Problem 4-83/4-84/4-85/ Engineering Mechanics Materials

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Engineering Mechanics problem with solution
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4–83. The wires AB and AC are made of steel, and wire AD is made of copper. Before the 150-lb force is applied, AB and AC are each 60 in. long and AD is 40 in. long. If the temperature is increased by 80F, determine the force in each wire needed to support the load. Take
E st = 29(10 3 ) ksi, E cu = 17(10 3 ) ksi, a st = 8(10 -6
)/F,
a cu = 9.60(10 -6
)/F. Each wire has a cross-sectional area of 0.0123 in2

4–84. The center rod CD of the assembly is heated from T1 = 30°C to T2 = 180°C using electrical resistance heating. At the lower temperature T1 the gap between C and the rigid bar is 0.7 mm. Determine the force in rods AB and EF caused by the increase in temperature. Rods AB and EF are made of
steel, and each has a cross-sectional area of 125 mm 2 . CD is made of aluminum and has a cross-sectional area of 375 mm 2 .
Est = 200 GPa, Eal = 70 GPa, and
aal = 23(10 −6 )/°C.

4–85. The center rod CD of the assembly is heated from T1 = 30°C to T2 = 180°C using electrical resistance heating. Also, the two end rods AB and EF are heated from
T1 = 30°C to T2 = 50°C. At the lower temperature T1 the gap between C
and the rigid bar is 0.7 mm. Determine the force in rods AB and EF caused by the increase in temperature. Rods AB and
EF are made of steel, and each has a cross-sectional area of 125 mm 2 . CD is made of aluminum and has a cross-sectional area of 375 mm 2 . Est= 200 GPa, Eal= 70 GPa, ast= 12(10 −6)/°C and aal = 23(10 −6 )/°C.