468_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

468_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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462 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.10-9 Beam with an overhand Sum moments about A & Solve for R B Sum forces in vertical direction M B ±² 2.16 * 10 4 lb-ft M B ±² P (4 ft) ² q (4 ft) 2 2 V max ± 1.1 * 10 4 lb at B V max ± R B ² ( P + q 4 ft) R A ± 6.4 * 10 3 lb R A ± q (16 ft) + 2 P ² R B R B ± 1.88 * 10 4 lb R B ± q a 4 3 L b 2 1 2 + P (8 ft + 16 ft) 12 ft q ± 1200 lb ft P ± 3000 lb s allow ± 18 ksi t allow ± 11 ksi L ± 12 ft Find moment at D (at Load P between A and B ) Required section modulus: Lightest beam is (from Table E-2(a)) Check max. shear stress ; Select S 8 * 23 beam t max ± 3674 6 11,000 psi so ok for shear t max ± V max 8 It 1 bh 2 ² bh 1 2 + th 1 2 2 h 1 ± h ² 2 t f h 1 ± 7.15 in. h ± 8 in. t f ± 0.425 in. t ± 0.441 in. b ± 4.17 in. S ± 16.2 in. 3 I ± 64.7 in. 4 S 8 * 23 S ± M max s allow S ± 14.4 in. 3 M max ± | M B | M max ± 2.16 * 10 4 lb-ft M D ± 1.28 * 10 4 lb-ft M D ± R A 8 ft ² q (8 ft) 2 2 (b) M AXIMUM LOAD BASED UPON SHEAR STRESS t max ± V max 8 It 1 bh 2 ² bh 1 2 + th 1 2 2 V max ± R A ± 3 8 qL t allow ± 50 MPa Bending stress governs: q max ± 184.7 kN/m ; ; q max ± 247 kN/m q max ± 64 t allow It w 3 L 1 bh 2 ² bh 1 2 ³ t w h 1 2 2 ± 3 qL 64 It 1 bh 2 ² bh 1 2
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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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