State of stress at a critical pt of a strained solid:

The state of stress at a critical pt of a strained solid is specified  through σ_x = 70 kN/mm², σ_y = - 50 kN/mm² and t_xy = 45 kN/mm². If the strength of the solid in tension, compression, & shear are specified as 120 kN/mm², 90 kN/mm² & 75 kN/mm² respectively, check the safety of the component.

 Solution

Given  σ_x = 70 kN/mm²

σ_y = - 50 kN/mm²

t_xy = 45 kN/mm²

= 85 - 65 N/mm²

Maximum shear stress, t_max  =   (s₁     - s₂ )/2 = 85 - (- 65)/2

= 75 N/mm²

All of the stresses are in the strength limits of the solid and therefore, the solid is safe.

Factor of safety in tension = 120/85 = 1.412

Factor of safety in compression = 90/65 = 1.3846

Factor of safety in compression = 75/75 = 1

Now, compressive stresses  & maximum tensile  are well in strength limits, maximum shear stress has reached the strength limit and therefore if the state of stress is proportionally raised the solid will fail in shear.