Civil Engineering Reference
In-Depth Information
Figure 7.3
Estimation of effective transverse compression
shear stress
v
that the shear element can withstand. This calls for the
solution of equations governing the equilibrium, compatibility and material
behaviour of the shear element. These equations can be obtained from the
equations of the softened truss model theory for a reinforced concrete
element carrying general two-dimensional stresses.
7.3
Softened truss model
7.3.1
Fundamental assumptions
A reinforced concrete element is subjected to shear stresses and normal
stresses as shown in
Figure 7.4.
The directions of the longitudinal and
transverse steel bars are designated as the
l
-and t-axes, respectively, forming
the
l
-t co-ordinate system. Accordingly, the normal stresses are denoted by
s
l
t
lt
.
After the development of diagonal cracks, the concrete struts are
subjected mainly to compression and the steel bars act as tension links, thus
forming a truss action. The compression struts are oriented in the d-axis,
which is inclined at an angle
and
s
t
and the shear stresses are
to the longitudinal steel bars. This direction
is also assumed to be the direction of the principal compressive stress and
strain of the concrete element. Taking the direction perpendicular to the d-
axis as the r-axis, a d-r co-ordinate system in the direction of the principal
stresses and strains is established. The normal principal stresses in the d- and
a
