866_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

866_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 11Ch11.qxd 9/27/08 860 2:21 PM Page 860 CHAPTER 11 Columns Problem 11.3-17 The truss ABC shown in the figure supports a vertical load W at joint B. Each member is a slender circular steel pipe (E = 30,000 ksi) with outside diameter 4 in. And wall thickness 0.25 in. The distance between supports is 23 ft. Joint B is restrained against displacement perpendicular to the plane of the truss. Determine the critical value Wcr of the load. B 100 mm W 40° A 55° C 7.0 m Solution 11.3-17 FREE-BODY DIAGRAM OF JOINT B E 30000 ksi L 23 ft d2 4 in. t 0.25 in. d1 d2 2t I p 4 1d 2 64 u1 d1 4 d 12 40° L AB L AB L BC L BC LP 3.50 in. 5.200 in.4 I u2 55° © Fhoriz sin a u2 b sin(180° u1 u2) 18.912 ft LP sin a u1 b sin(180° u1 u2) 14.841 ft Critical loads Pcr– AB Pcr– BC Problem 11.3-18 p2EI L2 AB 2 p EI L2 BC Q © Fhoriz 0 FAB cos1u12 0 FAB sin1u12 FBC cos1u22 FBC sin1u22 0 W 0 SOLVE THE TWO EQUATIONS W W 1.7361FAB 1.3004 FBC CRITICAL VALUE OF THE LOAD W BASED ON MEMBER AB: Q Wcr– AB 1.7361Pcr–AB Wcr– AB 51.90 k BASED ON MEMBER BC: Pcr– AB 29.89 k Pcr–BC 48.55 k A truss ABC supports a load W at joint B, as shown in the figure. The length L1 of member AB is fixed, but the length of strut BC varies as the angle u is changed. Strut BC has a solid circular cross section. Joint B restrained against displacement perpendicular to the plane of the truss. Assuming the collapse occurs by Euler buckling of the strut, determine the angle u for minimum weight of the strut. Wcr–BC 1.3004Pcr⇣– BC Wcr 51.9 k 63.13 k min(Wcr– AB,Wcr– BC) Wcr Wcr– BC ; Member AB governs A B u W C L1 ...
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