868_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

868_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 11.3-19 An S steel cantilever beam AB is supported by a steel tie rod at B has shown. The tie rod is just taut when a roller support is added at C at a distances S to the left of B , then the distributed load q is applied to beam segment AC . Assume and neglect the self weight of the beam and tie rod. See Table E-2(a) in Appendix E for the properties of the S -Shape beam. (a) What value of uniform load q will, if exceeded, result in buckling of the tie rod if L 1 =6 ft, S = 2 ft, H = 3 ft, d = 0.25 in.? (b) What minimum beam moment of inertia I b is required to prevent buckling of the tie rod if ? (c) For what distances S will the tie rod be just on the verge of buckling if ? q ± 200 lb/ft, L 1 ± 6 ft, H ± 3 ft, d ± 0.25 in. S ± 2 ft d ± 0.25 in., H ± 3 ft, L 1 ± 6 ft, q ± 200 lb/ft, E ± 30 * 10 6 psi 6 * 12.5 862 CHAPTER 11 Columns Solution 11.3-19 Analyze 1st degree statically-indeterminate beam by letting force in tie rod be a redundant Released beam AB with the uniform load
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Unformatted text preview: q S 6 * 12.5 I b 22.0 in. 4 P cr p 2 EI r H 2 P cr 43.81 lb A r 0.049 in. 2 A r p 4 d 2 I r 191.7 * 10 6 in. 4 I r p 64 d 4 q 200 lb ft H 3 ft d 1 4 in. L 1 6 ft E 30 * 10 6 psi F ROM APPENDIX G Shortening in tie rod Compatibility equation (a) F OR ; q max 142.4 lb ft * 1 s 2 A r L 1 + 3 HI b 2 From (1) q max 8 Q sA r 1 L 1 s 2 3 Q P cr s 2.0 ft Q sqA r 1 L 1 s 2 3 8 1 s 2 A r L 1 + 3 HI b 2 (1) QH EA r q 1 L 1 s 2 3 24 EI b c Qs 3 3 EI b + Qs 1 L 1 s 2 s 3 EI b d d B d B d r d r QH EA r d B Qs 3 3 EI b + Qs ( L 1 s ) s 3 EI b S L 1 Tie rod, diameter d S 6 12.5 H B A q D C L 1 = 6 ft S B A q S L 1 = 6 ft B Q A Released beam AB with the redundant Q From appendix G d B q 1 L 1 s 2 3 24 EI b 11Ch11.qxd 9/27/08 2:21 PM Page 862...
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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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