Shear strain energy theory for the failure of a material at elastic limit, is due to A. Rankine B. Guest or Trecas C. St. Venant D. Von Mises

The correct answer is: D. Von Mises

The von Mises yield criterion is a theory of plasticity that states that a material will yield when the equivalent stress reaches a critical value. The equivalent stress is a measure of the combined effects of tension, compression, and shear stress on a material.

The von Mises yield criterion is named after Richard von Mises, a German-American engineer and mathematician who developed the theory in the early 20th century. The von Mises yield criterion is widely used in engineering to predict the failure of materials.

The other options are incorrect because they do not represent the von Mises yield criterion.

• Rankine’s theory of failure is a theory of plasticity that states that a material will yield when the maximum principal stress reaches a critical value.
• Guest’s theory of failure is a theory of plasticity that states that a material will yield when the maximum shear stress reaches a critical value.
• St. Venant’s theory of failure is a theory of plasticity that states that a material will yield when the maximum shear strain reaches a critical value.