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

p5.9 The assembly shown in Figure P5.9 consists of rod (1) and
tube (2), both made of steel (E = 30,000 ksi). The tube is attached
to a fixed support at C. A rigid end plate is welded to the tube at B,
and the rod is welded to the end plate. The rod is solid, with a diameter
d 1 = 0.375 in. The tube has an outside diameter D 2 = 2.25 in.
and a wall thickness t 2 = 0.125 in. The dimensions of the assembly
are a = 60 in. and b = 32 in. Determine the horizontal deflection at
rod end A for an applied load P = 4 kips.
D 2
c
A
FIGURE p5.8
B
End
plate
FIGURE p5.9
a
Tube (2)
p5.10 The system shown
in Figure P5.10 consists of a
rod, a spring, a tube, and a
fixed base. Polymer rod (1) is
attached to rod cap A at its
upper end and passes freely
through the spring, tube cap
B, tube (2), and the fixed
base to rod end D, where a
load P is applied. The load
applied at rod end D is transmitted
by the rod to rod cap
A, causing the spring to compress.
The force in the spring
is then transmitted to the
tube, in which it creates compressive
deformation. The
a
C
(1)
P
b
t 2
d 1
b
C
B
Rod (1)
Fixed support
Rod cap A
A
Tube
L 2 (2)
L 1
Fixed
base
polymer rod (1) has a diameter d 1 = 12 mm, an elastic modulus E 1 =
1,400 MPa, and a length L 1 = 640 mm. The linear compression
spring has a spring constant k = 850 N/mm. Tube (2) has an outside
k
FIGURE p5.10
P
Tube cap B
Rod (1)
C
Rod end D
P
Spring
diameter D 2 = 50 mm, an inside diameter d 2 = 46 mm, an elastic
modulus E 2 = 900 MPa, and a length L 2 = 350 mm. For an applied
load P = 750 N, determine the vertical displacement of (a) rod cap
A, (b) tube cap B, and (c) rod end D relative to C.
p5.11 The mechanism shown in Figure P5.11 consists of rigid
bar ABC pinned at C to nylon [E = 200 ksi] rod (1), which has a
diameter 0.25 in. and a length L 1 = 14 in. The linear compression
spring, which is placed between the base of the mechanism at E and
a rigid plate at D, has a spring constant k = 940 lb/in. The base is
rigid and fixed in position, and rigid bar ABC is horizontal before
the load P is applied. Rod (1) is attached to plate D at the lower end
of the spring. The nylon rod passes freely through the compression
spring and through a hole in the base at E. Determine the value of
load P that is needed to deflect end A downward by 2.0 in. Use dimensions
a = 9.0 in., b = 3.0 in., and c = 5.0 in.
L 1
(1)
c
FIGURE p5.11
C
p5.12 The wooden pile
shown in Figure P5.12 has a
diameter of 100 mm and is
subjected to a load P = 75 kN.
Along the length of the pile
and around its perimeter, soil
supplies a constant frictional
resistance w = 3.70 kN/m. The
length of the pile is L = 5.0 m
and its elastic modulus is E =
8.3 GPa. Calculate
E
(a) the force F B needed at
base of the pile for
equilibrium.
(b) the magnitude of the
downward displacement
at A relative to B.
k
D
b
Base
B
p5.13 A 1 in. diameter steel [E = 29,000 ksi and γ = 490 lb/ft 3 ]
rod hangs vertically while suspended from one end. The length of
the rod is 320 ft. Determine the change in length of the bar due to
its own weight.
p5.14 A homogenous rod of length L and elastic modulus E is a
truncated cone with diameter that varies linearly from d 0 at one end
y
a
Rigid bar
FIGURE p5.12
P
A
B
F B
w
L
A
P
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