Moment And Shear Calculator

Example Data Table

Formula Used

For vertical equilibrium, the calculator uses ΣFy = 0. For a simply supported beam, RA + RB = total downward load.

For moment equilibrium about the left support, RB × L = Σ(P × a) + Σ(W × x̄) + ΣM.

Section shear is V(x) = RA − loads left of x. Section moment is M(x) = RA × x − moments of loads left of x.

A linear distributed load uses q(t) = q0 + (q1 − q0)(t − a)/(b − a). Its resultant is the area under that load.

How To Use This Calculator

1. Enter the total beam length.
2. Select simply supported or cantilever support behavior.
3. Enter the section location where shear and moment are needed.
4. Add point loads as one row per load.
5. Add distributed loads using start and end positions.
6. Use one unit system for every value.
7. Press the calculate button and read the result above the form.
8. Download the CSV or PDF report when needed.

Why Moment And Shear Checking Matters

Moment and shear checks help engineers understand beam behavior before a member is sized. A load creates vertical force, support reaction, shear variation, and bending demand. Each value changes along the span. A clear calculator reduces mistakes during early design, homework, review, and field planning.

What This Tool Evaluates

This tool accepts point loads, uniform loads, partial uniform loads, linear loads, and applied couples. It uses static equilibrium to find reactions. It then samples the beam at many stations. The largest absolute shear and moment are reported. The table also shows values at selected positions, so users can review the diagram shape without drawing it manually.

Good Inputs Give Better Results

Use one consistent unit system. Enter length in feet or meters. Enter forces in pounds, kilonewtons, or matching units. Place every load from the left support or fixed end. Keep positions between zero and the total span. For distributed loads, the start location should be smaller than the end location. For triangular loads, enter the starting and ending intensities.

Reading The Output

Positive shear means the left segment tends to move upward at the cut. Positive moment usually represents sagging action. Negative moment usually represents hogging action. Reaction signs show whether a support pushes upward or would need restraint. The maximum values are useful for quick checks, but detailed design still needs code rules, load combinations, material limits, and serviceability checks.

Practical Design Use

The station table can be exported for worksheets, reports, and comparison notes. The downloaded values help build shear and moment diagrams in another program. You can increase the number of stations for smoother curves. You can also evaluate a specific section by entering its distance from the left end. This is useful near supports, under concentrated loads, and around distributed load boundaries.

Helpful Limitations

The calculator is a statics tool. It does not replace structural judgment. It assumes idealized supports and vertical loading. It does not check lateral torsional buckling, deflection, vibration, bearing, connection strength, or local code requirements. Use the result as a transparent calculation aid. Verify final designs with qualified review when safety matters. Always record assumptions, units, load directions, and support choices for review later checks.

FAQs