The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 61 GPa] with a cross-sectional area of A₁ = 810 mm². Bar (2) is a bronze alloy [E = 103 GPa] with a cross-sectional area of A2 = 470 mm². Assume L₁=2.4 m, L₂=3.1 m, a=0.7 m, b=1.9 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 5.8-mm clearance in the pin connection at A. If a load of P = 44 kN is applied at B, determine: (a) the normal stresses 0₁, 02, in both bars (1) and (2). (b) the normal strains &1, 82, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) A a L₁ B b (2) C L2 D

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 61 GPa] with a
cross-sectional area of A₁ = 810 mm². Bar (2) is a bronze alloy [E = 103 GPa] with a cross-sectional area of A₂ = 470 mm². Assume
L₁=2.4 m, L₂=3.1 m, a=0.7 m, b=1.9 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 5.8-mm
clearance in the pin connection at A. If a load of P = 44 kN is applied at B, determine:
(a) the normal stresses 0₁, 0₂, in both bars (1) and (2).
(b) the normal strains E1, E2, in bars (1) and (2).
(c) determine the downward deflection VA of point A on the rigid bar.
(1)
A
Answers:
(a) σ₁ =
(b) ₁ =
(C) VA =
i
a
i
i
L₁
B
P
b
(2)
MPa, 0₁ =
με,€2 =
mm.
L2
i
i
D
MPa.
με.
Transcribed Image Text:7 The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 61 GPa] with a cross-sectional area of A₁ = 810 mm². Bar (2) is a bronze alloy [E = 103 GPa] with a cross-sectional area of A₂ = 470 mm². Assume L₁=2.4 m, L₂=3.1 m, a=0.7 m, b=1.9 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 5.8-mm clearance in the pin connection at A. If a load of P = 44 kN is applied at B, determine: (a) the normal stresses 0₁, 0₂, in both bars (1) and (2). (b) the normal strains E1, E2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) ₁ = (C) VA = i a i i L₁ B P b (2) MPa, 0₁ = με,€2 = mm. L2 i i D MPa. με.
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