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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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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 W cr of the load. 860 CHAPTER 11 Columns Solution 11.3-17 Critical loads P cr BC p 2 EI L 2 BC P cr BC 48.55 k P cr AB p 2 EI L 2 AB P cr AB 29.89 k L BC 14.841 ft L BC L P sin a u 1 b sin(180° u 1 u 2 ) Q L AB 18.912 ft L AB L P sin a u 2 b sin(180° u 1 u 2 ) Q u 1 40° u 2 55° I p 64 1 d 2 4 d 1 4 2 I 5.200 in. 4 d 1 3.50 in. d 1 d 2 2 t t 0.25 in. d 2 4 in. L 23 ft E 30000 ksi F REE - BODY DIAGRAM OF JOINT B W A B C 40 ° 55 ° 7.0 m 100 mm S OLVE THE TWO EQUATIONS C RITICAL VALUE OF THE LOAD W B ASED ON MEMBER AB : B ASED ON MEMBER BC : Member AB governs ; W cr 51.9 k W cr min( W cr AB , W cr BC ) W cr BC 1.3004 P cr

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866_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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