Civil Engineering Reference
In-Depth Information
Figure 5.24
Flow chart for proportional loadings
5.4.6 Example Problem 5.4 for Proportional Loading
5.4.6.1 Problem Statement
A nonprestressed 2-D element was designed by the equilibrium (plasticity) truss model in
Example Problem 5.1 (see Section 5.1.5 and Figure 5.3), and then analyzed by the Mohr
compatibility truss model in Example Problem 5.2 (see Section 5.3.4 and Figure 5.10). This
2-D element is subjected to a set of membrane stresses
σ
=
2.13 MPa (tension),
σ
t
=−
2.13
MPa (compression) and
3.69 MPa. Assuming that this set of stresses is applied in a
proportional manner, we can now analyze the nonlinear behavior of this 2-D element by the
rotating angle softened truss model (RA-STM). Particular interest is placed in the stress and
strain conditions at the first yield of steel and at the ultimate load stage.
τ
t
=
