05-03ChapGere.0002

05-03ChapGere.0002 - 322 A-PDF Stresses in Beams (Basic...

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Problem 5.7-2 A tall signboard is supported by two vertical beams consisting of thin-walled, tapered circular tubes (see figure). For purposes of this analysis, each beam may be represented as a cantilever AB of length L 5 8.0 m subjected to a lateral load P 5 2.4 kN at the free end. The tubes have constant thickness t 5 10.0 mm and average diameters d A 5 90 mm and d B 5 270 mm at ends A and B , respectively. Because the thickness is small compared to the diameters, the moment of inertia at any cross section may be obtained from the formula I 5 p d 3 t /8 (see Case 22, Appendix D), and therefore the section modulus may be obtained from the formula S 5 p d 2 t /4. At what distance x from the free end does the maximum bending stress occur? What is the magnitude s max of the maximum bending stress? What is the ratio of the maximum stress to the largest stress s B at the support? Solution 5.7-2 Tapered circular tube 322 CHAPTER 5 Stresses in Beams (Basic Topics) Wind load P = 2.4 kN
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