Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 8.1, Problem 8.15P
The inner ring A has an inner radius r1 and outer radius r2. The outer ring B has an inner radius r3 and an outer radius r4, and r2 > r3. If the outer ring is heated and then fitted over the inner ring, determine the pressure between the two rings when ring B reaches the temperature of the inner ring. The material has a modulus of elasticity of E and a coefficient of thermal expansion of α
.
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The center rod CD of the assembly is heated from T₁ = 30 °C to T₂ = 165
°C using electrical resistance heating. At the lower temperature T₁ the gap
between C and the rigid bar is 0.7 mm. Rods AB and EF are made of
steel, and each has a cross-sectional area of 125 mm². CD is made of
aluminum and has a cross-sectional area of 375 mm². Est = 200 GPa,
Eal = 70 GPa, and cal = 23 (10-) /°C.
(Figure 1)
Figure
0.7 mm
240 mm
300 mm
Determine the force in the rod AB caused by the increase in temperature.
Express your answer to three significant figures and include the appropriate units.
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Determine the force in the rod EF caused by the increase in temperature.
Express your answer to three significant figures and include the appropriate units.
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The bar has a cross-sectional area A, length L, modulus of elasticity E, and coefficient of thermal expansion a. The temperature of the bar changes uniformly along its length from TA at A to TB at B so that at any point x alongthe bar T = TA + x(TB - TA)>L. Determine the force the bar exerts on the rigid walls. Initially, no axial force is in the bar and the bar has a temperature of TA.
The central bar CD of the assembly is heated from 30 ° C to 180 ° C by means of an electrical resistance. Also the two bars AB and EF are heated from 30 ° C to 50 ° C. At the lower temperature of 30 ° C, the space between C and the rigid bar is 0.7 mm.
Determine the force in bars AB and EF caused by the increase in temperature. Bars AB and EF are made of steel and each has a cross-sectional area of 125 mm ^ 2; CD is aluminum with a cross-sectional area of 375 mm ^ 2. Steel = 200GP; Ealuminum = 70 GPa; alpha steel = 12 X10 ^ -6 (1 / ºC); alpha aluminum = 23 X10 ^ -6 (1 / ° C).
Chapter 8 Solutions
Mechanics of Materials (10th Edition)
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