Deflection Under Load Calculator

Analyze beam bending for point, uniform, and custom loading cases. View results instantly with charts. Plan stronger members using clear engineering checks and comparisons.

Calculator Inputs

Used only for the offset point load case.
Example: use 360 for an L/360 check.
Reset

Formula Used

This calculator uses classic Euler-Bernoulli beam equations for small elastic deflections. Internal calculations convert all values to SI units.

1) Simply supported beam with center point load

Maximum deflection: δmax = P L3 / 48 E I

2) Simply supported beam with offset point load

Reactions: RL = P b / L, RR = P a / L, where b = L - a.

For x ≤ a: y(x) = P b x (L2 - b2 - x2) / 6 L E I

For x ≥ a: y(x) = P a (L - x) (2 L x - x2 - a2) / 6 L E I

3) Simply supported beam with full uniform load

Maximum deflection: δmax = 5 w L4 / 384 E I

4) Cantilever beam with end point load

Maximum deflection: δmax = P L3 / 3 E I

5) Cantilever beam with full uniform load

Maximum deflection: δmax = w L4 / 8 E I

Symbols: P = point load, w = uniform load intensity, L = span, E = Young’s modulus, I = second moment of area.

How to Use This Calculator

  1. Choose the beam case that matches your support and loading condition.
  2. Enter the beam span and pick the correct span unit.
  3. Enter either the point load or the distributed load value.
  4. For offset loading, provide the distance from the left support.
  5. Enter Young’s modulus for the beam material.
  6. Use a custom inertia value or calculate inertia from section geometry.
  7. Set an allowable deflection ratio such as L/360.
  8. Click Calculate Deflection to show results above the form.
  9. Review the graph, reactions, peak deflection location, and serviceability status.
  10. Use the CSV or PDF buttons to export the results.

Example Data Table

Beam Case Span Load E I Approx. Max Deflection
Simply supported center point 4.0 m 12 kN 200 GPa 8,000,000 mm⁴ 10.00 mm
Simply supported offset point at 1.5 m 4.0 m 15 kN 200 GPa 8,000,000 mm⁴ 11.50 mm
Simply supported full uniform load 5.0 m 3.5 kN/m 200 GPa 8,000,000 mm⁴ 17.80 mm
Cantilever end point 2.5 m 8 kN 200 GPa 8,000,000 mm⁴ 26.04 mm
Cantilever full uniform load 2.5 m 2.0 kN/m 200 GPa 8,000,000 mm⁴ 6.10 mm

FAQs

1) What does this calculator estimate?

It estimates beam deflection under common support and load cases. It also reports reactions, stiffness, peak location, slopes, and a serviceability comparison.

2) Which beam cases are included?

It covers simply supported beams with center point, offset point, and uniform loads, plus cantilever beams with end point and full uniform loads.

3) Can I enter my own moment of inertia?

Yes. Choose the custom inertia mode when you already know the section property from a handbook, design sheet, or manufacturer catalog.

4) Why is cantilever deflection often larger?

Cantilevers are fixed at one end and free at the other. That condition makes them much more flexible than simply supported beams under similar loading.

5) What is an allowable deflection ratio?

It is a serviceability target such as L/240, L/360, or L/480. The calculator compares actual deflection with that limit and flags the result.

6) Does the graph show the real beam shape?

It shows the analytical elastic deflection curve for the chosen load case. It is idealized and does not include cracking, yielding, or connection slip.

7) Can I use steel, aluminum, or timber properties?

Yes. Enter the correct Young’s modulus and section inertia for your material and member geometry, and the tool will recalculate the response.

8) What assumptions should I remember?

This tool assumes linear elastic behavior, constant cross section, small deflections, and standard beam theory. Use detailed structural analysis for critical design work.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.