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EDUCATIONAL STUFFS

An Ocean of Information

August 26, 2021February 18, 2025

STRENGTH OF MATERIALS- Thermal Stresses and Strains

THERMAL STRESSES AND STRAINS

  • If the temperature of a body is lowered or raised its dimensions will decrease or increase correspondingly. If these changes, however, are checked the stresses thus developed in the body are called temperature stresses (Thermal Stresses) and corresponding strains are called temperature strains (Thermal Strains).
  • If the object is subjected to uniform changes in temperature, the sides of the object will change. If “α” is the coefficient of thermal expansion or contraction, the uniform thermal strain is given by

 εt = α . (t2 – t1)
or
εt = α . Δt

where,  Δt = (t2 – t1) = Change in temperature

  • Consider a bar of length L, subjected to uniform increase in temperature (Δt), the bar being free to expand. Then the increase in the length of the bar. Then the increase in the length of the bar is,

εt . L = α . Δt . L

  • Conditions for Thermal Stress
    • Thermal gradient must be there
    • Expansion or contraction due to thermal gradient is restricted partially or fully.

 

Total stress developed in a component = Mechanical Stress + Thermal Stress

In presence of thermal variation when dimensional stability is required during the functionality of a component, INVAR (Nickel and Steel Alloy) is selected as a material for that component because it have least coefficient of thermal expansion.

αInvar = 1.2 x 10-6 / °C

αDiamond = 1.1 x 10-6 / °C

Diamond is not used because of its high cost.

Coefficient of thermal expansion for various common materials:

αSteel = 12 x 10-6 / °C

αCopper = 16 x 10-6 / °C

αBrass = 20 x 10-6 / °C

αAluminum = 23 x 10-6 / °C

 

CASE I: FREE EXPANSION

In this case, when the bar is heated or cooled than the bar is free to expand.

 

thermal stresses

 

Change in dimension along x-axis, (𝛿th)x = α . ΔT . L

Change in dimension along y-axis, (𝛿th)y =  α . ΔT . d

Change in dimension along z-axis, (𝛿th)z = α . ΔT . d

Thermal Strain, (εth)x = (εth)y = (εth)z = α . ΔT

Thermal Stress, (σTh)x = (σTh)y = (σTh)z = 0

On heating the bar its length will increase and in this case the expansion of the bar is not restricted so no Thermal Stress will be there.

 

 

CASE II: COMPLETELY RESTRICTED EXPANSION IN ONE DIRECTION

In this case, the bar is not allowed to expand when there is expansion or contraction due to change in temperature.

 

thermal stresses

 

Total change in length= Change in length due to Thermal Stress + Change in length due to Normal Stress = 0

(𝛿L)Total = (𝛿Th) + (𝛿Al) = 0

α . ΔT . L – [frac up=”RL” down=”AE”] = 0

α . ΔT . L = [frac up=”RL” down=”AE”]

R = α . ΔT . A . E

Thermal Stress, σTh = [frac up=”R” down=”A”] = α . ΔT . E

  • When temperature rises, σTh is compressive in nature.
  • When temperature falls, σTh is tensile in nature.

From the above equation of thermal stress it can be concluded that the thermal stress is independent of the dimension of the member.

 

CASE III: PARTIALLY RESTRICTED EXPANSION

In this case, the bar is allowed to expand partially.

 

thermal stresses

 

Total change in length= Change in length due to Thermal Stress + Change in length due to Normal Stress = λ

(𝛿L)Total = (𝛿Th) + (𝛿Al) = λ

α . ΔT . L – [frac up=”RL” down=”AE”] = λ

[frac up=”RL” down=”AE”] = α . ΔT . L – λ

Thermal Stress, σTh = ([frac up=”α . ΔT . L – λ” down=”L”]) . E

Thermal Stress, σTh = ([frac up=”𝛿Th – λ” down=”L”]) . E

where, λ = Expansion permitted by the flexible supports

 

 

RELATED VIDEOS THERMAL STRESSES AND STRAINS:

 

 

 

 

For More Information:- CLICK HERE

DIPLOMA Strength of Materials aluminumbrasschange in lengthchange in temperaturecompletely restricted expansioncompressivecopperdiamonddiplomaengineeringfree expansionIndustry Applicationsinvarlengthmaterialmaterial sciencematerialsmechanicalmechanical engineeringmechanical stressmechanicspartially restricted expansionpolymerpolymer technologys.o.msomsteelstellstrainStrain Calculationstrengthstrength of materialstressstress analysisTemperature Changestemperature straintemperature stresstensilethermal contractionthermal expansionthermal gradientthermal strainThermal Strainsthermal stressThermal Stresses

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