696_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

696_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 690 11:06 AM Page 690 CHAPTER 8 Applications of Plane Stress RESULTANT FORCES ACTING ON AB P weight of AB and BC P qL T torque due to weight of BC T L (qL) a b 2 pgLd2/4 (2) qL2 2 PL (3) bending moment at A MA PL /2 0 sy sA txy sA sA 2 + a b + t2 A 2 A2 tA (8) Substitute (8) into (7): pgL2d 2 8 MA sx s1 gL2 (6 + 140) d 2gL2 (3 + 110) d (9) Substitute from (5) and (6) and simplify: 3pgL2d2/8 3PL /2 (4) s1 STRESSES AT THE TOP OF THE BAR AT A sA sA 2gL2 (3 + 110) s1 SOLVE FOR d normal stress due to MA M(d/2) I (10) M(d/2) pd 4/64 12gL2 d 32M pd 3 tA tA pd 4/32 2gL2 d 16T pd 3 g (6) 490 lb/ft3 L 20 in. d T(d/2) ; (11) SUBSTITUTE NUMERICAL VALUES INTO EQ. (11): shear stress due to torque T T(d/2) Ip (5) d 1.50 in. 0.28356 lb/in.3 s1 932 psi ; STRESS ELEMENT ON TOP OF THE BAR AT A s1 s1 A principal tensile stress (maximum tensile stress) sx + sy + 2 a sy sx 2 2 b + t2 xy (7) Problem 8.5-14 A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (see figure). The tank has radius r 50 mm and wall thickness t 3 mm. The internal pressure p 3.5 MPa and the torque T 450 N # m. What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 72 MPa? T P T P ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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