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

p15.28 Three loads are applied to the rectangular tube shown in
Figure P15.27a/28a. The load magnitudes are P = 175 kN, Q = 60 kN,
and R = 85 kN. The dimensions of the tube, as shown in Figure
P15.27b/28b, are b = 150 mm, d = 200 mm, t = 10 mm, and z K =
50 mm. The location of load P is also shown in this figure. Use
a = 125 mm, and determine the normal and shear stresses that act at
point K. Show these stresses on a stress element.
p15.29 Concentrated loads of P x = 33 kips, P y = 29 kips, and
P z = 46 kips are applied to the cantilever beam in the locations and
directions shown in Figure P15.29a/30a. The beam cross section
shown in Figure P15.29b/30b has dimensions b = 9 in. and d = 4 in.
Using the value a = 6.4 in., determine the normal and shear stresses
at point H. Show these stresses on a stress element.
z
y
K
H
a
P z
b
P y
x
y
FIGURE p15.31a/32a
36 mm
P y
K
y
H
12 mm
H
x
7 mm
z
d
P z
b
a
a
P x
a
a
a
54 mm
z
K
226 mm
FIGURE p15.29a/30a
160 mm
12 mm
FIGURE p15.31b/32b
K
b
5
y
b
3
H
p15.32 Consider the cantilever beam shown in Figure P15.31a/
32a. The dimensions of the beam cross section and the location of
point H are shown in Figure P15.31b/32b. Use the values a = 2.15 m,
b = 0.85 m, P y = 13 kN, and P z = 6 kN, and determine the normal
and shear stresses acting at point H.
d
FIGURE p15.29b/30b
b
x
p15.33 A circular tube with an outside diameter of 4.0 in. and
a wall thickness of 0.083 in. is subjected to loads P x = 1,360 lb,
P z = 950 lb, and T = 8,420 lb · in. as shown in Figure P15.33.
Using a = 6 in., determine the normal and shear stresses that exist
at (a) point H and (b) point K.
y
p15.30 Concentrated loads of P x = 33 kips, P y = 29 kips, and
P z = 46 kips are applied to the cantilever beam in the locations and
directions shown in Figure P15.29a/30a. The beam cross section
shown in Figure P15.29b/30b has dimensions b = 9 in. and d = 4 in.
Using the value a = 6.4 in., determine the normal and shear stresses
at point K. Show these stresses on a stress element.
p15.31 Consider the cantilever beam shown in Figure P15.31a/
32a. The dimensions of the beam cross section and the location of
point K are shown in Figure P15.31b/32b. Use the values a = 2.15 m,
b = 0.85 m, P y = 13 kN, and P z = 6 kN, and determine the normal
and shear stresses acting at point K.
Pz P x
T a
H K
z
FIGURE p15.33
x
653