Analyze beam shear stress with practical section options. Review formulas, examples, and unit conversions quickly. Download results as CSV and PDF for documentation needs.
| Section | Input Summary | Average Stress | Stress at Neutral Axis |
|---|---|---|---|
| Rectangle | V = 12 kN, b = 50 mm, h = 150 mm | 1.60 MPa | 2.40 MPa |
| Solid Circle | V = 8 kN, d = 80 mm | 1.59 MPa | 2.12 MPa |
| Hollow Circle | V = 18 kN, Do = 120 mm, Di = 80 mm | 2.86 MPa | 5.58 MPa |
General shear formula: τ = VQ / (Ib)
V is the internal shear force.
Q is the first moment of area above or below the point.
I is the second moment of area about the neutral axis.
b is the material width at the evaluation line.
Rectangle: A = bh, I = bh³ / 12, Q at neutral axis = bh² / 8, τmax = 3V / (2A)
Solid circle: A = πd² / 4, I = πd⁴ / 64, τmax = 4V / (3A)
Hollow circle: A = π(Do² − Di²) / 4, I = π(Do⁴ − Di⁴) / 64
Average shear stress: τavg = V / A
For built-up or irregular sections, use the custom mode with known A, Q, I, and b.
Use custom mode for channels, tees, I-sections, or any section where you already know A, Q, I, and local thickness.
Transverse shear stress acts inside a beam when a shear force is present. It is important near supports, load points, and web regions. Many failures begin when a designer checks bending stress but ignores shear. This calculator helps engineers review both average and peak shear values quickly.
Shear stress is not uniform across a section. In a rectangle, the stress is zero at the outer surface and highest at the neutral axis. In circular sections, the distribution is also curved. Hollow sections often produce higher local values because the effective wall width becomes smaller. That is why section geometry matters in beam design.
Mechanical engineers use shear checks in shafts, brackets, pins, and machine frames. Civil engineers use them in beams, bridge members, lintels, and truss connections. Fabrication teams also use them when reviewing plates, webs, and built-up sections. A fast calculator reduces mistakes during preliminary design and report preparation.
The core relationship is τ = VQ / (Ib). This equation links the internal shear force to the section geometry at the exact point being checked. Q depends on the area above the point. I depends on the whole cross section. b is the local material width where stress is evaluated. Small input errors in Q or b can change the final answer a lot.
Always keep units consistent. Compare the computed stress with the allowable shear strength of the material. Check both average and maximum values when standard formulas are available. For complex sections, use the custom mode with trusted section properties from a handbook, drawing, or analysis model. Clear shear checks improve safety, documentation, and design confidence.
It is the internal stress created by a shear force acting across a beam or member. It varies through the cross section and often peaks near the neutral axis.
Stress is not spread uniformly through most sections. The average value uses total area, but the real distribution concentrates stress more heavily in certain regions.
Use custom mode when the section is irregular or built-up, or when you already know area, first moment, second moment, and local thickness from drawings or software.
Yes. Choose inches for geometry and lbf for force. The calculator converts the values internally and can return stress in psi if needed.
No. It is meant for fast engineering checks. Final design still needs correct load cases, support conditions, code rules, and material limits.
Q measures how much area lies above or below the point being checked, multiplied by its centroid distance. It strongly affects local shear stress.
Yes, through custom mode. Enter the correct web thickness, section moment of inertia, and first moment at the point of interest.
Internal shear force is usually highest near supports. That often makes transverse shear stress more critical there than in the midspan region.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.