175_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

175_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.5.qxd 9/25/08 3:00 PM Page 169 SECTION 2.5 Thermal Effects 169 Problem 2.5-20 A plastic cylinder is held snugly between a rigid plate and a foundation by two steel bolts (see figure). Determine the compressive stress p in the plastic when the nuts on the steel bolts are tightened by one complete turn. Data for the assembly are as follows: length L 200 mm, pitch of the bolt threads p 1.0 mm, modulus of elasticity for steel Es 200 GPa, modulus of elasticity for the plastic Ep 7.5 GPa, cross-sectional area of one bolt As 36.0 mm2, and cross-sectional area of the plastic cylinder Ap 960 mm2. Steel bolt L Solution 2.5-20 Plastic cylinder and two steel bolts COMPATIBILITY EQUATION L 200 mm P 1.0 mm Es 200 GPa As 36.0 mm2 (for one bolt) Ep 7.5 GPa Ap 960 mm2 s p s elongation of steel bolt shortening of plastic cylinder np p (Eq. 2) FORCE-DISPLACEMENT RELATIONS n 1 (See Eq. 2-22) EQUILIBRIUM EQUATION ds PsL EsAs dp PpL Ep Ap (Eq. 3, Eq. 4) SOLUTION OF EQUATIONS Substitute (3) and (4) into Eq. (2): Pp L PsL + Es As Ep Ap np Solve simultaneously Eqs. (1) and (5): Ps Pp Pp tensile force in one steel bolt compressive force in plastic cylinder 2Ps Pp (Eq. 1) 2npEs AsEp Ap L(Ep Ap + 2Es As) (Eq. 5) ...
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