Shear Stress Calculator Formula
Understand the math behind the shear stress calculator. Each variable explained with a worked example.
Formulas Used
Average Shear Stress
avg_shear = v_n / areaVariables
| Variable | Description | Default |
|---|---|---|
shear_force | Shear Force (V)(kN) | 50 |
area | Cross-Sectional Area (A)(mm^2) | 3000 |
v_n | Derived value= shear_force * 1000 | calculated |
How It Works
Average Shear Stress
Shear stress arises from forces acting parallel to a cross-section.
Formula
tau_avg = V / A
where V is the internal shear force and A is the cross-sectional area resisting the shear. For beams, the actual shear stress distribution is parabolic (maximum at the neutral axis), and the peak value for a rectangle is 1.5 times the average.
Worked Example
A steel plate connection with 3000 mm^2 shear area carries 50 kN.
- 01Convert force: 50 kN = 50,000 N
- 02tau = 50,000 / 3,000 = 16.67 MPa
Frequently Asked Questions
How does shear stress differ from bending stress?
Bending stress acts perpendicular to the cross-section (normal stress) and varies linearly from the neutral axis. Shear stress acts parallel to the section and varies parabolically, peaking at the neutral axis.
What is the maximum shear stress in a rectangular beam?
The peak shear stress in a rectangular cross-section is tau_max = 1.5 V / A, occurring at the neutral axis. This calculator gives the average value V/A.
What is a typical shear yield strength?
Shear yield is approximately 0.577 times the tensile yield strength (von Mises criterion). For A36 steel with 250 MPa tensile yield, shear yield is about 144 MPa.
Ready to run the numbers?
Open Shear Stress Calculator