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

p4.8 Rigid bar ABC is supported by member (1) at B and by a
pin connection at C, as shown in Figure P4.8. Member (1) has a
cross-sectional area of 1.25 in. 2 and a yield strength of 40 ksi. The
pins at B, C, and D each have a diameter of 0.5 in. and an ultimate
shear strength of 72 ksi. Each pin connection is a double-shear connection.
Specifications call for a minimum factor of safety in member
(1) of 1.67 with respect to its yield strength. The minimum factor
of safety required for pins B, C, and D is 3.0 with respect to the
pin ultimate shear strength. Determine the allowable load P that
may be applied to the rigid bar at A. Use overall dimensions of a =
54 in. and b = 110 in.
P
a
(1)
A B C
FIGURE p4.8
D
p4.9 In Figure P4.9, rigid beam AB is subjected to a distributed
load that increases linearly from zero to a maximum intensity of w B =
17.5 kN/m. Beam AB is supported by a single-shear pin connection at
joint A and by a double-shear connection to member (1) at joint B.
Member (1) is connected to the support at C with a double-shear pin
connection. Use dimensions of a = 2.8 m, b = 1.0 m, and c = 1.2 m.
(a) The yield strength of member (1) is 340 MPa. A factor of
safety of 1.67 with respect to the yield strength is required for
the normal stress of member (1). Determine the minimum
cross-sectional area required for member (1).
(b) The ultimate shear strength of the material used for pins A, B,
and C is 270 MPa. A factor of safety of 2.50 with respect to
the ultimate shear strength is required for the pins, and all
three pins are to have the same diameter. Determine the
minimum pin diameter that may be used.
A
FIGURE p4.9
a
p4.10 Beam AB is supported as shown in Figure P4.10/11. Tie
rod (1) is attached at B and C with double-shear pin connections,
while the pin at A is attached with a single-shear connection. The
pins at A, B, and C each have an ultimate shear strength of 54 ksi,
and tie rod (1) has a yield strength of 36 ksi. A uniformly distributed
b
B
w B
b
C
c
load w = 1,800 lb/ft is applied to the beam as shown. Dimensions
are a = 15 ft, b = 30 in., and c = 7 ft. A factor of safety of 2.5 is
required for all components. Determine
(a) the minimum required diameter for tie rod (1).
(b) the minimum required diameter for the double-shear pins at B
and C.
(c) the minimum required diameter for the single-shear pin at A.
p4.11 Beam AB is supported as shown in Figure P4.10/11. Tie
rod (1) has a diameter of 50 mm, and it is attached at B and C with
24 mm diameter double-shear pin connections. The pin connection
at A consists of a 40 mm diameter single-shear pin. The pins at A,
B, and C each have an ultimate shear strength of 520 MPa, and tie
rod (1) has a yield strength of 280 MPa. A uniformly distributed
load w is applied to the beam as shown. Dimensions are a = 4.0 m,
b = 0.5 m, and c = 1.5 m. A minimum factor of safety of 2.5 is required
for all components. What is the maximum loading w that
may be applied to the structure?
p4.12 The idler pulley mechanism shown in Figure P4.12 must
support belt tensions of P = l30 lb. Rigid bar ABC is supported by
rod (1), which has a diameter of 0.188 in. and a yield strength of
35,000 psi. Rod (1) is connected at A and B with 0.25 in. diameter
pins in double-shear connections. A 0.25 in. diameter pin in a singleshear
connection holds rigid bar ABC at support C. Each pin has an
ultimate shear strength of 42,000 psi. Overall dimensions of the
mechanism are a = 12 in., b = 9 in., c = 7 in., and d = 3 in. Determine
(a) the factor of safety for rod (1) with respect to its yield strength.
(b) the factor of safety for pin B with respect to its ultimate shear
strength.
(c) the factor of safety for pin C with respect to its ultimate shear
strength.
P
y
C
A
x
FIGURE p4.10/11
D
P
FIGURE p4.12
60°
b
d
c
(1)
a
w
B
Rigid
bar
C
a
(1)
B
c
b
A
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