Shear and Moment Diagram Calculator (Free SFD & BMD)

How to Draw Shear and Moment Diagrams

The calculator above draws both diagrams for you, but the same steps work by hand and are worth knowing for statics, mechanics of materials and the FE exam:

Find the support reactions from equilibrium: ΣF_y = 0 and ΣM = 0 about one support.
Draw the shear diagram from left to right. Jump up by each upward reaction, jump down by each point load, and slope down by w under a distributed load.
Draw the moment diagram by adding up the area under the shear diagram. The moment starts at zero at a free end or pinned end.
Mark the maximum moment where the shear crosses zero, and check that the moment returns to zero (or to the fixed-end moment) at the far end.

Rules of Thumb for Checking Your Diagrams

Load on the segment	Shear diagram	Moment diagram
No load	Horizontal line	Straight sloped line
Uniform load w	Straight line, slope −w	Parabola (2nd degree)
Linearly varying load	Parabola	Cubic curve
Point load P	Sudden jump of P	Kink (change in slope)
Applied moment M₀	No change	Sudden jump of M₀

Worked Examples

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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For standard cases you can also read the maximum shear and moment straight from the beam formula tables.

Shear and Moment Diagram FAQ

What is a shear and moment diagram?

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It is a pair of graphs along the length of a beam. The shear diagram shows the internal shear force V at every section and the moment diagram shows the internal bending moment M. Together they show where a beam is most highly stressed.

How are the shear and moment diagrams related?

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The slope of the moment diagram equals the shear (dM/dx = V), and the change in moment between two points equals the area under the shear diagram between them. The slope of the shear diagram equals the distributed load (dV/dx = −w).

What shape do the diagrams take?

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Under no load the shear is constant and the moment is a straight line. Under a uniform load the shear is a straight sloped line and the moment is a parabola. A point load makes a jump in shear and a kink in moment; an applied moment makes a jump in the moment diagram.

Can I generate diagrams for cantilevers and overhangs?

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Yes. Use a fixed support for a cantilever, or place pin and roller supports anywhere along the beam for overhangs and multi-span beams.

Shear and Moment Diagram Calculator