Shear and Moment Diagram Calculator
Interactive Beam Calculator (Simply Supported)
Point Loads (kip, downward positive)
0 kip
0 kip
0 kip·ft
0 kip
Critical values
How to Calculate Shear Force & Bending Moment Diagrams (2026 Guide)
Understanding shear and moment diagram calculator methods is essential for structural analysis. Below we break down the exact process used in this tool — from equilibrium to final diagrams.
Step-by-step procedure (for any simply supported beam)
- Determine reactions using ΣM = 0 and ΣFy = 0.
- Shear diagram construction: start from left reaction, subtract loads (point loads and area under distributed load).
- Moment diagram: integrate shear diagram (area under shear curve = change in moment).
- Identify critical points (zero shear, max moment).
Example calculation (our default beam)
Length = 10 ft, UDL = 1 kip/ft, point load P = 10 kip at 5 ft. Total UDL force = 10 kips → Reactions: R₁ = (P*(L-a)/L)+(wL/2) = (10*5/10)+(10/2)=5+5=10 kip, R₂ = (P*a/L)+(wL/2) = (10*5/10)+5=10 kip. Shear just left of point load: 10 - (1*5)=5 kip; after point load: -5 kip. Max moment occurs where shear changes sign: at x=5ft → M = R₁*5 - w*5²/2 = 10*5 - 12.5 = 37.5 kip·ft. Our calculator delivers exact values.
Quick reference table: common load types & diagram shapes
| Load type | Shear diagram shape | Moment diagram shape |
|---|---|---|
| Point load | Rectangular jump | Linear (V-shape) |
| Uniform distributed load | Linear slope | Parabolic |
| Triangular load | Parabolic | Cubic |
Why use our shear and moment diagram calculator with solution?
Unlike generic tools, our calculator provides both graphical diagrams and numerical verification, ideal for homework, FE exam prep, or real-world beam sizing. All calculations follow AISC/ASCE guidelines and update for 2026 academic curricula.
Frequently Asked Questions
A tool that computes shear force and bending moment values along a beam and draws diagrams, helping engineers identify maximum stresses.
Yes. It uses equilibrium equations and is perfect for preliminary design, homework, and review. Always verify with professional software for final designs.
This version focuses on simply supported beams (most common). We plan to add frame and hinge support in 2026 updates. For now, it's ideal for basic beam analysis.
Positive moment causes compression on top fibers (sagging). Our calculator uses standard engineering sign convention (positive moment up).
The reaction and critical values are shown numerically; the graphs visually represent shear & moment. Upgrade to detailed solution steps coming soon.
Simply add multiple point loads using the "Add point load" button. The calculator superposition principle handles any combination.
Engineering verification checklist (shear & bending moment diagrams)
- ✔️ ΣFy = 0 → sum of reactions equals total applied loads.
- ✔️ ΣM about any point = 0 (moment equilibrium verified).
- ✔️ Shear diagram jumps downward by magnitude of downward point loads.
- ✔️ Moment diagram slope matches shear value at every section.
- ✔️ Moment at pinned supports = 0.
- ✔️ Area under shear diagram between supports = net moment change (should be zero for simply supported).
Use this quick method to manually check any beam shear and moment diagram calculator results — including ours.