Shear Moment Calculator

Shear force and bending moment diagrams are the starting point for sizing any beam. Set the span and supports, add your loads, and this calculator solves the reactions and draws both diagrams, marking the maximum shear and moment — with deflection too if you enter the material and section properties.

What shear and moment diagrams show

Shear force at a point is the sum of the vertical forces on one side of it; bending moment is the sum of their moments about that point. Plotted along the beam, the shear diagram shows where the beam is most likely to fail in shear (near supports and heavy point loads) and the moment diagram shows where bending stress peaks. The key relationships: the slope of the moment diagram equals the shear, so maximum moment occurs where shear crosses zero; a point load makes the shear jump; a distributed load makes the shear slope and the moment curve.

Worked example

A 6 m simply supported beam carries a 20 kN point load 2 m from the left support and a uniform load of 5 kN/m along its full length. Total load is 50 kN; taking moments about the left support gives a right reaction of 21.67 kN and a left reaction of 28.33 kN. The shear drops from 28.33 kN, crosses zero at the point load, and the maximum moment is 46.67 kN·m at 2.00 m — the same values the calculator shows with its default loads.

Standard beam formulas

Loads combine by superposition: the diagrams for several loads are the sum of the diagrams for each load alone, which is exactly how the calculator adds them.

Overhangs and cantilevers

Moving a support in from the end creates an overhang. Loads on the overhang lift the far support and create negative (hogging) moment over the support, which puts the top of the beam in tension — important for reinforced concrete and for timber joists with notches. A cantilever has a single fixed support that resists both force and moment; its maximum moment is at the fixed end.

Checking your answer

• The reactions must add up to the total load (vertical equilibrium).
• The shear diagram should return to zero at the right-hand end.
• The moment should be zero at a pin, roller or free end, and equal the fixed-end moment at a fixed support.
• The maximum moment should fall where the shear crosses zero, or at a support.
• Compare with a standard formula for the simplest version of your case.

Point loads versus distributed loads

A point load represents something concentrated — a post, a wheel, a machine foot — and produces a sudden step in the shear diagram and a sharp corner in the moment diagram. A distributed load represents something spread out — floor loads, snow, the beam’s own weight — and produces a sloping shear line and a curved moment diagram. Real loads are often a mix, and a partial distributed load (from and to positions) lets you model loads over only part of the span.

From moment to beam size

Once you know the maximum moment, the required section modulus is S = M ÷ allowable bending stress (or M ÷ design strength in limit-state design). For the worked example, 46.67 kN·m with an allowable stress of 165 MPa needs S ≈ 283 cm³, which points to a small steel I-section; a timber beam needs a much deeper section because its allowable stress is lower. Shear capacity, deflection, lateral buckling and bearing at the supports must also be checked — the diagrams here are the first step, not the whole design.

Deflection

Enter the modulus of elasticity E and second moment of area I to plot the deflected shape. In SI, enter E in GPa (steel ≈ 200, softwood ≈ 8–12) and I in cm⁴; in US units, E in ksi (steel ≈ 29,000) and I in in⁴. Deflection limits such as span/360 for floors are common serviceability checks — the calculator shows the ratio L/Δ.

What’s in the template pack

• Beam formula reference sheet (simply supported, cantilever, fixed and overhanging cases)
• Excel beam worksheet: reactions, shear and moment at 20 points with a chart
• Printable hand-calculation worksheet with free-body diagram grid
• Section properties table for rectangular and I-sections
• Load take-down worksheet

The calculator is free; the pack is a one-time download.

AI-assisted content

This page and the templates were drafted with AI assistance and reviewed by Kedop. They are for education and preliminary checks — structural designs must be checked by a qualified engineer against the applicable codes.