Civil Engineering Reference
In-Depth Information
Figure 4.3
Stresses on elements in typical reinforced concrete beams
t
coordinate, a shear stress is considered
positive if it causes a counter-clockwise rotation of the element, while shear stress is negative
if it causes a clockwise rotation of the element.
In the graphical representation of the Mohr circle in Figure 4.2(b), a rotation of an angle
α
1
in an element is represented by a rotation of 2
According to Equation (4.24) in the stationary
−
α
1
from the reference point A to the rotating
point C. For a 90
◦
rotation in the element, point C would have rotated 180
◦
from the reference
point A to point B. Point B, therefore, should represent a shear stress of negative
τ
t
(
−
τ
t
)as
indicated in Figure 4.2(b).
The right-hand support of a typical reinforced concrete beam is shown in Figure 4.3(a). Two
concrete elements, A and B, are indicated and are shown separately in Figure 4.3(b) and (c).
Element A is taken in the
t
coordinate of the steel bars and element B in the principal 1-2
coordinate of the applied stresses. The stresses on these two elements have been indicated in a
qualitative sense with regard to sign. We will now find how to draw a Mohr circle to represent
the stresses on these two elements.
The stresses on element A are shown in Fig. 4.4(b). The shear stress,
−
−
τ
t
, on the top face
is based on the sign convention given in Fig. 4.4(a). Figure 4.4(a) is obtained by applying
τ
t
=−
τ
t
to the basic sign convention shown in Fig. 4.1(a). A Mohr stress circle is constructed
graphically in Fig. 4.4 (c).
