Equilibrium (Plasticity) Truss Model - Unified Theory of Concrete Structures - page 50

Figure 2.14 Interaction surface for shear, torsion, and bending

replaces the first two interaction surfaces and, therefore, Equation (2.94) governs. Figure 2.14
also shows that the longitudinal steel in one wall will yield when the member fails on one
of the three interaction surfaces. On the interaction curves of any two interaction surfaces,
however, the longitudinal steel in two adjacent walls will yield. At the two peak points where
all three surfaces intersect, all the longitudinal steel will yield.
It should be pointed out that the relationship between shear and torsion is not linear. This
is because the plasticity truss model allows the

α r angle to vary in each of the four walls of
a member, such that both the longitudinal and transverse steel will yield and the capacity of
the member is maximized. As a result, the plasticity truss model always provides an upper
bound solution.
If the compatibility condition of a RC member is considered, some of the steel may not
yield and the predicted capacity may not be reached. Such situations will be discussed in
subsequent chapters. However, tests have shown that the interaction relationships predicted
by the plasticity truss model could be conservative, even when the steel does not yield in
one direction. Perhaps this theoretical nonconservative behavior is counteracted by the strain
hardening of the yielded mild steel bars.
It should also be pointed out that the interaction surfaces based on the plasticity truss model
have been shown by tests to be nonconservative near the region of pure torsion. The theoretical
torque may overestimate the test results by 20%. This nonconservative behavior is caused by
the overestimation of the lever arm area A o , if it is calculated according to the centerline of
the hoop bars. Detailed discussion of this problem will be given in Chapter 7.