Calculator
Example Data Table
| Beam | Load case | Span | Load | Section | Expected note |
|---|---|---|---|---|---|
| Simply supported | Point load | 6 m | 20 kN at 3 m | 3 m | Maximum moment occurs at midspan. |
| Simply supported | Uniform load | 8 m | 5 kN/m | 4 m | Maximum moment occurs near the center. |
| Cantilever | Uniform load | 4 m | 3 kN/m | 0 m | Maximum moment occurs at the fixed end. |
| Simply supported | Triangular load | 5 m | Peak 6 kN/m | 2.5 m | Reactions depend on load direction. |
Formula Used
Simply supported point load: RA = P(L - a) / L, RB = Pa / L.
Moment before load: Mx = RAx.
Moment after load: Mx = RAx - P(x - a).
Simply supported uniform load: RA = RB = wL / 2.
Moment at section: Mx = RAx - wx² / 2.
Maximum moment: Mmax = wL² / 8.
Cantilever point load: Mx = -P(a - x), when x is before the load.
Cantilever uniform load: Mx = -w(L - x)² / 2.
Triangular load: total load equals wpeakL / 2. Its centroid is L / 3 from the heavy end.
Stress check: stress = |M| / Z. In this tool, MPa uses kN·m and cm³.
Combined loading: the calculator uses superposition. Each load effect is added at the same section.
How to Use This Calculator
- Select the beam type.
- Select the load case.
- Enter span length.
- Enter the section position from the left support or fixed end.
- Enter point load, uniform load, or triangular load data.
- Add section modulus and allowable stress when a stress check is needed.
- Press calculate to view the result above the form.
- Use CSV or PDF download buttons to save the report.
Bending Moment Planning
A bending moment shows how a beam tends to bend at a chosen section. It is created by loads, supports, and distance. Engineers use it to choose beam size, check service limits, and compare support layouts. This calculator gives a quick mathematical check before deeper structural review.
Why the Result Matters
A beam can fail even when the total load seems small. The location of the load often matters more than the load alone. A point load near midspan creates a different curve than the same load near a support. A distributed load spreads demand over the span. A triangular load represents pressure that changes along the beam. These cases are common in floors, rafters, brackets, lintels, machine frames, and classroom examples.
What This Calculator Covers
The tool supports simply supported beams and cantilever beams. It accepts point loads, full span uniform loads, combined loading, and triangular loading. The section position lets you inspect a specific cut along the beam. The maximum moment is also estimated along the span. Optional section modulus and allowable stress fields add a capacity check. Use consistent units for every input.
Reading the Output
The left and right reactions show how the supports share load. For a cantilever, the fixed reaction and fixed-end moment are shown. The shear value helps locate where bending moment may peak. The bending moment at the chosen section is the main result. A positive value commonly means sagging for a simply supported beam. A negative value commonly means hogging for a cantilever.
Practical Notes
This calculator is a planning aid. It uses ideal beam assumptions. Real beams may include self weight, lateral torsion, connection eccentricity, shear deformation, cracked material, or code factors. Always check design rules before construction. For critical work, compare the result with a licensed engineer or an approved structural reference.
Choosing Better Inputs
Measure span between actual support points. Enter the load position from the left support or fixed end. Keep the section value within the beam length. Convert all values before entry. Do not mix feet with meters, or pounds with kilonewtons. When using stress checks, enter section modulus in cubic centimeters for the built-in MPa estimate. Review final values before saving reports.
FAQs
What is a bending moment?
A bending moment is the turning effect created inside a beam by external loads. It tells how strongly the beam wants to bend at a section.
Which beam types are supported?
The calculator supports simply supported beams and cantilever beams. These cover many basic classroom, workshop, and early design checks.
Can I calculate combined loads?
Yes. Choose the point load plus uniform load option. The calculator adds both effects by superposition at the selected section.
What units should I use?
Use one consistent unit system. For stress output, use kN for force, m for length, and cm³ for section modulus.
Why is cantilever moment negative?
The negative sign shows hogging action with the chosen convention. The absolute value is often used when comparing demand.
Where does maximum moment occur?
It depends on support type and loading. For many simply supported uniform loads, it occurs near midspan. For cantilevers, it often occurs at the fixed end.
Is this suitable for final structural design?
Use it for checking and learning. Final design should follow local codes, material rules, load factors, and professional review.
What do CSV and PDF downloads include?
They include input labels, reactions, shear, bending moment, maximum moment, and optional stress results for record keeping.