Shear Moment Diagram Calculator
Find the support reactions and maximum bending moment for a simply supported beam under a single point load, with the formula and a worked example.
Result
2,400 lb-ft
A 1,000 lb load at 4 ft on a 10 ft beam gives a max moment of 2,400 lb-ft
Quick Answer
This shear moment diagram calculator covers the simply supported beam with one point load only. For a 20 ft beam with a 1,000 lb load applied 8 ft from the left support, R1 = 1,000 × 12 ÷ 20 = 600 lb, R2 = 400 lb, and the maximum moment at the load point is 600 × 8 = 4,800 lb-ft.
What This Shear Moment Calculator Covers and Omits
This calculator applies to a single, specific structural case: a simply supported beam with two pin/roller supports and a single concentrated point load applied at one location along the span. It computes the two support reactions, the maximum bending moment at the load point, and the shear force in each span segment. This is the single point-load case only. The calculator does not handle distributed loads across the span, multiple point loads at different positions, cantilever beams, or fixed-end support conditions.
The Simply Supported Beam Formula for a Single Point Load
Left reaction: R1 = P × b ÷ L Right reaction: R2 = P × a ÷ L Max moment: M_max = R1 × a = P × a × b ÷ L
- Left reaction: R1 = P × b ÷ L
- Right reaction: R2 = P × a ÷ L
- Maximum bending moment: M_max = R1 × a = P × a × b ÷ L
- Location of M_max: directly under point load, at distance a from left support
How To Read Shear and Moment Results for a Supported Beam
Inputs
- Beam length L (ft): the clear span between support centerlines
- Point load P (lb): the concentrated force applied perpendicular to the beam axis
- Load position a (ft): the distance from the left support to where the load is applied
Steps
- Identify the beam span L between support centers.
- Determine the load P and its position a from the left support.
- Enter L, P, and a into the calculator.
- Read R1, R2, and M_max from the results.
- Use R1 for left support sizing, R2 for right support sizing, and M_max for bending stress and deflection checks.
Shear and Moment Values: A Complete Worked Example
A 20 ft simply supported beam under a 1,000 lb point load placed 8 ft from the left support.
- Calculate right segment b = 20 − 8 = 12 ft.
- Calculate left reaction: R1 = 1,000 × 12 ÷ 20 = 600 lb.
- Calculate right reaction: R2 = 1,000 × 8 ÷ 20 = 400 lb.
- Verify equilibrium: R1 + R2 = 600 + 400 = 1,000 lb.
- Calculate max moment: M_max = 600 × 8 = 4,800 lb-ft.
The left support carries 600 lb, the right support carries 400 lb, and maximum bending moment is 4,800 lb-ft at the load point.
When To Use This Shear Moment Diagram Calculator Tool
Use this calculator for a quick hand-check of a simply supported beam with one concentrated load in a preliminary design, homework verification, or teaching context. It is also useful for validating a structural software result on a simple reference case. Do not use it for final structural design of occupied structures; that requires a licensed structural engineer accounting for load combinations, beam self-weight, deflection limits, and material stress allowables. Do not apply the results to any beam configuration other than the single-point-load, simply-supported case described above.
Assumptions
- The beam is simply supported with one pin and one roller (no moment resistance at supports).
- A single concentrated point load P is applied at distance a from the left support.
- Beam self-weight is not included in the calculation; add self-weight as a separate distributed load if needed.
- The beam is straight, prismatic, and loaded in the plane of the web (no lateral-torsional effects).
Limitations
- Does not handle distributed loads (uniform, triangular, or partial); this is the single point-load case only.
- Does not handle multiple point loads; superpose separate calculations and add results only for linear-elastic beams.
- Does not handle cantilever, fixed-end, propped, or continuous beams.
- Does not compute deflection, stress, or section modulus requirements.
In Practice
The most useful check after calculating reactions is equilibrium verification: R1 + R2 must equal P. If they do not, the inputs are inconsistent (usually load position a is entered larger than span L). Doing this check by inspection before relying on the result takes seconds and confirms the setup is correct before using the reactions for support sizing.
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Frequently Asked Questions: Shear Moment Calculator
What is a simply supported beam?
A simply supported beam rests on two supports, one of which allows rotation and prevents vertical movement (a pin), and the other of which allows both rotation and horizontal movement (a roller). This configuration allows the beam to expand or contract freely and creates no moment reactions at the supports. It is the most basic and commonly used beam model in introductory structural analysis.
What is the maximum bending moment for a single point load?
For a point load P at distance a from the left support of a span L, the maximum bending moment is M_max = P × a × b ÷ L, where b = L − a. This maximum occurs directly under the load. When the load is at midspan (a = b = L/2), M_max simplifies to P × L ÷ 4.
How do I find bending stress from the maximum moment?
Bending stress f = M_max × c ÷ I, where c is the distance from the neutral axis to the extreme fiber and I is the moment of inertia of the cross-section. For a standard steel wide-flange section, these values appear in the AISC Steel Construction Manual. This calculator provides M_max; you apply the stress formula separately using the section properties of your chosen beam.
Can I add multiple point loads using this calculator?
For linear-elastic beams, you can run the calculator separately for each load and add the resulting reactions and moments by superposition. Run once for Load 1 at position a1, once for Load 2 at position a2, and sum the R1 values, sum the R2 values, and sum the M_max values (which only directly superpose if the loads are at the same position). For different load positions, sum the moments at the specific cross-section of interest, not the peak values from each run.
Why does the moment return to zero at the supports?
A simply supported beam has no moment resistance at either support. A pin or roller cannot exert a moment reaction on the beam. Since the external moment at each support is zero and the beam is in static equilibrium, the internal bending moment at both support points must also be zero. This is why the moment diagram starts and ends at zero for any simply supported beam.
Sources
Last updated: . Reviewed for accuracy against the formula shown above.