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

Spacer block
FIGURE p16.6
76 mm 76 mm
Double angles
L102 × 76 × 9.5
Long legs back-to-back
Spacer thickness
p16.7 A solid 0.5 in. diameter cold-rolled steel rod is pinned to
fixed supports at A and B as shown in Figure P16.7. The length of
the rod is L = 24 in., the rod’s elastic modulus is E = 30,000 ksi, and
its coefficient of thermal expansion is α = 6.6 × 10 −6 /°F. Determine
the temperature increase ∆T that will cause the rod to buckle.
p16.9 Rigid beam ABC is supported by a pinned connection at
A and by a 180 mm by 180 mm square timber post that is pin
connected at B and D, as shown in Figure P16.8/9. The length
dimensions of the beam are x 1 = 3.6 m and x 2 = 2.8 m. The timber
post has a length L = 4 m and an elastic modulus E = 12 GPa. If a
factor of safety of 2.0 with respect to buckling is specified, determine
the magnitude of the maximum distributed load w that may be
supported by the beam.
p16.10 A rigid beam is supported by a pinned connection at B
and by an inclined strut that is pin connected at A and C as shown
in Figure P16.10a. The dimensions of the structure are a = 3.5 m,
b = 2.5 m, c = 3.8 m, and e = 200 mm. Loads on the structure are
P = 13 kN and w = 150 kN/m. The strut is fabricated from two steel
[E = 200 GPa] L127 × 76 × 12.7 angles, which are oriented with the
long legs back-to-back, as shown in Figure P16.10b. The angles are
separated and connected by spacer blocks, which are s = 40 mm
thick. Determine
(a) the compressive force in the strut created by the loads acting
on the beam.
(b) the slenderness ratios for the strut about the strong and weak
axes of the double-angle shape.
(c) the minimum factor of safety in the strut with respect to
buckling.
A
FIGURE p16.7
L
p16.8 Rigid beam ABC is supported by a pinned connection at
A and by a timber post that is pin connected at B and D, as shown in
Figure P16.8/9. A distributed load of w = 2 kips/ft acts on the 14 ft
long beam, which has length dimensions x 1 = 8 ft and x 2 = 6 ft. The
timber post has a length L = 10 ft, an elastic modulus E = 1,800 ksi,
and a square cross section. If a factor of safety of 2.0 with respect
to buckling is specified, determine the minimum width required for
the square post.
B
c
e
y
P
A
Double angles
L127 × 76 × 12.7
Long legs back-to-back
a
b
w
B
x
w
FIGURE p16.10a
C
A B C
x 1
x2
L
(1)
Double angles
L127 × 76 × 12.7
Long legs back-to-back
D
Spacer block
s
FIGURE p16.8/9
FIGURE p16.10b
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