522_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

522_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 516 5:34 AM Page 516 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.3-8 The cross section of a composite beam made of aluminum y and steel is shown in the figure. The moduli of elasticity are Ea 75 GPa and Es 200 GPa. Under the action of a bending moment that produces a maximum stress of 50 MPa in the aluminum, what is the maximum stress ss in the steel? Aluminum 40 mm Steel z O 80 mm 30 mm Solution 6.3-8 Composite beam of aluminum and steel (2) Steel: b Es b 30 mm ha 40 mm All dimensions in millimeters. Ea (1) Aluminum: 75 GPa sa 50 MPa Use the base of the cross section as a reference line. 30 mm 200 GPa hs 80 mm ss h2 ? © yi Ai © Ai (40)(80)(80) + (100)(30)(40) (80)(80) + (30)(40) 49.474 mm TRANSFORMED SECTION (ALUMINUM) h1 120 h2 70.526 mm MAXIMUM STRESS IN THE ALUMINUM (1) (EQ. 6-15) sa s1 Mh1 IT MAXIMUM STRESS IN THE STEEL (2) (EQ. 6-17) Mh2n IT ss n Es Ea 200 75 2.667 ss sa h2n h1 ss Aluminum part is not changed. s2 1.8707 (50 MPa) (49.474)(2.667) 70.526 1.8707 ; 93.5 MPa Width of steel part nb (2.667)(30 mm) 80 mm Problem 6.3-9 A beam is constructed of two angle sections, each L 5 3 1/2, which reinforce a 2 8 (actual dimensions) wood plank (see the cross section shown in the figure). The modulus of elasticity for the wood is Ew 1.2 106 psi and for the steel is Es 30 106 psi. Find the allowable bending moment Mallow for the beam if the allowable stress in the wood is sw 1100 psi and in the steel is ss 12,000 psi. (Note: Disregard the weight of the beam, and see Table E-5a of Appendix E for the dimensions and properties of the angles.) 2 8 wood plank C y z 5 in. 3 in. Steel angles ...
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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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