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

Relations between E, G and K

The largest maximum shear strain and shear stress can be given by 

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

 Substituting  in terms of  we may write 

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

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    Substituting the above expressions for ε_x , ε_y and ε_z  we have.

and substituting   we have 

Combining this with   we  have 

Substituting   we may write the normal and shear stresses as

These equations are considered to be suitable in thermoelastic situations.