Shear Stress Calculator
Calculate shear stress from transverse loads and torsional forces
Calculate Shear Stress
Internal shear force at the section
Total cross-sectional area
Shear Stress Results
Formula used: τ = V/A
Calculation: τ = 0.0 kN / 0.00 cm²
Example Calculation
Steel Beam Under Transverse Load
Method: Average shear stress
Shear Force (V): 50 kN
Cross-sectional Area (A): 0.02 m² (200 cm²)
Calculation Steps
τ = V / A
τ = 50,000 N / 0.02 m²
τ = 2,500,000 Pa
τ = 2.5 MPa
Formula Reference
Transverse Loading
Average: τ = V/A
Exact: τ = VQ/(It)
Torsional Loading
τ = Tρ/J
Max: τ = TR/J
Typical Stress Values
Key Points
Maximum shear stress often occurs at neutral axis in beams
Torsional stress is maximum at outer surface of shafts
Longitudinal and transverse shear stresses are equal
Consider stress concentrations at geometric discontinuities
Understanding Shear Stress
What is Shear Stress?
Shear stress is the component of stress coplanar with a material cross-section. It arises from forces applied parallel or tangent to an area, causing the material to deform by sliding layers relative to each other without changing the volume.
Types of Shear Loading
- •Transverse: Forces perpendicular to beam axis
- •Torsional: Twisting moments about shaft axis
- •Punching: Concentrated loads causing shear failure
Mathematical Relationships
τ = V/A (average)
τ = VQ/(It) (exact)
τ = Tρ/J (torsion)
- τ: Shear stress (Pa)
- V: Shear force (N)
- A: Cross-sectional area (m²)
- Q: First moment of area (m³)
- I: Moment of inertia (m⁴)
- t: Width at point of interest (m)
- T: Applied torque (N⋅m)
- ρ: Radial distance (m)
- J: Polar moment of inertia (m⁴)
Design Note: Always check both normal and shear stresses. Failure can occur due to combined loading effects.