Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

Mechanical Engineering : Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

The document Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev is a part of Mechanical Engineering category.
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Relations between E, G and K

The largest maximum shear strain and shear stress can be given by Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

Considering now the hydrostatic state of stress and strain we may write

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev Substituting Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev in terms of Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev we may write 

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

 

Elementary thermoelasticity

So far the state of strain at a point was considered entirely due to applied forces. Changes in temperature may also cause stresses if a thermal gradient or some external constraints exist. Provided that the materials remain linearly elastic, stress pattern due to thermal effect may be superimposed upon that due to applied forces and we may write

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

It is important to note that the shear strains are not affected directly by temperature changes. It is sometimes convenient to express stresses in terms of strains. This may be done using the relation  Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev  Substituting the above expressions for εx , εy and εwe have.

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

and substituting  Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev we have 

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

Combining this with  Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev we  have Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

Substituting  Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev we may write the normal and shear stresses as

Strain Analysis (Part - 2) - Machine Design Mechanical Engineering Notes | EduRev

These equations are considered to be suitable in thermoelastic situations.

 

 

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