## Maximum shear stress, Civil Engineering

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Maximum shear stress:

The state of stress at a critical point of a strained solid is given by σx = 70 kN/mm2, σy = - 50 kN/mm2 and τxy = 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   σx = 70 kN/mm2

σy = - 50 kN/mm2

τxy = 45 kN/mm2

= 85 - 65 N/mm2

Maximum shear stress, τmax  =   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.

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