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455_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

455_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.8 Shear Stresses in Rectangular Beams 449 Solution 5.8-10 Simply supported wood beam L 1.2 m q g bh 181.44 N/m g 5.4 kN/m 3 S bh 2 6 1344 * 10 3 mm 3 A bh 33,600 mm 2 b 140 mm h 240 mm (a) A LLOWABLE BASED UPON BENDING STRESS Equate values of and solve for : or P 38.0 kN ; 0.3 P + 32.66 11,424 P 37,970 N P M max 11,424 N # m M max S s allow (1344 * 10 3 mm 3 )(8.5 MPa) ( P newtons; M N # m) 0.3 P + 32.66 N # m + (181.44 N/m)(1.2 m) 2 8 M max PL 4 + qL 2 8 P (1.2 m) 4 s allow 8.5 MPa s M max S P From Appendix F: Select in. beam (nominal dimensions) (b) R EPEAT ( A ) CONSIDERING THE WEIGHT OF THE BEAM R B 7.83 * 10 3 1b R B 7.725 * 10 3 1b + q beam L 2 q beam 20.964 1b ft g 35 1b ft 3 q beam g A A 86.25 in. 2 S 165.3 in. 3 ; 8 * 12 s max M S S req M max s allow S req 120.6 in. 3 beam is still satisfactory for shear. beam is still satisfactory for moment. ; Use 8 * 12 in. beam 8 * 12 S req M max s allow S req 122.3 in. 3 < S M max 2.293 * 10 4 1b-ft M max R B d qd 2 2 q total q + q beam q total
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Unformatted text preview: ± q + q beam q total ± 145.964 1b ft 8 * 12 A req ± 73.405 in. 2 < A V max ± R B A req ± 3 V max 2 t allow Problem 5.8-10 A simply supported wood beam of rectangular cross section and span length carries a concentrated load at midspan in addition to its own weight (see figure). The cross section has width and height . The weight density of the wood is . Calculate the maximum permissible value of the load if (a) the allowable bending stress is , and (b) the allowable shear stress is . 0.8 MPa 8.5 MPa P 5.4 kN/m 3 240 mm 140 mm P 1.2 m 0.6 m 0.6 m P 140 mm 240 mm 0.6 m 0.6 m P 140 mm 240 mm 05Ch05.qxd 9/25/08 2:29 PM Page 449...
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