is safer to have reinforcing steel yield before crushing (thus allowing for more

warning prior to failure), it is suggested that a more moderate arch angle be adopted in

construction. Additionally, barricades with larger arch angles are more prone to being

shear critical, which may result in sudden failures with little to no warning.

The simulated arch with negative curvature had a lower ultimate capacity than the

reference flat barricade due to nearly the entire cross-section being placed in direct tension

when pressured were applied. If a barricade were constructed poorly with the incorrect

direction of curvature, capacity would decrease; this deficiency could be mitigated by the

use of sufficient reinforcing steel which could act as a tensile net. Despite this, reversed

curvatures must be avoided in practice.

Figure 5.18: Pressures causing first cracking, yielding, and failure versus arch angle, θ


for each analysed case. Larger arch angles result in a stronger and stiffer barricade with

Arch Angle, α 100

less midspan deflection before failure. As previously mentioned, larger arch angles result

in higher compression stresses in the concrete for a given applied force, resulting in more

brittle behaviour. A peculiar, contrary result is the response of the 120◦ model, which

is more ductile than the 100◦ model and develops less axial forces for a given midspan

displacement. It is possible that because the 100◦ model places more demand on the

reinforcement (which has a higher Young’s modulus than concrete), its response is stiffer

than that of the 120◦ model which experiences lower steel stresses.

Axial forces develop at a faster rate with increasing arch angle but reach a peak at an

angle of 100◦. Because the cross-section is the same between all models, it would require

the same compressive force to cause concrete crushing. Thus, the peak axial force for all

models with an arch angle greater than 100◦ is approximately equal.

The strongest arch, the 160◦ model, has a 4.5-fold strength increase over the base flat

barricade with an approximate halving of peak midspan displacement.

The results for arches of angles greater than 80◦ differ from those found by Helinski et

al. [10]; in their simulations, these arches failed in shear and tensile separation at the

rock supports. While the Augustus-2 models did not fail in shear, models with large

arch angles did have more shear demand. Due to the simplifying assumptions made in

modelling arched barricades in Augustus-2 (namely, truss rods connecting beam elements

and strong Membrane support elements), further more detailed investigation of high arch

angles is warranted.

Arch Angle, α 101



Figure 5.19: Effect of varying barricade arch angle, θ

102

Chapter 6

Conclusions

Based on the parametric analysis, CPB barricade strength can vary by as much as 30%

depending on the Young’s modulus of the surrounding rock. Although other parameters

may have had a higher effect on capacity, the type of rock in a stope cannot be changed.

Barricade designs must therefore be scaled appropriately to account for boundary condi-

tions. Arched barricades are significantly stronger than flat ones: more than a doubling

in strength can be achieved with a moderate curvature. Because the arched barricades

were modelled in Augustus-2 did not use curved elements, some inaccuracy should be

expected with the corresponding results.

Of the material and geometric barricade properties, thickness and length have the

highest effects on capacity and displacement. Care should also be taken to properly

position the reinforcement within the concrete to support tensile stresses. Factors such

as reinforcement ratio and concrete compressive strength contribute little to capacity so

long as reasonable values are used.

Secondary moment (P-∆) effects can consume a significant amount of flexural capacity.

An iterative proof of concept simulation was performed in Augustus-2 to show both the

negative effects of P-∆ and a potential implementation method for future versions of the

software.

The equations derived for rock stiffness calculate a stiffness value based on the Young’s

modulus of the surrounding rock using theoretical solutions provided by Timoshenko

and Boussinesq for loaded areas on an infinite half space. Although the equations were

developed for simulating boundary conditions in Augustus-2, they can be applied in

practical situations where theoretical rock boundary displacements are desired.

103

Chapter 7

Recommendations

The following recommendations are made for future research:

Implement secondary moment effects in Augustus-2

Currently, Augustus-2 does not account for secondary moment effects (i.e. the P-∆

effect) in its simulations. Because this could significantly decrease the capacity of

the modelled barricades, it should be included to increase accuracy and minimize

unconservative overpredictions of strength. Such functionality would also improve

simulations results of other models subject to eccentric axial compressive loads.

Improve arch modelling capabilities in Augustus-2

Because Augustus-2 is not currently capable of modelling curved elements, truss rods

were used instead to arrange rectangular elements in a segmented circular layout.

Although simulations were performed to verify that the truss rod connections were

still able to properly simulate the behaviour of a typical beam, the model geometry

was still not representative of reality. If Membrane elements with high aspect ratios

could be used stably in simulations, this could improve accuracy.

Conduct experimental barricade tests

Experiments with actual barricade walls under CPB loading conditions would

provide an opportunity to not only verify Augustus-2 simulation results but to also

determine the in situ effects of rock wall stiffness. The impact of concrete shrinkage

could also be considered.

Investigate the effect of varying pressure distributions

All simulations in this thesis considered only uniformly distributed CPB pressures.

Because the paste is often poured in stages, it would be beneficial to determine the

104

effects of partial uniform pressure applied to barricades. Additionally, the profile of

the CPB pressure may not truly be uniform, which could affect behaviour.

Develop standard design methods

Currently, there are many different design methods for CPB barricades. After

experimental work is carried out, it is recommended that a design methodology

be established which accounts for various geometry and material properties. This

would minimize uncertainty and result in more efficient use of time and materials.

Determine interaction between parameters

The parametric study in this thesis only considered the variation of one parameter

at a time. To further characterize barricade behaviour, the effects of simultaneously

varying multiple parameters should be studied as their effects may not be merely

superimposed.

Investigate the effects of concrete shrinkage

Augustus-2 does not currently account for concrete shrinkage effects which could

affect barricade behaviour. Shrinkage cracking could adversely affect barricade

strength, particularly at boundary conditions where shear failures are of more

concern.

BIBLIOGRAPHY 105

Bibliography

[1] Bentz, E. C. private communication, 2012.

[2] Bentz, E. C. A shear-based analysis method for complex structures. In Federation

Internationale du Beton (fib) Proceedings (June 22-24, 2009).

[3] Bentz, E. C., Vecchio, F. J., and Collins, M. P. Simplified modified

compression field theory for calculating shear strength of reinforced concrete elements.

ACI Structural Journal (July-August 2006).

[4] Canadian Standards Association. CSA Standard A23.3-04 Design of Concrete

Structures, 2004.

[5] Collins, M. P., Bentz, E. C., and Sherwood, E. G. Where is shear reinforce-

ment required? a review of research results and design procedures. ACI Structural

Journal (September 2008), 590–600.

[6] Collins, M. P., and Mitchell, D. Prestressed Concrete Structures. Response

Publications, 1997.

[7] Davis, R. O., and Selvadurai, A. P. S. Elasticity and Geomechanics. Cambridge

University Press, 1996.

[8] Ganji, N. Simplified modeling of joint regions in reinforced concrete structures.

Master’s thesis, University of Toronto, 2008.

[9] Ghazi, S. Modeling of an underground mine backfill barricade. Master’s thesis,

University of Toronto, 2011.

[10] Helinski, M., Wines, D., Revell, M., and Sainsbury, D. Critical factors

influencing the capacity of arched fibrecrete bulkheads and waste rock barricades. In

Minefill 2011, 10th International Symposium on Mining with Backfill.

Bibliography 106

[11] Jaeger, C. Rock mechanics and engineering. Cambridge University Press, 1979.

[12] Revell, M. B., and Sainsbury, D. P. Advancing paste fill bulkhead design

using numerical modeling. In Minefill2007, 9th International Symposium on Mining

with Backfill.

[13] Revell, M. B., and Sainsbury, D. P. Paste bulkhead failures. In Minefill2007,

9th International Symposium on Mining with Backfill.

[14] Su, Y., Tian, Y., and Song, X. Progressive collapse resistance of axially-restrained

frame beams. ACI Structural Journal 106, 5 (September-October 2009).

[15] Thompson, B. D. Fieldwork report for paste backfill project at cayeli bakir mine,

turkey. Tech. rep., University of Toronto, 2010.

[16] Timoshenko, S., and Goodier, J. N. Theory of Elasticity. McGraw-Hill Book

Company, 1970.

[17] Vecchio, F. J., and Tang, K. Membrane action in reinforced concrete slabs.

Canadian Journal of Civil Engineering 17 (1990).

[18] Yeung, L. S. Y. A new finite element for reinforced concrete beam analyses

including shear. Master’s thesis, University of Toronto, 2008.

107

Appendices

108

Appendix A

Typical Augustus-2 Input Files

D:\Dropbox\MASc Thesis\Parametric\straight\Erock\35.new.job September-30-12 9:24 PM

Element Input File V2.0Analysis Definition title=Reference straight // title date=2012/08/30 // Date doneby=Drew Cheung // Doneby path = D:\Dropbox\MASc Thesis\Parametric\straight\Erock\ units=METRIC // units (METRIc / US)End

Node List 1 0 0 3 2 200 0 2 1 0 600 7 400 150 51 2 80 0 2 1 0 300 109 4400 0 3 2 200 0 2 1 0 600 115 0 -200 2 1 400 0 117 4400 -200 2 1 400 0 119 0 300 2 1 -200 0 121 4800 300 2 1 200 0 End

Restraint List 3 0 1 111 0 1 115 1 1 4 1 120 1 1 2 2 7 2 2 2 5 0.75 6 0.25 2 5 0.75 6 0.258 2 2 2 5 0.25 6 0.75 2 5 0.25 6 0.75107 2 2 2 109 0.75 110 0.25 2 109 0.75 110 0.25108 2 2 2 109 0.25 110 0.75 2 109 0.25 110 0.75119 2 2 2 1 0.5 2 0.5 2 1 0.5 2 0.5121 2 2 2 113 0.5 114 0.5 2 113 0.5 114 0.5End

Incident Beam 1 1 2 3 4 supportref.rsp 2 1 2 3 7 8 9 10 refstrong.rsp 3 1 2 6 13 14 15 16 ref.rsp 20 1 2 26 53 54 55 56 refstrong.rsp 4 1 2 30 61 62 63 64 ref.rsp 20 1 2 50 101 102 103 104 refstrong.rsp 3 1 2 53 109 110 111 112 supportref.rsp 2 1 2 End

Incident Truss 55 1 115 rot35.rsp STEEL 56 5 116 rot35.rsp STEEL 57 109 117 rot35.rsp STEEL 58 113 118 rot35.rsp STEEL 59 119 120 ax35.rsp STEEL 60 121 122 ax35.rsp STEEL End

Loads List 10 0 -.2 0 49 2 0 0 End

-1-

D:\Dropbox\MASc Thesis\Parametric\straight\Erock\refstrong.rsp September-30-12 9:30 PM

<?xml version="1.0" encoding="UTF-8" standalone="no" ?><!DOCTYPE suite_3g SYSTEM "r3g.dtd">

<document><r3g_beam name ="Reference"

doneby ="DC"date ="2012/8/31" >

<concrete fcp ="35.0"maxagg ="19.0"c_mod ="4" >

0.000 0.000.085 2.240.169 4.480.254 6.720.338 8.940.422 11.150.507 13.320.592 15.460.676 17.540.760 19.550.845 21.480.930 23.321.014 25.061.099 26.671.183 28.161.268 29.501.352 30.701.437 31.751.521 32.651.606 33.401.690 34.001.775 34.451.859 34.761.944 34.942.028 35.0050.000 35.00

</concrete><rebar fy ="400.0"

esh ="7.0"eu ="100.0" />

<prestress fu ="1860.0" /><sectionSOLID >

300.0 1000.00.0 1000.0 "Concrete 1"

</sectionSOLID><shapesection name ="RECT"

par1 ="1000.0"par2 ="300.0"par3 =" 0.0"par4 =" 0.0"par5 =" 0.0"par6 =" 0.0" />

<longreinfx z ="150.00"

-1-

D:\Dropbox\MASc Thesis\Parametric\straight\Erock\ref.rsp September-30-12 9:30 PM


<document><r3g_beam name ="Reference"

doneby ="DC"date ="2012/8/31" >

<concrete fcp ="35.0"maxagg ="19.0" />

<rebar fy ="400.0"esh ="7.0"eu ="100.0" />


300.0 1000.00.0 1000.0 "Concrete 1"



<longreinfx z ="150.00"type ="Steel 1"num ="3"A ="1500.0"Ai ="500.0"db ="25.2"dep ="0.00" />

<eleminfo L ="900.00"mido2 ="0.00"lplate ="150.00"rplate ="150.00" />

<sectloading BM ="-0.0"MM ="1.0" />

</r3g_beam></document>

-1-

D:\Dropbox\MASc Thesis\Parametric\straight\Erock\supportref.rsp September-30-12 9:29 PM


<document><r3g_beam name ="supportref"

doneby ="DC"date ="2012/8/31" >

<concrete fcp ="10000.0"maxagg ="0.0" />

<rebar fy ="400.0"esh ="7.0"eu ="100.0" />


600.0 1200.00.0 1200.0 "Concrete 1"



<longreinfx z ="300.00"type ="Steel 1"num ="3"A ="1500.0"bartitle ="25M"dep ="0.00" />

<transreinfz A ="1000.0"type ="Steel 1"pattern ="3"space ="250.0"disttop ="547.4"distbot ="52.6"A ="1000.0"bartitle ="25M"dep ="0.00"name ="stirrup" />




-1-

D:\Dropbox\MASc Thesis\Parametric\straight\Erock\ax35.rsp September-30-12 9:29 PM


<document><r3g_beam name ="rotref"

date ="2012/8/31" ><concrete fcp ="35.0"

maxagg ="19.0" /><rebar fy ="20000.0"

fu ="20000.0"esh ="100.0"eu ="100.0" />


400.0 0.1393.2 103.5 "Concrete 1"373.2 200.0 "Concrete 1"341.4 282.8 "Concrete 1"300.0 346.4 "Concrete 1"251.8 386.4 "Concrete 1"200.0 400.0 "Concrete 1"148.2 386.4 "Concrete 1"100.0 346.4 "Concrete 1"58.6 282.8 "Concrete 1"26.8 200.0 "Concrete 1"6.8 103.5 "Concrete 1"0.0 0.1 "Concrete 1"

</sectionSOLID><shapesection name ="CIRCLE"


<longreinfx z ="200.00"type ="Steel 1"A ="23.0"Ai ="23.0"db ="5.4"dep ="0.00"name ="outer" />




-1-

D:\Dropbox\MASc Thesis\Parametric\straight\Erock\rot35.rsp September-30-12 9:29 PM


<document><r3g_beam name ="rotref"

date ="2012/8/31" ><concrete fcp ="35.0"

maxagg ="19.0" /><rebar fy ="20000.0"

fu ="20000.0"esh ="100.0"eu ="100.0" />


400.0 0.1393.2 103.5 "Concrete 1"373.2 200.0 "Concrete 1"341.4 282.8 "Concrete 1"300.0 346.4 "Concrete 1"251.8 386.4 "Concrete 1"200.0 400.0 "Concrete 1"148.2 386.4 "Concrete 1"100.0 346.4 "Concrete 1"58.6 282.8 "Concrete 1"26.8 200.0 "Concrete 1"6.8 103.5 "Concrete 1"0.0 0.1 "Concrete 1"

</sectionSOLID><shapesection name ="CIRCLE"


<longreinfx z ="200.00"type ="Steel 1"A ="18.0"Ai ="18.0"db ="4.8"dep ="0.00"name ="outer" />




-1-

115

Appendix B

Parametric Modelling Data

100crack

7.7

yield

8.92

5crush

200crack

6.37

5yield

24.225

crush

400crack

23yield

66.3

crush

500crack

35.7

yield

124.95

crush

600crack

51yield

173.4

crush

vert

horiz

vert

horiz

vert

horiz

vert

horiz

vert

horiz

Data from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

thicker =

stronger but m

ore brittle

==============

‐0.194

00.19

40 ==============

‐0.055

00.05

50

==============

‐0.029

00.02

90

==============

‐0.026

00.02

60

==============

‐0.017

00.01

70

‐0.388

00.38

80

‐0.109

00.10

90

‐0.057

00.05

70

‐0.052

00.05

20

‐0.035

00.03

50

crack

yield

fail

Title

: Con

trol Chart

‐0.643

0.3

0.64

3‐0.3

Title

: Con

trol Chart

‐0.164

00.16

40

Title

: Con

trol Chart

‐0.086

00.08

60

Title

: Con

trol Chart

‐0.078

00.07

80

Title

: Con

trol Chart

‐0.052

00.05

20

100

7.7

8.92

58.92

5‐1.35

1.5

1.35

‐1.5

‐0.219

00.21

90

‐0.114

00.11

40

‐0.106

00.10

60

‐0.069

00.06

90

200

6.37

524

.225

33.15

X Axis T

itle: x‐axis

‐2.26

3.4

2.26

‐3.4

X Axis T

itle: x‐axis

‐0.292

0.1

0.29

2‐0.1

X Axis T

itle: x‐axis

‐0.165

0.2

0.16

5‐0.2

X Axis T

itle: x‐axis

‐0.183

0.8

0.18

3‐0.8

X Axis T

itle: x‐axis

‐0.088

00.08

80

300

12.25

4980

.85

Y Axis T

itle: y‐axis

‐3.168

5.5

3.16

8‐5.5

Y Axis T

itle: y‐axis

‐0.44

0.5

0.44

‐0.5

Y Axis T

itle: y‐axis

‐0.397

3.3

0.39

7‐3.3

Y Axis T

itle: y‐axis

‐0.439

5.6

0.43

9‐5.6

Y Axis T

itle: y‐axis

‐0.134

0.6

0.13

4‐0.6

400

2366

.313

2.6

‐4.091

7.7

4.09

1‐7.7

‐0.866

2.7

0.86

6‐2.7

‐0.724

8.2

0.72

4‐8.2

‐0.712

11.1

0.71

2‐11.1

‐0.292

4.3

0.29

2‐4.3

500

35.7

124.95

187.43

x‐axis

y‐axis

‐5.008

105.00

8‐10 x‐axis

y‐axis

‐1.263

4.8

1.26

3‐4.8

x‐axis

y‐axis

‐1.038

13.1

1.03

8‐13.1

x‐axis

y‐axis

‐1.003

17.3

1.00

3‐17.3

x‐axis

y‐axis

‐0.464

8.6

0.46

4‐8.6

600

5117

3.4

214.2

Line

type

: 0

‐5.898

12.2

5.89

8‐12.2Line

type

: 0

‐1.677

7.1

1.67

7‐7.1

Line

type

: 0

‐1.368

18.4

1.36

8‐18.4Line

type

: 0

‐1.286

23.5

1.28

6‐23.5Line

type

: 0

‐0.661

13.9

0.66

1‐13.9

700

68.75

229.5

252.45

00

00

‐6.817

14.5

6.81

7‐14.5

00

00

‐2.104

9.6

2.10

4‐9.6

00

00

‐1.688

23.6

1.68

8‐23.6

00

00

‐1.572

29.8

1.57

2‐29.8

00

00

‐0.863

19.6

0.86

3‐19.6

800

89.25

293.25

293.25

‐0.194

2.54

760.19

40.63

69‐7.714

16.7

7.71

4‐16.7

‐0.055

5.09

519

0.05

51.27

3798

‐2.532

12.1

2.53

2‐12.1

‐0.029

20.380

770.02

95.09

5193

‐2.013

292.01

3‐29

‐0.026

35.666

350.02

68.91

6588

‐1.861

36.2

1.86

1‐36.2

‐0.017

40.761

560.01

710

.190

39‐1.065

25.4

1.06

5‐25.4

900

112.2

326.4

‐0.388

5.1

0.38

81.27

5‐8.617

19.1

8.61

7‐19.1

‐0.109

10.2

0.10

92.55

‐2.959

14.7

2.95

9‐14.7

‐0.057

40.8

0.05

710

.2‐2.344

34.5

2.34

4‐34.5

‐0.052

71.4

0.05

217

.85

‐2.156

42.7

2.15

6‐42.7

‐0.035

81.599

980.03

520

.4‐1.27

31.3

1.27

‐31.3

1000

140.25

369.75

‐0.643

7.65

0.64

31.91

25‐9.576

22.9

9.57

6‐22.9

‐0.164

15.3

0.16

43.82

5‐3.366

17.1

3.36

6‐17.1

‐0.086

61.2

0.08

615

.3‐2.724

41.2

2.72

4‐41.2

‐0.078

107.1

0.07

826

.775

‐2.451

49.44

2.45

1‐49.44

‐0.052

122.4

0.05

230

.6‐1.477

37.4

1.47

7‐37.4

‐1.35

10.2

1.35

2.55

‐10.67

926

.410

.679

‐26.4

‐0.219

20.4

0.21

95.1

‐3.793

19.7

3.79

3‐19.7

‐0.114

81.600

010.11

420

.4‐3.327

53.4

3.32

7‐53.4

‐0.106

142.8

0.10

635

.7‐2.926

61.5

2.92

6‐61.5

‐0.069

163.2

0.06

940

.8‐1.689

43.6

1.68

9‐43.6

‐2.26

12.75

2.26

3.18

7530

.90

‐30.9

‐0.292

25.5

0.29

26.37

5‐4.204

22.1

4.20

4‐22.1

‐0.165

102

0.16

525

.5‐3.934

65.7

3.93

4‐65.7

‐0.183

178.5

0.18

344

.625

01‐3.567

793.56

7‐79

‐0.088

204

0.08

851

‐1.895

49.7

1.89

5‐49.7

‐3.168

15.3

3.16

83.82

5disp

axial

‐0.44

30.6

0.44

7.65

‐4.635

24.7

4.63

5‐24.7

‐0.397

122.4

0.39

730

.6‐4.538

784.53

8‐78

‐0.439

214.2

0.43

953

.550

01‐4.196

96.3

4.19

6‐96.3

‐0.134

244.8

0.13

461

.2‐2.11

56.1

2.11

‐56.1

‐4.091

17.85

4.09

14.46

25‐0.866

35.7

0.86

68.92

5‐5.052

27.3

5.05

2‐27.3

‐0.724

142.8

0.72

435

.7‐5.15

90.4

5.15

‐90.4

‐0.712

249.9

0.71

262

.475

01‐4.839

113.9

4.83

9‐113

.9‐0.292

285.6

0.29

271

.4‐2.455

67.6

2.45

5‐67.6

‐5.008

20.4

5.00

85.1

‐1.263

40.800

011.26

310

.2‐5.486

29.9

5.48

6‐29.9

‐1.038

163.2

1.03

840

.8‐5.762

102.8

5.76

2‐102

.8‐1.003

285.6

1.00

371

.399

99‐5.494

131.8

5.49

4‐131

.8‐0.464

326.4

0.46

481

.6‐2.943

85.1

2.94

3‐85.1

‐5.898

22.95

5.89

85.73

75‐1.677

45.9

1.67

711

.475

‐6.082

34.2

6.08

2‐34.2

‐1.368

183.6

1.36

845

.9‐6.386

115.5

6.38

6‐115

.5‐1.286

321.3

1.28

680

.324

99‐6.167

150.3

6.16

7‐150

.3‐0.661

367.2

0.66

191

.799

99‐3.431

102.6

3.43

1‐102

.6‐6.817

25.5

6.81

76.37

5‐2.104

50.999

992.10

412

.75

‐6.767

39.3

6.76

7‐39.3

‐1.688

204

1.68

851

‐7.014

128.2

7.01

4‐128

.2‐1.572

357

1.57

289

.250

01‐6.851

168.9

6.85

1‐168

.9‐0.863

408

0.86

310

2‐3.923

120.4

3.92

3‐120

.4‐7.714

28.05

7.71

47.01

25‐2.532

56.1

2.53

214

.025

‐7.456

44.5

7.45

6‐44.5

‐2.013

224.4

2.01

356

.1‐7.647

141

7.64

7‐141

‐1.861

392.7

1.86

198

.175

‐7.552

188

7.55

2‐188

‐1.065

448.8

1.06

511

2.2

‐4.426

138.5

4.42

6‐138

.5‐8.617

30.6

8.61

77.65

‐2.959

61.2

2.95

915

.3‐8.146

49.7

8.14

6‐49.7

‐2.344

244.8

2.34

461

.200

01‐8.287

153.9

8.28

7‐153

.9‐2.156

428.4

2.15

610

7.1

207.2

‐1.27

489.6

1.27

122.4

157.1

‐9.576

33.15

9.57

68.28

75‐3.366

66.3

3.36

616

.575

‐8.829

54.8

8.82

9‐54.8

‐2.724

265.2

2.72

466

.3‐8.936

167

8.93

6‐167

‐2.451

464.1

2.45

111

6.02

5‐1.477

530.4

1.47

713

2.6

‐10.67

935

.710

.679

8.92

5‐3.793

71.400

013.79

317

.85

‐9.528

609.52

8‐60

‐3.327

285.6

3.32

771

.4‐9.589

180.1

9.58

9‐180

.1‐2.926

499.8

2.92

612

4.95

‐1.689

571.2

1.68

914

2.8

‐4.204

76.5

4.20

419

.125

‐10.21

765

.210

.217

‐65.2

‐3.934

306

3.93

476

.5‐10.24

319

3.1

10.243

‐193

.1‐3.567

535.49

993.56

713

3.87

5‐1.895

611.99

991.89

515

3‐4.635

81.6

4.63

520

.4‐10.91

870

.510

.918

‐70.5

‐4.538

326.4

4.53

881

.600

01‐10.90

620

6.2

10.906

‐206

.2‐4.196

571.2

4.19

614

2.8

‐2.11

652.79

992.11

163.2

‐5.052

86.700

015.05

221

.675

75.8

‐5.15

346.8

5.15

86.7

219.6

‐4.839

606.9

4.83

915

1.72

5‐2.455

693.59

992.45

517

3.4

‐5.486

91.8

5.48

622

.95

‐5.762

367.2

5.76

291

.799

99‐5.494

642.6

5.49

416

0.65

‐2.943

734.39

992.94

318

3.6

‐6.082

96.9

6.08

224

.225

‐6.386

387.6

6.38

696

.9‐6.167

678.3

6.16

716

9.57

5‐3.431

775.19

993.43

119

3.8

‐6.767

102

6.76

725

.5‐7.014

408.00

017.01

410

2‐6.851

713.99

996.85

117

8.5

‐3.923

815.99

993.92

320

4‐7.456

107.1

7.45

626

.775

‐7.647

428.4

7.64

710

7.1

‐7.552

749.70

017.55

218

7.42

5‐4.426

856.8

4.42

621

4.2

‐8.146

112.2

8.14

628

.05

‐8.287

448.79

998.28

711

2.2

‐8.829

117.3

8.82

929

.325

‐8.936

469.2

8.93

611

7.3

‐9.528

122.4

9.52

830

.6‐9.589

489.6

9.58

912

2.4

‐10.21

712

7.5

10.217

31.875

‐10.24

351

010

.243

127.5

‐10.91

813

2.6

10.918

33.150

01‐10.90

653

0.39

9910

.906

132.6

ref

crack

49yield

196

700crack

68.75

yield

229.5close to sh

ear

800crack

89.25

yield

293.25

close to sh

ear

900crack

112.2

yield

NO

shear

1000

crack

140.25

yield

NO

shear

ref

crack

12.25yield

49vert

12.25

horiz

49vert

horiz

vert

horiz

vert

horiz

vert

horiz

vert

horiz

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

==============

‐0.033

00.03

30

==============

‐0.012

00.01

20

==============

‐0.009

00.00

90

==============

‐0.005

00.00

50

==============

‐0.005

00.00

50

==============

‐0.033

00.03

30

‐0.066

00.06

60

‐0.025

00.02

50

‐0.019

00.01

90

‐0.011

00.01

10

‐0.01

00.01

0‐0.066

00.06

60

Title

: Con

trol Chart

‐0.099

00.09

90

Title

: Con

trol Chart

‐0.037

00.03

70

Title

: Con

trol Chart

‐0.028

00.02

80

Title

: Con

trol Chart

‐0.016

00.01

60

Title

: Con

trol Chart

‐0.015

00.01

50

Title

: Con

trol Ch

‐0.099

00.09

90

‐0.132

00.13

20

‐0.05

00.05

0‐0.037

00.03

70

‐0.021

00.02

10

‐0.02

00.02

0‐0.132

00.13

20

X Axis T

itle: x‐axis

‐0.165

00.16

50

X Axis T

itle: x‐axis

‐0.062

00.06

20

X Axis T

itle: x‐axis

‐0.047

00.04

70

X Axis T

itle: x‐axis

‐0.027

00.02

70

X Axis T

itle: x‐axis

‐0.025

00.02

50

X Axis T

itle: x‐axis

‐0.165

00.16

50

Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

Y Axis T

itle: y‐axis

‐0.076

00.07

60

Y Axis T

itle: y‐axis

‐0.056

00.05

60

Y Axis T

itle: y‐axis

‐0.032

00.03

20

Y Axis T

itle: y‐axis

‐0.03

00.03

0 Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

‐0.477

2.3

0.47

7‐2.3

‐0.109

0.5

0.10

9‐0.5

‐0.067

00.06

70

‐0.037

00.03

70

‐0.035

00.03

50

‐0.477

2.3

0.47

7‐2.3

x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

x‐axis

y‐axis

‐0.221

3.8

0.22

1‐3.8

x‐axis

y‐axis

‐0.091

0.4

0.09

1‐0.4

x‐axis

y‐axis

‐0.043

00.04

30

x‐axis

y‐axis

‐0.039

00.03

90

x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

Line

type

: 0

‐0.345

7.7

0.34

5‐7.7

Line

type

: 0

‐0.161

2.8

0.16

1‐2.8

Line

type

: 0

‐0.048

00.04

80Line

type

: 0

‐0.044

00.04

40Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

00

00

‐1.346

10.9

1.34

6‐10.9

00

00

‐0.487

12.4

0.48

7‐12.4

00

00

‐0.263

6.6

0.26

3‐6.6

00

00

‐0.053

00.05

30

00

00

‐0.049

00.04

90

00

0‐1.346

10.9

1.34

6‐10.9

‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

‐0.012

45.856

770.01

211

.464

19‐0.641

17.9

0.64

1‐17.9

‐0.009

50.951

990.00

912

.738

‐0.365

10.6

0.36

5‐10.6

‐0.005

40.761

60.00

510

.190

4‐0.06

00.06

0‐0.005

50.952

030.00

512

.738

01‐0.055

00.05

50

‐0.033

9.79

076

0.03

3‐1.653

14.1

1.65

3‐14.1

‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

‐0.025

91.800

010.02

522

.95

‐0.795

23.5

0.79

5‐23.5

‐0.019

102

0.01

925

.5‐0.48

15.4

0.48

‐15.4

‐0.011

81.599

990.01

120

.4‐0.069

0.2

0.06

9‐0.2

‐0.01

102

0.01

25.5

‐0.064

0.2

0.06

4‐0.2

‐0.066

19.6

0.06

6‐1.955

17.3

1.95

5‐17.3

‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

‐0.037

137.7

0.03

734

.425

‐0.95

29.1

0.95

‐29.1

‐0.028

153

0.02

838

.25

‐0.598

20.5

0.59

8‐20.5

‐0.016

122.4

0.01

630

.6‐0.083

0.5

0.08

3‐0.5

‐0.015

153

0.01

538

.25

‐0.076

0.5

0.07

6‐0.5

‐0.099

29.4

0.09

9‐2.258

20.5

2.25

8‐20.5

‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

‐0.05

183.6

0.05

45.9

‐1.106

34.8

1.10

6‐34.8

‐0.037

204

0.03

751

.000

01‐0.719

25.8

0.71

9‐25.8

‐0.021

163.2

0.02

140

.8‐0.106

1.1

0.10

6‐1.1

‐0.02

204

0.02

51‐0.095

1.1

0.09

5‐1.1

‐0.132

39.2

0.13

2‐2.547

23.6

2.54

7‐23.6

‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

‐0.062

229.5

0.06

257

.375

‐1.256

40.4

1.25

6‐40.4

‐0.047

255

0.04

763

.75

‐0.84

31.1

0.84

‐31.1

‐0.027

204

0.02

751

‐0.175

4.3

0.17

5‐4.3

‐0.025

255

0.02

563

.75

‐0.135

3.1

0.13

5‐3.1

‐0.165

490.16

5‐2.85

26.8

2.85

‐26.8

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

‐0.076

275.4

0.07

668

.850

01‐1.41

46.2

1.41

‐46.2

‐0.056

306

0.05

676

.5‐0.956

36.2

0.95

6‐36.2

‐0.032

244.8

0.03

261

.200

01‐0.246

7.6

0.24

6‐7.6

‐0.03

306

0.03

76.5

‐0.212

7.5

0.21

2‐7.5

‐0.239

58.8

0.23

9‐3.141

303.14

1‐30

‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

‐0.109

321.3

0.10

980

.325

‐1.571

52.2

1.57

1‐52.2

‐0.067

357

0.06

789

.25

‐1.077

41.7

1.07

7‐41.7

‐0.037

285.6

0.03

771

.399

99‐0.304

10.3

0.30

4‐10.3

‐0.035

357

0.03

589

.250

01‐0.281

11.5

0.28

1‐11.5

‐0.477

68.6

0.47

7‐3.449

33.3

3.44

9‐33.3

‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

‐0.221

367.2

0.22

191

.8‐1.729

58.2

1.72

9‐58.2

‐0.091

408

0.09

110

2‐1.201

47.2

1.20

1‐47.2

‐0.043

326.4

0.04

381

.600

01‐0.362

13.1

0.36

2‐13.1

‐0.039

408

0.03

910

2‐0.333

14.6

0.33

3‐14.6

‐0.752

78.400

010.75

2‐3.746

36.5

3.74

6‐36.5

‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

‐0.345

413.1

0.34

510

3.27

5‐1.898

64.6

1.89

8‐64.6

‐0.161

459

0.16

111

4.75

‐1.318

52.5

1.31

8‐52.5

‐0.048

367.2

0.04

891

.800

01‐0.428

16.5

0.42

8‐16.5

‐0.044

459

0.04

411

4.75

‐0.386

17.9

0.38

6‐17.9

‐1.049

88.2

1.04

9‐4.066

40.1

4.06

6‐40.1

‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

‐0.487

459

0.48

711

4.75

‐2.138

74.7

2.13

8‐74.7

‐0.263

509.99

990.26

312

7.5

‐1.437

57.9

1.43

7‐57.9

‐0.053

408

0.05

310

2‐0.499

20.2

0.49

9‐20.2

‐0.049

510

0.04

912

7.5

‐0.446

21.7

0.44

6‐21.7

‐1.346

981.34

6‐4.578

46.8

4.57

8‐46.8

‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

‐0.641

504.9

0.64

112

6.22

5‐2.52

922.52

‐92

‐0.365

561

0.36

514

0.25

‐1.566

63.7

1.56

6‐63.7

‐0.06

448.8

0.06

112.2

‐0.567

23.8

0.56

7‐23.8

‐0.055

561.00

010.05

514

0.25

‐0.51

25.9

0.51

‐25.9

‐1.653

107.8

1.65

3‐5.133

54.2

5.13

3‐54.2

‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

‐0.795

550.79

990.79

513

7.7

‐2.922

110.4

2.92

2‐110

.4‐0.48

612.00

010.48

153

‐1.693

69.6

1.69

3‐69.6

‐0.069

489.6

0.06

912

2.4

‐0.635

27.5

0.63

5‐27.5

‐0.064

612.00

010.06

415

3‐0.574

300.57

4‐30

‐1.955

117.6

1.95

5‐5.673

61.4

5.67

3‐61.4

‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

‐0.95

596.70

010.95

149.17

512

8.8

‐0.598

663

0.59

816

5.75

78.9

‐0.083

530.39

990.08

313

2.6

‐0.708

31.3

0.70

8‐31.3

‐0.076

663

0.07

616

5.75

‐0.641

34.3

0.64

1‐34.3

‐2.258

127.4

2.25

8‐6.215

68.6

6.21

5‐68.6

‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

‐1.106

642.6

1.10

616

0.65

‐0.719

714.00

010.71

917

8.5

‐0.106

571.20

010.10

614

2.8

‐0.773

34.8

0.77

3‐34.8

‐0.095

714

0.09

517

8.5

‐0.699

38.1

0.69

9‐38.1

‐2.547

137.2

2.54

7‐6.765

75.9

6.76

5‐75.9

‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

‐1.256

688.5

1.25

617

2.12

5‐0.84

764.99

990.84

191.25

‐0.175

612

0.17

515

3‐0.846

38.7

0.84

6‐38.7

‐0.135

765

0.13

519

1.25

‐0.764

42.3

0.76

4‐42.3

‐2.85

147

2.85

‐7.32

83.3

7.32

‐83.3

‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

‐1.41

734.4

1.41

183.6

‐0.956

816.00

010.95

620

4‐0.246

652.8

0.24

616

3.2

‐0.911

42.2

0.91

1‐42.2

‐0.212

816.00

010.21

220

4‐0.831

46.6

0.83

1‐46.6

‐3.141

156.8

3.14

1‐7.88

90.7

7.88

‐90.7

‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

‐1.571

780.30

011.57

119

5.07

5‐1.077

867

1.07

721

6.75

‐0.304

693.6

0.30

417

3.4

‐0.976

45.7

0.97

6‐45.7

‐0.281

867.00

010.28

121

6.75

‐0.89

50.5

0.89

‐50.5

‐3.449

166.6

3.44

9‐8.44

98.2

8.44

‐98.2

‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.7‐1.729

826.2

1.72

920

6.55

‐1.201

918

1.20

122

9.5

‐0.362

734.4

0.36

218

3.6

‐1.048

49.6

1.04

8‐49.6

‐0.333

918

0.33

322

9.5

‐0.952

54.6

0.95

2‐54.6

‐3.746

176.4

3.74

6‐9.011

105.7

9.01

1‐105

.7‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.4‐1.898

872.1

1.89

821

8.02

5‐1.318

968.99

991.31

824

2.25

‐0.428

775.2

0.42

819

3.8

‐1.115

53.3

1.11

5‐53.3

‐0.386

968.99

990.38

624

2.25

‐1.022

59.2

1.02

2‐59.2

‐4.066

186.2

4.06

6‐9.587

113.4

9.58

7‐113

.4‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

‐2.138

918

2.13

822

9.5

‐1.437

1020

1.43

725

5‐0.499

816.00

010.49

920

4‐1.183

571.18

3‐57

‐0.446

1020

0.44

625

563

.4‐4.578

196

4.57

8‐10.16

712

110

.167

‐121

‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.6‐2.52

963.89

992.52

240.97

5‐1.566

1071

1.56

626

7.75

‐0.567

856.8

0.56

721

4.2

‐1.258

61.1

1.25

8‐61.1

‐0.51

1071

0.51

267.75

‐5.133

205.8

5.13

3‐10.75

712

8.6

10.757

‐128

.6‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.4‐2.922

1009

.82.92

225

2.45

‐1.693

1122

1.69

328

0.5

‐0.635

897.6

0.63

522

4.4

‐1.329

651.32

9‐65

‐0.574

1122

0.57

428

0.5

‐5.673

215.6

5.67

3‐11.36

813

6.4

11.368

‐136

.4‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.2‐1.879

1173

1.87

929

3.25

‐0.708

938.39

990.70

823

4.6

69‐0.641

1173

0.64

129

3.25

‐6.215

225.4

6.21

5‐11.99

214

4.2

11.992

‐144

.2‐6.765

235.2

6.76

558

.8‐0.773

979.19

990.77

324

4.8

‐0.699

1224

0.69

930

6‐6.765

235.2

6.76

5‐7.32

245

7.32

61.250

01‐0.846

1020

0.84

625

5‐0.764

1275

0.76

431

8.75

‐7.32

245

7.32

‐7.88

254.8

7.88

63.700

01‐0.911

1060

.80.91

126

5.2

‐0.831

1326

0.83

133

1.5

‐7.88

254.8

7.88

‐8.44

264.6

8.44

66.150

01‐0.976

1101

.60.97

627

5.4

‐0.89

1377

0.89

344.25

‐8.44

264.6

8.44

‐9.011

274.4

9.01

168

.6‐1.048

1142

.41.04

828

5.6

‐0.952

1428

0.95

235

7‐9.011

274.4

9.01

1‐9.587

284.2

9.58

771

.049

99‐1.115

1183

.21.11

529

5.8

‐1.022

1479

1.02

236

9.75

‐9.587

284.2

9.58

7‐10.16

729

410

.167

73.499

99‐1.183

1224

1.18

330

6‐10.16

729

410

.167

‐10.75

730

3.8

10.757

75.95

‐1.258

1264

.81.25

831

6.2

‐10.75

730

3.8

10.757

‐11.36

831

3.6

11.368

78.4

‐1.329

1305

.61.32

932

6.4

‐11.36

831

3.6

11.368

‐11.99

232

3.4

11.992

80.85

‐11.99

232

3.4

11.992

STEEL CE

NTR

OID

50crack

14.7

yield

69.825

crush

100crack

12.25yield

61.25crush

200crack

12.25yield

41.65crush

250crack

12.25yield

22.05crush

ref

crack

12.25yield

49crack

yield

fail

vert

horiz

vert

horiz

vert

horiz

vert

horiz

vert

horiz

5014

.769

.825

110.25

Data from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

100

12.25

61.25

85.75

==============

‐0.047

00.04

70 ==============

‐0.081

00.08

10

==============

‐0.033

00.03

30

==============

‐0.024

00.02

40

==============

‐0.033

00.03

30

150

12.25

4980

.85

‐0.095

00.09

50

‐0.163

0.3

0.16

3‐0.3

‐0.065

00.06

50

‐0.047

00.04

70

‐0.066

00.06

60

200

12.25

41.65

61.25

Title

: Con

trol Ch: Y‐Disp

lace

‐0.142

00.14

20 Title

: Con

trol Ch

‐0.358

1.2

0.35

8‐1.2

Title

: Con

trol Ch

‐0.098

00.09

80

Title

: Con

trol Ch

‐0.071

00.07

10

Title

: Con

trol Ch

‐0.099

00.09

90

250

12.25

22.05

51.45

‐0.197

00.19

70

‐0.761

4.3

0.76

1‐4.3

‐0.13

00.13

0‐0.095

00.09

50

‐0.132

00.13

20

X Axis T

itle: x‐axis

‐0.289

0.3

0.28

9‐0.3

X Axis T

itle: x‐axis

‐1.238

8.4

1.23

8‐8.4

X Axis T

itle: x‐axis

‐0.165

00.16

50

X Axis T

itle: x‐axis

‐0.119

00.11

90

X Axis T

itle: x‐axis

‐0.165

00.16

50

Y Axis T

itle: y‐axis

‐0.425

10.42

5‐1

Y Axis T

itle: y‐axis

‐1.724

131.72

4‐13

Y Axis T

itle: y‐axis

‐0.29

0.8

0.29

‐0.8

Y Axis T

itle: y‐axis

‐0.142

00.14

20

Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

‐0.595

2.2

0.59

5‐2.2

‐2.229

182.22

9‐18

‐0.96

8.6

0.96

‐8.6

‐0.176

0.1

0.17

6‐0.1

‐0.477

2.3

0.47

7‐2.3

x‐axis

y‐axis

®y"ÌUÈxF

‐0.783

3.7

0.78

3‐3.7

x‐axis

y‐axis

‐2.751

23.2

2.75

1‐23.2

x‐axis

y‐axis

‐1.453

14.3

1.45

3‐14.3

x‐axis

y‐axis

‐0.604

50.60

4‐5

x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

Line

type

: 0

‐0.978

5.3

0.97

8‐5.3

Line

type

: 0

‐3.279

28.5

3.27

9‐28.5Line

type

: 0

‐1.958

20.2

1.95

8‐20.2Line

type

: 0

‐2.146

27.4

2.14

6‐27.4Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

00

00

‐1.177

71.17

7‐7

00

00

‐4.429

43.6

4.42

9‐43.6

00

00

‐2.419

25.6

2.41

9‐25.6

00

00

‐2.529

32.4

2.52

9‐32.4

00

00

‐1.346

10.9

1.34

6‐10.9

‐0.047

14.686

140.04

73.67

1535

‐1.378

8.7

1.37

8‐8.7

‐0.081

24.476

890.08

16.11

9223

‐5.636

58.4

5.63

6‐58.4

‐0.033

9.79

076

0.03

32.44

769

‐2.88

31.1

2.88

‐31.1

‐0.024

7.34

307

0.02

41.83

5768

‐2.938

37.8

2.93

8‐37.8

‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

‐0.095

29.4

0.09

57.35

‐1.58

10.5

1.58

‐10.5

‐0.163

490.16

312

.25

‐6.882

75.1

6.88

2‐75.1

‐0.065

19.6

0.06

54.9

‐3.344

36.5

3.34

4‐36.5

‐0.047

14.7

0.04

73.67

5‐3.372

43.5

3.37

2‐43.5

‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

‐0.142

44.1

0.14

211

.025

‐1.782

12.3

1.78

2‐12.3

‐0.358

73.499

980.35

818

.375

‐8.182

92.2

8.18

2‐92.2

‐0.098

29.4

0.09

87.35

‐3.761

41.4

3.76

1‐41.4

‐0.071

22.05

0.07

15.51

25‐3.869

50.4

3.86

9‐50.4

‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

‐0.197

58.8

0.19

714

.7‐1.985

14.1

1.98

5‐14.1

‐0.761

980.76

124

.5‐9.547

110.1

9.54

7‐110

.1‐0.13

39.2

0.13

9.8

‐4.235

47.1

4.23

5‐47.1

‐0.095

29.4

0.09

57.35

‐4.365

57.4

4.36

5‐57.4

‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

‐0.289

73.5

0.28

918

.375

‐2.194

162.19

4‐16

‐1.238

122.5

1.23

830

.625

128.7

‐0.165

490.16

512

.25

‐4.688

52.5

4.68

8‐52.5

‐0.119

36.75

0.11

99.18

75‐4.865

64.4

4.86

5‐64.4

‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

‐0.425

88.2

0.42

522

.05

‐2.418

18.2

2.41

8‐18.2

‐1.724

147

1.72

436

.75

‐0.29

58.8

0.29

14.7

‐5.201

58.9

5.20

1‐58.9

‐0.142

44.1

0.14

211

.025

‐5.358

71.2

5.35

8‐71.2

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

‐0.595

102.9

0.59

525

.725

‐2.638

20.2

2.63

8‐20.2

‐2.229

171.5

2.22

942

.875

‐0.96

68.6

0.96

17.15

‐5.775

66.2

5.77

5‐66.2

‐0.176

51.45

0.17

612

.862

5‐5.856

78.1

5.85

6‐78.1

‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

‐0.783

117.6

0.78

329

.4‐2.87

22.5

2.87

‐22.5

‐2.751

196

2.75

149

‐1.453

78.399

991.45

319

.6‐6.365

746.36

5‐74

‐0.604

58.8

0.60

414

.7‐6.349

84.9

6.34

9‐84.9

‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

‐0.978

132.3

0.97

833

.075

01‐3.553

31.3

3.55

3‐31.3

‐3.279

220.5

3.27

955

.125

01‐1.958

88.2

1.95

822

.05

‐6.976

82.4

6.97

6‐82.4

‐2.146

66.15

2.14

616

.537

5‐6.84

91.6

6.84

‐91.6

‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

‐1.177

147

1.17

736

.75

‐4.167

39.1

4.16

7‐39.1

‐4.429

245

4.42

961

.25

‐2.419

98.000

012.41

924

.5‐7.584

90.6

7.58

4‐90.6

‐2.529

73.499

992.52

918

.375

‐7.336

98.5

7.33

6‐98.5

‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

‐1.378

161.7

1.37

840

.425

‐4.801

47.1

4.80

1‐47.1

‐5.636

269.5

5.63

667

.374

99‐2.88

107.8

2.88

26.95

‐8.192

98.9

8.19

2‐98.9

‐2.938

80.849

992.93

820

.212

5‐7.833

105.3

7.83

3‐105

.3‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

‐1.58

176.4

1.58

44.1

‐5.467

55.5

5.46

7‐55.5

‐6.882

294

6.88

273

.5‐3.344

117.6

3.34

429

.4‐8.804

107.1

8.80

4‐107

.1‐3.372

88.200

013.37

222

.05

‐8.331

112

8.33

1‐112

‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

‐1.782

191.1

1.78

247

.775

01‐6.177

64.7

6.17

7‐64.7

‐8.182

318.5

8.18

279

.625

‐3.761

127.4

3.76

131

.85

‐9.42

115.4

9.42

‐115

.4‐3.869

95.549

993.86

923

.887

5‐8.829

118.8

8.82

9‐118

.8‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

‐1.985

205.8

1.98

551

.45

‐6.919

74.4

6.91

9‐74.4

‐9.547

343

9.54

785

.75

‐4.235

137.2

4.23

534

.3‐10.04

312

3.8

10.043

‐123

.8‐4.365

102.9

4.36

525

.725

‐9.328

125.6

9.32

8‐125

.6‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

‐2.194

220.5

2.19

455

.125

‐7.681

84.3

7.68

1‐84.3

‐4.688

147

4.68

836

.75

‐10.67

613

2.2

10.676

‐132

.2‐4.865

110.25

4.86

527

.562

5‐9.828

132.3

9.82

8‐132

.3‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

‐2.418

235.2

2.41

858

.800

01‐8.445

94.3

8.44

5‐94.3

‐5.201

156.8

5.20

139

.214

0.7

‐5.358

117.6

5.35

829

.4‐10.33

413

910

.334

‐139

‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

‐2.638

249.9

2.63

862

.475

‐9.257

105.1

9.25

7‐105

.1‐5.775

166.6

5.77

541

.65

‐5.856

124.95

5.85

631

.237

5‐10.83

714

5.8

10.837

‐145

.8‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

‐2.87

264.6

2.87

66.15

‐10.07

811

5.8

10.078

‐115

.8‐6.365

176.4

6.36

544

.100

01‐6.349

132.3

6.34

933

.075

‐11.34

152.5

11.34

‐152

.5‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.7‐3.553

279.3

3.55

369

.824

99‐10.90

112

6.5

10.901

‐126

.5‐6.976

186.2

6.97

646

.55

‐6.84

139.65

6.84

34.912

515

9.2

‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.4‐4.167

294

4.16

773

.5‐11.74

113

7.3

11.741

‐137

.3‐7.584

196

7.58

449

.000

01‐7.336

147

7.33

636

.75

‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

‐4.801

308.7

4.80

177

.175

‐8.192

205.8

8.19

251

.45

‐7.833

154.35

7.83

338

.587

51‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.6‐5.467

323.4

5.46

780

.85

‐8.804

215.6

8.80

453

.9‐8.331

161.7

8.33

140

.425

‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.4‐6.177

338.1

6.17

784

.525

‐9.42

225.4

9.42

56.35

‐8.829

169.05

8.82

942

.262

5‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.2‐6.919

352.8

6.91

988

.200

01‐10.04

323

5.2

10.043

58.8

‐9.328

176.4

9.32

844

.1‐6.765

235.2

6.76

558

.8‐7.681

367.5

7.68

191

.874

99‐10.67

624

510

.676

61.25

‐9.828

183.75

9.82

845

.937

5‐7.32

245

7.32

61.250

01‐8.445

382.2

8.44

595

.55

‐10.33

419

1.1

10.334

47.775

‐7.88

254.8

7.88

63.700

01‐9.257

396.9

9.25

799

.225

‐10.83

719

8.45

10.837

49.612

5‐8.44

264.6

8.44

66.150

01‐10.07

841

1.6

10.078

102.9

‐11.34

205.8

11.34

51.45

‐9.011

274.4

9.01

168

.6‐10.90

142

6.3

10.901

106.57

5‐9.587

284.2

9.58

771

.049

99‐11.74

144

111

.741

110.25

‐10.16

729

410

.167

73.499

99max steel stress 4

38.6

max steel stress 4

24.3

max steel stress 4

00.6

max steel stress 4

05.5

‐10.75

730

3.8

10.757

75.95

fcm

0.41

fcm

0.12

‐11.36

831

3.6

11.368

78.4

‐11.99

232

3.4

11.992

80.85

REINFO

RCEM

ENT RA

TIO

0crack

12.25

yield

NO

crush

0.2crack

12.25yield

14.7

crush

0.4crack

12.25

yield

19.6

crush

0.6crack

12.25

yield

30.625

crush

0.8crack

12.25

yield

39.2

crush

1.2crack

49yield

55.125

crush

vert

horiz

vert

horiz

vert

horiz

vert

horiz

vert

horiz

vert

horiz

Data from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

==============

‐0.008

00.00

80 ==============

‐0.016

00.01

60

==============

‐0.033

00.03

30

==============

‐0.049

00.04

90

==============

‐0.066

00.06

60

==============

‐0.082

00.08

20

‐0.016

00.01

60

‐0.033

00.03

30

‐0.066

00.06

60

‐0.099

00.09

90

‐0.132

00.13

20

‐0.166

00.16

60

Title

: Con

trol Chart

‐0.025

00.02

50 Title

: Con

trol Ch

‐0.049

00.04

90

Title

: Con

trol Chart

‐0.099

00.09

90

Title

: Con

trol Chart

‐0.148

00.14

80

Title

: Con

trol Chart

‐0.239

0.3

0.23

9‐0.3

Title

: Con

trol Chart

‐0.556

2.9

0.55

6‐2.9

‐0.033

00.03

30

‐0.066

00.06

60

‐0.132

00.13

20

‐0.256

0.4

0.25

6‐0.4

‐0.843

60.84

3‐6

‐1.179

8.7

1.17

9‐8.7

X Axis T

itle: x‐axis

‐0.041

00.04

10 X Axis T

itle: x‐axis

‐0.082

00.08

20

X Axis T

itle: x‐axis

‐0.167

00.16

70

X Axis T

itle: x‐axis

‐0.885

7.1

0.88

5‐7.1

X Axis T

itle: x‐axis

‐1.512

13.1

1.51

2‐13.1

X Axis T

itle: x‐axis

‐1.861

15.6

1.86

1‐15.6

Y Axis T

itle: y‐axis

‐0.049

00.04

90 Y Axis T

itle: y‐axis

‐0.099

00.09

90

Y Axis T

itle: y‐axis

‐0.277

0.6

0.27

7‐0.6

Y Axis T

itle: y‐axis

‐1.465

13.5

1.46

5‐13.5

Y Axis T

itle: y‐axis

‐2.169

20.3

2.16

9‐20.3

Y Axis T

itle: y‐axis

‐2.566

22.9

2.56

6‐22.9

‐0.058

00.05

80

‐0.115

00.11

50

‐1.044

10.1

1.04

4‐10.1

‐2.04

20.1

2.04

‐20.1

‐2.824

27.6

2.82

4‐27.6

‐3.257

30.1

3.25

7‐30.1

x‐axis

y‐axis

‐0.066

00.06

60 x‐axis

y‐axis

‐0.132

00.13

20

x‐axis

y‐axis

‐1.636

18.4

1.63

6‐18.4

x‐axis

y‐axis

‐2.667

27.6

2.66

7‐27.6

x‐axis

y‐axis

‐3.618

37.2

3.61

8‐37.2

x‐axis

y‐axis

‐3.951

37.3

3.95

1‐37.3

Line

type

: 0

‐0.074

00.07

40Line

type

: 0

‐0.148

00.14

80Line

type

: 0

‐2.255

27.3

2.25

5‐27.3Line

type

: 0

‐3.551

39.9

3.55

1‐39.9Line

type

: 0

‐4.759

52.6

4.75

9‐52.6Line

type

: 0

‐4.725

45.8

4.72

5‐45.8

00

00

‐0.082

00.08

20

00

00

‐0.169

00.16

90

00

00

‐2.853

35.8

2.85

3‐35.8

00

00

‐4.422

524.42

2‐52

00

00

‐5.88

67.9

5.88

‐67.9

00

00

‐6.046

62.9

6.04

6‐62.9

‐0.008

2.44

769

0.00

80.61

1923

‐0.091

00.09

10

‐0.016

4.89

538

0.01

61.22

3845

‐0.229

10.22

9‐1

‐0.033

9.79

076

0.03

32.44

769

‐3.476

44.3

3.47

6‐44.3

‐0.049

14.686

140.04

93.67

1535

‐5.29

64.1

5.29

‐64.1

‐0.066

19.581

510.06

64.89

5378

‐7.012

83.3

7.01

2‐83.3

‐0.082

24.476

90.08

26.11

9225

‐7.38

80.2

7.38

‐80.2

‐0.016

4.9

0.01

61.22

5‐0.099

00.09

90

‐0.033

9.8

0.03

32.45

‐1.926

26.4

1.92

6‐26.4

‐0.066

19.6

0.06

64.9

‐4.094

52.8

4.09

4‐52.8

‐0.099

29.4

0.09

97.35

‐6.159

76.2

6.15

9‐76.2

‐0.132

39.200

010.13

29.80

0003

‐8.156

98.9

8.15

6‐98.9

‐0.166

490.16

612

.25

‐8.756

98.1

8.75

6‐98.1

‐0.025

7.35

0.02

51.83

75‐0.107

00.10

70

‐0.049

14.7

0.04

93.67

5‐0.099

29.4

0.09

97.35

‐4.691

61.3

4.69

1‐61.3

‐0.148

44.1

0.14

811

.025

‐7.038

88.5

7.03

8‐88.5

‐0.239

58.8

0.23

914

.7‐9.318

114.7

9.31

8‐114

.7‐0.556

73.5

0.55

618

.375

‐10.17

911

6.3

10.179

‐116

.3‐0.033

9.8

0.03

32.45

‐0.115

00.11

50

‐0.066

19.6

0.06

64.9

‐0.132

39.2

0.13

29.8

‐5.293

69.9

5.29

3‐69.9

‐0.256

58.8

0.25

614

.7‐7.922

100.8

7.92

2‐100

.8‐0.843

78.4

0.84

319

.6‐10.49

413

0.6

10.494

‐130

.6‐1.179

98.000

011.17

924

.5‐11.66

613

4.9

11.666

‐134

.9‐0.041

12.25

0.04

13.06

25‐0.123

00.12

30

‐0.082

24.5

0.08

26.12

5‐0.167

490.16

712

.25

‐5.908

78.4

5.90

8‐78.4

‐0.885

73.500

010.88

518

.375

‐8.807

113.1

8.80

7‐113

.1‐1.512

981.51

224

.5‐11.69

114

6.7

11.691

‐146

.7‐1.861

122.5

1.86

130

.625

‐0.049

14.7

0.04

93.67

5‐0.132

00.13

20

‐0.099

29.4

0.09

97.35

‐0.277

58.8

0.27

714

.7‐6.509

876.50

9‐87

‐1.465

88.2

1.46

522

.05

‐9.701

125.6

9.70

1‐125

.6‐2.169

117.6

2.16

929

.4‐2.566

147

2.56

636

.75

‐0.058

17.15

0.05

84.28

75‐0.14

00.14

0‐0.115

34.3

0.11

58.57

5‐1.044

68.6

1.04

417

.15

‐7.115

95.6

7.11

5‐95.6

‐2.04

102.9

2.04

25.725

‐10.60

713

8.2

10.607

‐138

.2‐2.824

137.2

2.82

434

.3‐3.257

171.5

3.25

742

.875

‐0.066

19.6

0.06

64.9

‐0.148

00.14

80

‐0.132

39.2

0.13

29.8

‐1.636

78.399

991.63

619

.6‐7.721

104.3

7.72

1‐104

.3‐2.667

117.6

2.66

729

.4‐11.50

215

1.7

11.502

‐151

.7‐3.618

156.8

3.61

839

.2‐3.951

196

3.95

149

‐0.074

22.05

0.07

45.51

25‐0.156

00.15

60

‐0.148

44.1

0.14

811

.025

‐2.255

88.2

2.25

522

.05

‐8.34

112.8

8.34

‐112

.8‐3.551

132.3

3.55

133

.075

‐4.759

176.4

4.75

944

.1‐4.725

220.5

4.72

555

.125

01‐0.082

24.5

0.08

26.12

5‐0.177

3.1

0.17

7‐3.1

‐0.169

490.16

912

.25

‐2.853

98.000

012.85

324

.5‐8.945

121.5

8.94

5‐121

.5‐4.422

147

4.42

236

.75

‐5.88

196

5.88

49‐6.046

245

6.04

661

.250

01‐0.091

26.95

0.09

16.73

75‐0.229

53.9

0.22

913

.475

‐3.476

107.8

3.47

626

.95

‐9.556

130.2

9.55

6‐130

.2‐5.29

161.7

5.29

40.425

01‐7.012

215.6

7.01

253

.9‐7.38

269.5

7.38

67.375

01‐0.099

29.4

0.09

97.35

‐1.926

58.8

1.92

614

.7‐4.094

117.6

4.09

429

.4‐10.16

413

910

.164

‐139

‐6.159

176.4

6.15

944

.1‐8.156

235.2

8.15

658

.8‐8.756

294

8.75

673

.5‐0.107

31.85

0.10

77.96

25‐4.691

127.4

4.69

131

.850

01‐10.74

914

9.9

10.749

‐149

.9‐7.038

191.1

7.03

847

.775

‐9.318

254.8

9.31

863

.7‐10.17

931

8.5

10.179

79.625

‐0.115

34.3

0.11

58.57

5‐5.293

137.2

5.29

334

.3‐11.35

215

9.8

11.352

‐159

.8‐7.922

205.8

7.92

251

.450

01‐10.49

427

4.4

10.494

68.6

‐11.66

634

311

.666

85.750

01‐0.123

36.75

0.12

39.18

75‐5.908

147

5.90

836

.75

‐11.93

517

2.8

11.935

‐172

.8‐8.807

220.5

8.80

755

.125

01‐11.69

129

411

.691

73.5

‐0.132

39.2

0.13

29.8

‐6.509

156.8

6.50

939

.2‐9.701

235.2

9.70

158

.8‐0.14

41.649

990.14

10.412

5‐7.115

166.6

7.11

541

.65

‐10.60

724

9.9

10.607

62.475

‐0.148

44.1

0.14

811

.025

‐7.721

176.4

7.72

144

.100

01‐11.50

226

4.6

11.502

66.15

‐0.156

46.55

0.15

611

.637

5‐8.34

186.2

8.34

46.55

‐0.177

490.17

712

.25

‐8.945

196

8.94

549

‐9.556

205.8

9.55

651

.45

‐10.16

421

5.6

10.164

53.9

‐10.74

922

5.4

10.749

56.35

‐11.35

223

5.2

11.352

58.800

01‐11.93

524

511

.935

61.25

ref

crack

12.25

yield

49vert

horiz

1.4crack

12.25

yield

62.475

crush

1.6crack

12.25

yield

69.825

crush

1.8crack

12.25

yield

77.175

crush

2crack

12.25

yield

83.3

First crack

Yield

Failure

Data from

Graph

00

00

vert

horiz

vert

horiz

vert

horiz

vert

horiz

012

.25

12.25

==============

‐0.033

00.03

30

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

0.2

12.25

14.7

14.7

‐0.066

00.06

60

==============

‐0.082

00.08

20

==============

‐0.082

00.08

20

==============

‐0.049

00.04

90

==============

‐0.066

00.06

60

0.4

12.25

19.6

61.25

Title

: Con

trol Chart

‐0.099

00.09

90

‐0.165

00.16

50

‐0.165

00.16

50

‐0.099

00.09

90

‐0.132

00.13

20

0.6

12.25

30.625

66.15

‐0.132

00.13

20

Title

: Con

trol Chart

‐0.502

2.3

0.50

2‐2.3

Title

: Con

trol Chart

‐0.456

1.8

0.45

6‐1.8

Title

: Con

trol Chart

‐0.148

00.14

80

Title

: Con

trol Chart

‐0.221

00.22

10

0.8

12.25

39.2

73.5

X Axis T

itle: x‐axis

‐0.165

00.16

50

‐1.087

7.5

1.08

7‐7.5

‐0.97

6.1

0.97

‐6.1

‐0.228

0.2

0.22

8‐0.2

‐0.488

0.2

0.48

8‐0.2

112

.25

4980

.85

Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

X Axis T

itle: x‐axis

‐1.715

13.7

1.71

5‐13.7

X Axis T

itle: x‐axis

‐1.56

11.6

1.56

‐11.6

X Axis T

itle: x‐axis

‐0.459

1.8

0.45

9‐1.8

X Axis T

itle: x‐axis

‐0.856

1.9

0.85

6‐1.9

1.2

12.25

55.125

85.75

‐0.477

2.3

0.47

7‐2.3

Y Axis T

itle: y‐axis

‐2.355

202.35

5‐20

Y Axis T

itle: y‐axis

‐2.158

17.4

2.15

8‐17.4

Y Axis T

itle: y‐axis

‐0.749

4.2

0.74

9‐4.2

Y Axis T

itle: y‐axis

‐1.268

4.8

1.26

8‐4.8

1.4

12.25

62.475

85.75

x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

‐3.009

26.6

3.00

9‐26.6

‐2.753

23.1

2.75

3‐23.1

‐1.073

71.07

3‐7

‐1.696

8.4

1.69

6‐8.4

1.6

12.25

69.825

91.875

Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

x‐axis

y‐axis

‐3.651

33.1

3.65

1‐33.1

x‐axis

y‐axis

‐3.353

293.35

3‐29

x‐axis

y‐axis

‐1.413

10.1

1.41

3‐10.1

x‐axis

y‐axis

‐2.124

12.2

2.12

4‐12.2

1.8

12.25

77.18

95.5

00

00

‐1.346

10.9

1.34

6‐10.9

Line

type

: 0

‐4.303

39.7

4.30

3‐39.7Line

type

: 0

‐3.974

35.1

3.97

4‐35.1Line

type

: 0

‐1.752

13.3

1.75

2‐13.3Line

type

: 0

‐2.554

16.1

2.55

4‐16.1

212

.25

83.3

98‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

00

00

‐4.97

46.5

4.97

‐46.5

00

00

‐4.589

41.1

4.58

9‐41.1

00

00

‐2.092

16.4

2.09

2‐16.4

00

00

‐2.988

202.98

8‐20

‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

‐0.082

24.476

90.08

26.11

9225

‐6.171

61.5

6.17

1‐61.5

‐0.082

24.476

90.08

26.11

9225

‐5.225

47.4

5.22

5‐47.4

‐0.049

14.686

140.04

93.67

1535

‐2.435

19.7

2.43

5‐19.7

‐0.066

19.581

510.06

64.89

5378

‐3.416

243.41

6‐24

‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

‐0.165

490.16

512

.25

‐7.478

78.1

7.47

8‐78.1

‐0.165

490.16

512

.25

‐6.299

60.2

6.29

9‐60.2

‐0.099

29.4

0.09

97.35

‐2.769

22.8

2.76

9‐22.8

‐0.132

39.200

010.13

29.80

0003

‐3.855

283.85

5‐28

‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

‐0.502

73.500

010.50

218

.375

‐8.83

95.1

8.83

‐95.1

‐0.456

73.499

990.45

618

.375

‐7.597

76.3

7.59

7‐76.3

‐0.148

44.1

0.14

811

.025

‐3.114

26.1

3.11

4‐26.1

‐0.221

58.8

0.22

114

.7‐4.295

324.29

5‐32

‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

‐1.087

981.08

724

.5‐10.24

611

2.7

10.246

‐112

.7‐0.97

97.999

990.97

24.5

‐8.945

92.8

8.94

5‐92.8

‐0.228

58.8

0.22

814

.7‐3.45

29.3

3.45

‐29.3

‐0.488

78.4

0.48

819

.6‐4.75

36.1

4.75

‐36.1

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

‐1.715

122.5

1.71

530

.625

‐1.56

122.5

1.56

30.625

‐10.38

110

9.8

10.381

‐109

.8‐0.459

73.499

990.45

918

.375

‐3.793

32.6

3.79

3‐32.6

‐0.856

98.000

010.85

624

.5‐5.207

40.3

5.20

7‐40.3

‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

‐2.355

147

2.35

536

.750

01‐2.158

147

2.15

836

.75

‐0.749

88.2

0.74

922

.05

‐4.154

364.15

4‐36

‐1.268

117.6

1.26

829

.4‐5.674

44.5

5.67

4‐44.5

‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

‐3.009

171.5

3.00

942

.875

‐2.753

171.5

2.75

342

.875

‐1.073

102.9

1.07

325

.725

‐4.501

39.3

4.50

1‐39.3

‐1.696

137.2

1.69

634

.3‐6.207

48.8

6.20

7‐48.8

‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

‐3.651

196

3.65

149

‐3.353

196

3.35

349

‐1.413

117.6

1.41

329

.4‐4.853

42.7

4.85

3‐42.7

‐2.124

156.8

2.12

439

.2‐7.183

547.18

3‐54

‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

‐4.303

220.5

4.30

355

.125

01‐3.974

220.5

3.97

455

.125

‐1.752

132.3

1.75

233

.075

01‐5.208

46.1

5.20

8‐46.1

‐2.554

176.4

2.55

444

.1‐8.213

65.4

8.21

3‐65.4

‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

‐4.97

245

4.97

61.25

‐4.589

245

4.58

961

.249

99‐2.092

147

2.09

236

.75

‐5.572

49.5

5.57

2‐49.5

‐2.988

196

2.98

849

‐9.354

77.5

9.35

4‐77.5

‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

‐6.171

269.5

6.17

167

.375

‐5.225

269.5

5.22

567

.375

‐2.435

161.7

2.43

540

.425

‐6.017

54.1

6.01

7‐54.1

‐3.416

215.6

3.41

653

.9‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

‐7.478

294

7.47

873

.5‐6.299

294

6.29

973

.499

99‐2.769

176.4

2.76

944

.1‐6.753

62.9

6.75

3‐62.9

‐3.855

235.2

3.85

558

.8‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

‐8.83

318.5

8.83

79.625

‐7.597

318.5

7.59

779

.625

‐3.114

191.1

3.11

447

.775

‐7.522

72.2

7.52

2‐72.2

‐4.295

254.8

4.29

563

.700

01‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

‐10.24

634

310

.246

85.75

‐8.945

343

8.94

585

.750

01‐3.45

205.8

3.45

51.450

01‐8.306

81.6

8.30

6‐81.6

‐4.75

274.4

4.75

68.6

‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

‐10.38

136

7.5

10.381

91.875

‐3.793

220.5

3.79

355

.125

‐9.117

91.2

9.11

7‐91.2

‐5.207

294

5.20

773

.5‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

‐4.154

235.2

4.15

458

.8‐10.00

410

1.3

10.004

‐101

.3‐5.674

313.6

5.67

478

.4‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.7‐4.501

249.9

4.50

162

.474

99‐6.207

333.2

6.20

783

.299

99‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.4‐4.853

264.6

4.85

366

.15

‐7.183

352.8

7.18

388

.2‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

‐5.208

279.3

5.20

869

.825

01‐8.213

372.4

8.21

393

.1‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.6‐5.572

294

5.57

273

.5‐9.354

392

9.35

498

‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.4‐6.017

308.7

6.01

777

.175

‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.2‐6.753

323.4

6.75

380

.85

‐6.765

235.2

6.76

558

.8‐7.522

338.1

7.52

284

.525

01‐7.32

245

7.32

61.250

01‐8.306

352.8

8.30

688

.2‐7.88

254.8

7.88

63.700

01‐9.117

367.5

9.11

791

.875

01‐8.44

264.6

8.44

66.150

01‐10.00

438

2.2

10.004

95.549

99‐9.011

274.4

9.01

168

.6‐9.587

284.2

9.58

771

.049

99‐10.16

729

410

.167

73.499

99‐10.75

730

3.8

10.757

75.95

‐11.36

831

3.6

11.368

78.4

‐11.99

232

3.4

11.992

80.85

LENGTH

1crack

127.4

yield

132.3crush

2crack

83.3

yield

102.9crush

3crack

61.3

yield

134.8crush

5crack

44.1

yield

235.2crush

6crack

34.3

yield

291.6crush

vert

127.4

horiz

132.3

vert

41.65

horiz

51.45

vert

20.433

33ho

riz44

.933

33vert

8.82

horiz

47.04

vert

5.71

6667

horiz

48.6

Data from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

==============

‐0.002

00.00

20 ==============

‐0.014

00.014

0 ==============

‐0.024

00.024

0 ==============

‐0.076

00.07

60

==============

‐0.126

00.12

60

‐0.003

00.00

30

‐0.029

00.02

90

‐0.048

00.04

80

‐0.151

00.15

10

‐0.252

00.25

20

Title

: Con

trol Chart

‐0.005

00.00

50 Title

: Con

trol Chart

‐0.043

00.04

30

Title

: Con

trol Chart

‐0.073

00.07

30

Title

: Con

trol Chart

‐0.236

00.23

60

Title

: Con

trol Chart

‐0.534

1.1

0.534

‐1.1

‐0.006

00.00

60

‐0.057

00.05

70

‐0.097

00.09

70

‐0.446

1.1

0.44

6‐1.1

‐1.126

5.1

1.12

6‐5.1

X Axis T

itl: x‐axis

‐0.008

00.00

80 X Axis T

itl: x‐axis

‐0.072

00.07

20

X Axis T

itl: x‐axis

‐0.122

00.12

20

X Axis T

itl: x‐axis

‐0.897

4.6

0.89

7‐4.6

X Axis T

itl: x‐axis

‐1.791

10.2

1.79

1‐10.2

Y Axis T

itle: y‐axis

‐0.01

00.01

0 Y Axis T

itle: y‐axis

‐0.094

0.1

0.09

4‐0.1

Y Axis T

itle: y‐axis

‐0.179

0.3

0.17

9‐0.3

Y Axis T

itle: y‐axis

‐1.378

8.7

1.37

8‐8.7

Y Axis T

itle: y‐axis

‐2.477

15.6

2.47

7‐15.6

‐0.011

00.01

10

‐1.414

22.3

1.414

‐22.3

‐0.489

3.6

0.48

9‐3.6

‐1.875

13.2

1.87

5‐13.2

‐3.162

21.2

3.16

2‐21.2

x‐axis

y‐axis

‐0.013

00.01

30 x‐axis

y‐axis

‐1.88

30.1

1.88

‐30.1

x‐axis

y‐axis

‐0.835

7.5

0.83

5‐7.5

x‐axis

y‐axis

‐2.383

17.8

2.38

3‐17.8

x‐axis

y‐axis

‐3.851

26.8

3.85

1‐26.8

Line

type

: 0

‐0.014

00.014

0Line

type

: 0

‐2.322

37.7

2.32

2‐37.7Line

type

: 0

‐1.175

11.5

1.17

5‐11.5Line

type

: 0

‐2.893

22.5

2.89

3‐22.5Line

type

: 0

‐4.543

32.5

4.54

3‐32.5

00

00

‐0.016

00.01

60

00

00

‐2.771

45.3

2.77

1‐45.3

00

00

‐1.531

15.9

1.53

1‐15.9

00

00

‐3.404

27.3

3.404

‐27.3

00

00

‐5.227

385.22

7‐38

‐0.002

4.89

544

0.00

24.89

544

‐0.018

00.01

80

‐0.014

14.686

140.01

47.34

307

‐3.219

533.21

9‐53

‐0.024

12.238

450.024

4.07

9483

‐2.042

232.04

2‐23

‐0.076

14.686

140.07

62.93

7228

‐3.916

32.1

3.91

6‐32.1

‐0.126

17.133

830.12

62.85

5638

‐5.925

43.7

5.92

5‐43.7

‐0.003

9.8

0.00

39.8

‐0.019

00.01

90

‐0.029

29.4

0.02

914

.7‐3.671

60.7

3.67

1‐60.7

‐0.048

24.5

0.04

88.16

6667

‐2.597

31.1

2.59

7‐31.1

‐0.151

29.4

0.15

15.88

‐4.453

37.1

4.45

3‐37.1

‐0.252

34.3

0.25

25.71

6667

‐6.614

49.3

6.61

4‐49.3

‐0.005

14.7

0.00

514

.7‐0.021

00.02

10

‐0.043

44.1

0.04

322

.05

‐4.125

68.4

4.12

5‐68.4

‐0.073

36.75

0.07

312

.25

‐3.135

393.13

5‐39

‐0.236

44.1

0.23

68.82

‐4.973

424.97

3‐42

‐0.534

51.45

0.534

8.57

5‐7.322

55.1

7.32

2‐55.1

‐0.006

19.599

760.00

619

.599

76‐0.022

00.02

20

‐0.057

58.8

0.05

729

.4‐4.583

76.1

4.58

3‐76.1

‐0.097

49.000

010.09

716

.333

34‐3.675

46.9

3.67

5‐46.9

‐0.446

58.8

0.44

611

.76

‐5.496

46.9

5.49

6‐46.9

‐1.126

68.600

011.12

611

.433

34‐8.048

618.04

8‐61

‐0.008

24.5

0.00

824

.5‐0.024

00.024

0‐0.072

73.500

010.07

236

.750

01‐5.043

83.8

5.04

3‐83.8

‐0.122

61.25

0.12

220

.416

67‐4.216

54.8

4.21

6‐54.8

‐0.897

73.500

010.89

714

.7‐6.032

526.03

2‐52

‐1.791

85.749

991.79

114

.291

67‐8.777

66.8

8.77

7‐66.8

‐0.01

29.4

0.01

29.4

‐0.026

00.02

60

‐0.094

88.199

990.094

44.1

‐5.506

91.6

5.50

6‐91.6

‐0.179

73.499

990.17

924

.5‐4.758

62.8

4.75

8‐62.8

‐1.378

88.2

1.37

817

.64

‐6.614

57.7

6.61

4‐57.7

‐2.477

102.9

2.47

717

.15

‐9.533

72.8

9.53

3‐72.8

‐0.011

34.3

0.01

134

.3‐0.027

00.02

70

‐1.414

102.9

1.414

51.45

‐5.972

99.4

5.97

2‐99.4

‐0.489

85.75

0.48

928

.583

33‐5.304

70.8

5.30

4‐70.8

‐1.875

102.9

1.87

520

.58

‐7.566

68.9

7.56

6‐68.9

‐3.162

120.05

3.16

220

.008

34‐10.71

784

.410

.717

‐84.4

‐0.013

39.2

0.01

339

.2‐0.029

00.02

90

‐1.88

117.6

1.88

58.8

‐6.44

107.1

6.44

‐107

.1‐0.835

97.999

990.83

532

.666

66‐5.85

78.8

5.85

‐78.8

‐2.383

117.6

2.38

323

.52

‐8.585

818.58

5‐81

‐3.851

137.2

3.85

122

.866

67‐12.28

810

0.7

12.288

‐100

.7‐0.014

44.1

0.01

444

.1‐0.03

00.03

0‐2.322

132.3

2.32

266

.15

‐6.911

114.9

6.91

1‐114

.9‐1.175

110.25

1.17

536

.75

‐6.403

86.9

6.40

3‐86.9

‐2.893

132.3

2.89

326

.46

‐9.616

93.3

9.61

6‐93.3

‐4.543

154.35

4.54

325

.725

‐0.016

490.01

649

‐0.032

00.03

20

‐2.771

147

2.77

173

.499

99‐7.578

124

7.57

8‐124

‐1.531

122.5

1.53

140

.833

34‐6.957

95.1

6.95

7‐95.1

‐3.404

147

3.404

29.4

‐10.66

410

5.6

10.664

‐105

.6‐5.227

171.5

5.22

728

.583

33‐0.018

53.9

0.01

853

.9‐0.034

00.034

0‐3.219

161.7

3.21

980

.85

‐8.065

131.9

8.06

5‐131

.9‐2.042

134.75

2.04

244

.916

67‐7.508

103.1

7.50

8‐103

.1‐3.916

161.7

3.91

632

.34

‐11.75

511

8.5

11.755

‐118

.5‐5.925

188.65

5.92

531

.441

67‐0.019

58.8

0.01

958

.8‐0.035

00.03

50

‐3.671

176.4

3.67

188

.199

99‐8.725

140.6

8.72

5‐140

.6‐2.597

147

2.59

748

.999

99‐8.071

111.3

8.07

1‐111

.3‐4.453

176.4

4.45

335

.28

‐6.614

205.8

6.614

34.3

‐0.021

63.7

0.02

163

.7‐0.037

00.03

70

‐4.125

191.1

4.12

595

.549

99‐9.223

148.5

9.22

3‐148

.5‐3.135

159.25

3.13

553

.083

33‐8.635

119.5

8.63

5‐119

.5‐4.973

191.1

4.97

338

.22

‐7.322

222.95

7.32

237

.158

33‐0.022

68.6

0.02

268

.6‐0.038

00.03

80

‐4.583

205.8

4.58

310

2.9

‐9.821

157.8

9.82

1‐157

.8‐3.675

171.5

3.67

557

.166

67‐9.201

127.7

9.20

1‐127

.7‐5.496

205.8

5.49

641

.16

‐8.048

240.1

8.04

840

.016

67‐0.024

73.500

010.024

73.500

01‐0.04

00.04

0‐5.043

220.5

5.04

311

0.25

‐10.32

216

5.8

10.322

‐165

.8‐4.216

183.75

4.21

661

.250

01‐9.768

136

9.76

8‐136

‐6.032

220.5

6.03

244

.1‐8.777

257.25

8.77

742

.875

‐0.026

78.399

990.02

678

.399

99‐0.044

00.044

0‐5.506

235.2

5.50

611

7.6

‐10.82

617

3.7

10.826

‐173

.7‐4.758

196

4.75

865

.333

33‐10.33

514

4.2

10.335

‐144

.2‐6.614

235.2

6.614

47.04

‐9.533

274.4

9.53

345

.733

33First crack

First y

ield

Failure

‐0.027

83.3

0.02

783

.3‐0.054

0.1

0.05

4‐0.1

‐5.972

249.9

5.97

212

4.95

‐11.33

818

1.6

11.338

‐181

.6‐5.304

208.25

5.304

69.416

67‐10.91

215

2.5

10.912

‐152

.5‐7.566

249.9

7.56

649

.98

‐10.71

729

1.55

10.717

48.591

671

127.4

137.2

137.2no

con

crete

‐0.029

88.2

0.02

988

.2‐2.1

38.8

2.1

‐38.8

‐6.44

264.6

6.44

132.3

‐11.91

419

0.5

11.914

‐190

.5‐5.85

220.5

5.85

73.500

01‐11.48

616

0.7

11.486

‐160

.7‐8.585

264.6

8.58

552

.919

99‐12.79

530

8.7

12.795

51.450

012

41.65

51.45

124.95

no con

crete

‐0.03

93.099

990.03

93.099

99‐6.911

279.3

6.91

113

9.65

‐6.403

232.75

6.40

377

.583

34‐9.616

279.3

9.61

655

.860

013

20.43

44.93

114.3

‐0.032

980.03

298

‐7.578

294

7.57

814

7‐6.957

245

6.95

781

.666

67‐10.66

429

410

.664

58.799

994

12.25

4980

.85

‐0.034

102.9

0.034

102.9

‐8.065

308.7

8.06

515

4.35

‐7.508

257.25

7.50

885

.749

99‐11.75

530

8.7

11.755

61.74

58.82

47.06

61.74

‐0.035

107.8

0.03

510

7.8

‐8.725

323.4

8.72

516

1.7

‐8.071

269.5

8.07

189

.833

336

5.72

48.6

51.45

‐0.037

112.7

0.03

711

2.7

‐9.223

338.1

9.22

316

9.05

‐8.635

281.75

8.63

593

.916

687

4.9

46.55

46.55

‐0.038

117.6

0.03

811

7.6

‐9.821

352.8

9.82

117

6.4

‐9.201

294

9.20

198

83.67

534

.91

‐0.04

122.5

0.04

122.5

‐10.32

236

7.5

10.322

183.75

‐9.768

306.25

9.76

810

2.08

339

2.72

228

.58

‐0.044

127.4

0.04

412

7.4

‐10.82

638

2.2

10.826

191.1

‐10.33

531

8.5

10.335

106.16

6710

2.45

23.52

‐0.054

132.3

0.054

132.3

‐11.33

839

6.9

11.338

198.45

‐10.91

233

0.75

10.912

110.25

‐2.1

137.2

2.1

137.2

‐11.91

441

1.6

11.914

205.8

‐11.48

634

311

.486

114.33

33

ref

crack

49yield

196

7crack

34.3

yield

NO

crush

8crack

29.4

yield

NO

crush

9crack

24.5

yield

NO

crush

10crack

24.5

yield

NO

vert

12.25

horiz

49vert

4.9

horiz

vert

3.67

5ho

rizvert

2.72

2222

horiz

vert

2.45

horiz

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

==============

‐0.033

00.03

30

==============

‐0.172

00.17

20

==============

‐0.194

00.194

0 ==============

‐0.206

00.20

60

==============

‐0.205

00.20

50

‐0.066

00.06

60

‐0.358

0.1

0.35

8‐0.1

‐0.394

00.394

0‐0.412

00.41

20

‐0.41

00.41

0 Title

: Con

trol Chart

‐0.099

00.09

90

Title

: Con

trol Ch: Co

ntrol Ch

‐0.851

2.4

0.85

1‐2.4

Title

: Con

trol Chart

‐0.833

1.6

0.83

3‐1.6

Title

: Con

trol Chart

‐0.781

0.9

0.78

1‐0.9

Title

: Con

trol Chart

‐0.685

0.3

0.68

5‐0.3

‐0.132

00.13

20

‐1.563

6.9

1.56

3‐6.9

‐1.539

5.5

1.53

9‐5.5

‐1.419

3.8

1.41

9‐3.8

‐1.176

21.17

6‐2

X Axis T

itl: x‐axis

‐0.165

00.16

50

X Axis T

itl: x‐axis

‐2.339

12.2

2.33

9‐12.2

X Axis T

itl: x‐axis

‐2.29

9.9

2.29

‐9.9

X Axis T

itl: x‐axis

‐2.114

7.4

2.11

4‐7.4

X Axis T

itl: x‐axis

‐1.801

4.8

1.80

1‐4.8

Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

Y Axis T

itle: y‐axis

‐3.131

17.8

3.13

1‐17.8

Y Axis T

itle: y‐axis

‐3.062

14.7

3.06

2‐14.7 Y Axis T

itle: y‐axis

‐2.844

11.3

2.844

‐11.3

Y Axis T

itle: y‐axis

‐2.444

7.7

2.44

4‐7.7

‐0.477

2.3

0.47

7‐2.3

‐3.922

23.4

3.92

2‐23.4

‐3.836

19.5

3.83

6‐19.5

‐3.574

15.3

3.574

‐15.3

‐3.102

10.9

3.10

2‐10.9

x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

x‐axis

y‐axis

y‐axis

‐4.712

29.1

4.71

2‐29.1

x‐axis

y‐axis

‐4.614

24.4

4.614

‐24.4 x‐axis

y‐axis

‐4.31

19.4

4.31

‐19.4

x‐axis

y‐axis

‐3.773

14.1

3.77

3‐14.1

Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

Line

type

: 0

‐5.506

34.8

5.50

6‐34.8Line

type

: 0

‐5.398

29.4

5.39

8‐29.4Line

type

: 0

‐5.051

23.5

5.05

1‐23.5Line

type

: 0

‐4.442

17.4

4.44

2‐17.4

00

00

‐1.346

10.9

1.34

6‐10.9

00

00

‐6.303

40.5

6.30

3‐40.5

00

00

‐6.175

34.3

6.17

5‐34.3

00

00

‐5.791

27.6

5.79

1‐27.6

00

00

‐5.106

20.7

5.10

6‐20.7

‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

‐0.172

17.133

830.17

22.44

769

‐7.105

46.2

7.10

5‐46.2

‐0.194

14.686

140.19

41.83

5768

‐6.961

39.2

6.96

1‐39.2

‐0.206

12.238

450.20

61.35

9828

‐6.533

31.8

6.53

3‐31.8

‐0.205

9.79

076

0.20

50.97

9076

‐5.778

245.77

8‐24

‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

‐0.358

34.3

0.35

84.9

‐7.911

51.9

7.91

1‐51.9

‐0.394

29.4

0.394

3.67

5‐7.75

44.2

7.75

‐44.2

‐0.412

24.5

0.41

22.72

2222

‐7.279

35.9

7.27

9‐35.9

‐0.41

19.6

0.41

1.96

‐6.451

27.3

6.45

1‐27.3

‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

‐0.851

51.45

0.85

17.35

‐8.726

57.6

8.72

6‐57.6

‐0.833

44.1

0.83

35.51

25‐8.544

49.1

8.544

‐49.1

‐0.781

36.75

0.78

14.08

3333

‐8.033

40.1

8.03

3‐40.1

‐0.685

29.4

0.68

52.94

‐7.128

30.6

7.12

8‐30.6

‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

‐1.563

68.6

1.56

39.8

‐9.556

63.4

9.55

6‐63.4

‐1.539

58.8

1.53

97.35

‐9.347

549.34

7‐54

‐1.419

491.41

95.44

4444

‐8.782

44.2

8.78

2‐44.2

‐1.176

39.2

1.17

63.92

‐7.803

347.80

3‐34

‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

‐2.339

85.75

2.33

912

.25

‐10.38

769

.110

.387

‐69.1

‐2.29

73.5

2.29

9.18

75‐10.15

859

10.158

‐59

‐2.114

61.250

122.114

6.80

5569

‐9.542

48.4

9.54

2‐48.4

‐1.801

491.80

14.9

‐8.484

37.3

8.484

‐37.3

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

‐3.131

102.9

3.13

114

.7‐11.25

174

.911

.251

‐74.9

‐3.062

88.200

013.06

211

.025

‐10.98

364

10.983

‐64

‐2.844

73.5

2.844

8.16

6667

‐10.30

852

.510

.308

‐52.5

‐2.444

58.8

2.444

5.88

‐9.172

40.7

9.17

2‐40.7

‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

‐3.922

120.05

3.92

217

.15

‐12.14

280

.912

.142

‐80.9

‐3.836

102.9

3.83

612

.862

5‐11.81

568

.911

.815

‐68.9

‐3.574

85.749

993.574

9.52

7777

‐11.08

356

.711

.083

‐56.7

‐3.102

68.599

993.10

26.85

9999

‐9.857

449.85

7‐44

‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

‐4.712

137.2

4.71

219

.6‐13.07

386

.913

.073

‐86.9

‐4.614

117.6

4.614

14.7

‐12.66

773

.912

.667

‐73.9

‐4.31

97.999

994.31

10.888

89‐11.87

360

.911

.873

‐60.9

‐3.773

78.400

013.77

37.84

0001

‐10.54

947

.310

.549

‐47.3

‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

‐5.506

154.35

5.50

622

.05

‐5.398

132.3

5.39

816

.537

5‐13.55

578

.913

.555

‐78.9

‐5.051

110.25

5.05

112

.25

‐12.66

665

12.666

‐65

‐4.442

88.200

014.44

28.82

0001

‐11.24

850

.711

.248

‐50.7

‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

‐6.303

171.5

6.30

324

.5‐6.175

147

6.17

518

.375

‐5.791

122.5

5.79

113

.611

11‐13.49

69.2

13.49

‐69.2

‐5.106

985.10

69.8

‐11.95

354

11.953

‐54

‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

‐7.105

188.65

7.10

526

.95

‐6.961

161.7

6.96

120

.212

5‐6.533

134.75

6.53

314

.972

22‐14.32

73.4

14.32

‐73.4

‐5.778

107.8

5.77

810

.78

‐12.67

657

.412

.676

‐57.4

‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

‐7.911

205.8

7.91

129

.4‐7.75

176.4

7.75

22.05

‐7.279

147

7.27

916

.333

33‐6.451

117.6

6.45

111

.76

‐13.41

160

.813

.411

‐60.8

‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

‐8.726

222.95

8.72

631

.85

‐8.544

191.1

8.54

423

.887

5‐8.033

159.25

8.03

317

.694

45‐7.128

127.4

7.12

812

.74

‐14.14

264

.214

.142

‐64.2

‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

‐9.556

240.1

9.55

634

.3‐9.347

205.8

9.34

725

.725

‐8.782

171.5

8.78

219

.055

56‐7.803

137.2

7.80

313

.72

‐14.88

867

.514

.888

‐67.5

‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

‐10.38

725

7.25

10.387

36.75

‐10.15

822

0.5

10.158

27.562

5‐9.542

183.75

9.54

220

.416

67‐8.484

147

8.484

14.7

‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

‐11.25

127

4.4

11.251

39.2

‐10.98

323

5.2

10.983

29.4

‐10.30

819

610

.308

21.777

78‐9.172

156.8

9.17

215

.68

‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

‐12.14

229

1.55

12.142

41.65

‐11.81

524

9.9

11.815

31.237

5‐11.08

320

8.25

11.083

23.138

89‐9.857

166.6

9.85

716

.66

‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.7‐13.07

330

8.7

13.073

44.1

‐12.66

726

4.6

12.667

33.075

‐11.87

322

0.5

11.873

24.5

‐10.54

917

6.4

10.549

17.64

‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.4‐14.48

632

5.85

14.486

46.55

‐13.55

527

9.3

13.555

34.912

5‐12.66

623

2.75

12.666

25.861

11‐11.24

818

6.2

11.248

18.62

‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

‐13.49

245

13.49

27.222

22‐11.95

319

611

.953

19.6

‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.6‐14.32

257.25

14.32

28.583

33‐12.67

620

5.8

12.676

20.58

‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.4‐13.41

121

5.6

13.411

21.56

‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.2‐14.14

222

5.4

14.142

22.54

‐6.765

235.2

6.76

558

.8‐14.88

823

5.2

14.888

23.52

‐7.32

245

7.32

61.250

01‐7.88

254.8

7.88

63.700

01‐8.44

264.6

8.44

66.150

01‐9.011

274.4

9.01

168

.6‐9.587

284.2

9.58

771

.049

99‐10.16

729

410

.167

73.499

99‐10.75

730

3.8

10.757

75.95

‐11.36

831

3.6

11.368

78.4

‐11.99

232

3.4

11.992

80.85

CONC CO

MP STR

5crack

24.5

yield

196crush

10crack

31.9

yield

191crush

20crack

39.2

yield

196

45crack

53.9

yield

191.1

55crack

58.8

yield

186.2

65crack

66.2

yield

183.8

vert

6.12

5ho

riz49

vert

7.97

5ho

riz47

.75

vert

9.8

horiz

49vert

13.475

horiz

47.775

vert

14.7

horiz

46.55

vert

16.55

horiz

45.95

Data from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

==============

‐0.065

00.06

50 ==============

‐0.05

00.05

0 ==============

‐0.04

00.04

0 ==============

‐0.045

00.04

50

==============

‐0.028

00.02

80

==============

‐0.02

00.02

0‐0.132

00.13

20

‐0.1

00.1

0‐0.08

00.08

0‐0.09

00.09

0‐0.056

00.05

60

‐0.039

00.03

90

Title

: Con

trol Chart

‐0.249

0.4

0.24

9‐0.4

Title

: Con

trol Chart

‐0.15

00.15

0 Title

: Con

trol Chart

‐0.119

00.11

90

Title

: Con

trol Chart

‐0.135

00.13

50

Title

: Con

trol Chart

‐0.084

00.08

40

Title

: Con

trol Chart

‐0.059

00.05

90

‐0.551

2.4

0.55

1‐2.4

‐0.265

0.5

0.26

5‐0.5

‐0.16

00.16

0‐0.193

0.1

0.19

3‐0.1

‐0.112

00.11

20

‐0.079

00.07

90

X Axis T

itle: x‐axis

‐0.912

50.91

2‐5

X Axis T

itle: x‐axis

‐0.535

2.5

0.53

5‐2.5

X Axis T

itle: x‐axis

‐0.251

0.4

0.25

1‐0.4

X Axis T

itle: x‐axis

‐0.455

2.2

0.45

5‐2.2

X Axis T

itle: x‐axis

‐0.14

00.14

0 X Axis T

itle: x‐axis

‐0.098

00.09

80

Y Axis T

itle: y‐axis

‐1.299

7.8

1.29

9‐7.8

Y Axis T

itle: y‐axis

‐0.845

5.2

0.84

5‐5.2

Y Axis T

itle: y‐axis

‐0.504

2.4

0.50

4‐2.4

Y Axis T

itle: y‐axis

‐0.905

6.6

0.90

5‐6.6

Y Axis T

itle: y‐axis

‐0.169

00.16

90

Y Axis T

itle: y‐axis

‐0.118

00.11

80

‐1.702

10.5

1.70

2‐10.5

‐1.172

8.1

1.17

2‐8.1

‐0.767

4.8

0.76

7‐4.8

‐1.359

11.3

1.35

9‐11.3

‐0.232

0.2

0.23

2‐0.2

‐0.138

00.13

80

x‐axis

y‐axis

‐2.123

13.2

2.12

3‐13.2 x‐axis

y‐axis

‐1.504

111.50

4‐11

x‐axis

y‐axis

‐1.062

7.6

1.06

2‐7.6

x‐axis

y‐axis

‐1.792

15.9

1.79

2‐15.9

x‐axis

y‐axis

‐0.413

1.7

0.41

3‐1.7

x‐axis

y‐axis

‐0.157

00.15

70

Line

type

: 0

‐2.561

15.8

2.56

1‐15.8Line

type

: 0

‐1.841

141.84

1‐14Line

type

: 0

‐1.363

10.5

1.36

3‐10.5Line

type

: 0

‐2.231

20.6

2.23

1‐20.6Line

type

: 0

‐0.747

50.74

7‐5

Line

type

: 0

‐0.186

0.1

0.18

6‐0.1

00

00

‐3.022

18.4

3.02

2‐18.4

00

00

‐2.183

16.9

2.18

3‐16.9

00

00

‐1.669

13.6

1.66

9‐13.6

00

00

‐2.673

25.4

2.67

3‐25.4

00

00

‐1.061

8.3

1.06

1‐8.3

00

00

‐0.235

0.3

0.23

5‐0.3

‐0.065

9.79

076

0.06

52.44

769

‐3.502

20.8

3.50

2‐20.8

‐0.05

9.79

076

0.05

2.44

769

‐2.526

19.9

2.52

6‐19.9

‐0.04

9.79

076

0.04

2.44

769

‐1.98

16.7

1.98

‐16.7

‐0.045

14.686

140.04

53.67

1535

‐3.12

30.3

3.12

‐30.3

‐0.028

9.79

076

0.02

82.44

769

‐1.347

11.3

1.34

7‐11.3

‐0.02

7.34

307

0.02

1.83

5768

‐0.318

0.8

0.31

8‐0.8

‐0.132

19.6

0.13

24.9

‐4.008

23.1

4.00

8‐23.1

‐0.1

19.6

0.1

4.9

‐2.881

22.9

2.88

1‐22.9

‐0.08

19.6

0.08

4.9

‐2.3

19.9

2.3

‐19.9

‐0.09

29.4

0.09

7.35

‐3.564

35.3

3.56

4‐35.3

‐0.056

19.6

0.05

64.9

‐1.64

14.5

1.64

‐14.5

‐0.039

14.7

0.03

93.67

5‐0.602

3.6

0.60

2‐3.6

‐0.249

29.4

0.24

97.35

‐4.545

25.3

4.54

5‐25.3

‐0.15

29.4

0.15

7.35

‐3.239

25.8

3.23

9‐25.8

‐0.119

29.4

0.11

97.35

‐2.614

23.1

2.61

4‐23.1

‐0.135

44.1

0.13

511

.025

‐4.188

434.18

8‐43

‐0.084

29.4

0.08

47.35

‐1.936

17.7

1.93

6‐17.7

‐0.059

22.05

0.05

95.51

25‐0.857

6.3

0.85

7‐6.3

‐0.551

39.2

0.55

19.8

‐5.114

27.5

5.11

4‐27.5

‐0.265

39.2

0.26

59.8

‐3.613

28.8

3.61

3‐28.8

‐0.16

39.2

0.16

9.8

‐2.933

26.3

2.93

3‐26.3

‐0.193

58.8

0.19

314

.7‐5.008

54.1

5.00

8‐54.1

‐0.112

39.2

0.11

29.8

‐2.235

20.9

2.23

5‐20.9

‐0.079

29.4

0.07

97.35

‐1.061

8.4

1.06

1‐8.4

‐0.912

490.91

212

.25

‐5.708

29.6

5.70

8‐29.6

‐0.535

490.53

512

.25

‐3.993

31.7

3.99

3‐31.7

‐0.251

490.25

112

.25

‐3.243

29.4

3.24

3‐29.4

‐0.455

73.5

0.45

518

.375

‐5.809

655.80

9‐65

‐0.14

490.14

12.25

‐2.536

24.3

2.53

6‐24.3

‐0.098

36.75

0.09

89.18

75‐1.303

111.30

3‐11

‐1.299

58.8

1.29

914

.7‐6.335

31.6

6.33

5‐31.6

‐0.845

58.8

0.84

514

.7‐4.383

34.7

4.38

3‐34.7

‐0.504

58.8

0.50

414

.7‐3.555

32.5

3.55

5‐32.5

‐0.905

88.2

0.90

522

.05

‐6.619

766.61

9‐76

‐0.169

58.8

0.16

914

.7‐2.82

27.4

2.82

‐27.4

‐0.118

44.1

0.11

811

.025

‐1.504

13.2

1.50

4‐13.2

‐1.702

68.599

991.70

217

.15

‐6.997

33.5

6.99

7‐33.5

‐1.172

68.599

991.17

217

.15

‐4.779

37.6

4.77

9‐37.6

‐0.767

68.6

0.76

717

.15

‐3.878

35.7

3.87

8‐35.7

‐1.359

102.9

1.35

925

.725

‐7.443

87.2

7.44

3‐87.2

‐0.232

68.599

990.23

217

.15

‐3.127

30.8

3.12

7‐30.8

‐0.138

51.45

0.13

812

.862

5‐1.731

15.6

1.73

1‐15.6

‐2.123

78.4

2.12

319

.6‐7.696

35.4

7.69

6‐35.4

‐1.504

78.4

1.50

419

.6‐5.187

40.4

5.18

7‐40.4

‐1.062

78.400

011.06

219

.6‐4.195

38.9

4.19

5‐38.9

‐1.792

117.6

1.79

229

.4‐8.267

98.5

8.26

7‐98.5

‐0.413

78.4

0.41

319

.6‐3.427

34.2

3.42

7‐34.2

‐0.157

58.8

0.15

714

.7‐1.959

18.1

1.95

9‐18.1

‐2.561

88.199

992.56

122

.05

‐8.436

37.1

8.43

6‐37.1

‐1.841

88.2

1.84

122

.05

‐5.621

43.3

5.62

1‐43.3

‐1.363

88.2

1.36

322

.05

‐4.525

42.2

4.52

5‐42.2

‐2.231

132.3

2.23

133

.075

‐9.106

110

9.10

6‐110

‐0.747

88.199

990.74

722

.05

‐3.832

39.3

3.83

2‐39.3

‐0.186

66.150

010.18

616

.537

5‐2.189

20.7

2.18

9‐20.7

‐3.022

98.000

013.02

224

.5‐9.266

399.26

6‐39

‐2.183

982.18

324

.5‐6.223

48.2

6.22

3‐48.2

‐1.669

98.000

011.66

924

.5‐4.988

47.4

4.98

8‐47.4

‐2.673

147

2.67

336

.75

‐9.948

121.5

9.94

8‐121

.5‐1.061

981.06

124

.5‐4.365

46.6

4.36

5‐46.6

‐0.235

73.499

990.23

518

.375

‐2.399

232.39

9‐23

‐3.502

107.8

3.50

226

.95

‐10.13

141

.710

.131

‐41.7

‐2.526

107.8

2.52

626

.95

‐6.937

54.3

6.93

7‐54.3

‐1.98

107.8

1.98

26.95

‐5.571

54.6

5.57

1‐54.6

‐3.12

161.7

3.12

40.425

01‐10.8

133.1

10.8

‐133

.1‐1.347

107.8

1.34

726

.95

‐4.91

544.91

‐54

‐0.318

80.850

010.31

820

.212

5‐2.611

25.4

2.61

1‐25.4

‐4.008

117.6

4.00

829

.4‐2.881

117.6

2.88

129

.4‐7.641

60.3

7.64

1‐60.3

‐2.3

117.6

2.3

29.4

‐6.152

61.6

6.15

2‐61.6

‐3.564

176.4

3.56

444

.1‐11.65

514

4.8

11.655

‐144

.8‐1.64

117.6

1.64

29.4

‐5.445

61.4

5.44

5‐61.4

‐0.602

88.2

0.60

222

.05

‐2.847

28.1

2.84

7‐28.1

‐4.545

127.4

4.54

531

.85

‐3.239

127.4

3.23

931

.85

‐8.379

668.37

9‐66

‐2.614

127.4

2.61

431

.85

‐6.735

68.6

6.73

5‐68.6

‐4.188

191.1

4.18

847

.775

‐1.936

127.4

1.93

631

.85

‐5.987

68.8

5.98

7‐68.8

‐0.857

95.549

990.85

723

.887

5‐3.067

30.6

3.06

7‐30.6

‐5.114

137.2

5.11

434

.3‐3.613

137.2

3.61

334

.3‐9.496

70.7

9.49

6‐70.7

‐2.933

137.2

2.93

334

.3‐7.332

75.7

7.33

2‐75.7

‐5.008

205.8

5.00

851

.450

01‐2.235

137.2

2.23

534

.3‐6.518

76.1

6.51

8‐76.1

‐1.061

102.9

1.06

125

.725

‐3.315

33.4

3.31

5‐33.4

‐5.708

147

5.70

836

.75

‐3.993

147

3.99

336

.75

‐3.243

147

3.24

336

.75

‐7.93

82.6

7.93

‐82.6

‐5.809

220.5

5.80

955

.125

‐2.536

147

2.53

636

.75

‐7.068

83.8

7.06

8‐83.8

‐1.303

110.25

1.30

327

.562

5‐3.63

37.4

3.63

‐37.4

‐6.335

156.8

6.33

539

.2‐4.383

156.8

4.38

339

.2‐3.555

156.8

3.55

539

.2‐8.543

89.7

8.54

3‐89.7

‐6.619

235.2

6.61

958

.8‐2.82

156.8

2.82

39.2

‐7.608

91.2

7.60

8‐91.2

‐1.504

117.6

1.50

429

.4‐4.027

42.8

4.02

7‐42.8

‐6.997

166.6

6.99

741

.65

‐4.779

166.60

074.77

941

.650

17‐3.878

166.6

3.87

841

.65

‐9.173

96.9

9.17

3‐96.9

‐7.443

249.9

7.44

362

.475

‐3.127

166.6

3.12

741

.65

‐8.158

98.8

8.15

8‐98.8

‐1.731

124.95

1.73

131

.237

5‐4.442

48.6

4.44

2‐48.6

‐7.696

176.4

7.69

644

.100

01‐5.187

176.4

5.18

744

.1‐4.195

176.4

4.19

544

.1‐9.805

104.1

9.80

5‐104

.1‐8.267

264.6

8.26

766

.150

01‐3.427

176.4

3.42

744

.1‐8.711

106.5

8.71

1‐106

.5‐1.959

132.3

1.95

933

.075

‐4.845

54.1

4.84

5‐54.1

‐8.436

186.2

8.43

646

.550

01‐5.621

186.2

5.62

146

.55

‐4.525

186.2

4.52

546

.55

‐10.44

911

1.5

10.449

‐111

.5‐9.106

279.3

9.10

669

.824

99‐3.832

186.2

3.83

246

.55

‐9.264

114.2

9.26

4‐114

.2‐2.189

139.65

2.18

934

.912

5‐5.246

59.6

5.24

6‐59.6

‐9.266

196

9.26

649

.000

01‐6.223

196

6.22

349

‐4.988

196

4.98

849

.000

01‐11.16

911

8.7

11.169

‐118

.7‐9.948

294

9.94

873

.499

99‐4.365

196

4.36

549

.000

01‐9.82

122

9.82

‐122

‐2.399

147

2.39

936

.75

‐5.648

65.2

5.64

8‐65.2

‐10.13

120

5.8

10.131

51.450

01‐6.937

205.8

6.93

751

.450

01‐5.571

205.8

5.57

151

.45

‐10.8

308.7

10.8

77.175

‐4.91

205.8

4.91

51.45

‐10.38

129.8

10.38

‐129

.8‐2.611

154.35

2.61

138

.587

5‐6.05

70.8

6.05

‐70.8

‐7.641

215.6

7.64

153

.900

01‐6.152

215.6

6.15

253

.900

01‐11.65

532

3.4

11.655

80.85

‐5.445

215.6

5.44

553

.900

01‐10.93

813

7.5

10.938

‐137

.5‐2.847

161.7

2.84

740

.425

‐6.449

76.3

6.44

9‐76.3

‐8.379

225.4

8.37

956

.350

01‐6.735

225.4

6.73

556

.35

‐5.987

225.4

5.98

756

.350

01‐11.50

414

5.4

11.504

‐145

.4‐3.067

169.05

3.06

742

.262

5‐6.863

82.1

6.86

3‐82.1

‐9.496

235.2

9.49

658

.8‐7.332

235.2

7.33

258

.8‐6.518

235.2

6.51

858

.800

01‐3.315

176.4

3.31

544

.1‐7.267

87.7

7.26

7‐87.7

ref

crack

49yield

196

‐7.93

245

7.93

61.250

01‐7.068

245

7.06

861

.25

‐3.63

183.75

3.63

45.937

5‐7.672

93.3

7.67

2‐93.3

vert

12.25

horiz

49‐8.543

254.8

8.54

363

.7‐7.608

254.8

7.60

863

.700

01‐4.027

191.1

4.02

747

.775

‐8.085

99.1

8.08

5‐99.1

Data from

Graph

00

00

‐9.173

264.6

9.17

366

.150

01‐8.158

264.6

8.15

866

.15

‐4.442

198.45

4.44

249

.612

5‐8.497

104.9

8.49

7‐104

.9 ==============

‐0.033

00.03

30

‐9.805

274.4

9.80

568

.6‐8.711

274.4

8.71

168

.600

01‐4.845

205.8

4.84

551

.450

01‐8.911

110.7

8.91

1‐110

.7‐0.066

00.06

60

‐10.44

928

4.2

10.449

71.05

‐9.264

284.2

9.26

471

.05

‐5.246

213.15

5.24

653

.287

5‐9.323

116.5

9.32

3‐116

.5 Title

: Con

trol Chart

‐0.099

00.09

90

‐11.16

929

411

.169

73.500

01‐9.82

294

9.82

73.5

‐5.648

220.5

5.64

855

.125

‐9.739

122.3

9.73

9‐122

.3‐0.132

00.13

20

‐10.38

303.8

10.38

75.950

01‐6.05

227.85

6.05

56.962

5‐10.15

712

8.2

10.157

‐128

.2 X Axis T

itle: x‐axis

‐0.165

00.16

50

‐10.93

831

3.6

10.938

78.400

01‐6.449

235.2

6.44

958

.8‐10.57

134

10.57

‐134

Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

Crack

Yield

Failure

‐11.50

432

3.4

11.504

80.85

‐6.863

242.55

6.86

360

.637

51‐10.98

913

9.9

10.989

‐139

.9‐0.477

2.3

0.47

7‐2.3

56.12

549

51.45

‐7.267

249.9

7.26

762

.475

‐11.41

214

5.9

11.412

‐145

.9 x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

107.97

547

.75

58.8

‐7.672

257.25

7.67

264

.312

51‐11.83

415

1.8

11.834

‐151

.8Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

209.8

4971

.05

‐8.085

264.6

8.08

566

.15

00

00

‐1.346

10.9

1.34

6‐10.9

3512

.25

4980

.85

‐8.497

271.95

8.49

767

.987

51‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

4513

.475

47.775

80.85

‐8.911

279.3

8.91

169

.825

‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

5514

.746

.55

80.85

‐9.323

286.65

9.32

371

.662

49‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

6516

.55

45.95

82.688

‐9.739

294

9.73

973

.500

01‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

‐10.15

730

1.35

10.157

75.337

5‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

‐10.57

308.7

10.57

77.175

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

‐10.98

931

6.05

10.989

79.012

5‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

‐11.41

232

3.4

11.412

80.849

99‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

‐11.83

433

0.75

11.834

82.687

5‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.7‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.4‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.6‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.4‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.2‐6.765

235.2

6.76

558

.8‐7.32

245

7.32

61.250

01‐7.88

254.8

7.88

63.700

01‐8.44

264.6

8.44

66.150

01‐9.011

274.4

9.01

168

.6‐9.587

284.2

9.58

771

.049

99‐10.16

729

410

.167

73.499

99‐10.75

730

3.8

10.757

75.95

‐11.36

831

3.6

11.368

78.4

‐11.99

232

3.4

11.992

80.85

Ref

eren

ce c

ase

E_RO

CK25

crack

49yield

176.4crush

30crack

49yield

176.4crush

35crack

49yield

186.2crush

45crack

49yield

196crush

50crack

49yield

205.8crush

55crack

49yield

205.8crush

60crack

49yield

215.6crush

65crack

49yield

215.6crush

vert

12.25

horiz

44.1

vert

12.25

horiz

44.1

vert

12.25

horiz

46.55

vert

12.25

horiz

49vert

12.25

horiz

51.45

vert

12.25

horiz

51.45

vert

12.25

horiz

53.9

vert

#VALUE!

horiz

53.9

#VALUE!

‐53.9

Data from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00

==============

‐0.034

00.03

40 ==============

‐0.033

00.03

30 ==============

‐0.033

00.03

30 ==============

‐0.033

00.03

30 ==============

‐0.032

00.03

20 ==============

‐0.032

00.03

20 ==============

‐0.032

00.03

20 ==============

‐0.032

00.03

20

‐0.067

00.06

70

‐0.067

00.06

70

‐0.066

00.06

60

‐0.065

00.06

50

‐0.065

00.06

50

‐0.065

00.06

50

‐0.064

00.06

40

‐0.064

00.06

40

Title

: Con

trol Chart

‐0.101

00.10

10 Title

: Con

trol Chart

‐0.1

00.1

0 Title

: Con

trol Chart

‐0.099

00.09

90 Title

: Con

trol Chart

‐0.098

00.09

80 Title

: Con

trol Chart

‐0.097

00.09

70 Title

: Con

trol Chart

‐0.097

00.09

70 Title

: Con

trol Chart

‐0.096

00.09

60 Title

: Con

trol Chart

‐0.096

00.09

60

‐0.134

00.13

40

‐0.133

00.13

30

‐0.133

00.13

30

‐0.131

00.13

10

‐0.13

00.13

0‐0.129

00.12

90

‐ 0.128

00.12

80

‐0.127

00.12

70

X Axis T

itl: x‐axis

‐0.17

00.17

0 X Axis T

itl: x‐axis

‐0.168

00.16

80 X Axis T

itl: x‐axis

‐0.167

00.16

70

X Axis T

itl: x‐axis

‐0.165

00.16

50

X Axis T

itl: x‐axis

‐0.163

00.16

30 X Axis T

itl: x‐axis

‐0.162

00.16

20

X Axis T

itl: x‐axis

‐0.161

00.16

10

X Axis T

itl: x‐axis

‐0.159

00.15

90

Y Axis T

itle: y‐axis

‐0.254

0.2

0.25

4‐0.2

Y Axis T

itle: y‐axis

‐0.248

0.3

0.24

8‐0.3

Y Axis T

itle: y‐axis

‐0.245

0.3

0.24

5‐0.3

Y Axis T

itle: y‐axis

‐0.237

0.3

0.23

7‐0.3

Y Axis T

itle: y‐axis

‐0.232

0.3

0.23

2‐0.3

Y Axis T

itle: y‐axis

‐0.23

0.3

0.23

‐0.3

Y Axis T

itle: y‐axis

‐0.226

0.3

0.22

6‐0.3

Y Axis T

itle: y‐axis

‐0.222

0.3

0.22

2‐0.3

‐0.568

1.9

0.56

8‐1.9

‐0.519

20.51

9‐2

‐0.506

2.3

0.50

6‐2.3

‐0.466

2.5

0.46

6‐2.5

‐0.441

2.5

0.44

1‐2.5

‐0.432

2.6

0.43

2‐2.6

‐0.389

2.2

0.38

9‐2.2

‐0.368

2.1

0.36

8‐2.1

x‐axis

y‐axis

‐0.895

3.8

0.89

5‐3.8

x‐axis

y‐axis

‐0.828

4.3

0.82

8‐4.3

x‐axis

y‐axis

‐0.8

4.7

0.8

‐4.7

x‐axis

y‐axis

‐0.729

5.2

0.72

9‐5.2

x‐axis

y‐axis

‐0.7

5.4

0.7

‐5.4

x‐axis

y‐axis

‐0.682

5.7

0.68

2‐5.7

x‐axis

y‐axis

‐0.638

5.7

0.63

8‐5.7

x‐axis

y‐axis

‐0.616

5.8

0.61

6‐5.8

Line

type

: 0

‐1.253

6.1

1.25

3‐6.1

Line

type

: 0

‐1.172

71.17

2‐7

Line

type

: 0

‐1.109

7.4

1.10

9‐7.4

Line

type

: 0

‐1.012

8.3

1.01

2‐8.3

Line

type

: 0

‐0.949

8.4

0.94

9‐8.4

Line

type

: 0

‐0.92

8.8

0.92

‐8.8

Line

type

: 0

‐0.881

9.2

0.88

1‐9.2

Line

type

: 0

‐0.832

9.2

0.83

2‐9.2

00

00

‐1.642

8.6

1.64

2‐8.6

00

00

‐1.513

9.7

1.51

3‐9.7

00

00

‐1.447

10.5

1.44

7‐10.5

00

00

‐1.294

11.5

1.29

4‐11.5

00

00

‐1.227

11.9

1.22

7‐11.9

00

00

‐1.172

12.2

1.17

2‐12.2

00

00

‐1.117

12.8

1.11

7‐12.8

00

00

‐1.069

131.06

9‐13

‐0.034

9.79

076

0.03

42.44

769

‐2.01

112.01

‐11

‐0.033

9.79

076

0.03

32.44

769

‐1.854

12.5

1.85

4‐12.5

‐0.033

9.79

076

0.03

32.44

769

‐1.772

13.6

1.77

2‐13.6

‐0.033

9.79

076

0.03

32.44

769

‐1.588

151.58

8‐15

‐0.032

9.79

076

0.03

22.44

769

‐1.504

15.4

1.50

4‐15.4

‐0.032

9.79

076

0.03

22.44

769

‐1.438

161.43

8‐16

‐0.032

9.79

076

0.03

22.44

769

‐1.366

16.7

1.36

6‐16.7

‐0.032

9.79

076

0.03

22.44

769

‐1.304

16.9

1.30

4‐16.9

‐0.067

19.6

0.06

74.9

‐2.378

13.4

2.37

8‐13.4

‐0.067

19.6

0.06

74.9

‐2.194

15.3

2.19

4‐15.3

‐0.066

19.6

0.06

64.9

‐ 2.096

16.6

2.09

6‐16.6

‐0.065

19.6

0.06

54.9

‐1.877

18.4

1.87

7‐18.4

‐0.065

19.6

0.06

54.9

‐1.764

18.8

1.76

4‐18.8

‐0.065

19.6

0.06

54.9

‐1.701

19.7

1.70

1‐19.7

‐0.064

19.6

0.06

44.9

‐1.617

20.6

1.61

7‐20.6

‐0.064

19.6

0.06

44.9

‐1.543

20.9

1.54

3‐20.9

‐0.101

29.4

0.10

17.35

‐2.732

15.8

2.73

2‐15.8

‐0.1

29.4

0.1

7.35

‐2.535

18.1

2.53

5‐18.1

‐0.099

29.4

0.09

97.35

‐2.404

19.5

2.40

4‐19.5

‐0.098

29.4

0.09

87.35

‐2.167

21.8

2.16

7‐21.8

‐0.097

29.4

0.09

77.35

‐2.037

22.4

2.03

7‐22.4

‐0.097

29.4

0.09

77.35

‐1.963

23.4

1.96

3‐23.4

‐0.096

29.4

0.09

67.35

‐1.865

24.5

1.86

5‐24.5

‐0.096

29.4

0.09

67.35

‐1.768

24.8

1.76

8‐24.8

‐0.134

39.200

010.13

49.80

0003

‐3.104

18.2

3.10

4‐18.2

‐0.133

39.2

0.13

39.8

‐2.861

20.8

2.86

1‐20.8

‐0.133

39.2

0.13

39.8

‐2.728

22.6

2.72

8‐22.6

‐0.131

39.2

0.13

19.8

‐2.443

25.1

2.44

3‐25.1

‐0.13

39.2

0.13

9.8

‐2.309

25.9

2.30

9‐25.9

‐0.129

39.2

0.12

99.8

‐2.213

272.21

3‐27

‐0.128

39.2

0.12

89.8

‐2.101

28.3

2.10

1‐28.3

‐0.127

39.2

0.12

79.8

‐2.004

28.8

2.00

4‐28.8

‐0.17

490.17

12.25

‐3.463

20.6

3.46

3‐20.6

‐0.168

48.999

990.16

812

.25

‐3.206

23.6

3.20

6‐23.6

‐0.167

490.16

712

.25

‐3.04

25.6

3.04

‐25.6

‐0.165

490.16

512

.25

‐2.733

28.5

2.73

3‐28.5

‐0.163

490.16

312

.25

‐2.569

29.3

2.56

9‐29.3

‐0.162

490.16

212

.25

‐2.475

30.7

2.47

5‐30.7

‐0.161

490.16

112

.25

‐2.349

32.2

2.34

9‐32.2

‐0.159

490.15

912

.25

‐2.228

32.6

2.22

8‐32.6

‐0.254

58.8

0.25

414

.7‐3.846

23.2

3.84

6‐23.2

‐0.248

58.8

0.24

814

.7‐3.537

26.4

3.53

7‐26.4

‐0.245

58.8

0.24

514

.7‐3.368

28.7

3.36

8‐28.7

‐0.237

58.8

0.23

714

.7‐3.01

31.8

3.01

‐31.8

‐ 0.232

58.8

0.23

214

.7‐2.843

32.9

2.84

3‐32.9

‐0.23

58.8

0.23

14.7

‐2.725

34.3

2.72

5‐34.3

‐0.226

58.8

0.22

614

.7‐2.584

362.58

4‐36

‐0.222

58.800

010.22

214

.7‐2.464

36.6

2.46

4‐36.6

‐0.568

68.6

0.56

817

.15

‐4.236

25.8

4.23

6‐25.8

‐0.519

68.599

990.51

917

.15

‐3.877

29.2

3.87

7‐29.2

‐0.506

68.600

010.50

617

.15

‐3.685

31.7

3.68

5‐31.7

‐0.466

68.6

0.46

617

.15

‐3.29

35.2

3.29

‐35.2

‐0.441

68.6

0.44

117

.15

‐3.104

36.4

3.10

4‐36.4

‐0.432

68.6

0.43

217

.15

‐2.988

38.1

2.98

8‐38.1

‐0.389

68.6

0.38

917

.15

‐2.822

39.8

2.82

2‐39.8

‐0.368

68.6

0.36

817

.15

‐2.688

40.5

2.68

8‐40.5

‐0.895

78.4

0.89

519

.6‐4.975

31.8

4.97

5‐31.8

‐0.828

78.4

0.82

819

.6‐4.299

334.29

9‐33

‐0.8

78.400

010.8

19.6

‐4.016

34.9

4.01

6‐34.9

‐0.729

78.4

0.72

919

.6‐3.585

38.8

3.58

5‐38.8

‐0.7

78.4

0.7

19.6

‐3.368

39.9

3.36

8‐39.9

‐0.682

78.4

0.68

219

.6‐3.24

41.7

3.24

‐41.7

‐0.638

78.4

0.63

819

.6‐3.071

43.7

3.07

1‐43.7

‐0.616

78.399

990.61

619

.6‐2.913

44.4

2.91

3‐44.4

‐1.253

88.2

1.25

322

.05

‐5.786

38.5

5.78

6‐38.5

‐1.172

88.2

1.17

222

.05

‐4.955

39.6

4.95

5‐39.6

‐1.109

88.200

011.10

922

.05

‐4.527

40.6

4.52

7‐40.6

‐1.012

88.2

1.01

222

.05

‐3.875

42.3

3.87

5‐42.3

‐0.949

88.2

0.94

922

.05

‐3.647

43.6

3.64

7‐43.6

‐0.92

88.200

010.92

22.05

‐3.495

45.4

3.49

5‐45.4

‐0.881

88.2

0.88

122

.05

‐3.31

47.6

3.31

‐47.6

‐0.832

88.2

0.83

222

.05

‐3.151

48.5

3.15

1‐48.5

‐1.642

97.999

991.64

224

.5‐6.589

45.1

6.58

9‐45.1

‐1.513

97.999

991.51

324

.5‐5.642

46.7

5.64

2‐46.7

‐1.447

97.999

991.44

724

.5‐5.152

485.15

2‐48

‐1.294

981.29

424

.5‐4.263

47.6

4.26

3‐47.6

‐1.227

97.999

991.22

724

.5‐3.926

47.3

3.92

6‐47.3

‐1.172

981.17

224

.5‐3.768

49.4

3.76

8‐ 49.4

‐1.117

98.000

011.11

724

.5‐3.552

51.5

3.55

2‐51.5

‐1.069

981.06

924

.5‐3.378

52.4

3.37

8‐52.4

‐2.01

107.8

2.01

26.95

‐7.4

51.8

7.4

‐51.8

‐1.854

107.8

1.85

426

.95

‐6.319

53.7

6.31

9‐53.7

‐1.772

107.8

1.77

226

.95

‐5.762

55.2

5.76

2‐55.2

‐1.588

107.8

1.58

826

.95

‐4.756

54.8

4.75

6‐54.8

‐1.504

107.8

1.50

426

.95

‐4.33

53.7

4.33

‐53.7

‐1.438

107.8

1.43

826

.95

‐4.083

54.4

4.08

3‐54.4

‐1.366

107.8

1.36

626

.95

‐3.803

55.6

3.80

3‐55.6

‐1.304

107.8

1.30

426

.95

‐3.61

56.5

3.61

‐56.5

‐2.378

117.6

2.37

829

.4‐8.217

58.6

8.21

7‐58.6

‐2.194

117.6

2.19

429

.4‐7

60.7

7‐60.7

‐2.096

117.6

2.09

629

.4‐6.379

62.4

6.37

9‐62.4

‐1.877

117.6

1.87

729

.4‐5.264

62.4

5.26

4‐62.4

‐1.764

117.6

1.76

429

.4‐4.791

61.2

4.79

1‐61.2

‐1.701

117.6

1.70

129

.4‐4.495

61.7

4.49

5‐61.7

‐1.617

117.6

1.61

729

.4‐4.137

61.9

4.13

7‐61.9

‐1.543

117.6

1.54

329

.4‐3.858

60.9

3.85

8‐60.9

‐2.732

127.4

2.73

231

.85

‐9.059

65.5

9.05

9‐65.5

‐2.535

127.4

2.53

531

.85

‐7.698

67.9

7.69

8‐67.9

‐2.404

127.4

2.40

431

.85

‐6.994

69.7

6.99

4‐69.7

‐2.167

127.4

2.16

731

.85

‐5.77

69.9

5.77

‐69.9

‐2.037

127.4

2.03

731

.85

‐5.243

68.6

5.24

3‐68.6

‐1.963

127.4

1.96

331

.85

‐4.929

69.4

4.92

9‐69.4

‐1.865

127.4

1.86

531

.85

‐4.523

69.5

4.52

3‐69.5

‐1.768

127.4

1.76

831

.85

‐4.199

684.19

9‐68

‐3.104

137.2

3.10

434

.300

01‐9.904

72.5

9.90

4‐72.5

‐2.861

137.2

2.86

134

.300

01‐8.393

758.39

3‐75

‐2.728

137.2

2.72

834

.3‐7.629

77.2

7.62

9‐77.2

‐2.443

137.2

2.44

334

.3‐6.275

77.4

6.27

5‐77.4

‐2.309

137.2

2.30

934

.300

01‐5.699

76.1

5.69

9‐76.1

‐2.213

137.2

2.21

334

.300

01‐5.354

775.35

4‐77

‐2.101

137.2

2.10

134

.3‐4.918

77.3

4.91

8‐77.3

‐2.004

137.2

2.00

434

.3‐ 4.561

75.8

4.56

1‐75.8

‐3.463

147

3.46

336

.75

‐10.76

679

.610

.766

‐79.6

‐3.206

147

3.20

636

.75

‐9.108

82.4

9.10

8‐82.4

‐3.04

147

3.04

36.75

‐8.258

84.6

8.25

8‐84.6

‐2.733

147

2.73

336

.75

‐6.779

84.8

6.77

9‐84.8

‐2.569

147

2.56

936

.750

01‐6.152

83.4

6.15

2‐83.4

‐2.475

147

2.47

536

.75

‐5.779

84.6

5.77

9‐84.6

‐2.349

147

2.34

936

.75

‐5.306

855.30

6‐85

‐2.228

147

2.22

836

.75

‐4.926

83.6

4.92

6‐83.6

‐3.846

156.8

3.84

639

.2‐11.64

186

.811

.641

‐86.8

‐3.537

156.8

3.53

739

.2‐9.824

89.7

9.82

4‐89.7

‐3.368

156.8

3.36

839

.2‐8.902

92.2

8.90

2‐92.2

‐3.01

156.8

3.01

39.200

01‐7.293

92.4

7.29

3‐92.4

‐2.843

156.8

2.84

339

.2‐6.615

916.61

5‐91

‐2.725

156.8

2.72

539

.2‐6.207

92.2

6.20

7‐92.2

‐2.584

156.8

2.58

439

.2‐5.697

92.8

5.69

7‐92.8

‐2.464

156.8

2.46

439

.2‐5.286

91.3

5.28

6‐91.3

‐4.236

166.6

4.23

641

.650

01‐3.877

166.6

3.87

741

.650

01‐10.55

197

.110

.551

‐97.1

‐3.685

166.6

3.68

541

.65

‐9.55

99.8

9.55

‐99.8

‐3.29

166.6

3.29

41.65

‐7.811

100.1

7.81

1‐100

.1‐3.104

166.6

3.10

441

.65

‐7.073

98.5

7.07

3‐98.5

‐2.988

166.6

2.98

841

.65

‐6.639

99.9

6.63

9‐99.9

‐2.822

166.6

2.82

241

.65

‐6.085

100.4

6.08

5‐100

.4‐2.688

166.6

2.68

841

.65

‐5.648

995.64

8‐99

‐4.975

176.4

4.97

544

.1‐4.299

176.4

4.29

944

.1‐11.28

310

4.5

11.283

‐104

.5‐4.016

176.4

4.01

644

.1‐10.20

310

7.4

10.203

‐107

.4‐3.585

176.4

3.58

544

.100

01‐8.328

107.7

8.32

8‐107

.7‐3.368

176.4

3.36

844

.1‐7.543

106.2

7.54

3‐106

.2‐3.24

176.4

3.24

44.100

01‐7.068

107.5

7.06

8‐107

.5‐3.071

176.4

3.07

144

.1‐6.483

108.3

6.48

3‐108

.3‐2.913

176.4

2.91

344

.1‐6.008

106.6

6.00

8‐106

.6‐5.786

186.2

5.78

646

.55

‐4.955

186.2

4.95

546

.55

‐4.527

186.2

4.52

746

.55

‐10.86

611

5.1

10.866

‐115

.1‐3.875

186.2

3.87

546

.55

‐8.853

115.5

8.85

3‐ 115

.5‐3.647

186.2

3.64

746

.55

‐8.011

113.8

8.01

1‐113

.8‐3.495

186.2

3.49

546

.550

01‐7.508

115.4

7.50

8‐115

.4‐3.31

186.2

3.31

46.55

‐6.876

116.1

6.87

6‐116

.1‐3.151

186.2

3.15

146

.550

01‐6.374

114.5

6.37

4‐114

.5‐6.589

196

6.58

949

‐5.642

196

5.64

249

‐5.152

196

5.15

249

‐11.53

112

2.8

11.531

‐122

.8‐4.263

196

4.26

349

‐9.382

123.3

9.38

2‐123

.3‐3.926

196

3.92

649

‐8.48

121.4

8.48

‐121

.4‐3.768

196

3.76

849

.000

01‐7.946

123.2

7.94

6‐123

.2‐3.552

196

3.55

249

‐7.272

124

7.27

2‐124

‐3.378

196

3.37

849

‐6.743

122.3

6.74

3‐122

.3‐7.4

205.8

7.4

51.45

‐6.319

205.8

6.31

951

.45

‐5.762

205.8

5.76

251

.45

‐4.756

205.8

4.75

651

.450

01‐9.916

131.1

9.91

6‐131

.1‐4.33

205.8

4.33

51.45

‐8.964

129.2

8.96

4‐129

.2‐4.083

205.8

4.08

351

.450

01‐8.393

131

8.39

3‐131

‐3.803

205.8

3.80

351

.449

99‐7.682

132.1

7.68

2‐132

.1‐3.61

205.8

3.61

51.45

‐7.109

130.2

7.10

9‐130

.2‐8.217

215.6

8.21

753

.9‐7

215.6

753

.9‐6.379

215.6

6.37

953

.9‐5.264

215.6

5.26

453

.900

01‐10.46

138.9

10.46

‐138

.9‐4.791

215.6

4.79

153

.900

01‐9.442

136.9

9.44

2‐136

.9‐4.495

215.6

4.49

553

.900

01‐8.837

139

8.83

7‐139

‐4.137

215.6

4.13

753

.9‐8.083

140.1

8.08

3‐140

.1‐3.858

215.6

3.85

853

.9‐7.481

138.2

7.48

1‐138

.2‐9.059

225.4

9.05

956

.35

‐7.698

225.4

7.69

856

.35

‐6.994

225.4

6.99

456

.35

‐5.77

225.4

5.77

56.35

‐11.00

214

6.9

11.002

‐146

.9‐5.243

225.4

5.24

356

.350

01‐9.924

144.9

9.92

4‐144

.9‐4.929

225.4

4.92

956

.35

‐9.285

147

9.28

5‐147

‐4.523

225.4

4.52

356

.350

01‐8.483

148.7

8.48

3‐148

.7‐4.199

225.4

4.19

956

.35

‐7.847

146.9

7.84

7‐146

.9‐9.904

235.2

9.90

458

.8‐8.393

235.2

8.39

358

.8‐7.629

235.2

7.62

958

.8‐6.275

235.2

6.27

558

.8‐11.55

155.2

11.55

‐155

.2‐5.699

235.2

5.69

958

.8‐10.40

615

3.2

10.406

‐153

.2‐5.354

235.2

5.35

458

.8‐9.729

155.5

9.72

9‐155

.5‐4.918

235.2

4.91

858

.8‐8.888

156.9

8.88

8‐ 156

.9‐4.561

235.2

4.56

158

.800

01‐8.218

155.1

8.21

8‐155

.1‐10.76

624

510

.766

61.250

01‐9.108

245

9.10

861

.250

01‐8.258

245

8.25

861

.25

‐6.779

245

6.77

961

.25

‐6.152

245

6.15

261

.25

‐10.89

416

1.2

10.894

‐161

.2‐5.779

245

5.77

961

.25

‐10.18

316

3.7

10.183

‐163

.7‐5.306

245

5.30

661

.25

‐9.297

165.2

9.29

7‐165

.2‐4.926

245

4.92

661

.25

‐8.592

163.4

8.59

2‐163

.4‐11.64

125

4.8

11.641

63.700

01‐9.824

254.8

9.82

463

.7‐8.902

254.8

8.90

263

.7‐7.293

254.8

7.29

363

.7‐6.615

254.8

6.61

563

.7‐11.39

116

9.3

11.391

‐169

.3‐6.207

254.8

6.20

763

.7‐10.63

917

1.9

10.639

‐171

.9‐5.697

254.8

5.69

763

.7‐9.706

173.5

9.70

6‐173

.5‐5.286

254.8

5.28

663

.7‐8.967

171.7

8.96

7‐171

.7‐10.55

126

4.6

10.551

66.15

‐9.55

264.6

9.55

66.15

‐7.811

264.6

7.81

166

.15

‐7.073

264.6

7.07

366

.149

99‐11.89

517

7.5

11.895

‐177

.5‐6.639

264.6

6.63

966

.149

99‐11.09

918

0.2

11.099

‐180

.2‐6.085

264.6

6.08

566

.15

‐10.12

182

10.12

‐182

‐5.648

264.6

5.64

866

.149

99‐9.345

180.2

9.34

5‐180

.2‐11.28

327

4.4

11.283

68.6

‐10.20

327

4.4

10.203

68.6

‐8.328

274.4

8.32

868

.599

99‐7.543

274.4

7.54

368

.6‐7.068

274.4

7.06

868

.6‐11.56

918

8.6

11.569

‐188

.6‐6.483

274.4

6.48

368

.599

99‐10.53

919

0.5

10.539

‐190

.5‐6.008

274.4

6.00

868

.600

01‐9.723

188.7

9.72

3‐188

.7‐10.86

628

4.2

10.866

71.049

99‐8.853

284.2

8.85

371

.05

‐8.011

284.2

8.01

171

.050

01‐7.508

284.2

7.50

871

.050

01‐6.876

284.2

6.87

671

.05

‐10.95

519

9.6

10.955

‐199

.6‐6.374

284.2

6.37

471

.05

‐10.09

919

7.7

10.099

‐197

.7‐11.53

129

411

.531

73.499

99‐9.382

294

9.38

273

.5‐8.48

294

8.48

73.5

‐7.946

294

7.94

673

.5‐7.272

294

7.27

273

.5‐11.38

720

8.1

11.387

‐208

.1‐6.743

294

6.74

373

.5‐10.48

620

6.3

10.486

‐206

.3ref

crack

49yield

196

‐9.916

303.8

9.91

675

.95

‐8.964

303.8

8.96

475

.95

‐8.393

303.8

8.39

375

.95

‐7.682

303.8

7.68

275

.949

99‐7.109

303.8

7.10

975

.95

‐10.88

214.9

10.88

‐214

.9vert

12.25

horiz

49‐10.46

313.6

10.46

78.4

‐9.442

313.6

9.44

278

.399

99‐8.837

313.6

8.83

778

.4‐8.083

313.6

8.08

378

.4‐7.481

313.6

7.48

178

.400

01‐11.57

522

3.3

11.575

‐223

.3 D

ata from

Graph

00

00

‐11.00

232

3.4

11.002

80.85

‐9.924

323.4

9.92

480

.85

‐9.285

323.4

9.28

580

.849

99‐8.483

323.4

8.48

380

.85

‐7.847

323.4

7.84

780

.849

99 ==============

‐0.033

00.03

30

‐11.55

333.2

11.55

83.300

01‐10.40

633

3.2

10.406

83.300

01‐9.729

333.2

9.72

983

.299

99‐8.888

333.2

8.88

883

.3‐8.218

333.2

8.21

883

.299

99‐0.066

00.06

60

‐10.89

434

310

.894

85.75

‐10.18

334

310

.183

85.750

01‐9.297

343

9.29

785

.75

‐8.592

343

8.59

285

.75

Title

: Con

trol Chart

‐0.099

00.09

90

‐11.39

135

2.8

11.391

88.2

‐10.63

935

2.8

10.639

88.2

‐9.706

352.8

9.70

688

.200

01‐8.967

352.8

8.96

788

.2‐0.132

00.13

20

‐11.89

536

2.6

11.895

90.65

‐11.09

936

2.6

11.099

90.649

99‐10.12

362.6

10.12

90.65

‐9.345

362.6

9.34

590

.650

01 X Axis T

itl: x‐axis

‐0.165

00.16

50

‐11.56

937

2.4

11.569

93.100

01‐10.53

937

2.4

10.539

93.099

99‐9.723

372.4

9.72

393

.1 Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

‐10.95

538

2.2

10.955

95.549

99‐10.09

938

2.2

10.099

95.550

01‐0.477

2.3

0.47

7‐2.3

‐11.38

739

2.00

0111

.387

98.000

02‐10.48

639

210

.486

98 x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

‐10.88

401.8

10.88

100.45

Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

‐11.57

541

1.6

11.575

102.9

00

00

‐1.346

10.9

1.34

6‐10.9

‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

70crack

49yield

225.4crush

fixed

crack

98yield

NO

SHEA

Rfree

crack

49yield

132.3crush

5crack

49yield

147crush

10crack

49yield

147crush

15crack

49yield

156.8crush

20crack

49yield

166.6crush

‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

vert

12.25

horiz

56.35

vert

24.5

SUP

horiz

at su

pvert

12.25

33.075

vert

12.25

horiz

36.75

vert

12.25

horiz

36.75

vert

12.25

horiz

39.2

vert

12.25

horiz

41.65

‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

Data from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

Data from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00 D

ata from

Graph

00

00

‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

==============

‐0.032

00.03

20 ==============

‐0.075

00.07

50 ==============

==============

‐0.034

00.03

40 ==============

‐0.034

00.03

40 ==============

‐0.034

00.03

40 ==============

‐0.034

00.03

40

‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

‐0.063

00.06

30

‐0.151

00.15

10

‐0.069

00.06

90

‐0.069

00.06

90

‐0.068

00.06

80

‐0.068

00.06

80

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

Title

: Con

trol Chart

‐0.095

00.09

50 Title

: Con

trol Chart

‐0.226

00.22

60 Title

: Con

trol Chart

Title

: Con

trol Chart

‐0.103

00.10

30 Title

: Con

trol Chart

‐0.103

00.10

30 Title

: Con

trol Chart

‐0.102

00.10

20 Title

: Con

trol Chart

‐0.102

00.10

20

‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

‐0.127

00.12

70

‐0.31

2.8

0.31

‐2.8

‐0.138

00.13

80

‐0.137

00.13

70

‐0.136

00.13

60

‐0.135

00.13

50

‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

X Axis T

itl: x‐axis

‐0.159

00.15

90 X Axis T

itl: x‐axis

‐0.441

18.1

0.44

1‐18.1

X Axis T

itl: x‐axis

X Axis T

itl: x‐axis

‐0.177

00.17

70 X Axis T

itl: x‐axis

‐0.176

00.17

60

X Axis T

itl: x‐axis

‐0.174

00.17

40

X Axis T

itl: x‐axis

‐0.172

00.17

20

‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

Y Axis T

itle: y‐axis

‐0.219

0.4

0.21

9‐0.4

Y Axis T

itle: y‐axis

‐0.631

59.2

0.63

1‐59.2

Y Axis T

itle: y‐axis

Y Axis T

itle: y‐axis

‐0.276

00.27

60 Y Axis T

itle: y‐axis

‐0.271

0.1

0.27

1‐0.1

Y Axis T

itle: y‐axis

‐0.264

0.2

0.26

4‐0.2

Y Axis T

itle: y‐axis

‐0.26

0.2

0.26

‐0.2

‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

‐0.361

2.1

0.36

1‐2.1

‐0.815

92.7

0.81

5‐92.7

‐0.717

0.1

0.71

7‐0.1

‐0.66

0.9

0.66

‐0.9

‐0.626

1.4

0.62

6‐1.4

‐0.593

1.7

0.59

3‐1.7

‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

x‐axis

y‐axis

‐0.593

5.9

0.59

3‐5.9

x‐axis

y‐axis

‐1.009

133.9

1.00

9‐133

.9 x‐axis

y‐axis

x‐axis

y‐axis

‐1.186

0.5

1.18

6‐0.5

x‐axis

y‐axis

‐1.098

1.9

1.09

8‐1.9

x‐axis

y‐axis

‐1.017

2.9

1.01

7‐2.9

x‐axis

y‐axis

‐0.956

3.4

0.95

6‐3.4

‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

Line

type

: 0

‐0.811

9.5

0.81

1‐9.5

Line

type

: 0

‐1.239

187

1.23

9‐187

Line

type

: 0

Line

type

: 0

‐1.715

1.1

1.71

5‐1.1

Line

type

: 0

‐1.604

3.1

1.60

4‐3.1

Line

type

: 0

‐1.444

4.6

1.44

4‐4.6

Line

type

: 0

‐1.366

5.5

1.36

6‐5.5

‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

00

00

‐1.038

13.4

1.03

8‐13.4

00

00

‐1.458

234.7

1.45

8‐234

.70

00

00

00

0‐2.25

1.7

2.25

‐1.7

00

00

‐2.077

4.3

2.07

7‐4.3

00

00

‐1.893

6.4

1.89

3‐6.4

00

00

‐1.77

7.7

1.77

‐7.7

‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

‐0.032

9.79

076

0.03

22.44

769

‐1.265

17.4

1.26

5‐17.4

‐0.075

24.494

0.07

56.12

35‐1.671

283.2

1.67

1‐283

.2‐0.017

4.89

538

0.01

71.22

3845

‐0.034

9.79

092

0.03

42.44

773

‐2.768

2.4

2.76

8‐2.4

‐0.034

9.79

076

0.03

42.44

769

‐2.554

5.5

2.55

4‐5.5

‐0.034

9.79

076

0.03

42.44

769

‐2.321

8.1

2.32

1‐8.1

‐0.034

9.79

076

0.03

42.44

769

‐2.171

9.8

2.17

1‐9.8

‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

‐0.063

19.6

0.06

34.9

‐1.485

21.4

1.48

5‐21.4

‐0.151

490.15

112

.25

‐1.884

332.6

1.88

4‐332

.6‐0.035

9.8

0.03

52.45

‐0.069

19.599

670.06

94.89

9918

‐3.294

33.29

4‐3

‐0.069

19.6

0.06

94.9

‐3.036

6.7

3.03

6‐6.7

‐0.068

19.6

0.06

84.9

‐2.752

9.9

2.75

2‐9.9

‐0.068

19.6

0.06

84.9

‐2.573

11.9

2.57

3‐ 11.9

‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

‐0.095

29.4

0.09

57.35

‐1.713

25.5

1.71

3‐25.5

‐0.226

73.5

0.22

618

.375

‐2.104

382.6

2.10

4‐382

.6‐0.052

14.7

0.05

23.67

5‐0.103

29.4

0.10

37.35

‐3.831

3.7

3.83

1‐3.7

‐0.103

29.4

0.10

37.35

‐3.523

7.9

3.52

3‐7.9

‐0.102

29.4

0.10

27.35

‐3.166

11.7

3.16

6‐11.7

‐0.102

29.4

0.10

27.35

‐2.978

14.1

2.97

8‐14.1

‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

‐0.127

39.2

0.12

79.8

‐1.941

29.7

1.94

1‐29.7

‐0.31

980.31

24.5

‐2.358

442.4

2.35

8‐442

.4‐0.07

19.6

0.07

4.9

‐0.138

39.2

0.13

89.8

‐4.373

4.3

4.37

3‐4.3

‐0.137

39.2

0.13

79.8

‐4.024

9.2

4.02

4‐9.2

‐0.136

39.2

0.13

69.8

‐3.605

13.5

3.60

5‐13.5

‐0.135

39.2

0.13

59.8

‐3.369

16.2

3.36

9‐16.2

‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.7‐0.159

490.15

912

.25

‐2.158

33.6

2.15

8‐33.6

‐0.441

122.5

0.44

130

.625

‐2.586

492.3

2.58

6‐492

.3‐0.087

24.5

0.08

76.12

5‐0.177

490.17

712

.25

‐5.84

55.84

‐5‐0.176

490.17

612

.25

‐4.619

10.8

4.61

9‐10.8

‐0.174

490.17

412

.25

‐4.038

15.3

4.03

8‐15.3

‐0.172

490.17

212

.25

‐3.782

18.5

3.78

2‐18.5

‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.4‐0.219

58.8

0.21

914

.7‐2.375

37.6

2.37

5‐37.6

‐0.631

147

0.63

136

.75

‐2.813

549.3

2.81

3‐549

.3‐0.104

29.4

0.10

47.35

‐0.276

58.799

990.27

614

.7‐7.915

7.2

7.91

5‐7.2

‐0.271

58.8

0.27

114

.7‐6.119

15.4

6.11

9‐15.4

‐0.264

58.8

0.26

414

.7‐4.655

18.1

4.65

5‐18.1

‐0.26

58.8

0.26

14.7

‐4.198

20.8

4.19

8‐20.8

‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

‐0.361

68.600

010.36

117

.15

‐2.603

41.8

2.60

3‐41.8

‐0.815

171.5

0.81

542

.875

‐3.063

605

3.06

3‐605

‐0.122

34.3

0.12

28.57

5‐0.717

68.6

0.71

717

.15

‐10.12

810

.510

.128

‐ 10.5

‐0.66

68.599

990.66

17.15

‐7.661

20.2

7.66

1‐20.2

‐0.626

68.600

010.62

617

.15

‐5.79

245.79

‐24

‐0.593

68.600

010.59

317

.15

‐4.973

25.7

4.97

3‐25.7

‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.6‐0.593

78.4

0.59

319

.6‐2.82

45.8

2.82

‐45.8

‐1.009

196

1.00

949

‐3.289

654.9

3.28

9‐654

.9‐0.139

39.2

0.13

99.8

‐1.186

78.400

011.18

619

.6‐1.098

78.4

1.09

819

.6‐9.273

25.2

9.27

3‐25.2

‐1.017

78.400

011.01

719

.6‐6.921

29.8

6.92

1‐29.8

‐0.956

78.399

990.95

619

.6‐5.955

32.3

5.95

5‐32.3

‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.4‐0.811

88.2

0.81

122

.05

‐3.038

49.9

3.03

8‐49.9

‐1.239

220.5

1.23

955

.125

‐3.52

705.5

3.52

‐705

.5‐0.156

44.1

0.15

611

.025

‐1.715

88.2

1.71

522

.05

‐1.604

88.2

1.60

422

.05

‐10.97

130

.510

.971

‐30.5

‐1.444

88.199

991.44

422

.05

‐8.076

35.8

8.07

6‐35.8

‐1.366

88.2

1.36

622

.05

‐6.917

38.8

6.91

7‐38.8

‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.2‐1.038

981.03

824

.5‐3.269

54.1

3.26

9‐54.1

‐1.458

245

1.45

861

.25

‐3.761

764.8

3.76

1‐764

.8‐0.179

490.17

912

.25

‐2.25

982.25

24.5

‐2.077

97.999

992.07

724

.5‐1.893

981.89

324

.5‐9.276

42.1

9.27

6‐42.1

‐1.77

981.77

24.5

‐7.903

45.4

7.90

3‐45.4

‐6.765

235.2

6.76

558

.8‐1.265

107.8

1.26

526

.95

‐3.49

58.2

3.49

‐58.2

‐1.671

269.5

1.67

167

.375

‐3.991

815.7

3.99

1‐815

.7‐0.22

53.9

0.22

13.475

‐2.768

107.8

2.76

826

.95

‐2.554

107.8

2.55

426

.95

‐2.321

107.8

2.32

126

.95

‐10.50

748

.510

.507

‐48.5

‐2.171

107.8

2.17

126

.95

‐8.915

52.2

8.91

5‐52.2

‐7.32

245

7.32

61.250

01‐1.485

117.6

1.48

529

.4‐3.718

62.5

3.71

8‐62.5

‐1.884

294

1.88

473

.5‐4.225

867.6

4.22

5‐867

.6‐0.285

58.8

0.28

514

.7‐3.294

117.6

3.29

429

.4‐3.036

117.6

3.03

629

.4‐2.752

117.6

2.75

229

.4‐11.76

254

.911

.762

‐54.9

‐2.573

117.6

2.57

329

.4‐9.937

59.1

9.93

7‐59.1

‐7.88

254.8

7.88

63.700

01‐ 1.713

127.4

1.71

331

.85

‐4.007

68.6

4.00

7‐68.6

‐2.104

318.5

2.10

479

.625

‐4.477

922.7

4.47

7‐922

.7‐0.527

63.7

0.52

715

.925

‐3.831

127.4

3.83

131

.85

‐3.523

127.4

3.52

331

.85

‐3.166

127.4

3.16

631

.85

‐2.978

127.4

2.97

831

.85

‐10.98

866

.110

.988

‐66.1

‐8.44

264.6

8.44

66.150

01‐1.941

137.2

1.94

134

.3‐4.343

76.2

4.34

3‐76.2

‐2.358

343

2.35

885

.75

‐4.733

978.7

4.73

3‐978

.7‐0.782

68.6

0.78

217

.15

‐4.373

137.2

4.37

334

.300

01‐4.024

137.2

4.02

434

.300

01‐3.605

137.2

3.60

534

.3‐3.369

137.2

3.36

934

.3‐9.011

274.4

9.01

168

.6‐2.158

147

2.15

836

.75

‐4.687

84.1

4.68

7‐84.1

‐2.586

367.5

2.58

691

.875

‐4.978

1032

4.97

8‐103

2‐1.036

73.5

1.03

618

.375

‐5.84

147

5.84

36.750

01‐4.619

147

4.61

936

.750

01‐4.038

147

4.03

836

.75

‐3.782

147

3.78

236

.75

‐9.587

284.2

9.58

771

.049

99‐2.375

156.8

2.37

539

.2‐5.029

91.9

5.02

9‐91.9

‐2.813

392

2.81

398

‐5.239

1086

.55.23

9‐108

6.5

‐1.333

78.4

1.33

319

.6‐7.915

156.8

7.91

539

.2‐6.119

156.8

6.11

939

.2‐4.655

156.8

4.65

539

.2‐4.198

156.8

4.19

839

.200

01‐10.16

729

410

.167

73.499

99‐2.603

166.6

2.60

341

.65

‐5.375

99.8

5.37

5‐99.8

‐3.063

416.5

3.06

310

4.12

5‐5.498

1148

5.49

8‐114

8‐1.635

83.3

1.63

520

.825

‐10.12

816

6.6

10.128

41.65

‐7.661

166.6

7.66

141

.65

‐5.79

166.6

5.79

41.65

‐4.973

166.6

4.97

341

.650

01‐10.75

730

3.8

10.757

75.95

‐2.82

176.4

2.82

44.1

‐5.713

107.5

5.71

3‐107

.5‐3.289

441

3.28

911

0.25

‐5.764

1204

.25.76

4‐120

4.2

‐1.937

88.2

1.93

722

.05

‐9.273

176.4

9.27

344

.100

01‐6.921

176.4

6.92

144

.1‐5.955

176.4

5.95

544

.1‐11.36

831

3.6

11.368

78.4

‐3.038

186.2

3.03

846

.550

01‐6.057

115.4

6.05

7‐115

.4‐3.52

465.5

3.52

116.37

5‐6.04

1262

.36.04

‐126

2.3

‐2.239

93.1

2.23

923

.275

‐10.97

118

6.2

10.971

46.55

‐8.076

186.2

8.07

646

.55

‐6.917

186.2

6.91

746

.55

‐11.99

232

3.4

11.992

80.85

‐3.269

196

3.26

949

‐6.414

123.5

6.41

4‐123

.5‐3.761

490

3.76

112

2.5

‐6.333

1324

.46.33

3‐132

4.4

‐2.546

982.54

624

.5‐9.276

196

9.27

649

‐7.903

196

7.90

349

.000

01‐3.49

205.8

3.49

51.45

‐6.758

131.4

6.75

8‐131

.4‐3.991

514.5

3.99

112

8.62

5‐2.83

102.9

2.83

25.725

First crack

First yield

Failure

‐10.50

720

5.8

10.507

51.450

01‐ 8.915

205.8

8.91

551

.45

‐3.718

215.6

3.71

853

.900

01‐7.102

140.1

7.10

2‐140

.1‐4.225

539

4.22

513

4.75

‐3.141

107.8

3.14

126

.95

512

.25

36.75

41.65

‐11.76

221

5.6

11.762

53.9

‐9.937

215.6

9.93

753

.9‐4.007

225.4

4.00

756

.350

01‐7.452

148.4

7.45

2‐148

.4‐4.477

563.5

4.47

714

0.87

5‐3.458

112.7

3.45

828

.175

1012

.25

36.75

46.55

‐10.98

822

5.4

10.988

56.35

‐4.343

235.2

4.34

358

.8‐7.805

156.7

7.80

5‐156

.7‐4.733

588

4.73

314

7‐3.75

117.6

3.75

29.4

1512

.25

39.2

53.9

‐4.687

245

4.68

761

.25

‐8.157

165.1

8.15

7‐165

.1‐4.978

612.5

4.97

815

3.12

5‐4.051

122.5

4.05

130

.625

2012

.25

41.65

56.35

‐5.029

254.8

5.02

963

.7‐8.51

173.5

8.51

‐173

.5‐5.239

637

5.23

915

9.25

‐4.39

127.4

4.39

31.85

2512

.25

44.1

63.7

‐5.375

264.6

5.37

566

.15

‐8.866

182.1

8.86

6‐182

.1‐5.498

661.5

5.49

816

5.37

5‐4.837

132.3

4.83

733

.075

3012

.25

44.1

68.6

‐5.713

274.4

5.71

368

.6‐9.224

190.9

9.22

4‐190

.9‐5.764

686

5.76

417

1.5

‐6.392

137.2

6.39

234

.335

12.25

46.55

73.5

‐6.057

284.2

6.05

771

.049

99‐9.576

200.1

9.57

6‐200

.1‐6.04

710.5

6.04

177.62

5‐8.389

142.1

8.38

935

.525

4012

.25

4980

.85

‐6.414

294

6.41

473

.5‐9.937

208.7

9.93

7‐208

.7‐6.333

735

6.33

318

3.75

‐10.59

114

710

.591

36.75

4512

.25

51.45

83.3

‐6.758

303.8

6.75

875

.949

99‐10.30

321

7.4

10.303

‐217

.4‐13.09

715

1.9

13.097

37.975

5012

.25

51.45

90.65

‐7.102

313.6

7.10

278

.400

01‐10.67

722

6.3

10.677

‐226

.3‐16.05

515

6.8

16.055

39.2

5512

.25

51.45

93.1

‐7.452

323.4

7.45

280

.850

01‐11.71

123

3.4

11.711

‐233

.4‐20.08

316

1.7

20.083

40.425

6012

.25

53.9

98‐7.805

333.2

7.80

583

.299

9965

12.25

53.9

102.9

‐8.157

343

8.15

785

.75

7012

.25

56.35

105.35

‐8.51

352.8

8.51

88.2

‐8.866

362.6

8.86

690

.649

99fixed

024

.518

3.79

SHEA

R‐9.224

372.4

9.22

493

.100

0180

24.5

183.79

‐9.576

382.2

9.57

695

.550

01‐9.937

392

9.93

797

.999

99free

012

.25

33.075

40.425

‐10.30

340

1.8

10.303

100.45

8012

.25

33.075

40.425

‐10.67

741

1.6

10.677

102.9

‐11.71

142

1.4

11.711

105.35

ARCH

ANGLE

20crack

51yield

240

40crack

54yield

351

60crack

58.8

yield

512.4

80crack

67.2

yield

828.8

100crack

84yield

1260

vert

12.686

57ho

riz59

.701

49vert

13.235

29ho

riz86

.029

41vert

14.033

41ho

riz12

2.29

12vert

15.483

87ho

riz19

0.96

77vert

18.421

05ho

riz27

6.31

58 D

ata from

Graph

00

00 D

ata from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

==============

‐0.116

1.5

0.11

6‐1.5

==============

‐0.103

2.8

0.10

3‐2.8

==============

‐0.21

7.7

0.21

‐7.7

==============

‐0.179

9.5

0.17

9‐9.5

==============

‐0.189

13.1

0.18

9‐13.1

‐0.271

3.8

0.27

1‐3.8

‐0.219

6.2

0.21

9‐6.2

‐0.752

350.75

2‐35

‐0.484

29.5

0.48

4‐29.5

‐0.456

34.7

0.45

6‐34.7

Title

: Con

trol Chart

‐0.951

19.7

0.95

1‐19.7 Title

: Con

trol Chart

‐0.616

21.9

0.61

6‐21.9

Title

: Con

trol Chart

‐1.417

67.9

1.41

7‐67.9

Title

: Con

trol Chart

‐0.909

58.4

0.90

9‐58.4

Title

: Con

trol Chart

‐0.802

65.7

0.80

2‐65.7

‐1.717

38.1

1.71

7‐38.1

‐1.097

41.1

1.09

7‐41.1

‐2.09

101.6

2.09

‐101

.6‐1.345

87.1

1.34

5‐87.1

‐1.149

95.6

1.14

9‐95.6

X Axis T

itle: x‐axis

‐2.5

56.8

2.5

‐56.8 X Axis T

itle: x‐axis

‐1.587

60.7

1.58

7‐60.7

X Axis T

itle: x‐axis

‐2.766

135.2

2.76

6‐135

.2 X Axis T

itle: x‐axis

‐1.779

116.2

1.77

9‐116

.2 X Axis T

itle: x‐axis

‐1.496

125.5

1.49

6‐125

.5 Y Axis T

itle: y‐axis

‐3.245

74.8

3.24

5‐74.8 Y Axis T

itle: y‐axis

‐2.086

80.6

2.08

6‐80.6

Y Axis T

itle: y‐axis

‐3.43

168.5

3.43

‐168

.5 Y Axis T

itle: y‐axis

‐2.204

145.4

2.20

4‐145

.4 Y Axis T

itle: y‐axis

‐1.84

155.3

1.84

‐155

.3‐4.017

93.3

4.01

7‐93.3

‐2.585

100.3

2.58

5‐100

.3‐4.109

201.9

4.10

9‐201

.9‐2.645

174.4

2.64

5‐174

.4‐2.194

185.5

2.19

4‐185

.5 x‐axis

y‐axis

‐4.844

114.2

4.84

4‐114

.2 x‐axis

y‐axis

‐3.071

119.6

3.07

1‐119

.6 x‐axis

y‐axis

‐4.776

235.5

4.77

6‐235

.5 x‐axis

y‐axis

‐3.076

203.3

3.07

6‐203

.3 x‐axis

y‐axis

‐2.542

215.3

2.54

2‐215

.3Line

type

: 0

‐5.918

144.2

5.91

8‐144

.2Line

type

: 0

‐3.557

139

3.55

7‐139

Line

type

: 0

‐5.452

270.3

5.45

2‐270

.3Line

type

: 0

‐3.521

232.3

3.52

1‐232

.3Line

type

: 0

‐2.901

245.3

2.90

1‐245

.30

00

0‐7.055

176.4

7.05

5‐176

.40

00

0‐4.06

158.8

4.06

‐158

.80

00

0‐6.163

309.3

6.16

3‐309

.30

00

0‐3.952

261.2

3.95

2‐261

.20

00

0‐3.251

275.1

3.25

1‐275

.1‐0.116

29.971

690.11

67.45

5644

‐8.214

209.3

8.21

4‐209

.3‐0.103

29.971

70.10

37.34

6005

‐4.555

178.7

4.55

5‐178

.7‐0.21

55.946

870.21

13.352

47‐6.883

349.2

6.88

3‐349

.2‐0.179

55.947

170.17

912

.891

05‐4.386

290.1

4.38

6‐290

.1‐0.189

69.933

950.18

915

.336

39‐3.601

304.9

3.60

1‐304

.9‐0.271

600.27

114

.925

37‐9.374

241.6

9.37

4‐241

.6‐0.219

600.21

914

.705

88‐5.102

202.5

5.10

2‐202

.5‐0.752

112

0.75

226

.730

31‐7.609

389.6

7.60

9‐389

.6‐0.484

112

0.48

425

.806

45‐4.835

319.1

4.83

5‐319

.1‐0.456

140

0.45

630

.701

75‐3.963

334.9

3.96

3‐334

.9‐0.951

900.95

122

.388

06‐18.82

537

6.7

18.825

‐376

.7‐0.616

900.61

622

.058

82‐5.681

228.5

5.68

1‐228

.5‐1.417

167.90

541.41

740

.072

88‐8.343

430.8

8.34

3‐430

.8‐0.909

168

0.90

938

.709

68‐5.266

348.3

5.26

6‐348

.3‐0.802

210

0.80

246

.052

63‐4.313

364.7

4.31

3‐364

.7‐1.717

120

1.71

729

.850

75‐1.097

120

1.09

729

.411

76‐6.27

255.3

6.27

‐255

.3‐2.09

224

2.09

53.460

62‐1.345

224

1.34

551

.612

9‐5.699

378

5.69

9‐378

‐1.149

280

1.14

961

.403

51‐4.663

394.6

4.66

3‐394

.6‐2.5

150

2.5

37.313

43‐1.587

150

1.58

736

.764

71‐6.866

282.3

6.86

6‐282

.3‐2.766

280

2.76

666

.825

78‐1.779

280

1.77

964

.516

13‐6.136

409.5

6.13

6‐409

.5‐1.496

350

1.49

676

.754

39‐5.015

424.6

5.01

5‐424

.6‐3.245

180

3.24

544

.776

12‐2.086

180

2.08

644

.117

65‐7.467

309.7

7.46

7‐309

.7‐3.43

336

3.43

80.190

93‐2.204

336

2.20

477

.419

36‐6.574

441.1

6.57

4‐441

.1‐1.84

420

1.84

92.105

26‐5.38

454.7

5.38

‐454

.7‐4.017

210

4.01

752

.238

81‐2.585

210

2.58

551

.470

58‐8.077

337.5

8.07

7‐337

.5‐4.109

391.99

994.10

993

.556

07‐2.645

392

2.64

590

.322

59‐7.014

473.6

7.01

4‐473

.6‐2.194

490

2.19

410

7.45

61‐5.727

485.2

5.72

7‐485

.2‐4.844

240

4.84

459

.701

5‐3.071

240

3.07

158

.823

53‐8.707

366

8.70

7‐366

‐4.776

448

4.77

610

6.92

12‐3.076

448

3.07

610

3.22

58‐7.454

506

7.45

4‐506

‐2.542

560

2.54

212

2.80

7‐6.073

516.8

6.07

3‐516

.8‐5.918

270

5.91

867

.164

19‐3.557

270

3.55

766

.176

47‐5.452

504

5.45

212

0.28

64‐3.521

504

3.52

111

6.12

9‐2.901

629.99

992.90

113

8.15

79‐7.055

300

7.05

574

.626

86‐4.06

300

4.06

73.529

4‐6.163

560

6.16

313

3.65

16‐3.952

559.99

993.95

212

9.03

22‐3.251

700

3.25

115

3.50

88‐8.214

330

8.21

482

.089

54‐4.555

330

4.55

580

.882

35‐6.883

616

6.88

314

7.01

67‐4.386

616

4.38

614

1.93

55‐3.601

769.99

993.60

116

8.85

96‐9.374

360

9.37

489

.552

23‐5.102

360

5.10

288

.235

29‐7.609

672

7.60

916

0.38

19‐4.835

672

4.83

515

4.83

87‐3.963

839.99

993.96

318

4.21

05‐18.82

539

018

.825

97.014

92‐5.681

390

5.68

195

.588

24‐8.343

728

8.34

317

3.74

7‐5.266

728.00

015.26

616

7.74

19‐4.313

909.99

994.31

319

9.56

1497

.014

92‐6.27

420

6.27

102.94

1217

3.74

7‐5.699

784

5.69

918

0.64

52‐4.663

980

4.66

321

4.91

23‐6.866

450

6.86

611

0.29

41‐6.136

840

6.13

619

3.54

84‐5.015

1050

5.01

523

0.26

31‐7.467

480

7.46

711

7.64

71‐6.574

896

6.57

420

6.45

16‐5.38

1120

5.38

245.61

41‐8.077

510.00

018.07

712

5‐7.014

952

7.01

421

9.35

48‐5.727

1190

5.72

726

0.96

49‐8.707

539.99

998.70

713

2.35

29First crack

First y

ield

Failure

‐7.454

1008

7.45

423

2.25

81‐6.073

1260

6.07

327

6.31

5813

2.35

29‐20

12.8

4865

.623

2.25

8127

6.31

580

12.25

4980

.85

2012

.69

59.7

9740

13.235

86.03

132.35

6014

.03

122.3

173.75

8015

.484

190.97

232.26

100

18.42

276.32

276.32

120

21.488

290.08

140

2533

0ref

crack

49yield

196

160

32.1

371.43

vert

12.25

horiz

49 D

ata from

Graph

00

00

==============

‐0.033

00.03

30

120crack

104

yield

NO

140crack

130

yield

NO

160crack

182

yield

‐0.066

00.06

60

vert

21.487

6ho

rizcrush

vert

25ho

rizvert

32.098

77ho

riz Title

: Con

trol Chart

‐0.099

00.09

90

Data from

Graph

00

00

Data from

Graph

00

00

Data from

Graph

00

00

‐0.132

00.13

20angle

arc length

bogus?

==============

‐0.162

10.4

0.16

2‐10.4

==============

‐0.137

10.2

0.13

7‐10.2

==============

‐0.162

14.3

0.16

2‐14.3

X Axis T

itle: x‐axis

‐0.165

00.16

50

204.02

‐20crack

51.2

sup

yield

192

‐0.328

21.2

0.32

8‐21.2

‐0.274

20.5

0.27

4‐20.5

‐0.323

28.6

0.32

3‐28.6

Y Axis T

itle: y‐axis

‐0.239

0.3

0.23

9‐0.3

404.08

vert

12.8

horiz

48 Title

: Con

trol Chart

‐0.545

37.6

0.54

5‐37.6

Title

: Con

trol Chart

‐0.42

32.3

0.42

‐32.3

Title

: Con

trol Chart

‐0.493

45.1

0.49

3‐45.1

‐0.477

2.3

0.47

7‐2.3

604.19

Data from

Graph

00

‐0.786

57.9

0.78

6‐57.9

‐0.585

46.8

0.58

5‐46.8

‐0.671

63.6

0.67

1‐63.6

x‐axis

y‐axis

‐0.752

4.9

0.75

2‐4.9

804.34

==============

0.02

40.3

X Axis T

itle: x‐axis

‐1.042

77.5

1.04

2‐77.5

X Axis T

itle: x‐axis

‐0.755

63.2

0.75

5‐63.2

X Axis T

itle: x‐axis

‐0.858

840.85

8‐84

Line

type

: 0

‐1.049

7.8

1.04

9‐7.8

100

4.56

0.04

80.6

Y Axis T

itle: y‐axis

‐1.291

97.2

1.29

1‐97.2

Y Axis T

itle: y‐axis

‐0.936

79.7

0.93

6‐79.7

Y Axis T

itle: y‐axis

‐1.055

103.6

1.05

5‐103

.60

00

0‐1.346

10.9

1.34

6‐10.9

120

4.84

Title

: Con

trol Chart

0.07

20.9

‐1.529

116.8

1.52

9‐116

.8‐1.105

95.8

1.10

5‐95.8

‐1.248

123.2

1.24

8‐123

.2‐0.033

9.79

076

0.03

32.44

769

‐1.653

14.1

1.65

3‐14.1

140

5.2

0.09

61.2

x‐axis

y‐axis

‐1.781

136.6

1.78

1‐136

.6 x‐axis

y‐axis

‐1.283

112.2

1.28

3‐112

.2 x‐axis

y‐axis

‐1.5

142.8

1.5

‐142

.8‐0.066

19.6

0.06

64.9

‐1.955

17.3

1.95

5‐17.3

160

5.67

X Axis T

itle: x‐axis

0.12

1.5

Line

type

: 0

‐2.031

156.2

2.03

1‐156

.2Line

type

: 0

‐1.461

128.1

1.46

1‐128

.1Line

type

: 0

‐1.706

162.4

1.70

6‐162

.4‐0.099

29.4

0.09

97.35

‐2.258

20.5

2.25

8‐20.5

Y Axis T

itle: y‐axis

0.14

41.8

00

00

‐2.298

176

2.29

8‐176

00

00

‐1.645

144.5

1.64

5‐144

.50

00

0‐1.926

181.9

1.92

6‐181

.9‐0.132

39.2

0.13

29.8

‐2.547

23.6

2.54

7‐23.6

0.16

82.1

‐0.162

51.950

930.16

210

.733

66‐2.545

195.8

2.54

5‐195

.8‐0.137

51.950

930.13

79.99

0563

‐1.827

160.6

1.82

7‐160

.6‐0.162

77.926

410.16

213

.743

63‐2.147

201.4

2.14

7‐201

.4‐0.165

490.16

512

.25

‐2.85

26.8

2.85

‐26.8

x‐axis

y‐axis

0.19

31.9

‐0.328

104

0.32

821

.487

6‐2.798

215.4

2.79

8‐215

.4‐0.274

104

0.27

420

‐2.012

176.7

2.01

2‐176

.7‐0.323

156

0.32

327

.513

23‐2.371

221

2.37

1‐221

‐0.239

58.8

0.23

914

.7‐3.141

303.14

1‐30

Line

type

: 0

0.23

72.4

‐0.545

156

0.54

532

.231

4‐3.055

235

3.05

5‐235

‐0.42

156

0.42

30‐2.201

192.8

2.20

1‐192

.8‐0.493

234

0.49

341

.269

84‐2.609

240.7

2.60

9‐240

.7‐0.477

68.6

0.47

717

.15

‐3.449

33.3

3.44

9‐33.3

00

00

0.30

72.9

‐0.786

208

0.78

642

.975

2‐3.326

254.8

3.32

6‐254

.8‐0.585

208

0.58

540

‐2.432

209

2.43

2‐209

‐0.671

312

0.67

155

.026

46‐2.83

260.4

2.83

‐260

.4‐0.752

78.400

010.75

219

.6‐3.746

36.5

3.74

6‐36.5

0.02

4‐6.393

960.02

41.59

849

0.48

94.8

‐1.042

260

1.04

253

.719

01‐3.577

274.5

3.57

7‐274

.5‐0.755

260

0.75

550

‐2.613

225.3

2.61

3‐225

.3‐0.858

390

0.85

868

.783

07‐3.086

279.9

3.08

6‐279

.9‐1.049

88.2

1.04

922

.05

‐4.066

40.1

4.06

6‐40.1

0.04

8‐12.8

0.04

83.2

0.71

16.9

‐1.291

312

1.29

164

.462

81‐3.836

294.1

3.83

6‐294

.1‐0.936

312

0.93

660

‐2.803

241.4

2.80

3‐241

.4‐1.055

468

1.05

582

.539

69‐3.314

299.4

3.31

4‐299

.4‐1.346

981.34

624

.5‐4.578

46.8

4.57

8‐46.8

0.07

2‐19.2

0.07

24.8

0.90

38.3

‐1.529

364

1.52

975

.206

61‐4.096

313.7

4.09

6‐313

.7‐1.105

364

1.10

570

‐2.997

257.5

2.99

7‐257

.5‐1.248

546

1.24

896

.296

3‐3.545

308.9

3.54

5‐308

.9‐1.653

107.8

1.65

326

.95

‐5.133

54.2

5.13

3‐54.2

0.09

6‐25.6

0.09

66.4

1.11

99.6

‐1.781

416

1.78

185

.950

41‐4.373

333.4

4.37

3‐333

.4‐1.283

416

1.28

380

‐3.192

273.6

3.19

2‐273

.6‐1.5

624.00

011.5

110.05

29‐3.775

338.4

3.77

5‐338

.4‐1.955

117.6

1.95

529

.4‐5.673

61.4

5.67

3‐61.4

0.12

‐32

0.12

81.35

111

‐2.031

468

2.03

196

.694

22‐4.659

353

4.65

9‐353

‐1.461

468

1.46

190

‐3.387

289.7

3.38

7‐289

.7‐1.706

702.00

011.70

612

3.80

95‐4.007

357.9

4.00

7‐357

.9‐2.258

127.4

2.25

831

.85

‐6.215

68.6

6.21

5‐68.6

0.14

4‐38.4

0.14

49.6

1.56

512

.3‐2.298

520

2.29

810

7.43

8‐4.912

372.7

4.91

2‐372

.7‐1.645

520

1.64

510

0‐3.584

305.9

3.58

4‐305

.9‐1.926

780

1.92

613

7.56

61‐4.239

377.4

4.23

9‐377

.4‐2.547

137.2

2.54

734

.300

01‐6.765

75.9

6.76

5‐75.9

0.16

8‐44.8

0.16

811

.21.81

213

.6‐2.545

572

2.54

511

8.18

18‐5.173

392.3

5.17

3‐392

.3‐1.827

571.99

991.82

711

0‐3.824

322.1

3.82

4‐322

.1‐2.147

858

2.14

715

1.32

28‐4.472

396.9

4.47

2‐396

.9‐2.85

147

2.85

36.75

‐7.32

83.3

7.32

‐83.3

0.19

3‐51.2

0.19

312

.82.02

714

.8‐2.798

624

2.79

812

8.92

56‐5.435

411.9

5.43

5‐411

.9‐2.012

624

2.01

212

0‐4.019

338.2

4.01

9‐338

.2‐2.371

936

2.37

116

5.07

94‐4.706

416.5

4.70

6‐416

.5‐3.141

156.8

3.14

139

.2‐7.88

90.7

7.88

‐90.7

0.23

7‐57.6

0.23

714

.42.24

416

‐3.055

676

3.05

513

9.66

94‐5.74

431.6

5.74

‐431

.6‐2.201

676

2.20

113

0‐4.21

354.4

4.21

‐354

.4‐2.609

1014

2.60

917

8.83

6‐4.942

436

4.94

2‐436

‐3.449

166.6

3.44

941

.65

‐8.44

98.2

8.44

‐98.2

0.30

7‐64

0.30

716

2.48

717

.2‐3.326

728

3.32

615

0.41

32‐6.001

451.3

6.00

1‐451

.3‐2.432

728

2.43

214

0‐4.408

370.5

4.40

8‐370

.5‐2.83

1092

2.83

192.59

26‐5.18

455.5

5.18

‐455

.5‐3.746

176.4

3.74

644

.100

01‐9.011

105.7

9.01

1‐105

.70.48

9‐70.4

0.48

917

.62.70

318

.3‐3.577

779.99

993.57

716

1.15

7‐6.262

470.9

6.26

2‐470

.9‐2.613

780.00

012.61

315

0‐4.607

386.6

4.60

7‐386

.6‐3.086

1170

3.08

620

6.34

92‐5.42

475

5.42

‐475

‐4.066

186.2

4.06

646

.55

‐9.587

113.4

9.58

7‐113

.40.71

1‐76.8

0.71

119

.22.92

119

.4‐3.836

832

3.83

617

1.90

08‐6.54

490.7

6.54

‐490

.7‐2.803

831.99

992.80

316

0‐4.806

402.7

4.80

6‐402

.7‐3.314

1248

3.31

422

0.10

58‐5.674

494.6

5.67

4‐494

.6‐4.578

196

4.57

849

‐10.16

712

110

.167

‐121

0.90

3‐83.2

0.90

320

.83.13

920

.5‐4.096

884

4.09

618

2.64

46‐6.826

510.5

6.82

6‐510

.5‐2.997

884

2.99

717

0‐5.006

418.8

5.00

6‐418

.8‐3.545

1326

3.54

523

3.86

24‐5.92

514.1

5.92

‐514

.1‐5.133

205.8

5.13

351

.45

‐10.75

712

8.6

10.757

‐128

.61.11

9‐89.6

1.11

922

.43.38

621

.6‐4.373

936

4.37

319

3.38

84‐3.192

936.00

013.19

218

0‐5.206

434.9

5.20

6‐434

.9‐3.775

1404

3.77

524

7.61

9‐5.673

215.6

5.67

353

.9‐11.36

813

6.4

11.368

‐136

.41.35

1‐96

1.35

124

3.60

422

.7‐4.659

987.99

994.65

920

4.13

22‐3.387

988.00

013.38

719

0‐5.407

451

5.40

7‐451

‐4.007

1482

4.00

726

1.37

56‐6.215

225.4

6.21

556

.350

01‐11.99

214

4.2

11.992

‐144

.21.56

5‐102

.41.56

525

.63.82

323

.8‐4.912

1040

4.91

221

4.87

6‐3.584

1040

3.58

420

0‐5.608

467.1

5.60

8‐467

.1‐4.239

1560

4.23

927

5.13

23‐6.765

235.2

6.76

558

.81.81

2‐108

.81.81

227

.24.04

824

.9‐5.173

1092

5.17

322

5.61

98‐3.824

1092

3.82

421

0‐5.81

483.2

5.81

‐483

.2‐4.472

1638

4.47

228

8.88

89‐7.32

245

7.32

61.250

012.02

7‐115

.22.02

728

.84.27

526

‐5.435

1144

5.43

523

6.36

36‐4.019

1144

4.01

922

0‐6.025

499.4

6.02

5‐499

.4‐4.706

1716

4.70

630

2.64

55‐7.88

254.8

7.88

63.700

012.24

4‐121

.62.24

430

.44.51

127

.2‐5.74

1196

5.74

247.10

75‐4.21

1196

4.21

230

‐6.226

515.6

6.22

6‐515

.6‐4.942

1794

4.94

231

6.40

21‐8.44

264.6

8.44

66.150

012.48

7‐128

2.48

732

4.86

627

.2‐6.001

1248

6.00

125

7.85

12‐4.408

1248

4.40

824

0‐5.18

1872

5.18

330.15

87‐9.011

274.4

9.01

168

.62.70

3‐134

.42.70

333

.65.31

630

.2‐6.262

1300

6.26

226

8.59

5‐4.607

1300

4.60

725

0‐5.42

1950

5.42

343.91

54‐9.587

284.2

9.58

771

.049

992.92

1‐140

.82.92

135

.25.79

32.2

‐6.54

1352

6.54

279.33

89‐4.806

1352

4.80

626

0‐5.674

2028

5.67

435

7.67

2‐10.16

729

410

.167

73.499

993.13

9‐147

.23.13

936

.86.29

134

.7‐6.826

1404

6.82

629

0.08

26‐5.006

1404

5.00

627

0‐5.92

2106

5.92

371.42

86‐10.75

730

3.8

10.757

75.95

3.38

6‐153

.63.38

638

.46.80

436

.429

0.08

26‐5.206

1456

5.20

628

037

1.42

86‐11.36

831

3.6

11.368

78.4

3.60

4‐160

3.60

440

7.33

139

.5‐5.407

1508

5.40

729

0‐11.99

232

3.4

11.992

80.85

3.82

3‐166

.43.82

341

.67.84

842

.4‐5.608

1560

5.60

830

0be

coming more shear critical, buto nly hits 0.6

80.85

4.04

8‐172

.84.04

843

.28.35

44.3

‐5.81

1612

5.81

310

4.27

5‐179

.24.27

544

.88.87

146

.4‐6.025

1664

6.02

532

04.51

1‐185

.64.51

146

.49.38

348

.3‐6.226

1716

6.22

633

04.86

6‐192

4.86

648

9.88

350

.133

05.31

6‐198

.45.31

649

.610

.452

5.79

‐204

.85.79

51.200

016.29

1‐211

.26.29

152

.86.80

4‐217

.66.80

454

.400

017.33

1‐224

7.33

156

7.84

8‐230

.47.84

857

.600

018.35

‐236

.88.35

59.200

018.87

1‐243

.28.87

160

.89.38

3‐249

.69.38

362

.49.88

3‐256

9.88

364

.000

0110

.4‐262

.410

.465

.6

123

Appendix C

Su et. al. Simulation Results

A2

Axial 1000 paper stiffness Axial 60 adjusted

vert horiz vert horiz

Data from Graph Data from Graph

============== axial disp ============== disp axial

0 ‐12.1

Title : Control Chart ‐72.7 0 Title : Control Chart 0.013003 ‐38.5

‐192.8 0.012983 0.02568 ‐72.2

X Axis Title : x‐axis ‐318.8 0.02556 X Axis Titl : x‐axis 0.03862 ‐106.8

Y Axis Title : y‐axis ‐430.5 0.038343 Y Axis Titl : y‐axis 0.05157 ‐141.3

‐517.8 0.051223 0.064523 ‐175.2

x‐axis y‐axis ‐582.5 0.06415 x‐axis y‐axis 0.077483 ‐204.3

Line type : 0 ‐630.8 0.077103 Line type : 0 0.09045 ‐231.2

0 0 0 0 ‐667.8 0.09007 0 0 0 0 0.103417 ‐257.1

‐3.895 90.55217 0.012983 90.55217 ‐355.2 0.10305 ‐3.901 80.00473 0.013003 80.00473 0.11639 ‐280.9

‐7.668 146.8708 0.02556 146.8708 ‐302.5 0.11663 ‐7.704 107.8398 0.02568 107.8398 0.129363 ‐303.3

‐11.503 195.2628 0.038343 195.2628 ‐278.7 0.129733 ‐11.586 125.6908 0.03862 125.6908 0.142337 ‐324

‐15.367 226.7152 0.051223 226.7152 ‐258.2 0.142793 ‐15.471 140.8542 0.05157 140.8542 0.155317 ‐344.3

‐19.245 245.6702 0.06415 245.6702 ‐238.9 0.155853 ‐19.357 154.8537 0.064523 154.8537 0.168293 ‐363.1

‐23.131 258.1199 0.077103 258.1199 ‐219.6 0.168927 ‐23.245 168.0817 0.077483 168.0817 0.181273 ‐357.7

‐27.021 266.6382 0.09007 266.6382 ‐20.7 0.18201 ‐27.135 179.0908 0.09045 179.0908 0.194753 ‐348.3

‐30.915 272.8213 0.10305 272.8213 ‐7.8 0.196123 ‐31.025 188.776 0.103417 188.776 0.207833 ‐343.6

‐34.989 163.6565 0.11663 163.6565 0 ‐34.917 197.3497 0.11639 197.3497 0.220893 ‐338.9

‐38.92 153.4815 0.129733 153.4815 ‐38.809 205.1498 0.129363 205.1498 0.23396 ‐333.7

‐42.838 149.7262 0.142793 149.7262 ‐42.701 212.2672 0.142337 212.2672 0.247037 ‐327.3

‐46.756 146.6364 0.155853 146.6364 ‐46.595 218.9237 0.155317 218.9237 0.260123 ‐319

‐50.678 143.5498 0.168927 143.5498 ‐50.488 224.8254 0.168293 224.8254 0.27323 ‐307.8

‐54.603 140.0697 0.18201 140.0697 ‐54.382 230.3396 0.181273 230.3396 0.286357 ‐259.8

‐58.837 66.00163 0.196123 66.00163 ‐58.426 167.0432 0.194753 167.0432 0.299913 ‐3.8

‐62.853 65.14833 0.20951 65.14833 ‐62.35 163.0602 0.207833 163.0602 0.314617 11.2

‐66.268 161.0004 0.220893 161.0004 0.328007 11.2

‐70.188 159.2363 0.23396 159.2363 0.341177 11.3

‐74.111 157.4876 0.247037 157.4876 0.354353 11.5

‐78.037 155.4841 0.260123 155.4841 0.367527 11.6

‐81.969 152.9413 0.27323 152.9413 0.380693 11.7

‐85.907 149.4586 0.286357 149.4586 0.39386 11.8

‐89.974 98.67216 0.299913 98.67216 0.407017 11.8

‐94.385 67.21954 0.314617 67.21954 0.420203 11.9

‐98.402 66.30299 0.328007 66.30299 0.433377 12

‐102.353 66.61988 0.341177 66.61988 0.446543 12.1

‐106.306 66.88845 0.354353 66.88845 0.459703 12.2

‐110.258 67.17238 0.367527 67.17238 0.472867 ‐10.9

‐114.208 67.4777 0.380693 67.4777 0.481237 ‐10.5

‐118.158 67.76095 0.39386 67.76095

‐122.105 68.07488 0.407017 68.07488

‐126.061 68.33515 0.420203 68.33515

‐130.013 68.61487 0.433377 68.61487

‐133.963 68.89952 0.446543 68.89952

‐137.911 69.18263 0.459703 69.18263

‐141.86 69.45695 0.472867 69.45695

‐144.371 3.29093 0.481237 3.29093

‐148.273 3.28621

‐152.175 3.25716

‐156.077 3.22762

‐159.979 3.21416

‐163.881 3.20319

‐167.783 3.17798

B1

Axial 1000 paper stiffness Axial 60

Vertical Horizontal Data from Graph Horizontal

Data from Graph ==============

============== disp axial disp axial

0 0 0 0 Title : Control Chart 0.01979 0 0 0

Title : Control Chart 0.019777 ‐51.6 51.6 ‐51.6 0.039377 ‐10.6 10.6 ‐10.6

0.03943 ‐127.1 127.1 ‐127.1 X Axis Title: x‐axis 0.058933 ‐29.4 29.4 ‐29.4

X Axis Title: x‐axis 0.05884 ‐213.3 212.4 ‐212.4 Y Axis Title: y‐axis 0.078607 ‐55.8 55.8 ‐55.8

Y Axis Title: y‐axis 0.07846 ‐282.7 244.8 ‐244.8 0.098293 ‐85.3 85.3 ‐85.3

0.09812 ‐331.8 145.4 ‐145.4 x‐axis y‐axis 0.117977 ‐115.3 112.1 ‐112.1

x‐axis y‐axis 0.11779 ‐365.9 130.5 ‐130.5 Line type : 0 0.13766 ‐140.1 107.8 ‐107.8

Line type : 0 0.137467 ‐390.9 123.4 ‐123.4 0 0 0 0 0.157337 ‐161.7 92.9 ‐92.9

0 0 0 0 0.157143 ‐409.8 116.9 ‐116.9 ‐5.937 49.12404 0.01979 49.12404 0.177017 ‐181.3 90.3 ‐90.3

‐5.933 53.37155 0.019777 53.37155 0.176827 ‐424.5 110.6 ‐110.6 ‐11.813 79.3871 0.039377 79.3871 0.196697 ‐198.8 89.3 ‐89.3

‐11.829 93.88904 0.03943 93.88904 0.19651 ‐436.2 104.3 ‐104.3 ‐17.68 93.07303 0.058933 93.07303 0.216387 ‐214.9 87.8 ‐87.8

‐17.652 121.272 0.05884 121.272 0.216193 ‐445.9 98.9 ‐98.9 ‐23.582 102.6188 0.078607 102.6188 0.236077 ‐229.5 86.1 ‐86.1

‐23.538 136.5284 0.07846 136.5284 0.23633 ‐226.8 94.5 ‐94.5 ‐29.488 111.2867 0.098293 111.2867 0.25577 ‐242.9 84.1 ‐84.1

‐29.436 144.1374 0.09812 144.1374 0.2562 ‐200.9 90.8 ‐90.8 ‐35.393 117.9481 0.117977 117.9481 0.275467 ‐255.3 82.3 ‐82.3

‐35.337 148.8909 0.11779 148.8909 0.276003 ‐189.8 87.8 ‐87.8 ‐41.298 123.5073 0.13766 123.5073 0.29517 ‐266.7 80.6 ‐80.6

‐41.24 152.3159 0.137467 152.3159 0.295823 ‐177.7 85.3 ‐85.3 ‐47.201 128.2296 0.157337 128.2296 0.31488 ‐277.3 79.1 ‐79.1

‐47.143 154.8414 0.157143 154.8414 0.31565 ‐165.1 83.2 ‐83.2 ‐53.105 132.3576 0.177017 132.3576 0.334593 ‐287.1 77.8 ‐77.8

‐53.048 156.8599 0.176827 156.8599 0.335523 ‐149.1 81.4 ‐81.4 ‐59.009 136.0471 0.196697 136.0471 0.354953 ‐296.2 76.6 ‐76.6

‐58.953 158.6159 0.19651 158.6159 0.356827 68.6 79.8 ‐79.8 ‐64.916 139.3723 0.216387 139.3723 0.374807 ‐313 75.3 ‐75.3

‐64.858 160.1414 0.216193 160.1414 0.37678 71.2 78.6 ‐78.6 ‐70.823 142.3239 0.236077 142.3239 0.39461 ‐320.7 72.1 ‐72.1

‐70.899 116.2315 0.23633 116.2315 0.396667 71.7 75.3 ‐75.3 ‐76.731 144.9371 0.25577 144.9371 0.41438 ‐322.5 69 ‐69

‐76.86 114.6198 0.2562 114.6198 0.41655 72.3 72 ‐72 ‐82.64 147.3376 0.275467 147.3376 0.43417 ‐325.4 67.1 ‐67.1

‐82.801 113.8638 0.276003 113.8638 0.436427 72.8 70.5 ‐70.5 ‐88.551 149.5186 0.29517 149.5186 0.453973 ‐325.8 66.1 ‐66.1

‐88.747 112.7214 0.295823 112.7214 0.45631 73.2 69.5 ‐69.5 ‐94.464 151.5273 0.31488 151.5273 0.473767 ‐325.6 65.3 ‐65.3

‐94.695 111.0857 0.31565 111.0857 0.476197 73.7 68.7 ‐68.7 ‐100.378 153.3798 0.334593 153.3798 0.493583 ‐326.1 64.8 ‐64.8

‐100.657 108.5377 0.335523 108.5377 0.49608 74.1 68.1 ‐68.1 ‐106.486 109.6136 0.354953 109.6136 0.513403 ‐324.3 64.3 ‐64.3

‐107.048 49.37662 0.356827 49.37662 0.515967 74.4 67.5 ‐67.5 ‐112.442 110.4674 0.374807 110.4674 0.533233 ‐322.1 63.9 ‐63.9

‐113.034 49.43325 0.37678 49.43325 0.535857 74.8 67 ‐67 ‐118.383 110.8634 0.39461 110.8634 0.553083 ‐318.1 63.2 ‐63.2

‐119 49.63043 0.396667 49.63043 0.555747 75 65.5 ‐65.5 ‐124.314 111.3725 0.41438 111.3725 0.572963 ‐311.8 61.6 ‐61.6

‐124.965 49.84537 0.41655 49.84537 0.575623 75.5 62.3 ‐62.3 ‐130.251 111.6637 0.43417 111.6637 0.595057 ‐301.2 60 ‐60

‐130.928 50.06274 0.436427 50.06274 0.595527 75.7 62.4 ‐62.4 ‐136.192 111.868 0.453973 111.868 0.615417 ‐49.5 59.3 ‐59.3

‐136.893 50.28269 0.45631 50.28269 0.61542 76 61.8 ‐61.8 ‐142.13 112.0647 0.473767 112.0647 0.635323 35.3 58.9 ‐58.9

‐142.859 50.4883 0.476197 50.4883 0.63531 76.3 61.3 ‐61.3 ‐148.075 111.9934 0.493583 111.9934 0.655213 35.5 58.6 ‐58.6

‐148.824 50.71212 0.49608 50.71212 0.655193 76.7 61.1 ‐61.1 ‐154.021 111.7714 0.513403 111.7714 0.675103 35.7 58.4 ‐58.4

‐154.79 50.93287 0.515967 50.93287 0.6751 76.9 60.8 ‐60.8 ‐159.97 111.2398 0.533233 111.2398 0.694997 36 58.3 ‐58.3

‐160.757 51.14385 0.535857 51.14385 0.694997 77.2 60.6 ‐60.6 ‐165.925 110.2269 0.553083 110.2269 0.7149 36.2 58.1 ‐58.1

‐166.724 51.35726 0.555747 51.35726 0.714887 77.5 60.4 ‐60.4 ‐171.889 108.3382 0.572963 108.3382 0.7348 36.4 57.9 ‐57.9

‐172.687 51.58128 0.575623 51.58128 0.734773 77.8 60.1 ‐60.1 ‐178.517 54.63169 0.595057 54.63169 0.754693 36.7 57.6 ‐57.6

‐178.658 51.78595 0.595527 51.78595 0.754683 78 59.3 ‐59.3 ‐184.625 51.92373 0.615417 51.92373 0.774583 36.9 56.7 ‐56.7

‐184.626 51.98836 0.61542 51.98836 0.774583 78.3 58.4 ‐58.4 ‐190.597 52.12277 0.635323 52.12277 0.794487 37.1 56.1 ‐56.1

‐190.593 52.20269 0.63531 52.20269 0.794477 78.5 57.9 ‐57.9 ‐196.564 52.33374 0.655213 52.33374 0.814387 37.3 55.7 ‐55.7

‐196.558 52.42475 0.655193 52.42475 0.814363 78.9 57.6 ‐57.6 ‐202.531 52.54673 0.675103 52.54673 0.834287 37.6 124.4 ‐124.4

‐202.53 52.61135 0.6751 52.61135 0.834273 79.3 57.4 ‐57.4 ‐208.499 52.75573 0.694997 52.75573 0.85418 37.8 125.7 ‐125.7

‐208.499 52.81106 0.694997 52.81106 0.854173 79.6 134.1 ‐134.1 ‐214.47 52.9401 0.7149 52.9401 0.874077 38 125.6 ‐125.6

‐214.466 53.01736 0.714887 53.01736 0.874073 79.9 157.5 ‐157.5 ‐220.44 53.13502 0.7348 53.13502 0.893983 38.3 125.4 ‐125.4

‐220.432 53.22706 0.734773 53.22706 0.893957 80.2 158.2 ‐158.2 ‐226.408 53.33186 0.754693 53.33186 0.913883 38.6 125.1 ‐125.1

‐226.405 53.41119 0.754683 53.41119 0.913853 80.3 158.1 ‐158.1 ‐232.375 53.54171 0.774583 53.54171 0.933783 38.7 124.9 ‐124.9

‐232.375 53.599 0.774583 53.599 0.933767 80.6 158 ‐158 ‐238.346 53.7253 0.794487 53.7253 0.953677 38.9 124.5 ‐124.5

‐238.343 53.79329 0.794477 53.79329 0.95367 80.8 157.9 ‐157.9 ‐244.316 53.91014 0.814387 53.91014 0.973573 39.1 124.1 ‐124.1

‐244.309 53.99131 0.814363 53.99131 0.973567 81.1 157.7 ‐157.7 ‐250.286 54.09857 0.834287 54.09857 0.99347 39.3 123.6 ‐123.6

‐250.282 54.17433 0.834273 54.17433 0.993457 81.4 157.5 ‐157.5 ‐256.254 54.28757 0.85418 54.28757 1.01338 39.5 123.1 ‐123.1

‐256.252 54.35195 0.854173 54.35195 1.01335 81.7 157.3 ‐157.3 ‐262.223 54.47924 0.874077 54.47924 122.5 ‐122.5

‐262.222 54.53672 0.874073 54.53672 1.033247 ‐157.1 157.1 ‐157.1 ‐268.195 54.65407 0.893983 54.65407 121.8 ‐121.8

‐268.187 54.73427 0.893957 54.73427 156.9 ‐156.9 ‐274.165 54.82705 0.913883 54.82705 121.1 ‐121.1

‐274.156 54.91596 0.913853 54.91596 156.7 ‐156.7 ‐280.135 55.0075 0.933783 55.0075 120.3 ‐120.3

‐280.13 55.08049 0.933767 55.08049 156.2 ‐156.2 ‐286.103 55.18819 0.953677 55.18819

‐286.101 55.25337 0.95367 55.25337 155.6 ‐155.6 ‐292.072 55.36775 0.973573 55.36775

‐292.07 55.42687 0.973567 55.42687 154.9 ‐154.9 ‐298.041 55.54298 0.99347 55.54298

‐298.037 55.6053 0.993457 55.6053 154.1 ‐154.1 ‐304.014 55.70552 1.01338 55.70552

‐304.005 55.78308 1.01335 55.78308 153.4 ‐153.4 ‐309.984 55.86867 1.03328 55.86867

‐309.974 55.95377 1.033247 55.95377 152.5 ‐152.5 ‐315.954 56.03765 1.05318 56.03765

‐313.092 61.31271 1.04364 61.31271 151.6 ‐151.6 ‐321.923 56.20341 1.073077 56.20341

‐318.999 61.14813 1.06333 61.14813 150.6 ‐150.6 ‐327.892 56.36868 1.092973 56.36868

‐324.906 60.96257 1.08302 60.96257 149.6 ‐149.6 ‐333.857 56.53363

‐330.814 60.75585 1.102713 60.75585 ‐339.828 56.67803

‐336.721 60.52773 1.122403 60.52773 ‐345.796 56.8281

‐342.629 60.27809 1.142097 60.27809

‐348.536 60.00688 1.161787 60.00688

‐354.443 59.71398 1.181477 59.71398

‐360.351 59.39931 1.20117 59.39931

‐366.258 59.06278 1.22086 59.06278

‐372.165 58.7043 1.24055 58.7043

‐378.073 58.32394 1.260243 58.32394

‐383.98 57.92157 1.279933 57.92157

‐389.887 57.49717 1.299623 57.49717

‐395.795 57.05053 1.319317 57.05053

‐401.702 56.58166 1.339007 56.58166

‐407.609 56.0905 1.358697 56.0905

‐413.517 0.79409 1.37839 0.79409

‐419.424 0.75716 1.39808 0.75716

‐425.332 0.74382 1.417773 0.74382

‐431.239 0.73081 1.437463 0.73081

‐437.147 0.7182 1.457157 0.7182

‐443.054 0.70598 1.476847 0.70598

‐448.961 0.69413 1.496537 0.69413

‐454.869 0.68263 1.51623 0.68263

‐460.776 0.67146 1.53592 0.67146

‐466.684 0.66062 1.555613 0.66062

‐472.591 0.65008 1.575303 0.65008

C2

Axial 1000 Axial 60

vert horiz Data from Graph horiz

Data from Graph disp axial ============== disp axial

============== 0 0 0 0 0 0 0 0

0.01975 ‐33.4 32.5 ‐32.5 Title : Control Chart 0.019775 ‐8.6 32.5 ‐32.5

Title : Control Chart 0.0395 ‐75.1 70.3 ‐70.3 0.039575 ‐22.6 70.3 ‐70.3

0.05935 ‐115.2 77.6 ‐77.6 X Axis Title: x‐axis 0.059475 ‐39.8 77.6 ‐77.6

X Axis Title: x‐axis 0.079245 ‐137.2 65.1 ‐65.1 Y Axis Title: y‐axis 0.07938 ‐57.3 65.1 ‐65.1

Y Axis Title: y‐axis 0.09916 ‐151 54.2 ‐54.2 0.099295 ‐70.8 54.2 ‐54.2

0.11909 ‐160.4 47.2 ‐47.2 x‐axis y‐axis 0.11922 ‐81.9 47.2 ‐47.2

x‐axis y‐axis 0.13903 ‐167.3 43.7 ‐43.7 Line type : 0 0.139155 ‐91.3 43.7 ‐43.7

Line type : 0 0.158975 ‐172.7 42 ‐42 0 0 0 0 0.15909 ‐99.3 42 ‐42

0 0 0 0 0.17872 ‐114.7 41.3 ‐41.3 ‐3.955 27.64249 0.019775 27.64249 0.17903 ‐106.2 41.3 ‐41.3

‐3.95 30.64527 0.01975 30.64527 0.19863 ‐107.4 41.1 ‐41.1 ‐7.915 42.50102 0.039575 42.50102 0.198975 ‐112.3 41.1 ‐41.1

‐7.9 51.84163 0.0395 51.84163 0.218535 ‐101.4 40.2 ‐40.2 ‐11.895 48.107 0.059475 48.107 0.218925 ‐117.9 40.2 ‐40.2

‐11.87 61.05107 0.05935 61.05107 0.23844 ‐96.7 38.1 ‐38.1 ‐15.876 52.9747 0.07938 52.9747 0.238875 ‐122.7 38.1 ‐38.1

‐15.849 64.468 0.079245 64.468 0.258345 ‐92.9 37.1 ‐37.1 ‐19.859 56.50575 0.099295 56.50575 0.25883 ‐127 37.1 ‐37.1

‐19.832 66.50816 0.09916 66.50816 0.27825 ‐89.6 36.7 ‐36.7 ‐23.844 59.13933 0.11922 59.13933 0.27832 ‐71.2 36.7 ‐36.7

‐23.818 67.90179 0.11909 67.90179 0.298155 ‐86.9 36.7 ‐36.7 ‐27.831 61.26606 0.139155 61.26606 0.298215 ‐69.8 36.7 ‐36.7

‐27.806 68.9147 0.13903 68.9147 0.31806 ‐83.6 36.6 ‐36.6 ‐31.818 62.96371 0.15909 62.96371 0.31813 ‐66.2 36.6 ‐36.6

‐31.795 69.7489 0.158975 69.7489 0.33796 ‐81.8 36.8 ‐36.8 ‐35.806 64.42544 0.17903 64.42544 0.338245 ‐82.9 36.8 ‐36.8

‐35.744 56.71375 0.17872 56.71375 0.357865 ‐79.2 37.1 ‐37.1 ‐39.795 65.72016 0.198975 65.72016 0.358155 ‐81.2 37.1 ‐37.1

‐39.726 54.62128 0.19863 54.62128 0.377765 ‐76.6 37.3 ‐37.3 ‐43.785 66.80882 0.218925 66.80882 0.378065 ‐79 37.3 ‐37.3

‐43.707 53.9863 0.218535 53.9863 0.39767 ‐74 37.8 ‐37.8 ‐47.775 67.75148 0.238875 67.75148 0.397975 ‐77 37.8 ‐37.8

‐47.688 53.70702 0.23844 53.70702 0.417575 ‐71 37.7 ‐37.7 ‐51.766 68.63973 0.25883 68.63973 0.41787 ‐75.2 37.7 ‐37.7

‐51.669 53.59356 0.258345 53.59356 0.43747 ‐68.4 36.1 ‐36.1 ‐55.664 55.00441 0.27832 55.00441 0.43588 ‐0.8 36.1 ‐36.1

‐55.65 53.59052 0.27825 53.59052 0.45524 40.9 34.7 ‐34.7 ‐59.643 54.40982 0.298215 54.40982 0.455695 ‐0.7 34.7 ‐34.7

‐59.631 53.63925 0.298155 53.63925 0.475005 40.4 34 ‐34 ‐63.626 53.8507 0.31813 53.8507 0.47551 ‐0.7 34 ‐34

‐63.612 53.72359 0.31806 53.72359 0.494795 40.5 33.7 ‐33.7 ‐67.649 31.44359 0.338245 31.44359 0.49532 0 33.7 ‐33.7

‐67.592 53.74492 0.33796 53.74492 0.51459 40.7 33.4 ‐33.4 ‐71.631 30.96113 0.358155 30.96113 0.515135 0 33.4 ‐33.4

‐71.573 53.77404 0.357865 53.77404 0.534385 40.8 33.2 ‐33.2 ‐75.613 30.56475 0.378065 30.56475 0.53495 0 33.2 ‐33.2

‐75.553 53.72995 0.377765 53.72995 0.55418 41 33 ‐33 ‐79.595 30.12401 0.397975 30.12401 0.55476 0 33 ‐33

‐79.534 53.62494 0.39767 53.62494 0.573975 41 32.9 ‐32.9 ‐83.574 29.62803 0.41787 29.62803 0.574575 0 32.9 ‐32.9

‐83.515 53.47573 0.417575 53.47573 0.593765 41.1 32.8 ‐32.8 ‐87.176 0.75593 0.43588 0.75593 0.59439 0 32.8 ‐32.8

‐87.494 53.19236 0.43747 53.19236 0.61356 41.2 32.8 ‐32.8 ‐91.139 0.69323 0.455695 0.69323 0.6142 0 32.8 ‐32.8

‐91.048 23.87395 0.45524 23.87395 0.63335 41.3 32.7 ‐32.7 ‐95.102 0.64206 0.47551 0.64206 0.634015 0 32.7 ‐32.7

‐95.001 23.84734 0.475005 23.84734 0.653145 41.5 32.7 ‐32.7 ‐99.064 0.58175 0.49532 0.58175 0.65383 0 32.7 ‐32.7

‐98.959 23.95012 0.494795 23.95012 0.67294 41.6 32.7 ‐32.7 ‐103.027 0.54027 0.515135 0.54027 0.67364 0 32.7 ‐32.7

‐102.918 24.06001 0.51459 24.06001 0.69273 41.7 32.8 ‐32.8 ‐106.99 0.51177 0.53495 0.51177 0.693455 0 32.8 ‐32.8

‐106.877 24.17138 0.534385 24.17138 0.71252 41.7 32.8 ‐32.8 ‐110.952 0.46126 0.55476 0.46126 0.71327 0 32.8 ‐32.8

‐110.836 24.28052 0.55418 24.28052 0.73231 41.8 32.5 ‐32.5 ‐114.915 0.44492 0.574575 0.44492 0.73308 0 32.5 ‐32.5

‐114.795 24.37862 0.573975 24.37862 0.752105 41.9 31.9 ‐31.9 ‐118.878 0.41458 0.59439 0.41458 0.752895 0 31.9 ‐31.9

‐118.753 24.47703 0.593765 24.47703 0.771895 42 31.4 ‐31.4 ‐122.84 0.37987 0.6142 0.37987 0.772705 0 31.4 ‐31.4

‐122.712 24.57562 0.61356 24.57562 0.79169 42.2 31.1 ‐31.1 ‐126.803 0.36263 0.634015 0.36263 0.79252 0 31.1 ‐31.1

‐126.67 24.67591 0.63335 24.67591 0.81148 42.3 30.8 ‐30.8 ‐130.766 0.34905 0.65383 0.34905 0.812335 0 30.8 ‐30.8

‐130.629 24.77858 0.653145 24.77858 0.83127 42.4 ‐134.728 0.31437 0.67364 0.31437 0.832145 0

‐134.588 24.87815 0.67294 24.87815 0.85106 42.4 ‐138.691 0.3086 0.693455 0.3086 0.85196 0

‐138.546 24.96583 0.69273 24.96583 0.87085 42.5 ‐142.654 0.27832 0.71327 0.27832 0.871775 0

‐142.504 25.05822 0.71252 25.05822 0.89064 42.6 ‐146.616 0.27502 0.73308 0.27502 0.891585 0

‐146.462 25.14878 0.73231 25.14878 0.91043 42.8 ‐150.579 0.24934 0.752895 0.24934 0.9114 0

‐150.421 25.2393 0.752105 25.2393 0.93022 42.9 ‐154.541 0.24545 0.772705 0.24545 0.931215 0

‐154.379 25.33324 0.771895 25.33324 0.950015 43 ‐158.504 0.22691 0.79252 0.22691 0.951025 0

‐158.338 25.42531 0.79169 25.42531 0.969805 43.2 ‐162.467 0.22379 0.812335 0.22379 0.97084 0

‐162.296 25.5151 0.81148 25.5151 0.989595 43.3 ‐166.429 0.20404 0.832145 0.20404 0.99065 0

‐166.254 25.59397 0.83127 25.59397 1.009395 23.6 ‐170.392 0.2023 0.85196 0.2023 1.010465 0

‐170.212 25.67683 0.85106 25.67683 0 0 ‐174.355 0.18531 0.871775 0.18531 1.03028 0

‐174.17 25.75767 0.87085 25.75767 0 0 ‐178.317 0.1836 0.891585 0.1836 1.05009 0

‐178.128 25.84057 0.89064 25.84057 0 0 ‐182.28 0.17208 0.9114 0.17208 1.069905 0

‐182.086 25.924 0.91043 25.924 0 0 ‐186.243 0.16969 0.931215 0.16969

‐186.044 26.00625 0.93022 26.00625 0 0 ‐190.205 0.15517 0.951025 0.15517

‐190.003 26.0899 0.950015 26.0899 0 0 ‐194.168 0.15335 0.97084 0.15335

‐193.961 26.16927 0.969805 26.16927 0 0 ‐198.13 0.14307 0.99065 0.14307

‐197.919 26.24813 0.989595 26.24813 ‐202.093 0.14229 1.010465 0.14229

‐201.879 12.9869 1.009395 12.9869 ‐206.056 0.13254 1.03028 0.13254

‐210.018 0.13123 1.05009 0.13123

‐213.981 0.12338 1.069905 0.12338

127

Appendix D

Vecchio and Tang Simulation Results

TV2 TV1 TV1 old TV1 new crack 29.2 yield 74.5

0 0 0 0 Data from Graph Data from Graph

2 15 2 20 ============== ==============

5 28 10 43

7.5 36 15 55 Title : Control Chart Title : Control Chart

9 40 18 61

11 52 19.1 63 X Axis Titl : x‐axis X Axis Titl : x‐axis

13 60 19.5 59 Y Axis Title: y‐axis Y Axis Title: y‐axis

16 69

18 73 x‐axis y‐axis x‐axis y‐axis

22.5 80 Line type : 0 Line type : 0

25 82.5 0 15.61609 0 15.61609 9E‐05 0 15.59739 0 15.59739 0.00039 0

27.5 85 ‐0.5 22.15574 0.5 22.15574 6.53974 ‐0.5 24.13129 0.5 24.13129 8.53429 0.85

30 87.5 ‐0.999 28.69465 0.999 28.69465 13.07865 ‐0.999 31.93258 0.999 31.93258 16.33558 1.6983

32.5 88.5 ‐1.498 33.58192 1.498 33.58192 17.96592 ‐1.497 36.55535 1.497 36.55535 20.95835 2.5449

35 88.5 ‐1.997 36.79436 1.997 36.79436 21.17836 ‐1.996 39.83085 1.996 39.83085 24.23385 3.3932

37.5 88.5 ‐2.495 39.32577 2.495 39.32577 23.70977 ‐2.494 42.61933 2.494 42.61933 27.02233 4.2398

40 89 ‐2.994 41.53744 2.994 41.53744 25.92144 ‐2.993 45.166 2.993 45.166 29.569 5.0881

42.5 89 ‐3.493 43.48075 3.493 43.48075 27.86475 ‐3.491 47.52072 3.491 47.52072 31.92372 5.9347

45 89 ‐3.991 45.39009 3.991 45.39009 29.77409 ‐3.99 49.78839 3.99 49.78839 34.19139 6.783

47.5 89 ‐4.49 47.14526 4.49 47.14526 31.52926 ‐4.489 51.99661 4.489 51.99661 36.39961 7.6313

50 88.5 ‐4.989 48.94612 4.989 48.94612 33.33012 ‐4.987 54.12089 4.987 54.12089 38.52389 8.4779

52.5 88.25 ‐5.488 50.55962 5.488 50.55962 34.94362 ‐5.485 56.23307 5.485 56.23307 40.63607 9.3245

55 87.75 ‐5.986 52.25674 5.986 52.25674 36.64074 ‐5.984 58.29198 5.984 58.29198 42.69498 10.1728

57.5 87.3 ‐6.485 53.80832 6.485 53.80832 38.19232 ‐6.482 60.29452 6.482 60.29452 44.69752 11.0194

60 86.9 ‐6.984 55.43998 6.984 55.43998 39.82398 ‐6.979 62.24336 6.979 62.24336 46.64636 11.8643

‐7.482 57.0138 7.482 57.0138 41.3978 ‐7.477 64.12067 7.477 64.12067 48.52367 12.7109

‐7.981 58.5186 7.981 58.5186 42.9026 ‐7.975 66.0028 7.975 66.0028 50.4058 13.5575

‐8.479 60.03481 8.479 60.03481 44.41881 ‐8.472 67.78382 8.472 67.78382 52.18682 14.4024

‐8.977 61.50855 8.977 61.50855 45.89255 ‐8.967 69.49208 8.967 69.49208 53.89508 15.2439

‐9.475 62.88391 9.475 62.88391 47.26791 ‐9.462 71.07138 9.462 71.07138 55.47438 16.0854

TV2 old TV2 new ‐9.973 64.34823 9.973 64.34823 48.73223 ‐9.955 72.51255 9.955 72.51255 56.91555 16.9235

Data from Graph Data from Graph ‐10.471 65.73816 10.471 65.73816 50.12216 ‐10.445 73.78256 10.445 73.78256 58.18556 17.7565

============== ============== ‐10.969 67.05191 10.969 67.05191 51.43591 ‐10.925 74.49463 10.925 74.49463 58.89763 18.5725

‐11.465 68.33606 11.465 68.33606 52.72006 ‐11.4 75.08162 11.4 75.08162 59.48462 19.38

Title : Control Chart Title : Control Chart ‐11.961 69.6013 11.961 69.6013 53.9853 ‐11.883 76.29959 11.883 76.29959 60.70259 20.2011

‐12.457 70.76345 12.457 70.76345 55.14745 ‐12.37 77.5927 12.37 77.5927 61.9957 21.029

X Axis Titl : x‐axis X Axis Titl : x‐axis ‐12.951 71.81094 12.951 71.81094 56.19494 ‐12.865 78.8686 12.865 78.8686 63.2716 21.8705

Y Axis Title: y‐axis Y Axis Title: y‐axis ‐13.443 72.74806 13.443 72.74806 57.13206 ‐13.36 80.10051 13.36 80.10051 64.50351 22.712

‐13.933 73.60334 13.933 73.60334 57.98734 ‐13.856 81.22137 13.856 81.22137 65.62437 23.5552

x‐axis y‐axis x‐axis y‐axis ‐14.417 73.8528 14.417 73.8528 58.2368 ‐14.352 82.33116 14.352 82.33116 66.73416 24.3984

Line type : 0 Line type : 0 ‐14.911 74.5057 14.911 74.5057 58.8897 ‐14.848 83.39728 14.848 83.39728 67.80028 25.2416

0 15.49848 0 0.00048 0 15.47779 0 ‐0.00021 0 ‐15.407 75.37974 15.407 75.37974 59.76374 ‐15.352 84.1898 15.352 84.1898 68.5928 26.0984

‐0.499 22.13287 0.499 6.63487 ‐0.499 24.14044 0.499 8.66244 0.8483 ‐15.904 76.35836 15.904 76.35836 60.74236 ‐15.856 85.06177 15.856 85.06177 69.46477 26.9552

‐0.999 28.75207 0.999 13.25407 ‐0.998 31.92145 0.998 16.44345 1.6966 ‐16.401 77.40611 16.401 77.40611 61.79011 ‐16.343 85.70577 16.343 85.70577 70.10877 27.7831

‐1.497 33.5287 1.497 18.0307 ‐1.496 36.51371 1.496 21.03571 2.5432 ‐16.898 78.2567 16.898 78.2567 62.6407 ‐16.838 86.69284 16.838 86.69284 71.09584 28.6246

‐1.995 36.7791 1.995 21.2811 ‐1.995 40.04649 1.995 24.56849 3.3915 ‐17.394 79.11808 17.394 79.11808 63.50208 ‐17.333 87.64605 17.333 87.64605 72.04905 29.4661

‐2.494 39.5309 2.494 24.0329 ‐2.493 43.25164 2.493 27.77364 4.2381 ‐17.891 79.96457 17.891 79.96457 64.34857 ‐17.828 88.50602 17.828 88.50602 72.90902 30.3076

‐2.992 41.94872 2.992 26.45072 ‐2.991 46.29996 2.991 30.82196 5.0847 ‐18.387 80.80995 18.387 80.80995 65.19395 ‐18.323 89.30877 18.323 89.30877 73.71177 31.1491

‐3.49 44.36461 3.49 28.86661 ‐3.489 49.294 3.489 33.816 5.9313 ‐18.884 81.65462 18.884 81.65462 66.03862 ‐18.819 90.06434 18.819 90.06434 74.46734 31.9923

‐3.989 46.61967 3.989 31.12167 ‐3.987 52.21726 3.987 36.73926 6.7779 ‐19.381 82.43725 19.381 82.43725 66.82125 ‐19.315 90.83148 19.315 90.83148 75.23448 32.8355

‐4.487 48.91768 4.487 33.41968 ‐4.486 55.1012 4.486 39.6232 7.6262 ‐19.885 82.6982 19.885 82.6982 67.0822 ‐19.81 91.5755 19.81 91.5755 75.9785 33.677

‐4.986 51.14243 4.986 35.64443 ‐4.984 57.98527 4.984 42.50727 8.4728 ‐20.383 83.22342 20.383 83.22342 67.60742 ‐20.305 92.19823 20.305 92.19823 76.60123 34.5185

‐5.484 53.34452 5.484 37.84652 ‐5.481 60.84474 5.481 45.36674 9.3177 ‐20.88 84.04531 20.88 84.04531 68.42931 ‐20.801 92.85798 20.801 92.85798 77.26098 35.3617

‐5.982 55.54479 5.982 40.04679 ‐5.979 63.67394 5.979 48.19594 10.1643 ‐21.377 84.83802 21.377 84.83802 69.22202 ‐21.296 93.44419 21.296 93.44419 77.84719 36.2032

‐6.48 57.71993 6.48 42.22193 ‐6.477 66.49121 6.477 51.01321 11.0109 ‐21.873 85.5383 21.873 85.5383 69.9223 ‐21.791 93.96476 21.791 93.96476 78.36776 37.0447

‐6.979 59.9086 6.979 44.4106 ‐6.975 69.27452 6.975 53.79652 11.8575 ‐22.369 86.2352 22.369 86.2352 70.6192 ‐22.286 94.48785 22.286 94.48785 78.89085 37.8862

‐7.477 62.0668 7.477 46.5688 ‐7.472 71.98963 7.472 56.51163 12.7024 ‐22.864 86.89317 22.864 86.89317 71.27717 ‐22.781 95.0275 22.781 95.0275 79.4305 38.7277

‐7.975 64.22147 7.975 48.72347 ‐7.968 74.68062 7.968 59.20262 13.5456 ‐23.36 87.54709 23.36 87.54709 71.93109 ‐23.277 95.24992 23.277 95.24992 79.65292 39.5709

‐8.473 66.36292 8.473 50.86492 ‐8.465 77.35587 8.465 61.87787 14.3905 ‐23.856 88.09715 23.856 88.09715 72.48115 ‐23.77 95.56373 23.77 95.56373 79.96673 40.409

‐8.971 68.4724 8.971 52.9744 ‐8.962 79.92995 8.962 64.45195 15.2354 ‐24.353 88.64254 24.353 88.64254 73.02654 ‐24.269 95.73162 24.269 95.73162 80.13462 41.2573

‐9.468 70.56644 9.468 55.06844 ‐9.457 82.42199 9.457 66.94399 16.0769 ‐24.849 89.16691 24.849 89.16691 73.55091 ‐24.766 96.10719 24.766 96.10719 80.51019 42.1022

‐9.966 72.61147 9.966 57.11347 ‐9.952 84.83689 9.952 69.35889 16.9184 ‐25.345 89.76467 25.345 89.76467 74.14867 ‐25.262 96.61883 25.262 96.61883 81.02183 42.9454

‐10.463 74.65991 10.463 59.16191 ‐10.445 87.18195 10.445 71.70395 17.7565 ‐25.841 90.26118 25.841 90.26118 74.64518 ‐25.758 97.10243 25.758 97.10243 81.50543 43.7886

‐10.96 76.68865 10.96 61.19065 ‐10.937 89.38706 10.937 73.90906 18.5929 ‐26.337 90.73612 26.337 90.73612 75.12012 ‐26.254 97.54716 26.254 97.54716 81.95016 44.6318

‐11.457 78.67369 11.457 63.17569 ‐11.427 91.37346 11.427 75.89546 19.4259 ‐26.833 91.19128 26.833 91.19128 75.57528 ‐26.748 97.95924 26.748 97.95924 82.36224 45.4716

‐11.954 80.58399 11.954 65.08599 ‐11.914 93.16514 11.914 77.68714 20.2538 ‐27.329 91.54445 27.329 91.54445 75.92845 ‐27.245 98.38892 27.245 98.38892 82.79192 46.3165

‐12.45 82.45999 12.45 66.96199 ‐12.388 94.77101 12.388 79.29301 21.0596 ‐27.824 91.96523 27.824 91.96523 76.34923 ‐27.74 98.80248 27.74 98.80248 83.20548 47.158

‐12.945 84.2594 12.945 68.7614 ‐12.864 96.63913 12.864 81.16113 21.8688 ‐28.319 92.32896 28.319 92.32896 76.71296 ‐28.235 99.21141 28.235 99.21141 83.61441 47.9995

‐13.439 86.03337 13.439 70.53537 ‐13.343 98.57572 13.343 83.09772 22.6831 ‐28.815 92.66666 28.815 92.66666 77.05066 ‐28.731 99.26773 28.731 99.26773 83.67073 48.8427

‐13.932 87.69211 13.932 72.19411 ‐13.827 100.6302 13.827 85.1522 23.5059 ‐29.311 93.07555 29.311 93.07555 77.45955 ‐29.226 99.55122 29.226 99.55122 83.95422 49.6842

‐14.426 89.34701 14.426 73.84901 ‐14.317 102.6759 14.317 87.19788 24.3389 ‐29.806 93.21559 29.806 93.21559 77.59959 ‐29.726 99.67683 29.726 99.67683 84.07983 50.5342

‐14.915 90.70584 14.915 75.20784 ‐14.811 104.6719 14.811 89.19391 25.1787 ‐30.3 93.36516 30.3 93.36516 77.74916 ‐30.223 100.0105 30.223 100.0105 84.41351 51.3791

‐15.405 92.18587 15.405 76.68787 ‐15.305 106.6462 15.305 91.16819 26.0185 ‐30.796 93.7135 30.796 93.7135 78.0975 ‐30.718 100.3851 30.718 100.3851 84.78807 52.2206

‐15.89 93.3578 15.89 77.8598 ‐15.799 108.556 15.799 93.07795 26.8583 ‐31.293 94.04916 31.293 94.04916 78.43316 ‐31.213 100.6891 31.213 100.6891 85.0921 53.0621

‐16.384 94.88244 16.384 79.38444 ‐16.293 110.4592 16.293 94.98123 27.6981 ‐31.791 94.2198 31.791 94.2198 78.6038 ‐31.71 101.0417 31.71 101.0417 85.44474 53.907

‐16.879 96.43159 16.879 80.93359 ‐16.787 112.3263 16.787 96.84832 28.5379 ‐32.288 94.48183 32.288 94.48183 78.86583 ‐32.207 101.3851 32.207 101.3851 85.78813 54.7519

‐17.375 98.04628 17.375 82.54828 ‐17.281 114.1509 17.281 98.67286 29.3777 ‐32.785 94.892 32.785 94.892 79.276 ‐32.704 101.7296 32.704 101.7296 86.13257 55.5968

‐17.871 99.6307 17.871 84.1327 ‐17.775 115.8946 17.775 100.41655 30.2175 ‐33.281 95.19745 33.281 95.19745 79.58145 ‐33.2 102.01 33.2 102.01 86.41303 56.44

‐18.368 101.2004 18.368 85.70236 ‐18.269 117.6519 18.269 102.17386 31.0573 ‐33.776 95.51102 33.776 95.51102 79.89502 ‐33.696 102.2948 33.696 102.2948 86.69784 57.2832 0.0700 , 2.113 30.18571

‐18.864 102.7172 18.864 87.21919 ‐18.763 119.3239 18.763 103.84587 31.8971 ‐34.272 95.82354 34.272 95.82354 80.20754 ‐34.202 102.4705 34.202 102.4705 86.87348 58.1434 0.1700 , 5.2469 30.86412

‐19.36 104.2239 19.36 88.72585 ‐19.257 120.912 19.257 105.434 32.7369 ‐34.768 96.15229 34.768 96.15229 80.53629 ‐34.707 102.7166 34.707 102.7166 87.11955 59.0019 0.2700 , 7.9537 29.45815

‐19.856 105.7033 19.856 90.20527 ‐19.753 122.367 19.753 106.88896 33.5801 ‐35.264 96.50584 35.264 96.50584 80.88984 ‐35.204 103.0153 35.204 103.0153 87.41833 59.8468 0.3650 , 10.6129 29.07644

‐20.352 107.159 20.352 91.66095 ‐20.302 60.19189 20.302 44.71389 34.5134 ‐35.761 96.79548 35.761 96.79548 81.17948 ‐35.7 103.2541 35.7 103.2541 87.65706 60.69 0.4502 , 12.8923 28.63683

‐20.848 108.6245 20.848 93.12648 ‐20.8 60.71018 20.8 45.23218 35.36 ‐36.256 96.9683 36.256 96.9683 81.3523 ‐36.196 103.4811 36.196 103.4811 87.88405 61.5332 0.5490 , 15.1717 27.63515

‐21.344 110.049 21.344 94.55095 ‐21.298 61.21377 21.298 45.73577 36.2066 ‐36.752 97.18995 36.752 97.18995 81.57395 ‐36.693 103.5767 36.693 103.5767 87.97972 62.3781 0.6478 , 17.3087 26.7192

‐21.84 111.4184 21.84 95.92041 ‐21.795 61.73482 21.795 46.25682 37.0515 ‐37.247 97.33687 37.247 97.33687 81.72087 ‐37.187 103.7108 37.187 103.7108 88.11382 63.2179 0.7506 , 19.1608 25.52731

‐22.336 112.8183 22.336 97.32034 ‐22.291 62.31932 22.291 46.84132 37.8947 ‐37.745 97.53095 37.745 97.53095 81.91495 ‐37.677 103.7842 37.677 103.7842 88.18722 64.0509 0.8494 , 20.823 24.51495

‐22.832 114.1437 22.832 98.64571 ‐22.787 62.89132 22.787 47.41332 38.7379 ‐38.243 97.69222 38.243 97.69222 82.07622 ‐38.174 103.9464 38.174 103.9464 88.34938 64.8958 0.9483 , 22.2953 23.51081

‐23.328 115.4129 23.328 99.91489 ‐23.282 63.42896 23.282 47.95096 39.5794 ‐38.741 97.88625 38.741 97.88625 82.27025 ‐38.671 104.2257 38.671 104.2257 88.62873 65.7407 1.0511 , 23.7201 22.56693

‐23.825 116.6431 23.825 101.1451 ‐23.777 63.96544 23.777 48.48744 40.4209 ‐39.237 98.10744 39.237 98.10744 82.49144 ‐39.168 104.4845 39.168 104.4845 88.88745 66.5856 1.1500 , 24.8126 21.57617

‐24.325 117.8579 24.325 102.3599 ‐24.272 64.51457 24.272 49.03657 41.2624 ‐39.733 98.40814 39.733 98.40814 82.79214 ‐39.665 104.6856 39.665 104.6856 89.0886 67.4305 1.2489 , 25.8101 20.66627

‐24.823 119.1196 24.823 103.6216 ‐24.768 65.05881 24.768 49.58081 42.1056 ‐40.228 98.58274 40.228 98.58274 82.96674 ‐40.16 104.9197 40.16 104.9197 89.32274 68.272 1.3477 , 26.7601 19.85613

‐25.32 120.3726 25.32 104.8746 ‐25.263 65.59637 25.263 50.11837 42.9471 ‐40.742 98.72816 40.742 98.72816 83.11216 ‐40.656 105.1271 40.656 105.1271 89.53012 69.1152 1.4506 , 27.6152 19.03709

‐25.816 121.6229 25.816 106.1249 ‐25.757 66.11995 25.757 50.64195 43.7869 ‐41.24 99.09559 41.24 99.09559 83.47959 ‐41.153 105.2433 41.153 105.2433 89.64627 69.9601 1.5497 , 28.2804 18.24895

‐26.311 122.8481 26.311 107.3501 ‐26.251 66.59896 26.251 51.12096 44.6267 ‐41.737 99.34652 41.737 99.34652 83.73052 ‐41.65 105.362 41.65 105.362 89.76498 70.805 1.6486 , 28.7556 17.44244

‐26.807 124.1826 26.807 108.6846 ‐26.746 67.1168 26.746 51.6388 45.4682 ‐42.234 99.56602 42.234 99.56602 83.95002 ‐42.147 105.5502 42.147 105.5502 89.95318 71.6499 1.7476 , 29.1359 16.67195

‐27.303 125.3735 27.303 109.8755 ‐27.241 67.63163 27.241 52.15363 46.3097 ‐42.732 99.70697 42.732 99.70697 84.09097 ‐42.643 105.6411 42.643 105.6411 90.04411 72.4931 1.8506 , 29.4212 15.8982

‐27.798 126.5166 27.798 111.0186 ‐27.736 68.12535 27.736 52.64735 47.1512 ‐43.228 99.88118 43.228 99.88118 84.26518 ‐43.141 105.8142 43.141 105.8142 90.21722 73.3397 1.9495 , 29.5642 15.16502

‐28.293 127.5549 28.293 112.0569 ‐28.23 68.59891 28.23 53.12091 47.991 ‐43.716 100.0125 43.716 100.0125 84.39649 ‐43.64 105.9582 43.64 105.9582 90.36119 74.188 2.0486 , 29.5646 14.43161

‐28.789 128.7267 28.789 113.2287 ‐28.725 69.0772 28.725 53.5992 48.8325 ‐44.212 100.263 44.212 100.263 84.64699 ‐44.136 106.0991 44.136 106.0991 90.50205 75.0312 2.1476 , 29.4701 13.72234

‐29.284 129.8079 29.284 114.3099 ‐29.22 69.57445 29.22 54.09645 49.674 ‐44.708 100.591 44.708 100.591 84.97504 ‐44.633 106.242 44.633 106.242 90.64502 75.8761 2.2506 , 29.1858 12.96801

‐29.779 130.8473 29.779 115.3493 ‐29.715 70.04581 29.715 54.56781 50.5155 ‐45.204 100.6814 45.204 100.6814 85.06544 ‐45.132 106.3739 45.132 106.3739 90.77686 76.7244 2.3496 , 28.8064 12.26013

‐30.275 131.8953 30.275 116.3973 ‐30.208 70.49542 30.208 55.01742 51.3536 ‐45.7 100.9341 45.7 100.9341 85.31805 ‐45.63 106.4931 45.63 106.4931 90.89606 77.571 2.4487 , 28.2371 11.53147

‐30.77 132.9071 30.77 117.4091 ‐30.702 70.93379 30.702 55.45579 52.1934 ‐46.198 100.9827 46.198 100.9827 85.36673 ‐46.127 106.564 46.127 106.564 90.96695 78.4159 2.5478 , 27.6204 10.84088

‐31.265 133.9138 31.265 118.4158 ‐31.197 71.39816 31.197 55.92016 53.0349 ‐46.694 101.0799 46.694 101.0799 85.46391 ‐46.625 106.6717 46.625 106.6717 91.07468 79.2625 2.6508 , 26.7663 10.09744

‐31.76 134.8933 31.76 119.3953 ‐31.692 71.8573 31.692 56.3793 53.8764 ‐47.19 101.1906 47.19 101.1906 85.57463 ‐47.122 106.6794 47.122 106.6794 91.08243 80.1074 2.7499 , 25.8647 9.405687

‐32.255 135.8624 32.255 120.3644 ‐32.186 72.31404 32.186 56.83604 54.7162 ‐47.687 101.3118 47.687 101.3118 85.69583 ‐47.619 106.744 47.619 106.744 91.14701 80.9523 2.8490 , 24.9156 8.745384

‐32.75 136.8211 32.75 121.3231 ‐32.681 72.76448 32.681 57.28648 55.5577 ‐48.184 101.4891 48.184 101.4891 85.87313 ‐48.117 106.839 48.117 106.839 91.24197 81.7989 2.9481 , 23.8241 8.081171

‐33.245 137.7686 33.245 122.2706 ‐33.176 73.21409 33.176 57.73609 56.3992 ‐48.682 101.6444 48.682 101.6444 86.02838 ‐48.614 106.8022 48.614 106.8022 91.20523 82.6438 3.0512 , 22.5901 7.403677

‐33.74 138.6855 33.74 123.1875 ‐34 20.52015 34 5.04215 57.8 ‐49.179 101.8124 49.179 101.8124 86.19642 ‐49.112 106.7262 49.112 106.7262 91.12924 83.4904 3.1504 , 21.2612 6.74873

‐34.236 139.6652 34.236 124.1672 ‐49.676 102.0155 49.676 102.0155 86.39948 ‐49.609 106.8471 49.609 106.8471 91.25006 84.3353 3.2495 , 19.9798 6.148577

‐34.73 140.4785 34.73 124.9805 ‐50.173 102.2165 50.173 102.2165 86.60052 ‐50.107 106.7618 50.107 106.7618 91.16476 85.1819 3.3486 , 18.6509 5.56976

‐35.225 141.2878 35.225 125.7898 ‐50.67 102.5651 50.67 102.5651 86.94913 ‐50.607 106.6606 50.607 106.6606 91.06359 86.0319 3.4478 , 17.4644 5.065375

‐35.72 142.0739 35.72 126.5759 ‐51.166 102.6389 51.166 102.6389 87.0229 ‐51.105 106.715 51.105 106.715 91.11796 86.8785 3.5509 , 16.2305 4.570813

‐36.215 142.8362 36.215 127.3382 ‐51.661 102.6961 ‐51.604 106.6967 51.604 106.6967 91.0997 87.7268 3.6500 , 15.139 4.147671

‐36.711 143.6579 36.711 128.1599 ‐52.157 102.8442 ‐52.103 106.5457 52.103 106.5457 90.94867 88.5751 3.6936 , 14.5695 3.944526

‐37.207 144.4305 37.207 128.9325 ‐52.653 103.1567 ‐52.601 106.5449 52.601 106.5449 90.94793 89.4217

‐37.702 145.2279 37.702 129.7299 ‐53.151 103.0607 ‐53.099 106.5727 53.099 106.5727 90.97573 90.2683

‐38.198 146.1293 38.198 130.6313 ‐53.648 103.1819 ‐53.596 106.5497 53.596 106.5497 90.9527 91.1132

‐38.693 146.987 38.693 131.489 ‐54.145 103.4931 ‐54.093 106.554 54.093 106.554 90.95703 91.9581

‐39.189 147.811 39.189 132.313 ‐54.642 103.4549 ‐54.592 106.5378 54.592 106.5378 90.94077 92.8064

‐39.684 148.6143 39.684 133.1163 ‐55.14 103.5863 ‐55.091 106.5456 55.091 106.5456 90.9486 93.6547

‐40.179 149.4178 40.179 133.9198 ‐55.638 103.6741 ‐55.591 106.432 55.591 106.432 90.83496 94.5047

‐40.674 150.2126 40.674 134.7146 ‐56.136 103.7486 ‐56.087 106.4661 56.087 106.4661 90.86908 95.3479

‐41.169 150.9815 41.169 135.4835 ‐56.633 103.857

‐41.664 151.6364 41.664 136.1384 ‐57.13 104.1719

‐42.159 152.3888 42.159 136.8908 ‐57.628 104.1297

‐42.653 153.0502 42.653 137.5522 ‐58.126 104.1795

‐43.181 73.5558 43.181 58.0578 ‐58.624 104.4297

‐43.676 73.94002 43.676 58.44202 ‐59.122 104.4608

‐44.171 74.31916 44.171 58.82116 ‐59.62 104.4401

‐44.666 74.67203 44.666 59.17403 ‐60.117 104.6302

‐45.161 75.03763 45.161 59.53963 ‐60.614 104.5854

‐45.657 75.42063 45.657 59.92263 ‐61.111 104.8266

‐46.153 75.78492 46.153 60.28692 ‐61.609 104.6673

‐46.647 76.1228 46.647 60.6248 ‐62.107 104.706

‐47.142 76.45691 47.142 60.95891 ‐62.604 104.784

‐47.637 76.7983 47.637 61.3003 ‐63.1 104.8428

‐48.133 77.14578 48.133 61.64778 ‐63.597 104.7945

‐48.628 77.49873 48.628 62.00073 ‐64.095 104.8551

‐49.123 77.85152 49.123 62.35352 ‐64.594 104.8414

‐49.619 78.19616 49.619 62.69816 ‐65.093 104.8767

‐50.114 78.51965 50.114 63.02165 ‐65.592 104.9227

‐50.609 78.79167 50.609 63.29367 ‐66.091 104.901

‐51.105 79.05779 51.105 63.55979 ‐66.59 104.8493

‐51.601 79.32696 51.601 63.82896 ‐67.088 104.8668

‐52.097 79.60295 52.097 64.10495 ‐67.587 104.8767

‐52.592 79.9214 52.592 64.4234 ‐68.085 104.8807

‐53.087 80.22719 53.087 64.72919 ‐68.581 104.8747

‐53.582 80.53143 53.582 65.03343 ‐69.078 104.8582

‐54.077 80.84759 54.077 65.34959 ‐69.576 104.8789

‐54.573 81.15853 54.573 65.66053 ‐70.075 104.8469

‐55.068 81.46652 55.068 65.96852 ‐70.574 104.7763

TV1 relative displacement of slab ends Data from Graph Data from Graph Data from Graph

Load (kN) Disp1 Disp2 Avg 2*avg ============== ============== ==============

0 0 0 0 0 0

15.597 0 0 0 0 0 Title: X‐Displacement Title: X‐Displacement Title : X‐Displacement

17.306 0 0 0 0 1.709

19.012 ‐0.001 0 0.0005 0.001 3.415 X Axis Title: mm X Axis Title: mm X Axis Titl : mm

20.717 ‐0.001 0 0.0005 0.001 5.12 Y Axis Title: Y Axis Title: Y Axis Title:

22.423 ‐0.002 0 0.001 0.002 6.826

24.129 ‐0.002 0 0.001 0.002 8.532 mm mm mm

25.834 ‐0.002 0.001 0.0015 0.003 10.237 Line type : 0 Line type : 0 Line type : 0

27.54 ‐0.003 0.001 0.002 0.004 11.943 0 15.597 0 15.597 0.001 ‐0.001 15.528

29.217 ‐0.003 0.001 0.002 0.004 13.62 0 17.306 0 17.306 0 0 21.031

30.669 ‐0.003 0.001 0.002 0.004 15.072 ‐0.001 19.012 0 19.012 ‐0.001 0.001 26.532

31.932 ‐0.003 0 0.0015 0.003 16.335 ‐0.001 20.717 0 20.717 0 0 31.405

33.052 ‐0.002 ‐0.001 0.0015 0.003 17.455 ‐0.002 22.423 0 22.423 0.004 ‐0.004 34.798

34.049 ‐0.001 ‐0.002 0.0015 0.003 18.452 ‐0.002 24.129 0 24.129 0.01 ‐0.01 37.447

34.969 0 ‐0.004 0.002 0.004 19.372 ‐0.002 25.834 0.001 25.834 0.019 ‐0.019 39.719

35.788 0.001 ‐0.005 0.003 0.006 20.191 ‐0.003 27.54 0.001 27.54 0.028 ‐0.028 41.675

36.574 0.002 ‐0.007 0.0045 0.009 20.977 ‐0.003 29.217 0.001 29.217 0.038 ‐0.038 43.381

37.29 0.004 ‐0.009 0.0065 0.013 21.693 ‐0.003 30.669 0.001 30.669 0.048 ‐0.048 45.064

37.974 0.006 ‐0.011 0.0085 0.017 22.377 ‐0.003 31.932 0 31.932 0.06 ‐0.06 46.737

38.656 0.008 ‐0.014 0.011 0.022 23.059 ‐0.002 33.052 ‐0.001 33.052 0.072 ‐0.072 48.244

39.249 0.01 ‐0.016 0.013 0.026 23.652 ‐0.001 34.049 ‐0.002 34.049 0.084 ‐0.084 49.85

39.876 0.012 ‐0.019 0.0155 0.031 24.279 0 34.969 ‐0.004 34.969 0.097 ‐0.097 51.303

40.455 0.015 ‐0.022 0.0185 0.037 24.858 0.001 35.788 ‐0.005 35.788 0.11 ‐0.11 52.808

41.009 0.017 ‐0.024 0.0205 0.041 25.412 0.002 36.574 ‐0.007 36.574 0.123 ‐0.123 54.223

41.571 0.02 ‐0.027 0.0235 0.047 25.974 0.004 37.29 ‐0.009 37.29 0.138 ‐0.138 55.692

42.106 0.022 ‐0.03 0.026 0.052 26.509 0.006 37.974 ‐0.011 37.974 0.152 ‐0.152 57.16

42.625 0.025 ‐0.033 0.029 0.058 27.028 0.008 38.656 ‐0.014 38.656 0.165 ‐0.165 58.474

43.189 0.028 ‐0.036 0.032 0.064 27.592 0.01 39.249 ‐0.016 39.249 0.18 ‐0.18 59.901

43.674 0.03 ‐0.039 0.0345 0.069 28.077 0.012 39.876 ‐0.019 39.876 0.195 ‐0.195 61.272

44.166 0.033 ‐0.043 0.038 0.076 28.569 0.015 40.455 ‐0.022 40.455 0.209 ‐0.209 62.511

44.686 0.036 ‐0.046 0.041 0.082 29.089 0.017 41.009 ‐0.024 41.009 0.225 ‐0.225 63.839

45.166 0.039 ‐0.049 0.044 0.088 29.569 0.02 41.571 ‐0.027 41.571 0.241 ‐0.241 65.183

45.653 0.042 ‐0.053 0.0475 0.095 30.056 0.022 42.106 ‐0.03 42.106 0.255 ‐0.255 66.447

46.114 0.045 ‐0.056 0.0505 0.101 30.517 0.025 42.625 ‐0.033 42.625 0.271 ‐0.271 67.756

46.589 0.048 ‐0.059 0.0535 0.107 30.992 0.028 43.189 ‐0.036 43.189 0.286 ‐0.286 68.947

47.077 0.051 ‐0.063 0.057 0.114 31.48 0.03 43.674 ‐0.039 43.674 0.302 ‐0.302 70.189

47.52 0.055 ‐0.066 0.0605 0.121 31.923 0.033 44.166 ‐0.043 44.166 0.318 ‐0.318 70.384

48.008 0.058 ‐0.07 0.064 0.128 32.411 0.036 44.686 ‐0.046 44.686 0.334 ‐0.334 71.04

48.447 0.061 ‐0.074 0.0675 0.135 32.85 0.039 45.166 ‐0.049 45.166 0.341 ‐0.341 71.555

48.909 0.065 ‐0.077 0.071 0.142 33.312 0.042 45.653 ‐0.053 45.653 0.354 ‐0.354 72.111

49.337 0.068 ‐0.081 0.0745 0.149 33.74 0.045 46.114 ‐0.056 46.114 0.377 ‐0.377 72.695

49.813 0.071 ‐0.085 0.078 0.156 34.216 0.048 46.589 ‐0.059 46.589 0.395 ‐0.395 73.352

50.238 0.075 ‐0.089 0.082 0.164 34.641 0.051 47.077 ‐0.063 47.077 0.413 ‐0.413 73.975

50.674 0.078 ‐0.092 0.085 0.17 35.077 0.055 47.52 ‐0.066 47.52 0.43 ‐0.43 74.593

51.117 0.082 ‐0.096 0.089 0.178 35.52 0.058 48.008 ‐0.07 48.008 0.446 ‐0.446 75.172

51.561 0.085 ‐0.1 0.0925 0.185 35.964 0.061 48.447 ‐0.074 48.447 0.477 ‐0.477 75.776

51.999 0.088 ‐0.104 0.096 0.192 36.402 0.065 48.909 ‐0.077 48.909 0.494 ‐0.494 76.028

52.43 0.092 ‐0.108 0.1 0.2 36.833 0.068 49.337 ‐0.081 49.337 0.512 ‐0.512 76.648

52.877 0.096 ‐0.112 0.104 0.208 37.28 exp 0.071 49.813 ‐0.085 49.813 0.531 ‐0.531 77.266

53.278 0.099 ‐0.116 0.1075 0.215 37.681 7.77E‐03 2.88 0.075 50.238 ‐0.089 50.238 0.549 ‐0.549 77.88

53.697 0.103 ‐0.12 0.1115 0.223 38.1 0.06 13.92 0.078 50.674 ‐0.092 50.674 0.566 ‐0.566 78.506

54.121 0.107 ‐0.124 0.1155 0.231 38.524 0.1098 19.8399 0.082 51.117 ‐0.096 51.117 0.585 ‐0.585 79.113

54.545 0.11 ‐0.128 0.119 0.238 38.948 0.1599 22.24 0.085 51.561 ‐0.1 51.561 0.603 ‐0.603 79.736

54.975 0.114 ‐0.131 0.1225 0.245 39.378 0.2099 24 0.088 51.999 ‐0.104 51.999 0.622 ‐0.622 80.319

55.398 0.118 ‐0.135 0.1265 0.253 39.801 0.2601 23.68 0.092 52.43 ‐0.108 52.43 0.64 ‐0.64 80.908

55.823 0.121 ‐0.14 0.1305 0.261 40.226 0.3103 23.52 0.096 52.877 ‐0.112 52.877 0.659 ‐0.659 81.514

56.231 0.125 ‐0.144 0.1345 0.269 40.634 0.3578 23.52 0.099 53.278 ‐0.116 53.278 0.678 ‐0.678 82.134

56.659 0.129 ‐0.148 0.1385 0.277 41.062 0.4079 24.96 0.103 53.697 ‐0.12 53.697 0.696 ‐0.696 82.741

57.075 0.133 ‐0.152 0.1425 0.285 41.478 0.4578 28.8 0.107 54.121 ‐0.124 54.121 0.715 ‐0.715 83.345

57.491 0.136 ‐0.156 0.146 0.292 41.894 0.5103 34.4 0.11 54.545 ‐0.128 54.545 0.734 ‐0.734 83.946

57.893 0.14 ‐0.16 0.15 0.3 42.296 0.5577 35.68 0.114 54.975 ‐0.131 54.975 0.753 ‐0.753 84.544

58.29 0.144 ‐0.165 0.1545 0.309 42.693 0.6078 37.28 0.118 55.398 ‐0.135 55.398 0.772 ‐0.772 85.137

58.682 0.148 ‐0.169 0.1585 0.317 43.085 0.6578 40.48 0.121 55.823 ‐0.14 55.823 0.792 ‐0.792 85.693

59.087 0.152 ‐0.173 0.1625 0.325 43.49 0.7079 42.08 0.125 56.231 ‐0.144 56.231 0.811 ‐0.811 86.272

59.496 0.156 ‐0.177 0.1665 0.333 43.899 0.7578 46.88 0.129 56.659 ‐0.148 56.659 0.829 ‐0.829 86.811

59.9 0.16 ‐0.181 0.1705 0.341 44.303 0.8103 52.48 0.133 57.075 ‐0.152 57.075 0.849 ‐0.849 87.382

60.289 0.164 ‐0.186 0.175 0.35 44.692 0.8601 57.44 0.136 57.491 ‐0.156 57.491 0.869 ‐0.869 87.95

60.696 0.167 ‐0.19 0.1785 0.357 45.099 0.9102 59.04 0.14 57.893 ‐0.16 57.893 0.888 ‐0.888 88.529

61.081 0.171 ‐0.194 0.1825 0.365 45.484 0.9604 60.64 0.144 58.29 ‐0.165 58.29 0.908 ‐0.908 89.096

61.47 0.175 ‐0.198 0.1865 0.373 45.873 0.9814 63.04 0.148 58.682 ‐0.169 58.682 0.927 ‐0.927 89.657

61.87 0.179 ‐0.203 0.191 0.382 46.273 0.152 59.087 ‐0.173 59.087 0.947 ‐0.947 90.206

62.242 0.183 ‐0.207 0.195 0.39 46.645 0.156 59.496 ‐0.177 59.496 0.968 ‐0.968 90.748

62.611 0.187 ‐0.211 0.199 0.398 47.014 0.16 59.9 ‐0.181 59.9 1.111 ‐1.111 90.81

62.977 0.192 ‐0.216 0.204 0.408 47.38 0.164 60.289 ‐0.186 60.289 1.176 ‐1.176 90.834

63.345 0.196 ‐0.22 0.208 0.416 47.748 0.167 60.696 ‐0.19 60.696 1.201 ‐1.201 91.085

63.73 0.2 ‐0.224 0.212 0.424 48.133 0.171 61.081 ‐0.194 61.081 1.229 ‐1.229 91.068

64.126 0.204 ‐0.228 0.216 0.432 48.529 0.175 61.47 ‐0.198 61.47 1.255 ‐1.255 91.127

64.491 0.208 ‐0.233 0.2205 0.441 48.894 0.179 61.87 ‐0.203 61.87 1.282 ‐1.282 91.233

64.882 0.212 ‐0.237 0.2245 0.449 49.285 0.183 62.242 ‐0.207 62.242 1.309 ‐1.309 91.332

65.255 0.216 ‐0.242 0.229 0.458 49.658 0.187 62.611 ‐0.211 62.611 1.337 ‐1.337 91.417

65.625 0.22 ‐0.246 0.233 0.466 50.028 0.192 62.977 ‐0.216 62.977 1.364 ‐1.364 91.576

66.002 0.224 ‐0.251 0.2375 0.475 50.405 0.196 63.345 ‐0.22 63.345 1.391 ‐1.391 91.723

66.37 0.228 ‐0.255 0.2415 0.483 50.773 0.2 63.73 ‐0.224 63.73 1.267 ‐1.267 91.514

66.735 0.232 ‐0.26 0.246 0.492 51.138 0.204 64.126 ‐0.228 64.126 1.228 ‐1.228 91.587

67.103 0.236 ‐0.264 0.25 0.5 51.506 0.208 64.491 ‐0.233 64.491 1.245 ‐1.245 91.729

67.435 0.241 ‐0.268 0.2545 0.509 51.838 0.212 64.882 ‐0.237 64.882 1.266 ‐1.266 91.911

67.782 0.245 ‐0.273 0.259 0.518 52.185 0.216 65.255 ‐0.242 65.255 1.289 ‐1.289 92.065

68.126 0.249 ‐0.277 0.263 0.526 52.529 0.22 65.625 ‐0.246 65.625 1.31 ‐1.31 92.237

68.471 0.253 ‐0.282 0.2675 0.535 52.874 0.224 66.002 ‐0.251 66.002 1.332 ‐1.332 92.451

68.814 0.258 ‐0.286 0.272 0.544 53.217 0.228 66.37 ‐0.255 66.37 1.354 ‐1.354 92.673

69.155 0.262 ‐0.291 0.2765 0.553 53.558 0.232 66.735 ‐0.26 66.735 1.374 ‐1.374 92.886

69.487 0.266 ‐0.295 0.2805 0.561 53.89 0.236 67.103 ‐0.264 67.103 1.396 ‐1.396 93.114

69.826 0.27 ‐0.3 0.285 0.57 54.229 0.241 67.435 ‐0.268 67.435 1.417 ‐1.417 93.339

70.132 0.275 ‐0.304 0.2895 0.579 54.535 0.245 67.782 ‐0.273 67.782 1.439 ‐1.439 93.56

70.455 0.279 ‐0.309 0.294 0.588 54.858 0.249 68.126 ‐0.277 68.126 1.46 ‐1.46 93.778

70.768 0.283 ‐0.313 0.298 0.596 55.171 0.253 68.471 ‐0.282 68.471 1.481 ‐1.481 94

71.077 0.288 ‐0.318 0.303 0.606 55.48 0.258 68.814 ‐0.286 68.814 1.502 ‐1.502 94.217

71.384 0.292 ‐0.323 0.3075 0.615 55.787 0.262 69.155 ‐0.291 69.155 1.524 ‐1.524 94.46

71.655 0.296 ‐0.327 0.3115 0.623 56.058 0.266 69.487 ‐0.295 69.487 1.545 ‐1.545 94.688

71.965 0.3 ‐0.332 0.316 0.632 56.368 0.27 69.826 ‐0.3 69.826 1.566 ‐1.566 94.849

72.243 0.304 ‐0.337 0.3205 0.641 56.646 0.275 70.132 ‐0.304 70.132 1.587 ‐1.587 95.049

72.536 0.309 ‐0.341 0.325 0.65 56.939 0.279 70.455 ‐0.309 70.455 1.608 ‐1.608 95.076

72.782 0.314 ‐0.346 0.33 0.66 57.185 0.283 70.768 ‐0.313 70.768 1.629 ‐1.629 95.104

73.042 0.318 ‐0.35 0.334 0.668 57.445 0.288 71.077 ‐0.318 71.077 1.651 ‐1.651 95.197

73.285 0.323 ‐0.355 0.339 0.678 57.688 0.292 71.384 ‐0.323 71.384 1.672 ‐1.672 95.352

73.549 0.327 ‐0.359 0.343 0.686 57.952 0.296 71.655 ‐0.327 71.655 1.698 ‐1.698 95.271

73.801 0.332 ‐0.364 0.348 0.696 58.204 0.3 71.965 ‐0.332 71.965 1.722 ‐1.722 95.26

74.047 0.336 ‐0.369 0.3525 0.705 58.45 0.304 72.243 ‐0.337 72.243 1.745 ‐1.745 95.369

74.278 0.341 ‐0.373 0.357 0.714 58.681 0.309 72.536 ‐0.341 72.536 1.767 ‐1.767 95.489

74.45 0.346 ‐0.378 0.362 0.724 58.853 0.314 72.782 ‐0.346 72.782 1.789 ‐1.789 95.605

74.41 0.355 ‐0.38 0.3675 0.735 58.813 0.318 73.042 ‐0.35 73.042 1.811 ‐1.811 95.709

74.45 0.372 ‐0.374 0.373 0.746 58.853 0.323 73.285 ‐0.355 73.285 1.834 ‐1.834 95.782

74.587 0.407 ‐0.348 0.3775 0.755 58.99 0.327 73.549 ‐0.359 73.549 1.857 ‐1.857 95.883

74.872 0.415 ‐0.349 0.382 0.764 59.275 0.332 73.801 ‐0.364 73.801 1.88 ‐1.88 95.993

75.147 0.421 ‐0.352 0.3865 0.773 59.55 0.336 74.047 ‐0.369 74.047 1.902 ‐1.902 96.114

75.239 0.415 ‐0.368 0.3915 0.783 59.642 0.341 74.278 ‐0.373 74.278 1.924 ‐1.924 96.24

75.181 0.398 ‐0.397 0.3975 0.795 59.584 0.346 74.45 ‐0.378 74.45 1.946 ‐1.946 96.352

75.256 0.389 ‐0.416 0.4025 0.805 59.659 0.355 74.41 ‐0.38 74.41 1.968 ‐1.968 96.477

75.511 0.392 ‐0.422 0.407 0.814 59.914 0.372 74.45 ‐0.374 74.45 1.99 ‐1.99 96.61

75.776 0.396 ‐0.427 0.4115 0.823 60.179 0.407 74.587 ‐0.348 74.587 2.012 ‐2.012 96.779

76.036 0.401 ‐0.432 0.4165 0.833 60.439 0.415 74.872 ‐0.349 74.872 2.033 ‐2.033 96.891

76.297 0.405 ‐0.436 0.4205 0.841 60.7 0.421 75.147 ‐0.352 75.147 2.055 ‐2.055 96.992

76.554 0.41 ‐0.441 0.4255 0.851 60.957 0.415 75.239 ‐0.368 75.239 2.077 ‐2.077 97.118

76.81 0.414 ‐0.446 0.43 0.86 61.213 0.398 75.181 ‐0.397 75.181 2.099 ‐2.099 97.245

77.075 0.418 ‐0.45 0.434 0.868 61.478 0.389 75.256 ‐0.416 75.256 2.12 ‐2.12 97.362

77.336 0.423 ‐0.455 0.439 0.878 61.739 0.392 75.511 ‐0.422 75.511 2.142 ‐2.142 97.486

77.585 0.427 ‐0.46 0.4435 0.887 61.988 0.396 75.776 ‐0.427 75.776 2.163 ‐2.163 97.596

77.847 0.432 ‐0.465 0.4485 0.897 62.25 0.401 76.036 ‐0.432 76.036 2.185 ‐2.185 97.724

78.107 0.436 ‐0.47 0.453 0.906 62.51 0.405 76.297 ‐0.436 76.297 2.206 ‐2.206 97.817

78.348 0.441 ‐0.474 0.4575 0.915 62.751 0.41 76.554 ‐0.441 76.554 2.227 ‐2.227 97.924

78.599 0.446 ‐0.479 0.4625 0.925 63.002 0.414 76.81 ‐0.446 76.81 2.248 ‐2.248 98.029

78.86 0.451 ‐0.484 0.4675 0.935 63.263 0.418 77.075 ‐0.45 77.075 2.269 ‐2.269 98.137

79.108 0.455 ‐0.489 0.472 0.944 63.511 0.423 77.336 ‐0.455 77.336 2.291 ‐2.291 98.246

79.362 0.46 ‐0.494 0.477 0.954 63.765 0.427 77.585 ‐0.46 77.585 2.312 ‐2.312 98.352

79.613 0.465 ‐0.499 0.482 0.964 64.016 0.432 77.847 ‐0.465 77.847 2.332 ‐2.332 98.409

79.863 0.47 ‐0.503 0.4865 0.973 64.266 0.436 78.107 ‐0.47 78.107 2.353 ‐2.353 98.488

80.094 0.475 ‐0.508 0.4915 0.983 64.497 0.441 78.348 ‐0.474 78.348 2.374 ‐2.374 98.616

80.32 0.48 ‐0.513 0.4965 0.993 64.723 0.446 78.599 ‐0.479 78.599 2.394 ‐2.394 98.644

80.545 0.485 ‐0.518 0.5015 1.003 64.948 0.451 78.86 ‐0.484 78.86 2.415 ‐2.415 98.716

80.77 0.489 ‐0.523 0.506 1.012 65.173 0.455 79.108 ‐0.489 79.108 2.435 ‐2.435 98.786

80.993 0.494 ‐0.528 0.511 1.022 65.396 0.46 79.362 ‐0.494 79.362 2.456 ‐2.456 98.855

81.212 0.499 ‐0.533 0.516 1.032 65.615 0.465 79.613 ‐0.499 79.613 2.476 ‐2.476 98.928

81.438 0.503 ‐0.538 0.5205 1.041 65.841 0.47 79.863 ‐0.503 79.863 2.496 ‐2.496 98.989

81.667 0.508 ‐0.544 0.526 1.052 66.07 0.475 80.094 ‐0.508 80.094 2.516 ‐2.516 99.051

81.89 0.512 ‐0.549 0.5305 1.061 66.293 0.48 80.32 ‐0.513 80.32 2.536 ‐2.536 99.109

82.116 0.517 ‐0.554 0.5355 1.071 66.519 0.485 80.545 ‐0.518 80.545 2.556 ‐2.556 99.171

82.325 0.521 ‐0.56 0.5405 1.081 66.728 0.489 80.77 ‐0.523 80.77 2.577 ‐2.577 99.23

82.545 0.526 ‐0.565 0.5455 1.091 66.948 0.494 80.993 ‐0.528 80.993 2.596 ‐2.596 99.284

82.763 0.531 ‐0.57 0.5505 1.101 67.166 0.499 81.212 ‐0.533 81.212 2.616 ‐2.616 99.34

82.969 0.535 ‐0.575 0.555 1.11 67.372 0.503 81.438 ‐0.538 81.438 2.635 ‐2.635 99.39

83.195 0.54 ‐0.58 0.56 1.12 67.598 0.508 81.667 ‐0.544 81.667 2.654 ‐2.654 99.44

83.401 0.545 ‐0.586 0.5655 1.131 67.804 0.512 81.89 ‐0.549 81.89 2.674 ‐2.674 99.488

83.603 0.549 ‐0.591 0.57 1.14 68.006 0.517 82.116 ‐0.554 82.116 2.693 ‐2.693 99.532

83.805 0.554 ‐0.596 0.575 1.15 68.208 0.521 82.325 ‐0.56 82.325 2.712 ‐2.712 99.58

83.891 0.548 ‐0.613 0.5805 1.161 68.294 0.526 82.545 ‐0.565 82.545 2.731 ‐2.731 99.627

83.829 0.518 ‐0.655 0.5865 1.173 68.232 0.531 82.763 ‐0.57 82.763 2.75 ‐2.75 99.671

84.042 0.519 ‐0.664 0.5915 1.183 68.445 0.535 82.969 ‐0.575 82.969 2.769 ‐2.769 99.716

84.27 0.523 ‐0.669 0.596 1.192 68.673 0.54 83.195 ‐0.58 83.195 2.787 ‐2.787 99.76

84.485 0.528 ‐0.674 0.601 1.202 68.888 0.545 83.401 ‐0.586 83.401 2.807 ‐2.807 99.816

84.685 0.534 ‐0.679 0.6065 1.213 69.088 0.549 83.603 ‐0.591 83.603 2.825 ‐2.825 99.849

84.9 0.539 ‐0.684 0.6115 1.223 69.303 0.554 83.805 ‐0.596 83.805 2.843 ‐2.843 99.895

85.091 0.545 ‐0.687 0.616 1.232 69.494 0.548 83.891 ‐0.613 83.891 2.862 ‐2.862 99.941

85.286 0.551 ‐0.691 0.621 1.242 69.689 0.518 83.829 ‐0.655 83.829 2.881 ‐2.881 99.987

85.342 0.575 ‐0.679 0.627 1.254 69.745 0.519 84.042 ‐0.664 84.042 2.899 ‐2.899 100.038

85.29 0.614 ‐0.651 0.6325 1.265 69.693 0.523 84.27 ‐0.669 84.27 2.918 ‐2.918 100.086

85.497 0.619 ‐0.656 0.6375 1.275 69.9 0.528 84.485 ‐0.674 84.485 2.936 ‐2.936 100.136

85.703 0.624 ‐0.661 0.6425 1.285 70.106 0.534 84.685 ‐0.679 84.685 2.957 ‐2.957 100.245

85.906 0.63 ‐0.666 0.648 1.296 70.309 0.539 84.9 ‐0.684 84.9 2.976 ‐2.976 100.281

86.105 0.634 ‐0.671 0.6525 1.305 70.508 0.545 85.091 ‐0.687 85.091 3.038 ‐3.038 100.222

86.301 0.64 ‐0.676 0.658 1.316 70.704 0.551 85.286 ‐0.691 85.286 3.228 ‐3.228 100.1

86.497 0.645 ‐0.681 0.663 1.326 70.9 0.575 85.342 ‐0.679 85.342 3.254 ‐3.254 100.151

86.691 0.65 ‐0.686 0.668 1.336 71.094 0.614 85.29 ‐0.651 85.29 3.276 ‐3.276 100.207

85.233 3.014 3.475 3.2445 0.619 85.497 ‐0.656 85.497 3.298 ‐3.298 100.266

TV2 Lateral rxn at slab end taken as axial force in slab exp Data from Graph

Load (kN) Axial Force (kN) NOTE: COMPRESSION IS POSITIVE FOR PLOTTING PURPOSES 2.9654 1.6189 ==============

0 0 0 8.2372 19.1781

15.47779 ‐0.00021 3.4 13.1796 26.5255 Title: Control Chart

31.92834 16.45034 4.6 18.1219 33.4994

40.2187 24.7407 3.7 23.0643 36.4882 X Axis Title: x‐axis

46.52364 31.04564 18.9 28.0066 38.1071 Y Axis Title: y‐axis

52.45502 36.97702 36.2 33.2784 39.1034

58.23001 42.75201 54.5 38.2208 39.8506 x‐axisy‐axis

63.9285 48.4505 73.2 43.1631 40.5977 Line type : 0

69.55088 54.07288 92.2 48.1054 41.0959 0 15.47779

75.00407 59.52607 111.2 53.0478 41.7186 ‐0.998 31.92834

80.30741 64.82941 130.2 57.9901 42.3412 ‐1.995 40.2187

85.26329 69.78529 149.1 63.2619 42.8394 ‐2.992 46.52364

89.71073 74.23273 167.9 68.2043 43.462 ‐3.988 52.45502

93.12569 77.64769 188 73.1466 43.9601 ‐4.984 58.23001

96.68891 81.21091 209 78.089 44.3336 ‐5.98 63.9285

100.76564 85.28764 227.4 83.0313 44.9564 ‐6.976 69.55088

104.83326 89.35526 246.2 87.9736 45.4545 ‐7.97 75.00407

108.72379 93.24579 265.3 93.2455 46.0772 ‐8.964 80.30741

112.48195 97.00395 284 98.1878 46.6999 ‐9.955 85.26329

116.04404 100.56604 302.6 103.1301 47.3225 ‐10.941 89.71073

119.44295 103.96495 321.4 108.0725 47.9452 ‐11.908 93.12569

122.47202 106.99402 340.2 113.0148 48.4433 ‐12.857 96.68891

118.2867 49.066 ‐13.822 100.7656

123.229 49.6886 ‐14.81 104.8333

128.1713 50.1868 ‐15.797 108.7238

133.1137 50.6848 ‐16.785 112.482

138.056 51.1831 ‐17.773 116.044

142.9984 51.8056 ‐18.761 119.443

148.2702 52.4284 ‐19.751 122.472

153.2125 53.0511 ‐20.799 60.72755

158.1549 53.7983 ‐21.795 61.73468

163.0972 54.5455

168.0395 55.1681

172.9819 55.9153

178.2537 56.6625

183.196 57.4097

188.1384 58.1569

193.0807 58.9041

198.0231 59.6513

203.2949 60.3985

208.2372 60.8965

213.1796 61.5192

218.1219 61.8929

223.0643 62.5156

228.0066 62.8892

233.2784 63.3873

238.2208 63.8854

243.1631 64.5081

248.1054 65.0062

253.0478 65.5044

257.9901 66.2516

263.2619 68.2441

268.2043 69.4894

273.1466 69.9875

278.089 70.2366

283.0313 70.4857

287.9736 70.7347

293.2455 70.8593

298.1878 71.1083

303.1301 71.3574

308.0725 71.8555

313.0148 73.1009

318.2867 74.4707

323.229 75.5915

328.1713 76.8369

333.1137 77.9577

338.056 79.0785

342.9984 80.3237

348.2702 81.5691

353.2125 82.6899

358.1549 83.8107

363.0972 84.807

368.0395 85.5542

372.9819 86.3014

378.2537 86.924

377.9242 89.0411

372.6524 88.6675

367.71 88.2939

362.7677 88.0448

357.8254 87.2976

352.883 86.4259

347.9407 85.5542

342.6689 84.4334

337.7265 83.5615

336.4086 83.3126

TV1

exp

TV2

exp

TV1

TV2

Lateral reaction at colum

n ba

se TV2

0.11

591.62

480.22

612.61

95load

rxn

load

rxn

Data

from

Graph

Data

from

Graph

0.63

894.44

230.74

94.93

950

0.2

00.1

==============

==============

1.13

447.09

411.24

457.59

1215

.596

825.9

15.477

793.7

01.62

999.49

711.74

9.99

4240

.018

268.5

31.928

345.9

0

Title

:Co

ntrol

Chart

Title

:Co

ntrol

Chart

0.32

642.14

472.12

5211

.568

42.23

5312

.065

650

.066

9510

.840

.218

77.6

24.048

262.34

2912

.119

72.62

0714

.137

22.73

0513

.722

358

.587

8113

.146

.523

649.1

34.096

95X

Axis

Title

:x‐axis

XAxis

Title

:x‐axis

4.33

4819

.450

43.11

6417

.369

43.25

3315

.461

866

.394

3715

.352

.455

0210

.642

.617

81Y

Axis

Title

:y‐axis

YAxis

Title

:y‐axis

6.32

7126

.533

13.63

9319

.772

33.74

8617

.533

273

.095

817

58.230

0112

.150

.424

378.34

6134

.194

14.13

4722

.092

44.24

3919

.438

676

.474

7718

.963

.928

513

.657

.125

8

x‐axisy

‐axis

x‐axisy

‐axis

10.3321

46.9794

4.63

0324

.91

4.73

9120

.929

681

.446

8920

.769

.550

8815

60.504

77Line

type

:0

Line

type

:0

12.351

54.722

95.12

5727

.313

5.23

4422

.752

185

.197

4522

.375

.004

0716

.565

.476

890

15

.596

820

15

.477

7914

.342

162

.797

45.62

1129

.633

15.72

9724

.574

788

.458

3423

.780

.307

4117

.969

.227

45‐1.996

40

.018

26‐0.998

31

.928

3416

.334

669

.714

96.11

6632

.119

6.25

2526

.480

191

.577

3824

.985

.263

2919

.372

.488

34‐3.991

50

.066

95‐1.995

40

.218

718

.328

375

.392

66.63

9534

.604

86.74

7728

.302

793

.957

9825

.789

.710

7320

.575

.607

38‐5.985

58

.587

81‐2.992

46

.523

6420

.351

79.747

77.13

4735

.929

97.24

3130

.291

195

.561

3626

.593

.125

7121

.777

.987

98‐7.976

66

.394

37‐3.988

52

.455

0222

.346

683

.772

67.62

9937

.669

67.73

8432

.196

697

.073

4427

.496

.688

9423

79.591

36‐9.96

73

.095

8‐4.984

58

.230

0124

.342

887

.218

98.12

5239

.326

38.23

3734

.102

98.801

4127

.910

0.76

5624

.381

.103

44‐11.87

9

76.474

77‐5.98

63

.928

526

.341

888

.020

68.62

0541

.397

68.72

8835

.841

799

.695

3128

.710

4.83

3225

.682

.831

41‐13.85

4

81.446

89‐6.976

69

.550

8828

.340

988

.904

99.14

3443

.551

89.25

1838

.078

810

1.00

2129

.410

8.72

3726

.883

.725

31‐15.85

85

.197

45‐7.97

75

.004

0730

.044

884

.090

49.63

8545

.291

39.74

8444

.544

810

2.30

5229

.911

2.48

1928

.185

.032

06‐17.82

8

88.458

34‐8.964

80

.307

4110

.133

947

.196

910

.243

846

.947

810

3.20

3230

.311

6.04

429

.386

.335

17‐19.81

91

.577

38‐9.955

85

.263

2910

.629

349

.351

110

.738

948

.604

510

3.84

8430

.811

9.44

2430

.487

.233

16‐21.79

1

93.957

98‐10.94

1

89.710

7311

.124

651

.339

611

.234

450

.592

910

4.65

5531

.387

.878

35‐23.77

95

.561

36‐11.90

8

93.125

7111

.619

953

.079

211

.729

752

.498

410

5.47

131

.888

.685

45‐25.75

8

97.073

44‐12.85

7

96.688

9412

.142

855

.565

12.252

554

.569

510

6.19

1332

.289

.500

97‐27.74

98

.801

41‐13.82

2

100.76

5612

.638

56.972

912

.747

856

.475

110

6.85

0232

.690

.221

29‐29.72

6

99.695

31‐14.81

10

4.83

3213

.133

359

.044

313

.243

158

.463

510

7.45

2433

90.880

23‐31.71

1

101.00

21‐15.79

7

108.72

3713

.628

660

.949

813

.738

560

.534

910

8.02

5533

.391

.482

35‐33.69

5

102.30

52‐16.78

5

112.48

1913

.903

861

.943

914

.233

862

.689

110

8.54

6233

.792

.055

52‐35.69

8

103.20

32‐17.77

3

116.04

414

.729

64.345

810

9.07

9933

.992

.576

22‐37.68

3

103.84

84‐18.76

1

119.44

2415

.251

966

.251

110

9.41

1134

.393

.109

91‐39.66

4

104.65

55‐19.75

1

122.47

0815

.747

168

.073

810

9.89

8534

.693

.441

14‐41.65

10

5.47

1‐20.79

9

60.726

0716

.242

369

.647

693

.928

47‐43.63

9

106.19

13‐21.79

5

61.734

4816

.737

571

.138

5‐45.62

7

106.85

02‐22.78

7

62.887

17.232

772

.712

3‐47.61

6

107.45

24‐23.77

7

63.962

6717

.727

974

.037

4‐49.60

5

108.02

55‐24.76

8

65.052

1218

.250

575

.445

3‐51.59

6

108.54

62‐25.75

7

66.118

0418

.745

676

.521

5‐53.58

7

109.07

9919

.240

777

.680

8‐55.57

7

109.41

1119

.735

878

.674

2‐57.56

4

109.89

8520

.230

879

.750

5‐59.55

6

110.34

1820

.753

480

.826

7‐57.93

4

20.460

3421

.248

481

.737

2‐59.79

9

20.392

8721

.743

582

.730

5‐61.66

4

20.357

2322

.238

683

.889

8‐63.53

20

.330

7222

.733

684

.800

2‐65.39

6

20.313

3223

.228

685

.793

6‐67.26

2

20.293

1423

.751

186

.786

924

.246

187

.448

524

.741

87.695

725

.235

988

.025

825

.730

788

.107

26.253

88.271

126

.747

888

.352

427

.242

688

.682

427

.737

588

.929

628

.232

389

.176

728

.727

189

.423

829

.249

589

.587

829

.744

188

.922

930

.128

85.604

9

132

Appendix E

P-Delta Simulation Results

1kN across

10kN

dow

n2kN across

10kN

dow

n3kN across

5kN across

10kN

across

Iteratio

n1

Iteratio

n1

Iteratio

n1

Iteratio

n1

Iteratio

n1

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

10

02

00

1.34

031

1340

3.1

10

01

10

02

00

2.68

062

2680

6.2

10

01

10

02

00

4.02

063

4020

6.3

10

01

10

02

00

6.69

935

6699

3.5

10

01

10

02

00

13.397

8113

3978

.11

00

13

0.01

994

0.01

568

40.01

994

‐0.022

351.32

037

1320

3.7

20

01

30.03

988

0.03

469

40.03

988

‐0.041

372.64

074

2640

7.4

20

01

30.05

981

0.05

374

0.05

981

‐0.060

373.96

082

3960

8.2

20

01

30.09

965

0.09

171

40.09

965

‐0.098

356.59

9765

997

20

01

30.19

933

0.18

678

40.19

933

‐0.193

3813

.198

4813

1984

.82

00

15

0.07

591

0.02

936

60.07

591

‐0.042

71.26

4412

644

30

0.13

2037

15

0.15

182

0.06

539

60.15

182

‐0.078

732.52

8825

288

30

0.26

4074

15

0.22

769

0.10

146

0.22

769

‐0.114

743.79

294

3792

9.4

30

0.39

6082

15

0.37

937

0.17

342

60.37

937

‐0.186

76.31

998

6319

9.8

30

0.65

997

15

0.75

880.35

355

60.75

88‐0.366

7512

.639

0112

6390

.13

01.31

9848

17

0.16

390.04

103

80.16

39‐0.061

051.17

641

1176

4.1

40

‐0.132

037

17

0.32

781

0.09

207

80.32

781

‐0.112

092.35

281

2352

8.1

40

‐0.264

071

70.49

164

0.14

318

0.49

164

‐0.163

113.52

899

3528

9.9

40

‐ 0.396

081

70.81

915

0.24

513

80.81

915

‐0.265

065.88

0258

802

40

‐0.659

971

71.63

841

0.50

038

1.63

841

‐0.520

1211

.759

411

7594

40

‐1.319

851

90.27

992

0.05

071

100.27

992

‐0.077

41.06

039

1060

3.9

50

0.12

644

19

0.55

984

0.11

476

100.55

984

‐0.141

452.12

078

2120

7.8

50

0.25

288

19

0.83

966

0.17

8810

0.83

966

‐0.205

473.18

097

3180

9.7

50

0.37

9294

19

1.39

90.30

684

101.39

9‐0.333

425.30

035

5300

3.5

50

0.63

1998

19

2.79

812

0.62

704

102.79

812

‐0.653

4710

.599

6910

5996

.95

01.26

3901

111

0.41

996

0.05

838

120.41

996

‐0.091

740.92

035

9203

.56

0‐0.126

441

110.83

991

0.13

344

120.83

991

‐0.166

81.84

071

1840

7.1

60

‐0.252

881

111.25

973

0.20

849

121.25

973

‐0.241

842.76

0927

609

60

‐0.379

291

112.09

892

0.35

854

122.09

892

‐0.391

794.60

043

4600

4.3

60

‐0.632

111

4.19

791

0.73

376

124.19

791

‐0.766

829.19

9991

999

60

‐1.263

91

130.58

001

0.06

405

140.58

001

‐0.104

080.76

0376

037

00.11

7641

113

1.16

001

0.14

812

141.16

001

‐0.188

151.52

061

1520

6.1

70

0.23

5281

113

1.73

985

0.23

218

141.73

985

‐0.272

192.28

078

2280

7.8

70

0.35

2899

113

2.89

891

0.40

024

142.89

891

‐0.440

163.80

044

3800

4.4

70

0.58

802

113

5.79

776

0.82

047

145.79

776

‐0.860

177.60

005

7600

0.5

70

1.17

594

115

0.75

607

0.06

772

160.75

607

‐0.114

420.58

424

5842

.48

0‐0.117

641

115

1.51

214

0.15

879

161.51

214

‐0.205

51.16

848

1168

4.8

80

‐0.235

281

152.26

801

0.24

986

162.26

801

‐0.296

551.75

262

1752

6.2

80

‐0.352

91

153.77

896

0.43

193

163.77

896

‐0.478

532.92

039

2920

3.9

80

‐0.588

021

157.55

768

0.88

718

167.55

768

‐0.933

535.84

013

5840

1.3

80

‐1.175

941

170.94

415

0.06

939

180.94

415

‐0.122

760.39

616

3961

.69

00.10

6039

117

1.88

829

0.16

547

181.88

829

‐0.218

840.79

233

7923

.39

00.21

2078

117

2.83

220.26

153

182.83

22‐0.314

91.18

843

1188

4.3

90

0.31

8097

117

4.71

906

0.45

362

184.71

906

‐0.506

881.98

029

1980

2.9

90

0.53

0035

117

9.43

768

0.93

388

189.43

768

‐0.986

93.96

013

3960

1.3

90

1.05

9969

119

1.14

023

0.06

906

201.14

023

‐0.129

10.20

008

2000

.810

0‐0.106

039

119

2.28

045

0.16

813

202.28

045

‐0.228

180.40

017

4001

.710

0‐0.212

081

193.42

041

0.26

7220

3.42

041

‐0.327

240.60

022

6002

.210

0‐0.318

11

195.69

920.46

529

205.69

92‐0.525

231.00

015

1000

1.5

100

‐0.530

041

1911

.397

730.96

057

2011

.397

73‐1.020

262.00

008

2000

0.8

100

‐1.059

971

211.34

056

0.06

672

221.34

006

‐0.133

440

011

00.09

2035

121

2.68

112

0.16

6822

2.68

012

‐0.233

520

011

00.18

4071

121

4.02

138

0.26

687

224.01

988

‐0.333

580

011

00.27

609

121

6.70

060.46

696

226.69

809

‐0.533

575E

‐06

0.05

110

0.46

0043

121

13.400

310.96

724

2213

.395

31‐1.033

610

011

00.91

999

123

1.34

031

‐0.033

360

012

0‐0.092

035

123

2.68

062

‐0.033

360

012

0‐0.184

071

234.02

063

‐0.033

350

012

0‐0.276

091

236.69

935

‐0.033

310

012

0‐0.460

041

2313

.397

81‐0.033

180

012

0‐0.919

991

130

0.07

603

113

00.15

2061

113

00.22

8078

113

00.38

0044

113

00.76

0005

114

0‐0.076

031

140

‐0.152

061

140

‐0.228

081

140

‐0.380

041

140

‐0.760

011

150

0.05

8424

115

00.11

6848

115

00.17

5262

115

00.29

2039

115

00.58

4013

116

0‐0.058

424

116

0‐0.116

851

160

‐0.175

261

160

‐0.292

041

160

‐0.584

011

170

0.03

9616

117

00.07

9233

117

00.11

8843

117

00.19

8029

117

00.39

6013

118

0‐0.039

616

118

0‐0.079

231

180

‐0.118

841

180

‐0.198

031

180

‐0.396

011

190

0.02

0008

119

00.04

0017

119

00.06

0022

119

00.10

0015

119

00.20

0008

120

0‐0.020

008

120

0‐0.040

021

200

‐0.060

021

200

‐0.100

021

200

‐0.200

011

210

01

210

01

210

01

210

5E‐07

121

00

122

00

122

00

122

00

122

0‐5E‐07

122

00

1

Iteratio

n2

%0.93

8034

Iteratio

n2

%0.93

8034

Iteratio

n2

%0.93

8065

Iteratio

n2

%0.93

8074

Iteratio

n2

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

10

02

00

1.42

885

1428

8.5

10

01

10

02

00

2.85

7728

577

10

01

10

02

00

4.28

609

4286

0.9

10

01

10

02

00

7.14

1671

416

10

01

10

02

00

14.282

5114

2825

.11

00

13

0.02

148

0.01

722

40.02

148

‐0.023

891.40

737

1407

3.7

20

01

30.04

295

0.03

777

40.04

295

‐0.044

442.81

475

2814

7.5

20

01

30.06

442

0.05

831

40.06

442

‐0.064

984.22

167

4221

6.7

20

01

30.10

734

0.09

944

0.10

734

‐0.106

037.03

426

7034

2.6

20

01

30.21

469

0.20

215

40.21

469

‐0.208

7414

.067

8214

0678

.22

00

15

0.08

180.03

217

60.08

18‐0.045

511.34

705

1347

0.5

30

0.14

0737

15

0.16

359

0.07

101

60.16

359

‐0.084

352.69

411

2694

1.1

30

0.28

1475

15

0.24

533

0.10

983

60.24

533

‐0.123

164.04

076

4040

7.6

30

0.42

2167

15

0.40

878

0.18

747

60.40

878

‐0.200

746.73

282

6732

8.2

30

0.70

3426

15

0.81

761

0.38

164

60.81

761

‐0.394

8313

.464

913

4649

30

1.40

6782

17

0.17

643

0.04

486

80.17

643

‐0.064

881.25

242

1252

4.2

40

‐0.140

737

17

0.35

286

0.09

974

80.35

286

‐0.119

752.50

484

2504

8.4

40

‐0.281

481

70.52

920.15

459

80.52

92‐0.174

593.75

689

3756

8.9

40

‐0.422

171

70.88

174

0.26

428

80.88

174

‐0.284

196.25

986

6259

8.6

40

‐0.703

431

71.76

359

0.53

859

81.76

359

‐0.558

412

.518

9212

5189

.24

0‐1.406

781

90.30

090.05

532

100.30

09‐0.082

011.12

795

1127

9.5

50

0.13

4705

19

0.60

179

0.12

399

100.60

179

‐0.150

682.25

591

2255

9.1

50

0.26

9411

19

0.90

254

0.19

264

100.90

254

‐0.219

313.38

355

3383

5.5

50

0.40

4076

19

1.50

378

0.32

9910

1.50

378

‐0.356

475.63

782

5637

8.2

50

0.67

3282

19

3.00

771

0.67

317

103.00

771

‐0.699

5911

.274

811

2748

50

1.34

649

111

0.45

074

0.06

357

120.45

074

‐0.096

930.97

811

9781

.16

0‐0.134

705

111

0.90

147

0.14

382

120.90

147

‐0.177

181.95

623

1956

2.3

60

‐0.269

411

111.35

201

0.22

405

121.35

201

‐0.257

392.93

408

2934

0.8

60

‐0.404

081

112.25

268

0.38

447

122.25

268

‐0.417

74.88

892

4888

9.2

60

‐0.673

281

114.50

548

0.78

562

124.50

548

‐0.818

669.77

703

9777

0.3

60

‐1.346

491

130.62

156

0.06

963

140.62

156

‐0.109

660.80

729

8072

.97

00.12

5242

113

1.24

311

0.15

927

141.24

311

‐0.199

311.61

459

1614

5.9

70

0.25

0484

113

1.86

442

0.24

8914

1.86

442

‐0.288

912.42

167

2421

6.7

70

0.37

5689

113

3.10

645

0.42

811

143.10

645

‐0.468

014.03

515

4035

1.5

70

0.62

5986

113

6.21

293

0.87

622

146.21

293

‐0.915

898.06

958

8069

5.8

70

1.25

1892

115

0.80

901

0.07

353

160.80

901

‐0.120

240.61

984

6198

.48

0‐0.125

242

115

1.61

802

0.17

042

161.61

802

‐0.217

131.23

968

1239

6.8

80

‐0.250

481

152.42

673

0.26

729

162.42

673

‐0.313

981.85

936

1859

3.6

80

‐0.375

691

154.04

340.46

098

164.04

34‐0.507

563.09

8230

982

80

‐0.625

991

158.08

667

0.94

528

168.08

667

‐0.991

616.19

584

6195

8.4

80

‐1.251

891

171.00

884

0.07

532

181.00

884

‐0.128

70.42

001

4200

.19

00.11

2795

117

2.01

766

0.17

733

182.01

766

‐0.230

710.84

004

8400

.49

00.22

5591

117

3.02

614

0.27

933

183.02

614

‐0.332

681.25

995

1259

9.5

90

0.33

8355

117

5.04

217

0.48

326

185.04

217

‐0.536

512.09

943

2099

4.3

90

0.56

3782

117

10.084

040.99

318

1810

.084

04‐1.046

174.19

847

4198

4.7

90

1.12

748

119

1.21

682

0.07

503

201.21

682

‐0.135

080.21

203

2120

.310

0‐0.112

795

119

2.43

364

0.18

008

202.43

364

‐0.240

130.42

406

4240

.610

0‐0.225

591

193.65

005

0.28

512

203.65

005

‐0.345

150.63

604

6360

.410

0‐0.338

361

196.08

178

0.49

514

206.08

178

‐0.555

061.05

982

1059

8.2

100

‐0.563

781

1912

.163

061.02

026

2012

.163

06‐1.079

932.11

945

2119

4.5

100

‐1.127

481

211.42

910.07

269

221.42

86‐0.139

410

011

00.09

7811

121

2.85

820.17

875

222.85

72‐0.245

470

011

00.19

5623

121

4.28

684

0.28

478

224.28

534

‐0.351

480

011

00.29

3408

121

7.14

285

0.49

681

227.14

035

‐0.563

40

011

00.48

8892

121

14.285

011.02

694

2214

.280

01‐1.093

280

011

00.97

7703

123

1.42

885

‐0.033

360

012

0‐0.097

811

123

2.85

77‐0.033

360

012

0‐0.195

621

234.28

609

‐0.033

350

012

0‐0.293

411

237.14

16‐0.033

30

012

0‐0.488

891

2314

.282

51‐0.033

170

012

0‐0.977

71

130

0.08

0729

113

00.16

1459

113

00.24

2167

113

00.40

3515

113

00.80

6958

114

0‐0.080

729

114

0‐0.161

461

140

‐0.242

171

140

‐0.403

521

140

‐0.806

961

150

0.06

1984

115

00.12

3968

115

00.18

5936

115

00.30

982

115

00.61

9584

116

0‐0.061

984

116

0‐0.123

971

160

‐0.185

941

160

‐0.309

821

160

‐0.619

581

170

0.04

2001

117

00.08

4004

117

00.12

5995

117

00.20

9943

117

00.41

9847

118

0‐0.042

001

118

0‐0.084

118

0‐0.126

118

0‐0.209

941

180

‐0.419

851

190

0.02

1203

119

00.04

2406

119

00.06

3604

119

00.10

5982

119

00.21

1945

120

0‐0.021

203

120

0‐0.042

411

200

‐0.063

61

200

‐0.105

981

200

‐0.211

951

210

01

210

01

210

01

210

01

210

01

220

01

220

01

220

01

220

01

220

01

Iteratio

n3

%0.99

6291

Iteratio

n3

%0.99

6291

Iteratio

n3

%0.99

6121

Iteratio

n3

Iteratio

n3

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

10

02

00

1.43

442

1434

4.2

10

01

10

02

00

2.86

884

2868

8.4

10

01

10

02

00

4.30

278

4302

7.8

10

01

10

02

00

7.16

939

7169

3.9

10

01

10

02

00

14.338

1314

3381

.31

00

13

0.02

158

0.01

731

40.02

158

‐0.023

991.41

284

1412

8.4

20

01

30.04

315

0.03

797

40.04

315

‐0.044

642.82

569

2825

6.9

20

01

30.06

471

0.05

861

40.06

471

‐0.065

274.23

807

4238

0.7

20

01

30.10

783

0.09

989

40.10

783

‐0.106

527.06

156

7061

5.6

20

01

30.21

567

0.20

312

40.21

567

‐0.209

7114

.122

4614

1224

.62

00

15

0.08

217

0.03

235

60.08

217

‐0.045

691.35

225

1352

2.5

30

0.14

1284

15

0.16

434

0.07

136

60.16

434

‐0.084

712.70

4527

045

30

0.28

2569

15

0.24

646

0.11

037

60.24

646

‐0.123

74.05

632

4056

3.2

30

0.42

3807

15

0.41

065

0.18

836

60.41

065

‐0.201

636.75

874

6758

7.4

30

0.70

6156

15

0.82

135

0.38

342

60.82

135

‐0.396

6213

.516

7813

5167

.83

01.41

2246

17

0.17

723

0.04

511

80.17

723

‐0.065

121.25

719

1257

1.9

40

‐0.141

284

17

0.35

445

0.10

022

80.35

445

‐0.120

242.51

439

2514

3.9

40

‐0.282

571

70.53

158

0.15

532

80.53

158

‐0.175

323.77

1237

712

40

‐0.423

811

70.88

571

0.26

549

80.88

571

‐0.285

46.28

368

6283

6.8

40

‐0.706

161

71.77

153

0.54

102

81.77

153

‐0.560

8212

.566

612

5666

40

‐1.412

251

90.30

223

0.05

562

100.30

223

‐0.082

31.13

219

1132

1.9

50

0.13

5225

19

0.60

445

0.12

457

100.60

445

‐0.151

262.26

439

2264

3.9

50

0.27

045

19

0.90

652

0.19

352

100.90

652

‐0.220

183.39

626

3396

2.6

50

0.40

5632

19

1.51

042

0.33

136

101.51

042

‐0.357

935.65

897

5658

9.7

50

0.67

5874

19

3.02

099

0.67

608

103.02

099

‐0.702

511

.317

1411

3171

.45

01.35

1678

111

0.45

269

0.06

3912

0.45

269

‐0.097

260.98

173

9817

.36

0‐0.135

225

111

0.90

537

0.14

447

120.90

537

‐0.177

831.96

347

1963

4.7

60

‐0.270

451

111.35

785

0.22

503

121.35

785

‐0.258

372.94

493

2944

9.3

60

‐0.405

631

112.26

240.38

6112

2.26

24‐0.419

334.90

699

4906

9.9

60

‐0.675

871

114.52

493

0.78

888

124.52

493

‐0.821

929.81

3298

132

60

‐1.351

681

130.62

418

0.06

998

140.62

418

‐0.110

010.81

024

8102

.47

00.12

5719

113

1.24

836

0.15

997

141.24

836

‐0.200

011.62

048

1620

4.8

70

0.25

1439

113

1.87

228

0.24

995

141.87

228

‐0.289

962.43

0524

305

70

0.37

712

113

3.11

954

0.42

986

143.11

954

‐0.469

764.04

985

4049

8.5

70

0.62

8368

113

6.23

913

0.87

971

146.23

913

‐0.919

398.09

980

990

70

1.25

666

115

0.81

235

0.07

3916

0.81

235

‐0.120

60.62

207

6220

.78

0‐0.125

719

115

1.62

470.17

115

161.62

47‐0.217

851.24

414

1244

1.4

80

‐0.251

441

152.43

673

0.26

838

162.43

673

‐0.315

071.86

605

1866

0.5

80

‐0.377

121

154.06

006

0.46

2816

4.06

006

‐0.509

373.10

933

3109

3.3

80

‐0.628

371

158.12

002

0.94

892

168.12

002

‐0.995

256.21

811

6218

1.1

80

‐1.256

661

171.01

291

0.07

569

181.01

291

‐0.129

070.42

151

4215

.19

00.11

3219

117

2.02

581

0.17

808

182.02

581

‐0.231

450.84

303

8430

.39

00.22

6439

117

3.03

835

0.28

044

183.03

835

‐0.333

81.26

443

1264

4.3

90

0.33

9626

117

5.06

251

0.48

512

185.06

251

‐ 0.538

362.10

688

2106

8.8

90

0.56

5897

117

10.124

740.99

689

1810

.124

74‐1.049

884.21

339

4213

3.9

90

1.13

1714

119

1.22

164

0.07

5420

1.22

164

‐0.135

450.21

278

2127

.810

0‐0.113

219

119

2.44

328

0.18

083

202.44

328

‐0.240

880.42

556

4255

.610

0‐0.226

441

193.66

449

0.28

624

203.66

449

‐0.346

270.63

829

6382

.910

0‐0.339

631

196.10

584

0.49

701

206.10

584

‐0.556

921.06

355

1063

5.5

100

‐0.565

91

1912

.211

21.02

420

12.211

2‐1.083

672.12

693

2126

9.3

100

‐1.131

711

211.43

467

0.07

307

221.43

417

‐0.139

790

011

00.09

8173

121

2.86

934

0.17

949

222.86

834

‐0.246

210

011

00.19

6347

121

4.30

353

0.28

5922

4.30

202

‐0.352

65E

‐06

0.05

110

0.29

4493

121

7.17

064

0.49

867

227.16

814

‐0.565

260

011

00.49

0699

121

14.340

631.03

067

2214

.335

63‐1.097

010

011

00.98

132

123

1.43

442

‐0.033

360

012

0‐0.098

173

123

2.86

884

‐0.033

360

012

0‐0.196

351

234.30

278

‐0.033

350

012

0‐0.294

491

237.16

939

‐0.033

290

012

0‐0.490

71

2314

.338

13‐0.033

170

012

0‐0.981

321

130

0.08

1024

113

00.16

2048

113

00.24

305

113

00.40

4985

113

00.80

991

140

‐0.081

024

114

0‐0.162

051

140

‐0.243

051

140

‐0.404

991

140

‐0.809

91

150

0.06

2207

115

00.12

4414

115

00.18

6605

115

00.31

0933

115

00.62

1811

116

0‐0.062

207

116

0‐0.124

411

160

‐0.186

611

160

‐0.310

931

160

‐0.621

811

170

0.04

2151

117

00.08

4303

117

00.12

6443

117

00.21

0688

117

00.42

1339

118

0‐0.042

151

118

0‐0.084

31

180

‐0.126

441

180

‐0.210

691

180

‐0.421

341

190

0.02

1278

119

00.04

2556

119

00.06

3829

119

00.10

6355

119

00.21

2693

120

0‐0.021

278

120

0‐0.042

561

200

‐0.063

831

200

‐0.106

361

200

‐0.212

691

210

01

210

01

210

5E‐07

121

00

121

00

122

00

122

00

122

0‐5E‐07

122

00

122

00

1

Iteratio

n4

%0.99

9756

Iteratio

n4

%0.99

976

Iteratio

n4

%0.99

9758

Iteratio

n4

Iteratio

n4

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

10

02

00

1.43

477

1434

7.7

10

01

10

02

00

2.86

953

2869

5.3

10

01

10

02

00

4.30

382

4303

8.2

10

01

10

02

00

7.17

113

7171

1.3

10

01

10

02

00

14.341

6214

3416

.21

00

13

0.02

158

0.01

732

40.02

158

‐0.023

991.41

319

1413

1.9

20

01

30.04

316

0.03

798

40.04

316

‐0.044

652.82

637

2826

3.7

20

01

30.06

473

0.05

863

40.06

473

‐0.065

294.23

909

4239

0.9

20

01

30.10

786

0.09

992

40.10

786

‐0.106

557.06

327

7063

2.7

20

01

30.21

573

0.20

319

40.21

573

‐0.209

7814

.125

8914

1258

.92

00

15

0.08

219

0.03

236

60.08

219

‐0.045

71.35

258

1352

5.8

30

0.14

1319

15

0.16

438

0.07

139

60.16

438

‐0.084

732.70

515

2705

1.5

30

0.28

2637

15

0.24

653

0.11

046

0.24

653

‐0.123

734.05

729

4057

2.9

30

0.42

3909

15

0.41

076

0.18

842

60.41

076

‐0.201

686.76

037

6760

3.7

30

0.70

6327

15

0.82

159

0.38

354

60.82

159

‐0.396

7313

.520

0313

5200

.33

01.41

2589

17

0.17

728

0.04

512

80.17

728

‐0.065

141.25

749

1257

4.9

40

‐0.141

319

17

0.35

455

0.10

025

80.35

455

‐0.120

272.51

498

2514

9.8

40

‐0.282

641

70.53

173

0.15

537

80.53

173

‐0.175

363.77

209

3772

0.9

40

‐0.423

911

70.88

596

0.26

556

80.88

596

‐0.285

476.28

517

6285

1.7

40

‐0.706

331

71.77

203

0.54

117

81.77

203

‐0.560

9712

.569

5912

5695

.94

0‐1.412

591

90.30

231

0.05

563

100.30

231

‐0.082

321.13

246

1132

4.6

50

0.13

5258

19

0.60

462

0.12

461

100.60

462

‐0.151

32.26

491

2264

9.1

50

0.27

0515

19

0.90

677

0.19

357

100.90

677

‐0.220

243.39

705

3397

0.5

50

0.40

5729

19

1.51

083

0.33

145

101.51

083

‐0.358

025.66

0356

603

50

0.67

6037

19

3.02

182

0.67

627

103.02

182

‐0.702

6811

.319

811

3198

50

1.35

2003

111

0.45

281

0.06

392

120.45

281

‐0.097

280.98

196

9819

.66

0‐0.135

258

111

0.90

561

0.14

451

120.90

561

‐0.177

871.96

392

1963

9.2

60

‐0.270

521

111.35

821

0.22

509

121.35

821

‐0.258

432.94

561

2945

6.1

60

‐0.405

731

112.26

301

0.38

6212

2.26

301

‐0.419

434.90

812

4908

1.2

60

‐0.676

041

114.52

615

0.78

909

124.52

615

‐0.822

139.81

547

9815

4.7

60

‐1.352

113

0.62

435

0.07

140.62

435

‐0.110

030.81

042

8104

.27

00.12

5749

113

1.24

869

0.16

002

141.24

869

‐0.200

051.62

084

1620

8.4

70

0.25

1498

113

1.87

277

0.25

002

141.87

277

‐0.290

032.43

105

2431

0.5

70

0.37

7209

113

3.12

036

0.42

997

143.12

036

‐0.469

874.05

077

4050

7.7

70

0.62

8517

113

6.24

078

0.87

993

146.24

078

‐0.919

618.10

084

8100

8.4

70

1.25

6959

115

0.81

256

0.07

392

160.81

256

‐0.120

630.62

221

6222

.18

0‐0.125

749

115

1.62

512

0.17

1216

1.62

512

‐0.217

91.24

441

1244

4.1

80

‐0.251

51

152.43

736

0.26

845

162.43

736

‐0.315

141.86

646

1866

4.6

80

‐0.377

211

154.06

110.46

292

164.06

11‐0.509

493.11

003

3110

0.3

80

‐0.628

521

158.12

211

0.94

915

168.12

211

‐0.995

486.21

951

6219

5.1

80

‐1.256

961

171.01

317

0.07

572

181.01

317

‐0.129

090.42

1642

169

00.11

3246

117

2.02

633

0.17

812

182.02

633

‐0.231

50.84

3284

329

00.22

6491

117

3.03

912

0.28

051

183.03

912

‐0.333

871.26

4712

647

90

0.33

9705

117

5.06

378

0.48

523

185.06

378

‐0.538

482.10

735

2107

3.5

90

0.56

603

117

10.127

290.99

712

1810

.127

29‐1.050

124.21

433

4214

3.3

90

1.13

198

119

1.22

195

0.07

543

201.22

195

‐0.135

470.21

282

2128

.210

0‐0.113

246

119

2.44

388

0.18

088

202.44

388

‐0.240

920.42

565

4256

.510

0‐0.226

491

193.66

540.28

631

203.66

54‐0.346

340.63

842

6384

.210

0‐0.339

711

196.10

735

0.49

712

206.10

735

‐0.557

041.06

378

1063

7.8

100

‐0.566

031

1912

.214

221.02

424

2012

.214

22‐1.083

92.12

7421

274

100

‐1.131

981

211.43

502

0.07

309

221.43

452

‐0.139

810

011

00.09

8196

121

2.87

004

0.17

954

222.86

903

‐0.246

26‐5E‐06

‐0.05

110

0.19

6392

121

4.30

457

0.28

597

224.30

307

‐0.352

670

011

00.29

4561

121

7.17

239

0.49

879

227.16

988

‐0.565

38‐5E‐06

‐0.05

110

0.49

0812

121

14.344

121.03

091

2214

.339

11‐1.097

255E

‐06

0.05

110

0.98

1547

123

1.43

477

‐0.033

360

012

0‐0.098

196

123

2.86

953

‐0.033

360

012

0‐0.196

391

234.30

382

‐0.033

350

012

0‐0.294

561

237.17

113

‐0.033

290

012

0‐0.490

811

2314

.341

62‐0.033

170

012

0‐0.981

551

130

0.08

1042

113

00.16

2084

113

00.24

3105

113

00.40

5077

113

00.81

0084

114

0‐0.081

042

114

0‐0.162

081

140

‐0.243

111

140

‐0.405

081

140

‐0.810

081

150

0.06

2221

115

00.12

4441

115

00.18

6646

115

00.31

1003

115

00.62

1951

116

0‐0.062

221

116

0‐0.124

441

160

‐0.186

651

160

‐0.311

116

0‐0.621

951

170

0.04

216

117

00.08

432

117

00.12

647

117

00.21

0735

117

00.42

1433

118

0‐0.042

161

180

‐0.084

321

180

‐0.126

471

180

‐0.210

741

180

‐0.421

431

190

0.02

1282

119

00.04

2565

119

00.06

3842

119

00.10

6378

119

00.21

274

120

0‐0.021

282

120

0‐0.042

571

200

‐0.063

841

200

‐0.106

381

200

‐0.212

741

210

01

210

‐5E‐07

121

00

121

0‐5E‐07

121

05E

‐07

122

00

122

05E

‐07

122

00

122

05E

‐07

122

0‐5E‐07

1

Iteratio

n5

%0.99

9986

Iteratio

n5

%0.99

9983

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

10

02

00

1.43

479

1434

7.9

10

01

10

02

00

2.86

958

2869

5.8

10

01

30.02

158

0.01

732

40.02

158

‐0.023

991.41

321

1413

2.1

20

01

30.04

316

0.03

798

40.04

316

‐0.044

652.82

642

2826

4.2

20

01

50.08

219

0.03

236

60.08

219

‐0.045

71.35

2613

526

30

0.14

1321

15

0.16

439

0.07

139

60.16

439

‐0.084

732.70

519

2705

1.9

30

0.28

2642

17

0.17

728

0.04

512

80.17

728

‐0.065

141.25

751

1257

5.1

40

‐0.141

321

17

0.35

456

0.10

025

80.35

456

‐0.120

272.51

502

2515

0.2

40

‐0.282

641

90.30

231

0.05

563

100.30

231

‐0.082

321.13

248

1132

4.8

50

0.13

526

19

0.60

463

0.12

461

100.60

463

‐0.151

32.26

495

2264

9.5

50

0.27

0519

111

0.45

282

0.06

392

120.45

282

‐0.097

280.98

197

9819

.76

0‐0.135

261

110.90

563

0.14

451

120.90

563

‐0.177

871.96

395

1963

9.5

60

‐0.270

521

130.62

436

0.07

140.62

436

‐0.110

030.81

043

8104

.37

00.12

5751

113

1.24

871

0.16

002

141.24

871

‐0.200

051.62

087

1620

8.7

70

0.25

1502

115

0.81

258

0.07

392

160.81

258

‐0.120

630.62

221

6222

.18

0‐0.125

751

115

1.62

514

0.17

1216

1.62

514

‐0.217

91.24

444

1244

4.4

80

‐0.251

51

171.01

318

0.07

572

181.01

318

‐0.129

090.42

161

4216

.19

00.11

3248

117

2.02

636

0.17

813

182.02

636

‐0.231

50.84

322

8432

.29

00.22

6495

119

1.22

196

0.07

543

201.22

196

‐0.135

480.21

283

2128

.310

0‐0.113

248

119

2.44

392

0.18

088

202.44

392

‐0.240

930.42

566

4256

.610

0‐0.226

51

211.43

504

0.07

309

221.43

454

‐0.139

810

011

00.09

8197

121

2.87

008

0.17

954

222.86

908

‐0.246

260

011

00.19

6395

123

1.43

479

‐0.033

360

012

0‐0.098

197

123

2.86

958

‐0.033

360

012

0‐0.196

41

130

0.08

1043

113

00.16

2087

114

0‐0.081

043

114

0‐0.162

091

150

0.06

2221

115

00.12

4444

116

0‐0.062

221

116

0‐0.124

441

170

0.04

2161

117

00.08

4322

118

0‐0.042

161

118

0‐0.084

321

190

0.02

1283

119

00.04

2566

120

0‐0.021

283

120

0‐0.042

571

210

01

210

01

220

01

220

01

20kN

across

30kN

across

40kN

across

45kN

across

48kN

across

FAIL AFTER

Reference data

No P‐de

ltaP‐de

ltano

n pd

% lost

Iteratio

n1

Iteratio

n1

Iteratio

n1

Iteratio

n1

Iteratio

n1

11.43

479

1.24

0.15

7089

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

Data

from

Graph

22.86

958

2.48

10.15

6622

10

02

00

26.795

3826

7953

.81

00

11

00

20

040

.193

2340

1932

.31

00

11

00

20

053

.591

0853

5910

.81

00

11

00

20

060

.289

9360

2899

.31

00

11

00

20

064

.309

4364

3094

.31

00

1==============

34.30

382

3.72

10.15

663

30.39

864

0.37

689

40.39

864

‐0.383

426

.396

7426

3967

.42

00

13

0.59

796

0.56

74

0.59

796

‐0.573

4539

.595

2739

5952

.72

00

13

0.79

729

0.75

713

40.79

729

‐0.763

4952

.793

7952

7937

.92

00

13

0.89

694

0.85

217

40.89

694

‐0.858

559

.392

9959

3929

.92

00

13

0.95

676

0.90

922

40.95

676

‐0.915

5463

.352

6763

3526

.72

00

15

7.17

113

6.2

0.15

6634

51.51

755

0.71

376

61.51

755

‐0.726

8125

.277

8325

2778

.33

02.63

9674

15

2.27

636

1.07

397

62.27

636

‐1.086

8937

.916

8737

9168

.73

03.95

9527

15

3.03

516

1.43

426

3.03

516

‐1.446

9650

.555

9250

5559

.23

05.27

9379

15

3.41

453

1.61

436

3.41

453

‐1.626

9956

.875

456

8754

30

5.93

9299

15

3.64

222

1.72

237

63.64

222

‐1.735

0260

.667

2160

6672

.13

06.33

5267

1

Title

:X‐Displacemen

t10

14.341

6212

.398

0.15

6769

73.27

673

1.01

068

3.27

673

‐1.030

223

.518

6523

5186

.54

0‐2.639

671

74.91

514

1.52

091

84.91

514

‐1.540

3235

.278

0935

2780

.94

0‐3.959

531

76.55

354

2.03

122

86.55

354

‐2.050

4247

.037

5447

0375

.44

0‐5.279

381

77.37

272.28

637

87.37

27‐2.305

4652

.917

2352

9172

.34

0‐5.939

31

77.86

427

2.43

947

87.86

427

‐2.458

556

.445

1656

4451

.64

0‐6.335

271

2028

.683

0924

.796

0.15

6763

95.59

613

1.26

742

105.59

613

‐1.293

5921

.199

2521

1992

.55

02.52

7783

19

8.39

425

1.90

7810

8.39

425

‐1.933

7231

.798

9831

7989

.85

03.79

1687

19

11.192

362.54

819

1011

.192

36‐2.573

8642

.398

7242

3987

.25

05.05

5592

19

12.591

362.86

838

1012

.591

36‐2.893

9147

.698

5747

6985

.75

05.68

754

19

13.430

873.06

051

1013

.430

87‐3.085

9750

.878

5650

8785

.65

06.06

6721

1X

Axis

Title

:mm

3043.02496

37.194

0.156772

118.39

571

1.48

421

128.39

571

‐1.516

9618

.399

6718

3996

.76

0‐2.527

781

1112

.593

652.23

466

1212

.593

65‐2.267

1327

.599

5827

5995

.86

0‐3.791

691

1116

.791

572.98

512

1216

.791

57‐3.017

2836

.799

5136

7995

.16

0‐5.055

591

1118

.890

463.36

035

1218

.890

46‐3.392

3541

.399

4741

3994

.76

0‐5.687

541

1120

.149

933.58

549

1220

.149

93‐3.617

4144

.159

544

1595

60

‐6.066

721

YAxis

Title

:xFffffff"@

4057.36612

49.592

0.156762

1311

.595

461.66

099

1411

.595

46‐1.700

3415

.199

9215

1999

.27

02.35

1865

113

17.393

282.50

149

1417

.393

28‐2.540

5122

.799

9522

7999

.57

03.52

7809

113

23.191

093.34

214

23.191

09‐3.380

6830

.399

9930

3999

.97

04.70

3754

113

26.089

933.76

225

1426

.089

93‐3.800

7734

.234

2000

70

5.29

1723

113

27.829

374.01

441

1427

.829

37‐4.052

8336

.480

0636

4800

.67

05.64

4516

145

64.521

6555

.791

0.15

6489

1515

.115

331.79

773

1615

.115

33‐1.843

711

.680

0511

6800

.58

0‐2.351

871

1522

.673

12.70

828

1622

.673

1‐2.753

8917

.520

1317

5201

.38

0‐3.527

811

1530

.230

873.61

883

1630

.230

87‐3.664

0723

.360

2123

3602

.18

0‐4.703

751

1534

.009

684.07

411

1634

.009

68‐4.119

1726

.280

2526

2802

.58

0‐5.291

721

1536

.277

134.34

728

1636

.277

13‐4.392

2328

.032

328

0323

80

‐5.644

521

mmxFffff

ff"@

4868

.822

9159

.51

0.15

6493

1718

.875

281.89

445

1818

.875

28‐1.947

057.92

0179

201

90

2.11

9925

117

28.313

072.85

503

1828

.313

07‐2.907

2511

.880

1611

8801

.69

03.17

9898

117

37.750

833.81

561

1837

.750

83‐3.867

4515

.840

2515

8402

.59

04.23

9872

117

42.469

644.29

5918

42.469

64‐4.347

5417

.820

2917

8202

.99

04.76

9857

117

45.301

14.58

408

1845

.301

1‐4.635

6119

.008

3319

0083

.39

05.08

7856

1Line

type

:0

1922

.795

31.95

115

2022

.795

3‐2.010

414.00

008

4000

0.8

100

‐2.119

931

1934

.193

122.94

174

2034

.193

12‐3.000

66.00

011

6000

1.1

100

‐3.179

91

1945

.590

923.93

234

2045

.590

92‐3.990

88.00

016

8000

1.6

100

‐4.239

871

1951

.289

744.42

764

2051

.289

74‐4.485

99.00

019

9000

1.9

100

‐4.769

861

1954

.709

224.72

483

2054

.709

22‐4.782

979.60

021

9600

2.1

100

‐5.087

861

0

00

021

26.800

381.96

783

2226

.790

37‐2.033

775E

‐06

0.05

110

1.83

9967

121

40.200

732.96

843

2240

.185

72‐3.033

965E

‐06

0.05

110

2.75

9958

121

53.601

093.96

904

2253

.581

08‐4.034

17‐5E‐06

‐0.05

110

3.67

9951

121

60.301

194.46

934

2260

.278

67‐4.534

270

011

04.13

9947

121

64.321

444.76

953

2264

.297

42‐4.834

340

011

04.41

595

11.24

‐0.998

0.99

81.24

2326

.795

38‐0.032

970

012

0‐1.839

971

2340

.193

23‐0.032

770

012

0‐2.759

961

2353

.591

08‐0.032

560

012

0‐3.679

951

2360

.289

93‐0.032

460

012

0‐4.139

951

2364

.309

43‐0.032

410

012

0‐4.415

951

2.48

1

‐22

2.48

113

01.51

9992

113

02.27

9995

113

03.03

9999

113

03.42

113

03.64

8006

13.72

1

‐33

3.72

114

0‐1.519

991

140

‐2.28

114

0‐3.04

114

0‐3.42

114

0‐3.648

011

4.96

‐4

44.96

150

1.16

8005

115

01.75

2013

115

02.33

6021

115

02.62

8025

115

02.80

323

16.2

‐5

56.2

160

‐1.168

011

160

‐1.752

011

160

‐2.336

021

160

‐2.628

031

160

‐2.803

231

7.43

9

‐66

7.43

917

00.79

201

117

01.18

8016

117

01.58

4025

117

01.78

2029

117

01.90

0833

18.67

9

‐77

8.67

918

0‐0.792

011

180

‐1.188

021

180

‐1.584

031

180

‐1.782

031

180

‐1.900

831

9.91

8

‐88

9.91

819

00.40

0008

119

00.60

0011

119

00.80

0016

119

00.90

0019

119

00.96

0021

111

.158

‐9

911

.158

200

‐0.400

011

200

‐0.600

011

200

‐0.800

021

200

‐0.900

021

200

‐0.960

021

12.398

‐10

1012

.398

210

5E‐07

121

05E

‐07

121

0‐5E‐07

121

00

121

00

113

.638

‐11

1113

.638

220

‐5E‐07

122

0‐5E‐07

122

05E

‐07

122

00

122

00

114

.877

‐12

1214

.877

16.117

‐13

1316

.117

Iteratio

n2

Iteratio

n2

Iteratio

n2

Iteratio

n2

17.357

‐14

1417

.357

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

Iteratio

n2

delta

Pd (N

mm)

coup

le fo

rce

18.597

‐15

1518

.597

10

02

00

28.564

8728

5648

.71

00

11

00

20

042

.847

6142

8476

.11

00

11

00

20

057

.129

757

1297

10

01

delta

Pd (N

mm)

coup

le fo

rce

10

02

00

68.555

9368

5559

.31

00

119

.837

‐16

1619

.837

30.42

937

0.40

763

40.42

937

‐0.414

1428

.135

528

1355

20

01

30.64

406

0.61

311

40.64

406

‐0.619

5442

.203

5542

2035

.52

00

13

0.85

873

0.81

859

40.85

873

‐0.824

9156

.270

9756

2709

.72

00

11

00

20

064

.271

3564

2713

.51

00

13

1.03

049

0.98

297

41.03

049

‐0.989

2567

.525

4467

5254

.42

00

121

.076

‐17

1721

.076

51.63

521

0.76

995

61.63

521

‐0.782

9826

.929

6626

9296

.63

02.81

355

15

2.45

283

1.15

826

62.45

283

‐1.171

1440

.394

7840

3947

.83

04.22

0355

15

3.27

038

1.54

657

63.27

038

‐1.559

2753

.859

3253

8593

.23

05.62

7097

13

0.96

611

0.92

134

40.96

611

‐0.927

6663

.305

2463

3052

.42

00

15

3.92

451.85

722

63.92

45‐1.869

8264

.631

4364

6314

.33

06.75

2544

122

.316

‐18

1822

.316

73.52

714

1.08

719

83.52

714

‐1.106

7625

.037

7325

0377

.34

0‐2.813

551

75.29

075

1.63

579

85.29

075

‐1.655

1637

.556

8637

5568

.64

0‐4.220

361

77.05

423

2.18

439

87.05

423

‐2.203

5150

.075

4750

0754

.74

0‐5.627

11

53.67

927

1.74

073

63.67

927

‐1.753

3760

.592

0860

5920

.83

06.33

0524

17

8.46

515

2.62

327

88.46

515

‐2.642

2360

.090

7860

0907

.84

0‐6.752

541

23.556

‐19

1923

.556

96.01

537

1.35

9710

6.01

537

‐1.385

8322

.549

522

5495

50

2.69

2966

19

9.02

313

2.04

622

109.02

313

‐2.072

133

.824

4833

8244

.85

04.03

9478

19

12.030

692.73

274

1012

.030

69‐2.758

3145

.099

0145

0990

.15

05.38

5932

17

7.93

613

2.45

869

87.93

613

‐2.477

7256

.335

2256

3352

.24

0‐6.330

521

914

.436

933.28

197

1014

.436

93‐3.307

3354

.119

5411

905

06.46

3143

124

.796

‐20

2024

.796

119.01

091

1.58

794

129.01

091

‐1.620

6519

.553

9619

5539

.66

0‐2.692

971

1113

.516

492.39

026

1213

.516

49‐2.422

6629

.331

1229

3311

.26

0‐4.039

481

1118

.021

793.19

256

1218

.021

79‐3.224

6239

.107

9139

1079

.16

0‐5.385

931

913

.534

683.07

601

1013

.534

68‐3.101

4650

.736

6750

7366

.75

06.05

9208

111

21.626

283.83

442

1221

.626

28‐3.866

2346

.929

6546

9296

.56

0‐6.463

141

26.035

‐21

2126

.035

1312

.425

831.77

248

1412

.425

83‐1.811

7916

.139

0416

1390

.47

02.50

3773

113

18.638

92.66

873

1418

.638

9‐2.707

724

.208

7124

2087

.17

03.75

5686

113

24.851

623.56

497

1424

.851

62‐3.603

5432

.278

0832

2780

.87

05.00

7547

111

20.274

713.59

373

1220

.274

71‐3.625

6443

.996

6443

9966

.46

0‐6.059

211

1329

.822

114.28

197

1429

.822

11‐4.320

2838

.733

8238

7338

.27

06.00

9078

127

.275

‐22

2227

.275

1516

.173

351.91

394

1616

.173

35‐1.959

8712

.391

5212

3915

.28

0‐2.503

771

1524

.260

232.88

2616

24.260

23‐2.928

1518

.587

3818

5873

.88

0‐3.755

691

1532

.346

673.85

124

1632

.346

67‐3.896

3824

.783

0324

7830

.38

0‐5.007

551

1327

.958

314.01

3114

27.958

31‐4.051

5336

.313

0436

3130

.47

05.63

3522

115

38.816

214.62

617

1638

.816

21‐4.671

0129

.739

7229

7397

.28

0‐6.009

081

28.515

‐23

2328

.515

1720

.168

072.01

305

1820

.168

07‐2.065

68.39

6883

968

90

2.25

495

117

30.252

363.03

293

1830

.252

36‐3.085

112

.595

2512

5952

.59

03.38

2448

117

40.336

124.05

2818

40.336

12‐4.104

5216

.793

5816

7935

.89

04.50

9901

115

36.390

34.33

558

1636

.390

3‐4.380

5527

.881

0527

8810

.58

0‐5.633

521

1748

.403

584.86

8718

48.403

58‐4.920

1120

.152

3520

1523

.59

05.41

191

29.755

‐24

2429

.755

1924

.326

042.07

055

2024

.326

04‐2.129

774.23

883

4238

8.3

100

‐2.254

951

1936

.489

363.12

085

2036

.489

36‐3.179

646.35

825

6358

2.5

100

‐3.382

451

1948

.652

074.17

113

2048

.652

07‐4.229

488.47

763

8477

6.3

100

‐4.509

91

1745

.378

494.56

275

1845

.378

49‐4.614

2918

.892

8618

8928

.69

05.07

3667

119

58.382

755.01

137

2058

.382

75‐5.069

3910

.173

1810

1731

.810

0‐5.411

91

30.995

‐25

2530

.995

2128

.569

872.08

723

2228

.559

86‐2.153

125E

‐06

0.05

110

1.95

5396

121

42.855

113.14

753

2242

.840

1‐3.213

5E‐06

0.05

110

2.93

3112

121

57.139

74.20

783

2257

.119

69‐4.272

845E

‐06

0.05

110

3.91

0791

119

54.733

984.69

629

2054

.733

98‐4.754

459.53

737

9537

3.7

100

‐5.073

671

2168

.567

945.05

607

2268

.543

92‐5.120

760

011

04.69

2965

132

.235

‐26

2632

.235

2328

.564

87‐0.032

940

012

0‐1.955

41

2342

.847

61‐0.032

740

012

0‐2.933

111

2357

.129

7‐0.032

510

012

0‐3.910

791

2164

.282

614.73

799

2264

.260

1‐4.802

82‐5E‐06

‐0.05

110

4.39

9664

123

68.555

93‐0.032

340

012

0‐4.692

971

33.474

‐27

2733

.474

130

1.61

3904

113

02.42

0871

113

03.22

7808

123

64.271

35‐0.032

410

012

0‐4.399

661

130

3.87

3382

134

.714

‐28

2834

.714

140

‐1.613

91

140

‐2.420

871

140

‐3.227

811

130

3.63

1304

114

0‐3.873

381

35.954

‐29

2935

.954

150

1.23

9152

115

01.85

8738

115

02.47

8303

114

0‐3.631

31

150

2.97

3972

137

.194

‐30

3037

.194

160

‐1.239

151

160

‐1.858

741

160

‐2.478

31

150

2.78

8105

116

0‐2.973

971

38.433

‐31

3138

.433

170

0.83

968

117

01.25

9525

117

01.67

9358

116

0‐2.788

111

170

2.01

5235

139

.673

‐32

3239

.673

180

‐0.839

681

180

‐1.259

531

180

‐1.679

361

170

1.88

9286

118

0‐2.015

241

40.913

‐33

3340

.913

190

0.42

3883

119

00.63

5825

119

00.84

7763

118

0‐1.889

291

190

1.01

7318

142

.153

‐34

3442

.153

200

‐0.423

881

200

‐0.635

831

200

‐0.847

761

190

0.95

3737

120

0‐1.017

321

43.393

‐35

3543

.393

210

5E‐07

121

05E

‐07

121

05E

‐07

120

0‐0.953

741

210

01

44.632

‐36

3644

.632

220

‐5E‐07

122

0‐5E‐07

122

0‐5E‐07

121

0‐5E‐07

122

00

145

.872

‐37

3745

.872

Iteratio

n3

Iteratio

n3

Iteratio

n3

220

5E‐07

147

.112

‐38

3847

.112

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

Iteratio

n3

Iteratio

n3

48.352

‐39

3948

.352

10

02

00

28.676

1128

6761

.11

00

11

00

20

043

.014

543

0145

10

01

10

02

00

57.352

1757

3521

.71

00

1de

ltaPd

(Nmm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

49.592

‐40

4049

.592

30.43

133

0.40

959

40.43

133

‐0.416

0928

.244

7828

2447

.82

00

13

0.64

70.61

605

40.64

7‐0.622

4842

.367

542

3675

20

01

30.86

264

0.82

254

0.86

264

‐0.828

8256

.489

5356

4895

.32

00

11

00

20

064

.521

6564

5216

.51

00

11

00

20

068

.822

9168

8229

.11

00

150

.831

‐41

4150

.831

51.64

269

0.77

351

61.64

269

‐0.786

5427

.033

4227

0334

.23

02.82

4478

15

2.46

405

1.16

361

62.46

405

‐1.176

4940

.550

4540

5504

.53

04.23

675

15

3.28

534

1.55

376

3.28

534

‐1.566

454

.066

8354

0668

.33

05.64

8953

13

0.97

051

0.92

575

40.97

051

‐0.932

0663

.551

1463

5511

.42

00

13

1.03

519

0.98

767

41.03

519

‐0.993

9467

.787

7267

7877

.22

00

152

.071

‐42

4252

.071

73.54

303

1.09

203

83.54

303

‐1.111

625

.133

0825

1330

.84

0‐2.824

481

75.31

459

1.64

306

85.31

459

‐1.662

4337

.699

9137

6999

.14

0‐4.236

751

77.08

601

2.19

408

87.08

601

‐2.213

1950

.266

1650

2661

.64

0‐5.648

951

53.69

609

1.74

875

63.69

609

‐1.761

3960

.825

5660

8255

.63

06.35

5114

15

3.94

245

1.86

578

63.94

245

‐1.878

3764

.880

4664

8804

.63

06.77

8772

153

.311

‐43

4353

.311

96.04

192

1.36

552

106.04

192

‐1.391

6522

.634

1922

6341

.95

02.70

3342

19

9.06

297

2.05

496

109.06

297

‐2.080

8333

.951

5333

9515

.35

04.05

5045

19

12.083

792.74

438

1012

.083

79‐2.769

9545

.268

3845

2683

.85

05.40

6683

17

7.97

188

2.46

959

87.97

188

‐2.488

6156

.549

7756

5497

.74

0‐6.355

111

78.50

329

2.63

498

8.50

329

‐2.653

8660

.319

6260

3196

.24

0‐6.778

771

54.551

‐44

4454

.551

119.04

981

1.59

446

129.04

981

‐1.627

1719

.626

319

6263

60

‐2.703

341

1113

.574

842.40

004

1213

.574

84‐2.432

4529

.439

6629

4396

.66

0‐4.055

051

1118

.099

573.20

561

1218

.099

57‐3.237

6739

.252

639

2526

60

‐5.406

681

913

.594

423.08

911

1013

.594

42‐3.114

5550

.927

2350

9272

.35

06.08

2556

19

14.500

663.29

593

1014

.500

66‐3.321

2954

.322

2554

3222

.55

06.48

8046

155

.791

‐45

4555

.791

1312

.478

241.77

947

1412

.478

24‐1.818

7816

.197

8716

1978

.77

02.51

3308

113

18.717

532.67

923

1418

.717

53‐2.718

1924

.296

9724

2969

.77

03.76

9991

113

24.956

443.57

896

1424

.956

44‐3.617

5332

.395

7332

3957

.37

05.02

6616

111

20.362

223.60

841

1220

.362

22‐3.640

3244

.159

4344

1594

.36

0‐6.082

561

1121

.719

633.85

007

1221

.719

63‐3.881

8847

.103

2847

1032

.86

0‐6.488

051

57.03

‐46

4657

.03

1516

.240

051.92

123

1616

.240

05‐1.967

1512

.436

0612

4360

.68

0‐2.513

311

1524

.360

282.89

353

1624

.360

28‐2.939

0818

.654

2218

6542

.28

0‐3.769

991

1532

.480

053.86

581

1632

.480

05‐3.910

9424

.872

1224

8721

.28

0‐5.026

621

1328

.076

244.02

885

1428

.076

24‐4.067

2636

.445

4136

4454

.17

05.65

4977

113

29.947

94.29

877

1429

.947

9‐4.337

0738

.875

0138

8750

.17

06.03

1962

158

.27

‐47

4758

.27

1720

.249

472.02

047

1820

.249

47‐2.073

028.42

664

8426

6.4

90

2.26

3419

117

30.374

483.04

407

1830

.374

48‐3.096

2312

.640

0212

6400

.29

03.39

5153

117

40.498

924.06

765

1840

.498

92‐4.119

3716

.853

2516

8532

.59

04.52

6838

115

36.540

354.35

197

1636

.540

35‐4.396

9327

.981

327

9813

80

‐5.654

981

1538

.976

274.64

365

1638

.976

27‐4.688

4829

.846

6429

8466

.48

0‐6.031

961

59.51

‐48

4859

.51

1924

.422

342.07

802

2024

.422

34‐2.137

244.25

377

4253

7.7

100

‐2.263

421

1936

.633

823.13

206

2036

.633

82‐3.190

856.38

068

6380

6.8

100

‐3.395

151

1948

.844

664.18

608

2048

.844

66‐4.244

428.50

751

8507

5.1

100

‐4.526

841

1745

.561

634.57

946

1845

.561

63‐4.630

9918

.960

0218

9600

.29

05.09

2723

117

48.598

944.88

653

1848

.598

94‐4.937

9320

.223

9720

2239

.79

05.43

2225

160

.75

‐49

4960

.75

2128

.681

122.09

4722

28.671

11‐2.160

59‐5E‐06

‐0.05

110

1.96

263

121

43.022

3.15

875

2243

.006

99‐3.224

215E

‐06

0.05

110

2.94

3966

121

57.362

184.22

277

2257

.342

16‐4.287

790

011

03.92

526

119

54.950

644.71

311

2054

.950

64‐4.771

269.57

101

9571

0.1

100

‐5.092

721

1958

.613

865.02

931

2058

.613

86‐5.087

3210

.209

0510

2090

.510

0‐5.432

231

61.99

‐50

5061

.99

2328

.676

11‐0.032

940

012

0‐1.962

631

2343

.014

5‐0.032

730

012

0‐2.943

971

2357

.352

17‐0.032

510

012

0‐3.925

261

2164

.532

914.75

4822

64.510

38‐4.819

635E

‐06

0.05

110

4.41

5943

121

68.834

925.07

401

2268

.810

9‐5.138

690

011

04.71

0328

163

.229

‐51

5163

.229

130

1.61

9787

113

02.42

9697

113

03.23

9573

123

64.521

65‐0.032

410

012

0‐4.415

941

2368

.822

91‐0.032

340

012

0‐4.710

331

64.469

‐52

5264

.469

140

‐1.619

791

140

‐2.429

71

140

‐3.239

571

130

3.64

4541

113

03.88

7501

115

01.24

3606

115

01.86

5422

115

02.48

7212

114

0‐3.644

541

140

‐3.887

51

160

‐1.243

611

160

‐1.865

421

160

‐2.487

211

150

2.79

813

115

02.98

4664

117

00.84

2664

117

01.26

4002

117

01.68

5325

116

0‐2.798

131

160

‐2.984

661

180

‐0.842

661

180

‐1.264

118

0‐1.685

331

170

1.89

6002

117

02.02

2397

119

00.42

5377

119

00.63

8068

119

00.85

0751

118

0‐1.896

118

0‐2.022

41

200

‐0.425

381

200

‐0.638

071

200

‐0.850

751

190

0.95

7101

119

01.02

0905

121

0‐5E‐07

121

05E

‐07

121

00

120

0‐0.957

11

200

‐1.020

911

220

5E‐07

122

0‐5E‐07

122

00

121

05E

‐07

121

00

122

0‐5E‐07

122

00

1Ite

ratio

n4

Iteratio

n4

Iteratio

n4

Iteratio

n4

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

delta

Pd (N

mm)

coup

le fo

rce

Iteratio

n4

10

02

00

28.683

0928

6830

.91

00

11

00

20

043

.024

9643

0249

.61

00

11

00

20

057

.366

1257

3661

.21

00

11

00

20

064

.537

3464

5373

.41

00

1de

ltaPd

(Nmm)

coup

le fo

rce

30.43

145

0.40

971

40.43

145

‐0.416

2228

.251

6428

2516

.42

00

13

0.64

718

0.61

623

40.64

718

‐0.622

6642

.377

7842

3777

.82

00

13

0.86

289

0.82

275

40.86

289

‐0.829

0756

.503

2356

5032

.32

00

13

0.97

079

0.92

602

40.97

079

‐0.932

3463

.566

5563

5665

.52

00

11

00

20

068

.839

6568

8396

.51

00

15

1.64

316

0.77

374

61.64

316

‐0.786

7727

.039

9327

0399

.33

02.82

5164

15

2.46

476

1.16

395

62.46

476

‐1.176

8340

.560

240

5602

30

4.23

7778

15

3.28

628

1.55

415

63.28

628

‐1.566

8554

.079

8454

0798

.43

05.65

0323

15

3.69

715

1.74

926

63.69

715

‐1.761

960

.840

1960

8401

.93

06.35

6655

13

1.03

548

0.98

797

41.03

548

‐0.994

2467

.804

1767

8041

.72

00

17

3.54

402

1.09

234

83.54

402

‐1.111

9125

.139

0725

1390

.74

0‐2.825

161

75.31

609

1.64

352

85.31

609

‐1.662

8837

.708

8737

7088

.74

0‐4.237

781

77.08

801

2.19

468

87.08

801

‐2.213

850

.278

1150

2781

.14

0‐5.650

321

77.97

412

2.47

028

87.97

412

‐2.489

356

.563

2256

5632

.24

0‐6.356

661

53.94

358

1.86

632

63.94

358

‐1.878

9164

.896

0764

8960

.73

06.78

0417

19

6.04

359

1.36

588

106.04

359

‐1.392

0122

.639

522

6395

50

2.70

3993

19

9.06

546

2.05

5510

9.06

546

‐2.081

3833

.959

533

9595

50

4.05

602

19

12.087

122.74

511

1012

.087

12‐2.770

6845

.279

4527

905

05.40

7984

19

13.598

173.08

993

1013

.598

17‐3.115

3750

.939

1750

9391

.75

06.08

4019

17

8.50

568

2.63

563

88.50

568

‐ 2.654

5860

.333

9760

3339

.74

0‐6.780

421

119.05

225

1.59

487

129.05

225

‐1.627

5819

.630

8419

6308

.46

0‐2.703

991

1113

.578

52.40

066

1213

.578

5‐2.433

0629

.446

4629

4464

.66

0‐4.056

021

1118

.104

453.20

643

1218

.104

45‐3.238

4839

.261

6739

2616

.76

0‐5.407

981

1120

.367

73.60

933

1220

.367

7‐3.641

2444

.169

6444

1696

.46

0‐6.084

021

914

.504

653.29

681

1014

.504

65‐3.322

1754

.335

5433

505

06.48

9607

113

12.481

531.77

991

1412

.481

53‐1.819

2216

.201

5616

2015

.67

02.51

3907

113

18.722

472.67

989

1418

.722

47‐2.718

8524

.302

4924

3024

.97

03.77

0887

113

24.963

013.57

984

1424

.963

01‐3.618

4132

.403

1132

4031

.17

05.02

7811

113

28.083

644.02

984

1428

.083

64‐4.068

2536

.453

736

4537

70

5.65

6322

111

21.725

483.85

106

1221

.725

48‐3.882

8647

.114

1747

1141

.76

0‐6.489

611

1516

.244

231.92

168

1616

.244

23‐1.967

612

.438

8612

4388

.68

0‐2.513

911

1524

.366

562.89

421

1624

.366

56‐2.939

7618

.658

418

6584

80

‐3.770

891

1532

.488

413.86

672

1632

.488

41‐3.911

8524

.877

7124

8777

.18

0‐5.027

811

1536

.549

764.35

316

36.549

76‐4.397

9627

.987

5827

9875

.88

0‐5.656

321

1329

.955

794.29

982

1429

.955

79‐4.338

1238

.883

8638

8838

.67

06.03

3397

117

20.254

582.02

094

1820

.254

58‐2.073

498.42

851

8428

5.1

90

2.26

395

117

30.382

133.04

477

1830

.382

13‐3.096

9312

.642

8312

6428

.39

03.39

595

117

40.509

124.06

858

1840

.509

12‐4.120

316

.857

1685

709

04.52

791

1745

.573

124.58

0518

45.573

12‐4.632

0418

.964

2218

9642

.29

05.09

3917

115

38.986

314.64

475

1638

.986

31‐4.689

5829

.853

3429

8533

.48

0‐6.033

41

1924

.428

382.07

849

2024

.428

38‐2.137

714.25

471

4254

7.1

100

‐2.263

951

1936

.642

883.13

276

2036

.642

88‐3.191

566.38

208

6382

0.8

100

‐3.395

951

1948

.856

734.18

701

2048

.856

73‐4.245

368.50

939

8509

3.9

100

‐4.527

91

1954

.964

234.71

416

2054

.964

23‐4.772

319.57

311

9573

1.1

100

‐5.093

921

1748

.611

194.88

764

1848

.611

19‐4.939

0420

.228

4620

2284

.69

05.43

351

2128

.688

092.09

517

2228

.678

08‐2.161

065E

‐06

0.05

110

1.96

3084

121

43.032

463.15

945

2243

.017

45‐3.224

925E

‐06

0.05

110

2.94

4646

121

57.376

134.22

371

2257

.356

11‐4.288

720

011

03.92

6167

121

64.548

64.75

586

2264

.526

08‐4.820

680

011

04.41

6964

119

58.628

355.03

043

2058

.628

35‐5.088

4510

.211

310

2113

100

‐5.433

51

2328

.683

09‐0.032

940

012

0‐1.963

081

2343

.024

96‐0.032

730

012

0‐2.944

651

2357

.366

12‐0.032

510

012

0‐3.926

171

2364

.537

34‐0.032

410

012

0‐4.416

961

2168

.851

665.07

513

2268

.827

64‐5.139

820

011

04.71

1417

113

01.62

0156

113

02.43

0249

113

03.24

0311

113

03.64

537

123

68.839

65‐0.032

340

012

0‐4.711

421

140

‐1.620

161

140

‐2.430

251

140

‐3.240

311

140

‐3.645

371

130

3.88

8386

115

01.24

3886

115

01.86

584

115

02.48

7771

115

02.79

8758

114

0‐3.888

391

160

‐1.243

891

160

‐1.865

841

160

‐2.487

771

160

‐2.798

761

150

2.98

5334

1

134

Appendix F

Element Angle Simulation Results

ECCENTRIC CANTI CHECK

N 1 E 1 E 0.5 E 2 E 3 E 4 E 5 E 6 E 7 E 8 E 10

Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph

============== ============== ============== ============== ============== ============== ============== ============== ============== ============== ==============

Title : Y‐Displacement Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Ch

X Axis Titl : mm X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis X Axis Titl : x‐axis

Y Axis Title: ®y"ÌUÈxF Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis

mm ®y"ÌUÈxF x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis

Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

‐0.413 3.53 0.413 ‐0.414 3.54838 0.414 ‐0.414 3.53034 0.414 ‐0.414 3.58206 0.414 ‐0.414 3.61318 0.414 ‐0.414 3.64027 0.414 ‐0.415 3.66268 0.415 ‐0.415 3.68122 0.415 ‐0.415 3.69392 0.415 ‐0.415 3.70247 0.415 ‐0.415 3.70208 0.415

‐0.829 5.397 0.829 ‐0.83 5.42802 0.83 ‐0.83 5.40322 0.83 ‐0.83 5.47372 0.83 ‐0.83 5.51363 0.83 ‐0.83 5.54722 0.83 ‐0.83 5.5744 0.83 ‐0.83 5.59473 0.83 ‐0.83 5.60788 0.83 ‐0.829 5.61353 0.829 ‐0.829 5.60157 0.829

‐1.241 6.876 1.241 ‐1.242 6.92242 1.242 ‐1.242 6.88844 1.242 ‐1.242 6.9851 1.242 ‐1.242 7.04104 1.242 ‐1.24 7.05483 1.24 ‐1.24 7.09692 1.24 ‐1.24 7.13031 1.24 ‐1.24 7.15459 1.24 ‐1.24 7.16958 1.24 ‐1.24 7.16936 1.24

‐1.653 8.212 1.653 ‐1.654 8.27069 1.654 ‐1.654 8.2298 1.654 ‐1.654 8.34669 1.654 ‐1.654 8.41073 1.654 ‐1.654 8.47613 1.654 ‐1.654 8.5218 1.654 ‐1.653 8.55795 1.653 ‐1.653 8.5836 1.653 ‐1.653 8.59672 1.653 ‐1.653 8.58902 1.653

‐2.066 9.393 2.066 ‐2.067 9.45959 2.067 ‐2.068 9.41506 2.068 ‐2.067 9.5415 2.067 ‐2.067 9.61321 2.067 ‐2.067 9.67322 2.067 ‐2.067 9.72154 2.067 ‐2.067 9.75842 2.067 ‐2.067 9.78309 2.067 ‐2.067 9.79584 2.067 ‐2.067 9.78302 2.067

‐2.48 10.391 2.48 ‐2.482 10.4623 2.482 ‐2.482 10.41848 2.482 ‐2.482 10.54664 2.482 ‐2.482 10.6154 2.482 ‐2.482 10.67145 2.482 ‐2.482 10.71505 2.482 ‐2.482 10.74608 2.482 ‐2.482 10.7583 2.482 ‐2.482 10.75905 2.482 ‐2.483 10.72433 2.483

‐2.897 11.197 2.897 ‐2.899 11.26983 2.899 ‐2.899 11.22891 2.899 ‐2.899 11.34092 2.899 ‐2.9 11.3943 2.9 ‐2.9 11.43658 2.9 ‐2.901 11.46016 2.901 ‐2.901 11.4844 2.901 ‐2.901 11.4993 2.901 ‐2.901 11.49236 2.901 ‐2.902 11.44332 2.902

‐3.316 11.821 3.316 ‐3.318 11.88615 3.318 ‐3.318 11.85028 3.318 ‐3.32 11.92958 3.32 ‐3.32 11.99389 3.32 ‐3.32 12.02105 3.32 ‐3.321 12.03857 3.321 ‐3.321 12.05896 3.321 ‐3.322 12.0521 3.322 ‐3.323 12.02503 3.323 ‐3.323 11.95554 3.323

‐3.738 12.25 3.738 ‐3.741 12.3031 3.741 ‐3.74 12.28678 3.74 ‐3.742 12.32566 3.742 ‐3.743 12.34592 3.743 ‐3.744 12.35479 3.744 ‐3.745 12.35303 3.745 ‐3.746 12.34511 3.746 ‐3.747 12.33329 3.747 ‐3.747 12.31172 3.747 ‐3.748 12.23372 3.748

‐4.162 12.531 4.162 ‐4.165 12.57185 4.165 ‐4.165 12.53828 4.165 ‐4.167 12.60037 4.167 ‐4.168 12.61488 4.168 ‐4.169 12.62897 4.169 ‐4.17 12.63104 4.17 ‐4.171 12.62172 4.171 ‐4.171 12.60114 4.171 ‐4.172 12.57012 4.172 ‐4.173 12.47842 4.173

‐4.588 12.749 4.588 ‐4.591 12.78021 4.591 ‐4.59 12.76396 4.59 ‐4.592 12.7996 4.592 ‐4.594 12.81132 4.594 ‐4.594 12.81865 4.594 ‐4.596 12.79885 4.596 ‐4.597 12.77629 4.597 ‐4.598 12.74366 4.598 ‐4.599 12.70298 4.599 ‐4.6 12.59679 4.6

‐5.014 12.871 5.014 ‐5.018 12.89263 5.018 ‐5.017 12.88491 5.017 ‐5.019 12.90143 5.019 ‐5.021 12.89133 5.021 ‐5.022 12.88309 5.022 ‐5.023 12.86711 5.023 ‐5.024 12.84232 5.024 ‐5.025 12.80901 5.025 ‐5.026 12.767 5.026 ‐5.027 12.65939 5.027

‐5.442 12.931 5.442 ‐5.445 12.95146 5.445 ‐5.444 12.94456 5.444 ‐5.447 12.95835 5.447 ‐5.448 12.95334 5.448 ‐5.45 12.93777 5.45 ‐5.451 12.91165 5.451 ‐5.452 12.88364 5.452 ‐5.453 12.84644 5.453 ‐5.454 12.80289 5.454 ‐5.455 12.69272 5.455

‐5.87 12.969 5.87 ‐5.874 12.97221 5.874 ‐5.873 12.96982 5.873 ‐5.875 12.97922 5.875 ‐5.877 12.97498 5.877 ‐5.878 12.96585 5.878 ‐5.879 12.94636 5.879 ‐5.88 12.91855 5.88 ‐5.881 12.8809 5.881 ‐5.882 12.83578 5.882 ‐5.883 12.7226 5.883

‐6.298 12.992 6.298 ‐6.302 12.98401 6.302 ‐6.301 12.98265 6.301 ‐6.303 13.00561 6.303 ‐6.305 12.98882 6.305 ‐6.306 12.97747 6.306 ‐6.307 12.98219 6.307 ‐6.308 12.92744 6.308 ‐6.309 12.89085 6.309 ‐6.31 12.84416 6.31 ‐6.31 12.73067 6.31

‐6.727 12.982 6.727 ‐6.731 12.98908 6.731 ‐6.73 12.98808 6.73 ‐6.732 13.01146 6.732 ‐6.733 12.99472 6.733 ‐6.734 13.0013 6.734 ‐6.735 12.98761 6.735 ‐6.736 12.93246 6.736 ‐6.737 12.8961 6.737 ‐6.738 12.85032 6.738 ‐6.738 12.73681 6.738

‐7.155 12.998 7.155 ‐7.159 13.00709 7.159 ‐7.158 12.99271 7.158 ‐7.16 13.00651 7.16 ‐7.162 12.99832 7.162 ‐7.162 13.0091 7.162 ‐7.163 12.98872 7.163 ‐7.165 12.93692 7.165 ‐7.165 12.89999 7.165 ‐7.166 12.85491 7.166 ‐7.166 12.74245 7.166

‐7.584 12.988 7.584 ‐7.587 13.00314 7.587 ‐7.587 12.99436 7.587 ‐7.589 13.00719 7.589 ‐7.59 13.01241 7.59 ‐7.591 12.9902 7.591 ‐7.592 12.97155 7.592 ‐7.593 12.94083 7.593 ‐7.593 12.90388 7.593 ‐7.594 12.85968 7.594 ‐7.594 12.74732 7.594

‐8.012 12.988 8.012 ‐8.016 13.00386 8.016 ‐8.015 12.99663 8.015 ‐8.017 13.00706 8.017 ‐8.018 13.00801 8.018 ‐8.019 12.99219 8.019 ‐8.02 12.97204 8.02 ‐8.021 12.94382 8.021 ‐8.021 12.90773 8.021 ‐8.022 12.86354 8.022 ‐8.022 12.753 8.022

‐8.44 13.001 8.44 ‐8.445 13.00036 8.445 ‐8.444 13.00573 8.444 ‐8.445 13.01823 8.445 ‐8.447 13.00901 8.447 ‐8.448 12.99665 8.448 ‐8.448 12.97478 8.448 ‐8.449 12.94708 8.449 ‐8.45 12.91129 8.45 ‐8.45 12.86765 8.45 ‐8.45 12.75754 8.45

‐8.869 12.995 8.869 ‐8.873 13.00496 8.873 ‐8.872 13.00642 8.872 ‐8.874 13.01512 8.874 ‐8.875 13.01004 8.875 ‐8.876 12.99899 8.876 ‐8.877 12.97762 8.877 ‐8.877 12.95221 8.877 ‐8.878 12.91974 8.878 ‐8.878 12.87825 8.878 ‐8.878 12.77073 8.878

‐9.298 12.993 9.298 ‐9.302 13.0076 9.302 ‐9.301 13.0069 9.301 ‐9.302 13.02526 9.302 ‐9.303 13.02352 9.303 ‐9.304 13.0172 9.304 ‐9.305 13.00156 9.305 ‐9.305 12.97626 9.305 ‐9.305 12.94337 9.305 ‐9.306 12.90215 9.306 ‐9.306 12.79529 9.306

‐9.726 13.018 9.726 ‐9.73 13.03447 9.73 ‐9.729 13.02593 9.729 ‐9.73 13.0487 9.73 ‐9.731 13.04813 9.731 ‐9.732 13.04131 9.732 ‐9.733 13.02542 9.733 ‐9.733 13.00109 9.733 ‐9.733 12.96836 9.733 ‐9.733 12.92731 9.733 ‐9.733 12.82055 9.733

‐10.154 13.043 10.154 ‐10.158 13.05936 10.158 ‐10.157 13.04923 10.157 ‐10.159 13.07054 10.159 ‐10.159 13.07231 10.159 ‐10.16 13.06576 10.16 ‐10.16 13.05294 10.16 ‐10.161 13.02613 10.161 ‐10.161 12.99339 10.161 ‐10.161 12.95192 10.161 ‐10.161 12.84528 10.161

‐10.583 13.064 10.583 ‐10.586 13.08248 10.586 ‐10.585 13.07725 10.585 ‐10.587 13.09417 10.587 ‐10.587 13.09616 10.587 ‐10.588 13.08975 10.588 ‐10.588 13.07802 10.588 ‐10.588 13.06516 10.588 ‐10.589 13.01757 10.589 ‐10.589 12.9763 10.589 ‐10.589 12.86936 10.589

‐11.011 13.087 11.011 ‐11.014 13.10558 11.014 ‐11.014 13.09749 11.014 ‐11.015 13.11741 11.015 ‐11.015 13.1196 11.015 ‐11.016 13.11509 11.016 ‐11.016 13.10125 11.016 ‐11.017 13.07374 11.017 ‐11.017 13.04123 11.017 ‐11.017 13.00011 11.017 ‐11.017 12.89303 11.017

‐11.439 13.109 11.439 ‐11.442 13.12885 11.442 ‐11.442 13.11888 11.442 ‐11.443 13.14029 11.443 ‐11.444 13.14263 11.444 ‐11.444 13.13771 11.444 ‐11.444 13.12402 11.444 ‐11.445 13.09679 11.445 ‐11.445 13.06411 11.445 ‐11.445 13.02282 11.445 ‐11.444 12.91563 11.444

‐11.867 13.131 11.867 ‐11.87 13.1526 11.87 ‐11.87 13.14363 11.87 ‐11.871 13.16136 11.871 ‐11.872 13.1651 11.872 ‐11.872 13.16024 11.872 ‐11.873 13.14342 11.873 ‐11.873 13.11963 11.873 ‐11.873 13.087 11.873 ‐11.873 13.04568 11.873 ‐11.872 12.93845 11.872

‐12.295 13.153 12.295 ‐12.299 13.17301 12.299 ‐12.298 13.16365 12.298 ‐12.299 13.18374 12.299 ‐12.3 13.18711 12.3 ‐12.3 13.18219 12.3 ‐12.301 13.16569 12.301 ‐12.301 13.14177 12.301 ‐12.301 13.10891 12.301 ‐12.301 13.06765 12.301 ‐12.3 12.96035 12.3

‐12.724 13.175 12.724 ‐12.727 13.1956 12.727 ‐12.726 13.18655 12.726 ‐12.727 13.20532 12.727 ‐12.728 13.20855 12.728 ‐12.728 13.2036 12.728 ‐12.728 13.19424 12.728 ‐12.729 13.16343 12.729 ‐12.729 13.13065 12.729 ‐12.729 13.08938 12.729 ‐12.728 12.98131 12.728

‐13.152 13.197 13.152 ‐13.155 13.21495 13.155 ‐13.155 13.20743 13.155 ‐13.156 13.22661 13.156 ‐13.156 13.22966 13.156 ‐13.156 13.2247 13.156 ‐13.156 13.21502 13.156 ‐13.157 13.1842 13.157 ‐13.157 13.15159 13.157 ‐13.157 13.11025 13.157 ‐13.156 13.0026 13.156

‐13.58 13.216 13.58 ‐13.583 13.23688 13.583 ‐13.583 13.22785 13.583 ‐13.584 13.24713 13.584 ‐13.584 13.2502 13.584 ‐13.584 13.24513 13.584 ‐13.584 13.24179 13.584 ‐13.585 13.20515 13.585 ‐13.585 13.17243 13.585 ‐13.584 13.13086 13.584 ‐13.584 13.02306 13.584

‐14.008 13.236 14.008 ‐14.011 13.25502 14.011 ‐14.011 13.24788 14.011 ‐14.012 13.26734 14.012 ‐14.012 13.27273 14.012 ‐14.012 13.26536 14.012 ‐14.013 13.24904 14.013 ‐14.013 13.22535 14.013 ‐14.013 13.19265 14.013 ‐14.012 13.15113 14.012 ‐14.011 13.04285 14.011

‐14.437 13.255 14.437 ‐14.44 13.27471 14.44 ‐14.439 13.26609 14.439 ‐14.44 13.28712 14.44 ‐14.44 13.29022 14.44 ‐14.441 13.28516 14.441 ‐14.441 13.26913 14.441 ‐14.441 13.24498 14.441 ‐14.441 13.2122 14.441 ‐14.44 13.17064 14.44 ‐14.439 13.06642 14.439

‐14.865 13.275 14.865 ‐14.868 13.29483 14.868 ‐14.868 13.28533 14.868 ‐14.868 13.30645 14.868 ‐14.868 13.31174 14.868 ‐14.869 13.30441 14.869 ‐14.869 13.28849 14.869 ‐14.869 13.26465 14.869 ‐14.869 13.23154 14.869 ‐14.868 13.18988 14.868 ‐14.867 13.09012 14.867

‐15.293 13.294 15.293 ‐15.296 13.31378 15.296 ‐15.296 13.30425 15.296 ‐15.296 13.32544 15.296 ‐15.297 13.33068 15.297 ‐15.297 13.32346 15.297 ‐15.297 13.30748 15.297 ‐15.297 13.28352 15.297 ‐15.297 13.25056 15.297 ‐15.296 13.2086 15.296 ‐15.295 13.10669 15.295

‐15.721 13.312 15.721 ‐15.724 13.33234 15.724 ‐15.724 13.32401 15.724 ‐15.725 13.34416 15.725 ‐15.725 13.34927 15.725 ‐15.725 13.34258 15.725 ‐15.725 13.33345 15.725 ‐15.725 13.30194 15.725 ‐15.725 13.26891 15.725 ‐15.724 13.22716 15.724 ‐15.722 13.12394 15.722

‐16.15 13.33 16.15 ‐16.153 13.35059 16.153 ‐16.152 13.34227 16.152 ‐16.153 13.36241 16.153 ‐16.153 13.36748 16.153 ‐16.153 13.36075 16.153 ‐16.153 13.3443 16.153 ‐16.153 13.32022 16.153 ‐16.153 13.28712 16.153 ‐16.152 13.24521 16.152 ‐16.15 13.13993 16.15

‐16.578 13.348 16.578 ‐16.581 13.36855 16.581 ‐16.581 13.35852 16.581 ‐16.581 13.3803 16.581 ‐16.581 13.38531 16.581 ‐16.581 13.37876 16.581 ‐16.581 13.36236 16.581 ‐16.581 13.33809 16.581 ‐16.581 13.30469 16.581 ‐16.58 13.26276 16.58 ‐16.578 13.15729 16.578

‐17.006 13.366 17.006 ‐17.009 13.3861 17.009 ‐17.009 13.37757 17.009 ‐17.009 13.39793 17.009 ‐17.009 13.40173 17.009 ‐17.009 13.39931 17.009 ‐17.009 13.37986 17.009 ‐17.009 13.35551 17.009 ‐17.009 13.32223 17.009 ‐17.008 13.28001 17.008 ‐17.006 13.17403 17.006

‐17.435 13.383 17.435 ‐17.437 13.40334 17.437 ‐17.437 13.39404 17.437 ‐17.438 13.4152 17.438 ‐17.438 13.41903 17.438 ‐17.437 13.4165 17.437 ‐17.437 13.39706 17.437 ‐17.437 13.37262 17.437 ‐17.437 13.33914 17.437 ‐17.436 13.29652 17.436 ‐17.434 13.18929 17.434

‐17.863 13.4 17.863 ‐17.866 13.42028 17.866 ‐17.865 13.41863 17.865 ‐17.866 13.43194 17.866 ‐17.866 13.43552 17.866 ‐17.866 13.43216 17.866 ‐17.866 13.41279 17.866 ‐17.865 13.38796 17.865 ‐17.865 13.35417 17.865 ‐17.864 13.31213 17.864 ‐17.862 13.20221 17.862

‐18.291 13.416 18.291 ‐18.294 13.43636 18.294 ‐18.294 13.42997 18.294 ‐18.294 13.4478 18.294 ‐18.294 13.45119 18.294 ‐18.294 13.4475 18.294 ‐18.294 13.42814 18.294 ‐18.293 13.40304 18.293 ‐18.293 13.36967 18.293 ‐18.292 13.32715 18.292 ‐18.29 13.21555 18.29

‐18.719 13.433 18.719 ‐18.722 13.45158 18.722 ‐18.722 13.44296 18.722 ‐18.722 13.46325 18.722 ‐18.722 13.46636 18.722 ‐18.722 13.46254 18.722 ‐18.722 13.44322 18.722 ‐18.722 13.41822 18.722 ‐18.721 13.3845 18.721 ‐18.721 13.34207 18.721 ‐18.718 13.22952 18.718

‐19.148 13.448 19.148 ‐19.15 13.46666 19.15 ‐19.15 13.45791 19.15 ‐19.151 13.47824 19.151 ‐19.15 13.48127 19.15 ‐19.15 13.48154 19.15 ‐19.15 13.45779 19.15 ‐19.15 13.43303 19.15 ‐19.149 13.39892 19.149 ‐19.149 13.35623 19.149 ‐19.146 13.243 19.146

‐19.576 13.463 19.576 ‐19.579 13.48146 19.579 ‐19.579 13.47267 19.579 ‐19.579 13.4929 19.579 ‐19.579 13.49677 19.579 ‐19.579 13.48787 19.579 ‐19.578 13.47226 19.578 ‐19.578 13.44724 19.578 ‐19.577 13.4132 19.577 ‐19.577 13.37034 19.577 ‐19.574 13.25632 19.574

‐20.004 13.477 20.004 ‐20.007 13.49585 20.007 ‐20.007 13.48714 20.007 ‐20.007 13.50724 20.007 ‐20.007 13.51013 20.007 ‐20.006 13.50959 20.006 ‐20.006 13.48646 20.006 ‐20.006 13.46122 20.006 ‐20.005 13.42698 20.005 ‐20.005 13.38389 20.005 ‐20.003 13.26461 20.003

‐20.433 13.492 20.433 ‐20.435 13.50995 20.435 ‐20.435 13.50128 20.435 ‐20.435 13.52128 20.435 ‐20.435 13.52382 20.435 ‐20.435 13.5164 20.435 ‐20.435 13.50008 20.435 ‐20.434 13.47488 20.434 ‐20.434 13.44051 20.434 ‐20.433 13.39743 20.433 ‐20.43 13.28694 20.43

‐20.861 13.505 20.861 ‐20.864 13.52374 20.864 ‐20.864 13.51509 20.864 ‐20.864 13.53503 20.864 ‐20.863 13.53765 20.863 ‐20.863 13.53001 20.863 ‐20.863 13.51359 20.863 ‐20.862 13.48817 20.862 ‐20.862 13.45363 20.862 ‐20.861 13.41051 20.861 ‐20.858 13.2985 20.858

‐21.289 13.519 21.289 ‐21.292 13.53729 21.292 ‐21.292 13.52864 21.292 ‐21.292 13.54831 21.292 ‐21.292 13.55107 21.292 ‐21.291 13.54325 21.291 ‐21.291 13.52677 21.291 ‐21.291 13.50125 21.291 ‐21.29 13.46667 21.29 ‐21.289 13.42342 21.289 ‐21.286 13.30994 21.286

‐21.718 13.532 21.718 ‐21.72 13.55009 21.72 ‐21.72 13.54174 21.72 ‐21.72 13.56285 21.72 ‐21.72 13.5644 21.72 ‐21.719 13.56048 21.719 ‐21.719 13.5396 21.719 ‐21.719 13.51395 21.719 ‐21.718 13.47921 21.718 ‐21.716 13.47654 21.716 ‐21.714 13.32173 21.714

‐22.146 13.545 22.146 ‐22.149 13.56285 22.149 ‐22.149 13.55416 22.149 ‐22.148 13.57473 22.148 ‐22.148 13.57689 22.148 ‐22.148 13.56862 22.148 ‐22.147 13.55202 22.147 ‐22.147 13.52631 22.147 ‐22.146 13.49143 22.146 ‐22.144 13.48716 22.144 ‐22.142 13.33315 22.142

‐22.575 13.557 22.575 ‐22.577 13.57523 22.577 ‐22.577 13.56654 22.577 ‐22.577 13.58689 22.577 ‐22.576 13.58902 22.576 ‐22.576 13.58487 22.576 ‐22.576 13.56413 22.576 ‐22.575 13.53826 22.575 ‐22.574 13.50347 22.574 ‐22.573 13.45881 22.573 ‐22.571 13.34428 22.571

‐23.003 13.569 23.003 ‐23.005 13.58704 23.005 ‐23.005 13.57859 23.005 ‐23.005 13.59877 23.005 ‐23.005 13.60085 23.005 ‐23.004 13.59245 23.004 ‐23.004 13.5758 23.004 ‐23.003 13.54991 23.003 ‐23.003 13.51503 23.003 ‐23.001 13.47392 23.001 ‐22.999 13.3554 22.999

‐23.431 13.58 23.431 ‐23.434 13.59874 23.434 ‐23.434 13.59014 23.434 ‐23.433 13.61026 23.433 ‐23.433 13.61435 23.433 ‐23.433 13.60389 23.433 ‐23.432 13.58721 23.432 ‐23.432 13.56126 23.432 ‐23.431 13.52633 23.431 ‐23.429 13.49956 23.429 ‐23.427 13.36617 23.427

‐23.86 13.592 23.86 ‐23.862 13.61005 23.862 ‐23.862 13.60151 23.862 ‐23.862 13.62147 23.862 ‐23.861 13.62546 23.861 ‐23.861 13.62646 23.861 ‐23.86 13.59824 23.86 ‐23.86 13.57216 23.86 ‐23.859 13.53711 23.859 ‐23.857 13.49528 23.857 ‐23.855 13.37659 23.855

‐24.288 13.603 24.288 ‐24.29 13.62099 24.29 ‐24.29 13.61246 24.29 ‐24.29 13.63232 24.29 ‐24.29 13.63624 24.29 ‐24.289 13.6258 24.289 ‐24.289 13.609 24.289 ‐24.288 13.58294 24.288 ‐24.287 13.5477 24.287 ‐24.285 13.51978 24.285 ‐24.283 13.38682 24.283

‐24.716 13.613 24.716 ‐24.719 13.63165 24.719 ‐24.719 13.62313 24.719 ‐24.718 13.64294 24.718 ‐24.718 13.64677 24.718 ‐24.718 13.63637 24.718 ‐24.717 13.61939 24.717 ‐24.716 13.59325 24.716 ‐24.715 13.55804 24.715 ‐24.714 13.51552 24.714 ‐24.711 13.40217 24.711

‐25.145 13.624 25.145 ‐25.147 13.64205 25.147 ‐25.147 13.63355 25.147 ‐25.147 13.65328 25.147 ‐25.146 13.65698 25.146 ‐25.146 13.6466 25.146 ‐25.145 13.62955 25.145 ‐25.144 13.6034 25.144 ‐25.144 13.56802 25.144 ‐25.142 13.53915 25.142 ‐25.139 13.41156 25.139

‐25.573 13.634 25.573 ‐25.575 13.65205 25.575 ‐25.576 13.64355 25.576 ‐25.575 13.66322 25.575 ‐25.574 13.66684 25.574 ‐25.574 13.65653 25.574 ‐25.573 13.6395 25.573 ‐25.573 13.61309 25.573 ‐25.572 13.57789 25.572 ‐25.57 13.53468 25.57 ‐25.567 13.42955 25.567

‐26.002 13.644 26.002 ‐26.004 13.662 26.004 ‐26.004 13.65355 26.004 ‐26.003 13.67386 26.003 ‐26.003 13.67665 26.003 ‐26.002 13.66617 26.002 ‐26.002 13.64903 26.002 ‐26.001 13.62279 26.001 ‐26 13.58789 26 ‐25.998 13.54874 25.998 ‐25.995 13.42358 25.995

‐26.43 13.653 26.43 ‐26.432 13.67156 26.432 ‐26.432 13.6631 26.432 ‐26.432 13.68268 26.432 ‐26.431 13.68605 26.431 ‐26.431 13.67564 26.431 ‐26.43 13.6585 26.43 ‐26.429 13.63189 26.429 ‐26.428 13.61346 26.428 ‐26.426 13.55782 26.426 ‐26.423 13.4469 26.423

‐26.858 13.663 26.858 ‐26.861 13.68099 26.861 ‐26.861 13.67252 26.861 ‐26.86 13.69271 26.86 ‐26.859 13.69527 26.859 ‐26.859 13.68496 26.859 ‐26.858 13.66758 26.858 ‐26.857 13.64123 26.857 ‐26.856 13.62181 26.856 ‐26.855 13.5666 26.855 ‐26.852 13.44653 26.852

‐27.287 13.672 27.287 ‐27.289 13.69002 27.289 ‐27.289 13.68137 27.289 ‐27.288 13.70172 27.288 ‐27.288 13.70712 27.288 ‐27.287 13.69393 27.287 ‐27.287 13.67655 27.287 ‐27.286 13.65006 27.286 ‐27.284 13.62171 27.284 ‐27.283 13.58328 27.283 ‐27.28 13.46312 27.28

‐27.715 13.681 27.715 ‐27.717 13.69909 27.717 ‐27.718 13.69043 27.718 ‐27.717 13.71004 27.717 ‐27.716 13.71315 27.716 ‐27.716 13.70252 27.716 ‐27.715 13.68535 27.715 ‐27.714 13.65874 27.714 ‐27.712 13.62997 27.712 ‐27.711 13.5913 27.711 ‐27.708 13.4629 27.708

‐28.144 13.69 28.144 ‐28.146 13.70779 28.146 ‐28.146 13.69918 28.146 ‐28.145 13.71867 28.145 ‐28.145 13.7217 28.145 ‐28.144 13.71129 28.144 ‐28.143 13.69372 28.143 ‐28.142 13.66706 28.142 ‐28.141 13.64595 28.141 ‐28.139 13.59904 28.139 ‐28.136 13.47887 28.136

‐28.572 13.698 28.572 ‐28.574 13.7163 28.574 ‐28.574 13.70769 28.574 ‐28.574 13.7271 28.574 ‐28.573 13.73008 28.573 ‐28.572 13.71962 28.572 ‐28.571 13.70219 28.571 ‐28.571 13.67538 28.571 ‐28.569 13.65374 28.569 ‐28.567 13.60669 28.567 ‐28.564 13.47853 28.564

‐29.001 13.706 29.001 ‐29.003 13.72566 29.003 ‐29.003 13.71605 29.003 ‐29.002 13.73538 29.002 ‐29.001 13.73817 29.001 ‐29.001 13.72782 29.001 ‐29 13.71034 29 ‐28.999 13.68357 28.999 ‐28.997 13.66141 28.997 ‐28.996 13.61427 28.996 ‐28.992 13.49408 28.992

‐29.429 13.715 29.429 ‐29.431 13.73329 29.431 ‐29.431 13.72423 29.431 ‐29.43 13.74349 29.43 ‐29.43 13.74416 29.43 ‐29.429 13.73584 29.429 ‐29.428 13.71822 29.428 ‐29.427 13.69138 29.427 ‐29.425 13.66881 29.425 ‐29.424 13.62174 29.424 ‐29.421 13.50116 29.421

‐29.857 13.723 29.857 ‐29.859 13.74182 29.859 ‐29.86 13.73218 29.86 ‐29.859 13.75139 29.859 ‐29.858 13.75406 29.858 ‐29.857 13.74367 29.857 ‐29.856 13.72598 29.856 ‐29.855 13.69914 29.855 ‐29.853 13.67608 29.853 ‐29.852 13.62159 29.852 ‐29.849 13.50801 29.849

‐30.286 13.73 30.286 ‐30.288 13.74905 30.288 ‐30.288 13.74001 30.288 ‐30.287 13.75913 30.287 ‐30.286 13.76284 30.286 ‐30.286 13.75134 30.286 ‐30.285 13.73358 30.285 ‐30.284 13.70665 30.284 ‐30.282 13.68328 30.282 ‐30.28 13.63629 30.28 ‐30.277 13.51467 30.277

‐30.714 13.738 30.714 ‐30.716 13.75662 30.716 ‐30.717 13.74766 30.717 ‐30.716 13.76673 30.716 ‐30.715 13.77031 30.715 ‐30.714 13.75882 30.714 ‐30.713 13.74104 30.713 ‐30.712 13.7139 30.712 ‐30.71 13.69019 30.71 ‐30.709 13.64319 30.709 ‐30.705 13.5215 30.705

‐31.143 13.745 31.143 ‐31.145 13.76408 31.145 ‐31.145 13.75514 31.145 ‐31.144 13.77437 31.144 ‐31.143 13.77767 31.143 ‐31.142 13.76611 31.142 ‐31.141 13.7483 31.141 ‐31.14 13.72128 31.14 ‐31.138 13.69717 31.138 ‐31.137 13.64985 31.137 ‐31.133 13.52805 31.133

‐31.571 13.752 31.571 ‐31.573 13.77139 31.573 ‐31.573 13.7625 31.573 ‐31.572 13.78174 31.572 ‐31.571 13.78484 31.571 ‐31.571 13.7733 31.571 ‐31.57 13.75538 31.57 ‐31.569 13.72831 31.569 ‐31.567 13.70389 31.567 ‐31.565 13.6565 31.565 ‐31.562 13.5346 31.562

‐32 13.759 32 ‐32.001 13.7785 32.001 ‐32.002 13.76967 32.002 ‐32.001 13.78886 32.001 ‐32 13.78906 32 ‐31.999 13.78032 31.999 ‐31.998 13.76233 31.998 ‐31.997 13.73526 31.997 ‐31.995 13.71046 31.995 ‐31.993 13.66308 31.993 ‐31.99 13.54046 31.99

‐32.428 13.766 32.428 ‐32.43 13.78541 32.43 ‐32.43 13.77658 32.43 ‐32.429 13.79574 32.429 ‐32.428 13.79868 32.428 ‐32.427 13.78726 32.427 ‐32.426 13.7692 32.426 ‐32.425 13.74215 32.425 ‐32.423 13.7169 32.423 ‐32.421 13.68295 32.421 ‐32.418 13.56069 32.418

‐32.857 13.773 32.857 ‐32.858 13.79233 32.858 ‐32.859 13.78343 32.859 ‐32.857 13.80399 32.857 ‐32.857 13.80252 32.857 ‐32.856 13.79396 32.856 ‐32.855 13.77593 32.855 ‐32.853 13.74917 32.853 ‐32.851 13.72319 32.851 ‐32.85 13.67535 32.85 ‐32.846 13.55271 32.846

‐33.285 13.78 33.285 ‐33.287 13.79921 33.287 ‐33.287 13.79036 33.287 ‐33.286 13.81083 33.286 ‐33.285 13.80934 33.285 ‐33.284 13.80044 33.284 ‐33.283 13.78244 33.283 ‐33.281 13.76843 33.281 ‐33.28 13.72946 33.28 ‐33.278 13.68148 33.278 ‐33.28 13.23334 33.28

‐33.714 13.787 33.714 ‐33.715 13.80586 33.715 ‐33.716 13.79707 33.716 ‐33.714 13.81741 33.714 ‐33.713 13.81598 33.713 ‐33.712 13.8069 33.712 ‐33.711 13.78874 33.711 ‐33.71 13.77425 33.71 ‐33.708 13.73551 33.708 ‐33.706 13.68758 33.706 ‐33.724 12.41947 33.724

‐34.142 13.793 34.142 ‐34.144 13.81231 34.144 ‐34.144 13.80443 34.144 ‐34.143 13.82386 34.143 ‐34.142 13.83 34.142 ‐34.141 13.8134 34.141 ‐34.14 13.79506 34.14 ‐34.138 13.7801 34.138 ‐34.136 13.74133 34.136 ‐34.138 13.47699 34.138 ‐34.162 11.82337 34.162

‐34.57 13.8 34.57 ‐34.572 13.81865 34.572 ‐34.572 13.81038 34.572 ‐34.571 13.83012 34.571 ‐34.57 13.82859 34.57 ‐34.569 13.8196 34.569 ‐34.568 13.80137 34.568 ‐34.566 13.78603 34.566 ‐34.566 13.66329 34.566 ‐34.582 12.60506 34.582 ‐34.599 11.28179 34.599

‐34.999 13.806 34.999 ‐35 13.82546 35 ‐35.001 13.81719 35.001 ‐34.999 13.83631 34.999 ‐34.999 13.83474 34.999 ‐34.998 13.82576 34.998 ‐34.996 13.80735 34.996 ‐34.995 13.79164 34.995 ‐35.009 12.81518 35.009 ‐35.02 11.99643 35.02 ‐35.034 10.79114 35.034

‐35.427 13.812 35.427 ‐35.429 13.83082 35.429 ‐35.429 13.82284 35.429 ‐35.428 13.84239 35.428 ‐35.427 13.84075 35.427 ‐35.426 13.83173 35.426 ‐35.425 13.81335 35.425 ‐35.436 13.03984 35.436 ‐35.448 12.16251 35.448 ‐35.457 11.46722 35.457 ‐35.472 10.23138 35.472

‐35.856 13.818 35.856 ‐35.857 13.83711 35.857 ‐35.858 13.82886 35.858 ‐35.856 13.84836 35.856 ‐35.855 13.84671 35.855 ‐35.854 13.83757 35.854 ‐35.861 13.35707 35.861 ‐35.875 12.37621 35.875 ‐35.884 11.63067 35.884 ‐35.892 10.97848 35.892 ‐35.906 9.84185 35.906

‐36.284 13.824 36.284 ‐36.286 13.84299 36.286 ‐36.286 13.83472 36.286 ‐36.285 13.85423 36.285 ‐36.284 13.85258 36.284 ‐36.284 13.77719 36.284 ‐36.3 12.68936 36.3 ‐36.312 11.82404 36.312 ‐36.32 11.17246 36.32 ‐36.328 10.49677 36.328 ‐36.342 9.35034 36.342

‐36.713 13.83 36.713 ‐36.714 13.84878 36.714 ‐36.715 13.84065 36.715 ‐36.713 13.85991 36.713 ‐36.712 13.85829 36.712 ‐36.724 13.05264 36.724 ‐36.738 12.08536 36.738 ‐36.746 11.38457 36.746 ‐36.756 10.65862 36.756 ‐36.764 10.0196 36.764 ‐36.786 8.47824 36.786

‐37.141 13.836 37.141 ‐37.143 13.85424 37.143 ‐37.143 13.84635 37.143 ‐37.142 13.86561 37.142 ‐37.147 13.47643 37.147 ‐37.163 12.39359 37.163 ‐37.173 11.61607 37.173 ‐37.182 10.87636 37.182 ‐37.193 10.11582 37.193 ‐37.199 9.57369 37.199 ‐37.226 7.77139 37.226

‐37.57 13.841 37.57 ‐37.571 13.8601 37.571 ‐37.572 13.85201 37.572 ‐37.57 13.87112 37.57 ‐37.586 12.7997 37.586 ‐37.6 11.8494 37.6 ‐37.609 11.1134 37.609 ‐37.622 10.19689 37.622 ‐37.627 9.69697 37.627 ‐37.643 8.68389 37.643 ‐37.665 7.22753 37.665

‐37.998 13.847 37.998 ‐38 13.86565 38 ‐38 13.85749 38 ‐38.008 13.3014 38.008 ‐38.023 12.26105 38.023 ‐38.035 11.36042 38.035 ‐38.045 10.60364 38.045 ‐38.055 9.85373 38.055 ‐38.067 9.02784 38.067 ‐38.083 7.94994 38.083 ‐38.095 7.11275 38.095

‐38.427 13.852 38.427 ‐38.429 13.82545 38.429 ‐38.429 13.86298 38.429 ‐38.447 12.61343 38.447 ‐38.46 11.71605 38.46 ‐38.471 10.8906 38.471 ‐38.482 10.05676 38.482 ‐38.491 9.38208 38.491 ‐38.508 8.18953 38.508 ‐38.521 7.25342 38.521 ‐38.524 6.94269 38.524

‐38.855 13.858 38.855 ‐38.869 13.143 38.869 ‐38.858 13.80257 38.858 ‐38.884 12.06321 38.884 ‐38.896 11.2069 38.896 ‐38.911 10.17423 38.911 ‐38.917 9.62725 38.917 ‐38.934 8.46592 38.934 ‐38.948 7.45964 38.948 ‐38.952 7.14634 38.952 ‐38.954 6.80079 38.954

‐39.286 13.739 39.286 ‐39.305 12.6458 39.305 ‐39.298 13.09765 39.298 ‐39.321 11.50625 39.321 ‐39.332 10.6735 39.332 ‐39.343 9.84196 39.343 ‐39.358 8.77998 39.358 ‐39.373 7.71541 39.373 ‐39.38 7.19963 39.38 ‐39.381 7.02033 39.381 ‐39.384 6.63465 39.384

‐39.725 13.074 39.725 ‐39.744 11.93177 39.744 ‐39.735 12.53773 39.735 ‐39.756 11.07196 39.756 ‐39.77 10.07056 39.77 ‐39.778 9.38904 39.778 ‐39.798 8.02512 39.798 ‐39.808 7.27218 39.808 ‐39.81 7.05429 39.81 ‐39.811 6.84982 39.811 ‐39.813 6.48233 39.813

‐40.162 12.566 40.162 ‐40.18 11.43015 40.18 ‐40.173 11.9528 40.173 ‐40.193 10.52266 40.193 ‐40.204 9.67841 40.204 ‐40.221 8.4688 40.221 ‐40.236 7.32277 40.236 ‐40.238 7.12639 40.238 ‐40.24 6.91073 40.24 ‐40.241 6.70875 40.241 ‐40.243 6.34557 40.243

‐40.6 11.908 40.6 ‐40.616 10.90898 40.616 ‐40.612 11.26118 40.612 ‐40.629 9.98302 40.629 ‐40.642 9.03313 40.642 ‐40.66 7.72499 40.66 ‐40.666 7.17631 40.666 ‐40.668 6.9541 40.668 ‐40.669 6.75465 40.669 ‐40.671 6.55536 40.671 ‐40.673 6.19808 40.673

‐41.039 11.219 41.039 ‐41.053 10.37057 41.053 ‐41.046 10.88015 41.046 ‐41.063 9.58282 41.063 ‐41.082 8.19064 41.082 ‐41.094 7.25754 41.094 ‐41.096 7.02349 41.096 ‐41.098 6.81101 41.098 ‐41.099 6.61436 41.099 ‐41.1 6.4174 41.1 ‐41.102 6.07665 41.102

‐41.473 10.844 41.473 ‐41.488 9.92358 41.488 ‐41.483 10.30419 41.483 ‐41.504 8.69224 41.504 ‐41.52 7.47461 41.52 ‐41.524 7.11366 41.524 ‐41.526 6.87827 41.526 ‐41.527 6.65682 41.527 ‐41.529 6.46164 41.529 ‐41.53 6.28151 41.53 ‐41.532 5.94455 41.532

‐41.91 10.315 41.91 ‐41.922 9.47211 41.922 ‐41.917 9.897 41.917 ‐41.943 7.94047 41.943 ‐41.952 7.20281 41.952 ‐41.954 6.95444 41.954 ‐41.955 6.74956 41.955 ‐41.957 6.53003 41.957 ‐41.958 6.3253 41.958 ‐41.959 6.14543 41.959 ‐41.961 5.82632 41.961

‐42.344 9.871 42.344 ‐42.363 8.57371 42.363 ‐42.351 9.49251 42.351 ‐42.379 7.30051 42.379 ‐42.381 7.05626 42.381 ‐42.383 6.81145 42.383 ‐42.385 6.59463 42.385 ‐42.387 6.39153 42.387 ‐42.388 6.20167 42.388 ‐42.389 6.02495 42.389 ‐42.391 5.70944 42.391

‐42.779 9.427 42.779 ‐42.802 7.82916 42.802 ‐42.792 8.55284 42.792 ‐42.809 7.14215 42.809 ‐42.811 6.91227 42.811 ‐42.813 6.68391 42.813 ‐42.815 6.45563 42.815 ‐42.816 6.26799 42.816 ‐42.817 6.08035 42.817 ‐42.818 5.89248 42.818 ‐42.82 5.59398 42.82

‐43.22 8.509 43.22 ‐43.237 7.24921 43.237 ‐43.231 7.80755 43.231 ‐43.239 7.00937 43.239 ‐43.241 6.75499 43.241 ‐43.243 6.52923 43.243 ‐43.244 6.33107 43.244 ‐43.246 6.11902 43.246 ‐43.247 5.93413 43.247 ‐43.248 5.77431 43.248 ‐43.249 5.47938 43.249

‐43.658 7.77 43.658 ‐43.666 7.10336 43.666 ‐43.665 7.2354 43.665 ‐43.669 6.8509 43.669 ‐43.671 6.62813 43.671 ‐43.672 6.40423 43.672 ‐43.674 6.20804 43.674 ‐43.675 5.9981 43.675 ‐43.676 5.81504 43.676 ‐43.677 5.65726 43.677 ‐43.679 5.36588 43.679

‐44.093 7.216 44.093 ‐44.096 6.97247 44.096 ‐44.095 7.07672 44.095 ‐44.098 6.72321 44.098 ‐44.1 6.48794 44.1 ‐44.102 6.28029 44.102 ‐44.103 6.08619 44.103 ‐44.105 5.8784 44.105 ‐44.106 5.69742 44.106 ‐44.107 5.54153 44.107 ‐44.108 5.25374 44.108

‐44.522 7.076 44.522 ‐44.526 6.81453 44.526 ‐44.525 6.94523 44.525 ‐44.528 6.58191 44.528 ‐44.53 6.363 44.53 ‐44.531 6.14488 44.531 ‐44.533 5.96546 44.533 ‐44.534 5.75993 44.534 ‐44.535 5.6063 44.535 ‐44.536 5.43932 44.536 ‐44.538 5.14277 44.538

‐44.952 6.932 44.952 ‐44.956 6.68693 44.956 ‐44.954 6.80259 44.954 ‐44.957 6.45601 44.957 ‐44.959 6.23932 44.959 ‐44.961 6.02397 44.961 ‐44.962 5.84574 44.962 ‐44.963 5.66603 44.963 ‐44.965 5.49066 44.965 ‐44.966 5.32569 44.966 ‐44.967 5.04499 44.967

‐45.382 6.802 45.382 ‐45.385 6.55953 45.385 ‐45.384 6.67445 45.384 ‐45.387 6.33139 45.387 ‐45.389 6.11688 45.389 ‐45.39 5.91563 45.39 ‐45.392 5.72728 45.392 ‐45.393 5.55184 45.393 ‐45.394 5.37624 45.394 ‐45.395 5.23797 45.395 ‐45.404 4.9361 45.404

‐45.811 6.675 45.811 ‐45.815 6.43259 45.815 ‐45.814 6.54705 45.814 ‐45.817 6.20806 45.817 ‐45.818 5.99564 45.818 ‐45.82 5.7962 45.82 ‐45.821 5.61011 45.821 ‐45.822 5.43652 45.822 ‐45.823 5.27535 45.823 ‐45.824 5.12639 45.824 ‐45.833 4.85142 45.833

‐46.241 6.548 46.241 ‐46.244 6.30947 46.244 ‐46.243 6.42164 46.243 ‐46.246 6.08582 46.246 ‐46.248 5.8757 46.248 ‐46.249 5.67826 46.249 ‐46.251 5.50671 46.251 ‐46.252 5.33489 46.252 ‐46.253 5.18792 46.253 ‐46.253 5.02813 46.253 ‐46.263 4.7567 46.263

‐46.671 6.422 46.671 ‐46.674 6.18638 46.674 ‐46.673 6.29734 46.673 ‐46.676 5.96608 46.676 ‐46.677 5.7695 46.677 ‐46.679 5.58708 46.679 ‐46.68 5.39165 46.68 ‐46.681 5.24669 46.681 ‐46.682 5.07649 46.682 ‐46.691 4.91874 46.691 ‐46.692 4.67403 46.692

‐47.1 6.298 47.1 ‐47.103 6.06397 47.103 ‐47.102 6.17471 47.102 ‐47.105 5.85789 47.105 ‐47.107 5.65141 47.107 ‐47.108 5.47098 47.108 ‐47.109 5.30292 47.109 ‐47.11 5.13447 47.11 ‐47.119 4.97846 47.119 ‐47.12 4.83394 47.12 ‐47.121 4.57995 47.121

‐47.53 6.175 47.53 ‐47.533 5.94444 47.533 ‐47.532 6.06554 47.532 ‐47.535 5.73912 47.535 ‐47.536 5.56046 47.536 ‐47.537 5.36873 47.537 ‐47.539 5.20222 47.539 ‐47.54 5.03564 47.54 ‐47.548 4.89308 47.548 ‐47.55 4.73865 47.55 ‐47.551 4.49882 47.551

‐47.959 6.053 47.959 ‐47.962 5.84988 47.962 ‐47.961 5.94434 47.961 ‐47.964 5.64716 47.964 ‐47.965 5.45715 47.965 ‐47.967 5.27984 47.967 ‐47.968 5.11491 47.968 ‐47.977 4.94989 47.977 ‐47.978 4.79691 47.978 ‐47.979 4.65548 47.979 ‐47.98 4.40717 47.98

‐48.389 5.945 48.389 ‐48.392 5.7442 48.392 ‐48.391 5.85116 48.391 ‐48.393 5.54297 48.393 ‐48.395 5.36781 48.395 ‐48.396 5.17928 48.396 ‐48.397 5.01607 48.397 ‐48.406 4.85263 48.406 ‐48.407 4.71322 48.407 ‐48.408 4.58475 48.408 ‐48.409 4.33864 48.409

‐48.818 5.852 48.818 ‐48.821 5.626 48.821 ‐48.82 5.73214 48.82 ‐48.822 5.45295 48.822 ‐48.824 5.25381 48.824 ‐48.825 5.09206 48.825 ‐48.834 4.93032 48.834 ‐48.836 4.76848 48.836 ‐48.837 4.61842 48.837 ‐48.837 4.49164 48.837 ‐48.838 4.25969 48.838

‐49.248 5.733 49.248 ‐49.25 5.53544 49.25 ‐49.25 5.62733 49.25 ‐49.252 5.35049 49.252 ‐49.253 5.15481 49.253 ‐49.254 4.9933 49.254 ‐49.264 4.83318 49.264 ‐49.265 4.67302 49.265 ‐49.266 4.54788 49.266 ‐49.266 4.41079 49.266 ‐49.267 4.19243 49.267

‐49.677 5.628 49.677 ‐49.68 5.43208 49.68 ‐49.679 5.5366 49.679 ‐49.681 5.26155 49.681 ‐49.683 5.07829 49.683 ‐49.692 4.90759 49.692 ‐49.693 4.74896 49.693 ‐49.694 4.60192 49.694 ‐49.695 4.46641 49.695 ‐49.695 4.34196 49.695 ‐49.696 4.10381 49.696

‐50.106 5.537 50.106 ‐50.109 5.34262 50.109 ‐50.108 5.43328 50.108 ‐50.11 5.16092 50.11 ‐50.112 4.9918 50.112 ‐50.121 4.81057 50.121 ‐50.123 4.65359 50.123 ‐50.123 4.5198 50.123 ‐50.124 4.397 50.124 ‐50.125 4.27335 50.125 ‐50.125 4.03763 50.125

‐50.536 5.434 50.536 ‐50.538 5.24125 50.538 ‐50.538 5.34381 50.538 ‐50.54 5.07369 50.54 ‐50.549 4.89386 50.549 ‐50.551 4.73832 50.551 ‐50.552 4.58254 50.552 ‐50.552 4.44988 50.552 ‐50.553 4.30554 50.553 ‐50.554 4.18372 50.554 ‐50.554 3.97205 50.554

‐50.965 5.344 50.965 ‐50.968 5.1532 50.968 ‐50.967 5.2424 50.967 ‐50.969 4.97493 50.969 ‐50.979 4.8089 50.979 ‐50.98 4.65481 50.98 ‐50.981 4.50046 50.981 ‐50.982 4.35768 50.982 ‐50.982 4.23736 50.982 ‐50.983 4.11663 50.983 ‐50.983 3.9031 50.983

‐51.394 5.243 51.394 ‐51.397 5.07824 51.397 ‐51.396 5.16682 51.396 ‐51.406 4.88917 51.406 ‐51.408 4.7366 51.408 ‐51.409 4.58367 51.409 ‐51.41 4.43055 51.41 ‐51.411 4.28896 51.411 ‐51.411 4.16973 51.411 ‐51.412 4.05009 51.412 ‐51.412 3.86043 51.412

‐51.824 5.167 51.824 ‐51.826 4.97939 51.826 ‐51.825 5.07936 51.825 ‐51.836 4.81622 51.836 ‐51.837 4.64118 51.837 ‐51.838 4.48978 51.838 ‐51.839 4.36119 51.839 ‐51.84 4.2208 51.84 ‐51.84 4.09169 51.84 ‐51.841 3.98384 51.841 ‐51.842 3.76823 51.842

‐52.253 5.08 52.253 ‐52.264 4.89355 52.264 ‐52.255 4.98049 52.255 ‐52.265 4.72009 52.265 ‐52.266 4.57016 52.266 ‐52.267 4.41993 52.267 ‐52.268 4.2924 52.268 ‐52.269 4.15326 52.269 ‐52.269 4.02525 52.269 ‐52.27 3.9184 52.27 ‐52.27 3.70428 52.27

‐52.682 4.983 52.682 ‐52.693 4.82055 52.693 ‐52.692 4.89462 52.692 ‐52.695 4.64833 52.695 ‐52.696 4.49955 52.696 ‐52.697 4.35074 52.697 ‐52.697 4.20227 52.697 ‐52.698 4.08636 52.698 ‐52.698 3.95941 52.698 ‐52.699 3.85345 52.699 ‐52.699 3.65148 52.699

‐53.12 4.907 53.12 ‐53.123 4.72436 53.123 ‐53.122 4.82161 53.122 ‐53.124 4.57722 53.124 ‐53.125 4.41816 53.125 ‐53.125 4.28212 53.125 ‐53.126 4.13456 53.126 ‐53.126 4.01973 53.126 ‐53.127 3.8948 53.127 ‐53.127 3.78902 53.127 ‐53.128 3.58902 53.128

‐53.549 4.822 53.549 ‐53.552 4.65284 53.552 ‐53.551 4.74914 53.551 ‐53.553 4.49488 53.553 ‐53.554 4.34913 53.554 ‐53.554 4.2138 53.554 ‐53.555 4.06683 53.555 ‐53.555 3.95374 53.555 ‐53.556 3.8398 53.556 ‐53.556 3.72512 53.556 ‐53.557 3.52715 53.557

‐53.979 4.749 53.979 ‐53.981 4.58143 53.981 ‐53.98 4.65376 53.98 ‐53.982 4.42553 53.982 ‐53.983 4.28023 53.983 ‐53.983 4.1464 53.983 ‐53.984 4.00836 53.984 ‐53.984 3.88823 53.984 ‐53.985 3.77544 53.985 ‐53.985 3.66176 53.985 ‐53.986 3.46604 53.986

‐54.408 4.678 54.408 ‐54.41 4.51088 54.41 ‐54.409 4.58249 54.409 ‐54.411 4.35601 54.411 ‐54.411 4.21232 54.411 ‐54.412 4.07848 54.412 ‐54.412 3.95689 54.412 ‐54.413 3.82367 54.413 ‐54.413 3.71116 54.413 ‐54.414 3.61974 54.414 ‐54.414 3.42503 54.414

‐54.837 4.606 54.837 ‐54.839 4.44133 54.839 ‐54.839 4.51221 54.839 ‐54.84 4.28702 54.84 ‐54.84 4.14449 54.84 ‐54.841 4.01243 54.841 ‐54.841 3.89106 54.841 ‐54.842 3.75933 54.842 ‐54.842 3.64822 54.842 ‐54.842 3.55716 54.842 ‐54.843 3.36466 54.843

‐55.266 4.513 55.266 ‐55.268 4.37166 55.268 ‐55.268 4.44242 55.268 ‐55.269 4.21859 55.269 ‐55.269 4.07744 55.269 ‐55.27 3.94625 55.27 ‐55.27 3.82644 55.27 ‐55.27 3.71584 55.27 ‐55.271 3.60579 55.271 ‐55.271 3.49522 55.271 ‐55.272 3.31457 55.272

‐55.695 4.443 55.695 ‐55.697 4.30253 55.697 ‐55.696 4.37275 55.696 ‐55.697 4.15127 55.697 ‐55.698 4.02129 55.698 ‐55.698 3.88061 55.698 ‐55.699 3.76274 55.699 ‐55.699 3.6524 55.699 ‐55.7 3.54313 55.7 ‐55.7 3.44407 55.7 ‐55.701 3.25514 55.701

‐56.124 4.396 56.124 ‐56.126 4.23393 56.126 ‐56.125 4.3036 56.125 ‐56.126 4.09472 56.126 ‐56.127 3.95511 56.127 ‐56.127 3.83719 56.127 ‐56.128 3.70779 56.128 ‐56.128 3.5997 56.128 ‐56.128 3.49161 56.128 ‐56.129 3.38302 56.129 ‐56.129 3.21553 56.129

‐56.553 4.327 56.553 ‐56.555 4.16645 56.555 ‐56.554 4.23522 56.554 ‐56.555 4.0279 56.555 ‐56.556 3.88933 56.556 ‐56.556 3.77222 56.556 ‐56.556 3.64426 56.556 ‐56.557 3.53718 56.557 ‐56.557 3.43013 56.557 ‐56.557 3.34255 56.557 ‐56.558 3.16655 56.558

‐56.982 4.258 56.982 ‐56.983 4.09925 56.983 ‐56.983 4.18964 56.983 ‐56.984 3.9615 56.984 ‐56.984 3.84583 56.984 ‐56.985 3.71615 56.985 ‐56.985 3.6022 56.985 ‐56.986 3.49564 56.986 ‐56.986 3.38973 56.986 ‐56.986 3.29223 56.986 ‐56.987 3.10829 56.987

‐57.411 4.19 57.411 ‐57.412 4.05366 57.412 ‐57.412 4.12229 57.412 ‐57.413 3.9176 57.413 ‐57.413 3.78135 57.413 ‐57.414 3.65474 57.414 ‐57.414 3.53962 57.414 ‐57.414 3.43392 57.414 ‐57.415 3.33924 57.415 ‐57.415 3.2326 57.415 ‐57.415 3.06971 57.415

‐57.84 4.122 57.84 ‐57.841 3.98737 57.841 ‐57.841 4.05508 57.841 ‐57.841 3.85185 57.841 ‐57.842 3.72686 57.842 ‐57.842 3.61264 57.842 ‐57.843 3.48728 57.843 ‐57.843 3.38279 57.843 ‐57.843 3.27921 57.843 ‐57.844 3.19295 57.844 ‐57.844 3.02177 57.844

‐58.269 4.066 58.269 ‐58.27 3.92286 58.27 ‐58.269 3.99924 58.269 ‐58.27 3.79804 58.27 ‐58.271 3.66306 58.271 ‐58.271 3.54958 58.271 ‐58.271 3.44682 58.271 ‐58.272 3.34292 58.272 ‐58.272 3.23829 58.272 ‐58.272 3.14407 58.272 ‐58.273 2.98429 58.273

‐58.697 4 58.697 ‐58.699 3.867 58.699 ‐58.698 3.93322 58.698 ‐58.699 3.73306 58.699 ‐58.699 3.62082 58.699 ‐58.7 3.49738 58.7 ‐58.7 3.38486 58.7 ‐58.701 3.28233 58.701 ‐58.701 3.18884 58.701 ‐58.701 3.10494 58.701 ‐58.701 2.93649 58.701

‐59.126 3.956 59.126 ‐59.127 3.82312 59.127 ‐59.127 3.88947 59.127 ‐59.128 3.68988 59.128 ‐59.128 3.55802 59.128 ‐59.129 3.45682 59.129 ‐59.129 3.33419 59.129 ‐59.129 3.23212 59.129 ‐59.13 3.14931 59.13 ‐59.13 3.05658 59.13 ‐59.13 2.89891 59.13

‐59.555 3.89 59.555 ‐59.556 3.75813 59.556 ‐59.556 3.82469 59.556 ‐59.557 3.62558 59.557 ‐59.557 3.50578 59.557 ‐59.557 3.39508 59.557 ‐59.558 3.2936 59.558 ‐59.558 3.19223 59.558 ‐59.558 3.10054 59.558 ‐59.558 3.01798 59.558 ‐59.559 2.85225 59.559

‐59.984 3.836 59.984 ‐59.985 3.70433 59.985 ‐59.985 3.77032 59.985 ‐59.985 3.5737 59.985 ‐59.986 3.46409 59.986 ‐59.986 3.34392 59.986 ‐59.986 3.24361 59.986 ‐59.987 3.14372 59.987 ‐59.987 3.06211 59.987 ‐59.987 2.97012 59.987 ‐59.988 2.8153 59.988

‐60.413 3.771 60.413 ‐60.414 3.64167 60.414 ‐60.413 3.70629 60.413 ‐60.414 3.53208 60.414 ‐60.415 3.41279 60.415 ‐60.415 3.3032 60.415 ‐60.415 3.20413 60.415 ‐60.415 3.10428 60.415 ‐60.416 3.0132 60.416 ‐60.416 2.93211 60.416 ‐60.416 2.76939 60.416

‐60.841 3.727 60.841 ‐60.842 3.59855 60.842 ‐60.842 3.66298 60.842 ‐60.843 3.48027 60.843 ‐60.843 3.37158 60.843 ‐60.844 3.25375 60.844 ‐60.844 3.15489 60.844 ‐60.844 3.05492 60.844 ‐60.844 2.97482 60.844 ‐60.845 2.88498 60.845 ‐60.845 2.73291 60.845

‐61.27 3.674 61.27 ‐61.271 3.54629 61.271 ‐61.271 3.60963 61.271 ‐61.272 3.43588 61.272 ‐61.272 3.31226 61.272 ‐61.272 3.21347 61.272 ‐61.273 3.11444 61.273 ‐61.273 3.01617 61.273 ‐61.273 2.92734 61.273 ‐61.273 2.84758 61.273 ‐61.274 2.68816 61.274

‐61.699 3.631 61.699 ‐61.7 3.50421 61.7 ‐61.7 3.56782 61.7 ‐61.7 3.37753 61.7 ‐61.701 3.26094 61.701 ‐61.701 3.16307 61.701 ‐61.701 3.06576 61.701 ‐61.702 2.96831 61.702 ‐61.702 2.88943 61.702 ‐61.702 2.80138 61.702 ‐61.702 2.65223 61.702

‐62.128 3.569 62.128 ‐62.129 3.45263 62.129 ‐62.128 3.51578 62.128 ‐62.129 3.32647 62.129 ‐62.129 3.22106 62.129 ‐62.13 3.12351 62.13 ‐62.13 3.02686 62.13 ‐62.13 2.92978 62.13 ‐62.13 2.84266 62.13 ‐62.131 2.76449 62.131 ‐62.131 2.62534 62.131

‐62.556 3.516 62.556 ‐62.557 3.4111 62.557 ‐62.557 3.45414 62.557 ‐62.558 3.28628 62.558 ‐62.558 3.17104 62.558 ‐62.558 3.07471 62.558 ‐62.559 2.97855 62.559 ‐62.559 2.88272 62.559 ‐62.559 2.80544 62.559 ‐62.559 2.71882 62.559 ‐62.56 2.58111 62.56

‐62.985 3.474 62.985 ‐62.986 3.36019 62.986 ‐62.986 3.41207 62.986 ‐62.987 3.23521 62.987 ‐62.987 3.13308 62.987 ‐62.987 3.03569 62.987 ‐62.987 2.94014 62.987 ‐62.988 2.85436 62.988 ‐62.988 2.75927 62.988 ‐62.988 2.69141 62.988 ‐62.988 2.54584 62.988

‐63.414 3.423 63.414 ‐63.415 3.31976 63.415 ‐63.415 3.36116 63.415 ‐63.415 3.19517 63.415 ‐63.416 3.10091 63.416 ‐63.416 2.98716 63.416 ‐63.416 2.89279 63.416 ‐63.416 2.81698 63.416 ‐63.417 2.73163 63.417 ‐63.417 2.65521 63.417 ‐63.42 2.50211 63.42

‐63.843 3.382 63.843 ‐63.844 3.26959 63.844 ‐63.844 3.32071 63.844 ‐63.844 3.14809 63.844 ‐63.844 3.05186 63.844 ‐63.845 2.94866 63.845 ‐63.845 2.86436 63.845 ‐63.845 2.77064 63.845 ‐63.845 2.69509 63.845 ‐63.845 2.61025 63.845 ‐63.849 2.47935 63.849

‐64.271 3.332 64.271 ‐64.272 3.22806 64.272 ‐64.272 3.27029 64.272 ‐64.273 3.11577 64.273 ‐64.273 3.01281 64.273 ‐64.273 2.91988 64.273 ‐64.273 2.82682 64.273 ‐64.274 2.73377 64.274 ‐64.277 2.64981 64.277 ‐64.274 2.58354 64.274 ‐64.277 2.44577 64.277

‐64.7 3.291 64.7 ‐64.701 3.17844 64.701 ‐64.701 3.23873 64.701 ‐64.701 3.07667 64.701 ‐64.702 2.96472 64.702 ‐64.702 2.87259 64.702 ‐64.702 2.78034 64.702 ‐64.702 2.70619 64.702 ‐64.706 2.63017 64.706 ‐64.706 2.54803 64.706 ‐64.706 2.41511 64.706

‐65.129 3.24 65.129 ‐65.13 3.13865 65.13 ‐65.13 3.1989 65.13 ‐65.13 3.02736 65.13 ‐65.13 2.92647 65.13 ‐65.131 2.83494 65.131 ‐65.131 2.74337 65.131 ‐65.135 2.66072 65.135 ‐65.135 2.58673 65.135 ‐65.135 2.51692 65.135 ‐65.135 2.37953 65.135

‐65.558 3.209 65.558 ‐65.559 3.089 65.559 ‐65.558 3.14951 65.558 ‐65.559 2.98858 65.559 ‐65.559 2.89778 65.559 ‐65.559 2.80677 65.559 ‐65.559 2.71566 65.559 ‐65.563 2.64012 65.563 ‐65.563 2.55817 65.563 ‐65.563 2.47754 65.563 ‐65.563 2.34695 65.563

‐65.986 3.169 65.986 ‐65.987 3.04977 65.987 ‐65.987 3.1099 65.987 ‐65.987 2.95961 65.987 ‐65.988 2.85062 65.988 ‐65.992 2.76035 65.992 ‐65.992 2.67004 65.992 ‐65.992 2.59748 65.992 ‐65.992 2.5158 65.992 ‐65.992 2.45293 65.992 ‐65.992 2.32485 65.992

‐66.415 3.119 66.415 ‐66.416 3.02028 66.416 ‐66.416 3.06042 66.416 ‐66.416 2.9119 66.416 ‐66.416 2.81311 66.416 ‐66.421 2.74379 66.421 ‐66.421 2.655 66.421 ‐66.421 2.57119 66.421 ‐66.421 2.49325 66.421 ‐66.421 2.4168 66.421 ‐66.421 2.29194 66.421

‐66.844 3.08 66.844 ‐66.845 2.97207 66.845 ‐66.844 3.03068 66.844 ‐66.849 2.87389 66.849 ‐66.845 2.785 66.845 ‐66.849 2.69589 66.849 ‐66.849 2.60669 66.849 ‐66.849 2.52629 66.849 ‐66.85 2.45446 66.85 ‐66.849 2.39834 66.849 ‐66.849 2.26312 66.849

‐67.272 3.05 67.272 ‐67.277 2.93366 67.277 ‐67.273 2.99198 67.273 ‐67.278 2.82694 67.278 ‐67.278 2.7387 67.278 ‐67.278 2.67389 67.278 ‐67.278 2.59356 67.278 ‐67.278 2.50573 67.278 ‐67.278 2.43781 67.278 ‐67.278 2.35981 67.278 ‐67.278 2.23084 67.278

‐67.701 3.002 67.701 ‐67.706 2.92752 67.706 ‐67.702 2.94398 67.702 ‐67.706 2.81905 67.706 ‐67.707 2.72914 67.707 ‐67.707 2.62317 67.707 ‐67.707 2.53526 67.707 ‐67.707 2.4647 67.707 ‐67.707 2.39956 67.707 ‐67.707 2.32282 67.707 ‐67.707 2.19726 67.707

‐68.13 2.963 68.13 ‐68.135 2.85769 68.135 ‐68.135 2.90575 68.135 ‐68.135 2.76164 68.135 ‐68.135 2.67454 68.135 ‐68.135 2.60646 68.135 ‐68.135 2.52207 68.135 ‐68.135 2.44979 68.135 ‐68.136 2.35962 68.136 ‐68.135 2.30077 68.135 ‐68.135 2.17532 68.135

‐68.563 2.916 68.563 ‐68.564 2.82061 68.564 ‐68.563 2.90028 68.563 ‐68.564 2.75353 68.564 ‐68.564 2.6647 68.564 ‐68.564 2.56032 68.564 ‐68.564 2.4898 68.564 ‐68.564 2.41202 68.564 ‐68.564 2.34109 68.564 ‐68.564 2.26403 68.564 ‐68.564 2.15025 68.564

‐68.991 2.911 68.991 ‐68.992 2.81371 68.992 ‐68.992 2.83016 68.992 ‐68.993 2.68796 68.993 ‐68.993 2.60207 68.993 ‐68.993 2.53829 68.993 ‐68.993 2.44717 68.993 ‐68.993 2.36953 68.993 ‐68.993 2.30021 68.993 ‐68.993 2.24565 68.993 ‐68.993 2.12004 68.993

‐69.42 2.849 69.42 ‐69.421 2.7458 69.421 ‐69.421 2.82451 69.421 ‐69.421 2.6797 69.421 ‐69.421 2.59209 69.421 ‐69.421 2.48943 69.421 ‐69.421 2.4339 69.421 ‐69.421 2.35413 69.421 ‐69.421 2.28353 69.421 ‐69.421 2.22023 69.421 ‐69.421 2.09208 69.421

‐69.849 2.844 69.849 ‐69.85 2.73907 69.85 ‐69.85 2.76491 69.85 ‐69.85 2.62435 69.85 ‐69.85 2.53944 69.85 ‐69.85 2.47778 69.85 ‐69.85 2.39681 69.85 ‐69.85 2.32301 69.85 ‐69.85 2.25792 69.85 ‐69.85 2.17322 69.85 ‐69.85 2.07023 69.85

‐70.278 2.775 70.278 ‐70.278 2.6906 70.278 ‐70.278 2.75892 70.278 ‐70.279 2.61581 70.279 ‐70.279 2.52928 70.279 ‐70.279 2.44609 70.279 ‐70.279 2.3522 70.279 ‐70.279 2.28449 70.279 ‐70.279 2.2133 70.279 ‐70.279 2.15481 70.279 ‐70.279 2.0458 70.279

‐70.706 2.769 70.706 ‐70.707 2.67888 70.707 ‐70.707 2.69139 70.707 ‐70.707 2.57017 70.707 ‐70.707 2.50254 70.707 ‐70.707 2.40215 70.707 ‐70.707 2.33881 70.707 ‐70.707 2.26946 70.707 ‐70.707 2.19163 70.707 ‐70.707 2.12424 70.707 ‐70.707 2.02069 70.707

‐71.135 2.71 71.135 ‐71.136 2.62676 71.136 ‐71.136 2.68502 71.136 ‐71.136 2.55998 71.136 ‐71.136 2.44262 71.136 ‐71.136 2.39028 71.136 ‐71.136 2.31299 71.136 ‐71.136 2.24399 71.136 ‐71.136 2.16667 71.136 ‐71.136 2.10592 71.136 ‐71.136 1.99891 71.136

‐71.564 2.704 71.564 ‐71.564 2.61959 71.564 ‐71.564 2.63653 71.564 ‐71.565 2.49904 71.565 ‐71.565 2.43216 71.565 ‐71.565 2.36409 71.565 ‐71.565 2.26742 71.565 ‐71.565 2.21888 71.565 ‐71.565 2.13448 71.565 ‐71.565 2.08133 71.565 ‐71.565 1.97491 71.565

‐71.993 2.655 71.993 ‐71.993 2.55478 71.993 ‐71.993 2.62985 71.993 ‐71.993 2.49032 71.993 ‐71.993 2.40595 71.993 ‐71.994 2.30821 71.994 ‐71.993 2.25391 71.993 ‐71.994 2.16813 71.994 ‐71.993 2.11783 71.993 ‐71.993 2.05191 71.993 ‐71.993 1.95048 71.993

N E 1 E 2 E 4 E 6 E 8

Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph Data from Graph

============== ============== ============== ============== ============== ==============

Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Chart Title : Control Ch

X Axis Title: x‐axis X Axis Title: x‐axis X Axis Title: x‐axis X Axis Title: x‐axis X Axis Title: x‐axis X Axis Title: x‐axis

Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis Y Axis Title: y‐axis

x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis x‐axis y‐axis

Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0 Line type : 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

‐0.209 2.54359 0.209 ‐0.209 2.53972 0.209 ‐0.209 2.54805 0.209 ‐0.209 2.56264 0.209 ‐0.209 2.57501 0.209 ‐0.209 2.58479 0.209

‐0.421 3.42257 0.421 ‐0.422 3.42211 0.422 ‐0.422 3.4342 0.422 ‐0.422 3.45686 0.422 ‐0.422 3.47629 0.422 ‐0.421 3.49193 0.421

‐0.632 4.17121 0.632 ‐0.633 4.1794 0.633 ‐0.633 4.19579 0.633 ‐0.633 4.22661 0.633 ‐0.632 4.25446 0.632 ‐0.632 4.27799 0.632

‐0.845 4.83106 0.845 ‐0.846 4.83693 0.846 ‐0.846 4.85835 0.846 ‐0.845 4.89823 0.845 ‐0.845 4.93362 0.845 ‐0.845 4.96475 0.845

‐1.056 5.47251 1.056 ‐1.057 5.48197 1.057 ‐1.057 5.50743 1.057 ‐1.057 5.5551 1.057 ‐1.056 5.59732 1.056 ‐1.056 5.63449 1.056

‐1.267 6.07182 1.267 ‐1.268 6.08416 1.268 ‐1.268 6.11308 1.268 ‐1.268 6.16686 1.268 ‐1.268 6.2154 1.268 ‐1.268 6.2586 1.268

‐1.479 6.63303 1.479 ‐1.48 6.64931 1.48 ‐1.48 6.68208 1.48 ‐1.48 6.74419 1.48 ‐1.48 6.8001 1.48 ‐1.48 6.84982 1.48

‐1.692 7.1751 1.692 ‐1.693 7.19177 1.693 ‐1.693 7.22607 1.693 ‐1.693 7.29033 1.693 ‐1.693 7.34926 1.693 ‐1.693 7.40208 1.693

‐1.906 7.6774 1.906 ‐1.907 7.69644 1.907 ‐1.907 7.73322 1.907 ‐1.907 7.80201 1.907 ‐1.907 7.86425 1.907 ‐1.907 7.92014 1.907

‐2.12 8.14797 2.12 ‐2.121 8.16983 2.121 ‐2.122 8.20829 2.122 ‐2.122 8.28029 2.122 ‐2.122 8.34625 2.122 ‐2.122 8.40452 2.122

‐2.335 8.58816 2.335 ‐2.337 8.61207 2.337 ‐2.337 8.65169 2.337 ‐2.337 8.72637 2.337 ‐2.337 8.79346 2.337 ‐2.337 8.85311 2.337

‐2.551 8.99914 2.551 ‐2.553 9.02573 2.553 ‐2.553 9.06526 2.553 ‐2.553 9.14067 2.553 ‐2.553 9.2089 2.553 ‐2.553 9.26895 2.553

‐2.767 9.37852 2.767 ‐2.769 9.40751 2.769 ‐2.769 9.44769 2.769 ‐2.77 9.52293 2.77 ‐2.77 9.59063 2.77 ‐2.77 9.65086 2.77

‐2.985 9.73046 2.985 ‐2.986 9.76104 2.986 ‐2.987 9.80137 2.987 ‐2.987 9.87553 2.987 ‐2.988 9.94182 2.988 ‐2.988 10.00012 2.988

‐3.202 10.05329 3.202 ‐3.204 10.08434 3.204 ‐3.205 10.12348 3.205 ‐3.205 10.1962 3.205 ‐3.206 10.26062 3.206 ‐3.206 10.31757 3.206

‐3.421 10.34817 3.421 ‐3.423 10.38013 3.423 ‐3.423 10.41866 3.423 ‐3.424 10.49029 3.424 ‐3.425 10.5521 3.425 ‐3.425 10.60556 3.425

‐3.64 10.618 3.64 ‐3.642 10.65024 3.642 ‐3.642 10.6875 3.642 ‐3.643 10.75599 3.643 ‐3.644 10.81593 3.644 ‐3.644 10.86795 3.644

‐3.859 10.86505 3.859 ‐3.862 10.89753 3.862 ‐3.862 10.93348 3.862 ‐3.863 10.9996 3.863 ‐3.864 11.05441 3.864 ‐3.864 11.1036 3.864

‐4.079 11.08956 4.079 ‐4.082 11.12095 4.082 ‐4.082 11.1557 4.082 ‐4.083 11.2192 4.083 ‐4.084 11.27361 4.084 ‐4.082 11.30661 4.082

‐4.3 11.29479 4.3 ‐4.302 11.32479 4.302 ‐4.303 11.35618 4.303 ‐4.304 11.41039 4.304 ‐4.302 11.44482 4.302 ‐4.302 11.48067 4.302

‐4.521 11.4612 4.521 ‐4.524 11.48745 4.524 ‐4.524 11.51414 4.524 ‐4.522 11.55007 4.522 ‐4.522 11.58878 4.522 ‐4.522 11.61801 4.522

‐4.743 11.59181 4.743 ‐4.745 11.61559 4.745 ‐4.743 11.62898 4.743 ‐4.743 11.67701 4.743 ‐4.743 11.72202 4.743 ‐4.742 11.76595 4.742

‐4.965 11.72706 4.965 ‐4.963 11.74204 4.963 ‐4.963 11.77808 4.963 ‐4.961 11.84206 4.961 ‐4.958 11.89532 4.958 ‐4.956 11.93971 4.956

‐5.178 11.88158 5.178 ‐5.18 11.91148 5.18 ‐5.178 11.95099 5.178 ‐5.174 12.00689 5.174 ‐5.172 12.05471 5.172 ‐5.169 12.08935 5.169

‐5.417 11.89516 5.417 ‐5.416 11.94139 5.416 ‐5.413 11.98321 5.413 ‐5.394 12.10409 5.394 ‐5.385 12.1897 5.385 ‐5.382 12.21858 5.382

‐5.667 11.89501 5.667 ‐5.667 11.93426 5.667 ‐5.666 11.96767 5.666 ‐5.647 12.07641 5.647 ‐5.604 12.24947 5.604 ‐5.597 12.29813 5.597

‐5.917 11.89496 5.917 ‐5.918 11.92974 5.918 ‐5.918 11.958 5.918 ‐5.91 12.03546 5.91 ‐5.853 12.22146 5.853 ‐5.811 12.34893 5.811

‐6.168 11.8934 6.168 ‐6.17 11.92383 6.17 ‐6.17 11.9488 6.17 ‐6.163 12.01957 6.163 ‐6.126 12.15826 6.126 ‐6.026 12.38498 6.026

‐6.168 0 6.168 ‐6.17 0 6.17 ‐6.17 0 6.17 ‐6.163 0 6.163 ‐6.126 0 6.126 ‐6.24 12.40972 6.24

‐6.454 12.4185 6.454

‐6.668 12.41483 6.668

‐6.882 12.41068 6.882

‐7.096 12.41694 7.096

‐7.311 12.41998 7.311

‐7.525 12.42435 7.525

‐7.739 12.42682 7.739

‐7.953 12.42897 7.953

‐8.167 12.43329 8.167

‐8.381 12.43555 8.381

‐8.596 12.43752 8.596

‐8.81 12.43972 8.81

‐9.024 12.45209 9.024

‐9.238 12.47052 9.238

‐9.452 12.48749 9.452

‐9.667 12.50446 9.667

‐9.881 12.52144 9.881

‐10.095 12.53717 10.095

‐10.309 12.55608 10.309

‐10.524 12.57272 10.524

‐10.738 12.58886 10.738

‐10.952 12.60482 10.952

‐11.166 12.62054 11.166

‐11.381 12.63615 11.381

‐11.595 12.65144 11.595

‐11.809 12.66662 11.809

‐12.023 12.68373 12.023

‐12.238 12.6986 12.238

‐12.452 12.71318 12.452

‐12.666 12.72776 12.666

‐12.88 12.7422 12.88

‐13.095 12.75647 13.095

‐13.309 12.77051 13.309

‐13.523 12.78457 13.523

‐13.737 12.79832 13.737

‐13.952 12.81183 13.952

‐14.166 12.82499 14.166

‐14.38 12.83657 14.38

‐14.594 12.84682 14.594

‐14.809 12.85616 14.809

‐15.023 12.86472 15.023

‐15.237 12.87246 15.237

‐15.451 12.87958 15.451

‐15.665 12.88601 15.665

‐15.88 12.89544 15.88

‐16.094 12.9039 16.094

‐16.308 12.91252 16.308

‐16.522 12.92096 16.522

‐16.737 12.92946 16.737

‐16.951 12.93743 16.951

‐17.165 12.94571 17.165

‐17.379 12.95364 17.379

‐17.594 12.96133 17.594

‐17.808 12.96897 17.808

‐18.022 12.97672 18.022

‐18.236 12.98419 18.236

‐18.45 12.99151 18.45

Influence of Rock Boundary Conditions on Behaviour of Arched and ...

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