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Mechanics of Materials CIVL 3322 / MECH 3322

Thermal Strain

Function Variation at Small Angles

Thermal Strain 2

0.07

0.09

0.11

0.13

0.15

0.17

0.19

4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

Func

tion

Valu

e

Angle in Degrees

Angle Ratio

Angle Sine

Angle Tangent

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Thermal Strain

¢ Thermal strains are strains that develop when a material is heated or cooled

¢ They can be the bane of an engineer’s existence if they are not considered

¢ Materials that fit perfectly at one temperature can rupture or fall out when their environmental temperature changes

Thermal Strain 3

Thermal Strain

¢ The problem can be made even worse when a combination of thermal strain and strains induced by loadings are combined

¢ Strains caused by thermal changes and strains caused by loadings are additive

Thermal Strain 4

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Thermal Strain

¢ Thermal strains are typically linear in nature ¢ A uniform change in strain will occur for

every degree change in temperature no matter where on the temperature scale it starts from

¢ Of course near the melting point this is severely violated

Thermal Strain 5

Thermal Strain

¢ The linear relationship for thermal strain is shown as

Thermal Strain 6

εT =αΔT

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Thermal Strain

¢ The subscript on the strain denotes that it is developed because of a thermal change

¢  α is a linear coefficient relating the rate at which strain changes with respect to a unit change in temperature

¢ ΔT is the change in temperature in degrees

Thermal Strain 7

εT =αΔT

Thermal Strain

¢ Take care which unit system you are working in, degrees F or degrees C

¢ Different α values will be used in each system

¢ Tables D.1a and D.1b show some typical coefficients of thermal expansion

Thermal Strain 8

εT =αΔT

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Thermal Strain

¢ Notice that the values are very small ¢ Don’t expect really large strains to be

developed through thermal changes

Thermal Strain 9

εT =αΔT

Thermal Strain

¢ Thermal strains are always axial strains ¢ No shear strains are developed in a single

material because expansion or contraction takes place in all directions at once

¢ There are not forces developed between layers

Thermal Strain 10

εT =αΔT

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Thermal Strain

¢ Because the material expands in all directions in the same way, thermal strains will appear in every direction

Thermal Strain 11

εT =αΔT

Problem P2.16

¢ A large cement kiln has a length of 400 ft and a diameter of 20 ft.

¢ Determine the change in length and diameter of the structural steel [αs = 6.5 x 10-6/°F] shell caused by an increase in temperature of 350°F.

Thermal Strain 12

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Problem P2.18

Thermal Strain 13

P02_021

Problem P2.21

Thermal Strain 14

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Homework

¢ P 2.19 ¢ P 2.20 ¢ P 2.22

Thermal Strain 15