670_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

670_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Maximum Stresses in Beams When solving the problems for Section 8.4, consider only the in-plane stresses and disregard the weights of the beams Problem 8.4-1 A cantilever beam of rectangular cross section is subjected to a concentrated load P ± 17 k acting at the free end (see figure). The beam has width b ± 3 in. and height h ± 12 in. Point A is located at distance c ± 2.5 ft from the free end and distance d ± 9 in. from the bottom of the beam. Calculate the principal stresses s 1 and s 2 and the maximum shear stress t max at point A . Show these stresses on sketches of properly oriented elements. Probs. 8.4-1 and 8.4-2 P c A b d h Solution 8.4-1 P ± 17 k c ± 2.5 ft b ± 3 in. d ± 9 in. h ± 12 in. v ± 0.3 S TRESS AT POINT A I ± 432 in. 4 M ±² Pc M 5.1 ³ 10 5 lb-in. V ± PV ± 1.7 ³ 10 4 lb y A ± 3 in. s x ± 3.542 ³ 10 3 psi Q ± 40.5 in. 3 t ± 531.25 psi t xy ± t s x ± 3.542 ³ 10 3 psi s y ± 0 t xy ± 531.25 psi P RINCIPAL STRESSES u p ± 8.35 deg u p ± 1 2 a tan a 2 t xy s x ² s y b tan 1 2 u p 2 ± 2 t xy s x ² s y ± 2 t xy s x ² s y ± 0.3 t ± VQ Ib Q ± bd
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