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

b
P
t
P
FIGURE p4.3
Splice plate
Bar
Bar
P
P
p4.6 The bell-crank mechanism shown in Figure P4.6 is supported
by a single-shear pin connection at B and a roller support at C.
A load P acts at an angle of θ = 40° at joint A. The pin at B has a
diameter of 0.375 in., and the bell crank has a thickness of 0.188 in.
The ultimate shear strength of the pin material is 28 ksi, and the
ultimate bearing strength of the crank material is 52 ksi. A minimum
factor of safety of 3.0 with respect to shear and bearing is required.
Assume that a = 9.0 in. and b = 5.0 in. What is the maximum
load P that may be applied at joint A of the bell crank?
p4.4 A bar with a rectangular cross section is connected to a
support bracket with a circular pin, as shown in Figure P4.4. The
bar has a width b = 40 mm and a thickness of 10 mm. The pin has
a diameter of 12 mm. The yield strength of the bar is 415 MPa, and
a factor of safety of 1.67 with respect to yield is required. The
bearing strength of the bar is 380 MPa, and a factor of safety of 2.0
with respect to bearing is required. The shear strength of the pin is
550 MPa, and a factor of safety of 2.5 with respect to shear failure
is required. Determine the magnitude of the maximum load P that
may be applied to the bar.
FIGURE p4.4
b
Bracket
P
Pin
Bar
p4.5 In Figure P4.5, member (1) has a cross-sectional area of
0.7 in. 2 and a yield strength of 50 ksi. Member (2) has a crosssectional
area of 1.8 in. 2 and a yield strength of 36 ksi. A factor of
safety of 1.67 with respect to yield is required for both members.
Use dimensions of a = 60 in., b = 28 in., c = 54 in., and d = 72 in.
Determine the maximum allowable load P that may be applied to
the assembly. Report the factors of safety for both members at the
allowable load.
A
d
p4.7 The bell-crank mechanism shown in Figure P4.7 is in equilibrium
for a load F 1 = 7 kN applied at A. Assume that a = 150 mm,
b = 100 mm, c = 80 mm, and θ = 55°. The bell crank has a thickness
t = 10 mm, and the support bracket has a thickness t b = 8 mm. The
pin at B has a diameter d = 12 mm and an ultimate shear strength of
290 MPa. The bell crank and the support bracket each have an ultimate
bearing strength of 380 MPa. Determine
(a) the factor of safety in pin B with respect to the ultimate shear
strength.
(b) the factor of safety of the bell crank at pin B with respect to
the ultimate bearing strength.
(c) the factor of safety in the support bracket with respect to the
ultimate bearing strength.
θ
(1)
A
a
A
B
b
FIGURE p4.6
θ
P
Bell crank
Bell crank
F 1 C
B
(2)
a
b
F 2
C
c
a
(1)
t
B
Bracket
B
d
b
C
(2)
P
t b
t b
c
Connection detail
FIGURE p4.5
FIGURE p4.7
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