247_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

247_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 241 SECTION 2.12 Elastoplastic Analysis 241 Solution 2.12-6 Truss consisting of five bars b b b At the plastic load, all five bars are stressed to the yield stress b F Sum forces in the vertical direction and solve for the load: 2b P 10 mm A pd2 4 Y 1 2 b + 2F a b+F 12 15 sYA (5 12 + 4 15 + 5) 5 2F a PP d 4.2031sYA 2 78.54 mm ; Substitute numerical values: (4.2031)(250 MPa)(78.54 mm2) PP 250 MPa YA ; 82.5 kN Problem 2.12-7 A circular steel rod AB of diameter d 0.60 in. is stretched tightly between two supports so that initially the tensile stress in the rod is 10 ksi (see figure). An axial force P is then applied to the rod at an intermediate location C. B A d (a) Determine the plastic load PP if the material is elastoplastic with yield stress Y 36 ksi. (b) How is PP changed if the initial tensile stress is doubled to 20 ksi? A P C Solution 2.12-7 Bar held between rigid supports POINT C: sYA sYA P —C¡ — d 0.6 in. Y 2sYA p (2) (36 ksi) a b (0.60 in.)2 4 20.4 k PP ; 36 ksi Initial tensile stress 10 ksi (a) PLASTIC LOAD PP The presence of the initial tensile stress does not affect the plastic load. Both parts of the bar must yield in order to reach the plastic load. (B) INITIAL TENSILE STRESS IS DOUBLED PP is not changed. ; B ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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