Civil Engineering Reference
In-Depth Information
8.
Compare the two values of
s
r
obtained in step 3 and step 7. If they
are within a small error, the assumed value of
e
r
is accepted and the
solution procedure continues at step 10.
9.
If the error in
s
r
is too large, iteration continues from step 2 to step
8 by sweeping through possible values of
e
r
.
10.
Calculate
g
lt
[Eqn (7.7c)] and
v
[Eqn (7.6c)].
11.
d with a suitable increment and repeat step 1 to step
10. In this way, the loading history of
v
vs.
Select another
e
g
lt
can be traced and the
maximum shear stress can be determined. The maximum shear
stress is defined as the shear strength
v
n
.
7.3.6
Accuracy
A total of 64 test specimens are available in the literature to compare with
the proposed theory. They were reported by Smith and Vansiotis (1982),
Kong, Robins and Cole (1970), and de Paiva and Siess (1965). The basic
data are listed in
Table 7.1.
The specimens were selected because they
satisfy the following conditions: i) the test specimen must fail in web shear
mode, not in bearing or flexural modes; ii) the test specimen must contain at
least a minimum amount of transverse web reinforcement specified in the
ACI Code (1989) to render the truss model applicable; iii) the span-depth
ratio
a/h
must be less than 2; and iv) the test specimens must be simply
supported at the bottom surface and the loads acting on the top surface of
the beam.
In calculating the longitudinal steel ratio of the shear element, the
longitudinal steel reinforcement provided at the bottom and the top of the
beam is also included. This is because the expansion of the element in the
longitudinal direction due to shear is restrained by the longitudinal steel in
the top and bottom bars. Thus tests on beams with no horizontal web
reinforcements can still be used for comparison. The effective depth of the
shear element
d
v
is taken as the distance between the centre of the
compression steel and the centre of the tension steel. When compression
steel reinforcement is not provided, the depth
d
' is estimated as 0.1
d.
The theoretical values of the normalised shear strength, (v
n
/
f
'
c
)
T
, are
computed according to the procedure outlined in the previous section. The
results are listed in
Table 7.2.
Using the ratio of calculated shear strength to
test shear strength
R
T
as an indicator, the mean and standard deviation of this
ratio for the 64 data are 1.028 and 0.094, respectively. The agreement
between theory and test is quite good. A comparison of the theoretical and
experimental shear strengths is also presented in
Figure 7.6.
The sensitivity of the shear strength to the magnitude of the effective
transverse compression is studied using the available test specimens. The
available test specimens are divided into nine groups based on the different
a/
h
ratios ranging from 0.33 to 1.29. These nine groups are identified in Table
7.1 as SA, SB, SC, K30, K25, K20, K15, K10, and PS. As the effective
