Calculator
Example Data Table
| Total Load (N) | Span (mm) | Inner Span (mm) | Width (mm) | Height (mm) | Modulus (GPa) | Max Moment (N·mm) | Stress (MPa) | Deflection (mm) |
|---|---|---|---|---|---|---|---|---|
| 2000 | 500 | 200 | 20 | 10 | 210 | 150000 | 450 | 11.7857 |
| 3000 | 600 | 240 | 25 | 12 | 200 | 270000 | 450 | 14.85 |
| 4500 | 750 | 300 | 30 | 15 | 205 | 506250 | 450 | 18.1098 |
Formula Used
For a symmetric four point bending setup, the total applied load is split into two equal point loads.
Load at each point: P/2
Distance from support to nearest load: a = (L - S) / 2
Support reactions: Rleft = Rright = P / 2
Maximum shear: Vmax = P / 2
Maximum bending moment: Mmax = R × a = P(L - S) / 4
Second moment of area for a rectangular section: I = bh3 / 12
Section modulus: Z = I / (h / 2) = bh2 / 6
Maximum bending stress: σ = M / Z = 6M / (bh2)
Midspan deflection: δ = P a (3L2 - 4a2) / (48EI)
Outer fiber strain: ε = σ / E
Use N for load, mm for dimensions, and GPa for modulus. The returned stress is in MPa, because 1 MPa equals 1 N/mm2.
How to Use This Calculator
- Enter the total force applied by the loading nose pair.
- Enter the full support span between the two supports.
- Enter the inner loading span between the two applied loads.
- Enter the rectangular section width and height.
- Enter the elastic modulus of the material.
- Press Calculate to show the result above the form.
- Review reactions, moment, stress, strain, and deflection.
- Use the graph to inspect the bending moment distribution.
- Download the result as CSV or PDF when needed.
About 4 Point Bending
A four point bending test is useful when you want a wider constant moment zone than a three point setup provides. Because the bending moment remains flat between the inner loads, the specimen experiences pure bending across that region. This makes the method helpful for comparing materials, studying cracking behavior, and estimating surface stress under a controlled geometry.
The calculator on this page assumes a simply supported beam with two equal point loads placed symmetrically. That arrangement gives equal support reactions and a clean piecewise bending moment diagram. The outer beam segments carry shear and rising moment, while the middle region carries constant moment. This is the reason four point bending is often selected for lab work, classroom demonstrations, and quick engineering checks.
Section shape matters because stiffness and stress depend on geometry. A taller section increases the second moment of area strongly, since height is raised to the third power in the rectangular formula. That means small depth changes can greatly reduce deflection and stress. Width still matters, but not as strongly as height for rectangular members.
The output values should be read together. Maximum moment shows the peak bending demand. Bending stress estimates the outer surface stress. Midspan deflection describes service behavior. Strain gives another view of material response and can be compared with measured strain gauge data. If your load positions are not symmetric, or if your section is not rectangular, a different model should be used.
FAQs
1. What does this calculator solve?
It solves symmetric four point bending for a rectangular section. It returns equal point loads, support reactions, maximum shear, maximum moment, stress, strain, and midspan deflection.
2. What is the total applied load here?
The calculator treats the entered value as the combined load from both inner loading points. Each point load is half of that total.
3. Why must inner loading span be smaller than support span?
The inner loads must lie between the supports. If the loading span equals or exceeds the support span, the geometry is no longer a valid four point bending setup.
4. Which section shape does this page use?
It uses a rectangular cross section. The formulas for inertia, section modulus, stress, and deflection are based on rectangular width and height inputs.
5. What units should I enter?
Enter load in newtons, dimensions in millimeters, and elastic modulus in gigapascals. The page converts modulus so stress appears in megapascals and deflection in millimeters.
6. What does the flat graph region mean?
The flat middle region in the moment diagram is the constant moment zone. In that interval, bending is pure and shear is zero for the ideal symmetric case.
7. Can I use this for nonrectangular sections?
Not directly. You would need the correct section properties for your shape, then adjust the stress and deflection formulas to match that geometry.
8. Why is section height so important?
Height strongly affects stiffness because inertia includes height cubed. A modest increase in depth can sharply reduce stress and deflection for the same load and span.