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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 243 243 SECTION 2.12 Elastoplastic Analysis Problem 2.12-9 The structure shown in the figure consists of a
horizontal rigid bar ABCD supported by two steel wires, one of length L
and the other of length 3L/4. Both wires have cross-sectional area A and
are made of elastoplastic material with yield stress Y and modulus of
elasticity E. A vertical load P acts at end D of the bar. L
A (a) Determine the yield load PY and the corresponding yield
displacement Y at point D.
(b) Determine the plastic load PP and the corresponding displacement
P at point D when the load just reaches the value PP.
(c) Draw a load-displacement diagram with the load P as ordinate
and the displacement D of point D as abscissa. 3L
4 B C D P
2b b b Solution 2.12-9 Rigid bar supported by two wires
FREE-BODY DIAGRAM A
Y E cross-sectional area EQUILIBRIUM: yield stress
MA modulus of elasticity 0 FB(2b)
2FB FC(3b) P(4b)
3FC 4P (3) DISPLACEMENT DIAGRAM FORCE-DISPLACEMENT RELATIONS
EA dB D 3
2 (1) 3FCL
4EA 2 (2) FC B EA (4, 5) Substitute into Eq. (1): COMPATIBILITY:
FC a L b
2FB (6) ...
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- Fall '11