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

p17.24 Figure P17.24 shows block D, weighing 200 lb, dropped
from a height h = 6 ft onto a wide-flange steel beam that spans L =
24 ft with a = 8 ft and b = 16 ft. The steel beam has a moment of
inertia I = 300 in. 4 , a depth d = 12 in., and an elastic modulus E =
29,000 ksi. Determine
(a) the dynamic load applied to the beam.
(b) the maximum bending stress in the beam.
(c) the beam deflection at B due to the falling block.
A
a
FIGURE p17.24
p17.25 A 75 lb block D at rest is dropped from a height h =
2 ft onto the top of the simply supported wooden beam. (See
Figure P17.25.) The cross section of the beam is square—8 in. wide
by 8 in. deep—and the modulus of elasticity of the wood is E =
1,600 ksi. The beam spans L = 14 ft and is supported at A and C by
springs that each have a stiffness k = 1,000 lb/in. Assume that the
springs at A and C do not restrain beam rotation. Compute
(a) the maximum beam deflection at B due to the falling block.
(b) the equivalent static load required to produce the same
deflection as that in part (a).
(c) the maximum bending stress in the timber beam.
A
k
D
L
2
FIGURE p17.25
B
h
h
p17.26 The 120 kg block (Figure P17.26) is falling at 1.25 m/s
when it is h = 1,400 mm above the spring that is located at midspan
of the simply supported steel beam. The beam’s moment of inertia
is I = 70 × 10 6 mm 4 , its depth is d = 250 mm, and its elastic modulus
is E = 200 GPa. L = 5.5 m is the beam span. The spring constant is
k = 100 kN/m. Calculate
(a) the maximum beam deflection at B due to the falling block.
(b) the equivalent static load required to produce the same
deflection as that in part (a).
(c) the maximum bending stress in the steel beam.
B
D
b
L
2
k
C
C
A
L
2
FIGURE p17.26
p17.27 The post AB shown in Figure P17.27/28 has a length L =
2.25 m. The post is made from a steel HSS that has a moment of inertia
I = 8.7 × 10 6 mm 4 , a depth d = 150 mm, a yield strength σ Y = 315 MPa,
and an elastic modulus E = 200 GPa. A block with a mass m = 25 kg
moves horizontally with a velocity v 0 and strikes the HSS post
squarely at B. If a factor of safety of 1.5 is specified for the maximum
bending stress, what is the largest acceptable velocity v 0 for the block?
L
p17.28 In Figure P17.27/28, the post AB, with length L = 4.2 m,
is made from a steel HSS with a moment of inertia I = 24.4 ×
10 6 mm 4 , a depth d = 200 mm, a yield strength σ Y = 315 MPa, and
an elastic modulus E = 200 GPa. A block with a mass m moves
horizontally with a velocity v 0 = 4.5 m/s and strikes the HSS post
squarely at B. A factor of safety of 1.75 is specified for the maximum
bending stress; determine the largest
acceptable mass m for the
d
block.
p17.29 The simply supported steel
beam shown in Figure P17.29 is struck
squarely at midspan by a 180 kg block
moving horizontally with a velocity v 0 =
2.5 m/s. The beam’s span is L = 4 m, its
moment of inertia is I = 15 × 10 6 mm 4 ,
its depth is d = 155 mm, and its elastic
modulus is E = 200 GPa. Compute
(a) the maximum dynamic load applied
to the beam.
(b) the maximum bending stress in the
steel beam.
(c) the maximum beam deflection at B
due to the moving block.
h
d
B
B
A
v0
FIGURE p17.27/28
m
v0
L
2
L
2
L
2
C
B
A
FIGURE p17.29
C
v 0
m
745