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Shear Reinforcement for Large Lightly Reinforced Concrete
Members
Yoichi Yoshida
A thesis submitted in conformîty with the requirements for the
Degree of Master of Applied Science Graduate Department of Civil
Engineering
University of Toronto
O Copyright by Yoichi Yoshida, 2000
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Shear Reinforcement for Large Lightly Reinforced Concrete
Members Master of Applied Science, 2000 Yoichi Yoshida Graduate
Department of Civil Engineering Universisr of Toronto
Abstract
To obtain expenmental data about the shear capacity of very
large concrete members,
four tests invofving 2m deep beams, which are believed to be the
largest bearn-type specimens
tested in North Amerka were conducted. The four sections studied
contained various arnounts
of shear reinforcement.
The following conclusions were arrived at fiom this study.
The specimen not containing transverse reinforcement failed at a
shear which was only
47% of the failure load predicted by the shear provisions of the
curent AC1 Building
Code.
Providing a small amount of shear reinforcement greatly enhanced
the response of the
beams in terms of shear capacity and ductility. For the same
total amount of stimps the
shear capacity increased as the spacing of transverse
reinforcement decreased.
The procedures in the CSA code based on The Modified Compression
Field Theory yield
generally good estimates of failure for al1 of the
specimens.
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Acknowledgments
First and foremost I would like to thank my s u p e ~ s o r ,
Professor Michael P. Collins for
giving me a chance to study and to do research with him on such
an interesting research topic. I
also appreciate his expertise and guidance he has given me
throughout this research.
1 want to express my appreciation to my fellow graduate students
here at the University
of Toronto for their fnendship, their suggestions on vanous
aspects of rny research, and their
generous assistance dunng the tests. Among them I name here only
my roommates:
Evan C. Bentz, Almila Uzel, Young-Joon Kim, and Cao Sheng.
The experimental project wouldn't have succeeded without the
help of the staff at the
Mark Huggins Structural Laboratory. 1 would like to take this
opportunity to express al1 my
gratitude for their professional expertise and kind support. 1
also thank Mr. Peter Leesti for his
constant care regarding my research.
My stay at Toronto as a graduate student was made possible by
Obayashi Corporation,
which 1 really thank for giving me the chance to study in Canada
for two years and for providing
continuous financial support dunng my stay.
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Table of Contents
Abstract Acknowledgments Table of Contents List of Tables List
of Figures List of Appendices 1 Introduction
........................................................................................................................
1
1.1 Background
....................................................................................................................
I 1.2 Research Objectives and Layout of Work
.......................................................................
3
2 Review of Related Work and Code Provisions
....................................................................
4
.................................................................................................
2.1 Review of Related Work 4
................................................................
2.1.1 Effect of Member Size on Shear Strength 4 2.1.2 Effect of
Minimum Shear Reinforcement on Shear Strength
................................... 6 2.1.3 Modified Compression
Field ïheory
.......................................................................
7 2.1.4 Large Bearn Tests at the University of Toronto
.............................................. 10 . .
2.2 Review of Code Provisions
...........................................................................................
1 3 2.2.1 AC1 3 18-99
............................................................................................................
13 2.2.2 C SA-A23 . 3-94 (Generai Method)
........................................................................
14
2.3 Brief Introduction of Analysis Program
.........................................................................
18 2.3.1 Response-2000
......................................................................................................
-18
3 Experimental Test Program
...............................................................................................
20 3.1 Specimen Details
.........................................................................................................
20 3.2 Matenal Properties
.......................................................................................................
-24
3.2.1 Concrete Properties
................................................................................................
24 3.2.2 S tee1 Properties
.....................................................................................................
-26
3 -3 Specimen Construction
..................................................................................................
2 7 3.3.1 Form-work
...................................................
..............,,,...................... ............. -27 3 .3 .2
Concrete Pour and Cure ..................... ... ........ .....
................................................... -30 3.3.3
Specimen Transportation
......................................................................................
3 1
3.4 Test Rig Details
.............................................................................................................
34 3.4.1 Instrumentation and Data Acquisition
....................................................................
34
...........................................................................
3 .4.2 Strain Gauges on Reinforcement -37 ...............*..
..*.*..*..........................*..*.....-..-.......................*.
3 -5 Load Procedure. ................... 3 9
3 -6 Reinforcement afker Test
................................................................................................
39 4 Test Results and Analysis
..................................................................................................
42
...........................................................................
4.1 Overview of Result of YB2000 Series 42
................................................................
4.2 Effect of Member Depth on Shear Strength -49
.................................................. 4.2.1 Effect
of Member Depth Observed in Test Result 49
..................................... 4.2.2 Prediction of Beam's
Shear Strength Using Design Codes 5 1
....................................... 4.3 Effect of Minimum S
heu Reinforcement on Shear Strength - 3 5 4.3.1 Effect of Minimum S
hear Reinforcemcnt in Test Results
...................................... .55 4.3.2 Prediction of
Beam's Shear Strength
.................................................................
60
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Table of Contents (Cont'd)
..................................................................................
5 Conclusions and Recommendations -62
...................................................................................................................
5.1 Conclusions 62
........................................................................................................
5.2 Recomrnendations -63 Appendices
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List of Tables
Table 2.1 Properties of BN Series Specimens
............................................................................
11 Table 2.2 Values of ,û and @ for Section Not Containing
Transverse Reinforcement .................. 16 Table 2.3 Values of
and 0 for Section Containing Transverse Reinforcement
......................... 17 Table 3.1 Dimensions of Anchor Heads
of T-headed bars
......................................................... 22 Table
3.2 Test S pecimen Details
..............................................................................................
-22 Table 3.3 Concrete Properties
...................................................................................................
-24 Table 3.4 Properties of Reinforcing Bars
...................................................................................
26 Table 4.1 Expenrnental Resuit for Bearns of YB Series and BN
Series ..................................... .48 Table 4.2
Expenmental Result for Beams not containing shear reinforcement
........................... 49 Table 4.3 Prediction for Specimens
without Transverse Reinforcement using AC1 3 18-99, CSA-
...................................................................................
A23.3-94, and Response-2000 53 Table 4.4 Experimental Result for
Beams of YB Senes
............................................................. 55
Table 4.5 Prediction for Specirnens of YB series using AC1 3 18-99,
CSA-A23.3-94, and
Response-2000
..........................................................................................................
61
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List of Figures
Figure 1.1 Example of Liquid Natural Gas Tanks Constructed in
Japan ...................................... 2 Figure 1.2 Example
of Box Structure of Tokyo Highway Underpass
.......................................... 2 Figure 2.1
Relationship between Shear Strength and Shear Span-Depth Ratio
(Adapted from
Re f 9)
......................................................................................................................
4 ....... Figure 2.2 Influence of Member Depth on Shear Strength at
Failure (Adapted fkom Re f 9) 5
Figure 2.3 Size Effect Curves Suggested by Researchers (Adapted
from Re f 3) ........................ 6 Figure 2.4 Modified
Compression Field Theory
........................................................................
8 Figure 2.5 Liuence of Mmber Dspth on Shear Stress at Failure
(tests by Shioya) (Adapted
from Ref. 3) .................................................
.. ..................................................... 9 Figure
2.6 Geometric Details of BN Senes
................................................................................
12 Figure 2.7 Values of Crack Spacing Parameter (Adapted fkom ReE
9) ...................................... -15 Figure 2.8 Values of
P and 8 for Section Not Containhg Transverse Reinforcement
(Adapted
from Ref. 9)
............................................................................................................
16 Figure 2.9 Values of ,O and 6 for Section Containing Transverse
Reinforcement (Adapted fkom
Ref. 9)
....................................................................................................................
-17 Figure 2.10 Examples of the Screens of Response-2000
............................................................ 19
Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6
Figure 3.7 Figure 3.8 Figure 3.9
T-headed bars
...........................................................................................................
21 Geometric Details of YB2000 Series Specimens
....................................................... 23 .
Strength Development of Concrete
...........................................................................
25 S hrinkage Strain Development
................................................................................
-25 Longitudinal Rebars in YB2000/4&6
.............................. ..
.................................... 26 Cross-sectional View of
Form-work
.........................................................................
2 7 Bottom Rebar Cage
..................................................................................................
2 8 Form-work
............................................................................................................
-29 Rollen used to move the specimens
.....................................................................
31
Figure 3.10 Transportation Set-Up
............................................................................................
32 Figure 3.11 Support
...................................................................................................................
32 Figure 3.12 Transporiation of Specimen
....................................................................................
33 Figure 3.13 Experirnental Test Set-Up
.......................................................................................
34
.................................................................
Figure 3 .14 Layout of LVDT's for Beam DeBedon 35 Figure 3.15 Gnds
of LVDT's
....................................................................................................
36
..............................................................................................
Figure 3.16 Zurich Target Layout 36 Figure 3.17 Measurement using
Zurich Gauges
.........................................................................
3 7 Figure 3.18 Strain Gauges in Specimens
....................................................................................
38
...............................................................
Figure 3.19 FaiIed End Reinforced by Dywidag Bars -40
.......................... Figure 3.20 Collapsed FIemiral
Compression Zone on the Side of YB2000/6 ..41
Figure 3 -2 1 Repaired Portion
..............................................................................................
41 ........ Figure 4.1 Load-Deflection Curves for YB2000/0,
YB2000/4, YB2000/6, and YB2000/9 -43
................. ........................... Figure 4.2 Crack
Pattern at the Final Load Stage of YB200010 .. 45
................................................. Figure 4.3 Crack
Pattern at the Final Load Stage of YB2000D 46
Figure 4.4 Crack Pattern at the Final Load Stage of YB200016
.................................................. 47 Figure 4.5
Crack Pattern at the Final Load Stage of YB2000/4
............................................... -47 Figure 4.6
Cornparison of Crack Patterns
..................................................................................
50 Figure 4.7 S hear Force-Deflection Curve for YB2000/0
........................................................... -52
vii
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List of Figures (Cont'd)
Figure 4.8 Variation of failure shear stress ratio with beam
depth .............................................. 54
......................................................................
Figure 4.9 Load-deflection curve for YB2000/4 3 6
......................................................................
Figure 4.10 Load-deflection curve for YB2000/6 56
.....................................................................
Figure 4.1 1 Load-deflection curve for YB2000/9 -57
Figure 4.12 Crack Pattern o f YB2000/4&6 at Load Stage Close
to Failure ................................ 58
................................................ Figure 4.13 Crack
Pattern o f YB2000/9 at Failure of YB2000/0 59
.............................................................
Figure 4.14 Shear force-deflection curve for YB2000/4 60
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List of Appendica
Appendu A Calculations of AC1 3 18-99 and CSA423.3-94 (General
Method) Code Predictions
.................................................................................
65
Appendix B Output of Experiment
.....................................................................
74
Appendk C Matenal Properties
........................................................................
140
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1 Introduction
1.1 Background
In recent years, some very large structures, containing members
whose depth is more than
lm, have been constmcted. Some examples include iiquid natural
gas tanks, one of which
contains a 9.8m deep bottom slab as shown in Figure 1.1. Figure
1.2 shows another example,
which is a box structure of a Tokyo highway underpass containing
a 1.25m deep member as its
roof slab. These deep members usually have smaiî or sometimes no
transverse reinforcement and
hence rely on the large contribution of concrete to shear
strength of the members. However the
fact that the shear stress at failure decreases for members with
larger depths has been known for
several decades and in 1967 Kani warned of the imporiance of
this effect of member depth on
shear strength with his paper entitled "How safe are our large
reinforced concrete beams?'. Since
then research on shear strength of concrete members has been one
of the most active research
topics and as a result of it some theones have been deveioped
and they afEord a capability to
explain shear behaviour rationally and also provide relatively
precise estimates of shear capacity.
However the applicability of these theories for very deep
members, say ones more than 2rn deep,
has not actually been assured by very many experiments due to
the practical ditfinilty of
constructing and testing such large specimens. Hence a reliable
shear design method for deep
memben with or without transverse reinforcement is still a
significant need in current praaice.
The additional concern is that in the afiermath of some major
earthquakes such as
Northridge Earthquake in California in 1994 and Hyogoken Nanbu
Earthquake in Japan in 1995
design loads for earthquake in many design specifications have
been increased. This change has
caused a need to retrofit existing concrete structures designed
with old design codes especially
for shear capacity. One of the reinforcing methods for these
deep slabs is the addition of
transverse reinforcement. While it is cost effective to minimire
the number of reinforcing bars
placed as shear reinforcement, most design codes require a
rather small spacing for such shear
reinforcement (e.g. In the AC1 and CSA codes this spacing may
not exceed 600m even for very
deep members). Although wider spacing is believed to decrease
the shear strength of members, it
is not clear how much and what kind of disadvantages sparsely
reinforced memben really have.
Hence the eKea of spacing of shear reinforcement in large
members also needs to be
investigated for a feasible repair scheme.
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Figure 1.1 Example of Liquid Natural Gas Tanks Constmcted in
Tapan
Figure 1.2 Example of Box Structure of Tolqo Highway
Underpass
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1.2 Research Objectives and Layout of Work
Considenng the situation briefly descnbed in the previous
section, the following
objectives were set at the beginning of this research.
1. Foiiowing the series of l m deep beam tests done at the
University of Toronto during the
last several years, obtain reliable experimental data about
shear strength of 2m deep
bems using normal mength concrete :O investigate the vdidity of
exisîLing analytical
models and design provisions
2. Xnvestigate the effect of minimum shear reinforcement on
shear strength of such deep
members
3. Examine the effect of spacing of shear reinforcement on shear
strength and behaviour of
deep concrete members
This thesis consists of the following chapters. Chapter 2 deals
with previous work in
pursuit of sirnilar objectives as this research in order to give
a background. Chapter 2 also
includes b k f explanations of shear provisions of some design
codes and an analytical program,
which were later examined with experirnental results. Then
Chapter 3 describes details of the
experimental program including design, construction, and
instrumentation of the 2m deep beam-
type specimens. Test results and verification of the code
provisions and the analytical program
are shown in Chapter 4. Finally Chapter 5 concludes this report
with some recomrnendations for
fiiture research.
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2 Review of Related Work and Code Provisions
2.1 Review of Related Work
In this section, previous research results are summarized about
the topics related to this
research. It must be noted first that memben considered in this
reseatch have relatively large
shear-span-to-depth ratios, a/d, so that they can be designed
using sectional analysis ( d d > 2.5
according to Figure 2.1). For shorter members compression struts
fom between the loading
point and the supports and the shear is carried by arch action.
The behaviour of these short
members can be dealt with based on the strut-and-tie mode1 and
hence this type of member,
which has no significant size effect, is not treated in this
thesis.
Figure 2.1 Relationship between Shear Strength and Shear
Span-Depth Ratio (Adapted f?om Ref. 9)
2.1.1 Effect of Member Ske on Shear Strength
Member size plays a significant role in determinhg the failure
shear stress of memben
without web reinforcement. This effect means that the shear
strengui of members doesn't
increase iineariy as the member depth increases. In other words,
for deeper members, the shear
stress at failure is smaller than it is for smaller members.
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This "size effect" in shear was investigated by Kani who
conducted a series of beam tests
with specimens varying in depth f?om 200mm to 1200mm. More
recently, Kani's observations
were extended by Shioya (shown as Shimizu in Figure 2.2) up to a
member depth of 3000mm.
Figure 2.2 shows the infiuence of member depth observed by
previous researches.
Figure 2.2 Infiuence of Member Depth on Shear Strength at
Failure (Adapted from Ref. 9)
The cause of the size effect is mostly agreed among many
researchers as being the wider
cracks which form in larger members. Since beams usualiy have
longitudinal reinforcement only
at the top and the bottom, their capability to control crack
distribution is very limited around the
mid-depth of the beams. From the observation of crack patterns
in specirnens he tested, Shioya
suggested that the spacing of diagonal cracks was approximately
the effective depth of the
specirnens. Some other researchers assume the crack spacing to
be half of the effective depth or
0.7(d - c) where c represents depth of compression zone. As can
be seen, crack spacing is nearly always related to member
depth.
Shce the crack width is estimated as a produd of crack spacing
and concrete strain, a
larger crack spacing results in wider cracks. One of the
consequences of wider cracks is a
reduction of interface shear transfer, which is one of the
mechanisms carrying shear in reidorced
concrete members. For normal strength concrete, the interface
shear transfer is known as
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addition, spacing requirement for shear reinforcement assures
srna11 crack width at the s e ~ c e
load level for durability of the members.
Yoon et al tested 750mm deep specimens with various concrete
strength to investigate
the concern that minimum shear reinforcement in cunent design
codes rnay not be enough for
members made fiom high strength concretes. As a part of their
project, normal strength concrete
specimens were also tested for cornparison. These exhibited very
ductile behaviour afker the
formation of diagonal cracks and also the crack widths in the
spechens were limiteci to very
smali values. They concluded that current requirements are
reasonable for members having
normal concrete strength.
Although test results with regard to minimum shear reinforcement
for large-size
specimens are very limiteci, current requirements may be
conservative for deeper beams as long
as they are constructed with normal strength concrete. Since the
required arnount as minimum
shear reinforcement is constant regardless of member sire, shear
carried by stirrups increases as
d does (See Y, terms in Eqn.2.1 and Eqn.2.3) while shear carried
by concrete doesn't increase
due to the size effect. Consequently there is sufficient reserve
strength provided by the shear
reinforcement required by the current requirements. This
conservative aspect of the existing
codes, in tum, leads to a possibility of smaller minimum
reidorcement and larger spacing than
ones the design codes demand for these larger members.
2.1.3 Modified Compression Field Theory
With the aim of developing a rational shear design method,
extensive research has been
done at the University of Toronto. With many results of membrane
specimens tested with the
Panel Tester and the Shear Element Tester, the Compression Field
Theory and Iater the Modified
Compression Field Theory (hereafler MCFT) were developed. In
this section, a brief explanation
of the MCFT is presented.
MCFT considen not oniy equilibrium but also compatibility and
stress-strain
relationships for cracked concrete element as shown in Figure
2.4. Assuming that angle of crack
inclination is equal to angle of principal compressive stress in
the elements, MCFT determines
the angle of crack inclination satisfjring compatibility
requirement. Concrete tension stsening
and compression softening are included in its stress-strain
relationships as show in Figure 2.4.
Aithough MCFT mainly deds with average values for strain and
stress as representative values
-
of stress and strain States, it aiso checks the capability of
shear transfer across the cracks by
calculating shear stress acting on crack surfaces.
A shear design method based on MCFT has been adopted by sorne
design codes in North
Amenca; the Ontario Highway B d g e Design Code, the Canadian
Standards Association
Concrete Design Code (CSA-A23.3-94), and the AASHTO LRFD
specifications.
Stresses ut Cracks:
pXf- =&+I mi6+ v,.eotO p, f'& =/, + v tan8 - vd tan8
Geomelrlc Conditions:
Crack Widths:
Average Stress-Average Stmin Aelatlonships:
Concrete:
i\ltowable Shear Slress on Crack
Figure 2.4 Modified Compression Field Theory
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MCFT explicitly accounts for the effect of member depth as
follows. Since MCFT
assumes wider crack spacing for deeper beams, it Ieads to larger
crack width, which is obtained
as a product of the crack spacing and average concrete strain.
Consequently it becomes more
likely that the specimen's shear strength will be Iimited by the
capacity of diagonal cracks to
transfer shear across the cracks. The wider the crack width
becomes, the smaller the shear
transfer capability becomes.
Size effect predicted with MCFT is s h o w in Figure 2.5 with
the experimenta.1 resrilts
done by Shioya. The curve indicated as Generai Method Prediction
is based on the MCFT. As
show in this figure, actual shear stress at failure for the 3m
(about 10 feet) deep barn member
was ody one-third of the shear stress at failure of the 200mm (8
inches) deep bearn.
2a ln. 0.6 12 In. (500 mm)
0.4
2.5 Influence of Member Depth on Shear Stress at Failure (tests
by Shioya) (Adapted fiom ReE 3)
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2.1.4 Large Beam Tests at the University of Toronto
M e r the development of design procedures based on the MCFT, an
experimental
program was initiated at the University of Toronto in order to
ve* the applicability of the
theory to members having depths up to lm. The largest specimens
tested in the program were lm
deep, 0.3m wide, and 6m long. The beam properties varied in
tenns of member sue, concrete
strength, longitudinal reinforcement ratio, the presence of
distributed reinforcernent over the
depth of the beam, and the presence of minimum qriantities of
shear reinforcement. Most of the
specimens had approximately 1% of longitudinal reinforcement.
Details of this project can be
found in Ref. 2 and 13.
Conclusions deduced fiom this senes of tests related to
objectives of this research are as
follows.
1. Tests of Iightly reinforced specimens with no transverse
reinforcement exhiited a
significant size effect. The effect was related to the beam's
capability to control crack
width and crack spacing rather than the absolute depth of the
mernbers.
2. The amount of longitudinal reinforcement had a significant
influence on shear
capacity. More longitudinal reinforcement resulted in larger
shear capacity of beams
without transverse reinforcernent due to better ability to
control crack width.
3. Providing a small amount of transverse reinforcement resulted
in significant gains in
terms of reserve strength and ductility.
4. The shear design method based on MCFT, known as "the General
Methoà" or "Beta
Method" (explained briefly in 2.2.2), yielded generally good
predictions for the bearns
and it represented the trend of the effixts of member size and
the amount and
distribution of longitudinal reinforcement which were found in
the tests.
5. On the contrary, a considerable number of the specimens
failed at loads lower than
those predicted by the procedures of the AC1 code (descnbed in
2.2.1). This was
prominent especially for members without transverse
reinforcement where the size
effect was dominant.
-
Among the beams tested in the program, four beams in BN senes
were selected to
compare with the results acquired in this 2m beam deep
experirnental program. Their properties
and the cross-sectional details are given in Table 2.1 and
Figure 2.6 respeaively.
Table 2.1 Properties of BN Series Specimens
Series 1 BN Senes s pecimen / ~ ~ 1 2 . 5 j ~ ~ 2 5 j BNSO 1
BNIOO
- -.
Beam Dimensions 1 1 - 1 1
Cross Sectionai Dimensions Width, k ( m m )
Shear Span Ratio, I ald 1 3.07 1 3.00 1 3.00 1 2.92
300
Shear Span a (mm)
~oncrete Cylinder Strength W a ) -
37.2 37.2 37.2 37.2
Height, h(mm) 1 125
Longitudinal Reinforcemen t 1 1 1
300
338
250
300
676
Bottom
300
500 1000
1350
3-Ml0 ( A = ~ o o ~ )
2700
3-MIS ( A = ~ o o ~ ' )
2-M20,l - M X ( A 4 ~OOIIUII~)
3-M30 ( ~ = 2 1 00m2)
-
BNIOO
BN50, BN25, and EN1 2 have dimensions 50%, 25%, and 12.5% of BNl
O0 respectively.
BNIOO BN50 Figure 2.6 Geometric Details of BN Series
-
2.2 Review of Code Provisions
In this section, shear provisions in two codes are briefly
reviewed. They are AC1
(American Concrete Institute) 3 18-99, CSA (Canadian Standard
Association) 4 2 3 . 3 -94.
2.2.1 AC1 318-99
AC1 318-99 predicts that the shear strength of a concrete member
is provided by the
concrete web and, if the member has shear reinforcement, by the
sh= reinforcement. The s h w
strength provided by concrete, V,, is taken as the same value
for beams with and without shear
reinforcement and was denved empiricdy from many experirnental
data. The shear
reinforcement contribution, V,, is calculated based on the 45'
tmss d o g y . As a result, for non-
prestressed concrete members with normal strength concrete and
transverse reinforcement is as
follows.
[mm and MPa] (Eqn. 2.1)
AC1 3 18-99 requires that minimum shear reinforcernent have to
be provided in members
where factored shear force exceeds one-half of V,. However slabs
and footings are excluded
from this requirement.
42 A, = 0.33- [mm and MPa] (Eqn. 2.2) fY
When shear reinforcement is placed, the spacing has to be less
than 610rnm (24") and
-
2.2.2 CSA423.3-94 (General Method)
CSA423.3 ado pted the General S hear Design Method (hereafter
cded General Method)
that is based on MCFT as one part of its shear provisions.
The expression of the General Method for shear capacity consists
of the concrete
contribution and shear reinforcement contribution in the same
manner as AC1 3 18-99. However
both contributions are computed based on MCFT satisfjmg
cornpatibiiity and stress-strain
relationship of cracked concrete. As a aeesult, General Method
has the ability to consider some
factors which AC1 doesn't such as strain in longitudinal
reinforcement, maximum aggregate size,
crack spacing, and so on.
The expression is as foUows.
v = v, + Y, =p + 4f,dv cote S
[mm and MPa] (Eqn. 2.3)
p is a measure to represent the ability of the concrete member
to carry tensile stresses across potentid diagonai cracks. Since P
determines the magnitude of concrete contribution, this General
Method is also called Beta Method. The angle of diagonal cracks, 0,
is assumed to be
the angle of principal compressive stress in cracked concrete
with respect to longitudinal
reinforcement.
For members without web reinforcement, Table 2.2 or Figure 2.8
provides P and 0 with respect to strain in longitudinal
reinforcement and the crack spacing parameter, %, which is
determineci by the layout of longitudinal reinforcement as show
in Figure 2.7. The values in the
table and the figure were denved for a maximum aggregate size of
19mm. However the values
can be used for other
inaead of using st.
aggregate sizes using an equivalent spacing parameter, s, by
Eqn. 2.4,
[mm] (Eqn. 2.4)
where a refers to a maximum aggregate size.
A table and a graph are also prepared for members with at least
minimum web
reinforcement (See Table 2.3 and Figure 2.9). In this case,
average shear stress induced at the
specific section should be referred to instead of the crack
spacing parameter.
-
After the determination of and B, the strain in longitudinal
reinforcement, E, has to be
checked if'its assumed value in detennining P and 6 is larger
than the one calculated by Eqn. 2.5. Othenvise the values for ,8
and 8 should be revised using the ones for a higher E,
[mm and MPa] (Eqn. 2.5)
For members subjected to relatively low shear stress levels, the
spacing of transverse
shear reinforcernent shall not exceed 0.7d or 600mm.
(II) Mmmkr wlthout atlrrups and wlth cont.ntrmted longltudinil
nlnlorwment
(III) Mmikrrrtth0ul8ürrtIpr butwtth ml( dlrtrlbuld longltudlnil
mlntorcmnent
Figure 2.7 Values of Crack Spacing Parameter (Adapted f?om Ref.
9 )
-
Table 2.2 Values of 1 and 0 for Section Not Containing
Transverse Reinforcement --
Longitudinal ~train, t; < < s < -
0.ooos o.oo10 0.001s 0.0020 0.263 0.214 0.183 0.161 32" 34. 36O
38"
0.235 0.183 0.156 O. 138 370 4 1" 43" 45"
Figure 2.8 Values of and 0 for S edon Not Containing Transverse
Reinforcement (Adapted f?om Ref 9 )
-
Table 2.3 Values of ,û and 8 for Section Containing Transverse
Reinforcement
Figure 2.9 Values of p and û for Section Containing Transverse
Reinforcement (Adapted nom Ref. 9)
-
2.3 Bnef Introduction of Analysis Program
Among the many programs for the analysis of reidorced concrete
structures developed at
the University of Toronto based on the MCFT, a sectional
anaiysis program was used for
analysis in this research.
2.3.1 Response-2000
Response-2000 has been devrlcped by Bentz as a part of his Ph.D.
research project under
the supervision of Collins. This is a two-dimensionai sectional
anaiysis program for beams and
columns. In this program, cross-sections are discretized into
concrete layers and longitudinal
reinforcing bar elements. Longitudinal strain in each of the
layers and elements follows the
comrnon assurnption of "plane sections remain plane".
The program finds out a satisfactory state for the longitudinal
strain distribution and the
shear stress distribution across the cross-section based on
MCFT. Even though it was developed
based on MCFT, it is capable of using some other concrete
matenal models suggested by other
researchers in tenns of compressive stress-strah curve, tension
stiffening, and compression
sofiening of concrete. In this research, default selection
automatically chosen by the program
was used throughout the analysis, which are:
Popovicsmiorenfeldt/Collins for compressive
stress-strain curve, Vecchio-Collins 1986 for compression
sofiening, Bentz 1999 for tension
stiffening. Tensile strength of concrete was calculated using
0.33JfC; rather than using the
value the program automatically gives.
In spite of being a sectional analysis program, Response-2000 is
able to predict full
member response such as deflected shapes and the Ioad-deflection
curve of a span by perforrning
sectional analysis for a number of sections dong the span and
then integrating the calculation
results. In this research this &naion was fully used to
analyze experimental results. However,
since Response-2000 can't take into account a combination of a
dead load and an applied load,
the analysis was undertaken by considenng only the applied
Ioad.
Response-2000 and its manual are available fieely for use fiom
the World Wide Web at
the address of http://www.ecf utoronto.ca/-bentz/rîk-htm.
-
heu on Cnek
-. - . .- - -
Figure 2.10 Exarnples of the Screens of Response-2000
-
3 Experimental Test Program
As descnbed in 2.1.1, the data accumulation of shear strength of
deep beams, especiaiiy
ones with over l m in depth, is very limited. Therefore an
experimental project involving tests of
2m deep beams was initiated as a part of this research. The
details of this test program are
explained in this chapter.
5 . Specimen Detaiis
Two lightly reinforced beam specimens were constmcted and tested
in the Mark Huggins
Stmchiral Laboratory at the University of Toronto. Table 3.2
sumrnarizes the properties of the
specimens and their geometric properties are given in Figure
3.2.
The dimensions of the specimens were 12m in length, 2m in depth,
and 300mm in width.
The size of the specimens was determined considenng the
laboratory layout and the capacity of
the indoor Crane. The length of shear span is 5 . 4 ~ which
resulted in a shear-span-to-effective
depth ratio of 2.86.
Both specimens contained 0.74% of bottom longitudinal
reinforcement provided by six
M30 rebars. Three M20 rebars at the top were placed in order to
provide some bending strength
against unexpected loads dunng moving of the large beams. Ail of
the covers and the spacings of
longitudinal reinforcement satisfied the requirements of the CSA
code.
Shear reinforcement was provided not by usual stirrups but by
T-headed bars (as shown
in Figure 3.1). T-headed bars have a round head at each end and
the heads are designed to work
as anchors. More importantly this anchorage syaem is easy to
place for deep slabs which these
specimens were intended to represent. The round heads had an
area equal to about 7 t h e s the
bar area and the dimensions of the heads are shown in Table 3.1.
The length of the bars was
about 1890mrn fiom inside to inside of the heads. Headed
Reinforcement Corp. in California
manufactured the bars used for this project.
Each end of the two specimens was designed to have a dEerent
configuration of shear
reinforcement with the intention of obtaining a total of four
different test regions. The fust
specirnen had no shear reinforcement in one of the ends and one
USA #9 T-headed bar at the
middle of the other end. The other specimen contained USA #6
T-headed bars at a spacing of
1350mm in an end and USA #4 T-headed bars at a spacing of 590mm
in the other end. The site
-
of the bars and their corresponding spacing were determined so
that each end has the minimum
Avf, shear reinforcement ratio required in AC1 3 18-99, which is
- - - 0.33MPa. 4"s
The target concrete strength was 30MPa and it had a maximum
aggregate size of 10mrn.
The four test regions were narned according to their depth and
the size designation of the
rebars used for the T-headed bars ("0" was used for
non-shear-reinforced end). For example
YB2000!9 contained #9 T-hendet! bar in it. The beans ncre
identified by a combinadon of the
names of both ofits ends, such as YB2000/0&9.
Figure 3.1 T-headed bars
-
Table 3.1 Dimensions of Anchor Heads of T-headed bars
. . . - . - .
Table 3.2 Test Specirnen Details
1 Beam 1 YB2000/0&9 YB2000/4&6
S pecimen
T-headed bar
Specirnen
YB2000/9 USA #9
(e28.7rnm)
75
20 Anchor Head
1 East End 1 West End 1 East End 1 West End
Diameter (mm)
Thickness (mm)
YB2000/6 USA #6
1 Shear Spm 1 cAnn
YB2000/4 USA #4
Cross Sectional Dimensions Width, b, (mm)
Height, h (mm) Beam Dimensions
t
1 Shear Span Ratio, a/d
( e 1 9 . lmm) . (+12.7mm) I
I t 1
55
17
300
1
Longitudinal Reinforcement
TOP
I I
Transverse Reinforcement 1 1 1 1
38
11
300
Bottom
d (mm)
Bar Designation
3-M20 (~=900mm')
Yield Strength fi W a )
S hear Reinfo r- cernent Ratio
f , A A s ma)
2000
34420 (~=900rnm~)
6-M3 O (A4200mrn2)
1890
2000
6-M3 O (~=4200rnm')
1890
USA #9 ( ~ ~ 4 5 r n r n ' )
2700
USA #6 (A,-285 mm2)
1350
I
USA #4 (A*= 1 27mm2)
590
-
Beam ~~2000/0&9 fi
Beam YB2000/4&6
Beam YB2000/0&9 Beam
EAST
Figure 3.2 Geometnc Details of YB2000 Series Specirnens
-
3.2 Material Properties
3.2.1 Concrete Properties
Dufferin Concrete, a local ready-mi. concrete plant, provided
the concrete for this
projea. Concrete cylinders were made at the pouring. Since a
total of two tmcks were needed to
cast the two specimens sirnultaneously, concrete cylinders were
taken fiom each truck to
determine the properties of each of the concretes. The volume of
the concrete ftom the fkst
truck, dled batch ttl, was 9m3 and one h m the second tmclg
called batch #2, was 6Sm3.
Theoretically the amount of 14.4m3 out of the total 15.5m3 was
used to cunstnict the two
specimens.
The development of the compressive strength was observed by
testing the cylinden at the
age of 7 days, 14 days and 28 days ( a h 21 days for batch #2)
using a load controlled test
machine. The strengths at the age of the tests were obtained
using a 4,448kN high stifniess test
machine (MTS) with its stress-strain responses. Properties of
the concrete are shown in Table
3.3. The stress-strain curves are presented in Appendk C.
In addition to the strength properties, the s W a g e strain for
the specimens was
monitored dunng the maturing process by recording the readings
of three strain gauges on the
longitudinal reinforcernent in each bearn. Figure 3.4 shows the
shrinkage strain development.
Final values were listed in Table 3.3.
Table 3.3 Concrete Properiies
S pecimen 1 YB2000/0 1 YB200019 1 YB2000/6 1 YB2000/4 -
Cast Date 1 - c t . 13, 1999 1 Oct. 13, 1999
YB2000/4&6 B eam
Test Date 1 Dec. 16, 1999 1 Dec. 17, 1999 1 Feb. 2,2000 [ Feb.
11,2000
YB2000/0&9
Age at Test Date 1 64 1 65 1 112 1 121
--
' Shrinkage Strain on Test Date
(microstrain)
f c o n Test Date
w a )
1 The average of the readings of the three strain gauges on
longitudinal reinforcement
Batch #l
Batch #2
35.4
3 1.8
3 5.4
3 1.8
37.3
34.5
37.7
35.0
-
56 84 112 Age of Concrete (Days)
Figure 3.3 Strength Developrnent of Concrete
-300 ' Figure 3.4 Shrinkage Strain Developrnent
-
3.2.2 Steel Properties
The stress-strain responses of steel coupons taken from the
rebars were obtained using a
1,000kN universal dynamic test machine (MTS). The properties are
s u d e d in Table 3.4.
M30 and M S O rebars were used as longitudinal reinforcernent
and USA #9, #6, and #4 rebars
were placed as shear reinforcement. The stress-strain responses
for the reinforcing bars are given
in Appendix C.
The stress-strain results for the M30 longitudinal rebars
hdicated that the bars may have
corne f b m different heats (named as type A and type B).
Therefore additional tensile tests were
undertaken for coupons cut f?om YB2000/4&6 afker its tests
so as to identify the strength of each
longitudinal rebar. The identified location is shown Ui Figure
3.5.
Table 3.4 Properties of Reinforcing Bars
South 1
Rebar Size
USA #4
USA #6
USA #9
M20
WeA
Figure Longitudinal Rebars in YB2000/4&6
Diameter '-)
12.7
19.1
28.7
19.5
IM301xI 29.9 ( 700
Cross- Sectional
Area (mm2)
127
285
645
300
462
Yield Stress a )
468
465
470
433
447
658
Ultimate Stress W a )
68 1
657
692
63 8
610
13.7
'train hardening
Strain wl
( d m ) 4.4
13.8
4.5
14.1
14.8
129 200000
Rupture Strain htt
(mdm)
113
132
132
148
129
Theoreticai Young's Modulus
W a )
200000
200000
200000
200000
200000
-
3.3 Specimen Construction
3.3.1 Form-work
The construction of form-work was commenceci at the end of June,
1999 after design
calculations were done so that it would hold the pressure of
fksh concrete safely during the pour.
The form-work was also designed so that the two spechens could
be cast sirnultaneously. The
forrn-work was presented schematically in Figure 3.6 and in more
detail in Figure 3.8.
2*6 lumber
Threaded steel rods
ma. 0.0 O Q O 0 0 0
Figure 3.6 Cross-sectional New of Fom-work
Shce the form-work was very long, it was designed to wnstnict it
as a series of five
panel cornponents. Four of the five panels were 8 feet
(2438rnrn) long and the last panel
measured 2247m.m. Ail walls were constmcted fiom ?4 hch sheets
of plywood specially
processed to be able to be reused for future pouring. The
extenor walls were stiffened by two-by-
sixes running vertically, while the rniddle walls, which were
shared by both specimens, were
reinforced by two-by-fours. The extenor waiis were supported
laterally at three points: a sheet of
plywood screwed to the base sheets at the bottom of the
fom-work, and doubled channels at the
middepth and aiso at the top. Threaded steel rods were used to
tie the both sides of the channels
together. To cut the fiction between concrete and the threaded
steel rods at the middepth, the
rods were covered by PVC pipes in the fonn-work
The construction of the fom-work consiaed of the following
procedures.
-
Firstly, a layer of base sheets was laid on the laboratory floor
by adjusting its elevation to
keep them nearly level throughout the entire length of the
forni-work. Then two rows of 3OOmm
wide plywood were screwed to the base sheets so that they would
provide a groove to hold the
bottom side of the middle walls. Then the middte waiis were
built on the base sheets.
After strain gauges were applied to longitudinal rebars, bottom
rebar cages were
assembled on the base sheets (Bearns YB2000/0&9 on the south
side and Beam YB2000/4&6 on
the north side). The location of each rebar was secured by means
of many sets of a 50mm hi&
plastic chair and a 5rnm thick plastic plates, 50mm concrete
cubes, and Ml0 bars as show in
Figure 3.7. After the T-headed bars were hooked and tied to the
longitudinal rebars the exterior
walls and end walk were built with the aid of the indoor Crane.
Then the doubled channels were
attached to the form-work with the threaded steel rods and the
plywoods were screwed at the
bottom as weI1.
Findly the top rebats, which were prefabricated with 300m long
Ml0 bars on the floor,
were hung nom the top threaded steel rods with wires. 300mm long
wood spacen were dso
placed in both beam forms at the top to keep the width unifonn
during the cast. AU surfaces of
the plywood contacting the concrete were oiled prior to their
installation.
In case of unbalanced lateral force by fiesh concrete pressure,
some support pipes were
placed outside of the form-work in order to provide extra
lateral raistance. The support pipes
were used to adjust the plumbness of the form-work as well.
\ Base Plywood Figure 3.7 Bottom Rebar Cage
-
3.3.2 Concrete Pour and Cure
Concrete was cast on October 13th 1999. Since the total volume
required to cast two of
the beams was about 14.4m3, two 9m3 tmcks were used to transport
the concrete from the
concrete plant. On the arriva1 of the trucks, the slump of the
concrete was checked and
superplasticizer was added to the rnk to ensure an appropriate
placement of the concrete.
A large concrete bucket with the capacity of 0.9m3, maneuvered
by the 10-ton Crane in
the labor;itory, was used for the connete pour. Concrcte was
evenly distributed h t o tha two
molds in the fom-work to avoid laterai displacement of the
form-work. As a result, when the
batch #1 concrete was poured both beams were cast up to almost
the same height. Hence the
batch #1 concrete was located at the bottom part of the two
beams, which was assumed to be
approximately 1.1 to 1.2m deep, and the rest of the beams was
made fkom batch #2 concrete (0.8
to 0.9m deep).
On the south side of the fom-work, a fïxed scaffolding covering
east side of the fom-
work was built in advance and the rest was covered by a rolling
tower so that people could climb
up on the fon-work. A 3m long vibrator was employed fiom the top
side of the forrn-work to
fulfill concrete in the form-work. The wooded spacen placed at
the top of the forrn-work were
removed when the pour was near completion. The pour started at 9
o'clock in the rnoming and
finished at approximately 1 o'clock.
M e r the initial setting of concrete, the specimens and
cylinders were covered with moist
burlap and plastic sheets to rninimize the moisture loss during
the cure. The beams were kept
under this condition for a week. M e r that the exterior walls
were split ofFfiom the specimens,
which were then cured in air dry condition until their
tests.
From shortly after the completion of the pour, three of the
strain gauges on longitudinal
reinforcement in each bearn were kept measured with a main
indicator for the purpose of
obtaining their shrinkage strain.
-
3.3.3 Specimen Transportrtion
Because each beam weighed almost 17 ton, the 10-ton crane of the
laboratory couldn't
carry the whole beam. Therefore the following procedure was
taken utilizing a total of four sets
of rollen (See Figure 3.9) in order to transport the beams from
the construction area to the
testing area under the Baldwin loading machine in the
laboratory.
Firstiy one of the ends of the specimen in the fom-work was
lifted by the crane and
shifted to the side of the form-work with the other end
remaining in the form-work. Then the
other end was lifted and shifted in the sarne way. Then each end
was set on a steel pedestal and
fastened to two bracing stnits of the pedestal with bolts. Pnor
to the transportation the laboratory
floor was cleaned and some lines were drawn on the floor as
guides. M e r two sets of rollers
were placed under each steel pedestal (See Figure 3-10), the
crane dragged the specimen laterally
to the testing position under the loading machine (See Figure
3.12).
M e r settling the specimen to the right position, the specimen
was unfastened from the
bracing stnits and supports (See Figure 3.1 1) were placed under
the specimen.
Figure 3.9 Rollers used to move the specimens
-
Figure 3.10 Transportation Set-Up
Figure 3.11 Support
-
Figure 3.12 Transportation of Specirnen
-
3.4 Test Rig Detrils
Because of the magnitude of force required for the tests and the
size of the specimens, a
5,400kN Baldwin universal test machine (load-control actuator)
was chosen for the tests. The
specimens were tested under the condition of three point
loading. Between the Baldwin jack and
the specimen, a rocker type support was placed in order to allow
only rotation there. Anticipating
large bearing stress under the loading jack, a steel plate (1
1.5" long, 12" wide, and 1" thick) was
placed undemeath the suppon. At each end of the specimens, a
steel rollet support was placed on
the steel holder providing free rotation and longitudinal
displacements. Mixed plaster was placed
at al1 supports in order to create tight comection; thereby
minimiUng stress concentrations due
to irregularities of the surface of the concrete.
3.4.1 Instrumentation and Data Acquisition
Figure 3.13 shows a photograph of the test set-up. Ail of the
sides of the specimens w
painted white with Bat latex paint to emphasize crack
patterns.
Figu ire 3.13 Experimental Test Set-Up
-
Ten LVDT's (Linear Varying Displacement Transfomiers) were
placed as shown in
Figure 3.14 to measure the deflected shape of the specimen. Two
of the LVDT7s, which were
able to measure î50mm, were mounted on each side of the specimen
at the midspan to see ifany
tilting occurs dunng testing and aiso to obtain more accurate
midspan deflection by taking the
average of both readings. The other eight LVDT's (A25mm) were
placed directly under the
centre-line of the beam.
Measured midspan deflettion at the second test of each b a n
(Le. Specimen YB200019
of Bearn YB2000/0&9, Specimen YB2000/4 of Beam
YB2000/4&6) was modified in the
following way. For those specimens the acquired data of midspan
deflection were replaced with
the deflection data of the first specirnen up to the maximum
load attained at the first test. And the
following data were shifted to make a load-deflection curve.
This adjustment was done to
counter the effects of cracks formed during the fint test.
Figure 3.14 Layout of LVDT's for Beam Deflection
On the nonh side six grids of LVDT's were located in order to
provide average shear
strain of the grids (See Figure 3.15). For compression stmt of
the grids, LVDT's measuring
*15mm were mounted and for tension struts LVDT's measuring
k25rnrn were employed. At the
rniddle of each bar, a d e r support was glued on the concrete
to prevent the bar from sagging.
-
L 1
1750 1500 1 500 1250 . 1250 1500 -- 1500 1750 A
EAST WEST
-
1900*1900rnm grid Figure 3.15 Grids of LMT' s
On the south side, a total of 164 mrich targets were giued to
capture the strain
distribution of the concrete surface. Hand-held mnch gauges were
used to measure the length of
horizontal, vertical, and diagonal spacings of the grids. Pnor
to the test, initial readings were
taken and strains in following load stages were cdculated by
subtracting the reading obtained at
the load stage from the initial reading. The meamred concrete
strains in d m units are
presented in Appendix B.
Dunng the tests, nirich reading was perfonned ody for the end
expected to fail at the test
except for the test of YB2000/6. At the test of YB2000/6, both
ends were measured because
there was a small possibility that YB2000/4 might fail first.
With the help of three people the
time taken to measure the grids in an end was about 25 minutes
at each load stage.
-- -
Figure 3.16 Zurich Target Layout
-
Figure 3.17 Measurement using Zurich Gauges
3.4.2 S train Gauges on Rein force ment
Reinforcement in the beam specimens was instnimented with many
strain gauges as
shown in Figure 3.18. S train gauges wit h 1Om long leadwires in
3-wire syaem, FLA-5- 1 1- 1 OLT,
produced by Tokyo Sokki Kenkyujo Co. Ltd. were used for the
project. The leadwires were tied
to rebars with reinforcing tapes and they ail came out fiom the
top of the specimen in the vicinity
of the centre support. For longitudinal rebars two strain gauges
were attached at the sarne
location on both sides of the rebar because of an expectation
that some of the strain gauges
would be destroyed dunng the pour. If both gauges s u ~ v e d
the strain at the location was
calculated by taking the average of the two gauges.
-
Strain Gauaes on Lonaitudinal Reinforcernent œ
Strain Gaucies on Transverse Reinforcement
B
South
Figure 3.18 Strain Gauges in Specimens
North
T'-heoded bar
?ries
tries
-
3.5 Load Procedure
The tests were done by applying a venical downward load at the
bearn's midspan until
ultimate conditions were attained. In order to keep the area
under the loading jack intact and to
test the other half span, Ioading was done very carefully
especially near failure. During the tests,
load stages were taken for measurement of crack width, crack
pattern, and zurich reading. The
applied load was leveled off at each load stage and decreased by
approximately 10 % of the load
for the salie of çafety duRng the load stage.
3.6 ReinforcementafterTest
Since each end contains a difEerent configuration of shear
reinforcement, &er the fks t
test of the beam, the failed end had to be reinforced to recover
the strength for the next test for
the other end. Five sets of Dywidag high-strength bars with a
diarneter of 1" were employed and
the failed end was strapped with them as shown in Figure 3.19.
During the test, width of major
cracks in the previously failed end was observed to confirm that
the reinforcing system was
working well.
At the fint test of Bearn YB2000/4&6, the fiexural
compression zone on the side of
YB2000/6 collapsed severely due to the siippage of a major shear
crack (See Figure 3.20). Hence
the cmshed zone was repaired in the following way. Firstly the
crushed zone was chipped off
and al1 unstable concrete was removed. Then a fast hardening
mortar, EMACO S88 CI, produced
by Master Builders Inc. was used to fil1 up the void. Two days
later two 4" mortar cyünders,
which were taken at the pour, were tested and the strength was
found to be more than the
strength of the original concrete. A % inch thick steel plate
was placed on the portion and it was
clamped to the specimen by two of the five sets of prestressing
bars. The portion after the repair
is s h o w in Figure 3.2 1.
-
Figure 3.19 Failed End Reinforced by Dywidag Bars
-
Figure 3.20 Collapsed Flexural Compression Zone on the Side of
YB200016
6 . d AG5
Figure 3.21 Repaired Portion
-
4 Test Results and Analysis
In this chapter, the test results are discussed. In addition,
some analysis was performed
and the results are compared to the expenmental results. The
validity of the code provisions for
shear strength is also investigated.
The shear forces shown in this chapter were calculated at the
cntical section for shear,
which is d, away from the applied load, considenng the effect of
the self-weight of the beam.
The shear force due to the self-weight of the beam, Va is
Vd = y.h*w*d,, = y-hw0.9d = 23.5kN/m3x2mx0.3mx0.9x1.89m =
24.0kN
This Vd was added to the half of the applied load to obtain the
shear force at the critical section.
4.1 Overview of Result of YB2000 Series
Table 4.1 shows main result obtained fiom the tests of YB2000
senes beams. To
investigate the effect of member depth on shear strength, four
beams in the BN series (See Table
2.1 for details of these beams) are listed in the table as well.
The Ioad-deflection curves acquired
fiom the tests are shown in Figure 4.1.
Beam YB2000/0&9 containhg Specimen YB2000/0 and YB2000/9 was
tested on
December 16th and 17th 1999. Specimen YB2000/0, with no
transverse reinforcement,
undenvent a very bnttle failure. Pnor to the fdure, flexural
cracks, which initially propagated
vertically, inclined their directions towards the loading point
as the load increased. Finaliy at a
load of 461 kN, the plot of load-deflection curve showed its
peak and went into the post-peak
stage. At the maximum load the defection was only 8.0mm at
midspan. That is the failure
deflection was 1/675th of the span.
M e r reinforcing the failed end, Specimen YB2000/9 was tested
on the following day.
The end showed a big improvement due to the addition of only one
bar of USA $9 and finally
carried an applied load of 897kN before the compression mne near
the loading point was pushed
up to collapse.
The next two tests were done in February 2000. Beam
YB2000/4&6 demonstrated a good
distribution of cracks than Beam YB2000/0&9. A similar
failure mode as Specimen YB2000/9
o c m e d on the side of Specimen YB2000/6 when a load of 1053kN
was applied. At failure of
YB2000/6 Specimen YB2000/4 seemed to be very close to failure
judghg from the high strains
in the transverse reinforcement and the very wide shear
cracks.
-
M e r the repair was done as explained in 3.6, SpecimenYB2000/4
was tested ten days
later. At an applied load of approximately l25OlcN (midspan
deflection of 45mm), the specimen
showed flexural yielding of longitudinal reinforcement and the
deflection continued to increase.
The magnitude of the load was almost the sarne as an estimate by
Response-2000 (it prediaed
that a load when the longitudinal reinforcernent starteci to
yield was 1220kN). Finally the
compression zone failed at a midspan defieaion of 94mq and the
maximum applied load
obtained during the flexural yielding was 1300M.
YB 2000 senes - Load vs. Deflection
Midspan Defiedion (mm) Figure 4.1 Load-Deflection Curves for
YB2000/0, YB2000/4, YB2000/6, and YB200019
-
The photographs in the following pages show cracking pattern
obtained at failwe of the
specimens. The shear failure loads labeled on the specimens in
the photos were calculated as the
shear force at 2m away from the loading point based on less
accurate reading from the operating
console of the testing machine. Their values are somewhat
difSerent fiom the ones s h o w later in
this chapter, which were obtained as the shear force at d, away
from the loading point based on
data from the computerized data acquisition system.
-
Figure 4.2 Crack Pattern at the Final Load Stage of YB2000/0
-
Figure 4.4 Crack Pattern at the Final Load Stage of YB2OOO/6
Figu
-
Table 4.1 Expenmental Result for Beams of YB Series and BN
Series
6, at
failure
1 The first value shows the strength of batch #1 of concrete and
the second one is for batch #2. 2 Failed in flexure
-
4.2 E f k t of Member Depth on Shear Strength
4.2.1 Effect of Member Depth Observeci in Test Result
The expenmental results of Specimen YB2000/0 and the specimens
in BN series clearly
shows the significant decrease in shear stress at fdure that
occurs as mernber size increases (See
Table 4.2). The specimens in this table aii contained about the
sarne percentage of longitudinal
reinforcement and their concrete strengths were also very
similar. This result atnrms the
importance of the effea of menber size and it is very simi1ar to
the result of Shioya (See Figure
2.5).
It is noted that as the member size Uicreases the strain in the
longitudinal reinforcement at
failure decreases. Thus large size elements are more likely to
fail in shear and hence it is
necessary to have an accurate prediction method for shear
strength of such members.
Table 4.2 Expenmental Result for Beams not containing shear
reinforcement
The fint value shows the strength of batch #1 concrete and the
second one is for batch #2.
Specimen
YB2000/0
BNlOO
BNSO
BN25
BN12
The Modified Compression Field Theory explains the eflect of
member depth by the
increase of effective crack spacing which results in large crack
widths and decreased shear
transfer capacity across the crack. The crack patterns of
Specimens YB2000/0, BN100, and
BN50 show very similar pattems regardless of the difference of
member depth (See Figure 4.6).
This indicates that the approach of MCFï to size effect is
correct because a member with larger
depth has larger spacing and wider cracks. For Specimen
YB200010, the crack spacing at the
d (mm)
1 890
925
450
225
110
6, at
failure
8.0
5.9
5.4
5 .O
2.6
f c W a )
35.4/3 1 -8 ' 37.2
37.2
37.2
37.2
EX
(X 10-~)
0.83
1 .O
1.5
1.7
2.5
vw (w 255
192
132
73
40
7-
0.45
0.69
0.98
1 .O8
1.21
-
middepth is almost d , which is approximately 1.8m according to
the calculation in Appendix A,
and the maximum crack width measured larger than Specimens BNlOO
and BNSO.
WEST YB2000/9 Içouth y ~ ~ o o o / o s . . . . . a
EAST
. . . . . . . . o . . . * . . . . . O . . . . .
25
- . - BNSO
Figure 4.6 Cornparison of Crack Patterns
-
4.2.2 Prediction of Beam's Shear Strength Using Design Codes
Even though the influence of mernber depth on Mure shear stress
has been discussed for
many years, not al design codes appreciate the eEect
sufficiently. In this section, a cornparison
between the experimental results and predictions using some
design codes are made. In addition,
the specirnens were analyzed using Response-2000. Table 4.3
shows the experimentd results and
estimation using AC13 18-99, CSA-A23.3-94, and
Response-2000.
The K I code predias ml! the shev apacity for the specimens with
relatively small
depths. However Specimens YB2000/0 (d=1890mm) and BNlOO
(d=925mm) had much smaiier
shear strength than the ones the AC1 code predicts. Therefore it
is of a considerable concem to
use the AC1 code for mernbers with no shear reinforcement which
are deeper than about 0.75m.
The AC1 code requires that beams contain a minimum area of shear
reinforcement if the factored
shear force exceeds O.Sc$,V, and this requirement usually
mitigates the concem for its
unconservative prediction. However, the trend of the size effect
shown in Table 4.2 indicates that
the actual strength can be less than 0.43 (=0.5$.=0.5x0.85)
times the predicted strength for
members with over 2m depths. Besides the 0.54,Vc requirement
does not apply to slabs and
footings. Therefore the shear design according to the AC1 code
possibly leads to very
unconservative design for large depth memben.
The CSA code, on the other hand, yields conservative predictions
for the BN senes and
gives a close but somewhat unconservative estimate for the
failed load of Specimen YB2000/0.
The unconservative aspect of the predictions seems to increase
as the rnember depth increases.
Hence funher improvernent to provide more accurate predictions
seems to be necessary for the
CSA method with more expenmental data for the shear strength of
larger specimens being
acquired.
Fairly accurate estimates were made by Response-2000 throughout
the range of member
size. Figure 4.7 compares the load-deflection curve obtained
fiom the test of YB200010 with the
curve calculated by Response-2000. Although the andysis result
doesn't take into account the
dead load of the specimen itself0.e. the curve starts at zero
point), the behaviour of the specimen
was wel1 reproduced by Response-2000 while it predicts somewhat
higher stifihess after initial
crac king.
-
Figure 4.8 shows variation of failure shear stress ratio ( ~ 1 6
, d f i ) with beam depth and
the prediction results. It is evident fkom Figure 4.8 that the
CSA code and Response-2000
represent size effect on shear strength relatively weil.
i
I 1
j
O 1 2 3 4 5 6 7 8 9 10
Midspan Deflecb'on (mm)
Figure 4.7 Shear Force-Deflection Curve for YB200010
-
Table 4.3 Prediction for Specimens without Transverse
Reinforcement using AC1 3 18-99, CSA-A23.3-94, and
Response-2000
Specimen
YB2000/0
b
BN100
SR,, at failure (mm)
5.7
-
Figure 4.8 Variation of failure shear stress ratio with bearn
depth
-
4.3 Effect of Minimum Shear Reinforcement on Shear Strength
4.3.1 Effect of Minimum Shear Reinforcement in Test Results
Table 4.4 summarizes the results of the specimens with
transverse reinforcement. Results
h m Specimen YB200010, which contains no transverse
reinforcernent, are aiso included. In
addition Figure 4.9 to Figure 4.11 compare the load versus
midspan deflection relationships of
YB200014, YB2000/6, and YB2000/9 with YB2000/0.
Table 4.4 Experimental Result for Bearns of YB Senes
1 The fist value shows the strength of batch #1 concrete and the
second one is for batch #2. 2 Failed in flexure
S p ecimen
L
YB200014
YB200016
YB200019
YB200010
Al1 of the specimens with transverse relliforcement showed a
signifiant increase in load
capacity and ductility in cornparison to Specimen YB200010.
Specimen YB2000/4 actuaily failed
d (mm)
1890
1890
1890
1890
in flexure at a load that was almost shear capacity judging fiom
the main readings of transverse
reinforcement. The shear capacity of Specimen YB2000/4 was at
least 2.64 tirnes as great as
Specimen YB200010 due to the presence of just minimum transverse
reinforcement. Specimen
f c W a )
35.4/31.8 ' 37.3134.5 ' 37.7135.0 ' 35.413 1.8 '
YB200016, which contained bigger T-headed bars spaced wider
apart than SpecimenYB2000/4,
gained less increase in shear strength but was still 2.16 times
as strong as YB2000/0. The one
s (m)
large T-headed bar in YB200019 resulted in this specimen being
1.85 times as strong as
YB2000/0. Moreover ail three specimens with T-headed bars fded
at a peak rnidspan deflection
PV fv @@a)
which was three to four times larger than that of Specimen
YB2000/0. These results prove that
this srnaii amount of shear reinforcement, A, = 0 . 3 3 Q 7 was
adequate to serve as minimum fY
b O
590 1 0.33
shear reinforcernent for these large specimens.
674
550
472
255
1350
2700
-
b at
failure
0.33
0.37
-
Ex
(XIO-~)
- * 34
27
8.0
I
- 2
2.1
1.5 I
0.83
-
Midspan Defiedion (mm) Figure 4.9 Load-deflection curve for
YE2000/4
O 5 10 15 20 25 30 35 40 45 50
Midspan Defiedion (mm) Figure 4.10 Load-deflection curve for
YB2000/6
-
Midspan Defiedion (mm) Figure 4.11 Load-deflection curve for
YB200019
The crack patterns of the specirnens with transverse
reinforcement (See Figure 4.3 to
Figure 4.5) show well distributed cracks compared to Specimen
YB2000/0. In addition it
indicates that more cracks and smaller crack widths as the
spacing of the shear reinforcement
becornes closer. This is clearly shown in the photographs of
YB2000/4&6 at the same load stage
(See Figure 4.12). In the photographs YB2000/4 end shows
relatively more distributed aacks
and its maximum crack width is 4.0rnm compared to 6.0mm at
almost the same location on
YB2000/6 side.
This crack behaviour is certainly one of the reasons why, while
keeping the sarne amount
of shear reinforcement, closer spaced shear reinforcement
results in a greater increase in shear
capacity. That is, the capability to control crack width of the
closer spaced shear reinforcement
resulted in bigger shear transfer across the cracks. Figure 4.13
shows the ability of a T-headed
bar to control cracks. In the photograph, though the side of
YB2000/0 has failed, the end with a
transverse bar has only a few cracks and no visible crack
crossing the bar.
-
Figure 4.12 Crack Pattern of YB2OOO/4&6 at Load Stage Close
to Failure
-
Figure 4.13 Crack Pattern of YB2OOOI9 at Failure of YB200010
-
4.3.2 Prediction of Beam's Shear Strength
Estimations of the shear capacity of the specimens were made
using AC1 318-99, CSA-
A23.3-94, and Response-2000. The results are surnmarized in
Table 4.5. It should be noted that
among the three specimens only YB200014 satisfies 600rnm maximum
spacing of shear
reinforcement requirement in these codes. The code predictions
for YB2000/6 and YB200019,
neglecting the violation of the limit, are shown to help in
judging the need for this requirement.
Table 4.5 shows a very good agreement of the failure ioad with
the prediction using the
CSA code while the AC1 code also made a relatively accurate
estimate considering that the reai
shear capacity was somewhat higher than the value shown in Table
4.5 as shear strength.
Previous research shows members with at least minimum shear
reinforcement are tess influenceci
by the size effect of member size. The AC1 code, which doesn't
consider this effect, can be used
with only a smail loss in safety for large memben with normal
strength concretes as long as they
satisQ the minimum shear reinforcement requirements.
Response-2000 gives somewhat conservative estimate for specimen
YB200014 and it
predicts that the specimen fails in shear rather than in flexure
as really occurred. Figure 4.14
compares the experimental result and analytical result using
Response-2000.
i
i
I 1 est Result 1 4 Response2000 Result
O 5 I O 15 20 25 30 35 40 45 50
Mfdspan Deflection (mm)
Figure 4.14 Shear force-deflection curve for YB2000/4
-
Table 4.5 Prediction for Specimens of YB series using AC1 3
18-99, CSA423.3-94, and Response-2000
1 Failed in flexure 2 Prediction for shear capacity
Specimen
YB200014
YB2000/6
YB200Ol9
f c ( M W
37.7 .
350
37,3 - 34.5
35.4
31.8
Vcw (kW
674 '
550
472
VACI (W
772
7512
764
742
776
746
Vcs A (W
655
639'
649
633
658
636
VR‘S- (W
563
562
548
547
572
571
cd VACI
0.87
0.90
0.72
0.74
0.6 1
0.63
VaqJ VCSA
1 .O3
1 .O5
0.85
O, 87
0.72
O. 74
Veld V R ~
1.20
1.20
1 .O0
1 .O1
0.83
0.83
6~ at failure
(mm)
1
34
27
g~apmv at failure
(mm)
30
30
30
3 1
30 b
3 1
-
5 Conclusions and Recommendations
5.1 Conclusions
1. It is possible for a 2m deep member made fiom approximately
35MPa concrete and not
containing transverse reinforcement to fd at the very low shear
stress of 0.45 MPa
Cornparisons with shdower specimens show that this fdure stress
is sigdcantiy
eEected by rnember depth due to iarger crack spacings and wider
crack widths.
AY 1' 2. The addition of a srnaii amount of shear reinforcement
(- = 0.33hPa) greatly b w s
improves the shear capacity and ductility of large members.
Midspan deflections at
failure for the specimens with minimum transverse reinforcement
were three to four times
larger than those for the specimen without transverse
relliforcement.
3. The increase in shear capacity due to the presence of shear
reinforcement varied fiom
85% to 164% depending on the spacing of transverse
reinforcement. As the spacing
becarne closer, the capacity becarne bigger because of the
better crack control ability.
However it is noted that adding only one transverse bar at the
rniddle of the haif span
dmost doubled the shear capacity of the specimen.
4. Methods based on The Modified Compression Field Theory,
CSA-A23.3-94 and
Response-2000, generally predict well the shear capacity for
members with or without
transverse reinforcement and the trend of the size effect was
followed by the methods.
S. It is of considerable concem that the AC1 code predicted
shear strength for the member
without reinforcement more than twice the experimentdly
determined faiiure load.
Recognizing that the AC1 code pemits slabs and footings not to
have shear reinforcement
until the applied factored Ioad exceeds the predicted shear
strength, the code may
possibly produce severely unconservative members especially for
large lightiy reinforced
elements,
-
5.2 Recommendations
1. Since not only member depth but aiso amount of longitudinal
reinforcement has a
sigmficant effect on the shear capacity of members, tests should
be conducted with large
specimens having amounts of longitudinal reinforcement different
than the 0.74% used in
this study. Other major parameters such as concrete strength
should also be investigated.
2. Although the minimum arnount of shear reinforcement has
proved to be enough for the
specirnens in tfiis resemh, specimens witth higher strengtfi
conmte should be tested to
check the validity of the current design requirements for
minimum shear reinforcement.
3. The results of this research indicate that the spacing of
shear reinforcement significantiy
influences shear strength. Experiments should be conducted to
accumulate more data on
this effea so that the current code rules which prohibit the use
of spacings greater than
600mrn even for very deep members can be verified.
-
References
1. AC1 Committee 3 18, "Building Code Requirements for
Reinforced Concrete (AC1 3 18-99) and Commentary AC1 3 18 R-99",
American Concrete Institute, Detroit, 1999
2. Angelakos, D., "The Influence of Concrete Strength and
Longitudinal Reinforcement Ratio on the Shear Strength of
Large-Size Reinforced Concrete Bearns with, and without, Transverse
Reinforcement", M.ASc. Thesis, University of Toronto, Department of
C ' i Engineering, 1999, 181pp.
3 . .ASCE-MI Cornmittee 445 on Shear and Torsion, ''Recent
Approaches to Sheat Design of S tmctural Concrete", Journal of
Structurai Enginee~g, Dec. 1998, pp. 1375-14 17
4. Bentz, E.C., "Sectional Analysis of Reinforced Concrete
Members," Ph.D. Thesis, Department of Civil Engineering, University
of Toronto, 2000, 3 10 pp.
5. Canadian Portland Cernent Association, "Concrete Design
Handbook", Ottawa, 1995
6. Collins, M.P. and Kuchma, D., "How safe Are Our Large,
Lightly Reinforced Concrete Bearns, Slabs, and Footings?', AC1
Structural Journal, Jui.-Aug. 1999, pp. 482490
7. Collins, M.P., Mitchell, D., Adebar, P., Vecchio, F.J., "A
General Shear Design Method", AC1 Structural Journal, Jan.-Feb.
1996, pp. 36-45
8. Collins, M.P., Mitchell, D., "Prestressed Concrete
Structures", Response Publications, Canada, 1997,766 pp.
9. CSA Cornmittee A23.3, "Design of Concrete Stnictures with
Explanatory Notes*, Canadian Standard Association, Rexdal+ 1994,
199 pp.
10. Kani, G.N. J., Wow Safe Are Our Large Reinforced Concrete
Beams?", AC1 Journal, Mar. 1967, pp. 128-141
11. Kuchma, D., Végh, P., Simionopoulos, K., Stanik, B., and
Collins, M.P., 'The Influence of Concrete Strength, Distribution of
Longitudinal Reinforcement, and Member Size, on the Shear Strength
of Reinforced Concrete Beams", CEB Bulletin d'Information No. 237,
pp. 209-229
12. Shioya, T., "Shear Properties of Large Reinforced Concrete
Membef, Special Report of Institute of Technology, Shi-
Corporation, No.25, Feb. 1989, 198pp.
13. Stanik, B ., 'The Infiuence of Concrete S trength,
Distribution of Longitudinal Reinf'orcement, Amount of Transverse
Reinforcement and Member Size on Shear Strength of Relliforced
Concrete Members", M.kSc. Thesis, University of Toronto, Depariment
of Civil Engineering, l998,7 1 1 pp.
14. Yoon, Y., Cook, W.D., Mitchell, D., "Minimum S hear
Reinforcement in Normai, Medium and Hi&-Strength Concrete
Bearns", AC1 Structural Journal V.93, NOS, Sept.-Oct. 1996,
pp.576-584
-
Appendix A
Calculations of AC1 3 18-99 and CSA43.3-94 (General Method) Code
Predictions
-
Estimation of Shear Failure Load Using CSA-A23.3-94 (Gened
Method)
Sam~Ie Calculation for S~ecimen YB2000/0
Concrete Strength: f ;=3 5.4 MPa (batch #1) Maximum Aggregate
Size: 10 mm Yield Strength of Longitudinal Rebars: 455 MPa (Average
of Type A and Type B) Shear Span Length: a=5.4m Unit Weight of
Concrete: 23.5 kN/rn3
1. Find the flexural lever arm, d,
a d,, =d--=1890- 455 x 6 x 7OO/(O.8O x 35.4 x3OO) 3 3
= 1777mm
2. Calculate sectionai forces due to dead load Critical section
for shear is taken d, away from the applied load.
VD =23 .5~0 .3~2 .0~ l.777=25.l kN MD=183.3 kNm
3. Calculate the equivalent crack spacing parameter, s,
Hence s,d2000mm, s,,=2000mrn
4. Assume a value for the strain in longitudinal reinforcemeni,
gr and select values for @ and 0 fiom Table 2.2
Assume e = 0.0005. From Table 2.2, P = 0.126 and O= 59'. x
354~300~1777/1000=399.7~ V, =/?J?;'b,,,dv =0.126 J-
The sectional forces acting on the critical section are
calculated as: Shear force due to the applied load
Y, -Y, =399.7 -25.1=374.6W Bending moment
Mu = M D +M, = M D +V'(a-dv) = 183.3 +374.6x(5.4 -1.777) =
1540.5kNm
-
5. Check the strain in longitudinal reinforcement
The strain in longitudinal reinforcement is calculated as:
This hdicates that our assumption was unconservative. We must
choose a bigger value for
6. Second Iteration
Assume E~ = 0.0009. From Table 2.2, P = 0.084 and 8= 66'. x
354~300~1777/1000=266.4kN V, = p a b W d Y = 0.084 4-
The sectional forces acting on the critical section are
calculated as: Shear force due to the appiied load
Vp = V, - V' = 266.4 - 25.1 = 241.3kN Bending moment Mu = M D +
M p =MD +Yp@-d , ) =l83.3+241.3~(5.4-1.777) = lOS7.SkMm
Check the arain in longitudinal reinforcement The strain in
longitudinal reinforcement is calculated as:
MM f dv + OSV, cot 9 Ex =
E A
- - 1057.5 x 106 / 1777 + 0.5 x 266.4 x 1000 x cot66O 200000 x 6
x 700
= 0.00078 < 0.0009 This indicates that our second assumption
was sornewhat conservative. However we can use this value as a
shear capacity of the section when we design this member.
Vu= 266.4kN
-
In this research, linear interpolation was used in selecting and
6 &om Table 2.2 for more accurate value for shear capacity. The
result is as foiiows.
/3 = 0.0945;O = 64.3*;~, = 0.000875 V, = 299.8W
Mu = M D +(V, -&)(a-d,) = 183.3+(299.8-25.1)(5.4-1.777)
=1178.5RNm Mu Id, +0.5V, cote 1178.5 x lo6/1777 +OS x 299.8 x
1000xcot64.3~
8, = - - EsAs 200000 x 6 x 700
= 0.000875
Therefore prediction by the CSA code is V2=300kN
-
Sample Calculation for Soecimen YB2000/4
Concrete Strength: Maximum Aggregate Size: Yleld Strength of
Longitudinal Reban: Yield Strength of Transverse Reban: Area of a
Transverse Rebar: Spacing of Transverse Rebars: Shear Span Length:
Unit Weight of Concrete:
f ,=37.7 MPa (batch #1) 10 mm 455 MPa (Average of M 3 O Type A
and Type B) 468 MPa (#4) 127 mm2 (a) 590mm a=5.4m 23.5 ]th/m3
1. Find the flexural lever arm, d,,
2. Calculate sectional forces due to dead load Critical section
for shear is taken d, away from the applied load.
VD =23.5~0.3~2.0~1.784=25.1 kN Mp183.2 kNm
3. Calculate the shear force
4. Select values for p and B fiom Table 2.3
V Assume E, a 0.0020 and 7 0.050. From Table 2.3, f l= 0.143 and
O= 43.0'.
f,
V, = 3286.lp + 179.7 cot 6 = 3286.1 x 0.143 + 179.7 x cot 43 .O0
= 662.6W The sectional forces acting on the critical section are
calculated as: Shear force due to the applied load
Vp = V, - V' = 662.6 - 25.1 = 637SW Bending moment Mu =MD + M, =
M D + Vp(a - d,) = 183.2 + 637.5 x (5.4 - 1.784) = 2488.4WVm
-
V 5. Check E, and -
L'
The strain in longitudinal reinforcement is calculated as:
v 662.6 x 1000/(300 x 1784) = o.o328 < o.o5o -= L' 37.7
This indicates that Our assumption of gX was somewhat
unconservative. We must choose a bigg