452_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 452_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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446 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.8-6 Beam of rectangular cross section width height length Uniform load intensity of load A LLOWABLE STRESSES and (a) S IMPLE BEAM B ENDING (1) S HEAR (2) Equate (1) and (2) and solve for : L 0 ± h a s allow t allow b ; L 0 q allow ± 4 t allow bh 3 L t max ± 3 V 2 A ± 3 qL 4 bh V max ± qL 2 A ± bh q allow ± 4 s allow bh 2 3 L 2 s max ± M max S ± 3 qL 3 4 bh 2 M max ± qL 2 8 S ± bh 2 6 t allow s allow q ± L ± h ± b ± (b) C ANTILEVER BEAM B ENDING (3) S HEAR (4) Equate (3) and (4) and solve for : NOTE: If the actual length is less than , the shear stress governs the design. If the length is greater than , the bending stress governs. L 0 L 0 L 0 ± h 2 a s allow t allow b ; L 0 q allow ± 2 t allow bh 3 L t max ± 3 V 2 A ± 3 qL 2 bh V max ± qL A ± bh q allow ± s allow bh 2 3 L 2 s max ± M max S ± 3 qL 2 bh 2 M max ± qL 2 2 S ± bh 2 6 Problem 5.8-7 A laminated wood beam on simple supports is built up by gluing together four 2 in. ² 4 in. boards (actual dimensions) to form a solid beam 4 in. ² 8 in. in cross section, as shown in the figure.
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Unformatted text preview: The allowable shear stress in the glued joints is 65 psi, and the allowable bending stress in the wood is 1800 psi. If the beam is 9 ft long, what is the allowable load P acting at the one-third point along the beam as shown? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft 3 .) 2 in . 2 in . 2 in . 4 in . P 2 in . 3 ft L 9 ft Solution 5.8-7 W EIGHT OF BEAM PER UNIT DISTANCE g 35 lb ft 3 q g A t allow 65 psi s allow 1800 psi h 8 in. A bh L 9 ft b 4 in. A LLOWABLE LOAD BASED UPON SHEAR STRESS IN THE GLUED JOINTS ; MAX . SHEAR STRESS AT NEUTRAL AXIS t VQ Ib t max 3 V 2 A q 7.778 1b ft 05Ch05.qxd 9/25/08 2:29 PM Page 446...
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