Lecture 2-Thermal Strain

8/14/2019 Lecture 2-Thermal Strain

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Thermal Strain


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When the temperature of a

component is increased or

decreased the material

respectively expands or

contracts.


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Thermal Expansion, (or the increase in

length) for most materials, resultsfrom an increase in temperature.

The extent of the expansion ( L)depends on the temperature change

( T), the length of the part (L0), andthe coefficient of thermal expansion

of the material involved.L = L0 T (linearexpansion)


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Typical values of coefficient oflinear expansion

Carbon Steel 12 x 10-6 /0C

Aluminium 24 x 10-6 /0C

Copper 17 x 10-6 /0C

Cast Iron 10 x 10-6 /0C

Brass 16 x 10-6 /0C

Bronze 18 x 10-6 /0C


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Thermal Strain

The thermal strain (T) is given

by:

T = L / L0

T = T

If this expansion or contraction is notresisted in any way then the processes

take place free of stress.


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If the changes in dimensions

are restricted, then stresses

termed temperature stresses

will be set up within the

material.


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Thermal Stress

The thermalstress (FT) is

given by:

FT = EwhereE Elasticmodulus

(a)Bar of initial length L;

(b)Elongation L due toheat;

(c)Thermal stress in


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For Large temperature changes,both and E vary withtemperature.

We shall assume that the

temperature changes aresufficiently small for and E to beconsidered as constants.


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Thermal Stress

In (c), when the bar

is subjected to

change in

temperature, the

total strain is zero,

i.e. the elastic strain

must be equal and

opposite to the

thermal strain, thus

(a)Bar of initial length L;

(b)Elongation L due toheat;

(c)Thermal stress in


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Differential thermal expansion

Results whenever there is a

temperature difference or gradient from

point to point in metals. The differential

occurs because most metals expand

with increasing temperature. If the

increase (or decrease) in temperature is

different in different sections of a

material, the sections will have

expanded to a different extent.


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Differential thermal expansion

In this case, the compressive andtensile stresses can result in thebending of the part, as shown below:


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Compound Bars


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In certain applications it is necessary to

use a combination of elements or bars

made from different materials, each

material performing a different

function, such as electric cables.


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Example:

In overhead electric cables, for example,

it is often convenient to carry the current

in a set of copper wires surrounding steel

wires, the latter being designed tosupport the weight of the cable over large

spans.


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When an external load W is applied tosuch a compound bar it is shared

between the individual component

materials in proportions depending on


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When two or more members are rigidlyfixed together so that they share the same

load and extend or compress the sameamount, the members form a compoundbar.

The stresses in each member arecalculated using the following:

1.The total load is the sum of the loads

taken by each member.2.The total load taken by each member isgiven by the product of its stress and itsarea.

3.The extension or contraction is the same


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Each member carries a portion of

the total load W proportional to its

EA/L value.

Force in member 1 :

If all members are of equal lengththe stress of one member (F1) is

given by:


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Stress in member 1:


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If the compound bar is subjected to

a temperature rise each material

will attempt to expand by different

amount.


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The two materials are now rigidly joined asa compound bar and subjected to the same

temperature rise, each material will attemptto expand to its free length position buteach will be affected by the movement ofthe other.

The higher coefficient of expansion material(brass) will therefore seek to pull the steelup to its free length position and converselythe lower coefficient of expansion material(steel) will try to hold the brass back to itsfree length position.

The result is an effective compression of the

brass from its free length position and an


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The tensile force applied to the shortmember by the long member is equal in

magnitude to the compressive forceapplied to the long member by the shortmember.

Tensile force in steel = compressive forcein brass

steel Asteel = brass Abrass

These are two equations with twounknowns which can be solvedsimultaneously to obtain

steeland

brass.

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Lecture 2-Thermal Strain