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415_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

415_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 4:59 AM Page 409 SECTION 5.5 Normal Stresses in Beams Problem 5.5-23 A small dam of height h 6 ft is constructed of vertical wood beams AB, as shown in the figure. The wood beams, which have thickness t 2.5 in., are simply supported by horizontal steel beams at A and B. Construct a graph showing the maximum bending stress smax in the wood beams versus the depth d of the water above the lower support at B. Plot the stress smax (psi) as the ordinate and the depth d (ft) as the abscissa. (Note: The weight density g of water equals 62.4 lb/ft3.) Steel beam A Wood beam t t Wood beam Steel beam h d B Side view Solution 5.5-23 Vertical wood beam in a dam h 2.5 in. g MAXIMUM BENDING STRESS 12 bt Section modulus: S 6 6 ft t 62.4 lb/ft3 smax Let b width of beam (perpendicular to the figure) Let q0 intensity of load at depth d q0 gbd q0 smax L RA RB x0 Mc q0d2 a1 6 d 2d d + b L 3L A 3L h 6 ft q0d2 6L q0d a3 6 d A 3L d b L smax gd3 t2 a1 6 q0d2 c a1 bt2 6 d) d 2d d bd + L 3L A 3L d 2d d b + L 3L A 3L (62.4)d3 (2.5)2 a1 0.1849d3(54 d RA(L Mmax S g bd ; SUBSTITUTE NUMERICAL VALUES: d depth of water (ft) (Max. d h 6 ft) L h 6 ft g 62.4 lb/ ft3 t 2.5 in. smax psi ANALYSIS OF BEAM Mmax Top view q0d2 a1 6 d b L d(ft) 0 1 2 3 4 5 6 d dd b + 6 9 A 18 9d + d 12d ) smax(psi) 0 9 59 171 347 573 830 ; 409 ...
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