693_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

693_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 11:06 AM Page 687 SECTION 8.5 Combined Loadings Problem 8.5-11 An L-shaped bracket lying in a horizontal plane A supports a load P 150 lb (see figure). The bracket has a hollow rectangular cross section with thickness t 0.125 in. and outer dimensions b 2.0 in. and h 3.5 in. The centerline lengths of the arms are b1 20 in. and b2 30 in. Considering only the load P, calculate the maximum tensile stress st, maximum compressive stress sc, and maximum shear stress tmax at point A, which is located on the top of the bracket at the support. 687 t = 0.125 in. b1 = 20 in. h = 3.5 in. b2 = 30 in. b = 2.0 in. P = 150 lb Solution 8.5-11 L-shaped bracket P 150 lb b1 t 0.125 in. 20 in. b2 STRESSES AT POINT A ON THE TOP OF THE BRACKET 30 in. 3.5 in. b t 2.0 in. T 2tAm s h Mc I FREE-BODY DIAGRAM OF BRACKET 4500 lb-in. 2(0.125 in.)(6.3281 in.2) (3000 lb-in.)(1.75 in.) 2.1396 in.4 2844 psi 2454 psi (The shear force V produces no stresses at point A.) STRESS ELEMENT AT POINT A (This view is looking downward at the top of the bracket.) STRESS RESULTANTS AT THE SUPPORT Torque: Moment: T Pb2 M Shear force: (150 lb)(30 in.) Pb1 V 4500 lb-in. (150 lb)(20 in.) P 3000 lb-in. 150 lb PROPERTIES OF THE CROSS SECTION For torsion: Am t)(h t) For bending: c h 2 1 (b 12 2t)(h 1 (bh3) 12 (1.875 in.)(3.375 in.) 6.3281 in.2 1.75 in. I (b 1 (2.0 in.)(3.5 in.)3 12 2.1396 in.4 2t)3 1 (1.75 in.)(3.25 in.)3 12 sx txy sy 0 t s 2454 psi 2844 psi ...
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