Question

# Which of the following theory is also known as Beltrami or Haigh’s theory?

• 1.Maximum Distortions Energy Theory
• 2.Maximum Strain Energy Theory
• 3.Maximum Shear Stress Theory
• 4.Maximum Principal Stress Theory
Option 2:Maximum Strain Energy Theory
Solution

Maximum strain energy theory is also known as Beltrami or Haigh’s theory.

## Beltrami or Haigh’s Theory

### Maximum Strain Energy Theory (Beltrami or Haigh’s Theory)

• The underlying premise of this theory is that strains can be recovered up to the elastic limit.
• The strain energy at the elastic limit under simple tension is equal to the strain energy per unit volume causing failure.

### Maximum principal stress theory(Rankine Theory)

• When the largest major stress in a straightforward tension test exceeds the ultimate strength, a material fails by fracturing.
• When the biggest Principal stress at that spot achieves maximal strength, the crack will begin at the point where the material is most severely stressed.
• This yielding theory and the experiment agree pretty poorly. The hypothesis has, however, been effectively applied to brittle materials.
• It is used to describe how brittle materials, such cast iron, shatter.

### Maximum shear stress theory (Guest & Tresca’s Theory)

This hypothesis states that a specimen will break under any combination of loads when the highest shear stress at any site reaches a failure value equivalent to the yielding value generated during an axial tensile or compressive test of the same material.

### Shear Strain Energy Theory (Von-Misses Theory)

• The Maximum Energy of Distortion theory is another name for it.
• The diameters of all three Mohr's circles are taken into account by the Von-Mises criterion for describing the yield onset in isotropic materials.
• Along with the Trescatheory, this theory offers the best congruence between experiment and theory and is quite popular.

### Maximum principal strain theory(St. Venant theory)

• This hypothesis states that yielding will occur in either simple tension or compression when the maximal primary strain just surpasses the strain at the tensile yield point.
• This hypothesis exaggerates how ductile material behaves.
• With the exception of biaxial tension in brittle materials, the theory does not match the experimental results satisfactorily.

Summary:

## Which of the following theory is also known as Beltrami's or Haigh’s theory?

Maximum strain energy theory is called Beltrami or Haigh’s theory. The energy that the material has absorbed during failure has been a single-valued function independent of the stress system that caused it.