456_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 456_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 450 9/25/08 2:29 PM Page 450 CHAPTER 5 Stresses in Beams (Basic Topics) (b) ALLOWABLE LOAD P BASED UPON SHEAR STRESS tallow V 0.8 MPa t qL P + 2 2 3V 2A P + 108.86 2 (181.44 N/m)(1.2 m) P + 2 2 P + 108.86 (N) 2 2At 2 V (33,600 mm2)(0.8 MPa) 3 3 Equate values of V and solve for P: or P 17,920 P 35.6 kN 35,622 N ; NOTE: The shear stress governs and Pallow 35.6 kN 17,920 N Problem 5.8-11 A square wood platform, 8 ft * 8 ft in area, rests on masonry walls (see figure). The deck of the platform is constructed of 2 in. nominal thickness tongue-and-groove planks (actual thickness 1.5 in.; see Appendix F) supported on two 8-ft long beams. The beams have 4 in. * 6 in. nominal dimensions (actual dimensions 3.5 in. * 5.5 in.). The planks are designed to support a uniformly distributed load w (lb/ft2) acting over the entire top surface of the platform. The allowable bending stress for the planks is 2400 psi and the allowable shear stress is 100 psi. When analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load w1 (lb/ft2) based upon the bending stress in the planks. (b) Determine the allowable platform load w2 (lb/ft2) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load wallow on the platform? (Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.) 8 ft 8 ft ...
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