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Temperature Effect On 1D Bar Element: Heat Transfer

This document discusses heat transfer and thermal stress in a 1D bar element. The bar has a temperature increase of ΔT which causes it to expand by an amount equal to αΔTL. This expansion results in an initial or thermal strain. The stress-strain graph is affected by this initial strain. The stiffness matrix is derived from potential energy and accounts for the thermal load vector. The thermal load vector expression is used to calculate the thermal load distribution in each element. Solving the global stiffness matrix and load vector equations provides the displacement and stress distribution across the elements due to the applied thermal load.

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Manda Ramesh Babu
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695 views9 pages

Temperature Effect On 1D Bar Element: Heat Transfer

This document discusses heat transfer and thermal stress in a 1D bar element. The bar has a temperature increase of ΔT which causes it to expand by an amount equal to αΔTL. This expansion results in an initial or thermal strain. The stress-strain graph is affected by this initial strain. The stiffness matrix is derived from potential energy and accounts for the thermal load vector. The thermal load vector expression is used to calculate the thermal load distribution in each element. Solving the global stiffness matrix and load vector equations provides the displacement and stress distribution across the elements due to the applied thermal load.

Uploaded by

Manda Ramesh Babu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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HEAT TRANSFER

Module 4
Temperature effect on 1D bar element

Lets us consider a bar of length L fixed at one end whose temperature


is increased to T as shown.

Because of this increase in temperature stress induced are called as


thermal stress and the bar gets expands by a amount equal to TL as
shown. The resulting strain is called as thermal strain or initial strain
In the presence of this initial strain variation of stress strain graph is as
shown below

We know that

Therefore
Therefore

Extremizing the potential energy first term yields stiffness matrix,


second term results in thermal load vector and last term eliminates that
do not contain displacement filed
Thermal load vector

From the above expression taking the thermal load vector lets
derive what is the effect of thermal load.
Stress component because of thermal load

We know  = Bq and o = T substituting these in above equation we


get
Solution:
Global stiffness matrix:

Thermal load vector:


We have the expression of thermal load vector given by

Similarly calculate thermal load distribution for second element


Global load vector:

From the equation KQ=F we have

After applying elimination method and solving the matrix we


have Q2= 0.22mm
Stress in each element:

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