Member AC of the following truss is subjected to a temperature change of +110°C. Calculate the displacements of node A and the forces in each member using the stiffness method. Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as A√2; the cross section area of AB as 5.0A. b) Ay 1.732 m Part 1. The displacements at joint A: a) A₂ = = 1 m mm mm Part 2. The force in each member: a) NAB= b) NAC c) NAD = KN KN KN B C A

Member AC of the following truss is subjected to a temperature change of +110°C. Calculate the displacements of node A and the forces in each member using the stiffness method. Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as A√2; the cross section area of AB as 5.0A. b) Ay 1.732 m Part 1. The displacements at joint A: a) A₂ = = 1 m mm mm Part 2. The force in each member: a) NAB= b) NAC c) NAD = KN KN KN B C A

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

Member AC of the following truss is subjected to a temperature change of +110 °C. Calculate the displacements of node A and the forces in each member using the
stiffness method.
Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as A√2; the cross section area of AB as 5.0A.
1.732 m
1 m
Part 1.
The displacements at joint A:
a) A₂ =
b) Ay =
mm
mm
Part 2.
The force in each member:
a) NAB =
b) NAC =
c) NAD
kN
kN
kN
A

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Step 1: Introducing Given Data

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Step 2: Calculate Force matrix of member 2 (AC)

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Solution

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Step 3: Calculate Stiffness matrix of member 1

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Step 4: Calculate Stiffness matrix of member 2 & 3

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Step 5: Calculate Global matrix

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Step 6: Using load displacement equation

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Step 7: Calculate displacement u1 & u2

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Step 8: Calculate the force in member 1 (AB)

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Step 9: Calculate the force in member 2 (AC)

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Step 10: Calculate the force in member 3 (AD)

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