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Strength of Materials by V. Ramasamy, P. Purushothama Raj

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3.5 STRAIN ENERGY IN TERMS OF PRINCIPAL STRESSES

Let the major and minor principal stresses in a strained material be σ1 and σ2 and of the same sign. Then, the principal strains are given as

 

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Strain energy per unit volume due to σ1, image

 

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Total strain energy per unit volume U = U1 + U2

 

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In the case of 3D principal stress (with same sign) condition, ...

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