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 ² (10 ³ 3 ) in. in. in. d o ± 6 in. d i ± 5.625 in. (a) F ORCES & STRESSES IN PIPE & ROD rod (Q) as the redundant ´ rel1 ± relative displ. between cut ends of rod due to 1/4 turn of nut rel1 ±³ np ends of rod move apart, not together, so this is ( ³ ) rel2 ± relative displ. between cut ends of rod due pair of forces Q A pipe ± p 4 (d o 2 ³ 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 µ rel2 ± 0 Q ± 0.672 kips F rod ± Q statics F pipe ±³ Q stresses c ±³ 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 ³ 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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