Page 203 - Bridge and Highway Structure Rehabilitation and Repair

178 SECTION 2 STRENGTHENING AND REPAIR WORK

Figure 4.21 Distribution of angle of inclination 0 at failure.
Computer results for shear failure from the above model were compared with experimental
results from high strength beams tested by four universities, Cornell, North Carolina, Toronto
and Imperial College London. The major outcome was that the values of 0 range from 20° to 48°
in the beams and unlike ACI model do not have a constant angle of 45° (Figure 4.21).
Strength comparisons: The ultimate shear capacity of the beam is considered to have been
reached when one of the following conditions is met:
Capacity of stirrups in tension is exceeded, i.e.,
/
yld 1
sy
Capacity of steel in tension is exceeded, i.e.,
/
yld 1
sx
Various notations are described in papers by Khan et al, listed in the bibliography.
High strength lightweight concrete beams with stirrups failed in shear in diagonal tension,
as would be expected for beams without stirrups.
Infl uence of parameters on beam behavior: It is observed that the ratio of V ntheory /V nACI ca-
pacity of two of the beams tested at Imperial College is below 1.0. The a/d ratios of such beams
are between 2 and 4.
Effect of
:
o
ACI equation for stress-strain relation is
3 0.00195 4 1.03 8 10 –4
o

3 0.002 4 0.00012 (f 1 6 3), f 1 3 ksi (20.8 Mpa)
0
c
c
The major parameters are:

the compressive strain at the peak stress
o
f the stress at which tensile fracture of concrete occurs.
cr
The ACI equation gives a higher value of
and thus overestimates the failure strain.
0
Conclusions of theoretical and test beam studies of shear failure:
1. The results confirm the variable angle truss model theory for beams failing in shear.

2. The effect of concretes having different tensile stresses f can be signifi cant on shear capac-
cr
ity of beam, concrete stresses, and steel strains. Like f 1, f is an important parameter.
c
cr
3. Load capacities using the MCFT for high strength lightweight aggregate concrete beams
show lesser agreement with experimental values. By using actual stress-strain curves in
compression and tension for the lightweight aggregate concrete, it is expected that differ-
ences will be smaller.
4. As f 1 values increase, ACI code shear capacities get more conservative.
c
5. It is seen that cracking planes may be located at angles as low as 20 degrees. Due to changes
in the orientation of cracking angles, stress patterns are modifi ed.
6. Effect of shear deflection also needs to be included at cracking stage in future studies.

7. Accurate evaluation of modulus of elasticity of concrete is important since Ec values are