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

p5.29 In Figure P5.29, a load P is supported by a structure
consisting of rigid bar BDF and three identical aluminum
[E = 10,000 ksi] rods, each having a diameter of 0.625 in. Use
dimensions of a = 72 in., b = 60 in., and L = 90 in. For a load
P = 16 kips, determine
a length L 2 = 32 in. Use dimensions of a = 14 in., b = 16 in., and
c = 18 in. For an applied load of P = 9 kips, determine
(a) the normal stresses in links (1) and (2).
(b) the deflection of end D of the rigid bar.
(a) the tensile force produced in each rod.
(b) the vertical deflection at B of the rigid bar.
A
B
a
C
(1) (2)
(3)
D
a
E
F
L
L 2
D
P
L 1 c
C
(1)
b
B
y,v
A
(2)
x,u
a
FIGURE p5.31
b
FIGURE p5.29
P
p5.30 A uniformly distributed load w is supported by a structure
consisting of rigid bar BDF and three rods, as shown in Figure
P5.30. Rods (1) and (2) are 0.75 in. diameter stainless steel rods
that have an elastic modulus E = 28,000 ksi and a yield strength
s Y = 36 ksi. Rod (3) is a 1.25 in. diameter bronze rod that has an
elastic modulus E = 16,000 ksi and a yield strength s Y = 48 ksi. Use
a = 4 ft and L = 9 ft. If a minimum factor of safety of 1.8 is specified
for the normal stress in each rod, calculate the maximum magnitude
of the distributed load w that can be supported.
p5.32 In Figure P5.32, polycarbonate bars (1) and (2) are attached
at their lower ends to a slider block at B that travels vertically
inside of a fixed smooth slot. Load P is applied to the slider
block. Each bar has a cross-sectional area of 85 mm 2 , a length of
1.25 m, and an elastic modulus E = 8 GPa. Use dimensions of
a = 1.15 m and b = 0.90 m. For an applied load of P = 1,700 N,
determine
(a) the forces in bars (1) and (2).
(b) the deflection at B of the slider block.
a
b
C
a
2a
A
(1)
(2)
A
C
E
Smooth slot
B
(1) (2)
(3)
L
P
B
D
F
FIGURE p5.32
FIGURE p5.30
p5.31 Links (1) and (2) support rigid bar ABCD shown in Figure
P5.31. Link (1) is bronze [E = 15,200 ksi] with a cross-sectional
area A 1 = 0.50 in. 2 and a length L 1 = 24 in. Link (2) is cold-rolled
steel [E = 30,000 ksi] with a cross-sectional area A 2 = 0.375 in. 2 and
w
p5.33 The pin-connected structure shown in Figure P5.33 consists
of two cold-rolled steel [E = 207 GPa] bars (1) and a bronze
[E = 105 GPa] bar (2) that are connected at pin D. All three
bars have cross-sectional areas of 650 mm 2 . A load P = 275 kN
is applied to the structure at D. Using a = 2.4 m and b = 3.2 m,
calculate
(a) the normal stresses in bars (1) and (2).
(b) the displacement of pin D.
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