Civil Engineering Reference
In-Depth Information
one of the two critical paths according to the resistance of the beam along
those paths as shown in Figure 3.15.
Figure 3.15
Ultimate strength of RC deep beams with solid web and practical regions for web
openings (under four-point loading) (Ray, 1980)
The Figure shows a typical deep beam under four-point loading and
includes the practical regions for web openings and the free-body diagrams
for critical load paths I and II. Critical path I lies wholly in a region of
external shear,
Q
u=
P
u
/2, whereas critical path II traverses partly through a
region having shear
Q
u
=
P
u
/2 and partly through region of shear
Q
u
=
P
u
/4.
However, it was observed (Singh, Ray and Reddy, 1980) that after formation
of initial diagonal cracks which usually entered into the region of shear,
Q
y
=
P
u
/4, the beam carried a substantial load before failing along the second
path. As such it is reasonable to assume that the shear causing failure along
path II is
Q
u
=
P
u
/4.
The ultimate strength equations for beam with web openings can be
written directly from Eqn (3.21) for critical path I:
for critical path II:
