Part 1 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 = 0.40 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 = 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 1.8 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 57 ksi. If a factor of safety of 2.7 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B. LI T A Bronze (1) B Aluminum (3) D Aluminum (2) P b L3 C L2

Part 1 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 = 0.40 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 = 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 1.8 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 57 ksi. If a factor of safety of 2.7 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B. LI T A Bronze (1) B Aluminum (3) D Aluminum (2) P b L3 C L2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Alloys

An alloy is an admixture of two or more metals or a metal and a non-metal. Since ancient times, man has been using alloys. Alloying helps to retain the properties of the parent matter, such as hardness, strength, toughness, ductility and is corrosion-resistant. Copper alloys such as brass have antimicrobial properties that help to fight against (Coronavirus disease 2019) COVID-19 and other hospital-acquired infections. Some common alloys are brass, bronze, solder steel, etc. Most alloys have a lower melting point than their constituents. This is due to the presence of a nonmetal as one of the constituents that behaves as an impurity and restricts the raise of melting point.

Question

Part 1
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 = 0.40 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 = 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 1.8 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 57 ksi. If a factor of safety of 2.7 is required for this double shear pin connection, determine the
minimum pin diameter that can be used at B.
LI
T
A
Bronze
(1)
B
Aluminum
(3)
D
Aluminum
(2)
P
b
L3
C
L2

Calculate the cross-sectional areas of the three rods.
Answers:
A₁ =
A₂ =
A3 =
Part 2
Answers:
allow,Br=
For a factor of safety of 1.8, calculate the allowable stresses in the bronze and the aluminum rods.
Gallow,Al =
Part 3
Answers:
P/F₁ =
in.²
P/F₂ =
in.2
P/F3 =
in.²
On a piece of paper, sketch a free body diagram (FBD) cut through rod (3) and also a FBD of the rigid bar. Using these, find a relationship between the force in rod 1 (F₁) and the applied load, P, a relationship between the force in rod 2 (F₂) and the applied load, P, and also a relationship between the force in
rod 3 (F3) and the applied load, P.
ksi
ksi

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