Shear Strength of Slab-Corner Column

Connections

by

Claudia Correa Agudelo

June 2003

Department of Civil Engineering and Applied Mechanics

McGill University

Montreal, Canada

A Thesis submitted to the Faculty of Graduate Studies

and Research in partial fulfillment of the requirements

for the degree of Master of Engineering

/ ' t

© Claudia Correa Agudelo, 2003

' • »

To my Mom and Dad

Shear Strength of Slab-Corner Column Connections

Abstract

The 1994 CSA Standard requires that slab-column connections be

designed for one-way shear and two-way shear action. Three full-scale slab and

corner column specimens were constructed and tested to failure to investigate

the influence of the size of corner column on the slab shear capacity. The

current design provisions of the 1994 CSA Standard and EC2-02 were compared

with the experimental results of the three specimens.

The experimental results indicate that the predictions for one-way shear

action are more accurate than the predictions for two-way shear action. The

beneficial effects of increasing the column size in improving the shear capacity

and mode of failure are demonstrated.

Resistance en Cisaillement de connexions dalle-colonne de coin

Resume

La norme CSA 1994 exige que les connexions dalles-colonnes soient

congues I'effet de cisaillement uni et bidirectionnel. Trois specimens de dalle et

colonne de coin en grandeur reelle ont ete construits et testes jusqu'a la rupture

afin d'evaluer I'influence de la taille des colonnes sur la resistance en

cisaillement des dalles. Les resistances calculees selon les normes CSA 1994

et EC2-02 ont ete comparees avec les resultats experimentaux des trois

specimens.

Les resultats experimentaux demontrent que les predictions pour I'effet de

cisaillement en une direction sont plus precises que les predictions pour I'effet

bidirectionnel. Les essais demontrent que la resistance en cisaillement

augmente avec la taille des colonnes.

Acknowledgements

The author would like to express her deepest thanks to Professor Mitchell

for his expert guidance and his continued encouragement, advice and support

throughout this research programme. The author would also like to thank Dr.

William Cook for his assistance and his helpful suggestions.

The research was carried out in the Jamieson Structures Laboratory at

McGill University. The author wishes to thank Ron Sheppard, John Bartczak,

Marek Przykorski and Damon Kiperchuk for their assistance in the construction

and testing of the specimens. The assistance of Zhenyu Li in the laboratory is

also appreciated.

The valuable help of the secretaries of the Civil Engineering Department,

particularly Ann Bless, Sandy Shewchuk-Boyd, Franca Delia Rovere, and Anna

Dinolfo was much appreciated during the course of this research project.

The author would also like to express her deepest gratitude to her

parents, and her sister Marisabel for their constant support. Finally, the author

would like to thank the Engineer Louis Brunet for his continuous encouragement,

help, patience and understanding.

Claudia Correa

May, 2003

Table of contents

Abstract Resume Acknowledgements List of Figures v List of Tables v List of Symbols ix

Chapter 1: Introduction and Literature Review 1

1.1 Introduction 1 1.2 Key Research Studies 2 1.3 North American Codes 12 1.4 European Codes 16 1.5 Research Objectives 18

Chapter 2: Experimental Programme 20

2.1 Description of Prototype Structure 20 2.2 Design of Test Specimens 20 2.3 Details of Test Specimens 22

2.3.1 Specimen S1 22 2.3.2 Specimen S2 22 2.3.3 Specimen S3 23

2.4 Construction Sequence 23 2.5 Material Properties 24

2.5.1 Reinforcing Steel 24 2.5.2 Concrete 24

2.6 Testing Procedure 27 2.6.1 Test Setup and Loading Apparatus 27 2.6.2 Instrumentation 28

Chapter 3: Experimental Results 46

3.1 Specimen S1 47 3.2 Specimen S2 49 3.3 Specimen S3 51

Chapter 4: Analyses and Comparison of Results 68

4.1 Comparison of Experimental Results 68 4.2 Comparison of Experimental Results with Code Predictions 72

IV

Chapter 5: Conclusions 80

5.1 Conclusions 80

References 82

List of Figures

Chapter 2

2.1 Plan of prototype flat plate structure 30 2.2 Reinforcement details for bottom steel in S1 31 2.3 Top reinforcement in Specimen S1 32 2.4 Detailed view of the joint in Specimen S1 33 2.5 Bottom reinforcement details for Specimen S2 34 2.6 Arrangement on top steel for Specimen S2 35 2.7 Detailed view of the joint in Specimen S2 36 2.8 Bottom reinforcement details for Specimen S3 37 2.9 Top steel for specimen for Specimen S3 38 2.10 Detailed view of the joint in Specimen S3 39 2.11 Overall view of the specimens before casting 39 2.12 Stress-strain curves for reinforcing bars 40 2.13 Compressive stress-strain responses for concrete 40 2.14 Shrinkage strain curve 41 2.15 Test Setup for specimens 42 2.16 Overall view of loading setup 43 2.17 Location of LVDTs 44 2.18 Position of strain gauges 45

Chapter 3

3.1 Load versus average deflection of Specimen S1 53 3.2 Strain distribution of top reinforcement in Specimen S1 at

key load stages 53 3.3 Flexural cracking on top surface of Specimen S1 at a

shear of 75.5 kN 54 3.4 Flexural shear cracks at a shear of 111.8 kN in Specimen

S1, north face 54 3.5 Maximum crack width for Specimen S1 55 3.6 Shear failure in Specimen S1, north face 56 3.7 Shear failure in Specimen S1, west face 56 3.8 Top surface after shear failure in Specimen S1 57 3.9 Overall view of shear failure in north face in Specimen S1

at shear of 125.6 kN 57 3.10 Load versus average deflection of Specimen S2 58 3.11 Strain distribution of top reinforcement in Specimen S2 at

key load stages 58 3.12 Flexural cracking on top surface of Specimen S2 at a

VI

shear of 75.2 kN 59 3.13 Flexural shear cracks at a shear of 113 kN in Specimen

S2, west face 59 3.14 Maximum crack width for Specimen S2 60 3.15 Shear failure in Specimen S2, north face 61 3.16 Shear failure in Specimen S2, west face 61 3.17 Top surface after shear failure in Specimen S2 62 3.18 Overall view of shear failure in north face in Specimen S2

at shear of 116.7 kN 62 3.19 Load versus average deflection of Specimen S3 63 3.20 Strain distribution of top reinforcement in Specimen S3 at

key load stages 63 3.21 Flexural cracking on top surface of Specimen S3 at a

shear of 67.1 kN 64 3.22 Flexural shear cracks at a shear of 120.9 kN in

Specimen S3, west face 64 3.23 Maximum crack width for Specimen S3 65 3.24 Flexure-shear failure in Specimen S3, north face 66 3.25 Flexure-shear failure in Specimen S3, west face 66 3.26 Top surface after flexure-shear failure in Specimen S3 67

Chapter 4

4.1 Load versus average deflection 77 4.2 Load versus average deflection 77 4.3 Variation of strength predicted by the 1994 CSA Standard

with the column size 78 4.4 Variation of strength predicted by the 1994 CSA Standard

and EC2-02 with the column size 79

VII

List of Tables

Chapter 2

2.1 Summary of reinforcing bar properties 24 2.2 Concrete mix design 25 2.3 Concrete properties 26

Chapter 4

4.1 4.2

4.3

4.4

Summary of key load stages for Specimens S1, S2 and S3 ....69 Maximum crack widths at peak loads for Specimens S1,

S2 and S3 71 Predicted failure loads for Specimens S1, S2 and S3

according to the 1994 CSA Standard 73 Predicted shear strength for the three specimens with

EC2-02 75

VIII

List of Symbols

Ac area of critical section

Asw area of shear reinforcing steel

b perimeter of loaded area

b0 critical shear perimeter

c size length of the square column

C nominal shear stress according to plastic limit analysis

Ci size of the edge column perpendicular to the edge of the slab (CT > c2)

c2 size of the edge column parallel to the edge of the slab

d effective depth

da maximum aggregate size

dst diameter of the column

e eccentricity of the applied load from the centroid of the column

ex eccentricity of the applied load in the x direction (ex > ey)

ey eccentricity of the applied load in the y direction

f'c concrete compressive strength

fc20o compressive strength measured on a 200 mm diameter cylinder

fck strength below which 5% of all possible strength measurements for the specified concrete may be expected to fall

fck cube compressive cube strength of concrete

Fct vertical component of the concrete tensile stresses

Fdow dowel-force of the flexural reinforcing bars

pun

vertical component of the forces in inclined prestressing tendons

punching load

fr modulus of rupture of concrete

fsp splitting strength of concrete

Fsw vertical component of the forces in the shear reinforcement

fsw stress of shear reinforcement

fuit ultimate strength of reinforcing steel

fy yield stress of steel reinforcement

fyk characteristic yield stress of reinforcing bars

h thickness of the slab

J polar moment of inertia of the critical section about its centroidal axis

jd flexural lever arm

k size effect factor

k^ k2empirical constants in Eq. (1.12)

k2 empirical constant in Eq. (1.28)

ls shear span

lx, ly lengths of projections of the critical section for two-way shear

m ultimate resisting moment

Mt design moment transferred to the column

Mu factored moment

n ratio of the area of the reinforcing steel in the loaded area over the total area of tensile reinforcement

nc stress concentration factor to account for the concrete strength under a multiaxial state of stress

IX

p

V

Vc

vr

applied axial force on slab

shear force

nominal punching shear strength provided by the concrete

factored shear stress resistance

Vfiex shear force at flexural ultimate strength

Vr factored shear stress resistance

Vest observed shear force at shear failure

Vu punching shear resistance

vu ultimate shear stress

Vu1 cracking shear force of the conical shell in Coulomb's law

Vu2 cracking shear force of the catenary shell in Coulomb's law

x height of compression zone at flexure in tagential direction when punching occurs

a inclination of the punching shear crack

as factor which adjusts vc for support dimensions

pc ratio of the long to the short dimensions of the column

ey yield strain of reinforcing steel

(j) strength reduction factor for shear

<t>o relationship between shear and moment capacity in the vicinity of the loaded area

<f>c resistance factor for concrete

yf fraction of unbalanced moment transferred by flexure

yv fraction of unbalanced moment transferred by eccentricity of shear

r\ reduction factor accounting for the influence of torsion

X factor accounting for concrete density

X ratio of the diameter of the column to the effective depth

A.0 empirical parameter

(Ltg tension reinforcement ratio

p flexural reinforcement ratio

ai principal tensile stresses in the concrete

co mechanical reinforcement ratio

t, size effect factor

\\i rotation

Chapter 1

Introduction and Literature Review

1.1 Introduction

Flat plates are very popular structural systems due to their architectural

versatility and the reduced construction time through the use of flying forms. The

shear strength of slabs in the vicinity of columns is governed by the more severe

of two conditions, either one-way shear or two-way shear action. According to

the 1994 CSA Standard for the "Design of Concrete Structures" (CSA 1994) it is

necessary to check for both of these types of failure modes when designing flat

plates. The objective of this thesis is to investigate the behaviour of two-way

slabs failing in shear around corner columns and to propose a method for

assessing the types of shear failures.

In this chapter, the design approaches of the 1994 CSA Standard (CSA

1994), the American Concrete Institute "Building Code Requirements for

Structural Concrete" (ACI 318-02), the German Design Standard (DIN 1045

1988), the British Standard 8110 (1997) and the Eurocode 2 (EC2-02) are

discussed and compared. In addition some of the key research studies leading

up to the code developments are also discussed.

1.2 Key Research Studies

Many researchers have studied the behaviour of reinforced concrete

elements subjected to shear. In 1902, the German engineer, E. Morsch (Morsch

1902) developed the following equation for nominal shear stress, v, in a beam

subjected to flexural cracking:

v = — (1.1) bjd

where V is the shear, b is the perimeter of the loaded area and jd is the flexural

lever arm.

Morsch also described the resisting mechanisms for shear in the form of a

truss idealization with parallel chords and compressive diagonals inclined at 45

degrees with respect to the longitudinal axis.

A few years later, A. N. Talbot presented the results of his research study

on reinforced concrete footings which has had a significant impact on design

practice. Talbot (1913) carried out experiments on 114 wall footings and 83

column footings. He calculated the shear stress in the footings around the

square columns from the following equation:

v = , V , (1.2) 4(c + 2d)jd

where c is the side length of the square column and d is the effective depth of the

footing.

Talbot found that the shear strength increased as the amount of tensile

reinforcement in the slabs was increased. Based on the specimens that failed in

shear, he concluded that the critical section was located at a distance of d from

the face of the column.

In 1933 Graf studied the shear strength of slabs loaded by concentrated

loads near the supports. He found that the shear capacity decreased as the load

was moved away from the supports and increased with increasing concrete

strength. Graf proposed the following formula for the shear stress in slabs:

v = — (1.3)

4ch

where h is the thickness of the slab.

He suggested that the flexural cracking might have some influence on the

shear strength.

In 1939 Richart and Kluge (1939) found that an increase of the flexural

strength of the slabs would result in increased shear strength.

In 1946, Forsell and Holmberg reported results of different tests that were

carried out over a period from 1926 to 1928. They assumed that the shear stress

distribution was parabolic and utilized a critical section at a distance of 0.5h from

the edges of the loaded area. Their expression for the maximum shear stress

was: 1 - 5 V M A\

bh

They also concluded that increasing the slab moments decreased the shear

strength.

Shear tests on mortar bridge deck slabs were reported at the University of

Illinois by Newmark, Siess et al. (1946). Their results indicated that the failure

loads were dependent on the same factors as the loads at first yielding.

In 1948, Richart (1948) concluded that shearing stresses at failure of slab-

column connections, calculated on a critical section located at a distance d from

the faces of the columns, varied generally from 0.05 f'c to 0.09 f'c.

In 1953, based on the results reported by Richart (1948), Hognestad

(1953) suggested that the shearing stresses be computed at zero distance from

the loaded area or column faces. Hognestad developed the following expression

for the shear stress at failure:

V v =

78bd

' -_ 0.07A

0.035 + fc+130psi (1.5)

where <|>o is the ratio ——, where Vtest is the observed shear force at shear Vflex

failure and Vfiex the shear force at flexural ultimate strength as computed by yield-

line theory.

In 1956, Elstner and Hognestad (1956) reported that the concentration of

the tension and compression reinforcement in the column region as well as the

effect of eccentricity of the applied load had no effect on the ultimate shearing

strength. The shearing strength was calculated as:

v = — — = 333 psi + 0 . 0 4 6 ^ (1.6) 7

8 b d 4>0

In 1957, an ultimate strength theory for shear was presented by Whitney

(1957), based on previous test results but ignoring those that involved bond

failure. He assumed that the shear strength is primarily a function of the ultimate

resisting moment, m, inside the "pyramid of rupture" whose surface makes 45

degrees with the column.

The shear strength at a distance d/2 from the perimeter of the loaded area

was given by

v = 100psi + 0.75^- P- (1.7)

where ls is the "shear span" which is the distance between the support and the

nearest edge of the loaded area in the case of a slab supported along the edges.

A good approximation of the ultimate shear stress was found by Scordelis,

Lin and May (1958), when using equations (1.6) and (1.7).

In 1961, Moe (1961) verified that there is an interaction between flexure

and shear which Elstner and Hognestad and Whitney had suggested (see Eq.

(1.6) and (1.7)).

Based on test results in the literature and on the results of tests on 43

slabs, tested under different conditions, he found that the shear force at the

calculated ultimate flexural capacity of the slab, Vfiex, was one of the parameters

governing the shear strength of slabs and footings. The concrete strength, f'c,

and the ratio of the side length of the loaded area to the slab thickness, c/d, were

also directly related to the calculation of the ultimate shearing strength which was

expressed as

r

bd

15 1-0.075-v

5.25bdJf'c

1+ y

15 1-0.075-d

5.25<|)c (1.8)

V flex

Moe concluded that the inclined cracking load should be determined on

the basis of stresses computed at a distance of d/2 from the periphery, while the

shear compression failure should be predicted on the basis of the stresses on the

periphery of the loaded area or column. Moe suggested that for design, the

shearing stresses should be calculated as:

v = 9.23-1.12-d

v = 2.5 + 10

fc f o r - < 3 d

fo r - > 3 d

(1.9a)

(1.9b)

At the same time, a rational mechanical model for the punching shear

failure of slabs was proposed by Kinnunen and Nylander in Europe. Based on

61 tests on circular slabs with circular column stubs, the model predicts the

ultimate load for both flexural and punching failures, and is also capable of

predicting the deformation of slabs at failure. The model involves the rigid

rotation of slab portions separated by radial cracks. This research was the basis

of the 1964 Swedish Building Code (1964) and had significant influence upon

European code considerations.

In 1975, Hawkins, Mitchell and Hanna (1975) found that concentrating the

reinforcement in the column region, within a distance of 1.5 times the slab

thickness on both sides of the column, improved the resistance to punching

shear, however the ductility was reduced (Hawkins and Mitchell 1979).

During the 1970's, limit analysis was applied to study all types of failure,

including brittle failures such as punching shear. One of these studies was

published in 1976 by Braestrup, Nielsen et al. (1976). Based on the theory of

plasticity, they assumed concrete as a perfectly plastic material. They used

Coulomb's law to predict the punching shear resistance, Vu, by comparing the

fracture energy of the conical shell with the work performed by the applied loads,

giving:

Vu = Vu1+Vu2 (1.10)

where Vui describes the cracking shear of the conical shell and VU2 gives the

cracking shear of the catenary shell.

In 1985 Regan (1985) discussed the punching shear resistance of

connections of slabs with edge and corner columns. Assuming that the

resistance to nodal forces and torsion at the slab edge are lost when torsion

cracking occurs, the pure bending resistance is the ultimate moment provided by

the reinforcement perpendicular to the edge.

Rankin and Long (1987) proposed a new formula to calculate the

punching shear strength, V, which involves the reinforcement ratio, p (equal to

As/bd) as follows:

V=1.66 7^7(c + d)d VlOOp (1.11)

In 1987 several tests were carried out by Bazant and Cao (1987), in order

to quantify the size effect on the punching shear resistance. This was based on

the concept that the punching load should be predicted by fracture mechanics

instead of plastic limit analysis because the failure does not occur simultaneously

along the ultimate failure surface. They concluded that the nominal stress at

failure decreases as the size increases and regarded this behaviour as a direct

confirmation of the size-effect law.

The punching load was proposed as:

v„ =C 1 + V M a 7

(1.12)

where vu is the nominal shear stress; d is the effective depth of the slab; X0 is the

empirical parameter characterizing the fracture energy of the material and the

shape of the structure; da is the maximum aggregate size; and C is the value of

the nominal shear stress according to plastic limit analysis and is calculated as

C = k1fc^1 + k 2 ^

where ki and k2 are empirical constants.

In 1989 Georgopoulos (1989) proposed a method for the calculation of the

punching shear strength and the angle of inclined cracking of a slab without

shear reinforcement. He assumed that approximately 75% of the punching shear

was carried by the principal tensile stresses a, in the concrete and could be

calculated from the vertical component of the resulting tensile force. Hence, the

punching shear was calculated as:

Vu =4.13a1d2cota - + 0.20 + 0.35cota (1.13) v2 J

where GAS given by 0.17 (fck, Cube)2/3; d is the effective depth; a is the inclination of

the inclined punching shear crack (tana = 0.056/co + 0.3); co is the mechanical

reinforcement ratio = p fyk/Wubei A, is dst/hm and dst is the diameter of the column.

Based on the model proposed by Shehata in 1985, a simplified method

was proposed by Shehata and Regan in 1990. They considered that the

punching region of a slab is divided into rigid radial segments that rotate around

the center of rotation located at the column face and at the level of the neutral

axis. To calculate the ultimate punching shear resistance, they defined three

critical states at which the frontal part of the radial segment fails to support the

force at the column face:

1. If the angle a of the compressive force reaches 20°, there are principal

tensile stresses in the compressed front part and failure occurs by splitting

of the concrete. Experimental and numerical data show that the angle of

inclination of the internal crack surface can be approximated as 20° from

the horizontal.

2. If the average radial strain on the compressed face reaches a value of

0.0035 at the column face, there is a radial crushing of the concrete.

3. If the tangential strain of the compressed face reaches 0.0035 at a

distance x from the column face, there is tangential crushing of the

concrete.

The rotation \\iu at which any of these critical states is first achieved, is required to

obtain the punching shear capacity, Vu, with the conditions of equilibrium on a

radial segment being satisfied. The resulting expression for the punching shear

capacity is:

Vu = 27idstxncf'ctan10o (1.14)

where dst is the diameter of the column; x is the height of compression zone at

flexure in tangential direction when punching occurs; and nc is the stress

concentration factor to account for the concrete strength.

In the same year, Broms (1990) modified the model of Kinnunen and

Nylander. In his theory Broms includes unsymmetrical punching and size effect.

At the same time, Bortolotti (1990) applied the theory of plasticity to

calculate the punching shear. A three-dimensional axi-symmetrical model and

rigid plastic material properties were assumed in using a modified Coulomb yield

criterion for the concrete.

Alexander and Simmonds (1992) developed a model that combines radial

arching action with the concept of a critical shear stress on a critical section

(beam action shear). For brittle punching failure, bond strength of the

reinforcement is seen as the significant factor limiting the beam action shear.

In 1996, Menetrey (1996) presented an analytical method to predict the

punching shear capacity. This method was based on experimental results that

show the influence of the punching cone inclination and the difference between

8

punching shear failures and flexural failures. This method considers the inclined

principal tensile stresses in the concrete. Considering also the contribution of

each type of reinforcement crossing the punching shear crack, the punching load

of a general slab is expressed as:

Fpun = Fct + Fdow + Fsw + Fp (1.15)

where Fct is the vertical component of the concrete tensile stresses obtained by

integrating the vertical components of the tensile stresses in concrete, Fd0w is the

dowel-force contribution of the flexural reinforcing bars, Fsw is the vertical

component of the forces in studs, stirrups or bent-up bars which are well-

anchored, and Fp is the resultant of the vertical components of the forces in

inclined prestressing tendons.

Theodorakopoulos and Swamy (2002) presented a method to predict the

ultimate punching shear strength of slab-column connections. The model is

applied to lightweight and normal weight concrete and both normal strength and

high strength concrete. Failure is assumed to occur when the tensile splitting

strength of the concrete is exceeded.

Research on the punching shear strength of edge and corner columns

was made by Andersson (1966) using yield line theory. Considering a nominal

shear stress located at a distance of d/2 from the column, he proposed the

following formula for the calculation of the punching shear stress:

V̂_ d2

v =

1 + 0.4e

MS d

1 + 1^ 6 e

+ -Tf

(1.16)

where V is the shear force; Ci and c2 are sizes of the column; d is the effective

depth and e is the eccentricity of the load from the centroid of the column.

Zaghlool and de Paiva (1973a) developed a theoretical method to analyse

the punching shear strength of a corner column connection considering the effect

of the c/d ratio, the MA/ ratio and the steel configuration in the section close to

the column. Zaghlool and de Paiva (1973b) reported on test results on slabs with

corner columns these results indicated the conservative predictions the ACI

Code.

Ingvarsson (1977) suggested a critical section passing through a point

located d/2 from the inner corner of the column and projecting at an angle of 45

degrees from the column face. This gives a critical perimeter b0 = d + V2 (bi +

b2). Based on one-way shear, an ultimate shear stress at failure was given as:

vu = r,^ (0.126 + 2.24p) Ji\ (1.17)

where rj is a reduction factor accounting for the influence of torsion expressed as

1 ri =

' e x -e y +0.5 (0 , -c 2 ) "

d +^2(0, +c2)

where the ex and ey are the eccentricities of the applied loads (MA/) and ex > ey

and C1 > c2; \ = 1.75 - 1.25 d > 1.0.

Regan and Braestrup (1985) describe the approach taken by Regan to

determine the punching shear resistance of edge and corner slab-column

connections. This approach involves considerations of different peripheries for

the minimum shear resistance, the maximum shear resistance and the flexural

resistance.

Walker and Regan (1987) carried out tests on 11 slabs with corner

columns, where some of the columns did not extend above the slab. They

observed that yield lines could form over the column so that the width for moment

transfer was reduced. The moment distribution obtained from the equivalent

frame analysis of the ACI and British Codes and those from the test results were

compared.

Based on 27 previous experimental results, Moehle (1988) proposed a

strength method of analysis assuming that if the total shear force in the

connection is less than 75 percent of the pure shear capacity, there is no

interaction between shear and moment. The method evaluates the shear

10

strength, which is critical in the section area located at a distance of d/2 from the

face of the column. The ultimate shear stress is calculated in MPa units as

v. =0.17 c

< 2 ^ 1 + — 3

fc <V0-33fc (1.18) c J

where pc is the ratio of the long to the short dimensions of the column.

The moment strength is calculated as the flexural strength provided by the

reinforcement placed within a band width of c2 + 2 Ci, where c2 is the size of the

column parallel to the edge of the slab and Ci is the dimension of the column

perpendicular to the edge (but not to exceed the distance from the inner face of

the column to the slab edge). Failure is determined from the critical failure mode,

that is shear or moment. This model was adopted by ACI-ASCE Committee 352

(1988) as an optional design model.

Test results of six slabs with edge columns were reported by Mortin and

Ghali (1991). The purpose of this research was to investigate the effectiveness

of providing stud-shear reinforcement on the capacity of slab-column

connections. Two of the specimens had no shear reinforcement and the

remaining four had different arrangements of shear studs.

Lim and Rangan (1995) developed a truss theory to predict the punching

shear strength in slabs with edge and corner columns. Nine specimens with

stud-shear reinforcement were tested.

Hammill and Ghali (1994) reported on tests of 5 slabs with corner

columns. The variables were the amount of shear reinforcement and the loading

procedure.

Based on experimental results, Elgabry and Ghali (1996) presented a

study of the distribution of ultimate stress along the perimeter of the critical

section for slabs with interior, edge and corner columns. Using elastic analysis,

they suggested a new equation for yv (the portion of unbalanced moment

transferred by eccentric shear stresses) that considers different shapes of the

critical section. The equation for edge and corner columns was as given by:

11

j - V i =0.4 (1.19a)

T - - = 1 - (2-s\ ( 1 1 9 b )

1 + 0.2

where lx, ly are lengths of projections of the critical section for two-way shear on

principal axes x and y, respectively.

Ghali and Megally (1999) carried out analytical studies and suggested

replacing the Jx and Jy in equation (1.27) by the second moment about the

centroidal principal axes of the critical section, lx and ly.

1.3 North American Codes

The first standard specifications prepared by the ACI Joint Committee

(ACI 1909) limited the allowable stress on the concrete in pure shear to 0.06 fc.

The shear stress was computed by the following formula:

v = ^ (1.20,

where the critical section was taken along the perimeter b of the loaded or

column area and h is the total slab thickness.

ACI reports in 1916 and 1917 (1916 and 1917) gave an allowable value

for the concrete punching shear stress in slabs of 0.075 f'c

The 1920 ACI Standard prescribed an allowable shear stress of 0.10 fc

computed at the support or loading faces for members failing in pure shear. For

diagonal tension failures the allowable shear stress was computed using formula

(1.1) at a distance of d/2 from the periphery of the loaded area or column, was

limited to 0.035 f c.

12

In the report of the 1924 ACI Joint Committee the shear stress was

calculated at a distance of (h-1!4 in.) from the periphery of the loaded area. The

allowable shear stress was given by

v = 0.02 f'c (1+n)< 0.03 f'c (1.21)

where n is the ratio of the area of the reinforcing steel in the loaded area over the

total area of tensile reinforcement.

The 1956 ACI Building Code allowed maximum shear stresses of 100 psi,

proportional to fc that was computed on a critical section at a distance of d from

the periphery of the loaded area. The limits were calculated as follows:

v< 0.03 f'c <100psi (1.22a)

if more than 50% of the flexural reinforcement passes through the periphery; or

v< 0.025 fc <85psi (1.22b)

if only 25% of the flexural reinforcement passes through the periphery of the

loaded area or reaction area.

Concentration of the flexural reinforcement in a narrow band across the column

was assumed to increase the shear strength.

A new procedure was proposed by ACI Committee 326 (1962) for

punching shear based on Moe's equation (Moe 1961), with the variable §0 taken

as unity for design. From tests by Diaz de Cossio (1960), it was shown that the

punching shear strength of slabs with a large ratio of column dimension to depth,

c/d, approached a value close to 1.9Jf7, with f'c in psi units. From test results,

assuming the ultimate shear stress as 4.0A/f'c and defining the critical section

located at a distance d/2 from the periphery of the loaded area, the punching

shear stress was expressed as

v = ^ - = 4.0Vf7 (1.23) bd

It was concluded that the punching shear strength was affected primarily

by three variables: concrete tensile strength, that is Jf\. , the ratio of the side

13

length of the loaded area to the effective depth of the slab, c/d, and the

relationship between shear and moment in the vicinity of the loaded area, <j>o.

In 1974, ASCE-ACI Committee 426 presented a state-of-the-art report on

the shear strength of reinforced concrete slabs. They concluded that the ultimate

shear capacity for normal-weight reinforced concrete slabs of 4yjf\ was only

appropriate for concrete with strengths less than 4000 psi (28 MPa). For higher

strengths the capacity depended on a power of f'c closer to the cube root rather

than the square root.

The 1995 ACI Code requires that for members without shear

reinforcement, the punching shear resistance must be sufficient such that:

VU<(|>VC (1.24)

where Vu is the factored shear force at the section being considered; (j> is the

strength reduction factor for shear (equal to 0.85), and Vc the nominal punching

shear strength provided by the concrete.

The Canadian Standard (CSA 1994) has adopted the same approaches

for punching shear. The equations given below are taken from the CSA

Standard and hence are in metric units and the resistance factors are treated

differently than in the ACI code.

Thus, in absence of shear reinforcement, the factored shear resistance is

the smallest of

v = v = ¥ r ¥ c

V = V = r v c

1 + — v Pcy

0.2A4cVf'c (1-25a)

^ + 0.2 V b o J

*.<Mf,c (L25b)

v r = v c = 0 . 4 ^ c V f c (1.25c)

where the variable pc was first introduced in the 1977 Code and is the ratio of

long side to short side of the column, concentrated load or reaction area; b0 is the

perimeter of the critical section and J\\ is limited to 100 psi (25/3 MPa).

14

The coefficient X allows for low density concrete and is equal to 1.0, 0.85

and 0.75 for normal-weight, semi-lightweight and lightweight concrete

respectively; <t>c is the resistance factor for concrete (equal to 0.6); ocs is 4 for

interior columns, 3 for edge columns, and 2 for corner columns.

When the columns or capitals become very large, equation (1.25b) may

govern.

It is specified in the 1994 CSA Standard that the unbalanced moment at a

slab-column connection must be transferred from the slab to the column by

eccentricity of shear and by flexure. Shear transfer is assumed to occur in a

critical section at a distance d/2 away from the face of the column, while the

fraction of unbalanced moment transferred by flexure is resisted by a width of

slab equal to the transverse column width c2, plus 1.5h on each side of the

column.

The fraction of unbalanced moment transferred by eccentricity of shear is

Yv = 1-Yf (1.26a)

where yf is the fraction transferred by flexure:

Yf - J N r— (1.26b) 1 +

(2^ b1

v3y

and bi and b2 are the lengths of the sides of the critical shear perimeter for

moment transfer.

The unbalanced moment transferred by eccentricity of shear is yv Mf,

where Mf is the unbalanced moment at the centroid of the critical section.

The factored shear stress on the critical transfer section is the sum of

stresses caused by transfer of direct shear and unbalanced moment between the

slab and the column as

V y, M QA y, M ^ v„ = -**- + YXe) J yvMue

A c v ° yx

(1.27)

15

where the subscripts x and y refer to centroidal principal axes of the shear critical

sections; (x,y) are coordinates of the point at which vf is maximum; Ac is the area

of critical section; J is defined as the polar moment of inertia of the critical section

about its centroidal axis.

1.4 European Codes

Many European codes are based on the theory of Kinnunen and Nylander

(1960). The punching shear resistance is calculated in most building codes by

evaluating the nominal shear stress on a specified control surface around the

loaded area or column, and comparing this with a concrete tensile strength.

Provisions for punching shear capacity of concrete for four of the European

codes are described below.

In the German design code (DIN 1045 1988), the effect of moment

transfer can be ignored if the spans of a panel do not differ by more than 33%.

The application of DIN 1045 is described by Albrecht (2002) and fib Bulletin 12

(2001).

The design model for the punching shear resistance without shear

reinforcement considers a shear capacity that is dependent on the concrete cube

strength and the flexural reinforcement ratio.

The punching shear is determined as

V c= 0.441 k2fCi2002/3ud (1.28)

where k2 = 0.7 i+A. 500

A 0.45Ju and | i g is the tension reinforcement ratio.

Eurocode 2 (EC2 2002), the CEB-FIP Model Code 90 (CEB 1990) and the

1996 FIP-Recommendations (FIP 1996) consider the concrete cylinder strength,

16

fck, the flexural reinforcement ratio, pt, the size effect (k) as a function of the

effective depth, d, and the shear capacity of the shear reinforcement, fsw Asw.

EC2-02 calculates the resistance to punching shear for members without

shear reinforcement at a critical section located at 2d from the face of the column

as

Vc = [0.18 k (100 pfck)1/3]ud (1.29)

where fci< has several values of strength based on the characteristic strength,

k = 1 + J—— < 2.0, p = ^pxpy < 0.02 and d = x y , being px, py, dx and dy the

reinforcement ratios and the effective depths, respectively, in the two orthogonal

directions. These equations are compared with the North American approaches

by Paultre and Mitchell (2003).

The British Standard 8110 (BS 8110 1997) considers the same

parameters as the EC-2 and the 1990 Model Code. BS 8110 assumes a shear

crack inclination of 33°, reducing the amount of shear reinforcement (fib Bulletin

12 2001).

The punching shear at a critical section located at 1.5d from the face of

the column is given as

Vc=[0.34k(100pfck)1 /3 ]ud (1.30)

where k = J and p < 0.03. Albrecht (2002) compares the BS 8110 code with

other codes.

Comparing the provisions for the punching shear for corner columns

without shear reinforcement for leads to the conclusion that all have a wide range

of results for all failure modes. This is due to the safety factors and the different

evaluations of the punching shear capacities. Also, European codes consider

the size effect and the effect of amount of longitudinal reinforcement, while the

2002 ACI Code (ACI 2002) and the CSA Standard (CSA 1994) do not account

for these effects.

17

With respect to the flexural reinforcement ratio and the concrete cylinder

strength, it is observed that the BS 8110-97 Code, the 1990 Model Code and the

1996 FIP-Recommendations give higher capacities than the ACI and CSA for

large flexural reinforcement ratios (p>1%) and lower capacities for lower

reinforcement ratios {fib Bulletin 12 2001 and Paultre and Mitchell 2003).

For relatively high concrete strengths, the German and the North

American codes give upper limits on the punching shear stress. The 2002 ACI

Code neglects the influence of the flexural reinforcement ratio and therefore

gives more conservative predictions for flexural reinforcement ratios greater than

1.5%.

The design of reinforced concrete slabs for punching shear is of great

importance, but the provisions for the design and analysis differ considerably

among the various European and American design codes. Therefore, research

and development of models, material and computer methods are needed in this

important area.

1.5 Research Objectives

The objectives of this research program are:

1. Design three full-scale slab-column specimens to investigate the shear

capacity at corner columns in accordance with the 1994 CSA Standard

A23.3. The main variable in this test series is the size of the corner

columns.

2. Design a testing apparatus capable of producing positive moments around

the free edges of the slab specimens and negative moments around the

columns.

3. Construct and test the three corner column-slab specimens.

18

Evaluate the performance of the specimens and recommend an

appropriate design approach.

19

Chapter 2

Experimental Programme

2.1 Description of Prototype Structure

The prototype structure was designed in accordance with the Canadian

Standards Association A23.3-94 (CSA 1994). The slab was designed for a

relatively high specified live load of 10 kPa and a superimposed dead load of 1.5

kPa. This resulted in a high percentage of reinforcement and a shear-critical slab

design.

The clear spans in both directions were 4.0 m and a total slab thickness of

150 mm was chosen. Analysis indicated that for an edge panel, the slab

moments are zero at a distance of 0.32 m from the face of the column with the

maximum positive in the slab occurring at a distance of 1.82 m from the column

face. In choosing the size of the test specimen it was decided to use a corner

slab specimen that cantilevered out a distance of 1.150 m from the column faces

(see Fig. 2.1).

2.2 Design of Test Specimens

Three full-scale specimens were constructed and tested to failure in the

Jamieson Structures Laboratory in the Department of Civil Engineering at McGill

University. The slab specimens were identified as Specimens S1, S2 and S3,

having square corner columns with sizes, c of 250 mm, 300 mm and 350 mm,

20

respectively. The columns were extended above and below the slab a distance

of 1.425m, giving a total column height of 3.0 m.

A minimum specified concrete compressive strength of 30 MPa was used

for the design of the slab and the column. The specified yield strength used for

the reinforcement was 400 MPa.

The clear cover on both top and bottom steel reinforcement in the slab

was 20 mm, with a 30 mm clear cover used for the ties in the column.

All the test specimens contained the same flexural steel in the slab and

the same column reinforcement. Eleven 10M bottom reinforcing bars were used

in both directions, providing a positive moment capacity of 158.4 kN for slab

specimens. Four 15M top bars were used resulting in a flexural capacity of 123.8

kN for the specimens.

Steel plates of dimensions 40 x 40 x 9 mm were welded at one end of the

bars to ensure that the reinforcement was properly anchored.

Additional top and bottom edge steel bars, 400 mm in length, were placed

along the loading edges at the same level as the flexural reinforcement. These

bars were used to avoid any local failures in the regions of the load application.

Five 10M bars in each direction were located in such a way that 3 of them were

in the zone of the loading plate and the two remaining covered the rest of the

span. Steel plates were welded at one end.

No shear reinforcement was provided in any of the slabs.

The column reinforcement consisted of four vertical 15M bars and 15 sets

of 10M ties at a spacing of 220 mm.

21

2.3 Details of Test Specimens

2.3.1 Specimen S1

The details of Specimen S1 are shown in Fig. 2.2. The column of

Specimen S1 had cross-sectional dimensions of 250 mm by 250 mm. The

overall dimensions of the slab were 1400 by 1400 by 150 mm.

Two of the 11-10M bottom bars were anchored inside the column in order

to satisfy the structural integrity requirements. Steel plates were welded at both

ends. The length of these bars was 1380 mm to allow for a cover of 20 mm in

the column. The remaining bars were 1300 mm long and they were equally

distributed at a spacing of 125 mm. Both the dimensions and the detailing of the

positive moment reinforcement are shown in Fig. 2.2.

The 4-15M bars on top were fully anchored with welded plates inside the

column allowing for a cover of 20 mm. Figure 2.3 shows the arrangement of the

top layer of reinforcement. Figure 2.4 shows the details of the reinforcing steel in

Specimen S1 just before casting the concrete.

2.3.2 Specimen S2

Specimen S2 had a 300 mm square column resulting in overall slab

dimensions of 1450 mm x 1450 mm x 150 mm. As shown in Fig. 2.5, 2-10M bars

were placed on the bottom of the slab into the column in both directions. The

structural integrity reinforcement was the same as that used in Specimen S1.

Nine additional 10M bottom bars were uniformly distributed in both directions.

Figure 2.6 shows the 4-15M top bars for negative moment, with a spacing

of 60mm within the column. The photograph in Fig. 2.7 shows a closeup of the

reinforcement near the column before casting.

22

2.3.3 Specimen S3

Specimen S3 had a 350 by 350 mm column and a 1500 by 1500 by 150

mm slab. The 11-10M bottom bars were equally distributed at 125 mm spacing.

Two of the 10M bars were 1480 mm long and continued into the column to

satisfy the requirements for structural integrity. The 15M negative moment bars

on top were all anchored into the column resulting in a spacing of 70 mm.

Figures 2.8 and 2.9 show the arrangement of both the bottom and top layers of

reinforcement, respectively. The detailed view of the joint in Specimen S3 is

shown in Fig. 2.10.

2.4 Construction Sequence

The test specimens were constructed simultaneously in the Jamieson

Structures Laboratory. The formwork was constructed with plywood. Figure 2.11

shows a photograph of the overall view of the three specimens before casting.

The lower columns of the three specimens were cast first with the same

concrete batch to provide rigidity to the system. Eight days later, concrete was

cast in the three slabs. All slabs were constructed with the same batch of

concrete to ensure that all specimens possessed the same material properties.

Six days later, the top columns were cast with the same mix design specified by

the supplier but adding 1 liter of flow-mix to the concrete. All specimens were

cured and then stored in the formwork until they were moved to the testing frame

a few days before testing.

23

2.5 Material Properties

2.5.1 Reinforcing Steel

The reinforcement used in the construction of each of the specimens was

in conformance with CSA Standard G30.18 (CSA 1992). All reinforcement was

weldable grade, hot-rolled, deformed bars with a minimum specified yield stress

of 400 MPa. Three sample coupons of each reinforcing bar size were tested in

order to determine their stress-strain characteristics. The test samples were 300

mm in length and the extensometer used to measure strains was 150 mm long.

Figure 2.12 shows typical stress-strain curves for these reinforcing bars and

Table 2.1 summarizes the average values of the mechanical properties.

Table 2.1 Summary of reinforcing bar properties

BAR SIZE

10M

15M

AREA

(mm2)

100

200

fy (MPa)

(std. Deviation)

450.5

(13.9)

469.7

(5.38)

6y (mm/mm)

(std. deviation)

0.00225

(...)

0.00235

(...)

fuit (MPa)

(std. deviation)

567.6

(8.03)

591.0

(1.94)

2.5.2 Concrete

The columns and slabs were cast with normal density concrete. All

batches had a specified 28-day compressive strength of 30 MPa. The maximum

aggregate size used was 20 mm, and the components and proportions of the

concrete mix design, as specified by the supplier, are presented in Table 2.2.

24

After casting, the specimens were covered with wet burlap and plastic to

prevent water loss and maintained at standard room temperatures. The slab

specimens were moist-cured for a period of 7 days. After 24 hours, specimens

used to determine the mechanical properties were demolded and stored in a

humid room.

Table 2.2 Concrete mix design

COMPONENT

TypelO cement (kg/m3)

Fine aggregate (kg/m3)

Coarse aggregate (20mm) (kg/m13)

Coarse aggregate (14mm) (kg/mJ)

Water (kg/m3)

Water-cement ratio

Superplasticizer (l/m3)

Retarding agent (l/mJ)

Air-entraining agent (l/nr5)

Water-reducing agent (l/mJ)

Slump (mm)

Air content (%)

COLUMN AND

SLABS

340

784

369

693

160

0.47

2.5

0.32

0.19

1.06

80

6.5

For each mix, a series of tests were conducted on the plastic and

hardened concrete. First, volumetric air content and slump were determined.

Then six cylinders of 150 mm diameter and 300 mm length were cast for each

specimen and for each batch of concrete to test the physical properties of the

corresponding hardened concrete. Three cylinders were used to test the

compressive strength, f'c, after 28-days of curing in a humid room. Typical 28-

25

day compressive stress-strain relationships for the concrete used in the slabs are

shown in Fig. 2.13. Three cylinders per specimen with the same dimensions

were cast at the same time in order to determine the splitting tensile strength of

the concrete, fsp. The modulus of rupture, fr, was determined from flexural beams

with dimensions of 100 x 100 x 400 mm. These specimens were subjected to

four-point loading. The results obtained are summarized in Table 2.3.

Table 2.3 Concrete properties

SPECIMEN

Lower column

Slab

Upper column

f c (MPa)

(std. dev.)

35.4

(1.36)

42.8

(0.90)

33.6

(0.47)

fr (MPa)

(std. dev.)

4.26

(0.33)

6.41

(0.12)

4.26

(0.64)

fsp (MPa)

(std. dev.)

3.2

(0.18)

3.5

(0.20)

3.4

(0.08)

A standard specimen of dimensions 80 mm by 80 mm by 280 mm was

used to take shrinkage measurements for each batch of concrete cast.

Measuring studs were placed at each end of the standard specimen to take

readings and determine the shrinkage. The specimen was cured in the humid

room to simulate the conditions at the interior of the full-scale specimens. The

variation of shrinkage in the specimens in time is shown in Fig. 2.14.

26

2.6 Testing Procedure

The formwork of each specimen was removed a few days before testing to

hold them in a stable position and to provide stiffness to the whole system. Each

specimen was moved with a crane fixed to the specimen at the center of gravity.

The slabs were moved inside a steel testing frame used to laterally restrain the

column. After placing in the test frame, strain gauges were calibrated until the

gage indicated zero strain.

2.6.1 Test Setup and Loading Apparatus

At the moment of testing, the ages of Specimens S1, S2 and S3 were 54,

69 and 83 days, respectively.

The base of the column was placed on a neoprene rubber pad and the top

of the column was bolted to the steel frame using threaded rods and angle

sections on two faces of the column.

From the analysis of the prototype structure, the points of inflexion were

located at a distance of 320 mm from the face of the column. To simulate the

loading effects that the slab would experience two loads were applied as

indicated in Fig. 2.15. Each load was applied through a distribution beam

attached below the slab. For this purpose, a square hollow structural section

HSS 152 x 152 x 11 mm was used to transmit the load to the test specimen.

Two steel plates with dimensions of 150 by 450 mm and 19.04 mm-thick were

placed at the top and the bottom of the slab, 25 mm from the edge of the slab

and centered along the face of the column (see Fig. 2.15). Eight holes were

drilled for 8 bolts connecting the slab, a spreader beam and the loading beam

and causing a positive bending moment along the free edges of the slab. The

loading beams were centrally located under the spreader beam in such a way

27

that the resultant forces of P/2 were located along the interior column faces at a

distance of 500 mm (see Fig. 2.15).

Monotonic static load was applied downward at the two loading points and

the load was measured by two load cells that reacted against the hydraulic jacks

under the reaction floor. The jacks were connected to a common hydraulic pump

such that the loads were equal at the two loading points. Incremental forces

were applied in steps until failure was achieved. The magnitude of the

increments was reduced at the higher load levels near failure. Figure 2.16 shows

a photograph of the test setup.

2.6.2 Instrumentation

During testing, loads and deflections were recorded and strains were

monitored at various locations along the flexural reinforcement to provide

detailed data of the behaviour of the specimens. The extension and width of the

cracks was measured at each load stage and they were marked by a pen for

better visibility.

Two load cells were used to measure the applied downward forces on the

slab at each loading jack during testing.

Vertical displacements were measured at several points on the slab and

the column using linear voltage differential transducers (LVDTs). The LVDTs

were clamped to a light steel frame attached to the column. LVDTs 1 through 4,

having a displacement range of ± 50 mm, measured the displacements of the

slab relative to the column (see Fig. 2.16). The position of the LVDTs is shown in

Fig. 2.17. Three LVDTs with a range of ± 15 mm (LVDTs 5, 6 and 7 in Fig. 2.17)

were clamped to the column and measured the movement of the bottom surface

of the slab relative to the column at the slab-column interface. Two of these

LVDTs were attached to the column at the centre of both interior column faces,

28

100 mm below the slab. Another LVDT was attached to the column and located

at the corner of the column as shown in Fig. 2.17.

Electrical resistance strain gauges were attached to the flexural

reinforcement to measure the strain in the bars. Strain gauges with a 5 mm

gauge length were installed during construction of the specimen on all of the

negative moment reinforcing bars and on two of the four structural integrity bars.

The strain gauges were located at the column interface in both directions of the

slab. The positioning of the strain gauges is shown in Fig. 2.18.

A computerized data acquisition system was used to record loads,

displacements and strains at frequent intervals during loading.

29

4000

IT

test specimen

•

Figure 2.1 Plan of prototype flat plate structure.

30

275 •+*•

100 150 tv—i

1125

a) Plan view

-1150-

________

20 (230

9-10M bars, L=1300

b) Section 1-1

1150

130

20

130

20"

- 2-1OM bars, L=1380

c) Section 2-2

rcement details for bottom steel in S1 31

2 5 0 -

250 — > i —

20

20

1150

1150

4-15M@50(typ.)

50

150

50

a) Plan view

20 230 1150

4-15M bars, L=1380

20

130

b) Section 1-1

Figure 2.3 Top reinforcement in Specimen S1

32

Figure 2.4 Detailed view of the joint in Specimen S1

33

325 -*k- 1125

a) Plan view

150 150 * 1150

< 9-10M bars, L=1300 b) Section 1-1

130

20"

2-10M bars, L=1430 c) Section 2-2

n~**~m reinforcement details for Specimen S2.

34

a) Plan view

20 280 H*-

-v-

1150

4-15M bars, L=1430

20

b) Section 1-1

Figure 2.6 Arrangement on top steel for Specimen S2.

35

Figure 2.7 Detailed view of the joint in Specimen S2.

36

1150

t ~20 350

1500

1150

i i

j

200

1500

-200 -A-

150<

— 1500 a) Plan view

1150

•* ' '"* r " i r B H y--~««nr |jBa

•y

9-10M bars, L=1300 • b) Section 1-1

1150 >

130

20

130

2cT

2-10M bars, L=1480 c) Section 2-2

m reinforcement details for Specimen S3. 37

350 -*•

20

t ~20 350

1150

1150 70

;

210

70 4-15M@70(typ.)

20 330 -*\* -A-—

a) Plan view

1150

- p e — o — o —

A -4-15M bars, L=1480

b) Section 1-1

20

1^fT

Figure 2.9 Top steel for Specimen S3.

38

Figure 2.10 Detailed view of the joint in Specimen S3.

Figure 2.11 Overall view of the specimens before casting.

39

700

ro a. 400-

jjj 300^ to

200 4

100-

0

t

I

15M bars

gauge length

1 1 1 1 1 1 —

0 0.02 0.04 0.06 0.08 0.1 0.12

Strain (mm/ mm)

0.14 0.16 0.18

Figure 2.12 Stress-strain curves for reinforcing bars.

50

40 -

30 -ro

Q.

in in a> 20

CO

10 -

J.

T Slab Bottom column Upper column

0.001 0.002 0.003

Strain (mm/mm) 0.004

i -

0.005 0.006

Figure 2.13 Compressive stress-strain responses for concrete.

40

0.6

E E E E

ro

CO

0.5 -

0.4 -!

0.3 4

/>: v . Slab

100 120

Time (days)

140 160 180 200

Figure 2.14 Shrinkage strain curve.

41

1150

A -

A -I P/2

« 500 •

c — •

a) Elevation view

1150

25

P/2

' P/2

3@90

40

o o o o

I 70 I

< 450 • " W

b) Plan view

Steel plate (150x450)

Steel plate (150X100)

Slab

150-25

i!:l

< 475 * 175

o o

o o

o o

o o

150

X

450

25

HSS 152X152X11 L=450

HSS152X152X11 L=725 Steel plate (150X150)

c) Detailed view of steel sections

Figure 2.15 Test setup for specimens. 42

HSS 152X152X11

Figure 2.16 Overall view of loading setup.

43

c —• * 5 0 0 • + 5 5 0 *•- 100

A -

100

5

-V-

-rAv,

I P/2

a) Elevation view

c — •

500

550

100

4 500 •

-B 0

[] 7

o o - oA o

• 1 o o o o

« 550 •

Q 3

100

o o

n

b) Plan view

Figure 2.17 Location of LVDTs.

44

North edge

CD U)

T3 <D

to

^L. X .

a) Top reinforcement

b) Bottom reinforcement

Figure 2.18 Position of strain gauges.

45

Chapter 3

Experimental Results

This chapter presents the results and observations from the tests

performed on the three slab specimens. The data recorded for each specimen

included the applied loads, reinforcing steel strains, deflections, and the crack

development and crack widths.

The examination of the behaviour of each specimen includes the

description of the overall behaviour using the load versus deflection response.

The loads reported in this chapter are the sum of the two point loads applied to

the slab, including the self-weight of the slab and the loading devices, as

explained in Chapter 2. The corresponding self-weight plus the weight of the

loading devices for Specimens S1, S2 and S3 was 9.6, 10.1 and 10.6 kN

respectively. The deflections are the average deflections that were measured in

two symmetrical points as shown in Fig. 2.17. During the tests, the loads were

increased in small increments until failure was reached.

The faces of the test specimens are referenced using specific

identification. The flexural cracking on the north face is controlled by the lower

steel of the top mat ("flexural weak direction") in Specimen S1. Hence, the west

face corresponds to the cracking in the "flexural strong direction" for this

specimen. The north face of Specimen S2 and S3 corresponds to cracks

observed in the "flexural strong direction", while the west face corresponds to

cracks observed in the "flexural weak direction".

A general description of the progression of the cracks with the total load is

presented as well as the maximum crack widths recorded at each load stage.

46

The development of the strains in the top reinforcing bars and in two of the

structural integrity reinforcement at the face of the column is discussed.

3.1 Specimen S1

Figure 3.1 shows the load versus deflection responses for Specimen S1.

Different load-deflection responses are given for the average of the measured

deflections at points 1 and 4 and for the average deflections at points 2 and 3.

The first flexural cracks appeared at a total load of 21.3 kN. These cracks

appeared on the top surface of the slab close to the inner corner of the column

and propagated towards both free edges of the slab. These cracks were visible

on the north and west faces at locations of 75 mm and 25 mm, respectively, from

the faces of the column. Figure 3.1 shows a significant drop in stiffness starting

at a load of 15.5 kN, due to cracking.

One positive moment crack appeared at 240 mm from the east edge of

the slab near the north face when the applied load was 51.2 kN. At a load of

64.1 kN another positive moment crack developed at a location of 155 mm from

the south edge of the slab.

With increasing load, new flexural cracks occurred on the top surface of

the slab as shown in Fig. 3.3. When the total load was 75.5 kN, the maximum

width of the cracks on the exposed north and west edges of the slab were 0.30

mm for flexural cracks and 0.25 mm for the torsional cracks.

The strains in the reinforcing bars were measured with strain gauges

located in line with the faces of the column. Typical results of the strain in the

steel showed that the reinforcing bar located in the outermost edge near the west

face (gauge #1) was the first one to reach the yield strain at a total load of 84.4

kN as is illustrated in Fig. 3.2. When the load was increased to 91.7 kN, the steel

47

located closer to the inner corner of the column near the north face, reached the

yield strain while the remaining bars were below yield.

At 105.9 kN, crushing of the concrete occurred on the bottom surface of

the slab near the inner corner of the column. In the next load stage, at 111.8 kN,

the first shear cracks appeared on the north face of the slab at a distance of 285

mm from the face of the column, as shown in Fig. 3.4. As apparent from Fig. 3.4,

the angle of inclination of the shear crack was 45 degrees from the plane of the

slab. The width of the major shear crack was initially 0.10 mm. Splitting of the

concrete due to high local in compressive stresses was observed at the inside

corner of the column immediately below the slab. When the first shear crack

appeared on the north face, all the reinforcing bars in that direction had already

reached their yield strain.

When the load was increased to 117.6 kN, the first shear crack appeared

on the west face but for this case, the two outer bars in the "flexural strong

direction" (gauges #1 and #4) had yielded, while the two inner bars (gauges #2

and #3) were just below their yield strain (see Fig. 3.2).

As failure approached, the top surface cracks widened and at a load of

121.4 kN, a brittle shear failure occurred (see Fig. 3.1). Figure 3.5 shows the

maximum crack width recorded at each load stage and Fig. 3.6, 3.7 and 3.8

show photographs of the north and west faces of the slab at failure and the crack

pattern on the top surface. From Fig. 3.6 and 3.7 is observed that the failure

shear crack on the north face spread to both the top and bottom surfaces of the

slab. On the west face, the shear crack failure propagated towards the bottom

face of the slab and reached the bottom surface at a distance of 230 mm from

the column face.

Figure 3.2 shows that yielding was reached in all but one of the top bars in

the "flexural strong direction" (at gauge #3) before failure. From Fig. 3.2, it is also

observed that the strains were higher in the reinforcement located near the north

face ("flexural weak direction").

48

Figure 3.1 shows that the vertical deflection of the slab relative to the

column at the edge of the slab (points 2 and 3), was twice the deflection

measured at the points where the load was applied (points 1 and 4). This

relationship remained relatively constant throughout the test. The average

deflections recorded were 17.9 mm and 34.9 mm at the peak load of 121.4 kN.

Figure 3.9 gives an overall view of the slab-column specimen after shear

failure had occurred.

3.2 Specimen S2

Specimen S2 behaved in a manner similar to that of slab S1. Figure 3.10

shows the load-average deflection curves, with the average deflections

calculated from the individual deflection readings for the four symmetrical points

in the slab. A gradual reduction in stiffness is observed in Fig. 3.10 after a load

of 15.3 kN was reached. One crack formed at a load of 18.2 kN on the top

surface of the slab and originated in the inner corner of the column. This crack

propagated toward the edge of the west face of the specimen, surfacing on the

side face at a distance of 68 mm from the face of the column, and extended

down the slab edge a distance of 20 mm.

The first positive moment crack occurred on the west face at a load of

66.1 kN and was located 220 mm from the south face of the slab. When the load

was increased to 75.2 kN, an additional positive moment crack appeared near

the north face of the slab at a distance of 232 mm from the east face.

With increased loading, the cracks located in the immediate vicinity of the

inner corner of the column increased in number and extended to the free edges

of the slab as shown in Fig. 3.12. On the north and west faces of the slab, the

flexural cracks became inclined indicating flexural-torsion cracks. At this stage,

when the applied load was 75.2 kN, the maximum width of the flexural cracks

49

was 0.75 mm, and the maximum torsional crack was 0.35 mm as it is observed in

Fig. 3.14.

Figure 3.11 shows the strain distribution of the top reinforcement at the

face of the column for Specimen S2. The two bars located at the extremities of

the west face (gauges #1 and #4 in the "flexural weak direction") reached their

yield strain simultaneously at a load of 82.8 kN.

When the load was increased to 98.1 kN, the bar closest to the inner

corner of the column (gauge #4 in the "flexural strong direction") yielded while the

remaining bars in the same direction were below yield. At this load, all of the

bars located in the other direction had yielded.

For Specimen S2, the first shear crack started at a load of 113 kN, on the

bottom face of the slab at a distance of 350 mm from the face of the column, with

the crack becoming flatter as it progressed upwards into the slab (see Fig. 3.13).

The width of this shear crack was 0.5 mm, while the maximum width for the

flexural cracks was 2.25 mm, as is shown in Fig. 3.14.

As for Specimen S1, crushing of the concrete was observed at the inner

corner of the column, just below the slab. When the load was maintained at

116.7 kN for 1 or 2 minutes, a punching shear failure occurred. The failure shear

crack on the north face extended horizontally parallel to the plane of the bottom

bars towards the column (see Fig. 3.15). On the west face of the slab, failure

took place with the initial shear crack extending towards the column (see Fig.

3.16).

Yielding of the top reinforcing bars was recorded in all the bars before

failure was reached, as is shown in Fig. 3.11. None of the bottom reinforcing

bars yielded.

During testing, the average deflections from points 1 and 4 were twice the

average deflections from points 2 and 3. (see Fig. 3.10). The maximum average

deflection recorded was 18.9 mm and 37.6 mm at a load of 105.6 kN after shear

50

failure occurred. These deflections were greater than those for S1, due to the

higher strains reached in the flexural reinforcement.

Figures 3.15, 3.16 and 3.17 show photographs of the slab at failure. The

overall view of the deformed shape of Specimen S2 is shown in Fig. 3.18.

3.3 Specimen S3

The behaviour of Specimen S3 was different than the other two

specimens due to the failure mode. The total load versus the average deflection

response of Specimen S3 is shown in Fig. 3.19.

The first change in stiffness occurred when the total load was 17.7 kN. A

gradual decrease of stiffness was observed when the load was increased to 31.9

kN (see Fig. 3.19). The first flexural crack occurred on the top surface of the slab

when the total load was 18.8 kN and it was visible at locations 110 and 176 mm

from the face of the column on the north and west faces of the slab, respectively.

The load was increased gradually and at 74.5 kN the first positive moment crack

appeared near the north face (that is in the "flexural strong direction") at a

location of 220 mm from the east face of the slab. At this stage, the maximum

crack widths were 0.10 mm for the torsional cracks and 0.65 mm for the wider

flexural cracks, as is shown in Fig. 3.23. There were no shear cracks at this load

level. The crack pattern of the slab when the total load was 67.1 kN is shown in

Fig. 3.21.

Figure 3.20 shows the measured strains in the reinforcement bars of

Specimen S3 at the same key load stages as for Specimens S1 and S2. Strain

gauge readings showed that the bars closer to the inner corner of the column

(gauge #4 locations) were the first to reach the yield strain at total loads of 74

and 93.2 kN in the north and west faces, respectively.

51

The first sign of a shear crack, with a width of 0.10 mm, appeared at a

total load of 120.9 kN on the west face at a location 395 mm from the face of the

column (see Fig. 3.22). Figure 3.20 shows that when the first shear crack

appeared, all the reinforcing bars had yielded in flexure.

At a total load of 120.9 kN, the maximum crack widths were 0.10 mm for

the torsional cracks and 2.0 mm for the flexural cracks on the top surface (see

Fig. 3.23). Close to failure, the shear cracks on the north face tended to become

horizontal near the bottom face of the slab near the column while on the west

face of the slab the angle of inclination with respect to the slab was larger.

The maximum load and the corresponding average deflections registered

during testing were 124.9 kN and 30.5 mm for the points 1 and 4 and 15.3 mm

for points 2 and 3, as is shown in Fig. 3.19. As for the other two specimens, Fig.

3.19 shows that the average deflections in the edges of the slab (points 1 and 4)

were about twice those at the points where the loads were applied (points 2 and

3). The magnitude of the measured strains increased appreciably in the bars

oriented in the north face, especially the bar closest to the inner corner of the

column (gauge #4).

Crushing was also observed at the inner corner of the lower column, and

on the bottom surface of the slab, which demonstrated that failure by flexure had

occurred. The primary mode of failure was by flexure followed by extensive

shear cracks in the slab that could not extend, probably due to the presence of

the plates of the loading apparatus (see Fig. 3.25).

Photographs of the specimen at failure are shown in Fig. 3.24, 3.25 and

3.26.

52

140

100

§ 60

20 -

Load vs. deflection (av. of points 2 & 3)

Load vs. deflection (av. of points 1 & 4)

D -

3 —E

4

10 15 20 25 Average deflection (mm)

30 35 40

Figure 3.1 Load versus average deflection of Specimen S1.

Ey

0.00235 Strain

0.004 (mm/mm)

Strain (mm/mm)

• First flex, crack A First yielding • First shear crack • Failure

A/-

Figure 3.2 Strain distribution of top reinforcement in Specimen S1 at key stages.

53

Figure 3.3 Flexural cracking on top surface of Specimen S1 at a shear of 75.5 kN.

Figure 3.4 Flexural shear cracks at a shear of 111.8 kN in Specimen S1, north face.

54

IHU "

100 -

T3

ro o 60 -

20 -

1

< 1 1 y

-1 1 1 1 1 1

Flexural crack Shear crack Torsion crack

1 1 1

0.2 0.4 0.6 0.8

Maximum crack width (mm)

Figure 3.5 Maximum crack width for Specimen S1.

55

Figure 3.6 Shear failure in Specimen S1, north face.

1 • IIP? S1 s-^HH&RISB ifB

9 I: y

^f ^^H

Figure 3.7 Shear failure in Specimen S1, west face.

56

Figure 3.8 Top surface after shear failure in Specimen S1

Figure 3.9 Overall view of shear failure in north face in Specimen S1 at shear of 125.6 kN.

57

i t u -

100 -

2

S e o -

20 -

Load vs. deflection (av. of points 2 & 3)

' 1 1 1

/ Load vs. deflection ^ (av. of points 1 & 4)

1 1

- •

3

o2

0 1

—I 1 —

o

4

10 15 20 25 30 Average deflection (mm)

35 40

Figure 3.10 Load versus average deflection of Specimen S2.

Ey

0.00235 Strain

0.004 (mm/mm)

• First flex, crack A First yielding • First shear crack • Failure

Strain (mm/mm)

Figure 3.11 Strain distribution of top reinforcement in Specimen S2 at key load stages.

58

Figure 3.12 Flexural cracking on top surface of Specimen S2 at a shear of 75.2 kN.

Figure 3.13 Flexural shear cracks at a shear of 113 kN in Specimen S2, west face.

59

140

100 -

ro ° 60

20

- •

- •

[ _ l

I ^

i r

/y

1 1 1 1 1

Flexural crack Shear crack Torsion crack

1 1 1

0.4 0.8 1.2 1.6

Maximum crack width (mm)

Figure 3.14 Maximum crack width for Specimen S2.

60

Figure 3.15 Shear failure in Specimen S2, north face.

Figure 3.16 Shear failure in Specimen S2, west face.

61

Figure 3.17 Top surface after shear failure in Specimen S2.

Figure 3.18 Overall view of shear failure in north face in Specimen S2 at shear of 116.7 kN.

62

ro

140 -

100

60

20

A A \ Load vs. deflection 1 J \ (av. of points 2 & 3)

1 1 1 1

Load vs. deflection \ (av. of points 1 & 4)

1 1 —

D2

0 1

3

i

4

— i — '

10 20 30 40 50 Average deflection (mm)

60 70

Figure 3.19 Load versus average deflection of Specimen S3.

Ey

0.00235

0.006

0.010

Strain (mm/mm)

0.00235 0.006 Strain

0.010 (mm/mm)

<>

• First flex, crack A First yielding • First shear crack • Peak load

Figure 3.20 Strain distribution of top reinforcement in Specimen S3 at key stages.

63

Figure 3.21 Flexural cracking on top surface of Specimen S3 at a shear of 67.1 kN.

Figure 3.22 Flexural shear cracks at a shear of 120.9 kN in Specimen S3, west face.

64

140

100 -

ro ° 60

20

Flexural crack Shear crack Torsion crack

-i 1 1- -i 1 1 1 1-0.4 0.8 1.2 1.6

Maximum crack width (mm)

Figure 3.23 Maximum crack width for Specimen S3.

65

Figure 3.24 Flexure-shear failure in Specimen S3, north face.

Figure 3.25 Flexure-shear failure in Specimen S3, west face.

66

Figure 3.26 Top surface after flexure-shear failure in Specimen S3.

67

Chapter 4

Analyses and Comparison of Results

In this chapter, the responses of the three specimens are compared with

each other and with the predictions obtained using the equations of the Canadian

Standard (CSA 1994). These comparisons provide information on the influence

of the size of the column and the length of the critical perimeter on the shear

strength.

The objective of this chapter is to determine if the provisions of the

Canadian Standard (CSA 1994) provide conservative shear strength predictions

for slab-corner column connections.

4.1 Comparison of Experimental Results

Load-deflection curves for the Specimens S1, S2 and S3, having the same

flexural reinforcement are shown in Fig. 4.1 and 4.2.

Figures 4.1 and 4.2 illustrate that a punching shear failure in Specimens

S1 and S2 resulted in a sudden decrease of the carrying load after the peak

loads had been reached at peak loads of 121.4 and 116.7 kN, respectively. For

Specimen S3, the maximum load reached was 124.9 kN corresponding to

flexural yielding. The post-peak response of Specimen S3 was characterized by

a smooth decrease of the carrying load with increasing displacement. Specimen

S3 had a maximum load that was 3 to 7% higher than the maximum loads for

Specimens S1 and S2.

68

The total loads recorded during testing with the corresponding average

deflections at different key stages, such as first flexural cracking, first yielding,

first shear crack and peak load, for the various specimens are summarized in

Table 4.1.

Table 4.1 Summary of key load stages for Specimens S1, S2 and S3.

SPECIMEN

S1

S2

S3

Load (kN)

Deflection (mm)

Load (kN)

Deflection (mm)

Load (kN)

Deflection (mm)

FIRST

FLEX.

CRACK

21.3

1.2

18.2

0.6

18.8

0.6

FIRST

YIELD

84.4

15.7

82.8

13.9

74

11.4

FIRST

SHEAR

CRACK

111.8

26.8

113

26.4

120.9

27.9

PEAK

LOAD

121.4

34.9

116.7

31.3

124.9

30.5

From Table 4.1, it is observed that Specimen S2 exhibited the smallest

load at first flexural cracking.

The strain gauges in the top reinforcement of the slab showed that the

steel bars in Specimen S3 reached the yield strain at a slightly lower load than

for Specimens S1 and S2.

Table 4.1 also shows that in Specimens S1 and S2, the failure shear crack

appeared at only 92 and 97% of the ultimate load, respectively. For Specimen

S3, which exhibited a different failure mode, the first shear crack appeared at

97% of the ultimate load. In both Specimens S1 and S2, the angle of inclination

between the failure shear crack and the plane of the slab was approximately 30

69

degrees. In Specimen S3 significant shear cracks with an angle of 45 degrees

developed before flexural yielding occurred. Menetrey (1996) presented an

analytical method to predict the punching shear capacity, which is influenced by

the inclination of the shear cracks. He concluded that inclined cracks with a low

angle indicate punching shear failure, while inclined cracks with larger angles

indicate primarily flexural yielding.

Specimen S2, with a larger column than Specimen S1, experienced

smaller deflections during testing due to the smaller flexural lever arm and the

increased stiffness of the slab-column connection. However, the maximum

deflection attained at failure for Specimen S1 was 2% higher than the deflection

at peak load (i.e., increasing from 34.9 to 35.5 mm) while the maximum

deflection for Specimen S2 increased from 31.3 mm at the peak load to a value

of 37.6 mm at failure (i.e., an increase of 20%). In contrast to these two

specimens, Specimen S3 reached a maximum deflection of 60.2 mm, that is

almost double the deflection at peak load (see Fig. 4.1). It is evident that

Specimen S3 had considerably greater ductility than the other two specimens.

It is surprising that Specimen S2, having a larger column than Specimen

S1, experienced a peak load that was slightly less than Specimen S1. This may

be due to the very brittle nature of punching shear failures.

In all the specimens, yielding of all top reinforcing bars was recorded

before failure occurred. Specimen S3 underwent general yielding of the negative

moment reinforcing bars before the ultimate capacity was reached. Zaghlool and

de Paiva (1973) found that punching shear is a secondary phenomenon that

develops only after yielding of the steel at the slab-column interface. They

predicted that the ultimate capacity depends primarily on p fy and the column

size, among others, and not on y[f\ .

From the results presented in Chapter 3, it is observed that the highest

strains occurred for the three specimens in the bar located closest to the inner

70

corner of the column in the "flexural weak direction". This seems to show that the

greatest stresses were concentrated at the inner corner of the column.

Representative crack patterns for the three specimens at failure loads are

shown in Fig. 3.8, 3.17 and 3.26. Figures 3.8 and 3.17 in Chapter 3 show that

there was not much difference in the crack pattern and mode of failure for

Specimens S1 and S2. For all specimens, the flexural cracks first appeared in

the immediate vicinity of the inner corner of the column. The only major

difference was the width of the failure cracks.

The increased column size of Specimen S3 had a favorable influence on

the failure mode, shifting from punching shear to flexural yielding. This

observation is evident from the crack pattern of the three specimens in Fig. 3.26

and in Table 4.2.

Table 4.2 shows the maximum crack widths at loads corresponding to

general yielding of the flexural steel.

Table 4.2 Maximum crack widths at peak loads for Specimens S1, S2 and S3.

SPEC.

S1

S2

S3

LOAD AT

GENERAL

YIELDING

(% OF PEAK LOAD)

121.4

(100)

116.7

(100)

112.2

(90)

MAXIMUM CRACK WIDTH AT

GENERAL YIELDING (mm)

Flexural

crack

0.35

2.25

1.75

Torsional

crack

0.3

0.5

0.1

Shear

crack

2.0

2.0

MODE OF

FAILURE

Flexure +

Punching

Flexure +

Punching

Flexure

71

As can be seen from Table 4.2, significant shear cracks were present in

Specimens S1 and S2 at the load stage corresponding general yielding of the

flexural steel. Both of these specimens failed by combined flexure and punching

shear. Specimen S3, with the largest column, exhibited flexural yielding and

large deflections and had no shear crack when general yielding occurred.

4.2 Comparison of Experimental Results with Code Predictions

According to the 1994 CSA Standard it is necessary to check the design

for both one-way shear and two-way shear action for corner slab-column

connections. For both types of failure, either one-way shear or shear combined

with moment transfer, the strength is strongly influenced by the size of the critical

section or periphery.

For one-way shear, the critical section of a square corner column is

assumed to be located along a straight line at a distance of d/2 from the inner

corner of the column. Ingvarsson (1973) analyzed shear failures at corner

columns on the basis of the slab action being similar to that of a diagonal beam.

This critical one-way shear periphery was also suggested by Hawkins and

Mitchell (1979). The 1994 CSA Standard requirements for one-way shear at

corner columns was based on the work of Hawkins and Mitchell. This results in a

length, bo, of the critical section for a square column of size c of (d + V2 c).

In two-way shear action the 1994 CSA Standard assumes that the critical

section is located at a distance d/2 from the perimeter of the column, resulting in

a critical perimeter, b0, of 2 (c + d/2).

The one-way shear strength is determined from the following equation:

72

Vc =0.166A(l)cA/fc b0d (4.1)

where X is a factor accounting for concrete density and the two-way shear

strength is calculated using Eq. (1.24) in Chapter 1.

The critical perimeters for both one-way and two-way action are shown in

Table 4.3. Table 4.3 also compares the strengths of the slab-column

connections observed in the tests with the values predicted by the 1994 CSA

Standard using Eq. (4.1) and (1.24) for both one-way and two-way, respectively.

In this comparison, a value of (j)c of 1.0 was used in the analysis of the test

results, allowing the nominal shear resistance, Vc, to be determined.

Table 4.3 Predicted failure loads for Specimens S1, S2 and S3 according to

1994 CSA Standard.

Spec.

S1

S2

S3

c

(mm)

250

300

350

h

(mm)

150

150

150

f'c

(MPa)

42.8

42.8

42.8

dave

(mm)

115

115

115

One-way

shear across

corner at d/2

bo

(mm)

822.1

963.5

1104.9

Vc

(kN)

102.7

120.3

138

One-way

shear at d/2

from column

faces

bo

(mm)

615

715

815

Vc

(kN)

77.1

89.6

102.2

Shear and

moment

transfer at

d/2

bo

(mm)

615

715

815

Vc

(kN)

63.8

80.9

99.1

Vu

(kN)

121.4

116.7

124.9

Table 4.3 shows that one-way shear resistance at d/2 from the inner

corner was found to give the best prediction for all three test specimens. The

ultimate strengths of the three specimens are also compared to the values

obtained from the 1994 Standard equations and are plotted against the column

size in Fig. 4.3.

73

As can be seen from Table 4.3 and Fig. 4.3, the one-way shear

predictions with a diagonal critical section located at d/2 from the inner corner

provide very good agreement with the experimental results for Specimen S1, with

the experimental shear capacity being 18% above the predicted one-way shear

capacity. The experimental shear strength for Specimen S2 was 3% below the

value predicted by the 1994 CSA Standard for one-way shear. Specimen S3

experienced flexural yielding and hence the predicted value for one-way shear in

Table 4.3 is not applicable. The total shear corresponding to the negative and

positive flexural nominal resistances provided in the weak flexural direction are

139.3 and 183.9 kN, respectively, for Specimen S3. In this case, the negative

moment capacity governs and is used in the analysis. The maximum moment

reached in the slab at the column face is 10% below the predicted nominal

flexural resistance. It is believed that torsion in the slab resulted in additional

tensions in the reinforcement on the side faces of the column, thus resulting in a

lower moment resistance.

It is noted that the prediction for one-way shear on a critical section at d/2

from the column faces provides a conservative prediction of the failure load. This

assumed failure mode provides a simple approach, using the same critical

section as for two-way shear, and provides a simpler method than the current

CSA method for cases with rectangular columns and rectangular slab panels.

Another advantage of using this critical section is that all of the current code

requirements for proximity to edge of slab and for presence of openings would

also apply.

Both Table 4.3 and Fig. 4.3 also show that the predicted strength for each

specimen in two-way action is conservative. It is noted that the ACI Code does

not consider the one-way shear failure at corner columns.

Table 4.4 provides a summary of the shear strength for the three

specimens as predicted by EC2-02. It is noted that EC2-02 takes account of the

effect of the flexural reinforcement ratio on the shear resistance. Figure 4.4 also

74

compares the experimental results with the failure loads predicted by the 1994

CSA Standard and EC2-02.

Table 4.4 Predicted shear strength for the three specimens with EC2-02.

SPEC.

S1

S2

S3

c

(mm)

250

300

350

f'c

(MPa)

42.8

42.8

42.8

Clave

(mm)

115

115

115

k

2

2

2

P

0.012

0.011

0.010

bo(u)

(mm)

611

661

706

Vc

(kN)

93.3

98.2

102.3

Vu

(kN)

125.9

122.7

133.1

The critical perimeter in EC2-02 is considered at 2d from the face of the

column to make the limiting shear stress more uniform for different column sizes.

This feature is apparent from Fig. 4.4.

The expression used in EC2-02 to predict the shear strength is a function

of the cube root of the reinforcement ratio and the cube root of the compressive

strength of the concrete and also considers the size effect as is seen in Eq. 1.29

in Chapter 1.

It can be observed in Table 4.4 and Fig. 4.4 that the shear strength

predicted by the 1994 CSA Standard and by EC2-02 show significant differences

and that the equations predicted by EC2-02 have smaller variation than the 1994

CSA Standard for different column dimensions.

Table 4.4 shows that EC2-02 conservatively predicts values of the shear

strength with the predictions being relatively independent of the column size.

From Fig. 4.4 is observed that for small column sizes, up to 200 mm, EC2-

02 gives a higher prediction than the one-way shear prediction of the 1994 CSA

Standard. For column sizes between 200 and 350 mm, EC2-02 predicts values

75

that are lower than the ones predicted by the 1994 CSA Standard for one-way

shear strength. When the size of the column is 350 mm and more, the critical

perimeter assumed in EC2-02 is constant because is taken as the lesser of 1.5 d

and 0.5 c. For column sizes greater than 350, the 1.5 d requirement controls.

Hence, EC2-02 predicts a maximum shear strength for a column size of 350 mm,

with the predicted strength being reduced slightly for column sizes above 350

mm, because the flexural reinforcement ratio is reduced.

It is also observed that for larger flexural steel ratios such as Specimen

S1, a brittle shear failure occurred accompanied by yielding of the tension steel

reinforcement. When the flexural reinforcement ratio was decreased, a ductile

flexural failure occurred accompanied by general yielding of the negative moment

steel. However, Alexander and Simmonds (1992) found that the shear strength

was relatively independent of the steel index p fy when punching shear failure

occurs.

76

140

100

g 60

20

30 40 50

Average deflection (mm)

Figure 4.1 Load versus average deflection.

140

100

8 60

20

toffy \ S3 £r S2^ ^

k si •

i ' 1 ' 1 1 ' —

c

D

3

,2

1 — t — '

10 20 30 40 50

Average deflection (mm)

60 70

Figure 4.2 Load versus average deflection.

77

250

200 -

T 150 -

c Q) i— -^ W

S 1 0 CH JC CO

50.

S3

S1 . S2

y

One way across corner

One-way at d/2 from column faces

Two-way Test Results

100 200 300 400

Column Size (mm)

500 600

Figure 4.3 Variation of strength predicted by the 1994 CSA Standard with the column size.

78

250

200 -

^ 150 -

c CD

co

ro 100 a) CO

50 -

S 3 . ' ' S2 y'

S1 • ,-' • -'"• y^

' ^^^ ..'' " " ^ * • * *

. ' ' ' *•*

1 1 1 1-

S ' S

s ' S

, • s s

• s

y ^-^"^

s ~^*^

- - One way across corner, CSA

— One-way at d/2 from column faces, CSA

--- Two-way, CSA EC2-02

• Test Results

1

100 200 300 400 500 600

Column Size (mm)

Figure 4.4 Variation of strength predicted by the 1994 CSA Standard and EC2-02 with the column size.

79

Chapter 5

Conclusions

5.1 Conclusions

The results of testing three full-scale slab-column specimens are used to

evaluate the shear capacity at corner columns and to compare the experimental

results with predictions using the requirements of the 1994 CSA Standard A23.3.

The main variable in this test series is the size of the corner columns. The slab

thickness and reinforcing details were kept constant for all three specimens.

The following observations and conclusions are made, based on the

experimental results and the strength predictions:

1. The one-way shear capacities and the two-way shear capacities were

used to predict the strength of the slab-column connections. The one-way

shear strengths provided a more accurate prediction of the shear failure

than the two-way shear predictions.

2. A practical approach, suitable for codification, would be to assume a one­

way shear failure on a critical section located at d/2 from the column

faces. This is the same critical section assumed for two-way shear.

3. Two of the specimens failed in a brittle manner, exhibiting a one-way

shear failure. Although torsional cracking was observed, the dominant

failure crack was clearly a one-way shear failure. The specimen with the

largest column exhibited ductile flexural yielding, having greater post-peak

80

deflections than the other two specimens. This flexural yielding was

followed by a one-way shear failure.

4. The size of the column was found to have also influence on the capacity of

the specimens although S2, with a larger column, experienced a peak

load that was slightly less than Specimen S1. In view of the limited

number of tests, it would be desirable to conduct further geometrically

similar column size-effect tests with larger slabs.

5. The code rules for the computation of punching shear for corner columns

without shear reinforcement differ considerably with respect to the

definition of the control perimeter and calculation of the nominal shear

stress. EC2-02 considers the size effect and the effect of amount of

longitudinal reinforcement, while the 1994 CSA Standard does not

account for these effects. With respect to the flexural reinforcement ratio,

it is observed that EC2-02 gives higher capacities than the 1994 CSA

Standard for large flexural reinforcement ratios (p>1.3%) and more

conservative shear strength for lower reinforcement ratios.

6. All punching failures occurred at connections where yielding of all top

reinforcing bars was recorded. For this and the above reason, it is

believed that the punching shear strength of slabs is a function of flexural

reinforcement ratio and the yield stress, p fy.

7. There are considerable difficulties in performing an analysis that accounts

for the additional tensions in the reinforcement due to torsion. Therefore,

further research and development of models, material and computer

methods are needed in this important area.

81

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