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 = 0.70in. Aluminum rod (3) has a diameter of d3 = 0.95in. 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 2.0 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 55 ksi. If a factor of safety of 2.5 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B.

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 = 0.70in. Aluminum rod (3) has a diameter of d3 = 0.95in. 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 2.0 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 55 ksi. If a factor of safety of 2.5 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

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 = 0.70in. Aluminum rod (3) has a diameter of d3= 0.95in. 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 2.0 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 55 ksi. If a factor of safety of 2.5 is required for this double shear pin
connection, determine the minimum pin diameter that can be used at B.
5
L₁
A₁ =
A₂ =
A
A3 =
i
Bronze
(1)
i
a
B
Aluminum
(3)
Calculate the cross-sectional areas of the three rods.
Answers:
D
Aluminum
(2)
L3
in.²
in.²
C
in.2
L2

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