454_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

454_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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448 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.8-9 (a) R B qL 2 + P L d L + M L R A 1.025 * 10 3 1b R A qL 2 + P d L M L s Allow 2250 psi t allow 160 psi L 10 ft d 3 ft q 125 1b ft P 75001b M 18500 ft-b A req 72.422 in. 2 t max 3 V 2 A A req 3 V max 2 t allow M max 2.261 * 10 4 1b-ft M max R B d qd 2 2 V max R B V max 7.725 * 10 3 1b R B 7.725 * 10 3 1b (b) F IND M BASED ON ALLOWABLE BENDING STRESS AT h/2 FROM NA AT LOCATION OF MAX . BENDING MOMENT , use to find location of zero shear where max. moment occurs M AX . MOMENT M m a qL 2 + M L b x m qx m 2 2 M m x m L 2 + M q L 1 2 q L + M L q x 0 d dx c a qL 2 + M L b x qx 2 2 d M ( x ) a qL 2 + M L b x qx 2 2 d dx M ( x ) 0 M m ( x m ) simplifying Equating both expressions & solving for M where ; M max 9.01 N # m M A s a a bh 2 6 b a 8 qL 2 b qL 2 2 s a 8 MPa M m also M m s a S M m s a a bh 2 6 b M m 1 8 q 1 qL 2 + 2 M 2 2 L 2 q a L 2 + M qL b 2 2 M m a qL 2 + M L b a L 2 + M q L b Problem 5.8-9 A wood beam AB on simple supports with span length equal to 10 ft is subjected to a uniform load of intensity 125 lb/ft acting along the entire length of the beam, a concentrated load of magnitude
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