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

mecmovies
ExAmpLE
m15.1 A tubular shaft of outside diameter D = 114 mm and
inside diameter d = 102 mm is subjected simultaneously to a
torque T = 5 kN · m and an axial load P = 40 kN. Determine
the principal stresses and the maximum shear stress at a
typical point on the surface of the shaft.
pRoBLEmS
p15.1 A solid 1.50 in. diameter shaft is subjected to a torque
T = 225 lb · ft and an axial load P = 5,500 lb, as shown in
Figure P15.1/2.
(a) Determine the principal stresses and the maximum shear
stress at point H on the surface of the shaft.
(b) Show the stresses of part (a) and their directions on an
appropriate sketch.
p15.3 A hollow bronze [E = 15,200 ksi; ν = 0.34] shaft with an
outside diameter of 2.50 in. and a wall thickness of 0.125 in. is
subjected to a torque T = 720 lb · ft and an axial load P = 1,900 lb,
as shown in Figure P15.3/4. Determine
(a) the strains e x , e y , and γ xy ,
(b) the principal strains e p1 and e p2 , and
(c) the absolute maximum shear strain at point H on the outer
surface of the shaft.
y
y
z
A
FIGURE p15.1/2
H
(1)
T
B
P
x
z
A
FIGURE p15.3/4
H
(1)
T
B
P
x
p15.2 A solid 19 mm diameter aluminum alloy [E = 70 GPa;
ν = 0.33] shaft is subjected to a torque T = 60 N · m and an axial
load P = 15 kN, as shown in Figure P15.1/2. Determine
(a) the strains e x , e y , and γ xy ,
(b) the principal strains e p1 and e p2 , and
(c) the absolute maximum shear strain at point H on the outer
surface of the shaft.
p15.4 A hollow bronze shaft with an outside diameter of 80 mm
and a wall thickness of 5 mm is subjected to a torque of T = 620
N · m and an axial load of P = 9,500 N, as shown in Figure P15.3/4.
(a) Determine the principal stresses and the maximum shear
stress at point H on the surface of the shaft.
(b) Show the stresses of part (a) and their directions on an
appropriate sketch.
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