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 mm^{2}
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/mm^{2} 3
Average shear stress = 0.6366 N/mm^{2}
Minimum shear stress = 0.849 N/mm^{2}