Civil Engineering Reference
In-Depth Information
Figure
7.4 Stress condition in reinforced concrete element
r-directions are
s
r
respectively. The concrete strut is also assumed to
carry a small tension in the r-direction,
s
d
and
s
r
.
It is assumed that the behaviour of the cracked concrete element may be
characterised by its overall average strain and stress. The assumption is based
on the availability of an empirical material law linking the average strain to the
average stress in the concrete. This material law will be described later. With
this assumption, the difficulty encountered in the characterisation of the local
behaviour between the cracks is bypassed. The average normal strains of
concrete in the longitudinal and transverse directions are assumed to be
identical to those in the longitudinal and transverse reinforcements.
7.3.2
Stress transformation (equilibrium)
From the three equilibrium conditions of the truss model, it can be shown (Hsu,
1984) that the stresses in the concrete satisfy Mohr's stress circle. Thus,
s
c
=
s
d
cos
2
a
+
s
r
sin
2
a
(7.3a)
(7.3b)
(7.3c)
s
tc
=
s
d
sin
2
a
+
s
r
cos
2
a
t
ltc
=(
s
d
-
s
r
)sin
a
cos
a
where
s
tc
are normal stresses in concrete in
l
and t-directions,
respectively (positive for tension);
s
lc
,
t
ltc
is shear stress in concrete in
l
-t co-
