Civil Engineering Reference
In-Depth Information
Figure 2.3
Geometric relationships in mohr circle
equilibrium equations will be called the
second type
of expression for Mohr stress circles
in Section 5.1.3.
2.1.2.3 Yielding of Reinforcement in 2-D Elements
The plasticity truss model is based on the assumption that both the longitudinal and the
transverse steel must yield before failure. In order to ensure this mode of failure, the shear ele-
ments are divided into two types: under-reinforced and over-reinforced. In an under-reinforced
element the yielding of steel in both directions occurs before the crushing of concrete, thus
satisfying the assumption of the plasticity truss model. In an over-reinforced element, however,
concrete crushes before the yielding of either the longitudinal or the transverse steel, or both,
thus violating the basic assumption. The state of stresses that divide the under-reinforced mode
of failure from the over-reinforced will be called the balanced condition. Under the balanced
condition, one of the two yielded steels just reach yield point when the concrete crushes at an
effective stress of
f
c
. The softening coefficient
varies from about 0.2 to 0.6 (this will be
studied in detail in Chapters 5 and 6). In this chapter we will take
ζ
ζ
ζ
as a constant 0.4, a crude
average value.
