Show that the distortional strain energy given by (6.1.17) is related to the octahedral shear stress (3.5.4)₂ by the relation:

Equation 6.1 .17

Equation 3.5 .4

Results from Exercise 3.5 may be helpful.

Data from exercise 3.5 

A two-dimensional state of plane stress in the x, y-plane is defined byσ_z = τ _yz = τ _zx = 0. Using general principal value theory, show that for this case the in-plane principal stresses and maximum shear stress are given by:

Transcribed Image Text:

Ud 31+v 2 E oct 3 4 oct