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

y
P
P
Q
b f
t f
A
x H
H
x
B C D
K
x K
E
y
L
4
FIGURE p15.20a/21a
L
4
L
4
L
4
y H
z
H
t w
d
t f
FIGURE p15.22b
b f
y
y H
y K
z
H
K
t w
d
p15.23 The bracket shown in Figure P15.23a/24a supports a
pulley that has a diameter D = 120 mm. The tension in the pulley
belt is P = 200 N, and the angle of the pulley belt is β = 30° as
shown. The bracket has dimensions a = 90 mm and c = 150 mm.
The cross-sectional dimensions of the bracket are b = 10 mm and
d = 30 mm as shown in Figure P15.23b/24b. Determine the principal
stresses and the maximum shear stress acting at point H. Show
these stresses on an appropriate sketch.
FIGURE p15.20b/21b
β
P
p15.21 The simply supported beam shown in Figure P15.20a/
21a supports three concentrated loads. The loads at B and C each
have a magnitude of P = 70 kN, and the load at D is Q = 260 kN.
The beam span is L = 10 m. The cross-sectional dimensions of the
beam as shown in Figure P15.20b/21b are b f = 300 mm, t f = 20 mm,
d = 500 mm, t w = 12 mm, and y K = 120 mm. Determine the principal
stresses and the maximum shear stress acting at point K, which is
located at x K = 1.75 m from the left-hand support. Show these
stresses on an appropriate sketch.
p15.22 The beam shown in Figure P15.22a is supported by a tie
bar at B and by a pin connection at C. The beam span is L = 7 m and
the uniformly distributed load is w = 22 kN/m. The tie bar at B has
an orientation of θ = 25°. The cross-sectional dimensions of the
beam shown in Figure P15.22b are b f = 130 mm, t f = 12 mm, d =
360 mm, t w = 6 mm, and y H = 50 mm. Determine the principal
stresses and the maximum shear stress acting at point H. Show
these stresses on an appropriate sketch.
c
H
y
K
a
x
FIGURE p15.23a/24a
b
H
d
d
6
z
d
4
K
FIGURE p15.23b/24b
D
x
P
y
A
θ
B
FIGURE p15.22a
x
4L
5
w
H
L
5
C
p15.24 The bracket shown in Figure P15.23a/24a supports a
pulley that has a diameter D = 6 in. The tension in the pulley belt is
P = 75 lb, and the angle of the pulley belt is β = 30° as shown. The
bracket has dimensions a = 4.5 in. and c = 7.5 in. The crosssectional
dimensions of the bracket are b = 0.5 in. and d = 1.5 in. as
shown in Figure P15.23b/24b. Determine the principal stresses and
the maximum shear stress acting at point K. Show these stresses on
an appropriate sketch.
633