Calculate Beam Shear Stress
Use consistent millimetre and kilonewton inputs for the displayed MPa result.
Example Data Table
A sample rectangular beam uses the neutral axis for maximum shear stress.
| Shear force | Width | Depth | y location | Calculated stress |
|---|---|---|---|---|
| 50 kN | 150 mm | 300 mm | 0 mm | 1.667 MPa |
| 75 kN | 200 mm | 400 mm | 0 mm | 1.406 MPa |
| 60 kN | 150 mm | 300 mm | 75 mm | 1.250 MPa |
Formula Used
General beam shear stress follows the elastic shear formula below.
τ is shear stress in N/mm² or MPa. V is the internal shear force in N. Q is the first moment of area in mm³. I is the second moment of area in mm⁴. b is the material width at the chosen level in mm.
For a rectangular section, the calculator derives I = bh³ / 12 and Q = b(h² / 8 − y² / 2). At the neutral axis, y equals zero and shear stress reaches its maximum value.
How to Use This Calculator
- Select rectangular mode for a solid rectangular beam.
- Enter the internal shear force for the checked beam location.
- Enter width, depth, and distance from the neutral axis.
- Choose manual mode for built-up, I-shaped, or irregular sections.
- Enter Q, I, and local width b from your section analysis.
- Add an optional allowable stress and safety factor for screening.
- Review the result, assumptions, and governing design standard.
Beam Shear Stress in Construction
What the result represents
Shear stress measures internal sliding force within a beam section. It develops when vertical loads create a changing bending moment. The result is usually expressed in megapascals. One MPa equals one newton per square millimetre. A beam can have acceptable bending stress while still needing a shear review.
Why the neutral axis matters
Stress is not uniform through most beam depths. In a solid rectangular beam, shear stress is zero at the top and bottom faces. It rises toward the neutral axis. The maximum value occurs at the neutral axis. The calculator accepts a distance from that axis. This helps show how stress changes at different levels.
Understanding the section properties
The VQ divided by Ib equation needs reliable section data. V is the internal shear at the checked location. Q describes the area on one side of the plane. I describes resistance to bending about the neutral axis. The local width b is important for I-beams. A thin web can produce higher shear stress than broad flanges.
Using rectangular mode
Choose rectangular mode for a solid timber, concrete, or steel rectangle. Enter the actual section width and depth. Enter zero for y to obtain maximum elastic shear stress. The calculator automatically finds Q and I. It also displays the average stress and rectangular maximum stress. These values make a quick reasonableness check easier.
Using manual mode
Use manual mode for shapes with flanges, voids, plates, or built-up components. Obtain Q, I, and b from a correct section analysis. Use the web thickness where shear passes through an I-shaped beam web. Do not substitute total flange width for web thickness. That mistake can understate web shear stress.
Design decisions need more checks
This calculator supports preliminary estimation. It does not select member sizes or verify code compliance. Check material grade, connection forces, shear buckling, bearing, deflection, load combinations, and construction conditions. Use the relevant project standard and approved design method. Independent review is important for safety-critical members.
Critical locations need review
Shear force peaks near supports, point loads, and load changes. Evaluate critical locations rather than relying on one section. For beams, reactions and internal force diagrams guide the governing shear value. Keep load paths, construction stages, and actions under review.
Frequently Asked Questions
1. What units does the calculator use?
Enter shear force in kN and dimensions in millimetres. The calculator converts force to N. The final shear stress is shown in MPa, which equals N/mm².
2. Where is shear stress highest in a rectangular beam?
For a solid rectangular section, elastic shear stress is highest at the neutral axis. It becomes zero at the free top and bottom surfaces.
3. Can this calculate an I-beam web stress?
Yes. Select manual mode. Use the section’s correct Q and I values, then enter the web thickness as b at the point being checked.
4. What is the first moment of area Q?
Q is the area above or below the calculation plane multiplied by the distance from that area’s centroid to the neutral axis. Its unit is mm³.
5. Is the displayed utilization a design approval?
No. It compares the calculated stress with the optional limit you entered. It does not replace code checks, material checks, load combinations, or professional judgement.
6. Why does web thickness affect stress?
A smaller local width carries the same shear flow through less material. Therefore, a thinner web generally develops higher shear stress.
7. Can I enter a negative y distance?
Yes. The sign identifies the side of the neutral axis. For a symmetrical rectangular section, equal positive and negative distances produce the same stress magnitude.
8. Does this include shear buckling?
No. Slender steel webs may require a separate shear buckling review. Use the applicable structural standard for web slenderness and stiffener requirements.
9. Can I use this for timber beams?
Yes, for a preliminary elastic stress estimate. Use timber-specific design values, adjustment factors, grain direction limits, and connection checks in the final design.
10. Why is the result shown in MPa?
Using N, mm, and section properties in mm-based units produces N/mm². This is numerically identical to MPa, a standard engineering stress unit.
11. What should I check after calculating shear stress?
Check the governing load combination, material resistance, local bearing, web buckling, connections, deflection, and project-specific detailing requirements before making final decisions.