In a two-dimensional stress system, the principal stresses are σ₁ = 200 N/mm² (tensile) and σ₂ (compressive). The yield stress in compression is 250 N/mm², with μ = 0.25. What will be the value of σ₂ according to the maximum normal strain theory?

Concept:

According to maximum Normal Strain (principal strain) theory:

Maximum principal strain due to loading = maximum principal strain due to elastic limit

σ₁ – μσ₂ = f_y

Wherein,

σ₁  and σ­₂ are principle stresses and f_y is the yield stress

Calculation:

Consider tensile stresses positive and compressive stresses negative.

Given,

σ₁ = 200 N/mm² (tensile) ; σ₂ =  σ (Compressive) ; μ = 0.25; f_y = 250 MPa

\(200 - 0.25 \times \left( { - \sigma } \right) = 250\)

⇒ σ = 200 MPa