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

assembly. The solid bronze post has a length L = 450 mm, a diameter
of 60 mm, and a modulus of elasticity E = 105 GPa. Compute
the maximum stress in the bronze post and the impact factor
(a) if the spring has a stiffness k = 5,000 N/mm.
(b) if the spring has a stiffness k = 500 N/mm.
p17.18 The 32 mm diameter rod AB shown in Figure P17.18
has a length L = 1.5 m. The rod is made of bronze [E = 105 GPa]
that has a yield stress σ Y = 330 MPa. Collar C moves along the rod
at a speed v 0 = 3.5 m/s until it strikes the rod end at B. If a factor of
safety of 4 with respect to yield is required for the maximum normal
stress in the rod, determine the maximum allowable mass for
collar C.
p17.21 The 120 kg block C shown in Figure P17.21 is dropped
from a height h onto a wide-flange steel beam that spans L = 6 m.
The steel beam has a moment of inertia I = 125 × 10 6 mm 4 , a depth
d = 300 mm, a yield stress σ Y = 340 MPa, and an elastic modulus
E = 200 GPa. A factor of safety of 2.5 with respect to the yield
stress is required for the maximum dynamic bending stress. If the
falling block produces the maximum allowable dynamic bending
stress, determine
(a) the equivalent static load.
(b) the maximum dynamic beam deflection at A.
(c) the maximum height h from which the 120 kg block C can be
dropped.
A
v 0
B
h
C
FIGURE p17.18
L
Collar C
A
FIGURE p17.21
L
B
p17.19 The block E has a horizontal velocity v 0 = 9 ft/s when it
squarely strikes the yoke BD that is connected to the 3/4 in. diameter
rods AB and CD. (See Figure P17.19/20.) The rods are made of
6061-T6 aluminum that has a yield strength σ Y = 40 ksi and an
elastic modulus E = 10,000 ksi. Both rods have a length L = 5 ft.
Yoke BD may be assumed to be rigid. What is the maximum allowable
weight of block E if a factor of safety of 3 with respect to yield
is required for the maximum normal stress in the rods?
p17.22 The overhanging beam ABC shown in Figure P17.22/23
is made from an aluminum I shape, which has a moment of inertia
I = 25 × 10 6 mm 4 , a depth d = 200 mm, and an elastic modulus E =
70 GPa. The beam spans are a = 2.5 m and b = 1.5 m. A block D
with a mass of 90 kg is dropped from a height h = 1.5 m onto the
free end of the overhang at C. Calculate
(a) the maximum bending stress in the beam.
(b) the maximum beam deflection at C due to the falling block.
A
B
D
h
E
v 0
A
B
C
a
b
C
D
FIGURE p17.22/23
FIGURE p17.19/20
L
p17.20 In Figure P17.19/20, the 20 lb block E possesses a horizontal
velocity v 0 when it squarely hits the yoke BD that is connected
to the 1/4 in. diameter rods AB and CD. Both rods are made
of 6061-T6 aluminum that has a yield strength σ Y = 40 ksi and an
elastic modulus E = 10,000 ksi, and both have a length L = 30 in.
Yoke BD may be assumed to be rigid. Calculate the maximum allowable
velocity v 0 of block E if a factor of safety of 3 with respect
to yield is required for the maximum normal stress in the rods.
p17.23 In Figure P17.22/23, the overhanging beam ABC, made
from an aluminum I shape, has a moment of inertia I = 25 ×
10 6 mm 4 , a depth d = 200 mm, and an elastic modulus E = 70 GPa.
The beam spans are a = 3.5 m and b = 1.75 m. A block D with a
mass of 110 kg is dropped from a height h onto the free end of the
overhang at C. If the maximum bending stress due to impact must
not exceed 125 MPa, compute
(a) the maximum dynamic load allowed at C.
(b) the impact factor n.
(c) the maximum height h from which the 110 kg block D can be
dropped.
744