How to use the shear and moment diagram calculator
- Choose the units: kN and meters, N and meters, kip and feet, or lb and feet.
- Enter the span between the supports. The left support is a pin and the right one is a roller.
- Add each load: a point load with its position, or a uniform load with its start and end. All loads act downward.
- Read the reactions, the largest shear, the largest bending moment and where it occurs, and use the table of shear and moment along the beam.
Formula
Left and right reactions come from equilibrium: the sum of forces is zero and the sum of moments about the left support is zero
Shear V(x) = left reaction minus the load to the left of x
Moment M(x) = left reaction x minus the moment of the loads to the left of x
The largest moment is at a point where the shear crosses zero
The values in the table are exact for the loads you enter. A uniform load makes the shear change in a straight line and the moment in a curve.
A 6 m beam with a uniform load of 2 kN/m
The total load is 2 x 6 = 12 kN, so each reaction is 6 kN. The shear starts at 6 kN at the left end and falls steadily to -6 kN at the right end, crossing zero at midspan. The largest shear is 6 kN near 0 m.
The largest bending moment is at midspan, where it equals w x L^2 / 8 = 2 x 36 / 8 = 9 kN m at 3 m. The table lists the shear and moment at points along the span, starting with 6 and 0 at x = 0.
Reading the diagrams
The shear diagram shows the internal vertical force at each point, and the moment diagram shows the internal bending. The moment is zero at both supports of a simply supported beam and is largest where the shear passes through zero. Beam size is chosen from the largest moment, and connections and the web are checked against the largest shear.
To see how far the same beam bends under the load, use the beam deflection calculator.
Limits of a simple beam
This page treats a single span with a pin at one end and a roller at the other. It does not cover cantilevers, continuous beams over several supports, fixed ends or loads that vary in a triangle. It does not check material strength, so it is a first step before a design check by a qualified person.
Loads such as a thermal change in length are separate. See the thermal expansion calculator.
Assumptions and limits
- The beam is a single straight span, simply supported with a pin at the left and a roller at the right.
- Loads are downward only, and the self weight of the beam is included only if you enter it as a load.
- Moment is positive when the beam sags.
- The page does not check strength, deflection or code requirements. A qualified person should check any structure.
Frequently asked questions
How do I find the reactions of a beam?
Take moments about one support to find the other reaction, then use the sum of vertical forces. The page does this for any mix of point and uniform loads.
Where is the maximum moment?
It is where the shear changes sign, which is the point where the shear diagram crosses zero. The page reports that position.
Can I use feet and pounds?
Yes. Choose lb and feet or kip and feet, and enter all loads and the span in those units.
Does it include the weight of the beam?
Only if you add it. Enter the beam weight per unit length as a uniform load over the whole span.