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 Influence of Concrete Strength on the
Behaviour of Bridge Pier Caps

by

March, 1997

Department of Civil Engineering and Applied Mechanics

McGill University
Montreal, Quebec
Canada

A thesis SUbmittéd to the Faculty of Graduate Studies and Research in partial fulfilment of the
requirements for the degree of Master of Engineering

C Gavin MacLeod, 1997

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 ABSTRACT
(
Two full-scale reinforced concrete bridge pier caps were constructed and tested to
investigate the influence of concrete strength on their behaviour. The amount of uniformly
distributed reinforcement required for crack control at service load levels was also varied in order
to investigate the suitability of current design approaches for these disturbed regions. ln addition.
strut-and-tie models. refined strut-and-tie models and non-linear finite element analyses are used
to predict the comp!ete bei,aviour of the test specimens.

(
( RÉsUMÉ

Deux châpiteaux de pont grandeur réelle en béton armé ont été construits et testés pour
étudier ('influence de la résistance du béton sur leur comportement. La quantité d'armature
distribuée uniformément, nécessaire pour contrôler les fissures sous charges de service. a été
variée pour déterminer si les approches de conception actuelles conviennent pour ces structures
spéciales. De plus, des modèles bielle et tirant simple. des modèles bielle et tirant plus détaillés
et des analy~es non-linéaires par éléments finis sont utilisés pour prédire le comportement complet
des spécimens d'essai.

(
ii
(
ACKNOWLEDGEMENTS

The author would like to thank Professar Denis Mitchell for bis competent supervision,
support and encouragement throughout this research programme. The author would aIso like to
express his gratitude to Dr. William Cook for his advice and assistance during this programme.

The efforts of Marek Przykorski, ROD Sheppard, John Bartczac and Damon Kiperchuk
in preparing the experiments are gratefully acknowledged. The author would also like to thanle
Homayoun Abrishami, Arshad Khan, Stuart Bristowe, Glenn Marquis, Peter McHarg and Pierre-
Alexandre Koch for their contributions in the construction and testing of the specimens.

The fmancial support provided by Concrete Canad~ a Network of Centres of Excellence

Program funded by the Minister of State, Science and Technology in Canada, is greatly
appreciated.

(
Hi
( TABLE OF CONTENTS

ABSTRACT
RÉSUMÉ ii
ACKNOWLEDGEMENTS Hi

LIST OF FIGURES vi
LIST OF TABLES viii
LIST OF SYMBOLS x

1. INTRODUCTION
1.1 Introduction 1
1.2 Disturbed Regions 1
1.3 Previous Research on Strut-and-Tie Modeis 4
1.4 Design Using Strut-and-Tie Models 10
1.5 ACI Design Approaches for Disturbed Regions 13
1.5.1 ACI Provisions for Deep Beams 13
1.5.2 ACI Provisions for Brackets and Corbeis 15
1.6 Experiments on Deep Beams. CorbeIs and Pier Caps 17
1.6.1 Deep Beams 18
1.6.2 CorbeIs 21
1.6.3 Pier Caps 23
1.7 Detailed Analysis Procedures 24
1.7.1 Refined Strut-and-Tie Models 24
1.7.2 Non-Linear Finite Element Analysis 26
1.8 High-Performance Concrete 30
1.8.1 Compressive Strength 30
1.8.2 Flexure and Axial Loads 33
1.8.3 Minimum Reinforcement for Aexure and Shear 34
1.8.4 Strut-and-Tie Provisions 35
1.9 Crack Widths and Crack Spacing 35
1.10 Research Objectives 38

(
iv
 2. EXPERIMENTAL PROGRAMME 39
( 2.1 Details of Specimens 39
2.2 Material Properties 43
2.2.1 Concrete 43
2.2.2 Reinforcing Steel 46
2.3 Test Setup and Instrumentation 48
2.4 Testing Procedure 51

3. EXPERIMENTAL RESULTS 53
3.1 Load-Detlection Responses 53
3.1.1 Specimen CAPN 53
3.1.2 Specimen CAPH 55
3.2 Development of Strains 55
3.2.1 Specimen CAPN 55
3.2.2 Specimen CAPH 62
3.3 Development of Cracking 69
3.1.L Specimen CAPN 70
3.1.2 Specimen CAPH 73

4. COMPARISONS AND ANALYSES OF RESULTS 76

4.1 Comparison of Responses of Normal- and High-Strength Concrete
Specimens 76
4.2 c'redictions of Results 83
4.2.1 Applicability of Plane-Sections Analysis 83
4.2.2 Simple Strut-and-Tie Models 83
4.2.3 Refined Strut-and-Tie Models 85
4.2.4 Non-Linear Finite Element Analysis Using Program FIELDS 88
4.3 Estima~es of Crack Widths 101

5. CONCLUSIONS . L03

REFERENCES 105

APPENDIX - EXPERIMENTAL DATA 109

(
v
( LIST OF FIGURES

1.1 Typical forms of cap beams and pier caps used in bridge construction 2
1.2 Examples of disturbed regions . 3
1.3 Stmt-and-tie modelling of a deep beam with a direct support and a tension
hanger support . 5
lA Influence of principal tensile strain, El' on compressive strength of
diagonally cracked coocrete 8
1.5 Compressive strength of strut versus orientation of tension lie passing
through stmt 8
1.6 Provisions for brackets and corbeIs 16
1.7 Applicability of strut-and-tie model for predicting series of beams tested by
Kani 19
1.8 Crack control reinforcement required with assumption of straight-line
compressive struts 25
1.9 Investigating the effect of distributed reinforcement 00 deep beams 25
1.10 Evaluating stresses at Gauss points in quadrilaterai element 27
1.11 Detennining average concrete tensile stress,/el • from strain, El 29
1.12 Investigating stress cond!t!on at crack interface 29
1.13 Influence of concrete strength on shape of stress-straÏD curve 32
1.14 Crack width parameters 36
1.15 Side-face cracks controlled by skin reinforcement 36

2.1 Test simulation of cantilever cap beams 40

2.2 Specimen details 41
2.3 Concrete properties 45
2A Typical stress-strain resopnses of reinforcing bars 47
2.5 Specimen CAPN under the MTS testing machine 49
2.6 Different bearing details of specimens CAPN and CAPH 50
2.7 LVDT locations 52
2.8 Strain gauge locations and crack width lines of measurement 52

3.1 Load-deflection responses of specimens 54

3.2 Strains in bottom bar of CAPN tension tie, determined from strain gauges 56
3.3 Strains distributed reinforcement of CAPN, determined from strain gauges 58
(
vi
 3.4 Longitudinal strains from LVDTs at mid-height and at the level of the tension
( tie ofCAPN 59
3.5 Responses of CAPN-A rosettes A6 and A7 60
3.6 Responses of CAPN-B rosettes 86 and 87 61
3.7 Strains in bonom bar of CAPH tension tie. determined from strain gauges 63
3.8 Strains distributed reinforcement of CAPH. determined from strain gauges 65
3.9 Longitudinal strains from LVDTs at mid-height and at the level of the tension
tie ofCAPH 66
3.10 Responses of CAPH-A rosettes A6 and A7 67
3.11 Responses of CAPH-B rosettes 86 and B7 68
3.12 Development of cracks in CAPN 71
3.13 CAPN after faHure 72
3.14 Development of cracks in CAPH 74
3.15 CAPH after failure 75

4.1 Comparison of load-deflection responses of specimens . 77

4.2 Flexural crack widths measured at the level of the tension tie in specimens 79
4.3 Diagonal crack widths measured at mid-height of specimens 80
4.4 Influence of distributed reinforcement ratio on crack control 81
4.5 Simple strut-and-tie model for specimen CAPN 84
4.6 Simple strut-and-tie model for specimen CAPH 84
4.7 Refined strut-and-tie models for specimen CAPN 86
4.8 Refined strut-and-tie models for specimen CAPH 87
4.9 Predicted load-deflection responses of specimens 89
4.10 Predictions of deflected shapes of specimens at maximum predicted loads 91
4.11 Predicted strains and stresses in specimen CAPN at a load of 920 kN 92
4.12 Predicted strains and stresses in specimen CAPH at a load of 920 kN 93
4.13 Predicted strains and stresses in specimen CAPN at a Joad of 2280 kN 94
4.14 Predicted strains and stresses in specimen CAPH at a Joad of 2280 kN 95
4.15 Predicted strains and stresses in specimen CAPN at a Joad of 4980 kN 96
4.16 Predicted strains and stresses in specimen CAPH at a load of 5340 kN 97
4.17 Predictions of stress development in main tension ties of specimens 99
4.18 Comparison of predictions of stress in main tension ties at general yield 100

(
vii
( LIST OF TABLES

1.1 Effective stress levels in struts . 7

1.2 Effective stress levels in nodal zones 10

2.1 Mix design for 35 MPa concrete 44

2.2 Mix design for 70 MPa concrete 44
2.3 Concrete properties 46
2.4 Reinforcing steel properties 48

4.1 Comparison of strut-and-tie predictions with measured loads at general

yielding 88
4.2 Comparison of refined strut-and-tie predictions and non-linear finite element
predictions with measured loads at general yielding 98
4.3 Comparison of predicted and measured crack widths and principal tensile
strains in the main tension ties of specimens 102
4.4 Comparison of predicted and measured diagonal crack widths and principal
tensile strains at mid-height of the specimens 102

A.l Readings from vertical LVDTs used to detennine the deflection of

specimen CAPN 110
A.2 Readings from LVDTs located at the level of the main tension tie in
specimen CAPN-A III
A.3 Readings from LVDTs located at the level of the main tension tie in
specimen CAPN-B 112
A.4 Readings from LVDTs located at mid-height of specimen CAPN-A 113
A.S Readings from LVDTs located at mid-height of specimen CAPN-B 114
A.6 Readings from LVDTs rosettes located in end A of specimen CAPN 115
A.7 Readings from LVDTs rosettes located in end B of specimen CAPN 116
A.8 Strains from strain gauges 10cated in end A of specimen CAPN 117
A.9 Strains from strain gauges located in end B of specimen CAPN 119
A.IO Readings from vertical LVDTs used to detennine the deflection of
specimen CAPH 121
A.ll Readings from LVDTs located at the level of the main tension tie in
specimen CAPH-A 122
A.12 Readings from LVDTs located at the level of the main tension tie in
( specimen CAPH-B 123

viii
 A.13 Readings from LVDTs located at mid-height of specimen CAPH-A 124
( A.14 Readings from LVDTs located at mid-height of specimen CAPH-B 125
A.15 Readings from LVDTs rosettes located in end A of specimen CAPH 126
A.16 Readings from LVDTs rosettes located in end B of specimen CAPH 127
A.17 Strains from strain gauges located in end A of specimen CAPH 128
A.18 Strains from strain gauges located in end B of specimen CAPH 130

(
ix
( LIST OF SYl\mOLS

a maximum aggregate size

a shear span
A effective area of concrete SUITounding each reinforcing bar
A e. q area of effective embedment zone of concrete where reinforcing bars can influence crack
widths
A cs effective cross-sectional area of concrete compression strut
AI area of reinforcement required to resist moment, Mu, in corbel
Ah area of horizontal stirrup reinforcement in corbel
An area of reinforcement required to resist horizontal tensile force, Nue' in corbel
As area of primary tension reinforcement
As area of reinforcing steel
A smin minimum area of fiexural reinforcement
A sr area of reinforcing steel in main tension tie
Av area of shear reinforcement perpendicular to axis of member within a distance s
A lf area of shear friction reinforcement
A vh area of shear reinforcement parallel to axis of member within a distance 52

b width of member
br width of tension zone of member
bw minimum effective web width within depth d
C clear concrete cover
C distance from extreme compression fibre to neutral axis
C force in compression strot
d distance from extreme compression fibre to centroid of tension reinforcement
da depth of compression strot
db diameter of reinforcing bar
de distance from extreme tension fibre to centre of closest bar
Ee modulus of elasticity of concrete
Es modulus of elasticity of reinforcing steel
E sr modulus of elasticity of tension tie reinforcement
fe concrete stress
f e' compressive strength of concrete

1er concrete cracking stress, equal to EcE cr

( feu limiting compressive stress in concrete compression strut

x
 fel average principal tensile stress in concrete
( !C2 average principal compressive stress in concrete
Ir moJulus of rupture of concrete
J:. average stress in reinforcing steel
fs ca1culted stress in reinforcement at specified loads
fs.cr stress in reinforcing steel across crack
f2ma:c limiting compressive stress of diagonally cracked concrete
h overall depth of beam
height of effective embedment of tension tie
distance of main tension reinforcement from neutral axis
distance of extreme tension fibre from neutral axis
post-peak decay tenn for stress-strain relationship of concrete
coefficient that characterizes bond properties of reinforcing bars used in CEB-FIP crack
width expression
k1 rcmforcing bar location factor used in development length expression
k2 coefficient to account for strain gradient used in CEB-FIP crack width expression
k2 reinforcement coating factor used in development length expression
k3 reinforcing bar size factor used in development length expression
lb length of bearing
ld development length of reinforcement
ldh straight embed.ment length
ln clear span
M cr cracking moment
Mf factored mom~nt at a section
A-fr factored moment res=Citance at a section
Mu design ultimate moment
n curve fitting factor for stress-strain relationship of concrete
N applied axial tension
horizontal tensile force
s spacing of shear reinforcement parallel to axis of member
s maximum spacing between longitudinal reinforcing bars
mean crack spacing
mean spacing of diagonal cracks
spacing of shear reinforcement perpendicular to axis of member

( T force in tension tie

xi
 nominal shear strength provided by concrete
( shear stress at crack interface
Vcima:c limiting shear stress along crack
Vn nominal shear strength at a section
Vs nominal shear strength provided by shear reinforcement
Vu factored shear force at a section
W average crack width. equal ta El S",

Wk characteristic crack width. equal to 1.7w",

w", mean crack width. equal ta EqS",
W mat maximum crack width
z limiting crack width parameter. equal to fs(dcA)113
Cl 1 ratio of average stress in rectangular compression block to concrete strength
{3 factor accounting for strain gradient. equal to ~ / hl

{31 ratio of depth of rectangular compression block ta depth to neutral axis

'Yc density of concrete
'Y:ry shear strain
Ây yield deflection
au ultimate deflection
Ee compressive strain
Ee ' strain in concrete at peak compressive stress
Ecj strain in concrete caused by stress
Eer strain in concrete at cracking
Es strain in reinforcing steel
Es. cr strain in reinforcing bar at crack location
E.t horizontal tensile strain
Ey strain in y-direction
El principal tensile strain
El largest tensile strain in effective embedrnent zone
EZ principal compressive strain
EZ smallest tensile strain in effective embedment zone
(J angle of principal compressive strain from horizontal
smallest angle between compression stmt and tension tie crossing Stnlt
effective coefficient of shear friction
factor to account for influence of high-strength concrete. equal ta 0.55 + 1.25//fc'

( p reinforcement ratio of primary tension reinforcement. equal ta As/bd

xii
 Pq AJA c. q
( Pw AJbwd
capacity reduction factor taken as 0.85 for shear
y

material resistance factor for concrete

material resistance factor for prestressing steel
rnaterial resistance factor for reinforcing steel

(
xiii
 CHAPTER 1
(

INTRODUCTION

1.1 Introduction
Figure 1. 1 shows sorne typica1 fonns of cap beams and pier caps used in bridge
construction. Although there is a variety of fonTIS for these types of elements, this research
programme will examine a pier cap of forro shown in Fig. 1.I(b), which is aIso representative
of the cantilever portions of the cap beam shown in Fig. l.l(a). This chapter first reviews the
behaviour and design of disturbed regions, highlighting the use of strut-and-tie models for design.
A review of experimental work carried out on deep beams, corbeis and pier caps is presented to
provide background information on the behaviour of disturbed regions which are sunilar to those
investigated in this research programme.

1.2 Disturbed Regions

Regions of a member in which the "plane-sections" assumption is appropriate are
sometimes referred to as B-regions (where B stands for beam or Bernoulli hypothesis). Other
regions of a member where the strain distribution is significantly non-linear are referred to as D-
regions, or disturbed regions (Schlaich et al. 1987). This non-linear distribution of strains is due
to a cornplex internaI flow of stresses adjacent to abrupt changes of cross-section or the presence
of concentrated loads or reactions. The two main design assumptions, that plane sections rernain
plane and that the shear stress can be assurned to be unifonn over the nominal shear area, are no
longer valid in disturbed regions.

Several examples of disturbed regions are shawn in Fig. 1.2. where the flow of
compressive stresses is shown by dashed lines, and tensile ties are indicated by solid Hnes.
Figure 1.2(a) shows how the presence of a support reaction interrupts the uniform diagonal
compression field in a simply supported "slender" beam with stirrups. The flow of compressive
stresses fan into the support causing a disturbed region near that location. Figure 1.2(b) shows
a deep beam subjected to concentrated loads. Because of the complex flow of stresses in this
( member, the entire member is a disturbed region. The flow of forces from the top of the bearn

1
(

:
1
/
1

(a) Continuous cap beam

(b) Cantilever cap beam

(c) Deep-water pier cap

Figure 1.1 Typical forms of cap beams and pier caps used in bridge construction

(
2
(

uniform
fan field
/ /0
-~r---.-:--~

'''-.. tension tie

(a) Simply supported beam

compressive
strut

..!.

~:.~~:~

~...
1::...
~

,
T1 tension tie T
(b) Deep beam

ttttt"
(c) Corbel

Figure 1.2 Examples of disturbed regions

,-
3
 to the reaction areas delineates concentrated compressive stresses as shown. The resisting
( mechanism, consisting of the flow of compressive stresses and the presence of the tension tie,
resembles a tied arch. The corbel shawn in Fig. 1.2(c) is a D-region characterized by
concentrated compressive stresses flowing from the bearing areas to the column. The horizontal
components of these diagonal compressive stresses must be equilibrated by tension in
reinforcement which is well-anchored at the outer edges of the bearing areas.

1.3 Previous Research on Strut-and-Tie Models

Truss models have been used since the tum of the century for the design of slender
reinforced concrete beams (Ritter 1899, Môrsch 1909). These early tmss models had a
compression chord and tension chord with diagonal compressive struts, typically assumed ta act
at 45 0 • These tmss models formed the basis of code developments in Europe and North America
for the design of slender beams. Recently. renewed interest bas been generated in truss models
as a design tool, not ooly for slender beams, but also for the design of disturbed regions.

A strut-and-tie model provides a simple tool for the design of disturbed regions, that is,
regions having a complex flow of stresses. The flow of forces in a disturbed region is idealized
using compressive struts ta represent the concentrated compressive stresses and reinforcement ta
represent the tension ties (see Fig. 1.2). Figure 1.3 illustrates the development of a stmt-and-tie
model for a deep beam with a direct support and a tension hanger support. The first step in
design is ta sketch the flow of compressive stresses, in the fonn of compressive struts, from the
location of the applied loads to the support regions. The next step is to sketch the tension tie
reinforcement required to complete the strut-and-tie model (see Fig. 1.3(a». The shaded areas
in Fig. 1.3(a) where compressive struts and tension ties meet are referred to as nodal zones.
These nodal zones are regions of multi-directionally stressed concrete. In arder ta examine the
equilibrium of the model, an idealized truss model is created as shown in Fig. 1.3(b). The
dashed lines represent the centreline of the compressive struts, and the solid lines are located at
the centroid of the tension tie reinforcement. The nodes of the idealized truss occur at the
intersections of the compressive struts and tension ties in the idealized tross model. One of the
main advantages of using strut-and-tie models is that the flow of forces cao be easily visualized
by the designer. Seme experience is required to determine the most efficient strut-and-tie model
for any given situation, as no unique solution exists. As this is a lower-bound solution technique,
all solutions will give cons~rvative resulrs provided that equilibrium is satisfied, applicable stress
limits are not exceeded and the reinforcement is capable of developing the required stress.
( Schlaich and Schâfer (1984) and Schlaich et al. (1987) suggest choosing the geometry of a SLrut-

4
( d -.-=.~~
-4-
1 -.. --~----- r , 0
~-~ --..:'-,,-'
,'---..
tÎ Î "'---..... ,.
~':".. .~
,
~
_CCC-node ~: l"sinO, + d.cosf).
J

CTT-node CCT-node - h

~
I tt;/',$inO. + Iteoso.
~,.' :~~, .

.... . "0
T
h..
.r....
. ' ==
- ..

-~-
(a) Strut-and-tie model

+
1

1
, CCC-node

.• '~ - _. - --- --- - -.. - -- ----- ----il,

"
.'
.'

"

1/
~
\
'-... CTT-node

(b) Truss idealization

Figure 1.3 Strut-and-tie modelling of a deep beam with a direct support

( and a tension hanger support

5
 and-tie model such that the angle of each compression diagonal is within ± 15 of the angle of
0

( the resultant of the compressive stresses obtained from an elastic analysis. While this approach
gives sorne guidance in choosing the model geometry. it should be noted that considerable
redistribution of stresses may occur after cracking.

Once the geometry of the strut-and-tie model has been chosen. forces in the truss
members can be found from equilibrium. The required amount of reinforcement for each tension
tie can then be determined while ensuring that this reinforcement is anchored in such a way to
transfer the required tension to the nodal zones of the truss. The dimensions of a concrete
compressive strut must be made large enough such that the calcuJated stress in the strut is less
than its limiting stress.

Considerable research has been carried out on limiting stresses in concrete compressive
struts and the influence of anchorage details on the dimensions of these struts. Thürliman et al.
(1983) and Marti (1985) concluded that the stress in the stmts be limited to 0.60//. while
Ramirez and Breen (1991) suggest a compressive stress limit of 2.49Vfc' (in MPa units).
Schlaich et al. (1987) proposed stress limits for the struts which depend upon the stress conditions
and the angle of cracking associated with the strut (see Table 1.1).

Vecchio and Collins (1986) developed expressions for the modified compression field
theory which accounted for the strain softening of diagonally cracked concrete (see Fig. 1.4).
The limiting compressive stress. f2ma.t. is given as:

f2ma.t
I.e' < F' (l.1)
- Je
0.8 + 170f l

where: le' = concrete compressive strength.

= principal tensile strain.

The following strain compatibility equation provides a means of determining the principal tensile
strain. El' in diagonally cracked concrete:

(1.2)

= horizontal tensile strain.

= principal compressive strain.
( 8 = angle of the principal compressive strain from horizontal.

6
(
1
Conditions of StnIt

Undisturbed and uniaxial state of

1
Effective
Stress Level

O.80/c'
td
Schlaich et
compressive stress mat may exist for al.
prismatic struts (1987)

Tensile strains and/or reinforcement

perpendicular to the axis of the strut may
0.68//
cause cracking parallel to the strut with
nonnaI crack width
Tensile strains andior reinforcement at
skew angles ta the axis of the strut may
0. 51 h-'
cause skew cracking with nonnaI crack
width
Skew cracks with extraordinary crack
width (expected if modeHing of the struts
depans significantly from the theory of 0. 34h-'

elasticity's flow of internaI stresses)

Uncracked llniaxially stressed struts of 1.0 "2ic' (a) MacGregor

fields (1997)

Struts cracked Iongitudinally due ta

bottle-shaped stress fields with sllfficient 0.80 "2/c'(a)
transverse reinforcement

Struts cracked longitudinally due to

bottIe-shaped stress fields without 0.65 "2/c'(a)
transverse reinforcement

Struts in cracked zone with transverse 0.60 "2/c' (a)

tensions from transverse reinforcement
.
(~) where "1 = 0.55 + 1.251[ï;
Table 1.1 Effective stress IeveIs 1Ii struts (adapted from Schlaich et al. 1987,
and MacGregor 1997)

(
7
( 1.----------Jz-_- - - - ,

l' ;;; - " )--.

f-, E,

.f..- ·········r······· \.
r

/' .. -
1 \ .. f
1 / h

_--#-~>
1 ~

""" 1
E'c

(a) Average concrete compressive stress,);, from strains El and Ez

1.2
f /!2maz

-I
1.0 ';. /

0.8 - -
f~
0.6
/r:: El

l' " 1
0.4·

0.2

00 2 4 6 8 10 12 14

(b) Reduction in compressive strength with increasing values of El

Figure 1.4 Influence of principal tensile strain. El,on compressive strength of diagonally
cracked concrete (Vecchio and Coilins 1986)

1.0 r - - - - - - - - - - - - - - - ,
t.L == 0.550 Pel'
,-
0.8 €: ~ -0.002 "'i·...
fi.
'",-
.. 1'._

\ ~'O: _~ /

r 0.6 " - oC _ E, -0.006 \ 1 l.

E~.E o.::,,~;I>"'CU
Jeu
rpch' 0.4 f:/ l 'E, -0.002 ••

€: --0.002

0.2 """ "

l" == o.an tPc lt
30· 45· 60· 75· 90·

~
Figure 1.5 Compressive strength of strut versus orientation of tension tie passing
through strut (Collins and Mitchell 1986)
(
g
 In order to apply the strain softening expression to diagonal compressive struts, for use
( in a strut-and-tie model, Collins and Mitchell (1986) gave the following expressions for the
limiting compressive stress in the struts:

(1.3)

where: feu = limiting compressive stress in the strut,

te' = concrete cylinder strength,

= principal tensile strain.

(l.4)

where: f2 = principal compressive strain in the strut, taken as 0.002,

= strain in the tension tie crossing the strut,
= smallest angle between the strut and the tension tie crossing the strut.

The variation of the compressive strength, feu. of a strut as a function of the angle, (Js' between
the strut and the tension tie passing through the strut is shown in Fig. 1.5.

It is aIso necessary to limit the compressive stress in the nodal zones of the strut-and-tie
mode!. The maximum compressive stress limits in nodal zones depend on the different straining
and confinement conditions of these zones. Figure 1.3 illustrates three types of nodes identified
as follows:

1. CCC - nodal zone bounded by compressive struts and bearing areas only,
2. CeT - node with a tension tie passing through it in only one direction, and
3. eTT - node with tension ties passing through it in more than one direction.
The two nodal zones in Fig. 1.3 located under the bearing areas at the top of the deep beam are
examples of CCC-nodes, that is, each node is bordered by a bearing area and two compressive
struts. The node above the direct support at the right end of the beam is an example of a eCT-
node since it contains one principal tension tie passing through the zone. The node at the indirect
support, located at near the bottom-Ieft corner of the deep beam shown in Fig. 1.3 is an example
of a CTT-node since two tension ties pass through it. These nodal zones must be chosen large
enough to ensure that stresses do not exceed the applicable stress limits. Table 1.2 outlines the
( effective stress limits for nodal zones as detennined by severa! researchers.

9
 Effective Proposed
( Conditions of Nodal Zone Stress Leve! by
1 1 1 1
CCC-nodes 0.85// Collins and
CCT-nodes 0.75/,:' Mitchell
(1986)
CTT-nodes 0.6°fc'
CCC-nodes 0.8Sfc' Schlaich et
Nades where reinforcement is anchored aL.
0.68fc'
in or crossing the node (1987)

Nades bounded by compression struts 1.0 Jl2f/(a) MacGregor

and bearing areas (1997)
Nodes anchoring one tension tie 0.85 Jl2fc'(3)

Nodes anchoring tension ties in more 0.75 Jl2fc'(3)

than one direction
(a) where '1 = O.sS + 1.2S1{ï:

Table 1.2 Effective stress levels in nodal zones (adaptP.d from Collins and Mitchell 1986.
Schlaich et al. 1987. and MacGregor 1997)

1.4 Design Using Strut-and-Tie Models

The CSA Standard A23.3 "Design of Concrete Structures for Buildings" (CSA 1984.
1994). the Ontario Highway Bridge Design Code (OHBDC 1991). the Canadian Highway Bridge
Design Code (CHBDC 1997, currently under development) and the AASHTO LRFD
specifications (AASHTO 1992) have adopted the stmt-and-tie design methods developed by
Collins and Mitchell (1986). In comparing different codes. it is important ta reaIize that the
Canadian standards use rnaterial resistance factors (cP c for concrete. cP s for reinforcing steel and
cPp for prestressing steel). while the O.S. codes use capacity reduction factors. (j), which depend
on the type of action. Both the CSA Standard and the CHBDC use the same rnaterial resistance
factors for steel with cP s = 0.85 and cPp = 0.90. The CSA Standard uses cP c = 0.60. while the
CHBDC uses cP c = 0.75. In this section reference will be made to the requirements of the
Canadian Highway Bridge Design Code. The CHBDC states that stmt-and-tie models shaH be
considered for the design of deep footings and pile caps or other situations in which the distance
between centres of applied load and the supporting reaction is less than twice the component
( thickness.

10
 The design procedure, with reference to the relevant code requirements, is summarized
( in the following steps.

1. Sketch the strut-and-tie model, assuming straight compression struts to model the flow
of forces from the points of application of the loads to the supports (see Fig. 1.3(a».

2. Choose the size of each bearing such that the limiting compressive stress of the adjacent
nodal zone is not exceeded. The nodal zone stresses are limited to 0.85 (jJcfc' for a CCC-
node, 0.75 epcfc' for a ·CCT-node, and O.60t/>cfc' for a CTT-node. The tension lie
reinforcement must be distributed over an effective area of concrete such that the force
in the tension tie does not exceed the appropriate stress limit, given above, times this
effective area.

For example, the bearing area of the direct support on the right end of the deep beam
shown in Fig. 1.3(a) is adjacent to a CCT-node, so the area of the bearing plate, lbb,
must be chosen large enough to ensure that the factored reaction force of the support does
not exceed O.75t/>cfc' lbb. In addition, the reinforcement making up the tension tie must
be detailed such that the effective area surrounding the bars (defmed as that area having
the same centroid as the tension tie, that is, hab) is large enough such that the tension in
the lie does not exceed 0.75 cP c!c' ha b.

3. Draw the truss model idealizing the strut-and-tie model (see Fig. 1.3(b». Ali nodes are
located at the intersections of the lines of action of struts, tension ties, applied loads and
bearing reactions.

In order to determine the lme of action of compressive struts, it is necessary to determine

the dimensions of the struts, such that the compressive stress limits are not exceeded.
Since the design of deep beams usually commences by considering equilibrium at the
location of maximum moment, it is useful to realize that the depth of the horizontal strut.
da. can be found by:

c (1.5)

where C = T = lPs/yAsl of the main tension tie.

The line of action of this strut is located a distance of d/2 from the top surface of the
beam (see Fig. 1.3). The CeT-node at the right-hand direct support of the deep beam
in Fig. 1.3 is located at the point of intersection of the Hnes of action of the vertical
( bearing force, and the horizontal tension tie. The CTT-node located at the left-hand

11
 hanging (indirect) support in Fig. 1.3 is located at the inters~ction of the centroids of the
( horizontal and vertical tension ties.

4. Calculate the factored forces in the truss mcmbers (compression struts and tension ties)
through statie equilibrium.

5. Choose tension tie reinforcement such that the caIculated tension force, T. in each tie
does not exceed tPsf.. Ast• where/y and An are the yield stress and cross-sectional area of
the tension tie reinforcement. Distribute this reinforcement over an effective area of
concrete at least equai to the force in the tie divided by the stress limit of the nodal lone
which anchors il. Figure 1.3(a) shows the effective anchorage area, hab. of the CCT-
node of the deep bearn.

6. Check the development of the reinforcement. For example, the tension tie reinforcement
in the deep beam shawn in Fig. 1.3(a) must be anchored over the length lb so that it is
capable of resisting the caIculated force in the tension tie, T. at the inner edge of the
bearing.

7. Check the compressive stresses in the struts. The dimensions of the strot shaii be large
enough to ensure that the calculated compressive force in the stmt does not exceed
tPcfeuA cs • where feu and A cs are the limiting compressive stress and effective cross-
sectional area of the strot. respectively. Equations 1.3 and 1.4 give the limiting
compressive stress in the strut. The limiting compressive stress, feu. decreases as the
principal tensile strain, El' increases as the angle, 8s'
increases. The principal strain, El'

between the strut and the tension tie passing through the strut decreases (see Fig. 1.5).
It is necessary to determine the area. A cs , of each strot. For example, the area of the
diagonal strut at the intersection with the nodal zone at the right-hand end of the deep
beam in Fig. 1.3(a) equals (lbsin8s + hacos8s}b. This stress must not exceed the limiting
compressive stress in the strut.fcu. as detennined by Eq. 1.3 and 1.4. In calcuJatingfcu'
the strain in the tension tie passing through the strut, Es, may be taken as the factored
force in the tie divided by cPsAstEst, where Est is the modulus of elasticity of the tension
tie reinforcement.

8. Choose crack control reinforcement. The CSA Standard and the CHBDC require the
inclusion of uniformly distributed reinforcement in the horizontal and vertical directions,
having minimum reinforcement ratios of 0.002 and 0.003. respectively, in arder to
control cracking. The maximum spacing of this uniformly distributed reinforcement is

( 300 mm.

12
 1.5 ACI Design Approaches for Disturbed Regions
(
The American Concrete Institute Standard 318-95 "Building Code Requirements for
Structural Concrete" (ACI 1995) bas separate provisions for the design of deep beams and for
the design of brackets and corbeis. These two different design approaches are discussed below.

1.5.1 ACI Provisions for Deep Beams

The ACI Standard requires that:

(1.6)

= factored shear force at the section considered.

= nominal shear strength at that section. and
= strength reduction factor. taken as 0.85 for shear.

The nominal shear strength is defined as:

(1.7)

= nominal shear strength provided by the concrete. and

= nominal shear strength provided by the shear reinforcement.
The ACI Code defmes a member as as deep beam when [,Id is less than 5 (where ln is
the c1ear span measured from face to face of supports). The shear strength. Vn' for deep flexural
members shaH not be taken greater than:

Vn ~ ~Jfc' bwd for ln Id < 2

(1.8)
Vn ~ I~ [ 10 + ; ) /1: bwd for 2~1,/d<5

At the upper limit of I,/d = 5. Vn ~ 0.83/// bwd (the same for ordinary beams).

The critica1 section for shear shaH be taken at a distance of 0.15 ln from the face of the
support for uniformly loaded beams. and at a distance of 0.50a (where a is the shear span) from
the support face for beams with concentrated loads. but shaH not he taken at a distance greater
( than d from the face of the support. Unless a more detailed calculation is made in accordance

13
 with Eq. 1.10. Vc shaH be computed as follows:
(
(1.9)

The nominal shear strength provided by the concrete may aIso be calculated as:

( 1.10)

where: Pw

except that the vaIue of the first bracketed term shaIl not exceed 2.5, and Vc shaH not be taken
greater than 0.50Jfc' bwd. Mu is the factored moment occurring simultaneously with Vu at the
criticaI section defined above. Where the factored shear force. Vu' exceeds the concrete
resistance. cP Vc' shear reinforcement shaH he provided to satisfy Eq. 1.6 and 1.7. where Vs shaIl
he computed by:

V = [Av
s S
[1 +ln
12
1d
] + A vh [1l-ln
5 12
1d
]]
.!y
d (1.11)
2

where: Av = area of shear reinforcement perpendicular to the flexural tension reinforcement

within a distance 5, and
= area of shear reinforcement paraIleI to the flexural tension reinforcement

within a distance 52' and

s = spacing of shear reinforcement in a direction parallel to the flexuraI tension
reinforcement, and
= spacing of shear reinforcement in a direction perpendicular to the flexural
tension reinforcement.

[n addition. the area of shear reinforcement. Av. shaH not be less than 0.0015 bws and s shaH not
exceed dIS, nor 500 rmn. and A vh shaH not be less than 0.0025 bw s2 and S2 shaH not exceed d13.
nor 500 mm. The shear reinforcement calculated for use at the critical section shaH also be used
throughout the span.

(
14
 1.5.2 ACI Provisions for Brackets and Corbeis
( The ACI Code limits the applicability of the design provisions for brackets and corbeIs
to cases where the shear span-to-depth ratio~ ald~ is not greater than unity. These brackets and
corbeis tend to act as trusses or deep beams rather than flexural members (see Fig. 1.6).
According to the Commentary, the upper limit of unity for a/d is specified because~ for larger
shear span-to-depth ratios~ the diagonal tension cracks are less steeply inclined and the use of
horizontal stirrups alone as shown in Fig. 1.6(b) may not he suitable. Also, the specified method
of design has only been validated experimentally for ald not exceeding unity, and for a factored
horizontal tensile force ~ Nuc~ not greater than the factored shear force, Vu. It is assumed that a
corbel may fail by shearing along the coIumn-corbel interface~ by yielding of the main tension
tie, by crushing or splitting of the compression strut~ or by localized shearing or bearing failure
under the loading plate. In order to limit the size and shape of the corbel, it must have a
minimum depth at the outside edge of the bearing area of 0.5d. This limit is specified so that
a premature failure will not occur due to the propagation of a major diagonal tension crack from
below the bearing area to the outer sloping face of the corbel. The section at the face of the
support shall be designed to resist a shear, Vu' a moment [V"a + Nuc(h-d)], and a horizontal
tensile force, Nuc~ simultaneously. In all design calculations~ ep is taken equal to 0.85 since the
behaviour of corbeis is predominantly controlled by shear.

The design procedure is surnmarized in the following steps:

1. Select the initial geometry of the corbel ensuring that the shear span-to-depth ratio, a/d,
does not exceed unity, and that the minimum depth at the outside edge of the bearing
area is 0.5 d. Also, the shear strength~ Vn~ shaH not exceed 0.2fe' bwd nor 5.5 hwd (in
Newtons).

2. Calculate the area of shear friction reinforcement~ A':f~ across the shear plane necessary
to resist the applied shear force~ Vu' as:

(1.12)

where J.L = 1.40 for normal weight concrete.

3. Determine the area of reinforcement, Af~ required to resist the moment at the face of
support of the corbel at the level of the primary reinforcement. It is necessary to
estimate the distance (h - li) from the top face of the corbel to the centroid of the main
( tension reinforcement. The design uItïrnate moment~ Mu~ to be resisted is:

15
(

----'\~-"T'"

tension tie 1 v.
"A.f, ~ 1---.1....-...., ~ -r
shear
plane
h
d

_____ ----L

- - - - ' \ : - - -.......

(a) Strut-and-tie action of corbel

'r----'/'----r-

a
bearing
plate
A. (primary
reinforcement)

d h

A.. (closed
stirrups or ties)

"-----/"----,0-...

(b) Detailing of corbel

Figure 1.& Provisions for brackets and corbeis

(
16
 (1.13)
(
The area of reinforcement~ Af~ necessary to resist Mu shaH be ca1culated in accordance
with the flexural provisions of Clauses 10.2 and 10.3 (ACI 1995) using a capacity
reduction factor. cP. of 0.85.

4. Calculate the area of reinforcement. An. required to resist the horizontal tensile force~

Nue. from:

(1.14)

where cP is taken as 0.85. The value of Nue shaH not be taken less than 0.2 Vu' unIess
special provisions are made to avoid tensile forces.

5. Calculate the total area of primary tension reinforcement. Ar~ from:

(l.15)

6. Provide a minimum area of primary tension reinforcement. Ensure chat p = Ar/bd is at

least equaI to 0.04(j/ If,)

7. CaIculate the total cross-sectionaI area of horizontal stirrup reinforcement~ Ah~ as:

( 1.16)

Distribute this reinforcement uniformly within two-thirds of the effective depth of the
corbel adjacent to the primary tension reinforcement.

1.6 Experiments on Deep Beams, Corbeis and Pier Caps

This section provides a brief summary of sorne of the experimentaI studies that have been
carried out by other researchers investigating the performance of deep bearns. corbeIs and pier
caps.

(
17
 1.6.1 Deep Beams
(
Figure 1.7 ilIustrates the manner in which the shear strength reduces as the shear span-to-
depth ratio, ald~ increases. This series of tests were carried out by Kani in the 1960's and are
reported by Kani et al. (1979). The beams in this series had the same flexuraI reinforcement and
no shear reinforcement. The two main variables were the shear span and the size of the bearing
plates. AIso shown in this figure are the predicted capacities (Collins and Mitchell 1991) using
the modified compression field theory and strut-and-tie models. This figure demonstrates that
for beams with ald less than about 2.5 strut-and-tie models give more accurate predictions. The
1995 ACI Code provides special provisions for deep f1exural members with clear span-to-depth
ratios, l,ld. less than 5, that is beams with ald less than 2.5 (see Section 1.5.1).

Franz and Niedenhoff (1963) used photoelastic model studies to investigate the stresses
in isotropic homogeneous deep beams before cracking. These beams had a uniformly distributed
load applied aIong their top surface and were simply supported. Franz and Niedenhoff found that
the smaller the span-to-depth ratio, the more pronounced the deviation of stress distribution from
that assumed by the Bernoulli hypothesis. For beams with a span-to-height ratio of one, the
extreme fibre tensile stress can be more than twice that predicted by traditional engineering beam
theory. It has aIso been demonstrated that the tlexural lever arm for the elastic solution is less
than 0.67 h, which corresponds to that for a slender beam (Park and Paulay 1975). Furthermore,
the internai lever arm for very deep beams does not significantly increase after cracking. For
very deep beams, Franz and Niedenhoff also found that the depth of the tension zone near the
bottom of the beam is relatively small (roughly 0.251 thick).

Franz and Niedenhoff (1963) also tested reinforced concrete pier cap specimens which
when inverted resemble simply supported deep beams. Two different reinforcing bar Iayouts
were investigated, one which had concentrated reinforcing bars representing a tension tie and the
other contained bent-up bars for the main tension reinforcement. The specimen with the
horizontal bars had a capacity which was 23 % higher than that with the bent-up bars due to the
larger amount of tension tie reinforcement at the inside edge of the bearing.

Leonhardt and Walther (1966) carried out experiments on deep beams to investigate the
influence of detailing of the reinforcement and the influence of type of loading. They made the
following conclusions and recommendations:

1. The main tension tie reinforcement should be distributed over a depth of 0.25 h - 0.051
from the bottom (tension) face, for cases where h S l.

(
18
(

-<;rSB o 152 x 76 x 9.5 mm plate

0.25
• 152 x 152 x 25 mm plate
-<>- 152 x 229 x ~1 mm plate

.57 v v
a
0.20
24 in
\.
. , 1;,
,
(610 mm)

!
v J;' = 27.2 MPa V
0.15
J;:: 372 MPa
max. agg. = 19 mm
d= 538 mm
b = 155 mm
A., =22IT mm2
0.10
.72

0.05
053 056 .79

strut-and-tie model - '- sectional model

a 1 2 3 4 5 6 7
ald

Figure 1.7 Applicability of strut-and-tie model for predicting series of beams tested
by Kani (adapted trom Collins and Mitchell 1991 )

(
19
 2. At least 80 % of the maximum calcuJated force in the main tension tie reinforcement
( should be developed at the inner face of the supports.
3. Small diameter bars of mechanical anchorages should be used as the main tension tie
reinforcement to prevent premature anchorage fallure.
4. A minimum web reinforcement ratio of0.2 % in both directions, as in reinforced concrete
walls, is adequate to control cracking. This reinforcement should be provided in the
fonn of small diameter bars.
5. Near the supports, closely spaced horizontal and vertical bars of the same size as the web
reinforcement should be provided.

In their tests of simply supported deep beams, the location of the application of load was
varied. For the case of a point load applied on the top surface at midspan, the load path
resembles a L~~j-arch. When a uniformly distributed [oad was suspended from the bottom of the
beam instead of being applied to the top (compression) face of the beam, a more severe loarling
condition was created. For this case, the load must first be transferred by vertical or inclined
tension reinforcement up to the compression region of the beam before it can be transferred ta
the supports by means of tied-arch action. Therefore, vertical stirrups must be provided to satisfy
this force requirement as weil as to control cracks.

Rogowsky et al. ( 1986) carried out tests on 7 simply supported and 17 two-span
continuous deep beams. Variables included: the shear span-to-depth ratio, the flexural
reinforcement ratio, the amount of vertical stirrups and the amount of horizontal web
reinforcement. Two main types of behaviour were observed. Neac failure, beams without
vertical stirrups or with minimum vertical stirrups approached tied-arch action regardIess of the
arnount of horizontal web reinforcement present. These beams failed suddenly with little plastic
deformation, while those with large amounts of vertical stirrups failed in a ductile manner.

The ACI Code provisions for deep beams (see Section 1.5.1) have been developed based
solely on past experiments of single-span, simply supported deep beams loaded on their top
(compression) face. Rogowsky et al. (1986) concluded that the ACI Code expressions gave
conservative results for the simply supported beams and the continuous beams with large amounts
of vertical reinforcement tested. However, these expressions proved unconservative for the
continuous beams without web reinforcement and for thase containing only horizontal web
reinforcement. They determined that the ACI Code predictions were unconservative due to the
fact that they are based on an incorrect mechanica1 model for the shear strength of deep beams.
Rogowsky and MacGregor (1986) proposed the use ofstrut-and-tie models as a more rational and

( consistent means of analyzing single- and muItiple-span deep beams.

20
 1.6.2 Corbeis
(
Franz and Niedenhoff (1963) carried out photoelastic experiments on corbeis having a
shear span-to-depth ratio, ald. of less than 1.0. These experimental studies of the elastic response
of corbeis indicated that:

1. The tensile stress along the top edge of the corbel is almost constant between the bearing
area and the face of the column.
2. The compressive stress flowing in from the bottom of the corbel into the column are
almost parallel and resemble a compressive strut.
3. Rectangular corbeIs exhibited a nearly stress free zone at the outer-bottom corner of the
corbel.

Franz and Niedenhoff developed a simple truss analogy based on their observations of
the stress trajectories. In addition, they gave the following detailing recommendations:

1. The primary tension reinforcement should be anchored at the outside face of the corbel.
They recommended providing the main tension reinforcement in the forro of closed
hoops.
2. A minimum amount of compression reinforcement, with appropriate ties to prevent
buckling, should be placed parallel to the compression face of the corbel.
3. A minimum amount of uniformly distributed reinforcement. having an area of at least
25 % of that provided by the primary tension reinforcement. should be provided.

In 1964. Kriz and Raths tested 195 corbeIs. of which 124 were subjected vertical loads
alone and 71 others were loaded vertica1ly and horizontally (Kriz and Raths 1965). The variables
studied in these tests included size and shape of the corbel. amount of main tension tie
reinforcement and its detailing. concrete strength. ratio of shear span to effective depth. and ratio
of horizontal to vertical loading. Kriz and Raths gave the following recommendations:

1. The ratio of the amount of main tension reinforcement to the gross cross-sectionai area
of the corbel shouid not be less than 0.004 in arder ta control cracking.
2. A cross bar should be welded to the main tension tie reinforcement near each end in
order ta provide proper anchorage (see Fig. 1.6(b». The size of this cross bar should
be at least equal ta the largest bar used in the main tension tie reinforcement. and it
should be located as near to the outer face of the corbel as caver requirements permit.
3. Closed horizontal stirrups should he provided having an area not less than 50 % of that
provided by the main tension tie reinforcement. These stirrups should be unifonnly
( distributed throughout the upper two-thirds of the effective depth of the corbel.

21
 4. The total depth of the corbel at the outer edge of the loading plate shonld be at least
( equal to one-haIf the depth of the corbel at the column face.
5. The outer edge of the bearing plate should be at least 50 mm from the outer face of the
corbel.
6. When corbeis are designed to resist horizontal forces, the steel bearing plates should be
welded to the main tension tie reinforcement to transfer the horizontal force directly to
these bars (see Fig. 1.6(b».
7. Bearing stresses at ultimate load should not exceed 0.5/e'.

Mast (1968) introduced the "shear-friction" concept for the design of corbeis. His goal
was to develop a simple rational approach based on physical models of behaviour which couId
be used in the design of a number of different concrete connections. The approach assumes
numerous failure planes for which reinforcement must be chosen to prevent failure along these
planes.

The shear-friction concept assumes that a crack interface has sorne roughness and hence.
as shear is applied. the deformations include not only sorne shear displacement along the crack
interface, but also some widening of the crack. The crack opening causes tension in the
reinforcement crossing the crack which is balanced by compressive stresses in the concrete across
the crack interface. The shear on the interface is assumed to be related to the compression across
the interface by a coefficient of friction, p., which depends on the roughness of the interface
surface. The nominal shear capacity is thus given as:

(1.6)

In determining the shear strength, Mast made the following assumptions:

1. The reinforcement crossing a crack is sufficiently anchored such that the bars can yield.
2. The cohesive strength of concrete is negligible.
3. The effective coefficient of shear friction, p., depends on the surface roughness but is
independent of concrete strength.

This concept was applied to test data reported by Kriz and Raths where the shear span-to-
depth ratio, a/d, was less than or equal to 0.7 and where the reinforcernent had yielded. The
shear-friction concept gave reasonably conservative strength predictions for both vertical and
cornbined vertical and horizontal loading cases.

Mattock et al. (1976) tested 28 reinforced concrete corbeIs subjected to vertical and
( horizontalloading. The variables included in these tests were: the ratio of shear span to effective

22
 depth, the ratio of horizontal to vertical load, the amounts of main tension tie and distributed
( reinforcement, concrete strength and type of aggregate.

The design procedure tirst introduced in the 1971 ACI Code was based on the research
of [(riz and Raths (1965) with later modifications to include the design procedure developed by
Mattock (1976) and Mattock et al. (1976). This approach is still in use today (see Section 1.5.2).

1.6.3 Pier Caps

AI-Soufi (1990) carried out an experimental investigation which involved testing six
reinforced concrete pier caps. Parameters which were varied in these specimens included: the
geornetry of the pier caps, the amount and distribution of uniform1y distributed reinforcement,
and the anchorage details of this reinforcement. He made the following conclusions and
recommendations :

1. After yielding of the main tension tie reinforcement, yielding spreads to the distributed
reinforcement.
2. The unifonnly distributed reinforcement contributes significantly to the strength and plays
a key role in controlling cracks.
3. Standard 90° end hooks may be provided to anchor the reinforcement of the main tension
tie provided that these bars cao develop their yield force at the inner edge of the bearing
plates.
4. The unifonnly distributed horizontal reinforcement may be provided in the fonn of U-
shaped stirrups properly lap spliced over the central region of the pier cap. The
unifonnly distributed vertical reinforcement may be provided in the form of closed
stirrups or lap-spliced U-shaped stirrups.
5. The column reinforcernent, which was extended into the pier cap, provided additional
horizontal (colUfiUl ties) and vertical reinforcernent in the central region of the pier cap.
This additional reinforcernent controlled cracks and provided sorne confmement for the
lap splices of the uniformly distributed horizontal reinforcement.

Strut-and-tie models provided a useful tool for evaluating the strength of these pier caps,
while non-linear finite element analysis provided a means of predicting behaviour at service load
levels (see Section 1.7.2).

(
23
 1.7 DetaiIed Analysis Procedures
(
This section discusses more detailed analysis procedures, including refmed strut-and-tie
modelling, and non-linear fmite element analysis.

1.7.1 Retined Strut-and-Tie Models

Simple strut-and-tie models typically assume that the compressive struts can be
represented by straight fines between loading and support bearing areas, and usually ignore the
contribution of unifonnly distributed reinforcement. More refmed strut-and-tie models attempt
to include the effects of bulging and curving compressive struts due to the presence of tensile
stresses in the concrete and uniformly distributed reinforcement. Accounting for the presence
of unifonnly distributed reinforcement also increases the total amount of tension tie
reinforcement, and hence the strength of the member.

Figure 1.8 shows a simply supported deep beam with a concentrated load applied on its
top surface. In Fig. 1.8(a), the flow of principal compressive and tensile stresses are indicated
with dashed and solid 1ines, respectively. The diagonal compressive struts bulge between the
loading point and the supports due to the presence of tensile stresses in the concrete. A possible
strut-and-tie model which accounls for this bulging action of the struts is presented in Fig. 1.8(b).
Design procedures have typically adopted a simpler assumption of straight compression struts in
combination with a minimum amount of reinforcement uniformly distributed in the horizontal and
vertical directions as shown in Fig. 1.8(c). This uniformly distributed reinforcement serves to
control cracking in disturbed regions (see Section 1.4).

In deep beam design, unifonnly distributed reinforcement corresponding to geometric

ratios of 0.002 to 0.003 is usually provided in the horizontal and vertical directions. Marti
(1985) investigated the role of this reinforcement in controlling cracks. permitting redistribution
of stresses after cracking and increasing the strength of the member. Figure 1.9 shows one-haif
of a deep beam which is subjected to a concentrated load applied on its top surface and with
simple supports at its ends. It is assumed that this beam has uniformly distributed reinforcemnt
in the vertical direction only. Figure 1.9(a) illustrates the arching and fanning of the compressive
stresses in the member. The presence of the uniformly distributed vertical reinforcement permits
the main compression strut to curve, thus fonning an arch, and aIso provides anchorage for the
fanning compression struts near the bottom of the beam. Figure 1.9(a) shows the variation of
the force in required in the main tension lie reinforcement. The main tension tie has a maximum
( force at the centre-line of the beam (point d) corresponding to the tensile force, T. In the region

24
(
crack
VV 1
VV control VV
steel
1

. ' ~~'''''' ,
\
1
--
.
.< ; / .. ,.' '

::<t~
,"
i\- l
1

. " ~. ' . :

·~.··"".·:··" . ··\.X .~
..
..
:
' / '. •
.'1
1
1:

·.. ··::>I . . / . . . .
: ..
.
;"
....

"
, '
' ~...
.
".

.
~
1
i
1

v v v v
T
v
T
v
(a) Flow of principal (b) Required tension (c) Assumption of straight
stresses ties compressive struts

Figure 1.8 Crack control reinforcement required with assumption of straight-line

compressive struts (adapted from Schlaich et al. 1987)

effective distributed V lie representing distributed

vertical reinforcement vertical reinforcement
a b a

-c -C

L
~.

:---....,&- ~ _ _~----l: - T ,.....--+-_ _"""-+....L...

1
~: T

v v
variation of
force in
longitudinal
reinforœment
a b d e a c e

(a) Arch and fan action (b) Strut-and-tie model

Figure 1.9 Investigating the effect of distributed reinforcement

on deep beams (adapted from Marti 1985)

(
25
 between points b and d, tbat is where uniformly distributed vertical reinforcement is present, the
( force in the longitudinal reinforcement changes as shown in Fig. 1.9(a). In the regions between
points a and b and between d and e the force in the main tension tie remains constant. As
pointed out by Marti (1985), the vertical distributed reinforcement allows curtailment of sorne
of the longitudinal tension tie reinforcement. Figure 1.9(b) shows the idealized strut-and-tie
model for this deep beam containing uniformly distributed vertical reinforcement. The uniformly
distributed vertical reinforcement bas been idealized as a tension tie at the centre of zone
containing vertical reinforcement. This idealization permits the compressive arch and
compressive fanning to be represented as shown in Fig. 1.9(b). AIso shown is the variation of
force in the longitudinal reinforcement as predicted by this refined strut-and-tie model.

While unifonnly distributed vertical reinforcement reduces the demand on the main
tension tie reinforcement close to the support region, its presence does not result in increased
member strength. This is due to the fact that the strength is controlled by the conditions at
midspan. The presence of unifonnly distributed horizontal reinforcemem assists the main tension
tie reinforcement and results in increased strength.

Although the simple strut-and-tie models are very useful in design and give conservative
strength predictions, for detailed analysis of the strength a more refmed strut-and-tie mode!,
including both the vertical and horizontal distributed reinforcement, gives more accurate strength
predictions .

1.7.2 Non-Linear Finite Element Analysis

As was mentioned in Section 1.2, it is not appropriate to design disturbed regions with
the usual beam theory assumptions. Elastic finite element analysis may be used to detennine the
stresses in a reinforced concrete member prior to cracking, however this type of analysis may not
be appropriate for predicting stresses in a cracked member as significant redistribution of stresses
occurs after cracking. In order to predict the full response (including post-cracking response) of
reinforced concrete members a computer program, FIELDS, was developed (Cook 1987, Cook
and Mitchell 1988) which combines two-dimensional non-linear finite element analysis with the
compression field theory (Collins and Mitchell 1980, 1986, and Vecchio and Collins 1986).

Triangular and quadrilateral elements are used to model the reinforced concrete member.
To account for significant non-linearities which may arise within a finite element, up ta four-by-
four Gauss quadrature may be chosen for an element. Figure 1.10 illustrates the method used
( to evaluate stresses correspondiag to a state of strain at each Gauss point (Cook and Mitchell

26
(

o ,0 --:- 0 '0

o d ,0 0 ~ Gauss point
/)
b cr ô." 0

-,'0 ,0

(a) Element with 4 x 4 quadrature

y "1/2

1
/
-8
/
.,: 1"
/

(b) State of strain at a single Gauss point

,,/,/~,/ t t _f_

"/ /
'"
'-
/
~ ./+-
,-'

,,/ hL' " /

'",-
-
-E. + !
E)/
=-1 l-
A..f:!
'"4:.1:1
/ / "'.../"'.../ "-...
A.zlu
~t,
t +
;

,
1

(c) Determining stresses at a Gauss point corresponding to a strain state

Figure 1.10 Evaluating stresses at Gauss points in quadrilateral element

(Cook and Mitchell 1988)

(
27
 1988). The principal tensile strain, El' the principal compressive strain, E2, the strain in the x-
( direction, Ex, the strain in the y-direction, Ey , and the principal compressive strain direction, 8,
are inter-related by the requirements of strain compatibility (see Fig. 1.1 O(b».

The average steel stresses,fu andlsy, at a Gauss point can easily be determined by using
the stress-strain relationships of the reinforcing steel. However, the average stresses in the
cracked concrete, IcI and feZ' are not as easy to detennine. The average principal compressive
stress, feZ' is not only a function of the principal compressive strain, E2, but is also dependent on
the principal tensile strain, El. As El increases!c2 decreases; this effect is known as strain
softening. Combining the Iimiting compressive stress for cracked concrete developed by Vecchio
and Collins (1986) and a parabolic concrete stress-strain curve gives the compressive stress-strain
relationship for cracked concrete (see Fig. 1.4(a» as:

(1.18)

where:

{3 (1.19)

and = strain in the concrete at peak compressive stress.

After cracking, the principal tensile stress in the concrete varies from zero at a crack location to
a maximum between cracks. Figure 1.11 shows the average principal tensile stress, Ici' plotted
against the principal tensile strain, El (Vecchio and Collins 1986) as:

(1.20)

where: E c = initial tangent modulus of the concrete,

= strain in the concrete at cracking, and

= concrete cracking stress = EcEcro

Figure 1.12 shows that the average principal tensile stress may be limited by yielding of
( reinforcement or by sliding along the crack interface (Vecchio and Collins (986). Between the

28
(
t

----~-

Figure 1.11 Determining average concrete tensile stress,!•• fram strain, El

(Vecchio and Collins 1986)

(a) Cracked reinforced (b) Transmitting shear

concrete element acrass crack interface

VIJIl
/.- .-
),' V""l

(c) Average stresses (d) Stress condition at

between cracks crack interface

Figure 1.12 Investigating stress condition at crack interface

(Vecchio and Collins 1986)

(
29
 cracks, the concrete and the steel are assumed to have average values of stress (see Fig. 1.12(c».
( while at a crack the tensile stress in the concrete is zero, the steel stress is a maximum, and a
shear stress vci may exist at the crack interface (see Fig. 1. 12(d). An approximate expression
for the shear stress limit along a crack bas been developed (Vecchio and Collins 1986) based on
the interface shear transfer tests conducted by Walraven (1981). This expression can be
simplified as:

O.18Jlc' (1.21)
vcimar = -=-:::""":"'""-=-::--~----:~
0.31 +24w/(a + 16)

where: w = average crack width in mm,

a = maximum aggregate size in mm.

Note that this is an empirical expression and that stresses are expressed in MPa units. The
average crack width can be assumed to equal the average crack spacing times fI' Since the stress
states shown in Fig. 1. 12(c) and (d) are statically equivaient, it is possible to determine whether
yielding of the reinforcement across the crack (Le. l:rc.cr or Isy.cr equals 1,) or sliding at the crack
interface (Le. vci equals vdnuu ) will result in a value Offel less than that given by Eq. 1.20.

Examples of the application of non-lïnear fmite element anaIysis applied to deep beams.
corbeis, dapped end beams and anchorage zones are given by Cook and Mitchell (1988) and
Collins and Mitchell (1991).

1.8 High-Performance Concrete

1.8.1 Compressive Strength

Advances in concrete technology over the past (WO decades have resulted in the
availability of ready-mixed concrete with compressive strengths as high as 100 MPa in several
North American cities. There is a need to investigate whether the design proceâures. developed
for use with normal-strength concretes. are applicable to the full range of high-strength concretes
currently available (Collins et al. 1993).

The traditional parabolic stress-strain curve for nonnal-strength concrete recommended

by Hognestad (1957) can be expressed as:

(
30
( (1.22)

This fonnula provides a reasonable approximation ta the stress-strain curve for nonnal-strength
concrete. However as concrete strength increases the compressive stress-straïn curve is near
y y

linear over the rising branch, and exhibits greater initial stiffness and decreased ductility (see Fig.
1.13). The parabola is too "rounded" to accurately represent this increased linearty and the more
brittle post-peak response of very high-strength concrete.

Thorenfeldt et al. (1987) introduced a post-peak decay term, k, to the stress-straîn

relationship developed by Popovics (1973) such that it could be applied ta wide range of concrete
strengths. This resulted in the following expression:

le Ee n (1.23)
y; E;. n -1 + (Ee/Ec'yilè

where: le = compressive stress,

le' = maximum compressive stress,

= compressive strain,
= compressive strain when/e reaches Je',
n = curve fitting factor, as n becomes higher, the rising portion of the curve
becomes more 1inear, and
k = post-peak decay term taken as 1 when El
y Ec' is less than l, and taken greater
than 1 when El Ec' exceeds 1.

Equation 1.23 givesfc as a function of Ee and involves four constants, namelY,J/, E/, n
and k. While these four constants cau all he determined from actual cylinder stress-strain curves,
in many design situations, ooly the cylinder strength, J:, is known. Collins and Porasz (1989),
and Collins and Mitchell (1991) suggest that for El Ee' > 1:

j,' (1.24)
n := O.8+~
17

k := 0.67 + Je' (1.25)

62

(
31
(

120

-cu
a.
~ 60
':::

40

20

o 0.002 0.004

Figure 1.13 Influence of concrete strength on shape of stress-strain curve

(
32
 Furthermore. knowing Je'. the peak strain. Ec', can be calculated as:
(
(1.26)

where EL = modulus of elasticity of concrete.

The 1994 CSA Standard gives an expression for Ec (in MPa), for concrete with 'Yc between 1500
and 2500 kg/m3 , as follows:

1.S

[ 2;~ ]
(1.27)
Ec = (3300 Jfc' +6900)

where 'Y e = concrete density (in kg/m3 )

From the vaIue of Je' the four constants in Eq. 1.24 through 1.27 can be used to develop
the stress-strain relationship given in Eq. 1.23.

1.8.2 Flexure and Axial Loads

The new rectangular stress block factors, CXl and f3 I , of the 1994 CSA Standard are
suitable for a wide range of concrete compressive strengths. It is assumed that a concrete stress
of CXl ifJeJc' is uniformly distributed from the extreme compression fibre into the member a
distance of {31 c, where c is the distance of the neutraI axis from the extreme compression fibre.
These factors now depend on the concrete cylinder strength as follows:

CXl = 0.85 -0.0015Ic' ~ 0.67 (1.28)

{3I = 0.97 -0.00251: ~ 0.67 (1.29)

The new factors are intended to account for bath the significant shape change in the stress-strain
curve as the concrete strength increases and the difference between the cylinder strength and the
in-situ concrete strength.

(
33
 1.8.3 Minimum Reinforcement for Flexure and Sbear
(
The 1994 CSA Standard requires a minimum amount of flexural reinforcement in arder
to give adequate reserve of strength after cracking and hence provide a ductile response. The
1994 CSA Standard requires that one of the following three provisions be satisfied:

1. The factored moment resistance, M r , must be such that:

(1.30)

2. Except for slabs and footings, provide a minimum area of flexural reinforcement, A smin '
as follows:

_ O.2Vfc' (1.31)
A smin - brh
fy

where: b l = width of tension zone of member.

3. The minimum reinforcement requirements given above may he waived provided mat me
factored moment resistance, M r , is at least one-third greater than the factored moment,
Mf·

The 1994 CSA Standard a1so requires a minimum amount of shear reinforcement which
is dependent on concrete strength. An increase in the concrete compressive strength leads to an
increase in the tensile strength, which in tum results in an increase in the cracking shear. This
increase in the cracking shear requires an increase in the minimum shear reinforcement in order
to ensure that the shear strength exceeds the cracking shear. The 1994 CSA Standard requires
a minimum area of shear reinforcement, Av. as follows:

(1.32)

where: bw = minimum effective web width.

s = spacing of shear reinforcement.

This requirement, together with the maximum spacing limits for shear reinforcement, is intended
to control inclined cracking at service load levels.

(
34
 1.8.4 Strut-and-Tie Provisions
(
The provisions for strut-and-tie models in the 1994 CSA Standard are the same as those
in the 1984 CSA Standard. The stress limit for a concrete strut? O.85cPcfc'. remains a linear
function of the concrete cylinder strength. MacGregor (1997) has introduced a factor. 1'2. to
account for the influence of high-strength concrete (see Tables 1.1 and 1.2).

The 1994 CSA Standard and the 1997 CHBDC provisions for strut-and-tie models require
minimum amounts of uniformly distributed reinforcement which are independent of concrete
strength (see Section 1.4).

1.9 Crack Widths and Crack Spacing

Concrete can only withstand small tensile strains before it cracks. As these cracks do not
form at equal spacings. crack widths may vary in size. and it is therefore appropriate to define
the mean crack width, wm' as:

(1.33)

where: sm = mean crack spacing? and

= strain in the concrete caused by stress.

The characteristic crack width (the width which only 5 % of the cracks will exceed). w,t. is
approximated by the CEB-FIP Model Code (CEB 1990) as wk = 1.7 Wm. The CEB-FIP Model
Code (CEB 1990) gives the following expression for the mean crack spacing:

(1.34)

where: c = clear concrete cover.

s = maximum spacing between longitudinal reinforcing bars? but shaH not be taken
as greater than 15db (where db is the diameter of the reinforcing bar),
Pq = A/A c.q ?

As = area of steel considered to be effectively bonded to the concrete.

Ac.,! = area of the effective embedment zone of the concrete where the reinforcing
bars cao influence crack widths (see Fig. 1.14(a»,

(
35
(

-1 4.t = shaded area

....- - - -...
s

(a) CEB-FIP expression

.-- neutral axis

/'
à--- -- J -- ---1

tension
steel
centroid ") A = shaded area
r number of bars
1
.t 1

,t
.1...--!.- ====:;:
- tension
face

(b) Gergely-Lutz expression

Figure 1.14 Crack width parameters

neutral
axis
1
1 \ skin reinforœment
, '"
1
If'>
-
h> 750 mm r-.. ~ -1. <> 1
1

.~ If
a;,.r S 200 mm i 1
1
:_<tj~ ; , J

l
1
... - .. ---r ~ ~ -.r \ , 1 \ \

•• • • •• --th-a
1h - d
/ ) 1 1 1 J

cross-section elevation

Figure 1.15 Side-face cracks controlled by skin reinforcement

(
36
 = coefficient that characterizes bond properties of reinforcing bars,
( = 0.4 for defonned bars
= 0.8 for plain bars
= coefficient to account for the strain gradient.
= 0.25 (El + EiJ/2EI' where El and E2 are the largest and smallest tensile strains
in the effective embedment zone, respectively.

The Gergely-Lutz expression (Gergely and Lutz 1968) estimates the maximum crack
width as:

(1.35)

where: {3 = factor accounting for strain gradient,

= 1.0 for unifonn strains
= h2 /h l for varying strains, where hl is the distance of the main tension
reinforcement from the neutral axis and ~ is the distance of the extreme tension
fibre from the neutral axis
ES. cr = strain in a reinforcing bar at a crack location,
de = distance from the extreme tension fibre to the centre of the closest bar, and
A = effective area of concrete surrounding each bar, taken as the total concrete
area in tension, which has the same centroid as the tension reinforcement,
divided by the number of reinforcing bars (see Fig. 1.14(b».

In the Gergely-Lutz expression, the strain in the reinforcement at a crack is taken as:

N
E
s.cr =E-
(1.36)
s

where: N = applied axial tension, and

Es = modulus of elasticity of steel.

The CEB-FIP Model Code. (CEB 1990) limits crack widths to 0.30 mm for structures
exposed to bath frost and de-icing conditions. The 1995 ACI Code and the 1994 CSA Standard
require the calculation of a crack width parameter, z, to determine if the crack widths would be
within acceptable limits. This crack width parameter is based on the Gergely-Lutz expression
(see Eq. 1.35) and is given as:

(
37
( (1.37)

where: fs = calculated stress in reinforcement at specified loads, may be taken as 0.61,.

The z-factor is limited to 30.000 N/mm for interior exposure and 25.000 N/mm for exterior
exposure. These limits correspond to maximum crack widths of 0.40 and 0.33 mm. respectively.
If epoxy-coated reinforcement is used the CSA Standard requires multiplication of the limiting
crack width parameter, z. by a factor of 1.2, based on the research of Abrishami et al (1995).
Figure 1.15 illustrates the requirement for skin reinforcement in the 1995 AC! Code and
the 1994 CSA Standard for members with an overaH depth. h, exceeding 750 mm. The required
longitudinal skin reinforcement shaH be uniformly distributed along the exposed side faces of the
member over a depth of 0.5h-2(h-d) from the principal reinforcement (see Fig. 1.(5). The total
area of such reinforcement shall be Ps~cs where A cs is the sum of the area of concrete in strips
along each exposed side face, each strip having a height of 0.5 h - 2 (h - d) and a width of twice the
distance from the side face to the centre of the skin reinforcement but not more than half the web
width. The minimum amount of skin reinforcement shall be such that Pst equals 0.008 or 0.010
for interior or exterior exposure. respectively. The maximum spacing of this skin reinforcement
is 200 mm.

1.10 Research Objectives

The objectives of this research programme are:

1. to study the complete behaviour of full-scale reinforced concrete cantilever cap

beams,
2. to investigate the suitability of current design approaches for these disturbed
regions.
3. to compare the predicted responses using simple strut-and-tie models, refined
strut-and-tie models aIid non-lïnear finite element analyses,
4. to investigate the influence of concrete strength on the behaviour of large
cantilever cap beams, and
5. to study the amount of uniformly distribllted reinforcement reqllired for crack
control at service load levels.

(
38
 CHAPTER2
(
EXPERIMENTAL PROGRAMME

Two full-scale cantilever cap beams were constructed and tested in order to study their
complete responses. These test specimens are representative of the cantilever portions of
continuous cap beams and of cantilever cap beams as shown in Fig. 2.1. These cantilever cap
beams were designed using the strut-and-tie approach of current codes (CSA 1994, CHBDC 1996
and AASHTO LFRD 1994). The amounts of unifonnly distributed horizontal and vertical
reinforcement were varied in order ta study their influence on crack control at service load levels.

The geometry of the cantilever cap bearns was chosen after studying a number of
drawings of typical cap beams (see Fig. 1.1). The loads at each bearing location for the
prototype bridge investigated were a service dead load of 460 kN and a service dead plus live
plus impact Ioad of 1140 kN.

2.1 Details of Specimens

Cap beam specimen CAPN was cast with normal strength concrete (design le' = 35 MPa),
while specimen CAPH was constructed with high-performance concrete (design le' = 70 MPa).
Both specimens have identical geometries. As shown in Fig. 2.2, each cap beam is 3350 mm
long, 750 mm wide and has cantilevers which extend 1300 mm from the faces of the 750 mm
square colurml. The depth of each cantilever is 900 mm at its end, increasing to 1100 mm over
a distance of 625 DUn from the end.

The reinforcement for both specimens was identical, with epoxy-coated bars used
throughout ta confonn to the requirements of the Canadian Highway Bridge Design Code
(CHBDC 1996) for corrosive environments. The main tension tie reinforcement was provided
by two layers of reinforcement, each containing 5 No.25 bars, with a clear vertical spacing of
35 mm. One layer of 5 No.25 bars served as the compression steel. The square column was
reinforced with 12 No.25 bars and confmed by sets of 3 No.IO column ties spaced at 300 mm
(see Fig. 2.2). The specimens had crack control reinforcement ratios of 0.18% and 0.30% in
( cantilever ends A and B, respectively (see Sections A-A and B-8). In end A, this reinforcement

39
(

(a) Prototype continuous cap beam

~ililfif'41- ... ' .-;..~;'}~~

~1'~~~

(b) Prototype cantilever cap beam (c) Test setup

Figure 2.1 Test simulation of cantilever cap beams

(
40
(
r4-No.10 7 - No. 10-.......
/double stirrups double stirrups"'-
-...--- r---------,.~ (vertical (vertical
. -j

·
distributed
reinforcement)
s =300
distnbuted
reinforcement)
s =175
1
1

1
'" 1

·
2- No. 15 4-No.15-
1--
·
1100 U-shaped bars U-shaped bars
(horizontal
distributed
(horizontal
distributed
·
reinforcement)
s =295
reinforcement)
s =177 ·
~ ~
~ .. ~i ~•
750

section A-A t
s ectJon B-B
Il

.[u_~L_u_[
- - -- ., ..........
.L

625
5 - No. 25
A- ,.....-B 1.
1 -
--

--?<1 "
;
ri
--

1
1 ~~ 1=
~ 1=== ~

~
1
1
;
~~ P--': ~--...:
:t--
'1
1'1
1 1

F = F=== ~p
1

!
i 1,1
I~
;
l, ~F= F== F==
i i
l
!~
li 1
, -

t=== =
_. i
1
1 i
Ji
I~
~~
1

i i 900

l
1
!
=== !
!
;F== = :

TU
k:'~
. --------,.
1

!
.. _.-

-::::=::::
-
1
1 1
1

! i
1
i
il
il
~
1
i
1
1
--L-

A
- 3350
L......B

10 - No. 25
(tension
reinforeement)
3 - No. 10
12 - No. 25 (column ties)
(column bars) 5 =300
i

I~I Il ~ 1 1 1 Ir:
1 -
1
r-
I
~'
1 •

! 1 1 1 1 1
1

i
L __.l _~1
1

1 ! 1
L 1 1
I~
1
1
- -
i
~ 1 J 1

Notes:
dimensions in mm
minimum cover 50 mm =

( Figure 2.2 Specimen details

41
 was provided by 4 double No.ID stirrups spaced at 300 mm in the vertical direction~ and 2
( U-shaped No.15 bars spaced at 295 mm in the horizontal direction. These spacings were reduced
to 175 mm for the 7 vertical double stirrups and 177 mm for the 4 horizontal crack control bars
in end B. A minimum caver of 50 mm was maintained throughout the specimens.

Ninety-degree end anchorages with free end extensions of 300 mm beyond the bend were
provided on all the No. 25 bars used for the main tension tie reinforcement. In order to fully
develop the reinforcement ify = 400 MPa), the code (CHBDC 1996) requires straight embedment
lengths, [(/h, of 430 mm and 304 mm beyond the hooks for specimens CAPN and CAPH,
respectively. The tension development lengili~ [d~ of the No. 25 bars in CAPN is determined as:

Id = 0.18kl~~.f,db
1er
(2.1)
= 0.18(1.0)(1.2)(1.0) 400 (25)
0.33,;35
= 1106 mm

= bar location factor, taken as 1.0.

= coating factor, taken as l.2 due to the epoxy-coated bars.
= bar size factor, taken as l.0 because bars are larger than No. 20.

Likewise, [d = 782 mm for the No. 25 bars of CAPH. The stress in the bar that can be
developed by the hook is [(1106 - 430)/1106] * 400 MPa = 244 MPa for specimen CAPN and
[(782 - 304)/782] * 400 MPa = 244 MPa for CAPH. Knowing the geometry of the bend and
the placement of the bearing pads (see Fig. 2.2), the available straight bar embedment length to
the inner edge of the bearing plate is 286 mm for the bottom layer and 226 mm for the bottom
layer of bars for CAPN. Therefore, the bottom layer of bars in CAPN is capable of developing
a stress of 244 MPa + 286/1106 * 400 MPa = 348 MPa. while the top bars can develop 326
MPa. Similarly the bottom and top bar layers of CAPH can develop 371 MPa and 340 MPa.
respectively. These calculations assume that the bond stress is uniform over the development
length, which results in a linear build-up of stress along Id' Although stresses greater than 400
MPa are expected during testing, these smaller embedment lengths were provided to investigate
the beneficial effects of the compressive bearing stress on the bond strength.

The horizontal distributed steel was lap spliced in the central regions of the specimens
where additional confinement 1S provided by the column ties which are typically continued into
the cap beam. Without considering the beneficial effects of the confinement provided by these
( column ties, the required lap splice length is calculated as 1.3 Id (CHBDC 1996), where:

42
( Id = 0.18(l.O)(1.2}(O.8) 400 (15)
0.33,;35
= 531 mm

Hence the required lap splice length for specimen CAPN is 1.3 x 531 mm = 690 mm.
Similarly, the required lap length for specimen CAPH, having a design compressive strength of
70 MPa is 488 mm. Full development of the horizontal bars was therefore achieved in the
central region of the cap beam. Over the constant-depth panions of the cap beam the venical
uniformly distributed reinforcement was provided by No. la double closed stirrups (see Fig. 2.2).
Because of the changing depth of the cap beam near its ends, it was necessary ta use double U-
shaped spliced stirrups over the tapered panions of the specimens. The required lap-splice length
for these U-shaped stirrups, using Eq. 1.1, is 460 mm for CAPN and 340 mm for CAPH. A
conservative value of 460 mm was used for bath specimens.

2.2 Materia! Properties

2.2.1 Concrete

Both specimens were cast with ready-mix concrete. The specified concrete strength for
CAPN was 35 MPa with a water ta cement ratio (w/c) of 0.40 and a maximum aggregate size
of 14 mm. The high perfonnance concrete of CAPH had a specified strength of 70 MPa, a w/c
of 0.28, and a la mm maximum aggregate size. Mix designs are presented in Tables 2.1 and
2.2, and the slump and air content measurements taken upon delivery are shawn in Table 2.3.
The test specimens, together with the control cylinders and flexural beams, were covered with
wet burlap and plastic sheeting a few hours after casting, and were kept moist. The test
specimens and the control specimens were stripped of their formwork 4 days after casting and
kept in the same air-cured conditions of the laboratory. The compressive strengths were
determined from the results of testing 3 standard, 150 mm diameter by 300 mm long, concrete
cylinders, and the splitting tensile strengths were taken as the average from 3 Brazilian tests on
150 mm cP by 300 mm cylinders. In addition, 3 fiexural beam tests were used ta determine the
average modulus of rupture. These flexural beam specimens measured 150 x 150 x 600 mm and
were subjected to third-point loading over a span of 450 mm. A summary of the results of the
cylinder and beam tests are presented in Table 2.3. Representative compressive stress-strain
curves for the 35 MPa and 70 MPa concretes are shown in Fig. 2.3(a). ln addition, shrinkage
strains were determined from externally applied strain targets on concrete beam specimens
measuring 100 x 100 x 400 mm. The strain targets were placed on these shrinkage specimens
( 24 hours after casting. The shrinkage strains determined from these measurements are shawn

43
( 1
Ingredient
1
Type
1
Quantity
1

cement 10 415 kg/m3

fine aggregate Lafarge St.-Gabriel 757 kg/m3
coarse aggregate 10-14 mm limestone 1003 kg/m3
water (total) 167 kg/m3
total density 2342 kg/m3
water reducer Pozzolith 200N 1346 mL
air-entraining agent Micro-Air 330 mL
superplasticizer Rheobuild 1000 2.7 L
retarder Pozzolith l00XR 375 mL
Table 2.1 Mix design for 35 MPa concrete

Ingredient Type Quantity

1 1 1 1

cement 10SF 3
480 kg/m

fine aggregate Lafarge St.-Gabriel 850 kg/m3

coarse aggregate 10 1I1.ID limestone 1015 kg/m)

water (total) 135 kg/m3

total density 2480 kg/m3
water reducer Pozzolith 200N 1630 mL
superplasticizer Rheobuild 1000 13.0 L
retarder Pozzolith lOOXR 780 ml

Table 2.2 Mix design for 70 MPa concrete

in Fig. 2.3(b). It is interesting to note that the 70 MPa concrete exhibited considerably higher
shrinkage strains in the first few days ailer casting than the 35 MPa concrete.

(
44
( 100
90
/ 70MPa
80 ,.
./
',,://
70 /'
.. , . /
m-
a.. 60
.//'

een
t/
/'
/'
./ 1
50 1

en V 35MPa

-
,/
Q)
--L i
~
40 e---
~
~---~// ~
en
i
30
//""
20
10
/y 1
,

V 1

0 100 200 300 400 500

microstrain

(a) representative stress-strain curves

600
70 MPa'\.,

500
-- -~
-- --~

--- -- -- --
~--
~_a_

----------
400 ~---r-- -~--~----
---_.
...........
c /
~
"lij
'- 1
êii 300 __ J _ _ _ _ r----~- f-----------------
a
'- f
u
·Ë 1

200 -

100
r
a 50 100 150 200 250
time (days)

(b) average shrinkage strains

Figure 2.3 Concrete Properties

(
45
( 1
Property
1
35MPa
1
70MPa
1

air content (%) 6.5 2.3

slump (mm) 160 200

average 28-day strength (MPa) 36.1 72.8
age at testing (days) 62 70
secant modulus (GPa) 32.4 27.3
characteristic peak strain (mm/m) 2.18 3.08
compressive strength at testing average 37.6 79.2
(MPa) std. dey. 1.1 0.8
splining tensile strength at testing average 3.2 5.2
(MPa) std.dev. 0.2 0.8
modulus of rupture at testing average 4.6 6.7
(MPa) std. dey. 0.3 0.3

Table 2.3 Concrete properties

2.2.2 Reinforcing Steel

Steel reinforcement consisted of No.lO, No.15 and No.25 epoxy-coated defonned bars
with a specified grade of 400 MPa. A minimum of 3 tensile samples were tested for each bar
size to determine their mechanical properties. Table 2.4 summarizes the average values and the
standard deviation of the yield and ultimate stresses and strains at strain hardening. strains at the
ultimate stress and the rupture strains. Figure 2.4 shows lypical stress-strain curves for the three
different bar sizes. The modulus of elasticity for all reinforcing steel has been taken as 200 GPa
for the purpose of bath design and analysis.

(
46
( 1,000
900
aoo

----- ------
700 -~
--...;;;-

Ci 600
Q.
~ 500
:g 400 ~
~
iii 300
200
100

o 0.02 0.04 0.06 o.oa 0.1 0.12 0.14 0.16

strain (mm/mm)

(a) No. 10 bars

1,000

700
900
aoo
~-

~--_._-

~
-1
1
j
Ci 600 ~------~
Q.
~ 500 r-.---- -
:g 400 t - - - - - - -
~ ... _-
iii 300
--
~-
1
200
100 ~-----

1
o 0.02 0.04 0.06 o.oa 0.1 0.12 0.14 0.16
strain (mm/mm)

(b) No. 15 bars

1,000

--
900 ---

aoo
700
f----

~
-- -
Ci 600
~-
0..
~ 500
:g 400 t------'--
~
iii 300 - - -
200 ~,

100
1

o 0.02 0.04 0.06 o.oa 0.1 0.12 0.14 0.16

strain (mm/mm)

(c) No. 25 bars

Figure 2.4 Typical stress-strain responses of reinforcing bars

(
47
 Property
( 1 1
No. 10
1
No.IS
1
No. 25
1
yield stress average 441.0 419.0 468.5
(MPa) std. dev. 2.7 1.0 7.1
elastic modulus (GPa) 200 200 200
strain at strain average 0.77 1.12 0.54
hardening (%) std. dev. 0.04 0.02 0.06
ultimate stress average 707.5 688.4 768.6
(MPa) std. dev. 2.2 2.9 1.2
strain at ultimate stress average 13.4 12.0 10.2
(%) std. dev. 0.2 0.5 0.1
rupture strain, average 14.1 16.0 13.5
over 200 mm (%) std. dev. 0.6 1.1 0.6
Table 2.4 Reinforcing steel properties

2.3 Test Setup and Instrumentation

The pier caps were installed upside-down under the Il,000 kN capacity MTS universal
testing machine (see Fig. 2.5). Figure 2.6 shows the loading arrangement at the top of the stub
column for each specimen. Load was transferred through the 559 mm diameter bottom platen
of the MTS's spherical seat, which in turn loaded (Wo plates. These plates had a total thickness
of 127 mm in order to ensure sufficient spreading of the load. The 51 mm thick bottom plate
measured 660 x 660 mm, and was seated with plaster to the top of the 750 x 750 mm stub
column. The size of this battam plate was chosen such mat the laad would be transmitted ta the
vertical column bars without loading the concrete cover.

The cap beams were simply supported on the laboratory strong floor. Figure 2.6 shows
the bearing details used for specimens CAPN and CAPH. Two 20 mm thick by 152 mm wide
by 600 mm long bearing plates were seated with a plaster mortar compound on the bottom of
CAPN. The bearing plates for specimen CAPH had a width of 76 mm, that is, one-half that
provided for CAPN due to the higher concrete compressive strength of specimen CAPH. These
600 mm long bearing plates were centred across the 750 mm wide cap beams such that they did
not bear on the cover concrete. The centre of the bearings was located 375 mm from the end
( faces of the cap beams (see Fig. 2.6). The bearing plates rested on a rocker, with a radius of

48
(

Figure 2.5 Specimen CAPN under the MTS testing machine

(
49
(

660
559

- -., -

1].1:-:
...L. __ ..
. ~.~.
;.,r~l_.

381

==-____________________ n 1&

~_--I

375 375

Notes·
dimensions in mm
1& = 152 mm for CAPN
1& =76 mm for CAPH
Figure 2.6 Different bearing details of specimens CAPN and CAPH

(
50
 250 mm, which in tum rested on two 152 mm diameter rollers sandwiched between two 76 mm
( thick steel plates.

Three Linear Voltage Differentiai Transducers (LVDT's) or extensometers were installed

to measure vertical displacements of the specimen at the supports and at mid-span (see Fig. 2.7).
The centre deflection reported is taken as the deflection from the LVDT at midspan (CV), minus
the average of the LVDT's at ends A and B (AV and BV), in arder to remove movements al the
supports. In addition, extensometers were used to determine average strains in the test
specimens. These LVDT's were anached to threaded rads which, in mm, were gIued in hales
drilled 50 mm into the concrete. Ten extensometers were positioned, as shown in Fig. 2.7, al
the level of the centroid of the tension steel, between the centres of the bearings. A second line
of eight extensometers was located at mid-height of the cap beam. Additional extensometers were
positioned, as shown if Fig. 2.7, to form 260 mm rosettes within the shear spans of the cap
beam. The purpose of these rosettes was to determine principal strains and their directions in the
diagonal compressive struts.

Figure 2.8 shows the locations of the twenty-two electrica l resistance strain gauges which
were glued to the reinforcing bars prior to casting. Twelve gauges were located on the bottom
layer of the main tension reinforcement, 6 on the centre and 6 on the outermost bar. These
gauges were positioned al the start of the hooks, al the inner edges of the bearing plates, and at
locations aIigned with the column faces (see Fig. 2.8). An additional ten gauges were glued ta
the horizontal and vertical distributed bars in the shear spans of the cap beams as shown.

2.4 Testing Procedure

The loading was displacement controlled at a rate of approximately 0.004 mm/sec.
Throughout the testing, load, displacement and strain readings were recorded at intervais of 25
kN or 0.1 mm, whichever came first. During the early stages of a test, load application was
haited, to create major 10ad stages, al increments of approximately 500 kN. At these load stages,
widths of cracks crossing the horizontal Hnes shown in Fig. 2.8 were measured using a crack
comparator, and the crack patterns were sketched and photographed. After yieIding of the main
tension reinforcement, Ioad stages were taken al increments of l to 2 mm of the mid-span vertical
deflection. The Ioading of the specimens continued until a significant decrease in load-carrying
capacity was observed.

(
51
(

A6D A7D B7D BBD

AB A9 B9 BB
AS 86

A6V A7V B7V B6V

447

Al A2 A3 A4 A5 85 B4 B3 82 81
~O3
~L..:

AV CV 8V
260
typo
Note:
dimensions in mm

Figure 2.7 LVDT locations

-------- ~.:~~-~~--- ~-~!

crack widths
measured on
these Iines
l
1
A1D
1
&A11 1 .. :~~--:-: _:--~::."-:-:--:-. ~81()--' .-.---":.--.-;..'--- .,.
&811
~--- -------~-~~_ .."~._-_.-:--.. _-..::- ... ~:. ----~ .
. B9 1
- - - - Ag - - - - - - - - - - - ---- -~--= -~--. -:-.:- - - - - - - - -"~.' ....)-: - - - - -:- -
."."-.. ): " - - - . -.. " B7
A7 / & B8 \1
&AB

~ T:- - --T-'"'; - - -.,... - - -"7~-"""=-~'=-~~---~:T".,....;~.--"7"..:-."':...,.._-::;---=".~-"~" ---r-

A1 & A2 A3 &A4 A5 & A6 85 & B6 83 & B4 B1 & 82

Figure 2.S Strain gauge locations and crack width Iines of measurement

(
52
 CHAPTER3
(

EXPERIMENTAL RESULTS

This chapter describes the experimental results of each specimen. Appendix A gives
more details of the measurements taken.

3.1 Load-Deflection Responses

The response is described in tenns of the applied shear on each shear span, which is
taken as one-half of the totalload applied to the top of the column. Figures 3.1(a) and (h) show
the shear vs. centre deflection responses for specimens CAPN and CAPH. respectively.

3.1.1 Specimen CAPN

First cracking of CAPN occurred in ends A and B simultaneously at a shear of 430 kN.
These flexural cracks which occurred on the bottom face of the cap beam. in line with the column
faces. resulted in a slight decrease in member stiffness (see Fig. 3.1(a». At a shear of 870 kN.
a major diagonal crack formed on each end, causing a slight drop in load and a reduction of the
stiffness. First yielding of the tension tie occurred at a shear of less than 2310 kN near the
location of the first flexural crack of end A. First yielding of the crack control reinforcement
occurred at a shear of 1350 kN for end A and 1740 kN for end B. General yielding of the
specimen occurred at a shear of 2510 kN and a centre deflection of 4.33 mm. A maximum shear
of 2920 kN (that is, a total applied load of 5840 kN) was reached at a deflection of 14.78 mm.
Failure occurred by diagonal crushing of the concrete at the re-entrant corner between the column
and end A of the cap beam followed by slippage along the diagonal crack which formed between
the re-entrant corner and the support of end A. This resulted in a drop of about 30 % of the load-
carrying capacity as shown in Fig. 3.1(a)

(
53
( 3,500

1
3,000
- concrete aush ng and shear slip
\
2,500
/v---
-z 2,000
f- ~rsl yielding of len sion tie
h
~
L-
eu {firsl yielding of end 8 d stributed steel '-;
f
CD 1
J:: 1,500 -
en

1,000
!
firstyi. Iding of end A dist ibuted steel
1
/
first diagon ,1 cracking

500

0
f-.-. first f1exural fcking

5
1

10 15
/ 20 25
centre defiection (mm)

(a) Specimen CAPN

3,500

3,000 f--------.--~ V \' Shearsl~alb-

-z
2,500
! fi~l yielding of
tel sIon tie
\

-
.::.:.
L-
m
2,000
t-w. yielding of
end 8 distributed stee
\

)
CD
oC
en
1,500
1- firstyie ding of
/
1,000
! endA( istributed steel

firsl diagon 1cracking

/
500 r--

1
first f1exural CI acking

0 5 10 15 20 25
centre deflection (mm)

(b) Specimen CAPH

Figure 3.1 Load-deflection responses of specimens

(
54
 3.1.2 Specimen CAPH
(
First cracking of CAPH occurred in end A at a shear of 490 kN, and resulted in a
significant decrease in member stiffness (see Fig. 3.1(b». The first crack in end B did not
develop until a shear of 570 kN was reached. These fiexural cracks were aligned with the
column faces and propagated from the bottom face of the cap beam. At a shear of 890 kN, a
major diagonal crack formed on end A which caused considerable load drop-off and a reduction
in stiffness. First yielding of the tension tie occurred al a shear of 2120 k:N near the location of
the first flexural cracks of end A. First yielding of the crack control reinforcement occurred at
a shear of 1360 k.N for end A and 1910 k.N for end B. General yielding of the specimen took
place at a shear of 2620 kN and a centre deflection of 4.06 mm. A maximum shear of 3000 kN,
or a total applied load of 6000 kN, was reached at a deflection of 9.36 mm. Failure occurred
by shear slippage along the diagonal crack which formed between the re-entrant corner and the
support of end A, with only minor signs of crushing near the re-entrant corner. This resulted
in a drop of approximately 38% of the load-earrying capacity as shown in Fig. 3.1(b)

3.2 Development of Strains

LVDT's were used to determine the average strains over the gauge lengths provided, and
the strain gauges, glued to the reinforcing bars, were used to determine local strains in the bars.

3.2.1 Specimen CAPN

Figure 3.2 shows the variation ofshear vs. horizontal strains measured in the bottom bars
of the main tension tie. The development of strains is shown at different locations of the main
tension tie for both ends A and B, with solid lines used to identify readings from gauges placed
on the outermost bar and dashed lines used to identify those readings from the innennost bar.
From gauges A5 and A6, as weIl as B3 and 84, it is clear that the outennost bars are strained
approximately the same amount as the innermost bars. Gauge 85 did not work during testing.
Gauges AS and A6, as well as gauge 86 (see Fig. 3.2(e) and (t), located close to where the first
flexural cracks formed, clearly indicate the change from pre-eracking to post-eracking stiffness
at a shear of 430 kN, corresponding to first flexural cracking. AlI of the strain measurements
on end A were lost after a shear of 1590 kN was reached due to a malfunction in the data
acquisition system. Up to this shear level of 1590 kN, end A experienced slightly greater strains
than end B. Gauge 86 indicates that first yielding of the tension tie in end B occurs at a shear
(
55
( yield yield
3,500 :
3.500
(a) 1 (b)
3.000 3,000

2.500 2,500
;r
~
Z 2.000
1 1 Z 2.000
=-i5 =-iU
0
.r:
ln
1,500
1
R CIJ
.r:
en
1.500

1,000
:
FIl 1 :tJrtnHll 1,000 rfTT~ =:t t :-~ttti
lU 1 i -F-1tlll.UI ~ : i ~ t li
I·! dJlI
1 1

500 A 1 (outer bar) - - 500 - - B1 (outer bar)

A2 (inner bar) - - - - - - B2 (inner bar)
1

0 2.000 4,000 6.000 8.000 a 2.000 4,000 6,000 B.OOO

microstrain microstrain

yield yield
3,500 ..----r---.----~-~~-_._-..., 3.500 r----r---r---,....---r---""'!""""-..,.---~_..

3.000
1
+---~t~~-~t--t----+----+---l
(c)
3,000 t---+---+--~.I ~ (d)
2.500
--t--f--r-
1 1 1

2,500 I---_+--ff-.~__+_--+-r-I'
__1 1

~ 2.000 ---r -
~ i _ - o -1._ _ L-
2.000 t------,tFi"--t---,----t-----~--"-·
i5 iUCIJ
o
.r: .r:
en 1 en

1.000 .-~'1_+--+-~~

500 1----+--+----'---- A3 (outer bar) - - 500 .--~.-_t_-"----l - - B3 (outer bar)

A4 (inner bar) - - - - - - 84 (inner bar)

a 2.000 4.000 6,000 8.000 o 2.000 4,000 6.000 B,OOO

microstrain micrcstrain

yield yield
3,500

3,000 ---- - ,
! (e)
3.500

3,000
_-_-~
1 LI
-_-_- ._-.. . ._-L.. . _ ~
(f)

,,
~

1
2.500 2.500 -
.:
Z 1
Z 1
,,
2.000 2.000
=-iU ,.
,Î ! =-iU 1
0
.r: 1.500 ~ 1,500 ,
1
• •
ln ln

llt[ TV
1

,
1,000 1,000 , •
1 : ;

500 AS (outer bar) - - 500

.. ,"
- - - B6 (inner bar)
/ A6 (inner bar) - - -
1 '

1 1 1 1

a 2.000 4,000 6.000 B,OOO a 2.000 4,000 6.000 B,OOO

microstrain micrcstrain

Figure 3.2 Strains in bottom bar of CAPN tension tie, determined trom strain gauges
(
56
 of2310 leN. that is, somewhat less man the shear corresponding to general yielding of2510 kN.
( Extrapolation of readings from gauges AS and A6 indicates that first yielding of the tension tie
in end A occurred at a shear of about 2260 kN. The readings from gauges B3 and B4 (see Fig.
3.2(d), Iocated at the inner edge of the bearing in end B, indicate that the strains at this location
were close to the yield strain at maximum shear level. At general yield of the specimen (2510
kN), these strains had ooly reached about 65% of their yield strain. Strains in the bars at the
start of the main tension tie hook (B 1 and B2) remained weIl below yield throughout the loading
(see Fig. 3.2(b».

Figure 3.3 shows the applied shear vs. the measured strains in the distributed
reinforcement. Gauges located on the distributed reinforcement in end A were lost after a shear
of 1590 kN. Gauges A10 and All, as weIl as BIO and B11. glued to the vertical legs of the
closed hoùps. experienced significant tensile strains after the first major diagonal cracking at a
shear of 870 kN. As can be seen from Fig. 3.3(a) and (b), gauges AI0 and 810, which were
glued to the outer hoop legs, experienced larger strains than gauges A Il and 8 Il. attached ta the
inner hoop legs. Gauges A7 through A9. and B7 and B8 were placed outside the region where
major diagonal cracks fonned. and therefore experienced very little straining (see Fig. 3.3(c) and
(d».

Figure 3.4 shows the strains determined from the sets of LVDT's placed along a line
corresponding to the mid-height of the cap beam. and at the level of the centroid of the tension
tie. The average strains determined from these LVDT readings are plotted for four different load
stages: at a loading corresponding ta full-service plus impact. at general yielding. at maximum
shear, and after failure. Aiso shown in Fig. 3.4 are the yield strains of the uniformly distributed
steel and the tension tie reinforcement. Figure 3.4(a) shows that some regions of the tension tie
had reached yield at a load corresponding to full-service plus impact, while the uniformly
distributed crack control reinforcement had a maximum strain of 76 % of its yield strain. At
general yield (see Fig. 3.4(b», the average strains exceeded the strain-hardening strain of 5.4
millistrain in three regions of the main tension tie steel. ln addition. yielding of the distributed
reinforcement at mid-height of the section occurred. At maximum shear (see Fig. 3.4(c» there
is a noticeable difference between ends A and B, with strains in end A reaching a maximum
strain of 2.83% in the main tension tie reinforcement in linc with the column face (this average
strain corresponds to a steel stress of about 600 MPa). The maximum strain achieved in the
stronger end (end B) was 1.46%. As can he observed in Fig. 3.4(d), the strains generally
decreased due to the drop-off in load after failure, with the exception of the regions where a
major diagonal crack fonned between the re-entrant corner and the support in end A.
(
57
 ~ ~

yield 1
3,500 yiold
i
~
3,500,1 1 1 1 i (a)
3,0001 1 Il 3,000 1 1 1: 1 1 1 (b) 1

2,500 1 2,500

Ci'
~ 2,00 a :i "~ 2,000 l,
I[
-iV
~ :
i:
:
A10 (outer leg) - -
-
êi 1
1
- - 810 (outer log)
œ A11 (Iooorlog) - - - ~ 1,500 1
.c : CI) 1 - - - 811 (ioner leg)
en :
1
i -l 1,000 1
1

1
500 .
500

1 1
o 2000 4000 6000 8000 o 2000 4000 6000 8000
microstrain microstrain
yleld yleld
VI 3,500
00 3,500

Il
-t
(c) (d)
3,000 3,000

1
2,500 2,500
Ci'
0-
~
2,000 ~ 2,000
A9 (horizontal) - - - -
iV
j

• ~
œ 1,500 1,500
.c

•
CI) CI)

1,000 - --
1,000 ~, - _-1 =._ _ ~~ 1

- 87 (outer log)
500 A7 (outer leg) -- 500
- - - 8B (looor log)
1 1
A8 (Innor log) ---
1
o 2000 4000 6000 8000 a 2000 4000 6000 8000
mlcrostrain microstraln

Figure 3.3 Strains in distributed reinforcement of CAPN. determined from strain gauges
 ~ ~

2V

~ yield =2 1 (dlslribuled sleel)

_ yield:; 2.3 (tension lie sleel)

l' 'r,
Il i
j
'f i IÎ
d.o ·1.1
1

t 0.0 1.6: 1.1 0.0 1,.0 0.0 Ill,i·"

1
i : i
1 r
! r
2.0 n n • 2.8.) n n Z.e :nn rin 1. ( nn u.;<; ~l '.
'il ~ , 1 1 !
U,It
··1

t
V (a) V =1120 kN (full service + Impact =1140 kN) V (b) V =2510 kN (general yleld)
lÀ
\0
- ; - - ; - .~ i
"1 : : : Il i,
1

.i
1
1
1 1
1

t 1
Î
1

1
1
1
1

il i,
l,
t 1
ri l .1
'1 1
1 1
'·l

]"
"
1 If J,l

(c) V =2920 kN (maximum shear) (d) V =2040 kN (after fallure)

Figure 3.4 Longitudinal strains from LVOTs at mid-height and the level of the tension Ue of CAPN (expressed in millistrain)
( 3.500
yield
3.500
yield

---
1
1
3.0JO

2.500
.... - -" ,
L
- -- 3.000

2.500
_.... --z:
: -}
~

Z
~ 2,000 1 Z 2.000
~
1
1
-1-I~
Cii
G)
.t= 1.500 _._- Cii
IJ
.t= 1.500 li
li)

1.000
. /
:

~
1

1
~7
AS
li)

1,000
-1'
1 1

i
500 ~---
_~_J_
A6 --- 500
1
r------
1

1 A7 -- 1
t
1
a 1
0
a 5.000 10,000 15.000 a 5.000 10.000 15.000
micrcstrair. microstrain

(a) horizontal strain, E, (b) vertical strain, E)'

3,500.....---......----,---.......-----. 3.500

3.000 ---t----_~~I-_-------~-+-------I 3.000 1

1

Z 2,500 ---~+---./--- L==i Z

2,500

2,000
- .............. - --~ '-----7
1
/
1

j
1

1
1
~ 2,000 : \ ~
Cii
~ 1.500
1.000
-~I-T-
1

I---t---
1 Cii
CI)
.c
li)
1,500

1,000
r--- t-----F- -
r----

500 I----I-----+I------+I--~{
1
1
500
1 1

o 5.000 10,000 15,000 20,000 0 -5.000 a 5,000 10,000

microstrain microstrain

(c) maximum principal strain, E, (d) minimum principal strain, E2

3.500 3,500

I-·---~-k-= f-----~-!~
\ L/F~
1 1

3.000 -_._-_._- ~ -

3.000 -

---1
1

~--- Ï'r
2.500 r-----'----- f------ 2.500 -
Z 2,000 - - -
Z 2,000
C ~
Cii
G)
1.500
iD
IJ
.c 1.500 \
.c
li)
j li)
)
1,000

500
1..('
1
1,000

500
- ~

-1- 1

a 5.000 10,000 15,000 20,000 o 10 20 30 40 50 60 70 ao 90

micrcstrain degrees

(e) shear strain, YIJ' (f) principal angle, (J2

Figure 3.5 Responses of CAPN-A rosettes AS and A7

(
60
( 3,500
yield
3.500
yield

1
3.000 3.000
-,.-- -~-- V-- -'- .... -- ~-~ ~/
2.500 - ... : / 2.500
,,--
Z
:. 2.000 '7
\ '
Z
:. 2.000 il
f 1
;;
ID
.r:.
en
1,500

1.000

500
Ji J 1&
-1 --- 86
ia
ID
.r:.
en
1,500

1.000

500
l-f: 1

1
~I

1 -- 87
a a 10.000 15.000
a
a
1
5.000 5.000 10.000 15.000
microstrain microstrain

(a) horizontal strain, E. (b) vertical strain, E.,

3.500 3,500
1

3,000 3,000
.- ..... ~-
Z 2.000
~
êii
ID
2.500

1.500
Z 2.000
:.
iaID
2.500

1.500
1
-..
'\
'\,.
;1
11 !

:-----J==
.r:. .r:.
en en
1.000 -~
500 500

0
a 5,000 10.000 15.000 20.000 -5.000 o 5.000 10.000
microstrain microstrain

(c) maximum principal strain. E, (d) minimum principal strain. E2

3.500 3.500
1 i
3.000

2.500 ~,
~-- ~---- ..
1
- 3.000

2.500
t- 1--
1

Z _-J'j z _J
:. 2.000 ~ 2.000
Cii
~ 1,500 1 êii
~ 1.500 l
en
1.000
/
7 CIJ

1.000
~ï7
1 1 1

1
500 500
1

o 5.000 10.000 15.000 20,000 o 10 20 30 40 50 60 70 80 90

microstrain degrees

(e) shear strain, Yrp (f) principal angle. ()2

Figure 3.6 Responses of CAPN-B rosettes 86 and 87

(
61
 Figures 3.5 and 3.6 show the shear vs. horizontal strain vertical strain, principal strains
y y

( shear strain and angle of minimum principal strain determined from the rosettes in ends A and
B, respectively. The strains determined from the rosettes were very small until a crack formed
within the gauge lengths of the LVDTYs. The fust diagonal cracks. which formed in ends A and
B at a shear of 870 kN, resulted in the development of significant principal tensile strains and
shear strains. These are the same cracks that caused the slight drop off in load as shown in Fig.
3.1(a). The shear vs. horizontal strain y E.fy and the shear vs. vertical strain, Er responses are
described in Fig. 3.5(a) and (b)y and Fig. 3.6(a) and (b), for ends A and B, respectively. Both
the horizontal and vertical strains in the region of the cap beam close 10 the column face
experienced a sudden increase in strains upon first diagonal cracking. In end A, the horizontal
strains are slightly larger than the vertical strains, with yielding of the uniformly distributed steel
in the horizontal and vertical directions taking place al a shear of 1350 kN and 1500 kN,
respectively. In end B, the strains were lower than in end A due to the larger amount of
unifonnly distributed reinforcement in end B. This reinforcement, in end B, yielded in the
horizontal and vertical directions at shears of 1740 kN and 1780 kN respectively. Both the
y

principal tensile strain, El' and the shear strain y "(:cr plots indicate that significant yielding took
place, resulting in very large principal tensile strains and shear strains, particularly in end A.
The principal tensile strain was greater than 2 %. resulting in very large cracks, and hence slip
along the crack interface occurred at shears greater than 2700 kN. In end B, the strains were
somewhat lower than those experienced in end A. with a maximum tensile strain of 1.28 % and
a maximum shear strain of 0.78%. For both ends A and B, the angle, 82y corresponding to the
minimum principal strain was close to 45 0 from the horizontal until significant yielding took
place, which resulted in the angle becoming steeper.

3.2.2 Specimen CAPH

Figure 3.7 shows the variation of shear vs. horizontal strains measured in the bottom bars
of the main tension tie. Solid lines are used to identify readings from gauges placed on the
outermost bar and dashed lines are used to identify those readings from the innermost bar. It can
be seen from gauges A3 through A6, and B3 through B6, that the strains in the outermost bars
are approximately the same as those in the innennost bars. Gauges AS and A6 located close to y

where the first flexural crack formed clearly indicate the change from pre-eracking to post-
y

cracking stiffness at a shear of 490 leN. corresponding to tirst flexural cracking (see Fig. 3.7(e».
Readings from gauges B5 and B6 indicate that the tirst flexural crack in end B did not form until

( a shear of 570 kN was reached (see Fig. 3.7(t). Straïns in the tension tie in cantilever end A

62
( yield yield
3,500 3.500
(a) (b)
3,000
1
1 i 1
3.000 1 1
"

,
1
1
1
2,500 ! 2,500 i
1

Z 2.000 ! ! 1
1 Z 2.000
~ ~
œ œ
(1]
.c 1,500 1
-r CD
.r; 1.500

•
IIJ 1

. -r ,-
~.:.'
IIJ

1,000
1 • 1 _ •. ~
-

1,000
fil ~~~O-t~H~~Th
t ::r:.-tt Pi ~ l ~ !"!'TtlHld.ll1
i 1 i1 1
500
1
A1 (outer bar) - - 500 r---f--+...:.-----1 - - B1 (outer bar)
: A2 (inner bar) - - - - - - 82 (inner bar)
1
1 i 1
1
1 1 1

a 2,000 4,000 6.000 8.000 a 2,000 4,000 6,000 8.000

microstrain microstrain

yield Yleld
3.500 3.500
1
(c) (d)
3,000 ..;. 3.000

2,500 2.500

Z 2,000 Z 2,000
~ ~
œ
(1]
di
CD
.c 1.500 .r; 1.500
IIJ IIJ

1.000 1,000
1 1
500 A3(outerbar) - - 500 - - 83 (outer bar)
A4 (inner bar) - - - - - - 84 (inner bar)

a 2,000 4,000 6,000 8,000 0 2,000 4,000 6,000 8,000

microstrain microstrain

yield yield
3,500 3,500
(e) (f)
-r-
: 1
1
3,000 ~~_2"" -
3.000
: j?'
2,500 ---t--- 2,500

~
~b
Z Z 2.000

ml_
~
2.000 ~
œ
(1]
èa
CD
.c 1,500 .r; 1,500
IIJ

1,000
_)1 fi)

1,000

500
Ir :
AS (outer bar) - -
AS (inner bar) - - -
500
1

a 2,000 4.000 6.000 8,000 0 2,000 4,000 6,000 8,000

microstrain microstrain

Figure 3.7 Strains in bottom bar of CAPH tension tie, determined trom strain gauges
(
63
 were slightly greater than those in end B. Gauges AS and A6 indicate mat first yielding of the
( tension tie occurred at a shear of about 2120 kN. that is, somewhat less chan the shear
corresponding to general yielding (2620 kN). At general yielding, the strains from gauges A3
and A4. located at the inDer edge of the bearing in end A, were at 85 % of their yield strain,
while strains from gauges B3 and B4 had only reached 76% of their yield strain (see Fig. 3.7(c)
and (d». The readings from gauges A3 and A4 indicate that, at the maximum shear, the strains
at this location were slightly greater than the yield strain, while strains from gauges B3 and B4
remained just below yield. Strains in the bars at the start of the main tension tie hooks (A 1, Al,
BI and 82) remained weIl below yield throughout the loading (see Fig. 3.7(a) and (b».

Figure 3.8 exhibits the applied shear vs. the measured strains in the distributed
reinforcement. Gauges AI0 and AIL, experienced significant venical tensile strains after the first
major diagonal cracking occurred at a shear of 890 kN. As cao be seen from Fig. 3.8(a), gauge
AlO which was glued to the outer hoop leg, experienced largtr strains than gauge AlI, located
on the inner hoop leg. Gauges BLO and B LI, experienced significant tensile strains at a shear of
1625 kN when a major inclined crack propagated up towards the re-entrant corner of end B (see
Fig. 3.8(b». Gauges A8, and B7 through B9 experienced very small strains as they were
positioned outside the region where major diagonal cracks fonned (see Fig. 3.8(c) and (d».

Figure 3.9 shows the strains determined from the lines of LVDT's positioned at mid-
height of the cap beam, and at the level of the centroid of the tension tie. The LVDT readings
indicate that the tension tie reinforcement in end A had reached yield at a location in line with
the column face at full service loading plus impact (see Fig. 3.9(a». At this load level, the crack
control reinforcement remained below yield. Figure 3.9(b) shows that strain hardening of the
tension tie occurred at the same location where first yielding was measured and yielding of the
distributed reinforcement at mid-height of the section was measured at general yield of the
specimen. Strains in end A are considerably greater than those of end B at this stage. At the
extremities of the mid-height line of measurement, the strains were close to zero throughout
loading until a diagonal crack formed through the outer gauge length at failure. At maximum
shear, mid-height strains in end A are roughly twice those in end B (see Fig. 3.9(c». Strains at
the level of the tension tie are largest at the locations of the major flexural cracks. The maximum
strains in ends A and B at the maximum shear were 2.62%. and 1.94%, respectively. The post-
failure strains decreased due to the drop in load, with the exception of the extreme Ieft reading
at mid-height due to the formation of the diagonal crack which caused failure (see Fig. 3.9(d».

Figures 3.10 and 3.11 show the shear vs. horizontal strain, venical strain. principal

( strains, shear strain and angle of minimum principal strain determined from the rosettes in encls

64
 ~ ~

i~i-r-'-­
n
yl.1d 1 3,500 i yield
i-r---'- ,
3.S00 l, 1 1 I ! (a) (b)
3,000

2,500

z
c z
c
m
.c.
1 A10 (outer leg) - - m
~ 1,500
- - 810 (outer leg)
UI Al1 (inner log) - - - - - - 811 (inner leg)

u----l -
500

o 2000 4000 6000 BOOO

1,000

SOO\

o
1

•
~

2000
-l 4000 6000 8000
mlcrostrain microstrain
yleld yleld
0\ 3,500
Vl 3,500 1

(c) (d)
3,000 1 3,000
1
1 1
2,500 1 - - -- - -t 2,500 1

1
1
~ 2,000 1
~ 2,0001
...
llJ - - - - B9 (horizontal)
!UI 1,500 ;::1== m 1,5001 -

~nHllli~
--
oC
f- UI

1,000

I [~ JJ ~
~
.in! -JIl~ 1,000II---

500 AB (inner leg) - - - 500 l-

-- 87 (outer leg)
1 1
- -- 8B (Inner leg)
1

° 2000 4000 6000 BODO a 2000 4000 6000 8000

mlcrostrain microstraln

Figure 3.8 Strains in distributed reinforcement of CAPH, determined from strain gauges
 ~ ~

2V

~ yield = 21 (dlslribuled sleel)

_ yield =23 (tension lie steel)

~ '.1
!
!
1 1.
t
1
l1 . li 1 1

0.1 1.6 1.3 0.0 1'.3 1.2 0.0 0.0 .. :1'

. : . i 1
',: 1:1
., 1

1 •
1 1 1
0.1 1.9 0.1 1 2.9,! 0.8 0.4 :2.0 2.2 0.0 ·O~ 1 :'
i

v (a) V - 1120 kN (full service + Impact - 1140 kN) v (b) V - 2620 kN (general yleld)

0\
0\
·1
"

1 1
1

!
1
1

,
!
1

• 1
j;
1
:1
i
1:1
Il

1
1
.,

:.,
I~'
l'Ir
U1 •
8.7110) "

.,
" 1 1: Iii"
1
·1 r1
'! H' ,
!I
f, ~

r"
1

~:1 il: .
'j
-; , L Il /i .
~ J,I

(c) V - 3000 kN (maximum shear) (d) V - 1840 kN (after failure)

Figure 3.9 Longitudinal strains from LVDTs at mid-height and the level of the tension tie of CAPH (expressed in millistrain)
( 3,500
yield
3.500
yield
1
1
3,000 3,000
..
i:
l
-;.-
~ 1;--!TI 1
.............. -..".

~/ ::--r
2.500 2,500
Z 2,000
l
l / 1
~ 2.000 1/
~
i; j
~
iiCI) iD
.s= 1.500 ~ 1,500
III

1.000
) UI

1,000
J~
~: lAS '-.1
500 i ---
AS
A7 --
500 1

1
0
1

o
a 5.000 10.000 15.000 o 5.000 10.000 15,000
microstrain microstrain

(a) horizontal strain t Es (b) vertical strain, El'

3.500
1
1

3.000 1

r-
~
....» ~--r~ 1

2,500 2.500 ~

Z 2,000
~
l
1 1 r---
J
,--
i
ca
CD
z;; 1.500
UI

1,000 J
J
!

500 r----
1
0
o 5.000 o 5,000 10.000 15,000
microstrain microstrain

(c) maximum principal strain, Et (d) minimum principal strain, E2

3,500 3.500

'~*'
" t-
\
3,000 -------. 3.000

z~
2,500 - - - - -

2.000 ----
f--
--
i
ru 1
z~
2.500

2.000
-c

-~
fi
'----- -r--- -
t- --

t=+=1
1

ii 1 1 iD
1! 1,500 f-~~-- ~ 1,500 --
III

1.000 - - -
UI

1.000 \.J.
500
1
500 i
o o
1

5.000 10.000 15,000 o 10 20 30 40 50 60 70 BO 90

microstrain degrees

(e) shear strain, y.,. (f) principal angle. (J2

Figure 3.10 Responses of CAPH-A rosettes A6 and A7

(
67
( 3.500
yield
3,500
yield

1
3,000 -~-J 3.000

2.500
t / Î
2.500
t 1 1

~ 11 z~ fi
VL-i&
2.000 f - - - . 2.000
a;
l! 1.500 ~--
....
ID
~ 1,500
1)
co
~86
li)

1,000 :: 1 1,000 1

, i
500 ' - - - B6 500

o
:
: 1 -
.
87
o
a 5,000 10.000 15,000 a 5.000 10,000 15,000
microstrain microstrain

(a) horizontal strain. El (b) vertical strain, E.,

3.500 r----.......------...I----,--~ 3.500

----J~--b· _-~I
z
3.000 -

2.500 -~_' r---~

--1 3,000

2.500
~
l 1
r r=
1
Z

=E
:. 2.000 - - - - - 1 1 :. 2.000
la }
~ 1.500 - - - - - ---t----t-i ---t 1! 1,500
1

--~-f-"---LI ~
ln

1,000 1,000
L __
li)
1

J-
500 . _ - - 500
o 1
L - - - - - ' - _........._ _.........._ ........._...:....._""'--~.
1

o
a 5,000 10,000 15,000 o 5,000 10,000 15,000
microstrain microstrain

(c) maximum principal strain, El (d) minimum principal strain, E2

3,500 3,500

3.000 _._._---

2.500
--~~ 3,000

2.500
p=--(1" ~ ~-

Z
:. 2.000 - - - -
1 1 z~ 2.000
,l
a;
CD
.J::.
1.500
--;J i
1! 1.500
,/

[
li) li)

- -
1.000 ~ 1,000

500 500

0
a 5,000 10.000 15.000 o 10 20 30 40 50 60 70 BO 90
microstrain degrees

(e) shear strain, }'I)' (f) principal angle, (J2

Figure 3.11 Responses of CAPH-B rosettes B6 and 87

(
68
 A and B, respectively. The strains determined from each rosette were very small UDtil a crack
( fonned within the rosette. Significant principal rensile strains and shear strains developed at a
shear of 890 kN, which corresponds to the formation of the fust diagonal crack in end A. This
is the same crack that caused the slight drop-off in loarl as shown in Fig. 3. 1(b). The rosettes
in end B did not register significant strains until the formation of the first diagonal crack in that
end at a shear of 1040 kN. The shear vs. horizontal strain and the shear vs. vertical strain
responses are described in Fig. 3.10(a) and (b), and Fig. 3.11(a) and (b), for ends A and B,
respectively. Both the horizontal and vertical strains in the cantilever ends near the column face
experienced sudden increases upon first diagonal cracking. [n end A, the horizontal strains were
somewhat larger than the vertical strains, with yielding of the unifonnly distributed steel in the
horizontal and vertical directions taking place at shears of 1360 kN and 1610 kN, respectively.
In end B. the strains were lower than in end A due to the larger amount of unifonnly distributed
reinforcement in end B. The horizontal distributed reinforcement in end B yielded at a shear of
1910 kN. while the vertical distributed reinforcement did not yield until a shear of 2730 kN.
Both the principal tensile strain and the shear strain plots show that significant yielding had taken
place resulting in very large principal tensile strains and shear strains, particularly in end A.

As can be seen from Fig. 3.10, significant strains were measured in CAPH-A rosette A7
when the shear reached the diagonal cracking shear of 890 kN. A maximum tensile strain of
1.4 % and a maximum shear strain of 0.7 % were reached during the rest. After this maximum
strain was reached, failure occurred by shear slippage as shown in Fig. 3.15. Significant strains
developed in rosette B7 of CAPH-B at shears greater than 1040 kN (see Fig. 3.11). This
corresponds to the formation of diagonal cracks through this rosette. A maximum tensile strain
of 0.65% and a maximum shear srrain of 0.69% were reached in end B.

The angles of minimum principal strain for both ends were considerably steeper (see Fig.
3.10(f) and 3. 11(f» than those reached in specimen CAPN (see Fig. 3.5(f) and 3.6(f».

3.3 Development of Cracking

Since one of the main objectives of this research programme is to examine the influence
of different amounts of unifonnly distributed reinforcement on crack control at service load
levels, particular care was taken to measure crack widths at aliload stages. In order to have a
consistent means of measuring crack widths, they were measured at locations where the cracks
crossed two horizontal lines, one at mid-depth of the cap beam and the other at the level of the

( centroid of the tension tie (see Fig. 2.8).

69
 3.3.1 Specimen CAPN
(
Figures 3.12(a) and (b) illustrate the change in cracking pattern and crack widths which
were measured over the full service load range for the cap beam. First cracking of specimen
CAPN occurred at a shear of 430 kN with the formation of two shon flexuraI cracks, near the
bottom of the specimen, in line with the column faces (see Fig. 3.12(a». As the shear was
increased to 460 kN, the load corresponding to the self-weight of the superstructure, the cracks
extended slightly but their widths had not changed significantly. Figure 3 . 12(b) shows the crack
pattern at a shear of 1120 kN, which corresponds closely to full service plus impact 10ading on
the superstructure. This crack pattern had essentiaIly developed at a shear of 870 kN, and as the
load was increased to 1120 kN, the cracks grew in width aIone. It can be seen from Fig. 3. 12(b)
that ends A and B had maximum diagonal crack widths of 0.20 and 0.25 mm, respectively, even
though end B had a larger amount of uniformly distributed reinforcement Cp = 0.003), than end
A (p = 0.0018). At this load level the maximum flexuraI crack width was 0.20 mm. It is noted
that the maximum diagonal crack width and the maximum flexural crack width were about the
same, and both are within acceptable limits for this member containing epoxy-eoated bars

As the shear was increased beyond 1120 kN, it was observed that cracks had formed at
nearly every hoop location along the bottom of the beam. Figure 3. 12(c) shows the crack pattern
at a shear of 2510 kN, corresponding to general yielding. The diagonal cracks had a maximum
width of 1.00 and 0.60 mm in ends A and B, respectively. For this loading case, well above the
service load range, the higher percentage of unifonnly distributed reinforcement in end B
provided better crack control. Minor crushing at bath re-entrant corners was observed at load
levels slightly higher than generaI yield.

The crack pattern at maximum shear is shawn in Fig. 3.12(d). In end A, a new major
diagonal crack formed with a width of 2.20 mm, while two existing diagonal cracks, aIso had
widths greater than 2.00 mm. Two of these cracks delineate the "bulging" of the newly formed
strut in end A (see Fig. 3.12(d».

At failure, a new 3.00 nun wide diagonal crack opened suddenly, delineating the strut
between the re-entrant corner and the bearing in end A, as shown in Fig. 3. 13. This was
followed immediately by major crushing near the re-entrant corner of end A (see Fig. 3.13).

(
70
 ~ ~

2V

·1

-l' ~ .'

l' 1

J f

1;
,. tt " 1
~,..,

':'t
o o
o01 o01
v (a) V =430 kN (superstructure dead Joad;: 460 kN) V (b) V;: 1120 kN (full service + impact;: 1140 kN)

~
l ,
" .q
1. -f

lf +~

...o ~
o
...
01

(c) V;: 2510 kN (generaJ yield) (d) V ;: 2920 kN (ma)(imum shear)

Figure 3.12 Development of cracks in CAPN (crack widths given in mm)

(

Figure 3.13 CAPN after failure

(
72
 3.3.2 Specimen CAPH
(
Figures 3. 14(a) and (b) ilIustrate the change in cracking pattern and crack widths which
were measured for the HPC specimen CAPH over its full service load range. First cracking of
specimen CAPH occurred in end A at a shear of 490 kN, slightIy higher than 460 kN, the load
corresponding to the superstructure dead Joad. This f1exural crack propagated from the bottom
of the specimen, in Hne with the column face, over a distance of approximately one-half metre
(see Fig. 3.14(a». This behaviour is typical of HPC as large amounts of energy are released
upon initial cracking due to the elevated tensile strength of the concrete. At a shear of 570 kN,
the tirst flexural crack in end B had formed in line with the column face. Figure 3.14(b) shows
the crack pattern at a shear of 1120 kN, which corresponds closely to full service load plus
impact loading on the superstructure. This crack pattern had essentially developed at a shear of
890 kN, with the only change taking place. as the [oad was increased to 1120 kN. being me
widening of the cracks. It can be seen from Fig. 3.14(b) that end A had a maximum diagonal
crack width of 0.45 mm. which is greater than permissible lirnits. The maximum diagonal crack
width in end B was only 0.25 mm, indicating that the higher percentage of uniformly distributed
reinforcement in this end provided sufficient crack control. The maximum flexural crack width
was 0.25 mm at mis load level, and splitting cracks could be observed along the main tension tie.

As the shear was increased beyond 1120 kN, nearly every hoop location along the bottom
of the beam had attracted a crack. Figure 3 .14(c) shows the crack pattern at a shear of 2620 kN,
the load corresponding to general yielding. The diagonal cracks had a maximum width of 1.25
and 0.60 mm in encis A and B, respectively.

The crack pattern at maximum shear is shown in Fig. 3.14(d). In end A. a new major
diagonal crack formed with a width of 1.25 mm between the re-entrant corner and the support
of end A. Just before failure occurred, minor crushing at both re-entrant corners was observed.
and a horizontal crack at the top of the cap beam directly under the column formed.

Figure 3.15 shows the crack pattern of specimen CAPH after failure. Failure was caused
by relative shear slip of 8.00 mm a10ng the newly formed diagonal crack in end A. A minor
amount of crushing also occurred near the top of this crack.

(
73
 ~
--
2V

.1' """--

i
1
1.
" 1
.~
1
M
;
1
J!
1 • ,~
1

-.r" i:'.
'i
il '1
o
(;)
(JI

v (a) V =490 kN (superstructure dead load = 460 kN) V (b) V =1120 kN (full service + impact = 1140 kN)
-..,J
J:o,.
l'

,1
1

.... .. ...... 0 ' " "'0 0 0 ......... 000 -'

m
o
oo 0
0
N
(JI
m
0
00 Ut Ut i»
0 (JI 0 00
:... W
(JI 0
NON
(JI
0 (JI
:." NW
0 (JIO
b
o
(c) V = 2620 kN (general yleld) (d) V = 3000 kN (maximum shear)

Figure 3.14 Development of cracks in CAPH (crack widths given in mm)

(

Figure 3.15 CAPH after failure

(
75
 CHAPTER4
(

COMPARISONS AND ANALYSES OF RE8ULTS

4.1 Comparison of Responses of Normal- and High-Strength Concrete

Specimens
Load-deformation responses of the two specimens are compared in Fig. 4.1. First
flexural cracking occurred at a shear of 430 kN for the normal-strength concrete specimen.
CAPN, and 490 kN for the high-strength concrete specimen. CAPH. The first diagonal cracking
in CAPN occurred at a shear of 870 kN, while the first inclined crack CAPH occurred at a shear
of 890 kN. While the high-strength concrete had about twice the compressive strength of the
normal-strength concrete. it is somewhat surprising that CAPH had only marginally higher
cracking loads. [t is important to realize that at the time of testing, the shrinkage strains in
specimens CAPN and CAPH were about 320 and 420 microstrain, respectively (see Fig. 2.3(b».
The higher expected restrained shrinkage stresses in specimen CAPH would cause a larger
reduction in the cracking (oad than that of specimen CAPN.

Specimen CAPN reached general yield at a shear of 2510 kN and exhibited a

displacement ductility, defined as the ultimate deflection divided by the yield deflection (du! dy).
of 3.4. Specimen CAPH exhibited a slightly stiffer response than specimen CAPN and yielded
at a shear of 2620 kN. However. this specimen was considerably less ductile than CAPN.
achieving an ultimate detlection of only 2.3 times ây. The failure of the normal-strength concrete
specimen was caused by crushing at the re-entrant corner of end A. followed by shear slip (see
Fig. 3.13). The high-performance concrete pier cap failed by shear slip along a diagonal crack
extending from the re-entrant corner to the support of end A (see Fig. 3.15).

Steel strains in cantilever ends A of bath specimens were generally slightly greater than
those of ends B. The strains measured on the tension tie reinforcement at the inside edges of the
bearing pads were significantly lower than those measured in line with the column faces. This
curtailment of stresses in the main tension tie is described in section 1.7. 1. The steel stresses
measured at the inner edge of the bearing in end A of each specimen was typically 69 % of those
measured in line with the column faces after significant cracking had occurred. In end B of each
( specimen, the stresses at the inner edge of the bearing were approximately 63 %. representative

76
(

3,500

_.' shearslip CAPN

3,000 ..-Jb41-----U- crushing and CAPH
shearslip

2,500

--
z
~

~
2,000 ,..
-- "l
cu /
al
L:- 1,500
w 1
/
1.000
1
1
500 .1
J
{

0 5 10 15 20 25
centre deflection (mm)

Figure 4.1 Comparison of load-deflection responses of specimens

(
77
 of the higher ratio of vertical distributed reinforcement. Most of the strain gauges located on the
( distributed reinforcement did not register large strains as they were located just outside the region
of significant diagonal cracking.

By comparing the horizontal strains at mid-height for specimens CAPN and CAPH (see
Fig. 3.4(a) and Fig. 3.9(a». at a load level corresponding to full service plus impact loading. the
following observations can be made:

1. End A of each specimen. which contained a distributed reinforcement ratio of 0.0018,

had a maximum horizontal strain in the cantilever portion of 1.6 millistrain.
2. End B of each specimen, containing a distributed reinforcement ratio of 0.003. had a
maximum horizontal strain of 1.1 millistrain for CAPN and 1.2 millistrain for CAPH.

At higher load levels the differences between these horizontal strains at mid-height of
ends A and B for both specimens became more significant.

The rosettes of specimen CAPN indicate that after cracking and up to a load of about
2700 kN the principal tensile and shear strains in ends A and B were virtually the same (see Fig.
3.5 and 3.6). At loads higher than 2700 kN, general yielding of the reinforcement resulted in
very large principal tensile and shear strains in end A. The angle of minimum principal strain
determined from rosettes A7 and B7 were roughly 45 0 • Principal tensile strains determined frOID

rosette A7 of the high-performance concrete specimen, CAPH, were considerably greater than
those detennined from rosette B7, while the shear strains were virtually the sarne in the two ends
(see Fig. 3.10 and 3.11). The angle of minimum principal strain determined frOID rosette B7 was
slightly steeper than that of A7.

Figure 4.2 compares the flexural crack widths measured at the level of the tension tie in
the normal- and high-strength concrete pier cap specimens. Crack widths are slightly higher in
the high-strength concrete specimen due in large part to the greater release of energy upon initial
cracking. Figure 4.3 compares the diagonal crack widths measured at mid-height of the normal-
and high-strength concrete specimens. It is clear that crack widths are considerably larger in end
A of the high-strength concrete specimen than in the nonnal-strengili concrete specimen, while
the crack widths in end B of each specimen are roughly the same.

Figures 4.4(a) and (b) compare the maximum diagonal crack widths in ends A and B of
specimens CAPN and CAPH, respectively. There was not a significant difference between the
crack widths of the two ends of CAPN under upper serviceability conditions (refer to Fig.
3. 12(b», and they were ail smaller than required by code limits. However, at higher load levels,
( the extra reinforcement in end B caused a moderate improvement in crack control over end A.

78
 ~ ~

3,500 3,500

3,000--- 3,000 --------- -------

2,500
""
2,500
----~-~

,. - -- ----
(

~
Z 2,000 }
C 2,000 l
/
iü t'
m
~
1,500 ~ 1,500 1
III III
/
1,000 1,000 1
1
CAPN-A / CAPN·B
500
CAPH-A
500
oJ
--
CAPH-B
---
0 0.5 1.0 1.5 2.0 o 0.5 1.0 1.5 2.0
maximum crack width (mm) maximum crack width (mm)

(a) Maximum crack widths

~ 3,500 3,500
\0
3,000
........::=---~.--- - -- .... ....
3,000
p--- - ......
......

2,500 2,500
Z
~ 2,000
Z
~ 2,000 1
...ftJ ...ftJ J
CI) CI)
~ 1,500 .&:. 1,500 ,/
III en 1
1
1,000 1,000
CAPN·B
500 500 --
CAPH-B
---
2 e 0 8 10
° 4
sum of crack widths (mm)
6 10 2 4
sum of crack widths (mm)
6

(b) Sum of crack widths

Figure 4.2 Flexural crack widths measured at the level of the tension tie in specimens
 ~
--
3,500 3,500

3,000 3,000
---- 1 1
2,500 2,500

Z
~ 2,000
Z 2,000
~
iü iüQ)
~ l,SaD oC 1,500
III III

1,000 1,000
CAPN-A CAPN-B
500 ---+------1 500
CAPH-A CAPH·B

a 0.5 1.0 1.5 2.0 0 0.5 1.0 1.5 2.0

maKimum crack width (mm) maximum crack width (mm)

(a) Maximum crack widths

OC! 3,500 3,500

0

t---- y ,....--
3,000 3,000
_i-""'" - .-

~
r--- ~

J'
2,500 2,500

Z
~

j
III
2,000 .

l,SaD

1,000
7:'
]/
J
1
1
Z
~

m
oC
III
2,000

1,500

l,DaO /
CAPN·A CAPN-B
500 --
CAPH·A
500 --
CAPH·B
1 1 1
--- ---
0 2 4 6 8 10 a 2 4 6 8 la
sum of crack wldths (mm) SUffi of crack wldths (mm)

(b) Sum of crack widths

Figure 4.3 Diagonal crack widths measured at mid-height of specimens

( 3,500

nn_l -11_----
3,000
-~ =o05l'- - ~__-I---------1'
2,500

-z
-
.:tt::.
~

ro
Q)
2,000

L:; 1,500
Ul

1,000

o 0.5 1.0 1.5 2.0

maximum diagonal crack width (mm)

(a) Normal-strength concrete specimen, CAPN

3,500 r-------~-----~-----r___----.....,

3,000 .. ------~f----_-------=Jlb-c-=-------t=::::;;::;::==----=· =..c

2,500 t-------+---~-:::::-----+-~"'----______II__----_t

-
g 2,000 J-------.........;..-~..::::.-----+-------+__-----_I

1,500 -~--I----~+--------j-------t------I
(

o 0.5 1.0 1.5 2.0

maximum diagonal crack width (mm)

(b) High-strength concrete specimen, CAPH

Figure 4.4 Influence of distributed reinforcement ratio on crack control

(
81
 Alternatively, a significant difference in crack control perfonnance of the (wo ends of CAPH
( could be observed at full service plus impact loading. A diagonal crack in end A had already
opened up to 0.45 mm, while the cracks in end B were weIl controlled (refer to Fig. 3.14(b».

ft is interesting to note that the high-strength concrete specimen has a post-cracking

stiffness which is only slightly higher than mat of the normal-strength concrete specimen (see Fig.
4.1). This resu1t is somewhat surprising since the tensile strength of the high-strength concrete
is about 1.6 times the tensile strength of the normal-strength concrete (see Table 2.3). The
reduced tension stiffening observed in the high-strength concrete specimen may be due to the
greater tendency for bond splitting cracks as cao be observed by comparing the crack patterns
of CAPN and CAPH (see Fig. 3.13 and 3.15). Azizinamini et al. (1993) have postulated that
high-strength concrete, due to its higher compressive strength, develops higher, more localized
bond stresses. This, together with the fact mat the bearing capacity of the concrete is related to
Je' whereas the tensile strength is related to Jfc' ' results in bond splitting of the concrete before
a uniform bond stress can be achieved. Abrishami et al. (1995) concluded that the presence of
epoxy-coating on reinforcement results in fewer flexural cracks, larger crack widths, more
splitting cracks and decreased ductility. In addition, Abrishami and Mitchell (1996) concluded
that bond splitting cracks reduce the tension stiffening in the concreœ and that after significant
deformations in the post-cracking range, the tension stiffening ofh.igh-strength concrete specimens
approaches that of normal-strength concrete specimens. The effects associated with the use of
high-strength concrete in combination with the use of epoxy-coated reinforcing bars has resulted
in a reduced tension stiffening, fewer flexural and diagonal cracks, bond splitting cracks and a
lower ductility.

c
82
 4.2 Predictions of Results
(
A number of different types of predictions were carried out to detennine the response of
the specimens tested.

4.2.1 Applicability of Plane-SectioDS Analysis

Although plane-sections analysis is not applicable for predicting the responses of disturbed
regions. it is of interest to compare the predicted cracking loads. using this method. with the
measured cracking loads.

The predicted shears corresponding to first flexural cracking, at mid-span of the

specimens. from plane-sections analyses were 462 kN and 66 L kN for specimens CAPN and
CAPH. respectively. These values are significantly higher than those measured during testing,
that is, 430 kN for CAPN and 490 kN for CAPH. The key reasons why these predictions are
unconservative are that the strain distribution in disturbed regions is significantly non-lïnear and
that concrete shrinkage strains were not given any consideration. The computer program
RESPONSE (Collins and Mitchell 1991) was used to carry out the sarne predictions including the
effect of concrete shrinkage strains. The shears corresponding to first flexural cracking including
shrinkage strains were predicted to be 304 kN and 476 kN for specimens CAPN and CAPH.
respectively. which are conservative predictions.

4.2.2 Simple Strut-and-Tie Models

Simple strut-and-tie models were developed to estabHsh preliminary predictions of the pier
cap yield strengths (see Fig. 4.5 and 4.6). Both specimens were govemed by yielding of the
main tensile tie. The main tension tie, which consists of 10 No. 25 bars with a yield stress of
468 MPa. has a yield force of 2340 kN. It is assumed that the Hnes of action of the diagonal
struts intersect the lines of action of the compressive resultants in the column (Le., at the quarter
points of the column). From equilibrium, the shear which corresponds to yielding of the main
tension tie is 1995 kN for specimen CAPN and 2050 kN for specimen CAPH (see Fig. 4.5 and
4.6). In these predictions, the material reduction factors were taken as 1.0. These models are
simple and no consideration is given to any strength enhancement provided by the distributed
reinforcement, particularly the horizontal bars. The predictions are therefore conservative.

(
83
( 2V = 3990 kN

et = 0.85(37.6 M a)(750 mm) = 98 mm

d= 997.5

T = 2340 kN
41.9°

v= 1995 kN v = 1995 kN
Figure 4.5 Simple strut & tie model for specimen CAPN

2V = 4100 kN

92S------l
..---------,"'-..;._...-'c'-~-----......--t------.-l-

d= 997.5

DI"-.,,-tt:- T-=-23-4-0-k_N_--------~~ 41.90 ,

v= 2050 kN v= 2050 kN
Figure 4.6 Simple strut & tie model for specimen CAPH
(
84
 4.2.3 Refined StnIt-and-Tie Models
(
The refmed strut-and-tie models shown in Fig. 4.7 and 4.8 account for the contribution
of the crack control reinforcement to the strength of the specimens. In addition ta the main
tensile tie at the bottom of the specimens~ additional ties are provided to represent the horizontal
and vertical distributed steel. These secondary tension ties are positioned at the centroids of the
effective horizontal and vertical uniformly distributed reinforcement. The refined strut-and-tie
models shawn in Fig. 4.7(a) and 4.8(a) model the response ofeach specimen as though they were
reinforced throughout with a reinforcement ratio of 0.00 18 for the distributed steel. These
details~ which were used in encis A of both test specimens. are modelled by a secondary
horizontal tension tie (4 legs of No. 15 bars) with a yield force of (800 mm2)(419 MPa)=340 kN
and vertical tension ties (3 sets of 4 legged No. 10 hoops) at each end with yield forces of (1200
mm2)(441 MPa)=530 kN. The predictions obtained from Fig 4.7(a) and 4.8(a) are representative
of the weaker side of each specimen and hence should be used when comparing with the actual
strengths. The refined strut-and-tie models shown in Fig. 4.7(b} and 4.8(b) model a distributed
reinforcement ratio of 0.003. which is the same reinforcement ratio contained in ends B of
specimens CAPN and CAPH. The yield forces of the horizontal and vertical tension ties in Fig.
4.7(b) and 4.8(b) were calculated to be 670 kN and 880 kN~ respectively. The predictions
obtained from Fig. 4.7(b) and 4.8(b) are presented in arder to demonstrate the how the strengths
would increase if the larger amount ofunifonnly distributed reinforcement (Le.• a ratio ofO.D03)
were present throughout the specimens.

The changing inclinations of the main diagonal struts in Fig. 4.7 and 4.8 are induced by
the presence of the vertical and horizontal distributed reinforcement. The tensile forces result
in discrete angular changes at the nodes where the secondary tension ties intersect the struts. The
resulting arching action provides steeper struts above the supports. ultimately resulting in higher
strengths. If more distributed steel were present. then the arching action would be even more
pronounced (see Fig. 4.7(b) and 4.8 (b».

This more detailed strut-and-tie model gives a better representation of the flow of
compressive stresses. The modelling of the flow of compressive stresses from the column into
the cap beam results in higher localized compressive stresses near the re-entrant corners and
secondary struts which represent the fanning compressive stresses anchored by the vertical
unifonnly distributed reinforcement. A comparison of Fig. 4.7 with 4.8 iIlustrates that the struts
for the high-strength concrete specimen are considerably smaller than those in the nonnal-strength
concrete specimen. This effect gives a slight increase in the capacity for the high-strength

( concrete specimen.

85
( 2V=4820 kN

T = 340 kN

T= 530 kN

_~,--_ _... T_=_2_3_4_0_k_N ----J"'__~~. 50.10

v = 2410 kN v= 2410 kN
(a) End A details

T = 670 kN

_-:-f:....---IIoL-------T-=-2-3-4-0-k-N-----~---~~. 54.8
0

V= 2540 kN V=2540 kN
(b) End 8 details

( Figure 4.7 Refined strut & tie models for specimen CAPN

86
 2V= 5120 kN
(

T = 340 kN

T = 530 kN

..,.'--_ _....... T-=-2-3-40-kN_----~t__--~ __ 51.2°

v= 2560 kN V= 2560 kN
(a) End A details

2V = 5420 kN

T = 670 kN

T =880 kN
~,--_ _..... T-=-2-3-4-0_kN_----~e__--__Jili ..... 55.4 0

v = 2710 kN v = 2710 kN
(b) End B details

( Figure 4.8 Refined strut & tie models for specimen CAPH

87
 Table 4.1 compares the predictions made with the simple strut-and-tie model and the
( refmed strut-and-tie model with the measured values of total load applied ta the pier caps at
general yield. In making these predictions, it was assumed that both encls of the cap beam were
reinforced with the smaller amount of uniformly distributed reinforcement, that is consistent with
end A, since end A will give a lower predicted load. It is apparent tbat the refined strut-ad-tie
models give excellent predictions of the load at general yielding. Accounting for the uniformly
distributed reinforcement can significantly increase the predicted yield load, while giving slightly
conservative predictions. It must be pointed out that the actual failure loads are somewhat higher
than the general yielding loads due to strain hardening in the reinforcement. The predictions
made with the strut-and-tie models neglected the effects of strain hardening.

Measured Simple Strut-and-Tie Refined Strut-and-Tie

Load at
Specimen Predicted Measured Predicted Measured
Yield
Yield Yield
(kN) Predicted Predicted
(kN) (kN)

CAPN 5020 3990 1.26 4820 1.04

CAPH 5240 4100 1.28 5120 1.02

Table 4.1 Comparison of strut-and-tie predictions with measured loads at general yielding

4.2.4 Non-Linear Finite Element Analysis Using Program FIELDS

Figure 4.9 compares the measured load-deflection responses with the predicted responses
obtained by using the non-linear finite element program FIELDS (Cook 1987, Cook and Mitchell
1988) for specimens CAPN and CAPH. ln predicting the responses the cracking stress was
adjusted to account for the size effect of these full-scale specimens. Using a cracking stress of
0.33 Jfc' for these specimens which experience significant diagonal cracking within the cantilever
portions of the cap beams, and assuming that the cracking stress is inversely proportional to the
fourth root of the size, then the cracking stress for these Il ()() mm deep members compared to
the 150 mm deep control specimens would be:

h ] 0.25
fer = [ capbœm 0.33Jf:
h conrrol (4.1)

( = 0.608 * 0.33 Jf;

88
( 3,500
measured
3,000
\ E~~~

2,500
/~
,!

z
~
2,000 ,1
,1 1
il
...eu
11)
..c 1,500
'1
,
,1
,/
1
1
1

'-;
en

1,000 -,./
,'1 )
!
500 Il
/' /
0
1
1

5 10
V
15 20 25
centre deflection (mm)

(a) Specimen CAPN

3,500
1

·Fv
measured
3,000
predicted
- - - --
2,500 .', rI
,'/
z ' 1J
1

\
r;
,

~
2,000 , /
...eu ,'j
11)
..c 1,500 " 11
en

1,000
~:r
// /
t
500 It---------t
/
0
1

5 10
1 15 20 25
centre deflection (mm)

(b) Specimen CAPH

Figure 4.9 Predicted and measured load-deflection responses of specimens

(
89
 As cao be seen from Fig. 4.9 the predicted responses for specimens CAPN and CAPH
( agree very weIl with the measured responses up to loads of 2490 kN and 2670 kN, respectively.
At these load levels. the non-linear analysis predicts local crushing at the re-entrant corner. The
load deflection responses up to cracking and from cracking up to the points where local crushing
is predicted. agree reasonably weil with the measured response. As can he seen from comparing
Fig. 4.9(a) and (b), the predictions over-estirnate the tension-stiffening, particularly for the high-
strength concrete specimen (see discussion in Section 4.1).

In arder to reduce the sensitivity due to local crushing, the elements at the re-entrant
corner were softened by specifying a compressive stress-strain curve having a peak strain equal
to 1.5 times the cylinder peak strain. The fmite element analysis gives an accurate prediction of
yielding, however since the analysis relies on a tangent stiffness mode!. it was unable to converge
after local crushing was predicted.

Figure 4.10 shows the deflected shapes of specimens CAPN and CAPH at the predicted
maximum load levels. It is apparent from this figure that the deformations are not symmetrical
about the centrelines of the pier caps due to the fact that end B of each specimen contains a
greater amount of uniformly distributed horizontal and vertical reinforcement.

Figures 4.11 through 4.16 show the predicted strains and concrete stresses for specimens
CAPN and CAPH at three different load levels. At the lower service load level, that is a total
applied load of 920 kN, for both the normal-strength and high-strength concrete specimens the
stresses are nearly elastic with ooly minor cracking predicted for specimen CAPN. In addition,
no distinct compressive strut action is apparent at this load level (see Fig. 4.11 and 4.12).
Figures 4.13 and 4.14 show the predicted strains and stresses at the upper service load level
corresponding to a total applied load of 2280 kN. Significant principal tensile strains are
predicted in both specimens at this load level. It is apparent that larger principal tensile strains
occur in end A than in end B due to the smaller amount of uniformly distributed reinforcement.

Figures 4.15 and 4.16 show the predicted strains and stresses at the maximum predicted
load levels. It is apparent that the principal tensile strains are larger for the diagonal cracks than
for the f1exural cracks. By observing the flow of compressive stresses it is apparent that more
direct compressive strut action is taking place close to failure. Sorne bulging of the compressive
struts between the column and the reaction bearings is apparent. The high-strength concrete
specimen CAPH exhibits struts having smaller widths and higher compressive stresses. The non-
Iinear finite-element analysis predicts a 7 % higher ultimate strength for CAPH than for CAPN.
The predicted strains in the tension tie for the high-strength concrete specimen are higher than
( those predicted for the normal-strength concrete specimen.

90
 2V=4980 kN
(

displacement scale:
5.00 mm

/
- 1-
-
i i 1 i 1
1

L 1 ! l r---------
T 1
: : -~
1
1 1
i \
i 1 1
-
1
! 1 i --t----~
- .
i
~~C :
1
----L--
i

v =2490 kN v= 2490 kN
(a) Specimen CAPN

2V= 5340 kN

displacement scale:
5.00 mm

V= 2670 kN V= 2670 kN
(b) Specimen CAPH

Figure 4.10 Predictions of deflected shapes of specimens at maximum

( predicted loads

91
( 2V= 920kN

1·1· .. .. ..,.
...
.... - -1- ... 1

suain scare:
.. ... .. .. ,. ... 0.75(10"")
--
.. .. ..,.. ., .. ~

~~.....ç .. ..•.. +
~ ; i + ~ 1
Il

il'
.Ir
··.. ,. •
'+" • ,
f f f ., 1"'~
+1· ·
1

~%%_~
.. .. +• + .,. -;---~L# r;-~
+
< ~---rlll~f:~
:Ir 1 ~ 4l 1 Il Il

· - ~
# 1-
.,.
1-

--.~~ If~I l ·~
..
Il l '"
1t 1 Il 1 1
, -.
1

~ :-t;" + • .,
-" -
·
It~·- _'!.
..
#
" " "
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" % .. 1 #
" It Il Il

!.. "'" .... '" '" .... .... ..

1 1

... ...
1

"- 'll. <lit .w A Il Il /1 III l i li li ~

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'll. 1
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+ ...
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'ft ~ Il

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--·
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1

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V =460 kN v = 460 kN
(a) Principal strains

2V= 920 kN

.-. f f f t .
.. + f + or . stress scale:
SMPa
.,. f f i t -t --
f ~ Je \ \
'J
.,.
~. ---
.......... ... --...... x
/ .;1' ~
• .;- .....
.;('
-,... .,
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..,. +.,. ,....i7~
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.....:""'~.~
". • • ~ ~ ~ ....- x ~ -...... '!lo
.~. r;~~f""':':...
.-. ... •--
<~",,~.
~
,
<'
~.

.. -. . ,.-1 • •
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Jt
JIf
JI('

;r
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}l
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.. ·... ·· · .
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"'-
.....
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·· . · · · ·
....
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... • • Il # Il 1 Il
",. ~ • Il • ~
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... ... . ...
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t-
1

V =460 kN V=460 kN
(b) Stresses in con crete

( Figure 4.11 Predicted strains and stresses in specimen CAPN at a load of 920 kN

92
( 2V= 920kN

!
~ !: ·1· · "*
... ... .. . ~ ... strain scare:
... .. ....
... 1 ... ... 0.75(10-.2)
--
...
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1'" ... ... .... ""

Il

li- Il ] ... - .. 'JI, .... 1 ... ... 1 ..

•
..
1 ...

• + • • • • • .. 1 .. ... Jr
Il
Jt li . . . . Je 1 -\'

V=460 kN
f 1
V=460 kN
(a) Principal strains

2V =920 kN

.~

1 f 1 f f i ""
... of t 1- oi' -to stress scare:
5MPa
.,. i f t Je t --
f- I .,. Je \ \
, ...
.,.+ .,... • )'r--..r---,
/ '\.
~
... ... N "'1.

~
~~). •
:..< ~ ..
~r'~i---·
;.. .: .~ .. -
~- 'C
.
..... .....-;'
\
0\-
itt
lit
0+
~

... • •
......
~

X'
.. x
-----
~

....
X

~
,
... ...
,.ft"

... • -.. ....

..-.
Of.
'#..,
"'-
~
, .,.
~
... ~
-+0

v.. $
f

'" • (~>t~r--,.
- ho-' ,- ----. "

... .. .. .. • ·
• Il X j ;r -1- "'- X '1.
• #1 #1 #1
,,~
.-~

... .. . .
• • · · " ... ... ... • •

.. .. . .
• • "
.. • " , , . . ... -- .. . • .. ...
Il

... .. . "
Il

... ...
'# :Ill a - #1 , li
*'

·· · ... ... •· •· ... ...· · ·· ." .. .... ,.. ,• •• ·• .. ......

- . .
• lit .-

... ·
... . , , ..
• , , , •
, - · ·· ·· . · . .. .. .. · 1
, ·· . "

-· ·• •• ... • . .. .... .. .. . .... .... .- .. "" · · ·. + . "

" · ·
,-
• 1 + f 1 ~ + + ~ ~ \ +
If +
.,. • It:
Jt
1 + ~ \
~ ~+I 1- + + + + + + + ,\~$ "'- ~

V=460 kN
T 1
V =460 kN
(b) Stresses in concrete

( Figure 4.12 Predicted strains and stresses in specimen CAPH at a load of 920 kN

93
( 2V=2280 kN

. + + + + .
· • . .. .. · strain scare:

• ... .. .. • •
0.75{10.,)
--
."
·
.. ·.. •
• ~

...-:- ~*~~
.......... ~ JK
~
•
""
ft
Il
1

•
il' _t-"
J'
" • ... • "
.,...-
~
•
~

...
• ..
'"
+
t
l&.
~
~
--• ...
~
"Ir f

-
• ,
~

1
1-
i-
~?:"
.,. .,. -
...· ·
,-.,' ,;~
~
.~ ... ,,~~ % 11
• ~ • + a ~

~ :--r;" ~ "', , ," .. ...

....j ~ ~
..
+ •
.. · ,..,,--- / ~ • • " , 1"' ..... i- -~-
• , , "'1'" ~ • .ft
,.-
11.1' ·
~ i " -....~
~
, .·.. •
~. i~ ~.
+ .... + ~

... ''lII.i' '" , "j~ ,- ....- "., /./ • , '*

-+ +- +
...
;:0.- ..... f +- Jtr ,fT JI'

.. .
JI'

...
... Il

... ", ~ --f-. ~ ......... "....., V· /./ ... • .. .,. ...

..... ..... ,.., /1/"'- 1/< . ... .
Jr .. j.. '" ,~ + + +
"-
... ,. .... ~.-....«., "- ~ "-+- r-l
"
• ... .. ... I~ . "' ,,-, -r- + +
-+- ~ V ~'
~ .....
V V ..... ....
' .., ...
...
...
JI'

" ... 1" 1-1

'-
• !'-,,; Î"#.. ~
r"-...,

~"- ;:.
":-1-'."-f-+-+-+-f--l-+-,
1
-t- -f- ~
' .. :.,....t-" -\- ;.--r .....l-'
~,""++-
~

....t-
....i-
· ··
,
~+- -+-
1-, :
t-" ~' L.~

·· .
,,:,ç'
1/ '.,< ~ ..
'....... _.\: . ~lf' ~~ +. ,
...
Ir

-T- -1-
• 1 .•

v= 1140 kN v = 1140 kN
(a) Principal strains

2V = 2280 kN

t· T ...,
~
f. l T
't
•
1

·.., ·.J- I, l ... ......·,

,
~
stress scale:

·, 1 ·-· · ,·.
SMPa
.J.
J
-\, --
'f )t X ~ ~ ~~
'/'" lA'" ...-r ~/- ~
"'~ .,.
~-:;.~
~ t"';- +. Yo~
..... "'.;...-:;
,
Ir

-
l '"
N
..\'" ~ 1.--; ~ ~
/
/
. / ;r
- , ,s X
/I~ .-
co

+ \
~
'f.... '-.
~ ~

---...... ~
-f.,
'f..
......
y. "":"'--r-...
-r!.r! ':;;-~
i'r{.! -'rS ~
" "- "
N .,< /" /-'
~.-;-- .. ~. .- /
· · , ...
lit ~~
", -.
.
-."
~ ,'<1' ,t? 1".."/ ;l + \ \. " ..... ~ le. '~.~~

· .. .
.." .. .. ·.. · ,
,," -/'. • • ....

.. · " "
+ ~ ~ ;t ," ,'" ~ '\. ~ Je .. ~ ~

..
j'

/ /
:' ~

.... .. .,.
-+
Jr ...
~

~
~;l

/.1 / /
;l / j/

// / .
, - . •
#>

.. .. .
#
,
+
+ + •
\
'IL .....
X
..\~
'..,.
~
.~
~

\
lt •
\ :lE • .,.
.. --
.. ..~ ...
.• . "- i\\\:C
~,r
...
•.,. f-
,
I/ / "
./
.•.. .. "- + t
.. t + .
% '\

• ··
.... 1/ / ... ~
•
.. . ":\l't ; .
~ t t t %
... . • .. .. ..
-- .
" 1 x ·..
"l /
.
- -
~

f 1 i f .. t .
f
+
f-
~ t
f
+
i- f
...
i t +
...
-t t
~

" " -1-

• ,~' ~
fo

• Ir

V= 1140 kN v = 1140 kN
(b) Stresses in concrete

( Figure 4.13 Predicted strains and stresses in specimen CAPN at a load of 2280 kN

94
( 2V = 2280 kN

. ···· ..Ir

... . -1 •
·· strain scale:
..
· ··* ·
O.75(10-J)
--
.. • • • •
- ... .
... •• •• •• ... ....
~ Il 3C
~...-:; + 1:'-'~
. · . · ·· . • ,,,
:li:' -\- '" ! •
N f -+
-. • • • •
~+- .Ir
" , l" ~ '1/1:
.. • .
a Il
, #
~
,.- #~~
- - 1If~
- li ';t~ '1/1: i"":::---
~~~
"- ~ ~f~
1t 1l
, ,. • 1"'", ' .......
• 1
, ,
"1 "-". If -:.__ Jt

· .."" . • • • · .
" If l'--c_
~~Jt ,'Il,'lL ~ + Jr ..-' ~ . Jt--~
-.

.. " " lt

~ .. 1". 'lL ...

"1"'1'" ... ... , ......

, 1"---.1',
1 .,
--- _.
""'J "''"t--
· ... --""
• :.-......
/

/1
,
.
tt
,
JI Jlltlt Jt
*'
. , . . . ...
i
+ ft i t + -'" 41._ +
,
JI Jt

..... " l', '---J" 1.. • + + .. ~..-'"

. ",- ""- "'I~

~f---
t ." 1... 1......
~- / 1·' 41 41 .... ..,.

~ . . 1- ... .. -+- _Il t + + + of ~ ~

.,., ,/ .." • ..,. .....
.. 1- "·1, .".~ ~'-. ... +1+ / ,. ·1* .- . ..
. ..
+ ~
""
~ Jr 1- .. . . --.!-,.
#.~ ~ - ..--l--+---""'+- -,,".
.Ir
. -t- -1- -+- -+- _....
,.\ -l-
~ . / ,,:'
-~. ~ ...Je" ..
,ro' ~

~ lt 1. + "...l~ . .
.... 1
- · · · · -+- , · -+- ..;-
1 ~
'1" 'Il
11 il

v= 1140 kN
T 1
v = 1140 kN
(a) Principal strains

2V= 2280 kN

· T, '7
t
'

1
l ·. stress scale:
5M?a

v =1140 kN V=1140kN
(b) Stresses in concrete

( Figure 4.14 Predicted strains and stresses in specimef'\ CAPH at a load of 2280 kN

95
( 2V=4980 kN

,.,
·... .... · ..· .. JI'

...
.. '1·
- ... r ~
strain scale:
3.75(10~)
--
.. .... .. .,.
......... ...-; ,..... • -1 ....
. • •, • -,
JI

3t
.,. ,..
1~
, •.- fi.

• ,
of.

.-
• JI'

. "
'Ilo ." If

• ~r ~
rt~"
~ + ~.~~~
" " -, ~
11. t f 1 fi fi
" .'-.:............ .
, ," Je': -11"
. 'At~
~. - ... ...
--:.'
'!".)!' if ..
" • ... ... ~'
~ 11(

. • • '"
Jr "..' ;1
./
1 ' ~
-. -~
!.
...
.~
'If

~ l"lt
+
_~"Il
" '"'
•
...
.. ·1 " " ....... ~ ~ ~ ,.. • t • •
• ~ ',,- ~ " ~
"Il
• t t •
'" ""
1

.-r
/ 1/"/ .
"
,< ,~" " ,"
,

...
1t
1t •
•
Jé-'~
lr

. '" P
1... Il Ar tt olt If 11( Il

""', ~
,
. . , ....... ...
+ i" ... '\loI ......
... • Ill. ... ... ..., ' - "c. "'- ..... - i -
,'"
'~ ~

~ \
+
...
t
-t
"
-t
...
-t ---
-t I-Y· x
w / /
JI' ./,/ '"
/./ 1 -# JI' JI' Jt
+
.;-
.... 1" . ·-"l' "---, "~
......

~ >--l-~ .li' K .... + + + ~~-- ~ ~ ... " /~/ /< , • <r .,.
.
,If
'4
... j. r-. ~', ' .. ~, -'.!-f- -1- -\- -\- ..... -\- *1- +- -\- ·\-1.-- ,'(' . / i/" ." ~ .. -1 + rt
'"
11. JI' 1. 1-«- " "'~I-l-- -f-- -~-r-f- -+- -1-- -1-- -l-I-+- -+- -i-- -1--1-\-1·\' .r1('" ,w:" f''' "·1'" ~

-T- t
V =2490 kN V= 2490 kN
(a) Principal strains

2V=4980 kN

f- f f t t · -t stress scale:
20MPa
f 1 i \ \ .\;

. . .v- :x ....... ..... ..

.
;~
./ x
/
~ .......
......... .............
--- ...
,
~

,
+1+ ...
• " • ",,< -" ..-• /'1(" .... 0+-
~

.
~ ":""1-.. .".
~ ~ '#.,. ~

)(
.~ ~x/
/""11.

/ .. / .. ;1 • , •
If
~< ~

•
•
.. ~
• X
~ X ""-
X ~
, ~ · .. ·
..
.« ,..: ... +
+ + .- ; ' 4"~ ,-" ~< ...
~ • of t
..
~ +
.
...'" ... ·
.
~ X
~
~
,~

+ +
... "4
,
. )f
;il" "
;(1/
"#. ~

~ ,
~'t(

...
• ... ~;t ,,'" ~ , , • ... .... op
...
op#
•
+ ...
.. #
li
-
.
. .. .. ..
.. • .. "
~ ~

~
• ~

•
'..." ~ JI JI
""
li:
·
ri! ~..: / p -+ 1- ~
"
~

..- .. +.. + ·+ . .. .."

... 10 4'

" · -1-
~ + ;t _1 10 -p -PI+ ...
~

V =2490 kN V=2490 kN
(b) Stresses in concrete

( Figure 4.15 Predicted strains and stresses in specimen CAPN at a Joad of 4980 kN

96
( 2V= 5340 kN

.... .. .. • .. '*
................. suain scaJe:
3.75(10 4 )

.., •
• ,+ +. ..
# ~

~~
Jt .li'
<tj.;l'l :.tIJt_~
... ... , -, , ",, ·. ..
-,...-;
-
...
+

~
1 + ...
"" te...... 1 ~
%
-I~
~
Ir

"" .,.
i-
"JI,
f-
f
...
..
f

Jt

,:!-!--_ ~ 1~
. .• - •
- '~ ......
~f--
·
...
""
• " ,t
to ...

"" "
'f '1- .,. 1& " 11>

~ i- .,.1 ....... .... " "___, '" l'-c- - f- ~ • + i

....
.
+ ""'ll. .... --.. ....., ' ___. " ~ -1-- ,-aL. • i
••
Jr
...
"" ......
., ''--f.-l..........-
....... !"
.. r-. .....- ' " ' " ~ ~-+- .
~ ".c..,.f"'''' .
--.Jl..- -t + +
.... -+ . of

"
t .... X
.....: :--.... '*-.. -I.r-..-- ....- ..Y'
"
~ -\- 4- .1-

... "" i'f :--... ~ .-

..-~ r- ·

v= 2670 kN
T
V=2670 kN
T
(a) Principal strains

2V= 5340 kN

L
, ,
l-
• f T ~

·/ -;f :.:. \. ·.. l

,
+ ./. 1r stress scale:
20MPa
! ~-

".. .'
..

--.. --........... --.......... -......

....r .~ ~ "
'fi' ..-~ j--..." c,.

........... ., 1- .. 1"'" ,Y "Y '-1..... ............. -/, , • .... ~:--:-.

~ __,.... Ir-'-
Ir

. ·..
,"'"
..
.... 11 :" ;f '.t .~
'«... ~ ~
~~~
" ";:-
- · • ·• ,
'.

~ Ir_" !. -: ---.; 't ;< /..( 1& ~ ~- '-.. ~ -;-~.~ $~--~

/1,(
"
~

. .. .
""
"_
11

'1 ...
...
Il
~

;< ~..( /"

,01'
/ " ....
/
/
,,-.(
~
.,. ·.. ·, ... "t ..
··..
~
•
~
~
"

'"\ X
",,- ~

~ x ...
Il
• "Il '" I--~_ ~--!
:lE
.~

...
-~

.. - ;t ,,"" / • .. • • • '.<. ~ X
f .. ".-.t / + t :(. % .. •

.,
i- Jl .JI' 1& +
.. .
.. 1

.. ... ... ~~ , '!<! )t .... op

• • • • •. • ~ \. ~ X ~ :li: • •
.. .
• ·..
• '1 a:t ~-l / / " ;( .... ... •
1& • • .... • ~ ~ \. \ ~ • +
+ ... "II
. f ir l
,(')l , "

·• ,.""
... li. ...
·
... . • •
• •
+ • •
f .t- If , Il ~ ~ \\Jt .-
.. .
~

..• • " •
~ )f • "1- t ... ... • X \~~
Hf ;1 li + 1- ~ ... ... ...
1- f- + + 4- Il \- f ....
" Jr 4t

V=2670 kN
T
V=2670 kN
1
(b) Stresses in concrete

( Figure 4.16 Predicted strains and stresses in specimen CAPH at a load of 5340 kN

97
 Figure 4.17 shows the development of stress in the main tension ties of specimens CAPN
( and CAPH. Stresses are plotted at applied shears of 460 kN and 1140 kN (the service load range
bounds). 2000 kN and at the maximum load predicted by the finite element analyses. The
predictions for both specimens indicate a significant stress drop-off within the region containing
the confinement reinforcement provided by the column ties. The measured strains are typically
somewhat higher than the predicted strains. It must be pointed out that the predicted strains
shown in the figure are "average" strains and therefore would be less than the strains measured
at or near cracks. The non-linear fmite element analyses provided excellent predictions of the
strains in the main tension tie at the inner edge of the bearing. The presence of unifonnly
distributed reinforcement results in a drop-off in stress from the location of maximum moment
towards the inner edge of the bearing. As can be seen from the measured and predicted stresses
the tension tie force decreases for locations close to the bearing due to the contribution of the
vertical uniformly distributed steel. The larger amounl of vertical reinforcement in end B results
in reduced force demands on the tension lie at the inner edge of the bearings. (see Fig. 4.(7).

Figure 4.18 compares the predicted stresses in the main tension tie using fmite element
analysis and refined strut-and-tie modelling with the stress computed from the measured steel
strains at maximum predicted loads. It can be seen that the reflned strut-and-tie model gives
reasonable predictions for these stresses.

Table 4.2 compares the predictions made using the refmed strut-and-tie model and the
predictions from the non-lînear fmite-element analysis with the measured values of total load
applied to the pier caps at general yield. Although the non-linear finite element analysis gives
slightly better predictions. the refined strut-and-lie model compares exceptionally weil with this
more sophisticated approach. It must be pointed out however that the non-linear finite element
analysis is capable of predicting strains and crack widths al service load levels.

Measured Rermed Strut-and-Tie Finite Element

Load at
Specimen Predicted Measured Predided Measured
Yield
Yield Yield
(kN) Predicted Predided
(kN) (kN)

CAPN 5020 4820 1.04 4940 1.02

CAPH 5240 5120 1.02 5240 1.00

Table 4.2 Comparison of refmed strut-and-tie predictions and non-linear finite element
predictions with measured loads at general yielding
(
98
( 2V

measured
1 1

predicted
- - - --

400 ----- ...

~ ~---,-:.L-_----~---~--.__,""-=_....,_=-=_-_--;:----~---"':::-o;=---------~

lU ,
a.
6 300
c_~_,!-.~,- __-~_ - - ---------------="--~-- __.._.__._~_":_:_:_:;-~-~~"""""'o:----.~------I
en
en ,, , ,
,,,' '
~
200
iii
100 ,,
,'- ----=-----------~---~
0

v v
(a) Specimen CAPN

2V

measured
1 1

500

cu
400
--------
a. 300
~
en
en
--- -------
~
200
i.ii
100 ---
0

v v
(b) Specimen CAPH

( Figure 4.17 Predictions of stress development in main tension ties

99
( 2V=4820 kN

measured

finite element

refined strut-and-tie

500

400 1 7
- - - -+ -...=.>-~,--= --------- ------.
-------- -----;::.~'-------------I
ca
a.. ,/
300
~
lI:I Il
lI:I 1
~
200 1
iii /
100

v = 2410 kN v = 2410 kN
(a) Specimen CAPN

2V= 5120 kN

•
1

measured

finite element

refined strut-and-tie

500~------- ---------------------------.=...,

ca
.... _---,.",-
400 J------l'F--:.;;:.-~=~=':...;~::..------::O"-_..=_----_=__--...._::~=-_=:::::=__----~
Q.
~ 300
lI:I
~ 200J----fLJ1-...---------------------------l+--~

ëii
100
O~-.c:...,..__II..-.,...."...,.----:,.,...___"_..".....,...::_____:'.......,===~=======~==.......,,,....=~~_____,~-~

v =2560 kN V= 2560 kN
(b) Specimen CAPH

c Figure 4.18 Predictions of stress development in main tension ties at general yield

100
 4.3 Estimates of Crack Widths
(
Tables 4.3 and 4.4 compare the measured principal tensile strains and crack widtbs with
those predicted using the results from the non-linear finite element analyses. The crack width
predictions were made for bath flexural and diagonal cracks. The expected flexural crack widths,
w. were determined from:

Wm = fcfsm (4.2)

where: Ecf = maximum predicted principal tensile strain at the level of the main tension tie.
= average crack spacing predicted from CEB expression (see Section 1.9).

The expected diagonal crack widths were determined from:

(4.3)

where: Ecf = maximum predicted principal tensile strain at mid-height of pier cap.

The predicted average spacing, smtJ. of the diagonal cracks is determined from (Collins and
Mitchell 1991):

sine + COS8] -1 (4.4)

[
Smz smv

where sna and smv are the crack spacings indicative of the crack control characteristics of the
horizontal and vertical distributed reinforcement, respectively. For sirnplicity smz and S mv were
taken as the spacings of reinforcement in the two directions and the angle of principal
compression, 8. was assumed to be 45 0 • In addition, the predicted crack widths were multiplied
by a factor of 1.2 to account for the influence of epoxy coating on the reinforcement (Abrishami
et al. 1995).

As can be seen from Table 4.3, the flexural crack widths predicted using non-linear finite
element analyses compare very weIl with the measured maximum crack widths.

The predicted widths of diagonal cracks can vary considerably from the crack widths
observed (see Table 4.4). One concem is that when applying normal procedures to the high
strength concrete specimen. the principal tensile strain and the crack width may be
underestirnated. This may be due to the larger energy released when cracks fonn in high-strength

c concrete members, which can lead ta the formation of longer and larger cracks. In addition this

101
 Load
( Specimen
(kN)
Epndi&ud
(10-;
EIMasund
(10-;
WpntlicUd
(mm)
WIMasurm
(mm)

CAPN-A 920 0.169 0.291 0.05 0.05

Sm = 248mm 2280 0.805 1.134 0.24 0.20
CAPN-B 920 0.107 0.144 0.03 0.05
Sm = 248 mm 2280 0.704 1.000 0.21 0.15
CAPH-A 920 0.037 0.064 - -
Sm = 248mm 2280 0.704 1.087 0.21 0.25
CAPH-B 920 0.037 0.067 - -
Sm = 248mm 2280 0.562 1.068 0.17 0.20

Table 4.3 Comparison of predicted and measured crack widths and principal tensile strains
in the main tension tie

Specimen Load EprtdiC1td EIMasurtd wprtdiœd wnuasurm

(kN) (loJ) (loJ) (mm) (mm)

CAPN-A 920 0.025 0 - -

sme=210mm 2280 2.174 2.459 0.55 0.30
CAPN-B 920 0.030 0 - -
sme= 124mm 2280 0.985 1.953 0.15 0.25
CAPH-A 920 0.019 0 - -
sme=210mm 2280 1.638 2.203 0.41 0.45
CAPH-B 920 0.019 0 - -
sme= 124mm 2280 0.585 1.096 0.09 0.25

Table 4.4 Comparison of predicted and measured diagonal crack widths and principal
tensile strains at mid-height

phenomenon may be due to the fact that the tension stiffening in high-strength concrete members
tends to approach that of norrnal-strength concrete members after significant cracking has
( developed (see Section 4.1).

102
• CHAPTER5

CONCLUSIONS

The conclusions arising from this research project are summarized as follows:

1. A reinforcement ratio for the unifonnly distributed steel of 0.002 was sufficient to control
cracking over the depth of the normal-strength concrete pier cap specimen. This amount
of reinforcement is required in the 1994 CSA Standard for controlling cracking in
disrurbed regions. Side A of the normal-strength concrete specimen contained a
reinforcement ratio of 0.00 18. and exhibited adequate crack control at service load levels.

2. A uniformly distributed steel reinforcement ratio of 0.003 was necessary to adequately

control cracking over the depth of the high-strength concrete pier cap specimen at service
load levels. F0r the high-strength concrete specimen. initial cracks tended to be longer
and wider than those observed in the nonnal-strength concrete specimen.

3. The high-strength concrete specimen had a slightly higher strength than the normal-
strength concrete specimen due to the smaller compressive struts in the high-strength
concrete pier cap. leading to a slightly larger effective depth. The high-strength concrete
pier cap specimen exhibited a 32 % lower ductility than the norma1-strength concrete
specimen.

4. Both the normal- and high-strength concrete specimen exhibited cracking loads which
were influenced by the large size of the specimens and by the restrained shrinkage
stresses. The cracking load of the high-strength concrete specimen was only slightly
higher than that of the normal-strength concrete specimen due to the higher shrinkage
strains experienced in the high-strength concrete.

5. Simple strut-and-tie models provided conservative estimates of the strength of the pier cap
specimens.

6. Retined strut-and-tie models which sirnulate the effect of the horizontal and vertical
distributed reinforcement, provided better estimates of the general yielding load of the
specimens than the simple strut-and-tie model. In the refined stmt-and-tie model, the
( inclusion of the horizontal tension tie representing the uniformly distributed horizontal

103
 reinforcement significantly increases the strength prediction. The vertical tension ties
( representing the uniformly distributed vertical reinforcement reduces the required force
in the main tension tie near the support bearings.

7. The predictions using non-linear finite element analyses gave accurate predictions of the
variation of stress in the main tension lie and provided a means of assessing the principal
tensile strains and crack widths at service load levels.

8. Reasonably accurate predictions of flexuraI crack widths were made by applying the usual
crack spacing assurnptions to the principal tensile strains abtained from the non-linear
finite element analyses.

9. More research is required ta accurately predict the inclined crack widths in very large
disturbed regions and to praperly account for the influence of high-strength cancrete on
inclined crack widths.

(
104
 REFERENCES
1
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Abrishami, H. H. and Mitchell. D. (1996), "influence of Splitting Cracks on Tension

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lOS
 Collins, M. P. and Porasz, A. (1989), "Shear Design for High Strength Concrete", CES
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 Mast, R. F. (1968), "Auxilliary Reinforcement in Concrete Connections", Proceedings
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3rd German edition by E. P. Goodrich, McGraw-Hill Book Co., New York, 1909, 368 pp.

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New York, 1975, 769 pp.

Popovics, S. (1973), "A Numerical Approach to the Complete Stress-Strain Curve of

Concrete". Cement and Concrete Research, Vol. 3, No. 5, May 1973, pp. 583-599.

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562-571.

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Schweizerische Bauzeitung, Vol. 33, No. 7, Feb. 1899, pp. 59-61.

Rogowsky. D. M. and MacGregor, J. G. (1986), "Design of Reinforced Concrete Deep

Beams", Concrete International, VoL 8, No. 8, August 1986, pp. 49-58.

Rogowsky, D. M., MacGregor, J. G. and Ong, S. Y. (1986), "Tests of Reinforced

Concrete Deep Beams", ACI Structural Journal, Vol. 83, No. 4, July-August 1986, pp. 614-623.

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Schlaich, J., Schâfer, K. and Jennewein, M. (1987), "Toward a Consistent Design of

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(
107
 Thorenfeldt, E., Tomaszewicz, A. and Jensen, J. J. (1987), "Mechanical Properties of
( High-Strength Concrete and Application in Design", Proceedings of the Symposium Udlization
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Vecchio, F. J. and Collins, M. P. (1986), "The Modified Compression Field Theory for
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1986, pp. 219-231.

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of the American Society of Civil Engineers, Vol. 107, No. 5Tll, Nov. 1981, pp. 2245-2270.

(
108
 APPENDIX
(

EXPERIMENTAL DATA

This appendix presents a summary of the experimental data recorded for the two pier cap
specimens. The data presented includes applied shear LVDT readings, and strains
y frOID the
electrical resistance strain gauges. Refer to Fig. 2.7 and 2.8 for descriptions of the
instrumentation.

(
109
( Sbear AV CV DV Disp.
(kN) (mm) (mm) (mm) (mm)
1 1 1 1 1 1
a a 0 0 a
246.0 -0.290 -0.432 -0.380 0.097
427.5 -0.460 -0.727 -0.640 0.177
615.5 -0.590 -1.123 -0.780 0.438
864.5 -0.740 -1.827 -1.010 0.952
1123.0 -0.900 -2.637 -1.250 1.562
1502.5 -1.140 -3.589 -1.480 2.279
1753.5 -1.250 -4.165 -1.650 2.715
1998.5 -1.380 -4.754 -1.820 3.154
2251.5 -1.500 -5.453 -1.910 3.748
2505.0 -1.610 -6.153 -2.040 4.328
2665.5 -1.700 -7.496 -2.140 5.576
2721.5 -1.750 -8.707 -2.190 6.737
2786.0 -1.750 -10.060 -2.220 8.075
2833.0 -1.730 -12.430 -2.250 10.440
2895.5 -1.630 -15.191 -2.200 13.276
2912.5 -1.580 -16.650 -2.140 14.790
2104.0 -1.690 -17.147 -1.940 15.332
Table A.l Readings from vertical LVDTs used to determine the deflection of
specimen CAPN

(
110
( Shear Al Al A3 A4 AS
(kN) (mm) (mm) (mm) (mm) (mm)
1 1 1 1 1 1 1
0 0 0 0 0 0
246.0 -0.003 -0.002 -0.003 0 0
427.5 -0.003 -0.005 -0.003 0.063 0
615.5 -0.003 -0.002 -0.003 0.223 -0.010
864.5 0.036 0.094 -0.046 0.527 -0.028
1123.0 0.021 0.460 -0.062 0.641 0.007
1502.5 -0.012 0.734 0.003 0.773 0.098
1753.5 -0.018 0.863 0.041 0.881 0.133
1998.5 -0.021 1.005 0.067 1.013 0.157
2251.5 -0.003 1.175 0.102 1.156 0.178
2505.0 0.054 1.334 0.146 1.334 0.189
2665.5 0.099 1.625 0.304 2.359 0.185
2721.5 0.375 2.076 0.472 2.994 0.157
2786.0 0.459 2.537 0.595 3.658 0.108
2833.0 0.541 3.241 0.732 4.855 -0.094
2895.5 0.683 3.921 0.849 6.137 0.046
2912.5 0.837 4.250 0.970 6.544 0.133
2104.0 1.620 3.246 0.905 6.280 0.067
Table A.2 Readings from L VDTs located at the level of the main tension tie in
specimen CAPN-A

(
111
c 1
Shear
(kN)
1
B5
(mm)
1
B4
(mm)
1
B3
(mm)
1
B2
(mm)
1
BI
(mm)
1

0 0 0 0 0 0
246.0 0.010 -0.005 -0.002 0 -0.003
427.5 0.038 -0.005 -0.007 0 -0.006
615.5 0.307 -0.121 -0.020 -0.002 -0.015
864.5 0.505 -0.068 -0.048 0.170 -0.006
1123.0 0.663 -0.074 -0.063 0.393 -0.021
1502.5 0.942 -0.163 -0.025 0.703 -0.086
1753.5 1.131 -0.205 -0.005 0.862 -0.126
1998.5 1.330 -0.268 0.005 1.091 -0.181
2251.5 1.627 -0.430 0.026 1.169 -0.033
2505.0 1.973 -0.614 0.043 1.219 0.087
2665.5 2.375 -0.823 0.089 1.289 0.206
2721.5 2.686 -0.907 0.132 1.271 0.288
2786.0 2.337 0.397 0.218 1.289 0.350
2833.0 2.131 1.766 0.586 1.544 0.589
2895.5 2.001 2.883 1.034 2.234 0.663
2912.5 1.935 3.392 1.291 2.575 0.676
2104.0 1.739 3.261 1.080 2.340 0.583
Table A.3 Readings from LVnTs located at the level of the main tension tie in
specimen CAPN-B

(
112
(
1
Shear
(kN) [ (::l 1
A7
(mm)
1
AS
(mm)
1
A9
(mm)
1
0 0 0 0 0
246.0 0 0 0 0
427.5 0.004 -0.003 0 0
615.5 0.007 -0.003 0.101 0.003
864.5 0.004 0.068 0.275 0.003
1123.0 0.004 0.365 0.260 0.003
1502.5 0.004 0.563 0.307 0
1753.5 0.007 0.652 0.373 0.003
1998.5 0.011 0.751 0.427 0.006
2251.5 0.004 0.889 0.499 0
2505.0 0.004 1.010 0.586 0.003
2665.5 0 1.258 1.108 0
2721.5 -0.105 2.048 1.351 0.003
2786.0 -0.161 2.495 1.648 0
2833.0 -0.230 3.066 2.050 -0.004
2895.5 0.171 3.229 2.535 0
2912.5 0.371 3.417 2.644 0
2104.0 2.359 1.421 2.473 -0.004
Table A.4 Readings from LVDTs located at mid-height of specimen CAPN-A

113
( Shear 89 B8 B7 B6
(kN) (mm) (mm) (mm) (mm)
1 1 1 1 1 1

0 0 0 0 0
246.0 -0.003 0 -0.004 0
427.5 0 0.004 0 0
615.5 -0.051 0.080 0 0
864.5 -0.109 0.242 0.072 0.003
1123.0 -0.106 0.249 0.227 0.003
1502.5 -0.109 0.309 0.402 0.003
1753.5 -0.102 0.366 0.484 0
1998.5 -0.098 0.422 0.593 0.007
2251.5 -0.102 0.464 0.794 -0.014
2505.0 -0.098 0.560 0.935 -0.049
2665.5 -0.102 0.616 1.080 -0.066
2721.5 -0.080 0.704 1.192 -0.115
2786.0 -0.080 1.106 1.314 -0.115
2833.0 -0.102 1.645 1.709 0.014
2895.5 -0.033 2.022 2.223 0.168
2912.5 -0.018 2.181 2.513 0.227
2104.0 -0.036 2.089 2.309 0.210
Table A.S Readings from LVOTs located at mid-height of specimen CAPN-B

(
114
c Shear
(kN)
A6
(mm)
A6V
(mm)
A6D
(mm)
A7
(mm)
A7V
(mm)
A7D
(mm)

0 0 0 0 0 0 0

246.0 0 0 0.005 0 0 0
427.5 0.004 0 0.005 -0.003 0 0.005
615.5 0.007 0.003 0.015 -0.003 0.004 0.011
864.5 0.004 -0.008 0 0.068 0.097 0.145
1123.0 0.004 -0.015 0 0.365 0.336 0.532
1502.5 0.004 -0.022 0 0.563 0.498 0.801
1753.5 0.007 -0.026 0 0.652 0.606 0.952
1998.5 0.011 -0.026 0 0.751 0.715 1.120

2251.5 0.004 -0.029 -0.005 0.889 0.856 1.322

2505.0 0.004 -0.033 -0.005 1.010 1.014 1.540
2665.5 0 -0.040 -0.011 1.258 1.192 1.843
2721.5 -0.105 0.243 1.402 2.048 0.956 2.963
2786.0 -0.161 0.414 1.787 2.495 0.985 3.512

2833.0 -0.230 0.672 2.280 3.066 1.065 4.274

2895.5 0.171 1.218 3.056 3.229 1.094 5.249

2912.5 0.371 1.800 3.768 3.417 1.148 6.072
2104.0 2.359 2.556 6.723 1.421 0.820 8.050

Table A.6 Readings from LVOT rosettes located in end A of specimen CAPN

(
115
( ~::)
Shear B7 B7D B6 B6V B6D
(kN) (mm) (mm) (mm) (mm) (mm)
1 1 1 1 1 1 1

0 0 0 0 0 0 0

246.0 -0.004 -0.003 0 0 0 0

427.5 0 0 0 0 0 0.005

615.5 0 0 0 0 0 0.005

864.5 0.072 0 0.155 0.003 0 0.005

1123.0 0.227 0.004 0.379 0.003 0 0.005

1502.5 0.402 0.368 0.654 0.003 -0.003 0

1753.5 0.484 0.449 0.797 0 0 0

1998.5 0.593 0.575 0.957 0.007 0.004 -0.035

2251.5 0.794 0.814 1.267 -0.014 0.004 0.125

2505.0 0.935 0.990 1.484 -0.049 0.004 0.393

2665.5 1.080 1.108 1.714 -0.066 -0.118 0.650

2721.5 1.192 1.226 1.851 -0.115 -0.114 0.787

2786.0 1.314 1.322 1.994 -0.115 -0.147 0.902

2833.0 1.709 1.524 2.395 0.014 -0.033 1.662

2895.5 2.223 1.587 2.734 0.168 0.101 1.936

2912.5 2.513 1.583 2.808 0.227 0.142 2.045

2104.0 2.309 1.583 2.590 0.210 0.142 1.805

Table A.7 Readings from LVOT rosettes localed in end B of specimen CAPN

(
116
 Al A2 A3 A4
( Shear
(IO~
AS A6
(kN) (10'> (10'> (10'> (10'> (10'>

0 0 0 0 0 0 0

246.0 -2 -4 0 4 44 46
427.5 -2 -6 2 8 210 254

615.5 -2 -8 6 14 496 520

864.5 -4 -6 36 66 812 834

1123.0 10 6 382 540 1052 1106

1502.5 44 26 NIA 986 1446 1526

1753.5 NIA NIA NIA NIA NIA NIA

1998.5 NIA NIA NIA NIA NIA NIA
2251.5 NIA NIA NIA NIA NIA NIA
2505.0 NIA NIA NIA NIA NIA NIA
2665.5 NIA NIA NIA NIA NIA NIA
2721.5 NIA NIA NIA NIA NIA NIA
2786.0 NIA NIA NIA NIA NIA NIA
2833.0 NIA NIA NIA NIA NIA NIA
2895.5 NIA NIA NIA NIA NIA NIA
2912.5 NIA NIA NIA NIA NIA NIA
2104.0 NIA NIA NIA NIA NIA NIA
Table A.S Strains from strain gauges located in end A of specimen CAPN

(
117
( Shear A7 AS A9 AlO Ali
(kN) (10' (IO~ (10~ (l0~ (IO~

0 0 0 0 0 0
246.0 -14 -12 8 4 4
427.5 -24 -20 18 10 8
615.5 -34 -32 32 -2 -2
864.5 -34 -28 20 14 18
1123.0 -60 -38 14 212 58
1502.5 -80 -46 22 338 124
1753.5 NIA NIA NIA NIA NIA
1998.5 NIA NIA NIA NIA NIA
2251.5 NIA NIA NIA NIA NIA
2505.0 NIA NIA NIA NIA NIA
2665.5 NIA NIA NIA NIA NIA
2721.5 NIA NIA NIA NIA NIA
2786.0 NIA NIA NIA NIA NIA
2833.0 NIA NIA NIA NIA NIA
2895.5 NIA NIA NIA NIA NIA
2912.5 NIA NIA NIA NIA NIA
2104.0 NIA NIA NIA NIA NIA
Table A.S (Cont 'd) Strains from strain gauges located in end A of specimen CAPN

(
118
( Shear BI B2 B3 B4 B5 B6
(kN) (10' (10' (10' (10' (10' (10'

0 0 0 0 0 NIA 0
246.0 -2 -4 4 6 NIA 42
427.5 -4 -6 4 10 NIA 100
615.5 -4 -10 6 14 NIA 440
864.5 -8 -10 24 42 NIA 722
1123.0 -10 -8 186 178 NIA 970
1502.5 10 8 642 554 NIA 1368
1753.5 24 14 872 758 NIA 1620
1998.5 48 22 1140 968 NIA 1878
2251.5 110 38 1462 1234 NIA 2180
2505.0 164 52 1612 1476 NIA 2506
2665.5 232 72 1828 1664 NIA 2740
2721.5 274 90 1882 1734 SIA 2776
2786.0 302 100 1950 1794 NIA 3138
2833.0 388 108 2168 1902 NIA 5698
2895.5 446 122 2220 1992 NIA 3054
2912.5 466 128 2266 2054 NIA 2998
2104.0 454 130 1802 1774 NIA 2638
Table A.9 Strains from strain gauges located in end B of specimen CAPN

(
119
• Shear
(kN)

0
87
(l0'>

0
B8
(10')

0
B9
(10'

NIA
810
(10'

0
Bl1
(lO~

246.0 -12 -12 NIA 4- -6

427.5 -20 -24 NIA -10 -14
615.5 -28 -36 NIA -28 -32
864.5 -22 -40 NIA 12 26
1123.0 -34 -54 NIA 410 148
1502.5 -64 -80 NIA 710 338
1753.5 -82 -100 NIA 882 458
1998.5 -100 -120 NIA 1080 598

2251.5 -112 -142 NIA 1376 796

2505.0 -114 -164 NIA 1564 956

2665.5 -94 -180 NIA 1730 1138

2721.5 -82 -192 NIA 1818 1268
2786.0 -70 -200 NIA 1802 1292

2833.0 440 -24 NIA 1378 1230

2895.5 612 54 NIA 1304 1260

2912.5 668 80 NIA 1244 1162

2104.0 636 106 NIA 1060 1016

Table A.9 (Cont 'd) Strains from strain gauges located in end B of specimen CAPN

(
120
( Shear AV CV BV Disp.
(kN) (mm) (mm) (mm) (mm)
1 1 1 1 1 1
0 0 0 0 0
495.5 -0.501 -0.781 -0.797 0.132
571.5 -0.516 -0.887 -0.858 0.200
745.5 -0.683 -1.361 -1.027 0.506
890.5 -0.804 -1.890 -1.088 0.944
1124.0 -1.047 -2.585 -1.303 1.410
1326.5 -1.213 -3.078 -1.441 1.751
1611.0 -1.426 -3.814 -1.594 2.304
1870.5 -1.593 -4.362 -1.717 2.707
2122.0 -1.745 -4.900 -1.840 3.108
2391.0 -1.896 -5.517 -1.947 3.596
2618.0 -1.987 -6.083 -2.054 4.063
2771.5 -2.185 -7.169 -2.162 4.996
2844.0 -2.337 -8.430 -2.208 6.158
2902.5 -2.504 -9.603 -2.208 7.247
2960.5 -2.640 -10.961 -2.223 8.530
2996.0 -2.716 -11.877 -2.208 9.415
2792.0 -2.868 -12.111 -2.177 9.589
2910.0 -3.749 -13.138 -2.100 10.214
1842.0 -8.364 -13.662 -1.886 10.690
Table A.IO Readings from vertical LVDTs used to determine the deflection of
specimen CAPH

(
121
( Shear Al 1'..2 A3 A4 AS
(kN) (mm) (mm) (mm) (mm) (mm)
1 1 1 1 1 1 1

0 0 0 0 0 0
250.0 0 0.003 0.003 0 0.004
495.5 -0.006 0 0.003 0.114 0.007
571.5 0.021 0.003 0.005 0.160 0.007
745.5 0.018 0.003 -0.010 0.349 0.129
890.5 0.027 0.204 -0.044 0.515 0.157
1124.0 0.015 0.443 0.008 0.664 0.175
1326.5 -0.054 0.682 0.054 0.790 0.195
1611.0 -0.084 0.864 0.088 0.933 0.223
1870.5 0.030 0.879 0.147 1.053 0.255
2122.0 0.072 0.959 0.173 1.179 0.290
2391.0 0.196 1.016 0.227 1.311 0.338
2618.0 0.280 1.093 0.292 1.477 0.394
2771.5 0.356 1.220 0.566 2.233 0.408
2844.0 0.416 1.419 0.739 3.143 0.356
2902.5 0.456 1.785 0.832 4.139 0.317
2960.5 0.631 2.316 0.963 5.175 0.049
2996.0 0.698 2.483 1.068 6.080 -0.090
2792.0 0.846 2.517 1.104 6.046 -0.125
2910.0 0.942 2.933 1.288 6.206 -0.160
1842.0 0.825 1.686 1.102 5.645 -0.237
Table A.II Readings from LVDTs located al the level of the main tension lie in
specimen CAPH-A

(
122
c 1
Sbear
(kN)

0
1
B5
(mm)

0
1
B4
(mm)

0
1
<:J 0
82
(mm)

0
1
BI
(mm)

0
1

250.0 -0.003 0 0 0 -0.006

495.5 -0.003 0 0 -0.007 0
571.5 -0.003 0 0.003 0.020 0.006
745.5 -0.014 0.315 0.013 0.013 0.003
890.5 0.028 0.419 0.333 -0.034 0.000
1124.0 0.087 0.451 0.499 0.115 -0.012
1326.5 0.140 0.498 0.552 0.211 -0.009
1611.0 0.189 0.582 0.600 0.027 0.166
1870.5 0.217 0.655 0.743 0.286 0.291
2122.0 0.241 0.745 0.852 0.313 0.350
2391.0 0.259 0.855 0.982 0.320 0.423
2618.0 0.280 0.960 1.134 0.333 0.500
2771.5 0.297 1.059 1.426 0.299 0.555
2844.0 0.304 1.405 1.871 -0.055 0.611
2902.5 0.304 1.783 2.525 -0.341 0.651
2960.5 0.217 2.402 3.760 -1.063 0.688
2996.0 0.185 2.763 4.500 -1.539 0.718
2792.0 0.157 2.763 4.528 -1.676 0.721
2910.0 0.154 2.800 4.665 -1.717 0.728
1842.0 0.080 2.501 4.123 -1.676 0.632

Table A.I2 Readings from LVDTs located at the level of the main tension tie in
specimen CAPH-B

(
123
c 1
Shear
(kN)
1
A6
(mm)
1
A7
(mm)
1
AS
(mm)
1
A9
(mm)
1
0 0 0 0 0
250.0 0 0 0.004 0
495.5 -0.017 0.007 0.004 0
571.5 0.029 0.014 0.033 -0.004
890.5 0 0.188 0.254 0
1124.0 0 0.367 0.297 0
1326.5 0.015 0.463 0.359 -0.004
1611.0 0 0.584 0.427 0.003
1870.5 -0.017 0.715 0.489 0.007
2122.0 -0.063 0.832 0.558 0.003
2391.0 -0.078 0.977 0.627 0.007
2618.0 -0.110 1.112 0.692 0.087
2771.5 -0.154 1.445 1.061 0.094
2844.0 -0.200 1.679 1.514 0.124
2902.5 -0.215 1.945 2.050 0.124
2960.5 -0.232 2.473 2.430 0.134
2996.0 -0.246 2.696 2.807 0.138
2792.0 0.324 2.601 2.677 0.138
2910.0 1.270 2.509 2.731 0.138
1842.0 1.767 1.977 2.452 0.107
Table A.t3 Readings from LVDTs located at mid-height of specimen CAPH-A

(
124
( Shear B9 B8 B7 B6
(kN) (mm) (mm) (mm) (mm)
1 1 1 1 1 1

0 0 0 0 0
250.0 0 -0.004 0 0
495.5 0 -0.004 0 -0.004
571.5 -0.007 -0.004 -0.003 -0.007
890.5 0.270 0.123 0 -0.004
1124.0 0.296 0.261 0 -0.004
1326.5 0.340 0.345 -0.003 -0.004
1611.0 0.402 0.462 0.033 0
1870.5 0.409 0.328 0.452 -0.014
2122.0 0.453 0.345 0.541 -0.018
2391.0 0.533 0.359 0.653 -0.032
2618.0 0.577 0.359 0.781 -0.046
2771.5 0.643 0.416 0.926 -0.060
2844.0 0.745 0.634 1.008 -0.067
2902.5 0.847 0.856 1.124 -0.074
2960.5 0.986 1.170 1.249 -0.077
2996.0 1.095 1.392 1.318 -0.091
2792.0 1.073 1.389 1.298 -0.098
2910.0 1.106 1.417 1.325 -0.091
1842.0 0.920 1.322 1.101 -0.081

Table A.14 Readings from LVDTs located at mid-height of specimen CAPH-B

(
125
( Shear A6 A6V A6D A7 A7V A7D
(kN) (mm) (mm) (mm) (mm) (mm) (mm)

0 0 0 0 0 0 0

250.0 0 -0.004 0 0 -0.004 0

495.5 -0.017 -0.004 -0.005 0.007 -0.004 0
571.5 0.029 -0.007 0.006 0.014 -0.004 0
745.5 0.015 -0.007 0.006 0.014 0 0
890.5 0 0 0.011 0.188 0.137 0.252
1124.0 0 -0.004 0.006 0.367 0.271 0.471
1326.5 0.015 0 0.011 0.463 0.347 0.605

1611.0 0 0 0.011 0.584 0.451 0.773

1870.5 -0.017 -0.004 -0.005 0.715 0.567 0.958
2122.0 -0.063 -0.007 -0.010 0.832 0.653 1.104
2391.0 -0.078 -0.007 -0.005 0.977 0.772 1.311
2618.0 -0.110 -0.011 -0.016 1.112 0.877 1.479
2771.5 -0.154 -0.015 -0.016 1.445 1.058 1.843
2844.0 -0.200 -0.018 -0.021 1.679 1.177 2.095
2902.5 -0.215 -0.018 -0.021 1.945 1.336 2.387
2960.5 -0.232 -0.040 -0.160 2.473 1.646 2.980
2996.0 -0.246 -0.047 -0.155 2.696 1.762 3.227
2792.0 0.324 0.440 0.572 2.601 1.729 3.042
2910.0 1.270 1.298 1.504 2.509 1.830 3.070
1842.0 1.767 5.643 4.469 1.977 1.585 2.538

Table A.15 Readings from LVOT rosettes located in end A of specimen CAPH

(
126
( shear B7 B7V D7D B6 B6V B6D
(kN) (mm) (mm) (mm) (mm) (mm) (mm)
1 1 1 1 1 1 1 1
0 0 0 0 0 0 0
250.0 0 0 0 0 0 0.005
495.5 0 0 -0.006 -0.004 -0.004 0
571.5 -0.003 -0.004 -0.006 -0.007 -0.004 0
745.5 0 -0.004 0.000 -0.004 0 0.005
890.5 0 -0.004 -0.011 -0.004 0 0.005
1124.0 0 0 -0.051 -0.004 0 0.005
1326.5 -0.003 -0.004 -0.063 -0.004 0.004 0
1611.0 0.033 0.066 0.092 0 -0.004 0.005
1870.5 0.452 0.243 0.532 -0.014 -0.015 -0.018
2122.0 0.541 0.268 0.629 -0.018 -0.019 -0.012
2391.0 0.653 0.357 0.738 -0.032 -0.041 -0.035
2618.0 0.781 0.434 0.882 -0.046 -0.071 -0.058
2771.5 0.926 0.489 1.025 -0.060 -0.085 -0.063
2844.0 1.008 0.489 1.094 -0.067 -0.093 -0.069
2902.5 1.124 0.544 1.179 -0.074 -0.093 -0.075
2960.5 1.249 0.541 1.254 -0.077 -0.097 -0.080
2996.0 1.318 0.544 1.300 -0.091 -0.104 -0.092
2792.0 1.298 0.544 1.294 -0.098 -0.104 -0.086
2910.0 1.325 0.544 1.311 -0.091 -0.104 -0.086
1842.0 1.101 0.515 1.094 -0.081 -0.085 -0.075
Table A.16 Readings from LVDT rosettes located in end B of specimen CAPH

(
127
 Al A4
( Shear Al A3 AS A6
(kN) (10') (10,> (10') (10'> (10~ (10')

0 0 a 0 0 0 0
250.0 -2 -2 8 10 32 34
495.5 -6 -6 12 12 400 288
571.5 4 -6 16 18 524 378
745.5 4 -la 18 22 702 544
890.5 4 -6 32 48 892 716
1124.0 4 -6 118 124 1176 942
1326.5 2 a 510 614 1398 1L94
1611.0 12 2 882 980 1722 1530
1870.5 30 la 1246 1346 1994 1828
2122.0 38 14 1460 1598 2326 2226
2391.0 60 22 1768 1896 2658 2580
2618.0 88 28 1992 2106 3020 2896
2771.5 120 36 2172 2268 5764 3476
2844.0 136 42 2266 2364 4826 3266
2902.5 148 46 2336 2502 4966 2476
2960.5 178 62 2532 2958 5152 2378
2996.0 202 74 2588 3112 4946 2376
2792.0 258 72 2602 3130 4888 2342
2910.0 328 76 2688 3888 4530 2192
1842.0 314 78 5288 7222 3848 1900
Table A.17 Strains from strain gauges located in end A of specimen CAPH

(
128
 A7 A8 Ale
( Shear A9 Al.l
(kN) (l0') (lO~ (10'> (l0') {lO6-;

0 NIA 0 NIA 0 0

250.0 NIA -6 NIA 4 2

495.5 NIA -20 NIA -2 -4

571.5 NIA -16 NIA -2 -6

745.5 NIA -24 NIA -26 -26
890.5 NIA -6 NIA 50 8
1124.0 NIA -16 NIA 224 80
1326.5 NIA -26 NIA 340 140
1611.0 NIA -38 NIA 460 220
1870.5 NIA -46 NIA 628 308
2122.0 NIA -54 NIA 744 376
2391.0 NIA -54 NIA 1050 414
2618.0 NIA -56 NIA 1216 444
2771.5 NIA -64 NIA 1332 494

2844.0 NIA -66 NIA 1418 568

2902.5 NIA -74 NIA 1464 744
2960.5 NIA -66 NIA 1512 1010
2996.0 NIA -60 NIA 1608 1088
2792.0 NIA 34 NIA 48 -1180
2910.0 NIA 148 NIA -26 -12

1842.0 NIA 272 NIA 0 206

Table A.17 (Cont 'd) Strains from strain gauges located in end A of specimen CAPH

(
129
• Shear
(kN)

0
BI
(IO~

0
82
(10'

0
B3
(l0'

0
B4
(10'

0
B5
(10'

0
B6
(10'

0
250.0 0 -4 2 4 30 34
495.5 -2 -6 6 8 56 64
571.5 -2 -8 6 10 70 82
745.5 -2 -12 6 14 688 644

890.5 -2 -6 12 32 874 782

1124.0 -2 -8 60 72 1090 988
1326.5 -2 -6 144 200 1282 1152
1611.0 16 0 806 702 1556 1510
1870.5 34 8 1164 1132 1832 L820
2122.0 46 12 L340 1362 2170 2098
2391.0 52 12 1554 1630 2536 2394
2618.0 72 18 L748 L846 2884 2606
2771.5 98 22 1892 1982 3248 2670
2844.0 116 24 1976 2040 4316 2762
2902.5 132 26 2046 2092 6818 2976
2960.5 144 28 2122 2140 6196 3554
2996.0 158 28 2190 2172 3794 5204
2792.0 160 30 2162 2146 3680 5174
2910.0 168 30 2170 2154 2846 4458
1842.0 154 30 1714 1674 2348 3806
Table A.18 Strains from strain gauges located in end B of specimen CAPH

130
 BIO
( Shear B7 B8 B9 Bll
(kN) (10~ (10~ (10~ (lO~ (10'>

0 0 0 0 0 0
250.0 0 0 6 10 -2
495.5 -4 2 8 16 -12
571.5 -4 4 12 10 -16
745.5 -10 2 16 -34 -64
890.5 2 12 4 -76 -94
1124.0 -4 14 4 -80 -118
1326.5 -4 16 2 -90 -136
1611.0 -22 8 8 -104 -160
1870.5 -12 20 -6 836 488
2122.0 -20 16 -4 820 682
2391.0 -22 18 0 994 916
2618.0 -20 20 0 1230 1266
2771.5 -26 10 -2 1436 1568
2844.0 -32 4 -2 1462 1734
2902.5 -34 2 0 1610 1934
2960.5 -38 -2 -2 1892 2226
2996.0 -40 -4 -2 1970 2422
2792.0 -40 -4 -2 1864 2418
2910.0 -42 -8 -4 1712 2454
1842.0 -32 -10 -8 992 2204
Table A.18 (Cont'd) Strains from strain gauges located in end B of specimen CAPH

c
131
 IMAGE EVALUATION
TEST TARGET (QA-3)

1.0 :~ ~
1==
~ ~Iii
~
L::.
nm2.2
Ii:. lIIII5a

111111.1 t ~ I~ 111111.8

11111
125
. 111111.4 il~ 1.6
- 150mm --.J-
J
1
~

,
1

1-..
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......

APPLIED _~ I~GE .ne

1
~ 1653 East Msin Street
~~ Rochester. NY 14609 U
_ _ Phone: 716/482-0300 SA
_ _ Fax: 7161288-5989

o 1993• ApplIed 1mage. lne:.. AlI RIgtIts ReseMId