Construction calculator
Enter Beam, Load, and Section Details
Use one consistent unit system. The load factor applies to all entered vertical loads and the applied end moment.
Example data
Sample Rectangular Beam Check
| Input | Sample value | Purpose |
|---|---|---|
| Beam length | 3 m | Defines the uniform-load and moment lever arm. |
| Point load | 10 kN at 3 m | Creates support shear and fixed-end moment. |
| Uniform load | 2 kN/m | Adds 6 kN of support shear. |
| Section | 150 mm × 300 mm | Supplies the rectangular shear area. |
| Allowable shear stress | 0.60 MPa | Sets the entered planning limit. |
Engineering method
Formula Used
Support shear
LF is the load factor. P values are point loads. w is the uniform line load. w0 and wL are triangular-load intensities.
Fixed-end moment
The triangular-load moment uses its resultant and centroid. End moment changes reported support moment. It does not add direct vertical shear.
Section shear stress
- Rectangular: τmax = 1.5V / (b × d).
- Solid circular: τmax = 4V / (3A).
- Symmetric I-section: τ = VQ / (I × tw) at the web neutral axis.
Workflow
How to Use This Calculator
- Choose metric or imperial units before entering values.
- Select the section shape that best represents the beam.
- Enter the cantilever length from the fixed support.
- Add vertical point loads and their distances from support.
- Enter uniform and triangular loads when they apply.
- Provide an applied end moment only when it exists.
- Enter the load factor and applicable allowable shear stress.
- Enter the active section dimensions and calculate.
- Review stress, capacity, utilization, and support moment together.
- Download the result, then complete code and connection checks.
Design context
Cantilever Beam Shear Stress Basics
Support Demand
Cantilever beams project from a fixed support. Loads create maximum shear at the wall, column, or bracket connection. This calculator estimates critical support shear. It also estimates section stress.
Why Shear Matters
Shear stress can damage the web, split timber, crack concrete, or overstress fasteners near a connection. Bending and deflection need separate checks. A beam may pass a shear check yet fail another design limit. Use the output within a complete review.
Loading Effects
The fixed-end shear equals the sum of vertical loads. Point loads contribute their full value. Uniform loads equal intensity times length. A triangular load contributes one-half of the start and end intensities multiplied by length. The entered load factor multiplies the total. End moments change support moment, but do not add vertical shear.
Section Behavior
The section shape changes stress distribution. A rectangular section has its greatest shear stress near the neutral axis. Its maximum value is one and one-half times average shear. A solid round section has a different distribution. Its maximum value equals four-thirds of average shear. An I-section concentrates much of the shear in its web. The calculator uses the VQ divided by It relationship at the neutral axis.
Reliable Inputs
Accurate dimensions are essential. Use net dimensions where holes, notches, corrosion, or coping reduce the effective section. Use web thickness for an I-section. Check that flange and web dimensions represent a symmetric shape. Enter consistent units. Metric inputs use kilonewtons, metres, millimetres, and megapascals. Imperial inputs use kips, feet, inches, and ksi.
Allowable Limits
Allowable shear stress should come from the applicable design standard, material grade, and load-duration rules. Do not invent a limit. Engineers may also apply resistance factors, safety factors, connection reductions, bearing checks, and combinations. This tool lets you enter a load factor for planning comparisons. It does not create a code-approved load combination.
Using the Result
Review utilization after calculation. A value below one hundred percent is below the entered limit. A value above one hundred percent needs a larger section, lower load, stronger material, or revised support arrangement. Keep enough margin for uncertainty and construction tolerances.
Site Checks
Construction conditions can alter the result. Temporary equipment, wet concrete, stored materials, vibration, and eccentric brackets may increase demand. Confirm load paths into the fixed support. Verify anchors, welds, bolts, reinforcement, and surrounding members. A qualified professional should confirm final details before work begins.
Common questions
Frequently Asked Questions
1. What is a cantilever beam?
A cantilever beam is fixed at one end and free at the other. Its fixed support resists the vertical shear, bending moment, and rotation caused by applied loads.
2. Where is shear usually greatest?
For a standard cantilever carrying downward loads, vertical shear is greatest at the fixed support. The calculator reports this support value because it commonly controls the shear check.
3. Does an end moment add vertical shear?
No. A pure applied end moment changes the fixed-end bending moment. It does not directly create vertical shear. The calculator still includes its magnitude in the reported support moment.
4. Why is a load factor included?
The load factor lets you compare a factored demand with an entered planning limit. Select it according to the governing method. This calculator does not select code load combinations for you.
5. What rectangular section formula is used?
The calculator uses τmax = 1.5V divided by bd. This gives the maximum elastic shear stress for a solid rectangular section at its neutral axis.
6. How is I-section shear calculated?
It uses τ = VQ divided by I times web thickness. The calculation evaluates stress in the web at the neutral axis for a symmetric I-section.
7. Can this be used for steel, timber, or concrete?
It can estimate elastic section shear for those materials. Use a material-appropriate allowable stress and verify the relevant code rules, cracking assumptions, duration effects, and resistance factors.
8. Which units should I enter?
Metric mode expects kN, metres, millimetres, and MPa. Imperial mode expects kip, feet, inches, and ksi. Do not mix values from different systems.
9. Does the calculation design the connection?
No. It reports beam shear and fixed-end moment only. Design anchors, bolts, welds, reinforcing, bearing, and the supporting member using the applicable requirements.
10. What should I do above 100 percent utilization?
Reduce the load, increase effective section area, use stronger material, add support, or revise the beam arrangement. Then rerun all required strength and serviceability checks.
11. Is this result a final structural design?
Use it for preliminary checks. Confirm final beam designs with a qualified licensed engineer.