# Maximum Shear Stress Theory is also known as?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

(A) Beltrami and Haigh’s Theory

(B) Guest’s theory

(C) St. Venant’s Theory

(D) Rankine Theory

Maximum Shear Stress Theory is also known as Guest’s theory. Maximum Shear Stress Theory is successfully used with ductile materials. According to this hypothesis, a failure can be predicted to happen when the highest shear stress in a system of complex stress equals the maximum shear stress in a system of simple tension. Below is a relationship between the theories of failure, the appropriate materials, and a graphic representation.

### Maximum Shear Stress Theory Or Guest & Tresca’s Theory

In a uniaxial tensile test, the principal stress at the yield point will be σ1=σy, σ2=σ0, σ3=σ0,

where σy= yield stress

So, maximum shear stress at yielding for the uniaxial test, τuniaxial=σ1/2=σy/2.

Then according to maximum shear stress theory, for no failure:

τmax(biaxial or triaxial) ≤ τuniaxial

τmax≤ σy/2

For design, the maximum shear stress formula is given as

τmax≤ (σy/F.O.S)/2

where F.O.S = factor of safety

Summary:

## Maximum Shear Stress Theory is also known as? (A) Beltrami and Haigh’s Theory (B) Guest’s theory (C) St. Venant’s Theory (D) Rankine Theory

Guest’s theory is another name for the maximum shear stress hypothesis. When the highest shear stress in a system of complex stress equals the highest shear stress in a system of simple tension, a failure can be foreseen, goes this theory.

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