697_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

697_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 691 691 SECTION 8.5 Combined Loadings Solution 8.5-14 Cylindrical tank r 50 mm T 450 N # m t 3.0 mm sallow p 3.5 MPa 72 MPa Units: sx pr t sy CROSS SECTION A 2prt IP 3 942.48 mm2 2p(50 mm)(3.0 mm) 2pr t 2.3562 MPa, P 58.333 MPa Tr IP txy 3 2p(50 mm) (3.0 mm) newtons (450 N # m)(50 mm) 2.3562 * 106 mm4 9.5493 MPa 106 mm4 MAXIMUM TENSILE STRESS STRESSES IN THE WALL OF THE TANK smax sallow + 2[ 72 or 72 MPa sx + sy + 2 A 43.750 + (530.52 * 10 2( 28.250 a 6 sy sx 2 2 b + t2 xy )P 6 14.583 + (530.52 * 10 )P]2 + ( 9.5493)2 0.00053052P 14.583 + 0.00053052 P)2 + 91.189 Square both sides and simplify: sx 494.21 pr P + 2t A SOLVE FOR P (3.5 MPa)(50 mm) P + 2(3.0 mm) 942.48 mm2 29.167 MPa + 1.0610 * 10 0.014501 P 3 Pmax P 34.1 kN 34,080 N OR ; P z Problem 8.5-15 A post having a hollow circular cross section supports a horizontal load P 240 lb acting at the end of an arm that is 5 ft long (see figure). The height of the post is 27 ft, and its section modulus is S 15 in.3 Assume that outer radius of the post, r2 4.5 in., and inner radius r1 4.243 in. (a) Calculate the maximum tensile stress smax and maximum in-plane shear stress tmax at point A on the outer surface of the post along the x-axis due to the load P. Load P acts in a horizontal plane at an angle of 30° from a line which is parallel to the ( x) axis. (b) If the maximum tensile stress and maximum in-plane shear stress at point A are limited to 16,000 psi and 6000 psi, respectively, what is the largest permissible value of the load P? 5 ft 30° P = 240 lb 27 ft x A y ...
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