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

pRoBLEmS
p9.11 A 0.375 in. diameter solid steel shaft supports two pulleys
as shown in Figure P9.11. The shaft has a length L = 9 in., and the
load applied to each pulley is P = 60 lb. The bearing at A can be
idealized as a pin support, and the bearing at D can be idealized as
a roller support. Determine the magnitude of the maximum horizontal
shear stress in the shaft.
(a) the shear stress at point A, which is located at y A = 80 mm
below the centroid of the wide-flange shape.
(b) the maximum horizontal shear stress in the wide-flange shape.
y
P
V
t w
t f
z
d
A B C D
y A
A
L
3
L
3
L
3
P FIGURE p9.11
p9.12 A 25 mm diameter solid steel shaft supports loads P A =
1,000 N, P C = 3,200 N, and P E = 800 N, as shown in Figure P9.12.
Assume that L AB = 80 mm, L BC = 200 mm, L CD = 100 mm, and
L DE = 125 mm. The bearing at B can be idealized as a roller support,
and the bearing at D can be idealized as a pin support. Determine
the magnitude and location of
(a) the maximum horizontal shear stress in the shaft.
(b) the maximum tensile bending stress in the shaft.
b f
p9.15 The extruded cross section shown in Figure P9.15 is subjected
to a shear force V = 420 N. The dimensions of the cross section
are b = 40 mm, d = 60 mm, and t = 4 mm. Determine
(a) the value of Q associated with point H, located at a = 13 mm
above the lower surface of the cross section.
(b) the horizontal shear stress at point H.
(c) the maximum horizontal shear stress in the cross section.
t
(typ)
y
FIGURE p9.14
d
3
344
P A
A
L AB
B
FIGURE p9.12
L BC
L CD
p9.13 An aluminum alloy pipe with an outside
diameter of 4.0 in. and a wall thickness of
3/16 in. cantilevers upward a distance L = 18 ft,
as shown in Figure P9.13. The pipe is subjected
to a wind loading that increases from w A =
12 lb/ft at its base to w B = 20 lb/ft at its tip.
P C
(a) Compute the value of Q for the pipe.
(b) What is the maximum vertical shear
stress in the pipe?
p9.14 The internal shear force at a certain
section of a steel beam is V = 215 kN. The
beam cross section shown in Figure P9.14
has dimensions b f = 300 mm, t f = 19 mm,
d = 390 mm, and t w = 11 mm. Determine
C
D
w B
L DE
w A
P E
B
A
E
FIGURE p9.13
L
a
H
z
b
V
p9.16 The beam cross section shown in Figure P9.16 is subjected
to a shear force V = 215 kN. The dimensions of the cross
section are b = 150 mm, d = 210 mm, and t = 6 mm. Determine
(a) the horizontal shear stress at point H, located at a = 60 mm
below the upper surface of the cross section.
(b) the maximum horizontal shear stress in the cross section.
d
a
H
z
b
2
y
V
b
2
d
3
d
3
t
(typ)
FIGURE p9.15
FIGURE p9.16