Rigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.45 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.85in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft. (a) Determine the magnitude of load P that can safely be applied to the structure if a minimum factor of safety of 1.7 is required. (b) Determine the deflection of point D for the load determined in part (a). (c) The pin used at B has an ultimate shear strength of 59 ksi. If a factor of safety of 3.1 is required for this double shear pin connection, determine the minimum pin diameter that can be used a
Rigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.45 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.85in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft. (a) Determine the magnitude of load P that can safely be applied to the structure if a minimum factor of safety of 1.7 is required. (b) Determine the deflection of point D for the load determined in part (a). (c) The pin used at B has an ultimate shear strength of 59 ksi. If a factor of safety of 3.1 is required for this double shear pin connection, determine the minimum pin diameter that can be used a
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Rigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.45 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.85in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft.
(a) Determine the magnitude of load P that can safely be applied to the structure if a minimum factor of safety of 1.7 is required.
(b) Determine the deflection of point D for the load determined in part (a).
(c) The pin used at B has an ultimate shear strength of 59 ksi. If a factor of safety of 3.1 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B.
Transcribed Image Text:Rigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of
aluminum rod (3). Bronze rod (1) has an elastic modulus of E₁ = 15,000 ksi and a diameter of d₁ = 0.45 in. Aluminum rod (2) has an
elastic modulus of E₂ = 10,000 ksi and a diameter of d₂ = 0.85in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength
of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a 2.5 ft, b=1.5 ft, L₁= 6 ft, L₂-8 ft, and L3-3 ft.
(a) Determine the magnitude of load P that can safely be applied to the structure if a minimum factor of safety of 1.7 is required.
(b) Determine the deflection of point D for the load determined in part (a).
(c) The pin used at B has an ultimate shear strength of 59 ksi. If a factor of safety of 3.1 is required for this double shear pin
connection, determine the minimum pin diameter that can be used at B.
T
Aluminum
(2)
L
Bronze
(1)
A
B
Aluminum
(3)
L3
Calculate the cross-sectional areas of the three rods.
Answers:
A₁ =
in.2
A₂ =
A3=
i
in.²
in.²
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