Determine the value of the maximum shear stress:

A circular beam of 100 mm diameter is subjected to a shear force of 5 kN. Determine the value of the maximum shear stress & also draw the shear stress distribution diagram.

            Beam Cross-section                 Shear Stress Distribution

Figure

Solution

Diameter of beam = 100 mm

Area of cross section of beam = (π/4) × (100)² = 7854 mm²

Shear force, F = 5 kN = 5000 N

We have,

              τ _max    =  (4/3) × (F/ Cross-sectional area)

∴   τ _max = ( 4/3) × (5000 /7854)= 0.849 N/mm²    3         

Average shear stress = 0.6366 N/mm²           

Minimum shear stress = 0.849 N/mm²