Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

p3.16 Compound axial member ABC shown in Figure P3.16 has
a uniform diameter d = 1.50 in. Segment (1) is an aluminum [E 1 =
10,000 ksi] alloy rod with length L 1 = 90 in. Segment (2) is a copper
[E 2 = 17,000 ksi] alloy rod with length L 2 = 130 in. When axial
force P is applied, a strain gage attached to copper segment (2)
measures a normal strain of ε 2 = 2,100 µin./in. in the longitudinal
direction. What is the total elongation of member ABC?
been decreased by 30°F, the total strain in bar (1) is measured as
570 µε (elongation). Assume dimensions of a = 12 in. and b = 20 in.
Determine
(a) the magnitude of load P.
(b) the average shear stress in pin B.
A
P
L 1
P
(1)
A
Aluminum
FIGURE p3.16
B
(2)
L 2
Copper
C
P
d
C
L 1 (1)
D
FIGURE p3.18
b
Rigid
plate
B
a
p3.17 An aluminum alloy [E =
L
70 GPa; ν = 0.33; α = 23.0 ×
10 −6 /°C] plate is subjected to a
tensile load P as shown in Figure
P3.17. The plate has a depth d =
260 mm, a cross-sectional area
P
d
A = 6,500 mm 2 , and a length L = FIGURE p3.17
4.5 m. The initial longitudinal
normal strain in the plate is zero. After load P is applied and the
temperature of the plate has been increased by ∆T = 56°C, the longitudinal
normal strain in the plate is found to be 2,950 µε.
Determine
(a) the magnitude of load P.
(b) the change ∆d in plate depth.
p3.18 The rigid plate in Figure P3.18 is supported by bar (1)
and by a double-shear pin connection at B. Bar (1) has a length
L 1 = 60 in., a cross-sectional area A 1 = 0.47 in. 2 , an elastic modulus
E = 10,000 ksi, and a coefficient of thermal expansion of α = 13 ×
10 −6 /°F. The pin at B has a diameter of 0.438 in. After load P
has been applied and the temperature of the entire assembly has
p3.19 In Figure P3.19, member (1) is an aluminum bar that
has a cross-sectional area A = 1.05 in. 2 , an elastic modulus
E = 10,000 ksi, and a coefficient of thermal expansion of α =
12.5 × 10 −6 /°F. After a load P of unknown magnitude is applied
to the structure and the temperature is increased by 65°F, the
normal strain in bar (1) is measured as −540 µε. Use dimensions
of a = 24.6 ft, b = 11.7 ft, and c = 14.0 ft. Determine the magnitude
of load P.
A
Rigid bar
c
FIGURE p3.19
a
C
D
Strain
gage
(1)
B
b
P
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