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Unformatted text preview: Sec_2.8-2.12.qxd 242 9/25/08 11:44 AM Page 242 CHAPTER 2 Axially Loaded Members Problem 2.12-8 A rigid bar ACB is supported on a fulcrum
at C and loaded by a force P at end B (see figure). Three
identical wires made of an elastoplastic material
(yield stress Y and modulus of elasticity E) resist the load P.
Each wire has cross-sectional area A and length L.
(a) Determine the yield load PY and the corresponding
yield displacement Y at point B.
(b) Determine the plastic load PP and the corresponding
displacement P at point B when the load just reaches
the value PP.
(c) Draw a load-displacement diagram with the load
P as ordinate and the displacement B of point B
as abscissa. L
A C B
P L a a a a Solution 2.12-8 Rigid bar supported by wires
(b) PLASTIC LOAD PP (a) YIELD LOAD PY
Yielding occurs when the most highly stressed wire
reaches the yield stress Y At the plastic load, all wires reach the yield stress.
3 ; At point A:
dA (sYA) a L
E At point B:
At point A:
dA dB 0 sYA
EA 3dA dY dP 3sYL
E ; (c) LOAD-DISPLACEMENT DIAGRAM ;
2E At point B:
dB 3dA 3sYL
2E ; PP
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- Fall '11