Template · Engineering
Beam deflection and bending calculator
Deflection, bending moment, shear and stress for simply supported and cantilever beams under point and uniform loads.
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XLSXCSVODSXMLNumbers| Beam deflection and bending calculator | ||
| Example data — replace the blue input cells with your own. | ||
| Beam and loads | ||
| Support condition | Simply supported | Simply supported (pin and roller) or cantilever (fixed at the left end, free at the right) |
| Span, L (m) | 6.00 | For a cantilever, the length from the fixed support to the free end |
| Point load, P (kN) | 10.00 | Simply supported: applied at midspan. Cantilever: applied at the free end. Enter 0 for none. |
| Uniformly distributed load, w (kN/m) | 2.00 | Over the whole span, for example the beam self-weight. Enter 0 for none. |
| Material and section | ||
| Material | Structural steel | Choose from the list (values are on the Materials tab) |
| Modulus from the Materials tab (GPa) | 200.0 | |
| Modulus override (GPa, optional) | Leave blank to use the value from the Materials tab | |
| Modulus used, E (GPa) | 200.0 | |
| Section width, b (mm) | 100 | |
| Section depth, h (mm) | 200 | Solid rectangular section only (see the Notes tab) |
Showing the first 16 of 36 rows and 3 of 3 columns. Cells with formulas show the formula on hover.
| Beam stations: deflection, moment, shear and stress | |||||||
| Values at 21 equally spaced stations, from the left end to the right end. Change the inputs on the Inputs tab. | |||||||
| Support condition | Simply supported | ||||||
| Span, L (m) | 6.00 | ||||||
| Point load, P (kN) | 10.00 | ||||||
| Uniform load, w (kN/m) | 2.00 | ||||||
| Flexural rigidity, EI (N·m²) | 13,333,333 | ||||||
| Elastic section modulus, S (mm³) | 666,667 | ||||||
| Station | x (m) | x ÷ L | Symmetric distance (m) | Deflection (mm) | Bending moment (kN·m) | Shear (kN) | Bending stress (MPa) |
| 0 | 0.00 | 0.00 | 0.00 | 0.000 | 0.00 | 11.00 | 0.0 |
| 1 | 0.30 | 0.05 | 0.30 | 0.908 | 3.21 | 10.40 | 4.8 |
| 2 | 0.60 | 0.10 | 0.60 | 1.794 | 6.24 | 9.80 | 9.4 |
| 3 | 0.90 | 0.15 | 0.90 | 2.638 | 9.09 | 9.20 | 13.6 |
Showing the first 16 of 38 rows and 8 of 8 columns. Cells with formulas show the formula on hover.
| Materials: modulus of elasticity | ||
| Example data — replace the blue input cells with your own. Values are typical handbook figures for preliminary sizing. | ||
| Material | Modulus, E (GPa) | Basis |
| Structural steel | 200.0 | Carbon steel, typical handbook value (standards give about 200 to 210 GPa) |
| Stainless steel 304 | 193.0 | Austenitic stainless steel, typical value |
| Aluminium 6061-T6 | 68.9 | Typical handbook value for 6061-T6 |
| Copper C11000 | 117.0 | Typical value, annealed |
| Brass C26000 | 100.0 | Cartridge brass, typical (about 97 to 110 GPa) |
| Titanium Ti-6Al-4V | 113.8 | Typical handbook value |
| Cast iron, grey | 110.0 | Typical; varies widely with grade |
| Concrete C30/37 | 33.0 | Secant modulus, EN 1992-1-1 Table 3.1 (Ecm) |
| Softwood timber, spruce (parallel to grain) | 10.0 | Typical mean value; grading changes it a lot |
| Glulam GL24h (parallel to grain) | 11.6 | Mean modulus E0,mean, EN 14080 |
| Hardwood, oak (parallel to grain) | 11.0 | Typical mean value |
| Acrylic (PMMA) | 3.2 | Typical handbook value (about 2.4 to 3.4 GPa) |
Showing the first 16 of 16 rows and 3 of 3 columns. Cells with formulas show the formula on hover.
| Beam deflection and bending calculator |
| Notes: what this workbook does, how to use it and the method behind it. |
| What it does |
| Calculates the support reactions, maximum bending moment, maximum shear, maximum deflection and maximum bending stress for a prismatic rectangular beam, either simply supported or cantilevered, carrying a point load and a uniformly distrib… |
| How to use it |
| 1. On the Inputs tab, choose the support condition and enter the span, point load and uniform load (use 0 for none). |
| 2. Choose the material. The modulus comes from the Materials tab; type an override only if you have a tested or supplier value. |
| 3. Enter the section width and depth in millimetres. The second moment of area and section modulus are calculated. |
| 4. Set the deflection limit (span divided by 360 or 240) and your allowable bending stress. |
| 5. Read the reactions, maximum moment, shear, deflection and stress, and the two checks. |
| 6. Open the Stations tab for the deflection, moment, shear and stress at 21 stations. Its maxima should match the closed-form results (check on the Inputs tab). |
| Formulas and method |
| Euler-Bernoulli beam theory: small deflections, linear elastic material, plane sections remain plane. |
Showing the first 16 of 39 rows and 1 of 1 columns. Cells with formulas show the formula on hover.
What does this template do?
This workbook calculates how a rectangular beam bends under load. Choose a simply supported beam or a cantilever, enter the span, a point load and a uniformly distributed load, then pick a material and a section size. The sheet works out the support reactions, the largest bending moment and shear, the maximum deflection and the maximum bending stress.
Each load case uses its standard closed-form result, and the two cases are added together by superposition. Deflection is checked against the span divided by 360 or 240, and stress against an allowable that you enter. A station table gives the deflection, moment, shear and stress at 21 points along the span, and a check confirms that its maxima match the closed-form results.
It suits preliminary sizing, teaching and quick checks of an idea. It does not replace a structural design: the sheet applies no load factors, buckling checks or connection design.
What’s inside
- Simply supported and cantilever cases, with point and uniform loads added by superposition
- Maximum deflection from PL³/48EI + 5wL⁴/384EI (simply supported) or PL³/3EI + wL⁴/8EI (cantilever)
- Deflection check against span ÷ 360 or span ÷ 240, chosen on the Inputs tab
- Modulus looked up by material with INDEX and MATCH from a 12-material table, or overridden
- 21-station table of deflection, moment, shear and stress, checked against the closed-form maxima
Which tabs does the workbook have?
| Tab | What it holds |
|---|---|
| Inputs | Support condition, span, loads, material, section size, deflection limit, and the closed-form results and checks. |
| Stations | Deflection, bending moment, shear and stress at 21 stations along the span, with a check against the closed-form maxima. |
| Materials | Modulus of elasticity for common structural materials, used by the material lookup on the Inputs tab. |
| Notes | What the workbook does, how to use it, the formulas, the assumptions and the professional-verification note. |
What formulas does this template use?
This template holds 183 formulas in 358 cells across 4 tabs, so 51% of its cells calculate. They use 6 distinct functions; the longest formula is 222 characters and 33 of them read from another tab.
| Function | Uses | What it does |
|---|---|---|
IF | 115 | one result when a test is true, another when false |
ABS | 25 | absolute value |
MIN | 22 | smallest value |
MAX | 6 | largest value |
INDEX | 1 | value at a position in a range |
MATCH | 1 | position of a value in a range |
Counted from the workbook itself. Only functions that Excel, LibreOffice Calc, Google Sheets and Apple Numbers evaluate the same way are used, so the formulas survive every download format.
How do you use it?
- On the Inputs tab, choose the support condition and enter the span in metres.
- Enter the point load and the uniform load in kN and kN/m. Use 0 for none.
- Choose the material, then enter the section width and depth in millimetres.
- Set the deflection limit (360 or 240) and your allowable bending stress.
- Read the reactions, maximum moment and shear, deflection and stress, and the checks.
What is it good for?
- Sizing a timber joist or steel beam for a first estimate
- Comparing the deflection of two section depths
- Teaching superposition and the standard beam formulas
- Checking whether a cantilever shelf or canopy meets a span limit
Questions about this sheet
Does the sheet include the beam's own weight?
No. Add the self-weight to the uniform load on the Inputs tab if it matters for your case.
Can I use an I-section or a hollow section?
The sheet is built for a solid rectangle. For other shapes, enter the second moment of area and section modulus by hand in place of the width and depth.
Which deflection limit should I use?
Enter 360 for L/360 or 240 for L/240. The design code or the client sets which limit applies.
Are the stresses design values?
No. The stress is elastic bending stress from M/S. The sheet applies no load factors, resistance factors or code reductions.