The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 76 GPa] with a cross-sectional area of A₁ = 820 mm². Bar (2) is a bronze alloy [E = 108 GPa] with a cross-sectional area of A₂ = 520 mm². Assume L₁=1.6 m, L₂=2.0 m, a=0.8 m, b=1.1 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 1.2-mm clearance in the pin connection at A. If a load of P = 49 kN is applied at B, determine: (a) the normal stresses 61, 62, in both bars (1) and (2). (b) the normal strains £1,2, 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 b (2) ! ! MPa, 0₁ = ! με, €2 = i mm. i ! MPa. με.

The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 76 GPa] with a cross-sectional area of A₁ = 820 mm². Bar (2) is a bronze alloy [E = 108 GPa] with a cross-sectional area of A₂ = 520 mm². Assume L₁=1.6 m, L₂=2.0 m, a=0.8 m, b=1.1 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 1.2-mm clearance in the pin connection at A. If a load of P = 49 kN is applied at B, determine: (a) the normal stresses 61, 62, in both bars (1) and (2). (b) the normal strains £1,2, 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 b (2) ! ! MPa, 0₁ = ! με, €2 = i mm. i ! MPa. με.

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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Question

The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 76 GPa] with a
cross-sectional area of A₁ = 820 mm². Bar (2) is a bronze alloy [E = 108 GPa] with a cross-sectional area of A₂ = 520 mm². Assume
L₁=1.6 m, L₂=2.0 m, a=0.8 m, b=1.1 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 1.2-mm
clearance in the pin connection at A. If a load of P = 49 kN is applied at B, determine:
(a) the normal stresses 01, 02, in both bars (1) and (2).
(b) the normal strains 1, 2, 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
L₁
B
b
(2)
! MPa, σ₁ =
!
L2
με, €2 =
! mm.
D
i
!
MPa.
με.

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Step 1: Mention the given data.

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Step 2: Draw the free body diagram.

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Step 3: Determine the tension in bar 1 and 2.

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Step 4: (a) Determine the normal stress.

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Step 5: (b) Determine the normal strain.

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Step 6: (c) Determine the downward deflection of point A.

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