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

p17.8 A solid stepped shaft made of 2014-T4 aluminum (G = 28
GPa) is shown in Figure P17.6/7/8. The diameters of segments (1)
and (2) are d 1 = 20 mm and d 2 = 12 mm, respectively. The segment
lengths are L 1 = 240 mm and L 2 = 180 mm. Determine the elastic
strain energy stored in the shaft when the maximum shear stress is
130 MPa.
p17.9 Determine the elastic strain energy of the prismatic
beam AB shown in Figure P17.9 if w = 6 kN/m, L = 5 m, and EI =
3 × 10 7 N ⋅ m 2 .
w
A
FIGURE p17.10
w
L
p17.11 Determine the elastic strain energy of the prismatic
beam shown in Figure P17.11 if P = 75 kN, L = 8 m, and EI =
5.10 × 10 7 N ⋅ m 2 .
B
x
A
B
x
P
L
FIGURE p17.9
x
p17.10 Determine the elastic strain energy of the prismatic
beam shown in Figure P17.10 if w = 4,000 lb/ft, L = 18 ft, and
EI = 1.33 × 10 8 lb ⋅ ft 2 .
A
FIGURE p17.11
L / 2
B
L / 2
C
17.6 Impact Loading
When the motion of a body is changed (i.e., the body accelerates), the force necessary to
produce the acceleration is called a dynamic force or a dynamic load. Following are some
examples of a dynamic load:
• the force that an elbow in a pipeline exerts on the fluid in the pipe to change its direction
of flow.
• the pressure on the wings of an airplane pulling out of a dive.
• the force of the wind on the exterior walls of a building.
• the weight of a vehicle as it rolls across a bridge.
• the force of a hammer striking the head of a nail.
• the collision of a ship and a bridge pier.
• the weight of a man jumping on a diving board.
A dynamic load may be expressed in terms of
• the mass of a body times the acceleration of its center of mass
• the rate of change of the momentum of a body, or
• the change in kinetic energy of a body.
A suddenly applied load is called an impact load. The last three examples of a dynamic
load are considered impact loads. In each example, one object strikes another such
that large forces are developed between the objects in a very short period. When subjected
to impact loading, the loaded structure or system will vibrate until equilibrium is established
if the material remains elastic.
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