460_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

460_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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454 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.9-2 Log bridge Diameter Find allowable load (a) B ASED UPON BENDING STRESS Maximum moment occurs when wheel is at midspan ( ). ; W 28,600 N 28.6 kN 0.625 W + 664.1 18,560 18,560 N # m M max S s allow (2.651 * 10 3 m 3 )(7.0 MPa) S p d 3 32 2.651 * 10 3 m 3 0.625 W + 664.1 (N # m) ( W newtons) W 4 (2.5 m) + 1 8 (850 N/m)(2.5 m) 2 M max WL 4 + qL 2 8 x L /2 W t allow 0.75 MPa s allow 7.0 MPa d 300 mm (b) B ASED UPON SHEAR STRESS Maximum shear force occurs when wheel is adja- cent to support . ; W 38,700 N 38.7 kN W + 1062.5 N 39,760 N 39,760 N V max 3 A t allow 4 3 4 (0.070686 m 2 )(0.75 MPa) t max 4 V max 3 A A p d 2 4 0.070686 m 2 W + 1062.5 N ( W newtons) V max W + qL 2 W + 1 2 (850 N/m)(2.5 m) ( x 0) Problem 5.9-3 A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the
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