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174_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

174_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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168 CHAPTER 2 Axially Loaded Members Solution 2.5-19 The figure shows a section through the pipe, cap and rod N UMERICAL PROPERTIES L ci 48 in. E s 30000 ksi E b 14000 ksi E c 12000 ksi t c 1 in. p 52 (10 3 ) in. in. in. d o 6 in. d i 5.625 in. (a) F ORCES & STRESSES IN PIPE & ROD one degree stat-indet - cut rod at cap & use force in rod (Q) as the redundant rel1 relative displ. between cut ends of rod due to 1/4 turn of nut rel1 np ends of rod move apart, not together, so this is ( ) rel2 relative displ. between cut ends of rod due pair of forces Q A pipe p 4 (d o 2 d i 2 ) A rod p 4 d r 2 d rel2 Q a L + 2t c E b A rod + L ci E c A pipe b d r 1 2 d w 3 4 n 1 4 A rod 0.196 in 2 A pipe 3.424 in 2 compatibility equation rel1 rel2 0 Q 0.672 kips F rod Q statics F pipe Q stresses c 0.196 ksi b 3.42 ksi (b) B EARING AND SHEAR STRESSES IN STEEL CAP b 2.74 ksi c 0.285 ksi ; t c F rod p d w t c ; s b F rod p 4 (d w 2 d r 2 ) ; s b F rod A rod ; s c F pipe A pipe Q np L ci + 2t c E b A rod + L ci E c A pipe Problem 2.5-19 A capped cast-iron pipe is compressed by a brass rod, as shown. The nut is turned until it is just snug, then add an additional
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Unformatted text preview: quarter turn to pre-compress the CI pipe. The pitch of the threads of the bolt is p ± 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses p and r will be produced in the cast-iron pipe and brass rod, respectively, by the additional quarter turn of the nut? (b) Find the bearing stress b beneath the washer and the shear stress c in the steel cap. L ci = 4 ft Steel cap ( t c = 1 in.) Cast iron pipe ( d o = 6 in., d i = 5.625 in.) Modulus of elasticity, E : Steel (30,000 ksi) Brass (14,000 ksi) Cast iron (12,000 ksi) Nut & washer ( ) d w = 3 4 — in. ( d r = 1 2 — Brass rod ) in. Sec_2.5.qxd 9/25/08 3:00 PM Page 168...
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