564_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

564_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 558 5:59 AM Page 558 CHAPTER 6 Stresses in Beams (Advanced Topics) Elastoplastic Bending y The problems for Section 6.10 are to be solved using the assumption that the material is elastoplastic with yield stress sY. b1 Problem 6.10-1 Determine the shape factor f for a cross section in the shape of a double trapezoid having the dimensions shown in the figure. Also, check your result for the special cases of a rhombus (b1 0) and a rectangle (b1 b2). h — 2 z C b1 b2 Solution 6.10-1 Double trapezoid SHAPE FACTOR f f Z S (EQ. 6-79) 2(2b1 + b2) 3b1 + b2 ; SPECIAL CASE – RHOMBUS Neutral axis passes through the centroid C. Use case 8, Appendix D. SECTION MODULUS S Iz h3 2 a b (3b1 + b2)/12 2 b1 h3 (3b1 + b2) 48 c h/2 S I c 0 f 2 SPECIAL CASE – RECTANGLE h2 (3b1 + b2) 24 PLASTIC MODULUS Z (EQ. 6-78) A h 2 a b (b1 + b2)/2 2 y1 y2 z h (b + b2) 21 1 h 2b1 + b2 a ba b 32 b1 + b2 A ( y + y2) 21 h2 (2b1 + b2) 12 b1 b2 f 3 2 h — 2 ...
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