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

p5.34 A pin-connected structure is loaded and supported as
shown in Figure P5.34. Member ABCD is a rigid bar that is horizontal
before a load P = 6 kips is applied at end D. Bars (1) and (2)
are made of steel [E = 30,000 ksi], and each bar has a crosssectional
area of 0.45 in. 2 . Dimensions of the structure are a = 220 in.,
b = 140 in., c = 100 in., and d = 220 in. Determine
(a) the normal stress in each bar.
(b) the downward deflection of end D of the rigid bar.
d
a
a
E
A
FIGURE p5.34
A
B
C
(2)
FIGURE p5.33
b
(1)
(1)
(1) (2)
Rigid bar
B
C
a b c
p5.35 A load P = 100 kN is supported by an assembly consisting
of rigid bar ABC, two identical solid bronze [E = 105 GPa] bars, and
a solid aluminum alloy [E = 70 GPa] bar, as shown in Figure P5.35.
The bronze bars (1) each have a cross-sectional area of 125 mm 2 and
D
P
P
D
a length L 1 = 2,400 mm. Aluminum bar (2) has a cross-sectional area
of 375 mm 2 and a length L 2 = 1,500 mm. Assume that a = 500 mm.
All bars are unstressed before the load P is applied; however, there is
a gap of D = 2 mm in the connection at B. Determine
(a) the axial forces in the bronze and aluminum bars.
(b) the downward deflection of rigid bar ABC.
p5.36 A bronze pipe (1) is to be connected to an aluminum alloy
pipe (2) at flange B, as shown in Figure P5.36. When the assembly is
put in place, however, a gap of D = 0.25 in. exists between the two
pipes. Bronze pipe (1) has an elastic modulus E 1 = 16,000 ksi, a crosssectional
area A 1 = 2.23 in. 2 , and a length L 1 = 5.0 ft. Aluminum alloy
pipe (2) has an elastic modulus E 2 = 10,000 ksi, a cross-sectional area
A 2 = 1.07 in. 2 , and a length L 2 = 9.0 ft. If bolts are inserted into the
flanges and tightened so that the gap at B is closed, determine
(a) the normal stresses produced in each of the members.
(b) the final position of flange B with respect to support A.
A
L1
L2
(1)
FIGURE p5.36
p5.37 Rigid bar ABCD shown in Figure P5.37 is supported by a
smooth pin at D and by vertical aluminum alloy [E = 10,000 ksi] bars
attached at joints A and C. Bar (1) was fabricated to its intended
length L 1 = 40 in. Bar (2) was intended to have a length of 60 in.; however,
its actual length after fabrication was found to be L 2 = 59.88 in.
To connect it to the pin at C on the rigid bar, bar (2) will need to
be manually stretched by D = 0.12 in. After bar (2) has been stretched
and connected to the pin at C, a load P = 20 kips is applied to the rigid
bar at B. Use the following additional properties and dimensions:
A 1 = A 2 = 0.75 in. 2 , a = 36 in., b = 54 in., and c = 48 in. Determine
(a) the normal stresses in bars (1) and (2).
(b) the deflection at A of the rigid bar.
Δ
B
(2)
C
a
a
(1)
(2)
L 2
L 1
(1)
(1)
(2)
L 2
A B Δ C
Rigid bar
L 1
Rigid bar C Δ
A
a
B
b c
P
FIGURE p5.37
D
FIGURE p5.35
P
p5.38 A 0.625 in. diameter steel [E = 30,000 ksi] bolt (1) is placed
in a copper [E = 16,000 ksi] tube (2), as shown in Figure P5.38. The
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