\[\tau=\frac{VQ}{It}\]
Variables
tau[τ]shear stress (Pa)
Vinternal shear force (N)
Qfirst moment of area (m³)
Isecond moment of area (m⁴)
tsection thickness at the point of interest (m)
Description
What is this formula?
The Shear Stress in Beams formula calculates the transverse shear stress at a specific location within a beam cross-section subjected to a shear force.
Unlike flexural stress, which is highest at the outer fibers, shear stress is usually highest near the neutral axis.
When to use it
Use this formula when evaluating:
- Structural steel beams
- Reinforced concrete beams
- Timber beams
- Built-up sections
- Bridge girders
Example
A beam carries an internal shear force of 120 kN.
Data:
V = 120,000 N
Q = 0.004 m³
I = 0.006 m⁴
t = 0.02 m
Formula:
τ = (VQ)/(It)
Substitution:
τ = (120,000 × 0.004)/(0.006 × 0.02)
τ = 4,000,000 Pa
Result:
τ = 4.0 MPa
Applications
- Beam design
- Structural analysis
- Bridge engineering
- Steel structures
- Timber engineering
- Reinforced concrete design