Civil Engineering Reference
In-Depth Information
The computed normalised shear strength
F
and
R
F
values are given
in Table 2. The mean value of
R
F
for Eqn (7.21) is 1.008 and the coefficient
of variation is 0.082. Also shown in
Table 7.2
is the ratio for the theoretical
shear strength from the softened truss model to the experimental shear
strength
R
T
The mean value and the coefficient of variation of
R
T
for the 63
specimens are 1.025 and 0.092, respectively. It is observed that the proposed
explicit formula gives as good a prediction as the more rigorous and
complicated theory. The shear strengths calculated from Eqn (7.21) and Eqn
(7.2) are plotted in
Figure 7.12
against the experimental shear strengths for
the 63 specimens. It is seen that only one of the data points falls slightly
below the lower 15% line. Eqn. (7.21) has also been compared to other
empirical formulas found in literature (Mau and Hsu, 1989). The
comparison shows that the proposed explicit formula has the least
coefficient of variation.
7.6
Conclusions
i) The softened truss model theory is shown to predict with reasonable
accuracy the shear strength of simply-supported beams with transverse web
reinforcement and having shear-span to height ratio
(a/h)
between 0.33 and 2.
ii) Three non-dimensionalised parameters are identified as having major
effect on the shear strength of deep beams. They are the shear span ratio, the
transverse reinforcement index, and the longitudinal reinforcement index.
The present theory predicts that the effectiveness of transverse
reinforcement decreases when the
a/h
ratio decreases from 2 to 0.5. For
small
a/h
ratio below 0.5, the transverse reinforcement is ineffective in
increasing the shear strength.
iii) An explicit formula is proposed for shear strength design. This non-
dimensional formula expresses the shear strength ratio as a function of shear
span ratio, (through
K
), longitudinal reinforcement index and transverse
reinforcement index. This formula has been calibrated to the available test
data in the following range: 0.95
£
L/d
£
3.3, 0
£r
v
l
=
A
vl
/
bS
2
£
0.0091, 0.0018
£r
t
£
0.0245. The compression steel ratio is within 0.92% and the concrete
cylinder compression strength is close to 3000 psi (21 MN/m
2
).
References
American Concrete Institute Committee 318. (1989)
Building Code Requirements for
Reinforced Concrete.
ACI 318-89, American Concrete Institute, Detroit.
Collins, M. (1973) Torque-twist characteristics of reinforced concrete beams, In
Inelasticity and
Non-Linearity in Structural Concrete.
University of Waterloo Press, Waterloo Ontario: 211
Han, K.J. and Mau, S.T.(1988) Membrane behaviour of r/c shell element and limits on the
reinforcement
J. Struct. Mechcs, Am. Soc. Civ. Engrs
114
No. 2: 425.
Hagai, T. (1983) Recent plastic and truss theory on the shear failure of reinforced concrete
members
Proc. Colloquium of Shear Analysis of RC Structures.
Japan Concrete Institute,
Tokyo: 29-83.
