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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
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):
Ep Ap np Solve simultaneously Eqs. (1) and (5):
Pp tensile force in one steel bolt
compressive force in plastic cylinder
(Eq. 1) 2npEs AsEp Ap
L(Ep Ap + 2Es As) (Eq. 5) ...
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