Free Beam Calculator: Shear & Bending Moment Diagrams

Support reactions, shear force diagram (SFD) and bending moment diagram (BMD) for 2D beams with pin, roller and fixed supports.

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How to Use the Beam Calculator

  1. 1

    Add supports

    Pin, roller or fixed, anywhere on the span.

  2. 2

    Apply loads

    Point loads, distributed loads and applied moments.

  3. 3

    Read the results

    Reactions, shear force diagram and bending moment diagram, solved with the direct stiffness method.

Worked Beam Examples

Hand calculations you can open in the calculator to check.

Example 1

Simply supported beam with a uniform load

A 6 m beam, pinned at the left end and on a roller at the right, carries 10 kN/m over its full length.

R_A = R_B
30 kN
M_max
45 kN·m
›Solution
  • Reactions: Total load = 10 × 6 = 60 kN, shared equally: R_A = R_B = 30 kN.
  • Shear: Shear starts at +30 kN, falls in a straight line, crosses zero at midspan (3 m) and ends at −30 kN.
  • Moment: Maximum moment is at the zero-shear point: M_max = wL²/8 = 10 × 6² / 8 = 45 kN·m at midspan. The diagram is a parabola.
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Example 2

Simply supported beam with a center point load

An 8 m simply supported beam carries a single 20 kN load at midspan.

R_A = R_B
10 kN
M_max
40 kN·m
›Solution
  • Reactions: By symmetry, R_A = R_B = 20 / 2 = 10 kN.
  • Shear: Shear is +10 kN from the left support to the load, then jumps down by 20 kN to −10 kN.
  • Moment: Moment rises linearly to M_max = PL/4 = 20 × 8 / 4 = 40 kN·m under the load, where shear changes sign. The diagram is a triangle.
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Example 3

Cantilever with a uniform load

A 3 m cantilever, fixed at the left end and free at the right, carries 5 kN/m over its full length.

R
15 kN
M_fixed
22.5 kN·m
›Solution
  • Reactions: Vertical reaction R = 5 × 3 = 15 kN; fixed-end moment M = wL²/2 = 5 × 3² / 2 = 22.5 kN·m.
  • Shear: Shear is 15 kN at the fixed end and falls linearly to zero at the free end.
  • Moment: Moment magnitude is largest at the support, 22.5 kN·m (hogging), and drops to zero at the free tip along a parabola.
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Sign Convention

Reactions
Upward is positive
Shear
Positive when the left side is pushed up
Moment
Sagging (tension on the bottom) is positive

Simple spans plot positive moment, cantilevers negative. Same as the FE Reference Handbook.

Beam Calculator FAQ

How do I draw a shear and moment diagram with this calculator?

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Add supports, add your point, distributed or moment loads, and the calculator plots the shear force diagram (SFD) and bending moment diagram (BMD) automatically.

Is this beam calculator free?

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Yes. It is a free online beam calculator and needs no sign-up.

What supports and loads are supported?

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Pin, roller and fixed supports, with point loads, distributed loads and applied moments.

Where is the maximum bending moment on a beam?

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The bending moment has a local maximum or minimum where the shear force diagram crosses zero.

Can it solve statically indeterminate beams?

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Yes. The solver uses the direct stiffness method, so continuous beams, propped cantilevers and fixed-fixed beams work the same way as simple spans.

Which units can I use?

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Switch between SI (m, N, N·m) and US customary (ft, kips, kip·ft or kip·in) units at any time; the results update instantly.

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