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

m15.3 The rectangular tube is subjected to a transverse shear
force V and a bending moment M, each acting in the direction
shown. Determine the bending stress, the transverse shear stress
magnitude, the principal stresses, and the maximum shear stress
acting at location H.
m15.4 The wide-flange shape is subjected to a transverse shear
force V and a bending moment M, each acting in the direction
shown. Determine the bending stress, the transverse shear stress
magnitude, the principal stresses, and the maximum shear stress
acting at location H.
FIGURE m15.3 FIGURE m15.4
pRoBLEmS
p15.12 The extruded flexural member shown in Figure P15.12a
is subjected to a shear force V = 3,600 N and a bending moment
M = 550 N · m. The cross-sectional dimensions of the shape are
shown in Figure P15.12b, where a = 15 mm, b = 8 mm, c = 30 mm,
and d = 42 mm. Determine the principal stresses and the maximum
shear stress acting at point H, which is located at h = 20 mm below
the upper surface of the member.
h
H
z
FIGURE p15.12a
a
H
b
z
c
FIGURE p15.12b
b
y
c
V
y
b
M
a
d
b
x
p15.13 The beam cross section shown in Figure P15.13a/14a
will consist of two square tubes that are welded to a rectangular
web plate. The dimensions of the cross section as shown in Figure
P15.13b/14b are d = 240 mm, t w = 12 mm, b = 80 mm, and t = 8.0 mm.
The beam is subjected to an axial force P = 30 kN, a shear force
V = 180 kN, and a bending moment M = 75 kN · m. Determine the
principal stresses and the maximum shear stress acting at point H,
located at y H = 90 mm above the z centroidal axis. Show these
stresses on an appropriate sketch.
z
H
K
y
V
M
FIGURE p15.13a/14a
P
x
Square tube
t
p15.14 The beam cross section shown in Figure P15.13a/14a
will consist of two square tubes that are welded to a rectangular
web plate. The dimensions of the cross section as shown in
z
y H
y K
Square tube
H
y
K
b
t w
Web
plate
FIGURE p15.13b/14b
b
d
b
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