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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 237 237 SECTION 2.12 Elastoplastic Analysis Elastoplastic Analysis
The problems for Section 2.12 are to be solved assuming that the material is
elastoplastic with yield stress Y, yield strain Y, and modulus of elasticity
E in the linearly elastic region (see Fig. 2-70). A u u C Problem 2.12-1 Two identical bars AB and BC support a vertical load
P (see figure). The bars are made of steel having a stress-strain curve that
may be idealized as elastoplastic with yield stress Y. Each bar has
cross-sectional area A.
Determine the yield load PY and the plastic load PP. B
P Solution 2.12-1 Two bars supporting a load P JOINT B
Structure is statically determinate. The yield load PY
and the plastic lead PP occur at the same time, namely,
when both bars reach the yield stress. (2
PY Problem 2.12-2 A stepped bar ACB with circular cross sections
is held between rigid supports and loaded by an axial force P at
midlength (see figure). The diameters for the two parts of the bar are
d1 20 mm and d2 25 mm, and the material is elastoplastic with
yield stress Y 250 MPa.
Determine the plastic load PP. YA) sin PP A P
2 YA sin d1 ; C L
2 d2 P L
2 B ...
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