Civil Engineering Reference
In-Depth Information
σ
t
=
Figure 4.13
RC element subjected to pure shear (assuming
0)
is more complicated because the equilibrium equations must involve the concrete shear stress
τ
12
. In contrast, the rotating angle theory has the advantage of simplicity and can be used to
study the effect of steel reinforcement through the
V
s
term, without the complication induced
by the concrete shear stress
12
.
τ
4.3.5 Mohr Stress Circles for RC Shear Elements
The state of stresses of a RC 2-D elements subjected to pure shear is illustrated in Figure 4.13
in terms of Mohr stress circles. These Mohr circles will further help our understanding of the
rotating angle theory and the fixed angle theory.
Figure 4.13(a) shows a RC element subjected only to an applied shear stress
τ
t
. Conse-
2 principal coordinate is oriented at 45
◦
quently, the 1
−
to the
−
t
coordinate of the steel
α
1
of 45
◦
. On the Mohr circle of applied stresses in Figure 4.13(a),
points A and B represent the vertical face (
bars, giving a fixed angle
0
◦
) with a shear stress of
α
1
=
+
τ
t
and the hori-
90
◦
) with a shear stress of
zontal faces (
α
1
=
−
τ
t
, respectively. Points C and D represent the
45
◦
) with a normal stress of
135
◦
) with
principal 1-face (
α
1
=
σ
1
and the principal 2-face (
α
1
=
a normal stress of
σ
2
, respectively. The first crack is expected to develop perpendicular to the
principal tension direction (1-direction) with an
α
1
angle of 45
◦
to the
−
t
coordinate.
After cracking, the smeared steel stresses,
ρ
f
and
ρ
t
f
t
, are activated. The post-cracking
principal
r
−
d
coordinate of the concrete element begins to deviate from the 1
−
2 coordinate
