02-03ChapGere.0013

02-03ChapGere.0013 - 6 psi E QUILIBRIUM EQUATION P s 5...

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118 CHAPTER 2 Axially Loaded Members Problem 2.5-17 A copper tube is fitted around a steel bolt and the nut is turned until it is just snug (see figure). What stresses s s and s c will be produced in the steel and copper, respectively, if the bolt is now tightened by a quarter turn of the nut? The copper tube has length L 5 16 in. and cross-sectional area A c 5 0.6 in. 2 , and the steel bolt has cross-sectional area A s 5 0.2 in. 2 The pitch of the threads of the bolt is p 5 52 mils (a mil is one-thousandth of an inch). Also, the moduli of elasticity of the steel and copper are E s 5 30 3 10 6 psi and E c 5 16 3 10 6 psi, respectively. Note: The pitch of the threads is the distance advanced by the nut in one complete turn (see Eq. 2-22). Solution 2.5-17 Steel bolt and copper tube Copper tube Steel bolt Copper tube Steel bolt L 5 16 in. p 5 52 mils 5 0.052 in. n 5 (See Eq. 2-22) Steel bolt: A s 5 0.2 in. 2 E s 5 30 3 10 6 psi Copper tube: A c 5 0.6 in. 2 E c 5 16 3 10
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Unformatted text preview: 6 psi E QUILIBRIUM EQUATION P s 5 tensile force in steel bolt P c 5 compressive force in copper tube P c 5 P s (Eq. 1) C OMPATIBILITY EQUATION d c 5 shortening of copper tube d s 5 elongation of steel bolt d c 1 d s 5 np (Eq. 2) 1 4 F ORCE-DISPLACEMENT RELATIONS (Eq. 3, Eq. 4) S OLUTION OF EQUATIONS Substitute (3) and (4) into Eq. (2): (Eq. 5) Solve simultaneously Eqs. (1) and (5): (Eq. 6) Substitute numerical values: P s 5 P c 5 3,000 lb S TRESSES Steel bolt: Copper tube: 5 5 ksi (compression) s c 5 P c A c 5 3,000 lb 0.6 in. 2 s s 5 P s A s 5 3,000 lb 0.2 in. 2 5 15 ksi (tension) P s 5 P c 5 npE s A s E c A c L ( E s A s 1 E c A c ) P c L E c A c 1 P s L E s A s 5 np d c 5 P c L E c A c d s 5 P s L E s A s P s P c P s P c np A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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