159_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

159_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 153 153 SECTION 2.5 Thermal Effects Problem 2.5-4 A steel rod of 15-mm diameter is held snugly (but without any initial stresses) between rigid walls by the arrangement shown in the figure. (For the steel rod, use 12 10 6/°C and E 200 GPa.) (a) Calculate the temperature drop T (degrees Celsius) at which the average shear stress in the 12-mm diameter bolt becomes 45 MPa. Washer, dw = 20 mm 12-mm diameter bolt ΔT B A (b) What are the average bearing stresses in the bolt and clevis at A and the washer (dw 20 mm) and wall (t wall 18mm) at B? 18 mm 15 mm Clevis, tc = 10 mm Solution 2.5-4 numerical properties dr 15 mm db 12 mm dw 20 mm tc 10 mm twall 18 mm b 45 MPa E 200 GPa 6 12 (10 ) solve for T ¢T (a) TEMPERATURE DROP RESULTING IN BOLT SHEAR STRESS T rod force E P T shear with shear stress t so t b tb p c ( Ea¢ T) dr2 d 2 4 pdb t P p2 2 db 4 ; T 24°C P p ( E a ¢ T) d2 and bolt in double r 4 P 2 AS 2t b db 2 ab E a dr ( E a ¢ T) p2 d 4r P 10.18 kN (b) BEARING STRESSES P 2 dbtc bolt and clevis s bc 2 bw 74.1 MPa p 1d 2 4w d r2 2 ; (a) Derive a formula for the compressive stress c in the bar. (Assume that the material has modulus of elasticity E and coefficient of thermal expansion ). Δ TB ΔT Problem 2.5-5 A bar AB of length L is held between rigid supports and heated nonuniformly in such a manner that the temperature increase T at distance x from end A is given by the expression T TBx 3 / L3 , where TB is the increase in temperature at end B of the bar (see figure part a). ; P washer at wall s bw E a ¢ T dr 2 ab 2 db 42.4 MPa bc 0 A B x L (a) ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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