Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 4.6, Problem 4.77P
The bar has a cross-sectional area A, length L, modulus of elasticity E, and coefficient of thermal expansion α. The temperature of the bar changes uniformly along its length from TA at A to TB at B so that at any point x along the 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
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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 wires AB and AC are made of steel, and wire AD is made of aluminum. Before the
300 kN force is applied, AB and AC are each 150 mm. long and AD is 100 mm. long. If the
temperature is increased by 30°C, determine the force in each wire needed to support the load.
Take Est =
200 GPa, Eal
= 70 GPa, st =
12 (10") / °C, aal = 23 (10") / °C. Each wire has a
cross-sectional area of 0.02 mm².
B
100 mm
45° 45°
150 mm
150 mm
A
300 kN
4-69. Three bars each made of different materials are
connected together and placed between two walls when the
temperature is T₁ = 12°C. Determine the force exerted
on the (rigid) supports when the temperature becomes
T₂ = 18°C. The material properties and cross-sectional
area of each bar are given in the figure.
Steel
Brass
dEst = 200 GPa
Ebr = 100 GPa
bast=12(10-6)/°C abr 21(106)/C α =
=
Aut= 200 mm² Abr = 450 mm²
pha2kn
300 mm-
4kn
-200 mm-
Prob. 4-69
Copper
Ecu = 120 GPa-44
17(10-6)/°C
Acu = 515 mm²
100 mm
Chapter 4 Solutions
Mechanics of Materials (10th Edition)
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