Enter Beam and Section Data
Use values for the selected section only. Stress is reported as MPa and psi.
Example Data Table
| Section | Applied Shear | Key Dimensions | Calculated Shear Stress |
|---|---|---|---|
| Rectangle | 60 kN | b = 200 mm, h = 300 mm | 1.50 MPa at neutral axis |
| Solid circle | 50 kN | d = 180 mm | 2.62 MPa at neutral axis |
| Symmetrical I-section | 80 kN | h = 300 mm, bf = 200 mm, tf = 15 mm, tw = 10 mm | 29.99 MPa in the web |
Formula Used
τ = VQ / (I b)
τ is shear stress. V is design shear. Q is first moment of area. I is the second moment of area. b is width at the selected level.
I = b h³ / 12Q(y) = b(h² / 4 − y²) / 2τmax = 3V / (2bh)
A = πd² / 4τmax = 4V / (3A)
I = 2[(bftf³ / 12) + bftf(h / 2 − tf / 2)²] + tw(h − 2tf)³ / 12
The calculator evaluates web shear at the neutral axis. It assumes equal top and bottom flanges.
How to Use This Calculator
- Choose the section geometry.
- Enter the applied shear force and load factor.
- Select matching force and length units.
- Enter only the dimensions needed for your selected shape.
- Add an allowable shear stress when utilization is needed.
- Press Calculate Shear Stress.
- Review the stress, section properties, and utilization result.
- Download CSV or save a PDF record when required.
Understanding Beam Shear Stress
Why Beam Shear Matters
Beam shear stress develops when transverse loads push one portion of a member past another. It is different from bending stress. Bending changes across the depth because of moment. Shear depends on the internal shear force and section geometry. Designers must check both actions during structural work.
Where Shear Is Highest
For a rectangular section, shear is greatest at the neutral axis. It falls to zero at the top and bottom surfaces. A circular member also reaches its highest value near the center. In an I-section, the web usually carries most shear. The flange area helps form the first moment, but the thin web creates higher stress. This is why web thickness deserves careful attention.
Using Section Properties Correctly
The general equation is tau equals VQ divided by Ib. V is the design shear force. Q is the first moment of area above or below the point. I is the second moment of area for the full section. b is the material width at that point. Each property must use matching units. This calculator converts force and dimensions before solving the equation. The result appears in megapascals and pounds per square inch.
Selecting Practical Inputs
Enter the largest shear force expected at the location. Apply a load factor only when your method requires one. Use the beam depth and width for a rectangle. Use the diameter for a solid circle. For an I-section, enter the overall depth, flange width, flange thickness, and web thickness. Custom mode is useful when a trusted section table already provides Q, I, and width values. Verify every measurement before relying on the output.
Interpreting the Result
Compare the calculated stress with the allowable value from the governing design standard. A utilization below one hundred percent indicates the entered limit is not exceeded. This is not a complete design check. Beams may also need bending, deflection, buckling, bearing, connection, fatigue, and vibration checks. Openings, notches, point loads, and support reactions can create local effects. Review those locations separately. Use approved material strengths, load combinations, and code rules for final engineering decisions.
Good records help. Save results with assumptions, units, and drawing references. This practice speeds later reviews. It reduces errors when load cases or section dimensions change during later project design updates.
Frequently Asked Questions
1. What is beam shear stress?
Beam shear stress is the internal stress created by transverse force. It resists sliding between adjacent layers of a beam. Its value depends on the shear force, the section shape, and the location within that section.
2. What formula does the calculator use?
The general formula is τ = VQ divided by Ib. The calculator uses simplified shape formulas where appropriate. It uses the full expression for the I-section and custom-section options.
3. Where is shear stress usually greatest?
It is usually greatest at or near the neutral axis. For an I-section, the critical location is commonly in the web at the neutral axis. Surface shear is zero for a simple rectangular beam.
4. Which units can I use?
You can use N, kN, lbf, or kip for force. You can use mm, cm, m, in, or ft for length. Use one selected length unit for every section value.
5. Why is a load factor included?
A load factor converts the entered force into a design force when your calculation method requires it. Enter 1.00 for an unfactored assessment. Use the factor required by your governing standard.
6. Can this result complete a beam design?
No. This tool evaluates beam shear stress only. A complete design can also require bending, deflection, buckling, bearing, connection, stability, fatigue, and code-specific resistance checks.
7. Why is I-section web shear high?
The web is often thin and lies near the neutral axis. Much of the section shear passes through this smaller width. That combination can produce stress much higher than stress in the flanges.
8. What rectangular position should I enter?
Enter zero to calculate maximum shear at the neutral axis. Enter a positive or negative distance to check another point. The position must remain within half the section depth.
9. How is utilization calculated?
Utilization equals calculated shear stress divided by entered allowable shear stress, multiplied by 100. It is shown only when you provide a positive allowable value. It does not replace design-code verification.
10. Is shear stress the same as bending stress?
No. Shear stress comes from transverse shear force. Bending stress comes from bending moment. Their distributions differ through a beam depth, so both should be checked at relevant locations.
11. When should an engineer review the calculation?
Seek qualified review for structural design, unusual sections, openings, concentrated reactions, high utilization, temporary works, or code-required documentation. Local conditions can change stress patterns significantly.
Always confirm final designs with a qualified structural engineer.