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

p9.42 The hat-shape extrusion shown in Figure P9.42 has dimensions
b = 50 mm, d = 40 mm, a = 30 mm, and t = 2 mm. A
vertical shear force V = 600 N acts on the cross section. Determine
(a) the shear stress at points A–D.
(b) the resultant horizontal force that acts between points A and B.
p9.45 Sheet metal is bent into the shape shown in Figure P9.45
and is then used as a beam. The shape has centerline dimensions
a = 120 mm, b = 80 mm, and t = 3 mm. A vertical shear force
V = 6,400 N acts on the cross section. Determine the shear stress
magnitude that acts in the shape at points A–D.
a
y
a
t
(typ)
A
y
z
V
D
b
C
B
t
t
A
t
d
FIGURE p9.42
z
B
C
b
V
60° 60°
D
b
a
FIGURE p9.45
p9.43 Sheet metal is bent into the shape shown in Figure P9.43
and is then used as a beam. The shape has dimensions b = 4.5 in.,
d = 7.0 in., a = 1.5 in., and t = 0.14 in. A vertical shear force V =
6,200 lb acts on the cross section. Determine the shear stress that
acts in the shape at points A–G.
t
(typ)
a
z
b
G
y
V
A
B
C
a
F
FIGURE p9.43
p9.44 Sheet metal is bent into the shape shown in Figure P9.44
and is then used as a beam. The shape has dimensions b = 80 mm,
d = 60 mm, a = 20 mm, and t = 3 mm. A vertical shear force V =
5,400 N acts on the cross section. Determine the shear flow at
points A–E.
E
D
d
p9.46 Sheet metal is bent into the shape shown in Figure P9.46
and is then used as a beam. The shape has centerline dimensions
b = 3.0 in., d = 4.5 in., a = 1.8 in., and t = 0.12 in. A vertical shear
force V = 480 lb acts on the cross section. Determine
(a) the shear stress that acts in the shape at points A–D.
(b) the resultant horizontal force acting on the cross-sectional
element between A and B.
A
z
a
b
B
C
D
V
y
b
E
FIGURE p9.46
p9.47 The thin-walled sheet pile cross section shown in Figure
P9.47 is subjected to a vertical shear force V = 175 kN. The shape
has centerline dimensions b = 160 mm, d = 350 mm, a = 120 mm,
and t = 12 mm. Determine
(a) the shear stress in the shape at points A–E.
(b) the resultant horizontal force acting on the cross-sectional
element between A and B.
a
t
(typ)
F
d
A
a
B
C
D
z
y
V
E
b
t
t
a
t
d
FIGURE p9.44
z
A
b
B
C
FIGURE p9.47
D
y
E
V
t
(typ)
a 2b a b
d
387