Maximum shear stress:

The state of stress at a critical point of a strained solid is given by σ_x = 70 kN/mm², σ_y = - 50 kN/mm² and τ_xy = 45 kN/mm². If the strength of the solid in tension, compression and shear are provided as 120 kN/mm², 90 kN/mm² and 75 kN/mm² correspondingly, verify the safety of the component.

Solution

Given   σ_x = 70 kN/mm²

σ_y = - 50 kN/mm²

τ_xy = 45 kN/mm²

= 85 - 65 N/mm²

Maximum shear stress, τ_max  =   σ₁  - σ₂/2 = 85 -(-65)/2

= 75 N/mm²

All the stresses are inside the strength limits of the solid and thus, 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

Here, maximum tensile and compressive stresses are well inside strength limits, maximum shear stress has reached the strength limit and thus if the state of stress is proportionally increased the solid will fail in shear.