703_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

703_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 11:06 AM Page 697 697 SECTION 8.5 Combined Loadings Problem 8.5-19 A cylindrical pressure vessel with flat ends is y0 subjected to a torque T and a bending moment M (see figure). The outer radius is 12.0 in. and the wall thickness is 1.0 in. The loads are as follows: T 800 k-in., M 1000 k-in., and the internal pressure p 900 psi. Determine the maximum tensile stress st, maximum compressive stress sc, and maximum shear stress tmax in the wall of the cylinder. T M M T x0 z0 Solution 8.5-19 Cylindrical pressure vessal Internal pressure: p 900 psi Bending moment: M 1000 k-in. Torque: T 800 k-in. Outer radius: r2 12 in. Wall thickness: t 1.0 in. Mean radius: r r2 t/2 Outer diameter: d2 d1 sy 11.5 in. 22 in. MOMENT OF INERTIA I p4 (d 64 2 Ip 2I d 4) 1 pr 2t Mr2 I 5175.0 psi 2506.8 psi 2668.2 psi pr t txy Tr2 Ip 24 in. Inner diameter: sx 10,350 psi 1002.7 psi PRINCIPAL STRESSES sx + sy s1, 2 ; 2 4 4787.0 in. A a sy sx 2 2 b + t2 xy 6509.1 psi ; 3969.6 psi s1 9574.0 in.4 s2 10,479 psi 2540 psi NOTE: Since the stresses due to T and p are the same everywhere in the cylinder, the maximum stresses occur at the top and bottom of the cylinder where the bending stresses are the largest. MAXIMUM SHEAR STRESSES PART (a). TOP OF THE CYLINDER t In-plane: t 3970 psi Out-of-plane: Stress element on the top of the cylinder as seen from above. s1 2 tmax or s2 2 t s1 2 5240 psi 5240 psi MAXIMUM STRESSES FOR THE TOP OF THE CYLINDER st tmax 10,480 psi 5240 psi sc 0 (No compressive stresses) ...
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