Enter Beam and Section Data
Use the governing internal vertical shear force at the section being checked.
Example Data Table
These examples show the expected input structure. They are not approved design values.
| Section | Shear force | Dimensions | Maximum shear stress |
|---|---|---|---|
| Rectangle | 120 kN | 200 mm × 400 mm | 2.250 MPa |
| Solid circle | 120 kN | 250 mm diameter | 3.259 MPa |
| Symmetric I-section | 120 kN | 200 × 400 × 20 × 10 mm | Use web calculation |
Formula Used
The general beam shear equation is τ = VQ / (Ib). Here, τ is shear stress, V is internal vertical shear force, Q is the first moment of the area above or below the evaluation point, I is the second moment of area, and b is the local section width.
For a rectangle, the neutral-axis maximum becomes τmax = 1.5V / A. For a solid circle, it becomes τmax = 4V / (3A). For a symmetric I-section, the calculator uses VQ divided by inertia and web thickness at the neutral axis.
The result is given in MPa because one newton per square millimetre equals one MPa. The optional allowable stress creates a utilization check only. It does not replace code-based member design.
How to Use This Calculator
- Select the beam cross-section that matches the checked location.
- Enter the governing internal shear force from your structural analysis.
- Select force and dimension units before entering section geometry.
- Enter dimensions for the gross or effective section, as required by your design standard.
- For a custom shape, enter consistent Q, I, and local width values in millimetres.
- Add allowable shear stress only when it matches the same material and load basis.
- Calculate, review the stress location, then compare it with a verified design resistance.
Beam Shear Stress in Practice
Why Shear Stress Matters
Beam shear stress is not distributed evenly across a cross-section. It changes with the first moment of area, local width, and internal shear force. The largest value usually occurs at the neutral axis. This location needs attention because it can control web thickness, timber sizing, or connection detailing.
A beam can carry bending and shear at the same time. Bending stress is often greatest near outer fibres. Shear stress follows a different pattern. For a rectangular section, stress reaches zero at the top and bottom faces. It peaks at mid-depth. The peak is one and one-half times the average shear stress. This difference is important when a narrow beam supports a high reaction.
I-Sections and Local Width
I-sections need closer review. Their flanges provide much of the bending resistance. The web usually transfers most vertical shear. Maximum stress therefore occurs in the web near the neutral axis. A thin web can become critical even when the overall section seems large. The calculator evaluates the web with the general shear equation. It uses the upper area moment, section inertia, and web thickness.
Material and Design Checks
Material behavior also matters. Steel, timber, concrete, and composite members respond differently to shear. Some materials fail through web yielding. Others split along grain or develop diagonal cracking. The result from this page is a stress demand. It is not a complete member design. Compare it with a properly selected allowable or design shear resistance. Apply the project code, load combinations, safety factors, and material limits before approval.
Units and Final Review
Units deserve careful checking. A force entered in kilonewtons must match dimensions converted to millimetres. The calculated value then appears in megapascals. The page also reports kilopascals and pounds per square inch. These extra values help when drawings, supplier data, or specifications use different systems. Do not mix a nominal force with factored resistance data. Keep the same design basis throughout the check.
Use the calculation during early sizing, peer review, and design verification. Enter the largest applicable internal shear force. Select the correct cross-section. Confirm all dimensions represent the actual resisting material. For built-up beams, consider holes, notches, welds, bolts, and reduced web areas. These details can raise local stress beyond the simple result. Seek a qualified structural engineer for final decisions, especially for public, occupied, or safety-critical structures. Recheck results before final approval.
Frequently Asked Questions
1. What is maximum shear stress in a beam?
It is the highest internal shear stress at a specific beam cross-section. It commonly occurs near the neutral axis. Its exact location and value depend on the section shape and local width.
2. Why is beam shear highest at the neutral axis?
The first moment of area is largest around the neutral axis. Surface fibres have no material beyond the free face, so their vertical shear stress approaches zero.
3. Does this calculation include bending stress?
No. It calculates shear stress only. A complete beam check may also require bending, deflection, bearing, buckling, vibration, connection, and serviceability verification.
4. Can I use this for timber beams?
Yes, for preliminary stress demand. Use the correct effective dimensions and compare the result against the applicable timber shear resistance, adjustment factors, notches, and grain-related limits.
5. Which force should I enter?
Enter the internal vertical shear force at the exact section being checked. This is often largest near supports, but load arrangement and beam continuity can change the critical location.
6. Why does an I-section use web thickness?
Most vertical shear passes through the web. At the neutral axis, the local width in the shear equation is the web thickness, which can produce a higher local stress.
7. Are holes and notches included?
No. Holes, notches, cope cuts, and similar details reduce effective area and can cause stress concentrations. Check them separately using the relevant design provisions.
8. What units does the calculator use internally?
For standard shapes, dimensions are converted to millimetres and force to newtons. This produces stress in MPa. Custom Q, I, and b inputs must already use mm³, mm⁴, and mm.
9. What does utilization mean?
Utilization equals calculated stress divided by entered allowable stress. A value at or below 100 percent indicates the demand does not exceed that entered comparison value.
10. Is a result below allowable stress automatically safe?
No. The comparison addresses only the provided shear stress limit. It does not confirm load combinations, material grade, durability, construction quality, or other required checks.
11. When should an engineer review the calculation?
Use professional review for final design, unusual geometry, public structures, high loads, damaged members, major alterations, or any project governed by structural regulations.
Always verify calculations before approving structural construction work onsite.