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The dissertation entitled “The Current Limitations of Displacement Based Design”, by TimothySullivan, has been approved in partial fulfilment of the requirements for the Master Degree in

Earthquake Engineering.

The report is intended to supplement the WG 2 “Displacement Based Design,” commission 7

of fib “seismic design.”

Mervyn Kowalsky ________________________________

Gian Michele Calvi ________________________________



Abstract

i

ABSTRACT

Displacement based design methods are emerging as the latest tool for performance based seismicdesign. Of the many different displacement based design procedures proposed in recent years there are

few that are developed to a standard suitable for implementation in modern design codes. Through

application to various case studies this report identifies and discusses the difficulties a designer may

encounter when trying to use displacement based design. It is hoped that by presenting these

limitations efforts will be made to develop the methods further so that designers can begin using the

methods with ease and confidence.

The report incorporates results for five different case studies designed in accordance with eight

different displacement based design methods.

The report focuses on three aspects of the design methods:

1. The relative ease or difficulty with which a design method can be applied and any apparent

limitations a method may have.

2. The required strength obtained for each method and how this compares with the other

methods.

3. The performance of the methods assessed by comparing the predicted ductility or drift values

for each case study with those obtained through time-history analyses.

The case studies indicate that the level of involvement required by the designer does vary considerably

between methods. Some methods are only applicable to certain structural types and others encounter

difficulties with irregular structural forms and flexible foundations. In most instances the designer is

required to make assumptions in order to proceed further and in other instances the method does

simply not facilitate design.



Abstract

ii

As a performance based design tool some methods are currently limited to specific earthquake levels

and others do not directly control non-structural damage.

The study proceeds by using each of the design methods to develop design strengths to satisfy a set of

design parameters. Despite all methods using the same set of design parameters, a large variation in

design strength is observed. It is shown that some methods require a design base shear more than five

times that of other methods.

After the designs are complete, non-linear time history analyses are conducted using models with the

strength as obtained for each design. The time-history analyses indicate that all the methods

successfully provide designs that ensure limit states are not exceeded. Despite the large variation in

design strength the variation in drifts observed between methods is relatively low.



Acknowledgements

iii

ACKNOWLEDGEMENTS

I thank all members of the Rose School at the University of Pavia, for their friendly assistance

throughout the entire Master course. I also thank North Carolina State University for their supportduring my six week stay in the summer of 2001. I thank my supervisors Mervyn Kowalsky and Gian

Michele Calvi who provided excellent encouragement and guidance. I also thank Nigel Priestley forhis valuable comments and input during preparation of this report. Lastly, I particularly thank my

family in New Zealand and my friends all over the world for their continuing kindness and friendship.



Index

iv

THE CURRENT LIMITATIONS OF DISPLACEMENT BASED

DESIGN

INDEX

ABSTRACT

ACKNOWLEDGEMENTS

INDEX

LIST OF TABLES

LIST OF FIGURES

1. INTRODUCTION

1.1 DESIGN CRITERIA

1.2 DESIGN ASSUMPTIONS

2. DESCRIPTION OF THE BUILDINGS CONSIDERED2.1 CASE STUDY 1 – WALL STRUCTURE

2.2 CASE STUDY 2 – WALL STRUCTURE WITH FLEXIBLE FOUNDATION2.3 CASE STUDY 3 –WALL STRUCTURE WITH IRREGULAR LAYOUT

2.4 CASE STUDY 4 – REGULAR RC MOMENT FRAME

2.5 CASE STUDY 5 – VERTICALLY IRREGULAR RC MOMENT FRAME

3. APPLICATION OF THE DESIGN METHODS

3.1 PANAGIOTAKOS AND FARDIS – DEFORMATION CONTROLLED

SEISMIC DESIGN

3.1.1 General Procedure3.1.2 Applied to Case Study 1 – Wall structure

3.1.3 Applied to Case Study 2 – Wall structure with flexible foundation

3.1.4 Applied to Case Study 3 – Wall structure with irregular layout

page

i

iii

iv

viii

ix

1

13

4

4

5

67

8

911

11

12

12

12



Index

v

3.1.5 Applied to Case Study 4 – Regular RC Frame Structure3.1.6 Applied to Case Study 5 – Vertically Irregular RC Frame Structure

3.2 BROWNING – PROPORTIONING METHOD FOR RC STRUCTURES

3.2.1 General Procedure3.2.2 Applied to Case Study 4 – Regular RC Frame Structure

3.3 ASCHHEIM AND BLACK – YIELD POINT SPECTRA FOR SEISMICDESIGN

3.3.1 General

3.3.2 Applied to Case Study 2 – Wall structure with flexible foundation3.3.3 Applied to Case Study 3 – Wall structure with irregular layout

3.3.4 Applied to Case Study 4 – Regular RC Frame Structure

3.3.5 Applied to Case Study 5 – Vertically Irregular RC Frame Structure

3.4 CHOPRA – DBD USING INELASTIC SPECTRA


3.4.2 Applied to Case Study 3 – Wall structure with irregular layout3.4.3 Applied to Case Study 4 – Regular RC Frame Structure


3.5 FREEMAN – CAPACITY SPECTRUM METHOD3.5.1 General

3.5.2 Applied to Case Study 1 – Wall structure3.5.3 Applied to Case Study 2 – Wall structure with flexible foundation




3.6 SEAOC – DIRECT DISPLACEMENT BASED DESIGN

3.6.1 General3.6.2 Applied to Case Study 1 – Wall structure




3.7 PRIESTLEY AND KOWALSKY – DIRECT DISPLACEMENT BASED

DESIGN3.7.1 General




3.8 KAPPOS AND MANAFPOUR – SEISMIC DESIGN WITH ADVANCEDANALYTICAL TECHNIQUES3.8.1 General


3.8.3 Applied to Case Study 4 – Regular RC Frame Structure3.8.4 Applied to Case Study 5 – Vertically Irregular RC Frame Structure

4. REQUIRED STRENGTH COMPARISONS

4.1 FLEXURAL STRENGTH4.1.1 Case Study 1 – Wall structure

1313

14

1415

16

16

1718

19

19

20

2021

21

22

2323

2425

25

25

25

26

2627

2727

27

27

28

28

2929

29

30

31

31

31

3132

33

3434



Index

vii

6.6 FREEMAN’S METHOD

6.7 THE SEAOC METHOD

6.8 PRIESTLEY’S METHOD

6.8.1 Distribution of strength in proportion to the wall length squared

6.8.2 Use of an assumed displacement profile

6.9 KAPPOS’ METHOD

7 SUMMARY

8 CONCLUSIONS

9 BIBLIOGRAPHY

ANNEX 1. Sample input files for Ruaumoko Time History Analyses

ANNEX 2. Calculations for the case studies (in form of excel spreadsheets on CD)

65

65

65

66

66

67

68

70

72



Index

viii

LIST OF TABLES

1.1 SEAOC Recommended Drift Limits associated with Basic Safety Objective 1.2 SEAOC Recommended Displacement Ductility Limits

2.1 Details of the regular moment frame.

3.1 Capacity Design and dynamic magnification recommendations.

4.1 Total Building Design Base Shear for each of the case studies.

4.2 Longitudinal Steel Percentages for Case Study 4 Columns 4.3 Longitudinal Steel Percentages for Case Study 5 Columns

5.1 Design Parameters for the Case Studies

5.2 Governing Design Parameters for Case Study 1 5.3 Drift and Ductility values obtained from Time History Analyses for Case Study 1

5.4 Governing Design Parameters for Case Study 2

5.5 Drift values obtained from Time History Analyses for Case Study 2 5.6 Ductility values obtained from Time History Analyses for Case Study 2

5.7 Governing Design Parameters for Case Study 3 5.8 Drift and Ductility values obtained from Time History Analyses for EQ-I of Case Study 3 5.9 Drift and Ductility values obtained from Time History Analyses for EQ-IV of Case Study 3

5.10 Governing Design Parameters for Case Study 4

5.11 Drift and ductility values obtained from Time History Analyses of Case Study 4 5.12 Governing Design Parameters for Case Study 5

5.13 Drift and ductility values obtained from Time History Analyses of Case Study 5



Index

x

6.3 Relationship between the structural dimensions, yield displacement and ductility developed considering

the role of initial stiffness used in Chopra’s design method 7.1 Author’s Assessment of the Displacement Based Design Procedures



Chapter 1. Introduction

1

1. INTRODUCTION

1.1 DESIGN CRITERIA

The aims of these case studies in displacement based design are threefold:

1. To assess the relative ease or difficulty with which the design methods can be applied and

any apparent limitations the methods may have.

2. To compare the required strength for each method.

3. To consider the performance of the methods by comparing the predicted ductility or drift

values for each case study with those obtained through time-history analysis.

Demand spectra for the case studies are taken from the SEAOC Blue Book (1999). The decision to use

spectra from the SEAOC bluebook is made arbitrarily and does not indicate a limitation of the

methods since any suite of spectra can be used. SEAOC provides displacement response spectra

(DRS), acceleration response spectra (ARS) and acceleration-displacement response spectra (ADRS)

for four different level earthquakes; EQ-I to EQ-IV. For design, the case studies utilise EQ-I,

corresponding to a frequent earthquake and EQ-IV, corresponding to a maximum earthquake. A basic

safety objective is assumed adequate for the building designs and consequently the required building

performance for each earthquake is:

• EQ-I The structural system yield mechanism is partially developed but damage is

generally negligible.

• EQ-IV Damage is major and for structural systems around 80% of the usable

inelastic displacement of the structure is expended. Extensive repairs are required and

may not be economically feasible.

(Refer to Appendix IB-2.3 of SEAOC Blue Book for further details and other levels.)




2

70% of the SEAOC EQ-I ground motion has been used for all case studies except Case Study 2 for

which the full EQ-I was used. Details of the case studies are provided in Chapter 2. The decision to

use a reduced EQ-I spectra was made after the design of Case Study 2 showed that the EQ-I event was

controlling the design in all methods. It was considered that the use of a strong EQ-I motion would not

reveal the benefits of effective displacement based design methods. The governing design parameter

for each method is presented with the time-history results for each case study in the performance

assessment of Chapter 5. It is seen that some methods are still controlled by EQ-I even when 70% of

the SEAOC Bluebook demand spectra is used. The PGA values associated with the different spectra

used for design are:

• 70% EQ-I Spectra PGA = 0.11g

• EQ-I Spectra PGA = 0.16g

• EQ-IV Spectra PGA = 0.66g

Design drift limits were also selected from the SEAOC Blue Book. These target values are

shown in Table 1.1 below.

Table 1.1 SEAOC Recommended Drift Limits associated with Basic Safety Objective

System Drift Values related to Earthquake Event

Concrete System EQ-I EQ-II EQ-III EQ-IV

Shear wall H/L=1 0.003 0.0055 0.008 0.010

H/L=2 0.004 0.008 0.012 0.015

H/L=3 0.010 0.019 0.028 0.035

Coupled Shear Wall 0.005 0.015 0.030 0.040

Moment Frame 0.005 0.015 0.030 0.040 For PBSE Design of standard occupancy structures

Some methods require that a system displacement ductility value be maintained. Table 1.2 presents the

SEAOC ductility values selected for use in these case studies. Note that the table does not provide

recommended ductility values for walls with aspect ratio between 5 and 10, nor for values of H/L

greater than 10. SEAOC consider that for high H/L ratio walls, the useful displacement ductility value

of these walls will be limited by the limiting drift ratio.

Table 1.2 SEAOC Recommended Displacement Ductility Limits

System Displacement Ductility Limits for EQ Level

Structural System EQ-I EQ-IV

Shear wall (1 < H/L < 5) 1.0 5.0

Shear wall (H/L = 10) 1.0 2.5

Coupled Shear Wall 1.0 8.0

Moment Resisting Frame 1.0 8.0




3

1.2 DESIGN ASSUMPTIONS

Realistic gravity loads are included in the case studies, however, these are only intended for design in

combination with the earthquake loading (with combined loadcase = 1.0G+1.0EQ). The gravity loads

are only used as axial loads for the wall case studies and are applied as uniformly distributed loads

along the beams of the frame case studies. Load cases other than earthquake combined with gravity

are not considered.

Material Properties adopted for design are:

f’c = 27.5 MPa

Ec = 28100 MPa Case Studies 1 & 2 and 32 000 MPa for Case Studies 3, 4 and 5.

f y = 400 MPa

Es = 200 000 MPa

Material strengths are not factored to dependable strength levels for design. Where capacity design is

required an overstrength factor of 1.4 is assumed.

Where a method requires that material strain limits be checked, but does not recommend limiting

values, the following are used:

For EQ-I Concrete compressive strain limit = 0.004

Steel tensile strain limit = 0.015

For EQ-IV Concrete compressive strain limit = 0.018

Steel tensile strain limit = 0.06

Where a method requires values for ultimate curvature for the wall design cases, they are obtained

directly from the expressions developed by Priestley and Kowalsky (1998).

To enable clear comparison between methods the case studies maintain the same dimensions and

member sizes for each design method. Details of the five case studies considered are presented in thefollowing chapter.



Chapter 2. Description of the buildings considered

4

2. DESCRIPTION OF THE BUILDINGS CONSIDERED

2.1 CASE STUDY 1 – WALL STRUCTURE

The first case study examines an 8 storey building with walls of equal dimensions in a regular layout

on a rigid foundation. The geometry and layout is shown in Figure 2.1 below.

Figure 2.1 Case Study 1: Wall structure with regular layout on rigid foundation

Earthquake

Six walls of 5m length,250mm in thickness

Neglect contribution of 3

perpendicular walls

(a) Plan view

Earthquake

Six walls of 5m length,250mm in thickness


perpendicular walls

(a) Plan view

Storey weight = 5000 kN eachWall axial load ratio = 0.01/storey

8 storeys at 3m each

Rigid foundation beam

(b) Elevation view

Walls respond as linked cantilevers

Storey weight = 5000 kN eachWall axial load ratio = 0.01/storey



(b) Elevation view





5

2.2 CASE STUDY 2 – WALL STRUCTURE WITH FLEXIBLE FOUNDATION

The second case study examines an 8 storey building similar to that of Case Study 1 but with a flexible

foundation. The geometry and layout is shown in Figure 2.2 below.

Figure 2.2 Case Study 2: Wall structure on flexible foundation

Storey weight = 5000 kN each

Wall axial load ratio = 0.01/storey


Earthquake

Six walls of 5m length,

250mm in thickness


perpendicular walls

Flexible foundation beam

K=5000MNm/rad per wall

(a) Plan view

(b) Elevation view


Storey weight = 5000 kN each



Earthquake

Six walls of 5m length,

250mm in thickness


perpendicular walls

Flexible foundation beam

K=5000MNm/rad per wall

(a) Plan view

(b) Elevation view





6

2.3 CASE STUDY 3 – WALL STRUCTURE WITH IRREGULAR LAYOUT

The third case study examines an 8 storey building with walls arranged in an irregular layout. The

geometry and layout is shown in Figure 2.3 below. This case study highlights the performance of

design methods when applied to a structure consisting of walls of different dimensions arranged in a

realistic layout.

Design of the individual walls requires distribution of base shear. Figure 2.3 shows the names assigned

to the walls of the structure. These names are referred to in Chapters 4 and 5 where the design

strengths and drift and ductility demands are presented. Chapter 3 describes how each method

addresses the torsion associated with this case study.

Figure 2.3 Case Study 3: Wall Structure with Irregular Layout. Plan view shown top with rear elevation

underneath.

3m 'Wall A' 6m 'Wall B' 3m 'Wall C'

8 storeys at 3m spacing

24m

20m

All walls 250mm thick

8m 'Wall G'8m 'Wall F'

8m ‘Wall K’8m 'Wall H'

3m ‘Wall D’

3m ‘Wall J’

EQ direction

3m ‘Wall E’

3m ‘Wall I’

X

Y

Storeyweight = 5000 kN each



Storeyweight = 5000 kN each





8

2.5 CASE STUDY 5 – VERTICALLY IRREGULAR RC MOMENT FRAME

The fifth case study examines an 8 storey frame building with a vertically irregular layout. The

geometry is shown in elevation in Figure 2.5 below. This case study considers the performance of

design methods with application to a vertically irregular but realistic structural shape. The building has

a regular layout in plan.

Figure 2.5 Case Study 5: Vertically irregular moment frame

9m 9m 9m9m9m

Beams 650mm deep.

Floors 3000kN each

Beams 800mm deep.

Floors 4000kN each

Beams 900mm deep.

Floors 5000kN each

All columns 800mm deep x

750mm wide.

Rigid foundation

7m

4m

4m

4m

4m

4m

4m

4m

Plan View:

Elevation:



Chapter 3. Application of the Design Methods

10

SEAOCYes Yes Recommends Paulay Priestley

capacity design procedure.

Priestley

Yes Yes Examples provided show that

capacity design & allowance for

higher modes should be made.

Kappos

No – allows for

strain hardening in

process but not for

material strengths

higher than the

dependable value.

No – inherent in the

time history analysis.

Method factors demand shears by

1.1 to allow for larger EQ than

predicted.

The capacity design procedure described by Paulay and Priestley (1992) is adopted for the case

studies. The effects of the capacity design can be seen directly in the calculations included in the

annex.

Capacity design requirements have little effect on the results of the frame case studies presented in

Chapter 4 because the study chooses to compare only the first floor design beam moments and

reinforcement requirements for the base of the ground storey columns. These members form part of

the desired beam side-sway mechanism and therefore their required flexural strength does not increase

with capacity design. However, the corner base columns were designed assuming that yielding would

occur only after the formation of overstrength of the beams. This assumption results in larger design

axial forces for the columns. The actions that are most affected by capacity design, such as the

member design shear forces and design moments for columns above the first floor are not presented.

During the inelastic time-history analyses the columns above the first floor are modelled elastically

with cracked section properties and the yielding members of the frame are modelled with infinite shear

strength.

For the wall case studies, capacity design magnifies the design shears to allow for overstrength and

dynamic magnification effects. A linear variation of moment resistance is provided from the required

base moment to zero at the top of the building.




11

3.1 PANAGIOTAKOS AND FARDIS – DEFORMATION CONTROLLED SEISMIC

DESIGN

The design method proposed by Panagiotakos and Fardis (1999) is a deformation calculation based

method using initial stiffnesses with response spectra. The general procedure is illustrated in the

flowchart, Figure 3.1, below.

3.1.1 General procedure

The method allows for checking of a target ductility (equal to 1) for a frequent earthquake (equivalent

to SEAOC EQ-I) and then requires that permissible inelastic rotations are not exceeded for a very rare

earthquake (SEAOC EQ-IV).

Figure 3.1 Flowchart for design procedure of Panagiotakos and Fardis’ method

5. Verify that chord rotation demands areacceptable and modify longitudinal and

transverse steel if necessary.

6. Check and proportion stirrups in joints to

accommodate E -IV ca acit desi n shears.

1. Elastic analysis for non-seismic actions &

“frequent earthquake” (EQ-I) with elastic

spectrum using uncracked sections.

2. Proportioning of steel in hinge locations and

then throughout the structure following the

rules of capacity design for actions from the

elastic anal sis of ste 1.

3. Elastic analysis for “life safety “ (EQ-IV)

earthquake with 5% damped elastic spectrum,

using secant-to-yield member stiffnesses for

antisymmetric bending.

4. Amplification of chord rotations obtained

from elastic analysis of step 3, to estimate

upper characteristic inelastic chord-rotation

demands. The amplification factors are given

in text of the method and were obtained from

extensive time-history analyses.




12

As a performance based design tool the method could appear restrictive, in the sense that only two

different events can be checked and that non-structural damage (affected by drift) is not controlled. It

is additionally restrictive that design for EQ-IV, the life safety earthquake, requires that either a

serviceability earthquake or ultimate static loads have already been designed for.

3.1.2 Applied to Case Study 1 – Wall structure

The first two steps in the method (as presented in Figure 3.1) are equivalent to force-based design

procedures and did not present any difficulties in application. Step 3 involves the use of secant-to-

yield member stiffnesses for which the method does not provide an expression for wall elements. For

the case studies, the design yield moment Mn and yield curvature φy, were determined and assuming

that bar slippage could be ignored, the effective stiffness EI was calculated as EI = Mn/φy.

Amplification factors required in step 4 of the method are a relatively easy and fast way to obtain

inelastic chord-rotation demands. However, the scaling factors are not provided for wall structures.

For the case study it was assumed that the amplification factors for ground storey columns could be

used.

The method does not recommend expressions for allowable ultimate rotations of wall structures, and

therefore the case study used approximate expressions given by Priestley and Kowalsky (2000).


The method does not provide advice for designing structures with flexible foundations. It was assumed

that the elastic model used in steps 1 & 3 could simply be modelled with a flexible foundation,

however, it is uncertain whether the same inelastic amplification factors still apply.


No recommendations for the design of wall structures with irregular layout were found and therefore

design proceeded as for Case Study 1. The initial elastic design distributes strength to the walls in

proportion to their length cubed, in accordance with traditional force-based design procedures.




13


Of all the case studies the method was most easily applied to the frame structures of case studies 4 and

5. This is because the method clearly presents data and equations for the application of the method for

frame structures. Inelastic rotation amplification factors and equations for the secant-to-yield member

stiffness and the allowable ultimate rotation of beams are clearly presented. This is in contrast to wall

structures where several assumptions must be made, as already discussed in Section 3.1.2.


No special recommendations for vertically irregular RC frames were found. This did not restrict the

ease in which the method could be applied however, since the same inelastic rotation amplification

factors and design equations as for the regular RC frame were utilised.

Although not examined as a case study in this report, Panagiotakos and Fardis (1999) investigate

frames with infill panels and provide several design recommendations for this irregular structural

form.




14

3.2 BROWNING – PROPORTIONING METHOD FOR RC STRUCTURES

The design method proposed by Browning (2001) is a target period method that aims to achieve a pre-

defined average drift limit. The general procedure is illustrated in the flowchart, Figure 3.2, below.

3.2.1 General procedure

Browning’s method is relatively fast and simple to use, although Browning (2001) writes that it is only

applicable to regular reinforced concrete frames. Neither inelastic rotation demands nor ductility limits

are controlled in the design process.

Figure 3.2 Flowchart of Browning’s method

Calculate Tt(Using displacement

response spectra and desired

drift limit)

Proportion Members

Calculate Ti(period of structure using gross

section properties)

Check:

Ti < Tt

Increase

Member Size

No

Yes

Check:

V b < Cy

IncreaseStrength of

Yielding

No

Yes

Check girder

strength > column

strength at joints

Increase

Column

strength

No

Yes

Provide Adequate Detailing to Avoid

Brittle Failure




15


In determining minimum base shear strength Browning provides an expression that includes an

acceleration factor and a strength reduction factor. It is unclear how sensitive the design would be to

assumptions for the amplification factor, and the case study used the value of 15/4 provided by

Browning for systems with 2% damping.

Consideration was also given to selection of the force reduction factor since many codes use

considerably different factors for identical structural types. For Case Study 4 a force reduction factor

of 8 was used corresponding to the SEAOC allowable ductility value for the appropriate performance

level and structural type considered.

Browning recommends using a structural model with gross section properties and the use of capacity

design and detailing.

The method does not provide advice on how the base shear for the model should be distributed to

determine member actions. It was therefore assumed that it should be proportioned with respect to

mass and height, in line with most modern code approaches.




16

3.3 ASCHHEIM AND BLACK – YIELD POINT SPECTRA FOR SEISMIC DESIGN

3.3.1 General

The yield point spectra method presented by Aschheim and Black (2000) permits design to a number

of performance criteria relatively quickly. As illustrated in the flowchart of Figure 3.3, and Figures 3.4

and 3.5, the method involves development of yield point spectra, which are used to define a

permissible design region considering target drift and ductility values.

Yield point spectra (YPS) plot the yield points for oscillators

having constant displacement ductility for a range of oscillator

periods on axes of yield strength and yield displacement.

Aschheim and Black (2000) suggest that yield strengths

corresponding to specified displacement ductilities can be

determined approximately from elastic spectra using smooth R-

µ-T relationships such as those defined by Miranda and Bertero

(1994). For the case studies, yield point spectra were developed

using the R-µ-T relationship as developed by Nassar and

Krawinkler(1992). This relationship enables allowance for strain

hardening.

R-µ-T relationships can also be used to obtain displacements

corresponding to specified displacement ductilities. However,

designers must note that YPS are a plot of inelastic yield strength

coefficients versus yield displacement. The method recommends

that yield displacements be obtained from the elastic period of

each oscillator and the inelastic pseudo-acceleration using the

relation:

2

2

=∆

π

T S a y

To permit design for various risk events in one step the

permissible design regions for the different earthquakes can be

plotted on the same axes. Then, with knowledge of the

structure’s yield displacement, the strength required to satisfy all

ductility and drift limits can be obtained from the graph in oneFigure 3.3 Flowchart of

Aschheim’s method

Develop Yield Point

Spectra (Cy vs. ∆y) for

various ductility levels µ .

Determine target

displacement ∆T, to satisfy

drift limit for desired riskevent.

Determine points onyield spectra where:

µ.∆y = ∆T

Define acceptable ductilitydemand and thereby identify

permissible design region.

Determine∆y for the structureand plot to determine required

yield strength.

Use conventionalStrength-Based Code

applications for

proportioning the lateralforce resisting system.

Choose ductility limit for

desired performance level




18

Figure 3.4 Development of Yield Point Spectra (YPS). YPS are developed for the different ductility levels

being considered. The drift control branch of the yield spectrum is formed knowing the equivalent SDOF

system displacement for a given drift limit, and dividing this displacement by the expected ductility.

Figure 3.5 Using the Yield Point Spectra to obtain minimum required strength.


The method does not make recommendations for the design of wall structures with irregular layout. In

accordance with the recommendations provided for regular structures, the required base strength is

Yield Point Spectra for EQ-IV

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.1 0.2 0.3 0.4 0.5

Yield Displacement (m)

Y i e l d S t r e n g t h C o e f f i c i e n t , C

Ductility = 2

Ductility = 4

Ductility = 8

Each yield displacement

multiplied by the ductility

give the peak

displacement.

Peak displacement of

0.40m this case

y∆ y∆2 y∆4

Connection of dots forms

drift control branch

Obtaining Base Shear Coefficient for EQ 1

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.000 0.050 0.100 0.150 0.200 0.250

Yield displacement (m)

Y i e l d s t r e n g t h c o e f f i c i e n t C

y

Acceptable design

region is above the

branches

Drift control

branch

Ductility control

branch

Enter with

y∆

Obtain

yC




19

obtained using a system yield displacement and associated system ductility. In an effort to ensure that

individual members of the structure do not undergo excessive ductility demands the yield

displacement of the system is assumed to be that of the longest wall (which has the smallest yield

displacement). The base shear so obtained is proportioned up the height of the structure in relation to

mass and height, and then distributed to the walls in proportion to their length cubed in line with

conventional force based design procedures as recommended by the design method.


The method presents no significant difficulties in application to the Regular RC Frame structure. The

yield displacement is estimated using the yield curvature equations provided by Priestley and

Kowalsky (2000) and assuming that the first floor beam will yield first. In contrast with the Direct

DBD method the design is relatively sensitive to the yield displacement assumed. Because the method

uses the yield displacement to obtain a base shear coefficient directly from demand spectra, as shown

in Figure 3.5, a small difference in yield displacement can result in large difference in design base

shear.

3.3.5 Applied to Case Study 5 – Vertically irregular RC Frame Structure

No special recommendations are made for the design of vertically irregular frame structures. However,

the method presents no significant difficulties in application. The yield displacement is estimated

using the yield curvature equations provided by Priestley and Kowalsky (2000) and assumes that the

first floor beam will yield first.

The method assumes that the structure will respond principally in the first mode. For irregular

structures the mass participation in the first mode and consequently the effective mass and yield

displacement may be significantly different than that of a regular RC frame of similar size. As shown

in Chapter 5, these approximations do not appear to have been too significant for this case study.

However, given that the nature of irregular structures is difficult to predict it may be appropriate to

perform a pushover analysis, as suggested by Aschheim and Black (2000) to obtain a better value for

the yield displacement.




21

3.4.2 Application to Case Study 2 – Wall with flexible foundation

The method provides no recommendations for the design of structures with flexible foundations.

Therefore, in applying the method to Case Study 2 iteration was performed. The system yield

displacement, consisting of the sum of displacements due to the limiting structural deformation and

that due to foundation rotation, was trialled until the resulting design base shear caused the same

system displacement. Due to the inherently iterative nature of Chopra’s method, the requirement for

successive iteration and re-iteration was time consuming.


The method does not make recommendations for the design of wall structures with irregular layout.

Because the method does not recommend how the design base yield strength is proportioned to the

structure it is assumed that strength is distributed in proportion to the wall length cubed, as is the

current practice.

During the iteration process for Case Study 3 it was noted that the method has difficulty iterating on

stiffness for a number of walls. At the end of each iteration the strength is distributed to the walls and

their cracked stiffness is determined as EI = Mn/φy. As these values of stiffness are used to distribute

the base shear at the end of the next iteration it emerges that the shear is distributed totally away from

the smaller walls to be carried entirely by the larger walls. For detailing purposes it was assumed that

minimum steel would then be provided to the smaller walls for which no demand is expected.

3.4.4 Application to Case Study 4 – Regular RC Frame Structure

No recommendations or examples are provided for frame structures. Therefore, to determine the

structural stiffness, cracked section properties were assumed for the beams and the columns. These

values were obtained considering the strength provided and the yield curvature of these members, as

described in Section 3.4.1. As every iteration requires that the design moments be obtained for each

member of the frame, the method is considerably more involved for frame structures versus “single

member” type structures.

One limitation with the current form of the method was observed in designing the frame structure for

the EQ-I level. For this case the code drift limit of 0.5% is less than the predicted yield drift of the

structure. Strictly following the steps of the method (see Figure 3.6) the allowable plastic drift, θP

should then be zero. As the design displacement, ∆D, is equal to: P Y D H θ +∆=∆ , it appears that the

design displacement should therefore equal the yield displacement. If the system displacement

associated with the code drift limit is less than the yield displacement, it becomes apparent that a

design displacement equal to the yield displacement would not prevent the code drift limit being




22

exceeded. For this report it was assumed that the method intends the target displacement to equal the

lesser of the yield displacement (as explained above) and the displacement associated with the code

drift limit.

If the design displacement is calculated strictly as recommended, the method appears to apply only to

cases where the target drift is less than the yield drift of the structure. This attribute becomes a

limitation if the drift limit is driven by non-structural damage requirements rather than material

inelastic rotation limits as appears to be the situation in Case Study 4.


No recommendations are provided for vertically irregular frame structures. Therefore, design

assumptions were similar to those made for the regular frame structure of Case Study 4.




23

3.5 FREEMAN – CAPACITY SPECTRUM METHOD

3.5.1 General

The method proposed by Freeman (1998) and outlined in Figure 3.7, appears best suited to checking

the performance of existing structures for which the member sizes and strengths are known. This is

because the method requires that a capacity spectrum for the structure is graphically superimposed

onto a suite of demand spectra for different ductility/damping levels as shown in Figure 3.8.

Freeman does not recommend a particular procedure

to develop demand spectra for different levels of

damping. For the relationship between ductility and

damping, Freeman references various papers, and for

the case studies the relationship provided in EC8

(1998) was utilised:

2/1

)5,(),(2

7

+∆=∆

ξ ξ T T

This relationship was necessary for the development

of spectra at different levels of damping and in

checking the capacity curve against the demand.

Freeman does not provide a recommended procedure

for the design of new structures for which the initial

strength is unknown. To overcome this in the case

studies, the 5% damped EQ-I spectra, for which the

structure is required to remain elastic, was used to

determine the minimum strength for a known

structural yield displacement. The structural yield

displacement was estimated using the relationships

provided by Priestley and Kowalsky (2000). Having

obtained an initial strength level, a capacity curve

beyond first yield could be developed and used to

check higher demand events.

Figure 3.7 Flowchart of main steps in

Freeman’s method




24

Freeman does not prescribe which risk events should be checked nor what an appropriate target

displacement should be. For the case studies, this enabled both the target drift and ductility values to be

considered in determining target displacements. Indeed, the designer can decide what limit states are

important and design for those.

No recommendation is made as to how the base shear should be distributed to the structure, and for the

case studies it was assumed to be with respect to mass and height, in line with most modern codes.

Figure 3.8 Example of the Freeman method - Superimposing a capacity spectrum onto the demand

spectra to check the building performance. In this case the point on the capacity curve with ductility

corresponding to a damping of 20.1% would cross a 20.1% damped demand curve, providing the design

coefficient of approximately 0.2g.

3.5.2 Application to case study 1 – Wall structure

During the design process for Case Study 1 it was found that the strength provided to satisfy EQ-I drift

and ductility criteria, was insufficient for the EQ-IV criteria. The method does not provide

recommendations on how the structure should be improved to satisfy the critical demands of EQ-IV.

For the case study it was assumed that the dimensions would not change and that the strength of the

structure should be increased uniformly. Because increasing the strength does not affect the yield

displacement the new design could simply scale the forces up until the end of the pushover curve

reached the demand curve corresponding to maximum allowable drift or ductility, whichever

governed.

Graphical Solution for Life Safety Earthquake

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.0 0.2 0.4 0.6 0.8 1.0

Spectral Displacement (m)

S p e c t r a l A c c e l e r a t i o n

( g ' s )

5%

10%

20%

12%

14%

16%

20.1%

22.6% at limit

18%

We see that the EQ

generates 0.33m

displacement at20.1% damping and

with Sa = 0.22g




25

3.5.3 Application to case study 2 – Wall structure with flexible foundation

Freeman does not provide recommendations for structures with flexible foundations. However, it is

assumed in the case studies that by performing a pushover analysis on a model with the appropriate

foundation rotational stiffness the foundation flexibility is adequately accounted for. To obtain the

initial strength, an iterative procedure was followed, whereby a system yield displacement was

guessed and used to obtain a base shear from the elastic response spectra. The moment associated with

this base shear and the consequent foundation rotation were determined and used to evaluate the

system yield displacement.

3.5.4 Application to case study 3 – Wall structure with irregular layout

No recommendations are provided for structures with irregular layout. In addition, for reasons cited in

section 3.5.1 it is uncertain how an initial strength should be assigned to the structure. Therefore, it is

assumed that current force-based procedures are adopted for distribution of strength. Freeman

recommends that a pushover curve is developed to the largest displacement practicable or to the point

where degradation of the overall system occurs. It is assumed that individual wall ductility demands

would be considered in defining the point of overall system degradation.

3.5.5 Applied to Case Study 4 –Regular RC Frame Structure

Several assumptions had to be made for the pushover analysis and development of a model for

pushover analysis is time consuming. The model was developed in Ruaumoko (Carr 2001) with

cracked stiffness of beam elements estimated using Priestley and Kowalsky (2000) yield curvature

equations and the relation EI = Mn/φy. Column interaction diagrams were developed using the Recman

(King et. al. 1986 and Mander et. al. 1988) moment curvature analysis program. The cracked stiffness

was assumed as 50%Ig and 60%Ig for the ground columns and columns above the first floor

respectively. Using the SEAOC drift limit and a factor of 1.4 recommended by Freeman the allowable

roof displacement was related to a displacement at an equivalent SDOF oscillator height. This

displacement was then used to determine the displacement ductility demand, which was compared

with the design value for ductility, and the minimum selected. To compare the pushover curve with the

demand spectra the ductility-damping relation as referenced by Priestley (2001) was utilised.


Freeman makes no special recommendations for vertically irregular frame structures. Design

incorporated similar assumptions as were made for Case Study 4. The procedure was not complicated

by the irregular nature of the structure.




26

3.6 SEAOC – DIRECT DISPLACEMENT BASED DESIGN

3.6.1 General

Application of the first of the displacement based design procedures

provided in the SEAOC Blue Book (1999) showed that the procedure

was relatively fast and easy to use to obtain the design base shear.

However, some limitations with the method are noted and several

assumptions had to be made, as detailed below.

As illustrated in Figure 3.9, the method designs for target drift values.

Ductility demands are not controlled. Four different risk events and

drift limits may be considered for design depending on the structural

performance objective.

As part of the design process, the target displacement is used on

spectra at the recommended system damping value. The EC8 (CEN

1996) relationship between damping and ductility was utilised to

convert the target displacement to a value consistent with a 5%

demand spectrum, however, any established relation could be used and

SEAOC make reference to Newmark for this purpose.

For wall structures the method is currently limited to three different

aspect ratios, and does not advise the designer what should be assumed

in the case of a different aspect ratio. For the case studies it was

assumed that interpolation of the data could be performed.

The method recommends that the design base shear be distributed over

the height of the structure with respect to the displaced shape or the

code redistribution with respect to mass and height. No

recommendations are provided for the relative stiffness of members

within the structure. For the case studies it was assumed that commonestimates for cracked section properties (Paulay & Priestley 1992)

should be used for members expected to yield.

Figure 3.9 Flowchart of

SEAOC method




27

3.6.2 Application to case study 1 – Wall structure

In applying the method to Case Study 1 an inconsistency was noted. The method recommends that the

yield strength of the system be obtained using an overstrength factor divided into the required

effective strength. SEAOC suggests a range of overstrength factors from 1.25 to 2.0, however, it does

not recommend a procedure through which to obtain these factors. With the effective strength known

it was noted that this assumed overstrength factor is likely to predict a yield strength inconsistent with

the yield strength obtained using the ductility demand and the post-yield stiffness ratio. For the case

studies an overstrength value of 1.4 was assumed for the design to EQ-IV and 1.0 for design to EQ-I.

3.6.3 Application to case study 2 – Wall structure with flexible foundations

SEAOC provides no guidance for the design of structures with flexible foundations. Due to the

prescriptive nature of the method it was found that allowance for foundation flexibility could not be

made. This is because the method determines a target displacement using prescribed factors and

assumes a ductility demand. These values are independent of a likely yield displacement or foundation

rotation. If the method had instead calculated the ductility value using yield displacement, and then

determined equivalent damping for this ductility demand, an appropriate effective period could have

been obtained. Despite this restriction in the preliminary design stage it is not likely that non-

conservative designs would be generated since the method would account for negative effects of

foundation flexibility during the pushover analysis.


The method does not make recommendations for the design of wall structures with irregular layouts. It

is assumed that the design distributes the base shear strength to the walls in the proportion to their

length cubed, in accordance with current force-based design practices. No recommendations are

provided for design of structures with walls of different aspect ratio.


The SEAOC method is fast and easy to apply to the regular frame structure of Case Study 4. The base

shear obtained from the design process detailed by SEAOC was then applied to a model of the frame

in SAP2000. The elements of the model had cracked stiffness as recommended by Paulay and

Priestley (1992).


SEAOC suggests that the effectiveness of the design procedure for irregular structures is likely to be

limited. In application the method presented no more difficulty than the regular frame structure,

however, Chapter 8 shows that the design did not perform very well for this case study.




28

3.7 PRIESTLEY AND KOWALSKY – DIRECT DISPLACEMENT BASED DESIGN

3.7.1 General

The method proposed by Priestley and Kowalsky (2000) is a relatively fast method that designs a

structure to satisfy a pre-defined drift level. The code drift limit and the drift corresponding to the

system’s inelastic rotation capacity are considered in the design process. The method does not directly

control the system ductility demand.

Figure 3.10 Flowchart of the method by Priestley and Kowalsky

Priestley suggests strain limits for two design states; serviceability and damage control. These two

damage limit states correspond to SEAOC Blue Book performance levels SP1 (EQ-I) and SP4 (EQ-

IV). The designer is able to define appropriate strain limits for design states other than SP1 and SP4

(for example SP2 and SP3).

Determine target

displacement ∆D

using drift limit and assumed

displacement profile.

Determine estimate for system

yield displacement ∆y, and

displacement ductility µ.

Using ξ determine target

displacement ∆D5, equivalent to

SDOF system with 5% damping.

Estimate system damping ξ,

using µ - ξ relationship.

Enter 5% damped DRS with ∆D5

and read off effective period Te.

Use Te & Me to obtain effectivestiffness Ke and thereby the

required base shear

V = Ke∆D

Determine effective mass Me,

Me = ∑mi∆i/∆D

Distribute base shear to structure

in proportion to the assumed

displacement profile.




29

3.7.2 Application to case study 2 – Wall structure with flexible foundations

The method provides only limited guidance for the design of structures with flexible foundations. The

guidance given recommends calculation of a system damping value that takes into account the

foundation flexibility. Therefore, in application, iteration was used whereby after distribution of

design base shear to the structure, the consequent foundation rotation was determined and used to

evaluate the system yield displacement. This was then used to determine the system ductility demand

and corresponding damping. An effective system period was then determined from which the stiffness

and strength could be obtained (in accordance with the normal procedure - see Figure 3.10. This

process was repeated until system damping values converged.


The method recommends base shear strength is distributed to the walls in the proportion to their length

squared. In development of the design displacement profile it is unclear whether to use the longest

wall, or some average length of all the walls. It was assumed that the longest of the walls should be

used. In accordance with an example presented by Priestley and Kowalsky (2000) for a structure with

varying wall lengths, the equivalent damping of the building was determined using the expected

damping of each wall factored by its length squared over the sum of the squared lengths of the walls. It

was assumed that transverse walls should not be considered in this evaluation of the effective damping

despite the load that they carry due to the twisting of the structure.


The method was relatively easy to apply to the regular frame structure. It was assumed that the yield

displacement would be governed by the yield curvature of the first floor beam. The yield displacement

is used to obtain an estimate for the system damping from the displacement ductility and the base

shear has been shown (Priestley and Kowalsky 2000) to be relatively insensitive to this value of

damping. Hence the method is not very sensitive to the yield displacement. However, in the design of

Case Study 4 for EQ1 an unusual scenario occurred whereby the target drift was less than the yield

drift. Therefore, the required strength was obtained by multiplying the effective stiffness, obtained

from the normal design procedure for a target drift, by the yield displacement. This effectively scales

the design shear up to an appropriate yield strength recognising that the yield drift was larger than the

design target drift. Design actions for individual elements were obtained by modelling the structurewith the predicted effective stiffness of each element and with the base of the ground floor columns

modelled as a pinned connection with the column yield moment applied statically, as described by

Priestley and Kowalsky (2000).




30

3.7.5 Application to case study 5 – Vertically Irregular Moment Frame.

Integral to Priestley’s method is the assumed displacement profile of the structure at the drift limit.

Displacement profiles have not been developed for irregular structures and therefore the method

cannot strictly be applied to Case Study 5. However, for the purpose of academic interest it was

proposed that the method be applied to Case Study 5 using the displacement profile for a regular

moment frame with number of bays equal to the average of the vertically irregular system. Design

assumptions then followed those as for the regular RC frame structure of Case Study 4.




32

Allowable plastic rotations were calculated using Priestley and Kowalsky (2000) equations and using

an approximation for the beam neutral axis depth of 0.235d.

Figure F3.11 Flowchart of method by Kappos and Manafpour


No special recommendations are made for vertically irregular frame structures, therefore the design

proceeded with similar assumptions as for Case Study 4.

Detailing so that

minimum steel is

provided and

construction

requirements met.

Obtain Basic

Strength Level

Construction of model with

yielding members and properties based on

reinforcement provided for

Basic Strength Level.

Time-Histories

scaled to EQ-II

level.

Alter membersizes &/or

reinforcement

Drift &ductility

demands OK?

Time-Historiesscaled to EQ-IV

level.

Yes

No

Design of Columns

Design for Shear

Detailing of all members

considering level of

inelasticity expected.

Time-history analysisfor EQ-IV

Time-history analysis

for EQ-II

Elastic Analysis for

EQ-I spectrum

allowing for moderatecracking

Flexural

design of

beams

Selection of appropriatetime-histories

(minimum of 3 recommended)



Chapter 4. Required Strength Comparison

33

4 REQUIRED STRENGTH COMPARISONS

The flexural strength, shear strength, and reinforcement content required by each method for each of

the case studies is now presented to illustrate how significant the differences in the methods can be.

Firstly, flexural strength requirements are compared through the use of bending moment diagrams that

allow for capacity design and dynamic magnification as summarised in Chapter 3. Secondly, the

design base shears for the structures at yield are summarised and capacity design shears up the height

of the buildings are also presented. Finally, the flexural reinforcement content for the columns of Case

Studies 4 and 5 are presented.

The performance of each method is assessed by non-linear time history analyses, the results of which

are presented in Chapter 5.

Chapter 6 will identify characteristics of the methods that account for the variation in design actions

presented in this chapter and the likely performance as predicted by the time history analyses of

Chapter 5.




34

4.1 FLEXURAL STRENGTH

4.1.1 Case Study 1 – Wall structure

Figure 4.1 Design Moments for RC Wall Structure with Rigid Foundation

4.1.2 Case Study 2 – Wall structure with Flexible Foundations

Figure 4.2 Design Moments for RC Wall Structure with Flexible Foundations

Design Moments for a single wall of Case Study 1

RC Wall with Rigid Foundation

01

2

3

4

5

6

7

8

0 5000 10000 15000 20000 25000 30000

Demand Moment (kNm)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

Pr PaCh

A Fr Se K

Design Moments for a single wall of Case Study 2

RC Wall Structure with Flexible Foundations

0

12

3

4

5

6

7

8

0 5000 10000 15000 20000 25000

Demand Moment (kNm)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

Pr

PaCh AFr Se K




35

4.1.3 Case Study 3 – Wall structure with irregular layout

Design bending moments are presented for the 3m ‘Wall A’, the 6m ‘Wall B’ and the 8m ‘Wall F’.

For the location of these walls, refer to Figure 3.3 in Section 3.3.

Figure 4.3 Design Moments for ‘Wall A’ of RC Wall Structure with Irregular Layout

Figure 4.4 Design Moments for ‘Wall B’ of RC Wall Structure with Irregular Layout

Design Bending Moments for 3m 'Wall A' of Case Study 3RC Wall Structure with Irregular Layout

0

1

2

3

4

5

6

7

8

0 2000 4000 6000 8000

Bending Moment (kNm)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

A PaPr SCh

Fr K

Design Bending Moments for 6m 'Wall B' of Case Study 3

RC Wall Structure with Irregular Layout

0

1

2

3

4

5

6

7

8

0 10000 20000 30000 40000 50000

Bending Moment (kNm)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

Freeman

K - Kappos

A PaPr SCh Fr K




38

4.2 SHEAR STRENGTH

Values for the building design base shear strength at yield for each of the methods and all case studies

are shown in Table 4.1 below. The distribution of the capacity design shears up the building height are

presented in sections 4.2.1 to 4.2.5 that follow.

Table 4.1 Total Building Design Base Shear for each of the case studies.

4.2.1 Case Study 1 – Wall structure

Figure 4.8 Capacity Design Shears for Case Study 1 – Wall Structure with Rigid Foundation

Method Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5

Panagiotakos 9480 7200 10987 13406 7131

Aschheim 3008 5755 4426 3732 4038

Chopra 3416 3750 2434 3077 6307

Freeman 4537 5419 5059 4499 4584SEAOC 4560 4560 3013 3596 3249

Priestley 2900 3494 3417 6136 7623

Kappos 5400 5562 8044 9627 4464

Browning N/A N/A N/A 13369 N/A

Building Design Base Shear

(Base Shear at 1st Yield, kN)

Capacity Design Shears for a single wall from Case Study 1

(Wall Structure with Rigid Foundation)

0

12

3

4

5

6

7

8

0 1000 2000 3000 4000

Capacity Design Shear (kN)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

Pr PaCh A Fr

SeK




39

4.2.2 Case Study 2 – Wall structure with Flexible Foundations

Figure 4.9 Capacity Design Shears for Case Study 2 – Wall Structure with Flexible Foundations

4.2.3 Case Study 3 – Wall structure with irregular wall layout

Figure 4.10 Capacity Design Shears for Case Study 3 – Wall Structure with Irregular Layout

Capacity Design Shear for a single wall of Case Study 2

(RC Wall Structure with Flexible Foundations)

0

1

2

3

4

5

6

7

8

0 1000 2000 3000 4000

Capacity Design Shear (kN)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

Pr PaCh AFr Se K

Capacity Design Shears for Case Study 3

Wall Structure with Irregular Layout

0

1

2

3

4

5

6

7

8

0 5000 10000 15000 20000 25000 30000

Shear (kN)

L e v e l

Pr - Priestley

S - SEAOC

Pa - Panagiotakos

A - Aschheim

Ch - Chopra

F - Freeman

K - Kappos

Pa AS FPr C K




40

4.2.4 Case Study 4 – Regular moment frame structure

Figure 4.11 Capacity Design Shears for Case Study 4 – Regular RC Frame

4.2.5 Case Study 5 – Vertically Irregular RC Moment Frame

Figure 4.12 Capacity Design Shears for Case Study 5 – Vertically Irregular RC Frame

Capacity Design Shear for Case Study 4

Regular RC Frame

0

1

2

3

4

5

6

7

0 5000 10000 15000

Shear (kN)

L e v e l

Pr - Priestley

S - SEAOC

Pa -Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

B - Browning

B PaK AS F Pr C

Capacity Design Shear for Case Study 5

Vertically Irregular RC Frame

0

1

2

3

4

5

6

7

8

0 2000 4000 6000 8000

Shear (kN)

L e v e l

Pr - Priestley

S - SEAOC

Pa -Panagiotakos

A - Aschheim

Ch - Chopra

Fr - Freeman

K - Kappos

PaK AS F Pr C




41

4.3 RELATIVE STEEL CONTENT AND STEEL DISTRIBUTION

Longitudinal reinforcement ratios are presented for the columns of the frame case studies. These

reinforcement ratios were determined using RECMAN (King et. al. 1986, Mander et. al. 1988)

moment-curvature analyses assuming that the reinforcing steel is distributed evenly to the top, bottom

and sides of the section.

4.3.1 Case Study 4 – Regular RC Moment Frame

Table 4.2 Longitudinal Steel Percentages for Case Study 4 Columns

4.3.2 Case Study 5 – Vertically Irregular RC Moment Frame

Table 4.3 presents the steel contents required by each method for Case Study 5. Some of the steel

contents are excessive and it is expected that in design different column dimensions would be selected.

However, the unrealistic steel contents are presented to highlight the substantial difference in the

strength required for each of the methods.

Table 4.3 Longitudinal Steel Percentages for Case Study 5 Columns

Method

Longitudinal

Steel Interior

Columns

Longitudinal

Steel Corner

Columns

Pana iotakos 1.4% 2.7%

Brownin 1.5% 2.6%

Aschheim 0.3% 0.3%

Cho ra 0.3% 0.3%

Freeman 0.3% 0.4%

SEAOC 0.3% 0.3%

Priestley 0.3% 0.4%

Kappos 0.5% 1.3%

minimum steel assumed = 0.3%

note Pangiotakos already designs columns for ductility reqmnts and

requires 50mm stirrup spacing.

Method

Longitudinal

Steel Interior

Columns

Longitudinal

Steel Corner

Columns

Pana iotakos 6.7% 9.9%

Aschheim 1.0% 1.8%

Chopra 2.3% 3.2%

Freeman 1.5% 2.3%SEAOC 0.8% 1.3%

Priestley 2.6% 3.7%

Ka os 1.3% 2.1%

minimum steel assumed = 0.3%

Assumes no max steel reinforcing content

Also assumes tension steel = side = comp steel



Chapter 5. Assessment of Performance

43

5. ASSESSMENT OF PERFORMANCE

An assessment of each method’s performance is made by comparing the actual target design

parameters with the parameters obtained through time-history analyses of the structures with strength

as per each design method. The assessments should be seen only as a indication of performance since

many simplifying assumptions are made in the modelling process and the methods have only been

applied to five different case studies.

5.1 TIME HISTORY INPUTS AND MODELLING APPROXIMATIONS

Three spectrum-compatible time-histories were generated using SIMQKE that is part of the

Ruaumoko program (Carr 2001). It is understood that real earthquake records are desirable for actual

design. However, because of the nature of these case studies, it was decided that artificial time-

histories would best match the design spectra and would therefore most clearly demonstrate the

performance of each method. A time step of 0.01s and duration of 20s were chosen for the

accelerograms. The response spectra for the three time-histories generated to match EQ-I are shown in

Figures 5.1 and 5.2.

The plot of the displacement response spectra show that the artificially generated time-histories do not

match the design spectra very well with fairly large deviations at longer periods. However, by

considering the average and the peak of the maximum values of response from the three time histories

it is expected that the design spectra will be adequately represented. Therefore, in the following

sections an “average” and a “peak” value of response for the three time history analyses are presented.

The non-linear time-history analysis program Ruaumoko (Carr 2001) is used to subject each of the

structures to the spectrum compatible accelerograms. The strengths obtained for each method are input




45

Schonbrich with an unloading stiffness factor of 0.5, reloading stiffness factor of 0.0 and reloading

power factor of 1.0. An explanation of these factors and the shape of the hysteresis model is presented

in the Ruaumoko user manual by Carr (2001).

Elastic damping is modelled for the structures using tangent stiffness Rayleigh damping of

5% applied to the 1st and 2

nd modes. P-delta effects are not considered.

5.1.1 Case Study 1 – Wall Structure

In modelling the wall structure, masses were placed at floor levels assuming the floors to be flexible

out-of-plane, and infinitely stiff in-plane. The strength required for the bottom storey was continued up

the full height of the building and a constant effective stiffness was used over the structure’s height.

5.1.2 Case Study 2 – Wall structure with flexible foundation.

Modelling of the wall structure with the flexible foundation required introduction of a base restraint

with finite rotational stiffness. Note that all the other case studies applied base restraints with infinite

stiffness assuming rigid foundation response.

5.1.3 Case Study 3 – Wall structure with irregular plan and rigid foundation.

Ruaumoko 3D was used to develop a model for the time history analysis of Case Study 3 with

assumptions similar to those of Case Study 1, but with the design strength provided for each level.

Walls perpendicular to the principal earthquake direction are modelled with elastic section properties.

5.1.4 Case study 4 – Regular RC frame structure

A model was developed in Ruaumoko that includes base storey columns with axial load interaction

diagrams, and effective stiffness before yield estimated as 50% Ig using recommendations from Paulay

& Priestley (1992). The columns above the ground floor were modelled as elastic members as yield

should be confined to the base columns and beams by the principles of capacity design. These elastic

columns were modelled with cracked stiffness of 60%Ig, in accordance with Kappos (2001) and

Paulay and Priestley (1992) recommendations.

5.1.5 Case Study 5 – Vertically irregular RC frame structure

A model is used in Ruaumoko making assumptions similar to those of the regular frame model of

Case Study 4.




46

5.2 TIME HISTORY DRIFT AND DUCTILITY VALUES

Peak drift and ductility values are obtained from the time history analyses. They should be compared

with the design parameters as presented in Table 5.1 below. Note that only one parameter will govern

the design of each method. As discussed in Chapter 3, not all parameters are used by all of the

methods.

Table 5.1 Design Parameters for the Case Studies

System Drift Values related to Earthquake Event

Structural System EQ-I Drift EQ-I Ductility EQ-IV Drift EQ-IV Ductility

Shear wall H/L>3 1.0% 1.0 3.5% 5.0

RC Moment Frame 0.5% 1.0 4.0% 8.0

Displacement ductility values are obtained from the analyses by taking the maximum displacement

recorded at an assumed effective height and dividing this by the yield displacement corresponding to

the effective height. For the wall case studies the yield displacement was estimated using the

relationships developed by Priestley and Kowalsky (2000). For the frame case studies the yield

displacement was taken from the pushover analysis performed for the Freeman design. It is noted here

that this yield displacement was shorter than that predicted by the yield displacement equations for

frames developed by Priestley and Kowalsky (2000). This is expected to be because in the Ruaumoko

model the columns above the ground floor are modelled with constant cracked stiffness and the beams

are modelled with a low effective cracked stiffness. The building elastic stiffness and consequently the

yield displacement is dependent on the cracked stiffness assumed for the columns. It is considered that

this scenario whereby the ratio of column and beam stiffness is significantly different than anticipatedoccurs because of inappropriate beam and column dimensions. If shallower beams had been used the

cracked stiffness would have been closer to that assumed when determining the design strengths for

individual elements.

Inter-storey drift values for the wall case studies are the maximum recorded at the top storey as

previous research as discussed by Priestley and Kowalsky (2000) has shown that for wall structures

the peak drift generally occurs at the top floor. For the frame case studies the maximum inter-storey

drift was computed from maximum displacements measured up the height of the building. The use of

the maximum floor displacements is expected to slightly underestimate the maximum inter-storey drift

as it ignores the role of higher mode effects at maximum response. However, it is expected that the

drift values are accurate enough to provide a good indication of the level of drifts developed in the

structure.




47

5.2.1 Case Study 1 – Wall Structure

It is of interest to know which design parameter each method predicted would be critical when

reviewing the drift and ductility values obtained from the time-history analyses. Table 5.2 presents the

parameters that governed the design of Case Study 1 for each method.

Table 5.2 Governing Design Parameters for Case Study 1

The drift and ductility values obtained from time-history analyses presented in Table 5.3 show that all

the methods were successful in maintaining the target design parameters for Case Study 1.

Table 5.3 Drift and Ductility values obtained from Time History Analyses for Case Study 1

5.2.2 Case Study 2 – Wall Structure with Flexible Foundation

When reviewing the drift and ductility values obtained from the time-history analyses it is of interest

to know which design parameter each method predicted would be critical. Table 5.4 presents the

parameters that governed the design of Case Study 2 for each method.


Parameter Governing Design

Panagiotakos EQ-I ductility = 1.0

Aschheim EQ-I ductility = 1.0

Chopra EQ-I code drift = 1.0%

Freeman EQ-IV ductility = 5.0

SEAOC EQ-IV code drift = 3.5%

Priestley EQ-IV inelastic rotation

Kappos EQ-I ductility = 1.0

Method

Peak Average Peak Average Peak Average Peak Average

Panagiotakos 0.47% 0.36% 0.63 0.49 1.6% 1.5% 2.7 2.4

Aschheim 0.75% 0.65% 1.05 0.88 3.1% 2.8% 6.1 5.5

Chopra 0.63% 0.62% 0.83 0.80 2.7% 2.5% 5.3 5.0

Freeman 0.61% 0.49% 0.74 0.63 2.7% 2.4% 5.4 4.6

SEAOC 0.61% 0.49% 0.74 0.63 2.7% 2.4% 5.4 4.6

Priestley 0.76% 0.65% 1.06 0.88 3.0% 2.8% 5.9 5.5Kappos 0.56% 0.45% 0.72 0.60 2.2% 1.9% 3.9 3.4

Note: The 'peak' value refers to the highest maximum value recorded from the three time-history analyses.

The 'average' value refers to the average of the maximum values recorded for each of the three time-history analyses.

time-history top storey

drift

time-history ductility

demand

EQ-I EQ-I EQ-IV EQ-IVtime-history ductility

demand

time-history top storey

drift


Panagiatakos EQ-I ductility = 1.0

Aschheim EQ-IV structural ductility = 5.0

Chopra EQ-I code drift = 1.0%

Freeman EQ-I ductility = 1.0

SEAOC EQ-IV code drift = 3.5%

Priestley EQ-IV inelastic rotation capacity

Kappos EQ-I ductility = 1.0

Method




48

The drift and ductility values obtained from the time-history analyses presented in Table 5.5 and Table

5.6 show that all the methods were successful in maintaining the target design parameters for Case

Study 2. It is apparent that even though design strengths varied by as much as 100% the maximum

drift values are not significantly different.

Table 5.5 Drift values obtained from Time History Analyses for Case Study 2

Table 5.6 Ductility values obtained from Time History Analyses for Case Study 2

The relatively higher ductility values recorded for the Chopra and Priestley design methods are

somewhat expected since the methods do not attempt to control the displacement ductility and rather

control the inelastic rotation demand to acceptable values.

We also note that even though the SEAOC method only controls the drift and does not allow for

foundation rotation in the design process, the ductility values obtained this case study appear to be

within acceptable levels.

Peak Average Peak Average

Panagiatakos 1.05% 0.74% 2.3% 2.0%

Aschheim 1.02% 0.79% 2.6% 2.4%

Chopra 0.82% 0.76% 3.1% 2.7%

Freeman 0.96% 0.78% 2.7% 2.6%

SEAOC 0.86% 0.74% 2.6% 2.6%

Priestley 1.01% 0.73% 3.1% 2.7%

Kappos 1.03% 0.79% 2.6% 2.4%

The 'peak' value refers to the highest maximum value recorded from the three time-history analyses.The 'average' value refers to the average of the maximum values recorded for each of the three time-history analyses.

EQ-I EQ-IV

top storey drift top storey drift

Peak Average Peak Average Peak Average

Panagiatakos 0.9 0.6 2.0 1.9 3.0 2.7

Aschheim 1.0 0.7 2.7 2.6 3.9 3.7

Chopra 0.8 0.8 4.3 3.8 5.8 5.0Freeman 0.9 0.7 3.3 3.0 4.8 4.3

SEAOC 0.9 0.7 3.2 3.1 4.5 4.3

Priestley 1.1 0.7 4.3 3.8 5.8 5.0

Kappos 1.0 0.7 2.5 2.5 3.7 3.6

The 'peak' value refers to the highest maximum value recorded from the three time-history analyses.


The 'structural ductility' refers to the ductility imposed on the structure accounting for the foundation rotation.

EQ-IV EQ-IVsystem ductility

demand

structural ductility

demand

EQ-Isystem ductility

demand




49

5.2.3 Case Study 3 – Wall Structure with irregular plan and rigid foundation

Table 5.7 presents the parameters that governed the design of Case Study 3 for each method.


The drift and ductility values shown in Figures 5.8 and 5.9 for Case Study 3 were obtained using an

inelastic model in Ruaumoko 3D. The results show that all the methods were successful in maintaining

the target design parameters. However, preliminary analyses for EQ1, obtained using a fibre element

model of the structure, suggested that the methods may underestimate ductility demands on individual

walls of the twisting structure. Although the fibre element model could not be used for the EQ-IV

level due to convergence problems, these observations correspond well with the points made in

Section 6.

The preliminary results disagree with the final results obtained from the Ruaumoko 3D model that

indicate the methods perform satisfactorily for the EQ-I level. This is despite both models having

similar uncracked periods of vibration in both axes of the building. It is felt that the fibre element

model provided a better representation of the cracked section properties at first yield, since actual

material properties were modelled with strain dependent stiffness at all strain levels, in contrast to the

frame element model developed in Ruaumoko that relied on estimates of the cracked stiffness based

on the strength and curvature at first yield.

Table 5.8 Drift and Ductility values obtained from Time History Analyses for EQ-I of Case Study 3


Panagiatakos EQ-I Ductility Limit = 1.0

Aschheim EQ-I Ductility Limit = 1.0

Chopra EQ-IV 8m Wall Inelastic Rotation

Freeman EQ-IV Ductility Limit = 5.0

SEAOC EQ-IV Drift Limit

Priestley EQ-IV 8m Wall Inelastic Rotation

Kappos EQ-I Ductility Limit = 1.0

Method

Peak Average Peak Average Peak Average Peak Average Peak AveragePanagiatakos 0.34 0.27 0.69 0.54 0.41 0.35 0.45% 0.35% 0.21% 0.18%

Aschheim 0.35 0.33 0.70 0.66 0.58 0.53 0.47% 0.43% 0.30% 0.27%

Chopra 0.35 0.33 0.70 0.66 0.58 0.53 0.46% 0.43% 0.30% 0.27%

Freeman 0.35 0.33 0.70 0.66 0.58 0.53 0.47% 0.43% 0.31% 0.27%

SEAOC 0.35 0.33 0.70 0.66 0.58 0.53 0.46% 0.43% 0.30% 0.27%

Priestley 0.35 0.33 0.70 0.66 0.58 0.53 0.46% 0.43% 0.30% 0.27%

Kappos 0.40 0.30 0.80 0.60 0.53 0.41 0.51% 0.40% 0.28% 0.21%

EQ-I Walls A, B & C EQ-I Walls F & G

Maximum Drift Maximum Drift

EQ-I 3m Wall A EQ-I 6m Wall B EQ-I 8m Wall F

Ductility Demand Ductility Demand Ductility Demand




50

Unfortunately, for many of the design methods minimum steel requirements controlled the strength

and stiffness of the walls. Minimum steel was taken as 0.18% (equal to 0.7/fy as from Paulay &

Priestley [1992]) and the yield curvatures were calculated explicitly for each of the walls with

minimum reinforcement and with known axial load (constant for all methods). Recall that the yield

curvature is used in the calculation of the cracked stiffness and consequently the results of the EQ-I

earthquake analyses are of little interest since the cracked stiffness values (and therefore the elastic

periods) are practically the same for all methods except the Panagiotakos and Kappos methods.

The results for EQ-IV presented in Table 5.9 are of more interest. Keep in mind that this was the

earthquake event that governed most of the methods. Note that the Priestley method receives the

largest average ductility demands, which may be attributed to the base shear distribution procedure,

however, it could also occur due to the irregular nature of the time-histories employed in the analyses.

Table 5.9 Drift and Ductility values obtained from Time History Analyses for EQ-IV of Case Study 3

5.2.4 Case Study 4 – Regular Moment Frame

Table 5.10 presents the parameters that governed the design of Case Study 4 for each method.


The drift and ductility values obtained from time-history analyses presented in Table 5.11 show that

the methods were successful in maintaining the target design parameters for Case Study 4.

Peak Average Peak Average Peak Average Peak Average Peak Average

Panagiatakos 1.48 1.30 2.97 2.60 2.51 1.95 1.72% 1.52% 1.04% 0.84%

Aschheim 1.87 1.71 3.73 3.41 4.34 3.83 2.11% 1.92% 1.90% 1.66%

Chopra 1.97 1.76 3.94 3.53 4.64 4.14 2.20% 2.06% 2.03% 1.89%

Freeman 1.75 1.64 3.50 3.29 4.00 3.64 1.98% 1.85% 1.74% 1.58%

SEAOC 1.97 1.76 3.94 3.53 4.64 4.14 2.20% 2.06% 2.03% 1.89%

Priestley 1.95 1.78 3.90 3.55 4.57 4.15 2.23% 2.06% 2.08% 1.88%

Kappos 1.50 1.38 2.99 2.77 2.57 2.34 1.70% 1.60% 1.09% 1.01%

Ductility Demand Ductility Demand Ductility Demand

EQ-IV Walls F & G

Maximum Drift Maximum Drift

EQ-IV 3m Wall A EQ-IV 6m Wall B EQ-IV 8m Wall F EQ-IV Walls A, B & C

Panagiatakos EQ-I Ductility & EQ-IV inelastic rotation demands

Aschheim EQ-I Drift Limit = 0.5%

Chopra EQ-I Drift Limit = 0.5%

Freeman EQ-I Drift Limit = 0.5%

SEAOC EQ-I Drift Limit = 0.5%

Priestley EQ-I Drift Limit = 0.5%

Kappos EQ-I Ductility Limit = 1.0

Browning EQ-I (threshold strength requirement)

Method Parameter Governing Design




52

Table 5.13 Drift and ductility values obtained from Time History Analyses of Case Study 5

5.3 DESIGN DISPLACEMENT VERSUS MAXIMUM RECORDED DISPLACEMENT

To highlight each method’s ability to control displacements the following bar charts compare the

design or “target” displacement with the maximum displacement recorded for the 3 time history

analyses of each case study. Each bar chart compares the displacements at the seismic level that

governed designed as identified in Section 5.2. Therefore, graphs that show a large variation in target

displacement include some methods that were governed by EQ-1 and others that were governed by

EQ-4. The comparison is made of displacements recorded at an assumed effective height, except in the

case of Browning’s method that designs to a roof displacement associated with a drift limit. Where a

method does not directly design for a target displacement, but rather for a certain displacement

ductility limit, then the displacement ductility limit is multiplied by the yield displacement to give the

appropriate target displacement.

It was shown in Section 5.1 that each of the time histories used for the analyses form an envelope

around the design spectra. Therefore, the maximum recorded displacement should be considered as an

upper bound to the peak displacement that would be observed if a time history exactly fitting the

demand spectra were used. The following bar charts show that the maximum recorded displacement

rarely exceeds the design displacement. This is perhaps the clearest means of demonstrating that the

displacement based design methods really do work.

Peak Average Peak Average Peak Average Peak Average

Panagiatakos 0.65% 0.48% 0.62 0.49 3.3% 2.7% 2.5 2.2

Aschheim 0.58% 0.53% 0.54 0.49 3.5% 2.8% 3.7 3.1Chopra 0.64% 0.53% 0.52 0.45 3.1% 2.8% 2.7 2.4

Freeman 0.60% 0.51% 0.58 0.51 3.1% 2.8% 3.2 2.9

SEAOC 0.69% 0.56% 0.62 0.51 3.6% 2.9% 4.1 3.1

Priestley 0.62% 0.46% 0.64 0.49 3.2% 2.9% 2.9 2.4

Kappos 0.64% 0.54% 0.57 0.50 3.1% 2.8% 3.4 3.0

The 'peak' value refers to the highest maximum value recorded from the three time-history analyses.


EQ-IVEQ-I EQ-I EQ-IV

Top storey Drift Ductility DemandTop storey DriftDuctility Demand




53

5.3.1 Displacement Based Design Performance for Case Study 1

Figure 5.3 shows that for Case Study 1 all the methods provide designs that ensure the maximum

displacements are below or not significantly above the target displacement used during design.

0.000 0.100 0.200 0.300 0.400 0.500 0.600

ISDC

YPS

INSPEC

CASPEC

SEAOC

DDBD

T-HIST

Target Displacement (m) Recorded Displacement (m)

Figure 5.3 Comparison of design displacement with maximum recorded displacement for Case Study 1



displacements are below or not significantly above the target displacement used during design.

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700

ISDC

YPS

INSPEC

CASPEC

SEAOC

DDBD

T-HIST






54



displacements are below the target displacement used during design.

0.000 0.100 0.200 0.300 0.400 0.500 0.600

ISDC

YPS

INSPEC

CASPEC

SEAOC

DDBD

T-HIST





displacements are below the target displacement used during design. Note that the target

displacements for the Panagiotakos and Kappos methods are large because they design to EQ-1

without the use of a design drift limit. Recall that the Browning displacements are those measured at

the roof level.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

ISDC

YPS

INSPEC

CASPEC

SEAOC

DDBD

T-HIST

ISIP






55



displacements are below the target displacement used during design. As was observed for the frame

structure of Case Study 4, the design of Case Study 5 was controlled by EQ-1 for all methods. Note

that the target displacements for the Panagiotakos and Kappos methods are again large because they

design to EQ-1 without the use of a design drift limit.

It has already been noted that the designs of the frame structures for Case Studies 4 and 5 are governed

by an EQ-1 drift limit that is less than the yield drift. This indicates that the drift limits suggested by

SEAOC for frames may be inappropriate, however, if displacement based design methods are to be

used in a performance based design approach it is important that they can design for any target drift,

whether this target drift is less or greater than the yield drift. For instance a performance based design

approach should be able to design a building that has special non-structural drift limit requirements

that may be less than the yield drift.

0 0.05 0.1 0.15 0.2 0.25

ISDC

YPS

INSPEC

CASPEC

SEAOC

DDBD

T-HIST





Chapter 6. Evaluation

57

Figure 6.1 Displacement response spectra showing linear relation between displacement and period

Secondly, consider the equation for the fundamental period of an SDOF oscillator given in 6-2.

K

M T π 2= (6-2)

where, M = Mass

T = Structural period

K = Stiffness

Using the argument, as presented by Priestley and Kowalsky (1998) and Priestley (1998), that stiffness

is proportional to strength, relation 6-3 is written.

V T 1∝ (6-3)

where, V = Strength

Finally, by combining relations 6-1 and 6-3 one obtains equation 6-4 that shows that the displacement

is proportional to the square root of the inverse of the strength.

V S d

1∝ (6-4)

This final relation corresponds with the results observed in these case studies. For instance, consider

the Aschheim and Panagiotakos results for Case Study 1.

The ratio of design strengths between methods is:

15.33008

9480

Asch base

Pan base ==V

V

And the ratio of EQ-1 peak drifts is:

806.1

1

65.0

36.0

Asch

Pan ==δ

δ

Linear relation for

medium length periods

Period, T (s)

Spectral

Displacement

Sd (m)

T1 T2




58

This ratio, as expected is approximately equal to the square root of the inverse of the strength,

2

1

1

2

81.1

1

77.1

1

15.3

1

Disp

Disp

V

V =≈==

In other case studies the displacements were even less dependent on strength than equation 6-4implies. For Case Study 2, the wall structure with flexible foundations, despite ratios of strength

between methods of more than two, the drifts vary by less than 35%.

The foundation flexibility, K fdtn, associated with Case Study 2 effectively reduces the total building

stiffness, K total, below the value of stiffness, K, associated with an equivalent structure having rigid

foundations, as shown in equation 6-5.

fdtntotal K K K

111+= (6-5)

Since a constant value of foundation stiffness is used for all the methods, it is apparent that the

foundation stiffness will act to reduce the ratio of actual stiffness between different methods. For

example, consider two structures that have a structural stiffness equal to 4.0 and 2.0 respectively,

giving a structural stiffness ratio of 2.0. The ratio of total building stiffness for these two structures on

a foundation with a constant stiffness equal to 1.0 is reduced from 2.0 to only 1.2.

The reduction of total stiffness due to foundation flexibility clearly accounts for the reduced influence

strength has on displacements for Case Study 2. However, in Case Studies 4 and 5 drift ratios are also

less than that predicted by relationship 6-4. This could be explained by the large elastic periods of

these structures. As a consequence of long elastic periods the structures do not need to develop large

levels of inelasticity before entering the equal displacement region of the response spectra (seen as the

flat portion of the spectra shown in Figure 6.1). Within the equal displacement region of the spectra

the structures are expected to have the same maximum displacements as is observed for some of the

methods with relatively low design strengths in Case Studies 4 and 5.

6.1.2 Inadequate strength distribution procedures for the EQ1 performance level

For the time-history analyses of Case Study 3 the Ruaumoko 3D model develops drifts and

displacements that indicate the design methods ensure target design parameters are maintained.

However, preliminary results for Case Study 3 obtained using a fibre element model indicated that the

drift and displacement ductility demands for the EQ1 performance level will generally be close to or

above the design limits. This observation is understandable when considering the base shear

distribution procedures adopted by the design methods, all of which do not consider individual wall

yield displacements in relation to the target displacement. All of the methods adopt well established




59

procedures such as those described in Paulay and Priestley (1992) that distribute the design base shear

to each wall in relation to its length cubed (or squared as in the Direct DBD method) with an

adjustment of this shear for torsion effects. To demonstrate why this procedure could be considered

inadequate, Figure 6.2 shows a reasonable target displacement for the EQ1 level in relation to

individual wall yield displacements. The “reasonable” target displacement is selected on the basis that

some ductility demand can be accepted in the critical element of the structure; in this case the 8m wall.

It is of significance that the target displacement is around half the yield displacements of the 3m walls

(Walls A and C from Case Study 3).

Figure 6.2 Possible serviceability target displacement for Case Study 3 in relation to the yield

displacements of the different length walls

We see that by neglecting to consider the yield displacements of the walls in the distribution procedure

the methods are unable to provide a system with sufficient stiffness to develop the design base shear at

the target displacement. The design base shear will instead be developed only when all the walls have

yielded, i.e. at the yield displacement of the smallest wall, in this case the 3m wall.

As the stiffness of the system is lower than intended with the design strength distributed in this

manner, the elastic period and consequently the peak displacement of the structure for the low

intensity earthquake is increased. This has the effect of increasing the displacement ductility demands

on the longest walls, for which yielding is expected before the target displacement is attained. It also

Force

(kN)

y∆ 8m wall y∆ 3m wall Displacement (m)

3m wall stiffness assumed by the

strength distribution procedures

Actual stiffness and therefore the available strength of 3m

wall is less than expected due to large yield displacement

8m WALL

3m WALL

Target displacement

for EQ1 level




60

increases the inter-storey drifts and therefore the non-structural damage increases for the whole of the

building.

An improved distribution procedure would include magnification of the distributed base shear for each

wall by considering the ratio of the yield displacement to the target displacement as described in the

following paragraphs.

6.1.2.1 Recommended design strength magnification for serviceability level earthquakes

To ensure that the strength of a wall structure at low intensity “serviceability” type earthquakes is as

intended, the following simple magnification for walls with yield displacement greater than the target

displacement is recommended.

Each wall is given yield strength V iy:

Di

yi

iiy V V ∆

∆= for Di yi ∆>∆

iiy V V = for Di yi ∆≤∆

where: =∆ yi Yield displacement of wall i

=iyV Yield strength of wall i

=iV Required strength of wall i at the target displacement as obtained

from the base shear distribution in proportion to the length cubed (or

squared as for the Direct DBD method)

=∆ Di target displacement for wall i

note: DCRi D Di R ∆≈±∆=∆ .θ

where: =∆ D Design displacement of the structure

=θ Twist of structure (zero for plan-regular structures)

=CRi R Distance from wall i to centre of rigidity of structure

This recommended magnification is applicable not only to torsionally irregular structures but to any

structure that has members with significant variation in yield displacement. For instance where a

structure has two 8m and two 3m walls on both sides of the building, equal distance from the centre of

mass, the same type of magnification is necessary. It is envisaged that the procedure could also be




61

extended to hybrid structures which have a combination of frames and walls, provided the yield

displacements for each of the structural elements is known.

6.1.3 Twist induced period lengthening

It is worth pointing out that no recommendations to account for twist-induced period lengthening

were found for any of the methods. This period lengthening occurs in structures such as Case Study 3

because the twist of the structure causes the centre of mass to displace further than the centre of

rigidity. For methods that use a target displacement to obtain the required stiffness, it appears that an

initial estimate of the twist could be used to increase the target displacement. This larger target

displacement would then result in a longer period being designed for. However, neglecting this twist is

unlikely to result in non-conservative design since the structure would essentially be given a shorter

period and higher strength than what is necessary to maintain the target displacement.

Those methods that proceed using the period of the structure implicitly allow for the building twist

lengthening the period of the structure provided that the model used to obtain the period adequately

models the twisting displacement of the mass.

The next part of this chapter discusses points particular to each method that are considered to account

for the variations in performance observed between the methods.

6.2 PANAGIOTAKOS AND FARDIS’ METHOD

Design actions for the method developed by Panagiotakos and Fardis (1999) are generally higher than

the other methods. This is due to the recommendation that an uncracked model of the structure be used

in the initial elastic design to EQ-I. Other methods, including force based design methods, recommend

the use of section properties modified to allow for cracking observed in structures at the point of yield.

An uncracked model is stiffer with shorter periods of vibration than an identical structure with cracked

section properties. Since typical acceleration response spectra are greater at short periods the stiffer

uncracked model attracts a high base shear coefficient. This observation explains why the design

strength for all methods was governed by the initial elastic design to EQ-I.

Panagiotakos and Fardis (1999) discuss the issue of using a cracked model in the presentation of the

method. They suggest that if a ‘serviceability’ earthquake is selected at a level of 30% to 50% of the

‘life safety’ one then internal forces will be about the same as those calculated from force-based

design for the elastic ‘life safety’ earthquake divided by force reduction factor R, or q, of around 5. In

the case studies the ratio between the EQ-IV and EQ-I acceleration response spectra is around 5.75.

Therefore, the high demands obtained for EQ-I are not the result of an unrealistically intense




63

6.4 ASCHHEIM’S METHOD

The method presented by Aschheim and Black (2000) is one of two methods examined here that use

inelastic spectra in the design process. It is also one of two methods that utilise ADRS format for

design purposes. The result of this combination is a method that allows design for several limits states

in one step once the spectra have been constructed. The method performs well maintaining the drift

and ductility limits and providing low base shear strength and consequently cost effective design in

relation to other methods.

Integral to the success of the method is a good estimate of yield displacement. In the case studies the

method has benefited from the use of yield displacements obtained using equations for yield curvature

presented by Priestley and Kowalsky (2000). When one considers the shape of the YPS it becomes

apparent that yield displacements more than say 20% from the actual displacement could result in an

increase or decrease in design shear strength by some 50%. Aschheim does suggest that designers can

obtain the yield displacement from pushover analysis, however, this requirement would add significant

time to an otherwise relatively fast design procedure.

6.5 CHOPRA’S METHOD

The method successfully limits the drift demands within the design limits, while providing only a low

level of strength.

The method is not complete as a design tool since it does not provide recommendations for structural

types other than SDOF oscillators, does not recommend a procedure for distribution of shear and does

not suggest procedures for structures with flexible foundations.

Curiously, the method as presented by Chopra (2001), does not detail the principles by which the

method achieves success other than to commend the use of inelastic spectra. During the design process

it was noted that the level of ductility of the SDOF oscillator does not affect the inelastic displacement

spectra at intermediate and long periods. This approximation was shown to be relatively accurate byMiranda and Bertero (2001) through a large number of inelastic time-history analyses. The method

takes advantage of this characteristic behaviour of SDOF oscillators by implicitly suggesting that

initial stiffness therefore governs the displacement response of a system. The system success then

comes from identifying the required initial elastic stiffness required to achieve the target displacement

and multiplying this by a good estimate for yield displacement.




64

Figure 6.3 Relationship between the structural dimensions, yield displacement and ductility developed

considering the role of initial stiffness used in Chopra’s design method

For a structure of given dimensions the yield displacement can be considered constant (Priestley and

Kowalsky 2000). Therefore, for such a structure a unique level of strength will exist that satisfies the

minimum initial stiffness as shown in Figure 6.3. After a designer chooses an acceptable plastic

rotation the target displacement can essentially be fixed and known immediately (an exception occurs

for structures with flexible foundations). Therefore, only one level of strength will satisfy the initial

stiffness that is obtained from the inelastic displacement response spectra.

Keeping the above points in mind, it is also worth noting that Chopra does not recommend a process

for estimation of member sizes. Interestingly, considering that initial elastic stiffness is believed to

control the displacement response, it should be possible to quickly optimise the strength and

proportions of the structure such that the drift limit corresponds to the inelastic rotation limit. For

instance, if structural drift controls the target displacement, dimensions could be increased and a

higher level of ductility developed. Alternatively, if inelastic rotation capacity is controlling, then

dimensions could be reduced and the strength and yield displacement increased. A complication with

this procedure is that the inelastic rotation capacity for larger members is less and as a consequence

even though they can afford lower strength they would need a higher percentage of confinement steel.

Obviously for the smaller walls the reverse is true, in that the percentage of confining steel required

Ductility demand will depend

on the yield displacement of

the structure.

Spectral

Displacement

Spectral

Acceleration

Structures with this initial

elastic stiffness will obtain

same peak displacement, umax.

umaxuy 1 uy 2 uy 3

Yield displacement reduces

with increasing member size.

Unique level of strength

exists for each size

structure to give umax.




65

for inelastic rotation could be reduced even though the longitudinal steel for strength would be

increased.

6.6 FREEMAN’S METHOD

The method developed by Freeman (1998) is intended for the assessment of existing structures. This

project utilised the method for design by using the EQ-I demand spectra to set the initial base shear

strength. Results indicate that the procedure performs well since target design parameters are not

exceeded and the required strength is not excessive. For wall structures with irregular layout it is

important that the pushover analysis identifies the critical elements of the structure rather than

considering the system drift and ductility values. After the assignment of strength initially, pushover

analysis for the EQ-I limit state for irregular structures is likely to improve the performance of the

design procedure. However, this additional task would make the procedure more time consuming.

6.7 THE SEAOC METHOD

The SEAOC (1999) method performs relatively well giving cost efficient design and in general

maintaining the target design parameters. One point where the method may be improved could be

through the identification of an approximate yield displacement for the structure.

Target displacements for the design drift limit could be checked against the yield displacement and the

required effective stiffness adjusted if necessary. It was seen in Case Study 5, where the system yield

drift of 1.0% was twice that of the design drift of 0.5%, that the effective stiffness calculated should

have been multiplied by the yield displacement to obtain the required yield strength. By multiplying

the calculated effective stiffness by the displacement corresponding to the target drift, the effective

stiffness provided was actually equal to half of that intended.

Yield displacement values would also enable the design of structures with flexible foundations since

system ductility and damping values could be calculated relatively quickly. Furthermore, yield

displacements would enable accurate calculation of the required initial stiffness and therefore the

required yield strength for the structure, rather than relying on an estimate for the overstrength factor.

6.8 PRIESTLEY’S METHODThe method developed by Priestley and Kowalsky (2000) performs well giving cost efficient design

while maintaining the target design parameters. Performance appears to be excellent in all case

studies. However as already noted, preliminary time-history analyses for EQ1 of Case Study 3

suggested that for low intensity earthquakes the method may benefit from alternative procedures for

the distribution of strength to walls of differing length.




66

6.8.1 Distribution of strength in proportion to the wall length squared

The initial performance assessment for Case Study 3 suggested that the Direct DBD method develops

higher displacements in relation to other methods. This is not surprising given the points made in

Section 6.1.2 and considering the recommended procedure of distributing the design base shear to the

walls in proportion to their length squared rather than their length cubed as done in the other DBD

methods. While this distribution procedure is most rational (Priestley and Kowalsky 2000) for

structural response where all walls are expected to be yielding, it causes larger displacements and

ductility demands for the frequent EQ-I than other methods with the same total design base shear. By

distributing the design base shear in proportion to the wall length squared, more strength is assigned to

the shorter 3m walls and less to the longer 8m walls in comparison to other design methods. As the

strength of the shorter walls cannot be fully developed at the EQ1 design displacement (refer Section

6.1.2) a smaller percentage of the design base shear can be developed at the design displacement in

comparison to other methods. The structure is consequently provided with much lower elastic stiffness

than anticipated and therefore develops larger displacements and ductility demands than desired.

6.8.2 Use of an assumed displacement profile

Another point regarding the Direct DBD method relates to the use of an assumed displacement profile.

The success of the direct DBD method relies, amongst other things, on the inelastic displacement

profile assumed at the design response. Currently, displacement profiles are provided by Priestley and

Kowalsky (2000) for wall structures assuming that the code drift limit governs design. Indeed, it has

been shown by Kowlasky (2001) that a code drift limit of 2.5% will be critical for the design of walls

with aspect ratio greater than 1. However, the data presented by Kowlasky (2001) also shows that if

the code drift limit is 3.5%, as recommended in the SEAOC Bluebook, then walls of aspect ratio

around 3 to 5 may well be governed by inelastic rotation capacity. Since this inelastic rotation demand

is likely to be developed at the base of a cantilever wall it is assumed that a linear displacement profile

would be utilised. However, a linear profile and perhaps the current displacement profile

recommended for cases where the code drift governs, would not account for higher mode effects that

can be rather significant as shown by the Kappos results presented in Chapter 4.1.1 and 4.1.2.

Despite the dependence of the method on an assumed displacement profile, the method performedwell for the vertically irregular frame structure of Case Study 5. It is noted however, that the design of

Case Study 5 was controlled by the EQ-1 drift limit and it would be interesting to consider the

performance of the method applied to a structure with even greater irregularity that is governed by the

EQ-IV event.




67

6.9 KAPPOS’ METHOD

Design in accordance with Kappos’ method (2001) ensured that the drift and ductility values obtained

from time-history analyses were well within the design limits.

It appears that the design procedure for EQ-I could be made more efficient since throughout the case

studies it was always the strength for EQ-I that governed the design. To improve the design procedure

for EQ-I the method should also take into account the drift limit. The potential benefit of this was seen

in Case Study 5 where the average maximum drift of the structure exceeded the recommended

maximums even though the ductility demand was well within the acceptable value. The method could

combine the drift check it performs for the fairly low intensity EQ-II event. The fact that Kappos

checks the drift for EQ-II but not EQ-I suggests that the method was disadvantaged by the SEAOC

Bluebook EQ-I drift limits that were shown to be less than the yield drift for the frame case studies.

The method could also adopt a check of material strains associated with acceptable damage at the

serviceability limit state rather than a ductility limit of 1.0 as done in other methods.

This method may be considered unnecessarily complex and time consuming for most design situations

since multiple time-history analyses are required. However, the method does provide a thorough

procedure that can be used when the likely inelastic response of a structure appears difficult to predict.



Chapter 7. Summary

68

7. SUMMARY

Four properties could be considered valuable to a displacement based design procedure:

• Simplicity – Methods that can be applied relatively quickly and easily are more likely to be

accepted by the design community.

• Versatility – Methods should be able to design a variety of structural forms for a range of

performance levels.

• Performance – Methods should be able to efficiently design a structure to deform to the

extent intended by the target design parameters.

• Completeness – Methods should provide enough information for the designer to be able to

proceed without making too many assumptions. If assumptions are frequently required the

method is prone to misinterpretation.

In applying each of the displacement based design procedures to five different case studies these

qualities have been assessed and are presented in Figure 7.1. Values from 1 to 5 are assigned to each

method for each property where:

• 1 = Very Poor

• 2 = Poor

• 3 = Acceptable

• 4 = Good

• 5 = Excellent

This assessment is obviously subjective and is intended to give the reader a quick impression of how

each method compares.



Chapter 7. Summary

69

Figure 7.1 Author’s Assessment of the Displacement Based Design Procedures

Assessment of the Displacement Based Design Methods

0

1

2

3

4

5

P

a n a g i o t a k o

s

B r o w

n i n g

A s c h h e i m

C h o p

r a

F r e e

m a n

S E A O

C

P r i e s t l e y

K a p p o s

SIMPLICITY VERSATILITY PERFORMANCE CLARITY/COMPLETENESS



Chapter 8. Conclusions

70

8. CONCLUSIONS

Eight different displacement based design procedures have successfully been applied to 5 different

structural forms. Application has highlighted the strengths and weaknesses of each of the methods. We

see that all the methods successfully maintain the target design parameters even though significant

variation in design strength exists.

It is considered that many of the DBD methods could benefit from the use of alternative target design

parameters that can still ensure accurate performance based design. The different target design

parameters adopted by the methods cause differences in design strengths and yet have relatively little

influence on performance. It would be interesting to compare the strengths obtained by the DBD

methods when they utilise a common target displacement, associated with an agreed set of design

parameters.

The large variation in design strengths between methods has a relatively low influence on peak

displacements due to the relationship between stiffness and displacement. The influence was observed

to reduce with the inclusion of foundation flexibility and where the response entered the equal

displacement range of the spectra.

A new design strength magnification procedure is proposed in Chapter 6 for the performance based

design of structures having walls of different length. The procedure aims to ensure that the stiffness

provided is as intended for design limits associated with seismic events of low intensity.

Limitations have been identified for all of the eight displacement based design methods considered.

These limitations can be considered as minor in some instances and rather major in others. However, it

is also considered that all of these limitations can easily be overcome now that they have been

identified.



Chapter 9. Bibliography

72

9. BIBLIOGRAPHY

1. Aschheim M.A. and Black E.F. (2000) "Yield Point Spectra for Seismic Design and

Rehabilitation" Earthquake Spectra, Vol. 16, No.2, 317-336.

2. Browning J.P. (2001) "Proportioning of Earthquake-Resistant RC Building Structures" Journal ofthe Structural Division, ASCE , Vol. 127, No.2, 145-151.

3. Carr, A.J. (2001) “Ruaumoko 3D Users Manual” University of Canterbury, Christchurch, NewZealand.

4. Chopra A.K. and Goel R.K. (1999) "Capacity-Demand-Diagram Methods Based on Inelastic

Design Spectrum" Earthquake Spectra, Vol. 15, No.4, 637-656.

5. CEN (1996) European Prestandard ENV 1998: Eurocode 8 – Design provisions for earthquake

resistance of structures. Comite Europeen de Normalisation, Brussels.

6. Chopra A.K. and Goel, R.K. (2001) "Direct Dispalcement-Based Design: Use of Inelastic vs.

Elastic Design Spectra" Earthquake Spectra, Vol. 17, No.1, 47-65.

7. Fajfar P. (2000) "A Nonlinear Analysis Method for Performance-Based Seismic Design"

Earthquake Spectra, Vol. 16, No. 3, 573-592.

8. Fenves (2001) “Structural Dynamics” Course material presented at the ROSE School, theEuropean School of Advanced Studies in Reduction of Seismic Risk, University of Pavia, Italy.

9. Fib TG7.2 (2002), Displacement-based design and assessment, Bulletin in printing.

10. Freeman S.A (1998) "The Capacity Spectrum Method as a Tool for Seismic Design", Proceedings

of the 11th European Conference on Earthquake Engineering, Sept 6-11, Paris.




73

11. Gulkan, P., and Sozen, M. (1974). "Inelastic Response of Reinforced Concrete Structures toEarthquake Motions." ACI Journal , Vol. 71, No.12, 604-610.

12. Kappos A.J. and Manafpour, A. (2001) "Seismic Design of R/C buildings with the Aid of

Advanced Analytical Techniques", Engineering Structures, Vol. 23.

13. King, D.J., Priestley, M.J.N. and Park, R. (1986) “Computer Programs for concrete column

design.” Res. Report 86/12, Department of Civil Engineering, University of Canterbury, New

Zealand.

14. Kowalsky M.J. (2001) “RC Structural Walls Designed According to UBC and Displacement

Based Design Methods” ASCE, Vol. 127, No. 5.

15. Lepage, A. (1997) “A method for drift-control in earthquake-resistant design of reinforced

concrete building structures.” PhD thesis, University of Illinois, Urbana, Illinois.

16. Mander, J.P., Priestley, M.J.N., and Park, R. (1988) “Theoretical stress-strain model for confinedconcrete.” Journal Structural Engineering ASCE, Vol. 114, No.8, 1804-1826.

17. Miranda, E. and Bertero, V.V. (1994). “Evaluation of Strength Reduction Factors for Earthquake-

Resistant Design”, Earthquake Spectra, Vol. 10, No.2.

18. Nassar and Krawinkler (1992) “Seismic design based on ductility and cumulative damage

demands and capacities” Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings, P. Fajfar and H. Krawinkler, Eds., Elsevier Applied Science, New York.

19. Panagiatakos T.B., Fardis M.N. (1999) "Deformation-Controlled Earthquake-Resistant Design of

RC Buildings" Journal of Earthquake Engineering, Vol. 3 No. 4, 498-518.

20. Paret, T.F, Sasaki, K.K., Eilbekc, D.H., Freeman, S.A. (1996). "Approximate inelastic procedures

to identify failure mechanisms from higher mode effects." 11th World Conference on Earthquake

Engineering , Acapulco, Mexico.

21. Paulay, T. (2000) “Understanding Torsional Phenomena in Ductile Systems” Bulletin of the New

Zealand National Society for Earthquake Engineering , New Zealand National Society forEarthquake Engineering, Silverstream. Vol. 33, No.4.

22. Paulay, T. and Priestley, M.J.N. (1992) “Seismic Design of Concrete and Masonry Buildings.”(John Wiley & Sons Inc. New York) 744 pp.

23. Priestley M.J.N and Calvi, G.M. (1997) “Concepts and procedures for direct displacement-based

design” Seismic Design Methodologies for the Next Generation of Codes, Fajfar and Krawinkler

(eds.), Balkema, Rotterdam, 171-181.




74

24. Priestley M.J.N and Kowalsky M.J. (1998). "Aspects of Drift and Ductility Capacity of CantileverStructural Walls.” Bulletin of the New Zealand National Society for Earthquake Engineering , New

Zealand National Society for Earthquake Engineering, Silverstream. Vol. 31, No.2

25. Priestley M.J.N and Kowalsky M.J. (2000). "Direct Displacement-Based Design of ConcreteBuildings" Bulletin of the New Zealand National Society for Earthquake Engineering , New

Zealand National Society for Earthquake Engineering, Silverstream. Vol. 33, No.4.

26. Priestley M.J.N (1998). "Brief Comments on Elastic Flexibility of Reinforced Concrete Frames,

and Significance to Seismic Design.” Bulletin of the New Zealand National Society for Earthquake Engineering , New Zealand National Society for Earthquake Engineering,

Silverstream. Vol. 31, No.4

27. Priestley M.J.N (2001) “Direct Displacement Based Design Fundamental Considerations”. Part of

course material presented at the ROSE School, the European School of Advanced Studies in

Reduction of Seismic Risk.

28. Qi, X. and Moehle, J.P. (1991) “Displacement design approach for reinforced concrete structures

subjected to earthquakes.” Struct. Res. Series No. 413, Civ. Eng. Studies, University of Illinois,

Urbana, Illinois.

29. SEAOC (1997) Seismic Design Manual. Vol. III (1997 UBC version)

30. SEAOC (1999) Recommended Lateral Force Requirements and Commentary, 7 th Ed.

31. Shibata, A., Sozen, M., (1976). "Substitute Structure Method for Seismic Design in R/C." Journal

of the Structural Division, ASCE , 102(1), 1-18.

32. Shimazaki, K. and Sozen, M.A. (1984). “Seismic drift of reinforced concrete structures.” Tech.Res. Rep. Of Hazama-Gumi, Tokyo, 145-166.



ANNEX 1

SAMPLE INPUT FILES FOR THE RUAUMOKO TIME HISTORY ANALYSES



RUAUMOKO INPUT FILE: Case Study 1 – Wall Structure with Rigid Foundation

EIGHT STOREY CONCRETE WALL WITH RIGID BASE - Aschheim- all units: kN T & m

2 0 1 0 1 0 0 0 0 0 ! Control Parameters9 8 2 8 1 2 9.81 5.0 5.0 0.01 19.99 1.0 ! Frame and Time-history

10 1 10 3 1 10 1.0 0.1 ! Output and Plotting Options

0 0 ! Iteration Control

NODES

1 0.0 0.0 1 1 1 0 0 0 02 0.0 3.0 0 0 0 0 0 0 0

3 0.0 6.0 0 0 0 0 0 0 0

9 0.0 24.0 0 0 0 0 0 0 0

ELEMENTS

1 1 1 22 2 2 3

3 2 3 4

4 2 4 55 2 5 6

6 2 6 7

7 2 7 88 2 8 9

PROPS1 FRAME

1 0 0 4 0 0 ! Parameters

28.1E6 10.7E6 1.25 0 0.379 0 0 0 0 0 ! Elastic properties with I tangent,

0.0 0.011 1.74 0 ! Bi-linear & Hinge length end 1

0 0 8523 -8523 ! Yield properties0.5 0.0 1.0 2 ! Takeda Parameters

2 FRAME ! Wall sections1 0 0 4 0 0 ! Parameters

28.1E6 10.7E6 1.25 0 0.379 0 0 0 0 0 ! Elastic properties with I tangent

0.0 0.011 1.5 0 ! Bi-linear & Hinge length end 1

0 0 8523 -8523 ! Yield properties0.5 0.0 1.0 2 ! Takeda Parameters

WEIGHT 02 833 0

3 833 0

4 833 0

5 833 06 833 0

7 833 0

8 833 09 833 0

LOADS

2 0.0 -3443 0.0 -344

4 0.0 -344

5 0.0 -3446 0.0 -344

7 0.0 -344

8 0.0 -3449 0.0 -344

EQUAKE

0 1 0.01 1.0



RUAUMOKO INPUT FILE: Case Study 3 – Wall Structure with Irregular Layout

EIGHT STOREY CONCRETE WALL WITH RIGID BASE - Panagiotakos - all units: kN T & m

2 1 0 0 0 0 0 0 ! Control Parameters108 88 34 8 1 2 9.81 5.0 5.0 0.01 19.99 1.0 ! Wall and Time-history Information

10 1 10 10 1.0 0.1 1.0 0 ! Output and Plotting Options

DEFAULT ! Transformation of Plot axes


NODES1 0.125 0 -10 1 1 1 1 1 1 0 0

2 1.5 0 -19.875 1 1 1 1 1 1 0 0

3 6 0 -0.125 1 1 1 1 1 1 0 0

4 10.5 0 -10 1 1 1 1 1 1 0 0

5 12 0 -8.5 1 1 1 1 1 1 0 0

6 12 0 -11.5 1 1 1 1 1 1 0 07 12 0 -19.875 1 1 1 1 1 1 0 0

8 13.5 0 -10 1 1 1 1 1 1 0 0

9 18 0 -0.125 1 1 1 1 1 1 0 010 22.5 0 -19.875 1 1 1 1 1 1 0 0

11 23.875 0 -10 1 1 1 1 1 1 0 0

12 0.125 3 -10 2 0 2 0 2 0 101 013 1.5 3 -19.875 2 0 2 0 2 0 101 0

14 6 3 -0.125 2 0 2 0 2 0 101 0

15 10.5 3 -10 2 0 2 0 2 0 101 016 12 3 -8.5 2 0 2 0 2 0 101 0

17 12 3 -11.5 2 0 2 0 2 0 101 0

18 12 3 -19.875 2 0 2 0 2 0 101 0

19 13.5 3 -10 2 0 2 0 2 0 101 0

20 18 3 -0.125 2 0 2 0 2 0 101 021 22.5 3 -19.875 2 0 2 0 2 0 101 0

22 23.875 3 -10 2 0 2 0 2 0 101 0

23 0.125 6 -10 2 0 2 0 2 0 102 024 1.5 6 -19.875 2 0 2 0 2 0 102 0

25 6 6 -0.125 2 0 2 0 2 0 102 0

26 10.5 6 -10 2 0 2 0 2 0 102 0

27 12 6 -8.5 2 0 2 0 2 0 102 028 12 6 -11.5 2 0 2 0 2 0 102 0

29 12 6 -19.875 2 0 2 0 2 0 102 0

30 13.5 6 -10 2 0 2 0 2 0 102 031 18 6 -0.125 2 0 2 0 2 0 102 0

32 22.5 6 -19.875 2 0 2 0 2 0 102 0

33 23.875 6 -10 2 0 2 0 2 0 102 0

34 0.125 9 -10 2 0 2 0 2 0 103 035 1.5 9 -19.875 2 0 2 0 2 0 103 0

36 6 9 -0.125 2 0 2 0 2 0 103 0

37 10.5 9 -10 2 0 2 0 2 0 103 038 12 9 -8.5 2 0 2 0 2 0 103 0

39 12 9 -11.5 2 0 2 0 2 0 103 0

40 12 9 -19.875 2 0 2 0 2 0 103 0

41 13.5 9 -10 2 0 2 0 2 0 103 042 18 9 -0.125 2 0 2 0 2 0 103 0

43 22.5 9 -19.875 2 0 2 0 2 0 103 0

44 23.875 9 -10 2 0 2 0 2 0 103 045 0.125 12 -10 2 0 2 0 2 0 104 0

46 1.5 12 -19.875 2 0 2 0 2 0 104 0

47 6 12 -0.125 2 0 2 0 2 0 104 048 10.5 12 -10 2 0 2 0 2 0 104 0

49 12 12 -8.5 2 0 2 0 2 0 104 050 12 12 -11.5 2 0 2 0 2 0 104 0

51 12 12 -19.875 2 0 2 0 2 0 104 0

52 13.5 12 -10 2 0 2 0 2 0 104 0



53 18 12 -0.125 2 0 2 0 2 0 104 054 22.5 12 -19.875 2 0 2 0 2 0 104 0

55 23.875 12 -10 2 0 2 0 2 0 104 0

56 0.125 15 -10 2 0 2 0 2 0 105 057 1.5 15 -19.875 2 0 2 0 2 0 105 0

58 6 15 -0.125 2 0 2 0 2 0 105 0

59 10.5 15 -10 2 0 2 0 2 0 105 0

60 12 15 -8.5 2 0 2 0 2 0 105 061 12 15 -11.5 2 0 2 0 2 0 105 0

62 12 15 -19.875 2 0 2 0 2 0 105 063 13.5 15 -10 2 0 2 0 2 0 105 0

64 18 15 -0.125 2 0 2 0 2 0 105 0

65 22.5 15 -19.875 2 0 2 0 2 0 105 0

66 23.875 15 -10 2 0 2 0 2 0 105 0

67 0.125 18 -10 2 0 2 0 2 0 106 068 1.5 18 -19.875 2 0 2 0 2 0 106 0

69 6 18 -0.125 2 0 2 0 2 0 106 0

70 10.5 18 -10 2 0 2 0 2 0 106 071 12 18 -8.5 2 0 2 0 2 0 106 0

72 12 18 -11.5 2 0 2 0 2 0 106 0

73 12 18 -19.875 2 0 2 0 2 0 106 0

74 13.5 18 -10 2 0 2 0 2 0 106 075 18 18 -0.125 2 0 2 0 2 0 106 0

76 22.5 18 -19.875 2 0 2 0 2 0 106 0

77 23.875 18 -10 2 0 2 0 2 0 106 078 0.125 21 -10 2 0 2 0 2 0 107 0

79 1.5 21 -19.875 2 0 2 0 2 0 107 0

80 6 21 -0.125 2 0 2 0 2 0 107 0

81 10.5 21 -10 2 0 2 0 2 0 107 0

82 12 21 -8.5 2 0 2 0 2 0 107 083 12 21 -11.5 2 0 2 0 2 0 107 0

84 12 21 -19.875 2 0 2 0 2 0 107 085 13.5 21 -10 2 0 2 0 2 0 107 0

86 18 21 -0.125 2 0 2 0 2 0 107 0

87 22.5 21 -19.875 2 0 2 0 2 0 107 0

88 23.875 21 -10 2 0 2 0 2 0 107 0

89 0.125 24 -10 2 0 2 0 2 0 108 090 1.5 24 -19.875 2 0 2 0 2 0 108 0

91 6 24 -0.125 2 0 2 0 2 0 108 0

92 10.5 24 -10 2 0 2 0 2 0 108 093 12 24 -8.5 2 0 2 0 2 0 108 0

94 12 24 -11.5 2 0 2 0 2 0 108 0

95 12 24 -19.875 2 0 2 0 2 0 108 0

96 13.5 24 -10 2 0 2 0 2 0 108 097 18 24 -0.125 2 0 2 0 2 0 108 0

98 22.5 24 -19.875 2 0 2 0 2 0 108 0

99 23.875 24 -10 2 0 2 0 2 0 108 0100 12 0 -10 1 1 1 1 1 1 0 0

101 12 3 -10 0 1 0 1 0 1 0 0

102 12 6 -10 0 1 0 1 0 1 0 0

103 12 9 -10 0 1 0 1 0 1 0 0104 12 12 -10 0 1 0 1 0 1 0 0105 12 15 -10 0 1 0 1 0 1 0 0

106 12 18 -10 0 1 0 1 0 1 0 0

107 12 21 -10 0 1 0 1 0 1 0 0108 12 24 -10 0 1 0 1 0 1 0 0

ELEMENTS1 1 1 12 0 0 X 0

2 3 2 13 0 0 Z 0

3 6 3 14 0 0 Z 04 2 4 15 0 0 X 0



5 5 5 16 0 0 Z 06 5 6 17 0 0 Z 0

7 4 7 18 0 0 Z 0

8 2 8 19 0 0 X 09 6 9 20 0 0 Z 0

10 3 10 21 0 0 Z 0

11 1 11 22 0 0 X 0

12 1 12 23 0 0 X 013 7 13 24 0 0 Z 0

14 10 14 25 0 0 Z 015 2 15 26 0 0 X 0

16 9 16 27 0 0 Z 0

17 9 17 28 0 0 Z 0

18 8 18 29 0 0 Z 0

19 2 19 30 0 0 X 020 10 20 31 0 0 Z 0

21 7 21 32 0 0 Z 0

22 1 22 33 0 0 X 023 1 23 34 0 0 X 0

24 11 24 35 0 0 Z 0

25 14 25 36 0 0 Z 0

26 2 26 37 0 0 X 027 13 27 38 0 0 Z 0

28 13 28 39 0 0 Z 0

29 12 29 40 0 0 Z 030 2 30 41 0 0 X 0

31 14 31 42 0 0 Z 0

32 11 32 43 0 0 Z 0

33 1 33 44 0 0 X 0

34 1 34 45 0 0 X 035 15 35 46 0 0 Z 0

36 18 36 47 0 0 Z 037 2 37 48 0 0 X 0

38 17 38 49 0 0 Z 0

39 17 39 50 0 0 Z 0

40 16 40 51 0 0 Z 0

41 2 41 52 0 0 X 042 18 42 53 0 0 Z 0

43 15 43 54 0 0 Z 0

44 1 44 55 0 0 X 045 1 45 56 0 0 X 0

46 19 46 57 0 0 Z 0

47 22 47 58 0 0 Z 0

48 2 48 59 0 0 X 049 21 49 60 0 0 Z 0

50 21 50 61 0 0 Z 0

51 20 51 62 0 0 Z 052 2 52 63 0 0 X 0

53 22 53 64 0 0 Z 0

54 19 54 65 0 0 Z 0

55 1 55 66 0 0 X 056 1 56 67 0 0 X 057 23 57 68 0 0 Z 0

58 26 58 69 0 0 Z 0

59 2 59 70 0 0 X 060 25 60 71 0 0 Z 0

61 25 61 72 0 0 Z 0

62 24 62 73 0 0 Z 063 2 63 74 0 0 X 0

64 26 64 75 0 0 Z 0

65 23 65 76 0 0 Z 066 1 66 77 0 0 X 0



67 1 67 78 0 0 X 068 27 68 79 0 0 Z 0

69 30 69 80 0 0 Z 0

70 2 70 81 0 0 X 071 29 71 82 0 0 Z 0

72 29 72 83 0 0 Z 0

73 28 73 84 0 0 Z 0

74 2 74 85 0 0 X 075 30 75 86 0 0 Z 0

76 27 76 87 0 0 Z 077 1 77 88 0 0 X 0

78 1 78 89 0 0 X 0

79 31 79 90 0 0 Z 0

80 34 80 91 0 0 Z 0

81 2 81 92 0 0 X 082 33 82 93 0 0 Z 0

83 33 83 94 0 0 Z 0

84 32 84 95 0 0 Z 085 2 85 96 0 0 X 0

86 34 86 97 0 0 Z 0

87 31 87 98 0 0 Z 0

88 1 88 99 0 0 X 0

PROPS

1 FRAME1 0 0 0 0 0 0 ! Wall H & K Floor 1

3.20E+07 1.28E+07 2 0 3.841 3.841 1.67 1.67 0 0 0 ! E G A Jxx Izz Iyy Asz Asy Sy Sz Wgt

0 0 0 0 0 0 10 10 ! Section end properties

2 FRAME1 0 0 0 0 0 0 ! Wall I & J Floor 1

3.20E+07 1.28E+07 0.75 0 0.224 0.224 0.625 0.625 0 0 0 ! E G A Jxx Izz Iyy Asz Asy Sy Sz Wgt0 0 0 0 0 0 10 10 ! Section end properties

3 FRAME

1 0 0 0 4 0 0 ! Wall A & C Floor 1

3.20E+07 1.28E+07 0.75 0 0.116 0.116 0.625 0.625 0 0 0 ! E G A Jxx Izz Iyy Asz Asy Sy Sz Wgt0 0 0 0 0 0 10 10 ! Section end properties

0.99 0.99 0.05 0.05 ! Bi-linear factors

1.61 0 0 0 ! Hinge lengths end 10 0 0 0 0 0 ! Axial and Torsion Yield

2863 -2863 2863 -2863 ! Yield properties

0.5 0.0 1.0 2 !Takeda Properties

4 FRAME

1 0 0 0 4 0 0 ! Wall B Floor 1

3.20E+07 12816000 1.5 0 1.096 1.0959 1.25 1.25 0 0 0 ! E G A Jxx Izz Iyy Asz Asy Sy Sz Wgt0 0 0 0 0 0 10 10 ! Section end properties

0.99 0.99 0.05 0.05 ! Bi-linear factors

1.94 0 0 0 ! Hinge lengths end 1

0 0 0 0 0 0 ! Axial and Torsion Yield18694 -18694 18694 -18694 ! Yield properties0.5 0.0 1.0 2.0 !Takeda Properties

5 FRAME1 0 0 0 4 0 0 ! Wall D & E Floor 1

32041000 12816000 0.75 0 0.165 0.1654 0.625 0.625 0 0 0 ! E G A Jxx Izz Iyy Asz Asy Sy Sz Wgt

0 0 0 0 0 0 10 10 ! Section end properties0.99 0.99 0.05 0.05 ! Bi-linear factors

1.61 0 0 0 ! Hinge lengths end 1

0 0 0 0 0 0 ! Axial and Torsion Yield4671 -4671 4671 -4671 ! Yield properties



56 765.4 0 765.457 187.5 0 187.5

58 453.0 0 453.0

59 390.5 0 390.560 390.5 0 390.5

61 390.5 0 390.5

62 531.1 0 531.1

63 390.5 0 390.564 453.0 0 453.0

65 187.5 0 187.566 765.4 0 765.4

67 765.4 0 765.4

68 187.5 0 187.5

69 453.0 0 453.0

70 390.5 0 390.571 390.5 0 390.5

72 390.5 0 390.5

73 531.1 0 531.174 390.5 0 390.5

75 453.0 0 453.0

76 187.5 0 187.5

77 765.4 0 765.478 765.4 0 765.4

79 187.5 0 187.5

80 453.0 0 453.081 390.5 0 390.5

82 390.5 0 390.5

83 390.5 0 390.5

84 531.1 0 531.1

85 390.5 0 390.586 453.0 0 453.0

87 187.5 0 187.588 765.4 0 765.4

89 765.4 0 765.4

90 187.5 0 187.5

91 453.0 0 453.0

92 390.5 0 390.593 390.5 0 390.5

94 390.5 0 390.5

95 531.1 0 531.196 390.5 0 390.5

97 453.0 0 453.0

98 187.5 0 187.5

99 765.4 0 765.4

LOADS

EQUAKE

0 1 0.01 1.0



54 8.5852 26.215 0 0 055 9.7028 4.267 0 0 0

56 9.7028 7.925 0 0 0

57 9.7028 11.583 0 0 058 9.7028 15.241 0 0 0

59 9.7028 18.899 0 0 0

60 9.7028 22.557 0 0 0

61 9.7028 26.215 0 0 062 17.7292 4.267 0 0 0

63 17.7292 7.925 0 0 064 17.7292 11.583 0 0 0

65 17.7292 15.241 0 0 0

66 17.7292 18.899 0 0 0

67 17.7292 22.557 0 0 0

68 17.7292 26.215 0 0 069 18.8468 4.267 0 0 0

70 18.8468 7.925 0 0 0

71 18.8468 11.583 0 0 072 18.8468 15.241 0 0 0

73 18.8468 18.899 0 0 0

74 18.8468 22.557 0 0 0

75 18.8468 26.215 0 0 076 26.8732 4.267 0 0 0

77 26.8732 7.925 0 0 0

78 26.8732 11.583 0 0 079 26.8732 15.241 0 0 0

80 26.8732 18.899 0 0 0

81 26.8732 22.557 0 0 0

82 26.8732 26.215 0 0 0

83 27.9908 4.267 0 0 084 27.9908 7.925 0 0 0

85 27.9908 11.583 0 0 086 27.9908 15.241 0 0 0

87 27.9908 18.899 0 0 0

88 27.9908 22.557 0 0 0

89 27.9908 26.215 0 0 0

90 36.0172 4.267 0 0 091 36.0172 7.925 0 0 0

92 36.0172 11.583 0 0 0

93 36.0172 15.241 0 0 094 36.0172 18.899 0 0 0

95 36.0172 22.557 0 0 0

96 36.0172 26.215 0 0 0

ELEMENTS

1 1 1 2

2 3 2 37 3 7 8

8 2 9 10

9 4 10 11

14 4 15 1615 2 17 1816 4 18 19

21 4 23 24

22 2 25 2623 4 26 27

28 4 31 32

29 1 33 3430 3 34 35

35 3 39 40

36 6 2 4137 8 3 42



38 10 4 4339 10 5 44

40 12 6 45

41 12 7 4642 12 8 47

43 5 41 48

44 7 42 49

45 9 43 5046 9 44 51

47 11 45 5248 11 46 53

49 13 47 54

50 6 48 10

51 8 49 11

52 10 50 1253 10 51 13

54 12 52 14

55 12 53 1556 12 54 16

57 6 10 55

58 8 11 56

59 10 12 5760 10 13 58

61 12 14 59

62 12 15 6063 12 16 61

64 5 55 62

65 7 56 63

66 9 57 64

67 9 58 6568 11 59 66

69 11 60 6770 13 61 68

71 6 62 18

72 8 63 19

73 10 64 20

74 10 65 2175 12 66 22

76 12 67 23

77 12 68 2478 6 18 69

79 8 19 70

80 10 20 71

81 10 21 7282 12 22 73

83 12 23 74

84 12 24 7585 5 69 76

86 7 70 77

87 9 71 78

88 9 72 7989 11 73 8090 11 74 81

91 13 75 82

92 6 76 2693 8 77 27

94 10 78 28

95 10 79 2996 12 80 30

97 12 81 31

98 12 82 3299 6 26 83



100 8 27 84101 10 28 85

102 10 29 86

103 12 30 87104 12 31 88

105 12 32 89

106 5 83 90

107 7 84 91108 9 85 92

109 9 86 93110 11 87 94

111 11 88 95

112 13 89 96

113 6 90 34

114 8 91 35115 10 92 36

116 10 93 37

117 12 94 38118 12 95 39

119 12 96 40

PROPS1 FRAME

2 0 0 4 0 0 ! E-P Ground Corner Columns

32.0E6 12.3E6 1.138 0.873 0.0539 0 ! Elastic properties with I cracked (50%Ig)0.00 0.035 0.469 0.469 ! Bi-linear & Hinge length end 1

-48350 -30000 4058 5674 5775 2798 6101 0 ! Yield SURFACE

0.5 0.0 1.0 2 ! Takeda Parameters

2 FRAME2 0 0 4 0 0 ! E-P Interior Ground Columns

32.0E6 12.3E6 1.022 0.787 0.0532 0 ! Elastic properties with I cracked (50%Ig)0.00 0.035 0.469 0.469 ! Bi-linear & Hinge length end 1

-39620 -30000 1491 4351 4386 1047 1980 0 ! Yield SURFACE


3 FRAME2 0 0 0 0 0 ! Elastic Upper Corner Columns

32.0E6 12.3E6 1.138 0.873 0.06475 0 ! Elastic properties with I cracked (60%Ig)

4 FRAME

2 0 0 0 0 0 ! Elastic Interior upper Columns


5 FRAME

1 0 1 4 0 0 ! 1st Floor E-P Beams

32.0E6 12.3E6 0.927 0.77 0.01687 0 ! Elastic properties with I tangent0.0 0.020 0.59 0.59 ! Bi-linear & Hinge lengths

-434 -434 -322 322 0 0 ! Fixed End Moments and Shears

0.0 0.0 1108 -1906 1108 -1906 ! Yield properties


6 FRAME ! 1st Floor Elastic beam joints

1 0 0 0 0 0 !

32.0E6 12.3E6 0.927 0.77 0.1337 0 ! Elastic properties

7 FRAME

1 0 1 4 0 0 ! 2nd Floor E-P Beams32.0E6 12.3E6 1.003 0.83 0.02306 0 ! Elastic properties with I tangent

0.0 0.020 0.59 0.59 ! Bi-linear & Hinge length end 1

-429 -429 -319 319 0 0 ! Fixed End Moments and Shears0.0 0.0 1509 -2295 1509 -2295 ! Yield properties




8 FRAME ! 2nd Floor Elastic beam joints

1 0 0 0 0 0 !32.0E6 12.3E6 1.003 0.83 0.1689 0 ! Elastic properties

9 FRAME

1 0 1 4 0 0 ! 3rd & 4th Floor E-P Beams32.0E6 12.3E6 0.813 0.67 0.01397 0 ! Elastic properties with I crck

0.0 0.020 0.59 0.59 ! Bi-linear & Hinge length end 1-429 -429 -319 319 0 0 ! Fixed End Moments and Shears



10 FRAME ! 3rd & 4th Floor Elastic Beam joints1 0 0 0 0 0 !


11 FRAME

1 0 1 4 0 0 ! Floors 5,6 Beams

32.0E6 12.3E6 0.555 0.46 0.0073 0 ! Elastic properties with I crck

0.0 0.020 0.59 0.59 ! Bi-linear & Hinge length end 1-429 -429 -319 319 0 0 ! Fixed End Moments and Shears



12 FRAME ! Floors 5,6 & 7 Elastic Beam joints

1 0 0 0 0 0 !


13 FRAME

1 0 1 4 0 0 ! Floor 7 Yielding Beams32.0E6 12.3E6 0.555 0.46 0.00484 0 ! Elastic properties with I crck





WEIGHT 0

18 3796 019 4469 0

20 4469 0

21 4469 0

22 4469 023 4469 0

24 4517 0

LOADS

1 0 0 0

2 0 -45 0

3 0 -45 04 0 -46 05 0 -46 0

6 0 -46 0

7 0 -46 08 0 -38 0

9 0 0 0

10 0 -91 011 0 -90 0

12 0 -91 0

13 0 -90 014 0 -90 0



RUAUMOKO INPUT FILE: Case Study 5 – Vertically Irregular Frame Structure

EIGHT STOREY Irregular RC Frame - all units: kN T & m

2 0 1 0 1 0 0 0 0 0 ! Control Parameters107 132 14 8 1 2 9.81 5.0 5.0 0.01 19.99 1.0 ! Frame and Time-history

10 1 10 3 1 10 1.0 0.1 ! Output and Plotting Options


NODES

1 0 0 1 1 12 9 0 1 1 1

3 18 0 1 1 1

4 27 0 1 1 1

5 36 0 1 1 1

6 45 0 1 1 1

7 0 7 0 0 08 0.4 7 0 0 0

9 8.6 7 0 0 0

10 9 7 0 0 011 9.4 7 0 0 0

12 17.6 7 0 0 0

13 18 7 0 0 014 18.4 7 0 0 0

15 26.6 7 0 0 0

16 27 7 0 0 017 27.4 7 0 0 0

18 35.6 7 0 0 0

19 36 7 0 0 0

20 36.4 7 0 0 0

21 44.6 7 0 0 022 45 7 0 0 0

23 0 11 0 0 0

24 0.4 11 0 0 025 8.6 11 0 0 0

26 9 11 0 0 0

27 9.4 11 0 0 0

28 17.6 11 0 0 029 18 11 0 0 0

30 18.4 11 0 0 0

31 26.6 11 0 0 032 27 11 0 0 0

33 27.4 11 0 0 0

34 35.6 11 0 0 0

35 36 11 0 0 036 36.4 11 0 0 0

37 44.6 11 0 0 0

38 45 11 0 0 039 0 15 0 0 0

40 0.4 15 0 0 0

41 8.6 15 0 0 0

42 9 15 0 0 043 9.4 15 0 0 0

44 17.6 15 0 0 0

45 18 15 0 0 046 18.4 15 0 0 0

47 26.6 15 0 0 0

48 27 15 0 0 049 27.4 15 0 0 0

50 35.6 15 0 0 051 36 15 0 0 0

52 0 19 0 0 0

53 0.4 19 0 0 0



7 3 7 238 3 10 26

9 3 13 29

10 3 16 3211 3 19 35

12 3 22 38

13 3 23 39

14 3 26 4215 3 29 45

16 3 32 4817 3 35 51

18 3 39 52

19 3 42 55

20 3 45 58

21 3 48 6122 3 51 64

23 3 52 65

24 3 55 6825 3 58 71

26 3 61 74

27 3 64 77

28 3 65 7829 3 68 81

30 3 71 84

31 3 74 8732 3 78 88

33 3 81 91

34 3 84 94

35 3 87 97

36 3 88 9837 3 91 101

38 3 94 10439 3 97 107

40 4 7 8

41 7 8 9

42 4 9 10

43 4 10 1144 7 11 12

45 4 12 13

46 4 13 1447 7 14 15

48 4 15 16

49 4 16 17

50 7 17 1851 4 18 19

52 4 19 20

53 7 20 2154 4 21 22

55 4 23 24

56 8 24 25

57 4 25 2658 4 26 2759 8 27 28

60 4 28 29

61 4 29 3062 8 30 31

63 4 31 32

64 4 32 3365 8 33 34

66 4 34 35

67 4 35 3668 8 36 37



69 4 37 3870 5 39 40

71 9 40 41

72 5 41 4273 5 42 43

74 9 43 44

75 5 44 45

76 5 45 4677 9 46 47

78 5 47 4879 5 48 49

80 9 49 50

81 5 50 51

82 5 52 53

83 10 53 5484 5 54 55

85 5 55 56

86 10 56 5787 5 57 58

88 5 58 59

89 10 59 60

90 5 60 6191 5 61 62

92 10 62 63

93 5 63 6494 5 65 66

95 11 66 67

96 5 67 68

97 5 68 69

98 11 69 7099 5 70 71

100 5 71 72101 11 72 73

102 5 73 74

103 5 74 75

104 11 75 76

105 5 76 77106 6 78 79

107 12 79 80

108 6 80 81109 6 81 82

110 12 82 83

111 6 83 84

112 6 84 85113 12 85 86

114 6 86 87

115 6 88 89116 13 89 90

117 6 90 91

118 6 91 92

119 13 92 93120 6 93 94121 6 94 95

122 13 95 96

123 6 96 97124 6 98 99

125 14 99 100

126 6 100 101127 6 101 102

128 14 102 103

129 6 103 104130 6 104 105



131 14 105 106132 6 106 107

PROPS1 FRAME

2 0 0 4 0 0 ! E-P Ground Corner Columns


0.00 0.027 0.600 0.600 ! Bi-linear & Hinge length end 1-38435 -15000 3092 3743 3666 2762 8902 0 ! Yield SURFACE


2 FRAME

2 0 0 4 0 0 ! E-P Interior Ground Columns


0.00 0.027 0.600 0.600 ! Bi-linear & Hinge length end 1-36011 -15000 2571 3200 3021 2002 6322 0 ! Yield SURFACE


3 FRAME

2 0 0 0 0 0 ! Elastic Upper Columns


4 FRAME ! 1st & 2nd Floor Elastic beam joints

1 0 0 0 0 0 !

32.0E6 12.3E6 0.691 0 0.0469 0 ! Elastic properties (assume zero shear deforamtion at joint)

5 FRAME ! 3rd 4th & 5th Floor Elastic Beam joints

1 0 0 0 0 0 ! (assume zero shear deforamtion at joint)

32.0E6 12.3E6 0.631 0 0.0334 0 ! Elastic properties

6 FRAME ! Floors 8,6 & 7 Elastic Beam joints

1 0 0 0 0 0 ! (assume zero shear deforamtion at joint)32.0E6 12.3E6 0.541 0 0.0183 0 ! Elastic properties

7 FRAME

1 0 1 4 0 0 ! 1st Floor E-P Beams

32.0E6 12.3E6 0.691 0.576 0.01296 0 ! Elastic properties with I tangent0.0 0.021 0.59 0.59 ! Bi-linear & Hinge lengths


0.0 0.0 1420 -1717 1420 -1717 ! Yield properties0.5 0.0 1.0 2 ! Takeda Parameters

8 FRAME

1 0 1 4 0 0 ! 2nd Floor E-P Beams32.0E6 12.3E6 0.691 0.576 0.01157 0 ! Elastic properties with I tangent

0.0 0.021 0.59 0.59 ! Bi-linear & Hinge lengths



9 FRAME1 0 1 4 0 0 ! 3rd Floor E-P Beams32.0E6 12.3E6 0.631 0.526 0.00890 0 ! Elastic properties with I crck




10 FRAME

1 0 1 4 0 0 ! 4th Floor E-P Beams

32.0E6 12.3E6 0.631 0.526 0.00817 0 ! Elastic properties with I crck0.0 0.021 0.59 0.59 ! Bi-linear & Hinge length end 1



74 800 077 800 0

78 750 0

81 750 084 750 0

87 750 0

88 750 0

91 750 094 750 0

97 750 098 750 0

101 750 0

104 750 0

107 750 0

LOADS

7 0 -11.1 0

10 0 -22.2 013 0 -22.2 0

16 0 -22.2 0

19 0 -22.2 0

22 0 -11.1 023 0 -11.1 0

26 0 -22.2 0

29 0 -22.2 032 0 -22.2 0

35 0 -22.2 0

38 0 -11.1 0

39 0 -11.1 0

42 0 -22.2 045 0 -22.2 0

48 0 -22.2 051 0 -11.1 0

52 0 -11.1 0

55 0 -22.2 0

58 0 -22.2 0

61 0 -22.2 064 0 -11.1 0

65 0 -11.1 0

68 0 -22.2 071 0 -22.2 0

74 0 -22.2 0

77 0 -11.1 0

78 0 -11.1 081 0 -22.2 0

84 0 -22.2 0

87 0 -11.1 088 0 -11.1 0

91 0 -22.2 0

94 0 -22.2 0

97 0 -11.1 098 0 -11.1 0101 0 -22.2 0

104 0 -22.2 0

107 0 -11.1 0

EQUAKE

0 1 0.01 1.0

PUSHOVER_PRESENTACION.pdf

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