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

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 K, located at y K = 60 mm below the z centroidal axis.
Show these stresses on an appropriate sketch.
p15.15 The cantilever beam shown in Figure P15.15a is subjected
to concentrated loads P x = 18 kips and P y = 32 kips. The
cross-sectional dimensions of the rectangular tube shape shown in
Figure P15.15b are b = 8 in., d = 12 in., and t = 0.25 in. Point H is
located at a distance a = 24 in. to the left of the concentrated loads.
Calculate the principal stresses and maximum in-plane shear stress
at point H for the following values of h:
(a) h = 4.0 in.
(b) h = 6.0 in.
(c) h = 8.0 in.
y
a
p15.17 Normal strain values e a = 740 me and e b = −180 me
were recorded with the two strain gages mounted at point H
on the aluminum alloy [E = 10,000 ksi; ν = 0.33] bar shown in
Fig ure P15.16/17. The dimensions of the bar are d = 2.50 in., t =
0.375 in., and L = 12 in. Gages a and b are oriented at β = 35° as
shown in the figure. Point H is located a distance h = 1.0 in. above
the bottom surface of the bar. Determine the magnitudes of loads
P x and P y .
p15.18 The beam shown in Figure P15.18/19 spans a distance
L = 30 in., and its cross-sectional dimensions are b = 1.0 in. and
d = 4.0 in. A load P = 12,000 lb is applied at midspan. Point K is
located at a distance a = 6 in. from the roller support at C. Calculate
the maximum compressive normal stress at point K for the following
values of k:
(a) k = 1.5 in.
(b) k = 2.0 in.
(c) k = 2.5 in.
P y
z H P x
FIGURE p15.15a
b
y
z
H
d
x
h
H θ
K
A B k C
a
a
L
2
FIGURE p15.18/19
P
L
2
H, K
b
d
h
y
L
2
β
b
t (typ.)
FIGURE p15.15b
p15.16 Loads P x = 13 kips and P y = 20 kips act on the titanium
alloy [E = 16,500 ksi; ν = 0.33] bar shown in Figure P15.16/17. The
dimensions of the bar are d = 4.0 in., t = 0.75 in., and L = 18 in.
Gages a and b are oriented at β = 40° as shown in the figure. Point
H is located a distance h = 1.5 in. above the bottom surface of the
bar. Determine the normal strains expected in gages a and b.
H
a
FIGURE p15.16/17
β
L
2
h
x
P y
P x
z
H
t
y
d
p15.19 A single strain gage is mounted on a simply supported
beam at point H as shown in Figure P15.18/19. The beam is made
of an aluminum alloy [E = 70 GPa; ν = 0.33], and it spans a distance
L = 1.0 m. The cross-sectional dimensions are b = 20 mm and
d = 60 mm. Point H is located at a distance a = 0.3 m from the pin
support at A, and the gage is aligned at an angle θ = 45° as shown.
If a load P = 9,000 N is applied at midspan, what strains should be
expected in the gage for the following values of h:
(a) h = 20 mm.
(b) h = 30 mm.
(c) h = 40 mm.
p15.20 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 = 25 kips, and the load at D is Q =
60 kips. The beam span is L = 32 ft. The cross-sectional dimensions
of the beam as shown in Figure P15.20b/21b are b f = 12.0 in., t f =
0.85 in., d = 20.0 in., t w = 0.50 in., and y H = 3.5 in. Determine the
principal stresses and the maximum shear stress acting at point H,
which is located at x H = 4 ft from the left-hand support. Show
these stresses on an appropriate sketch.
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