Simply Supported Beam Shear Force and Bending Moment Calculator
Input Parameters
Point Loads
Uniformly Distributed Loads
Triangular Loads
Applied Moment
Calculation Results
Support Reactions
Enter parameters and click Calculate to see results
Internal Forces at Evaluation Points
Enter parameters and click Calculate to see results
Step-by-Step Calculations
Enter parameters and click Calculate to see step-by-step calculations
Beam Visualization
What is Simply Supported Beam Bending Moment & Shear Calculator?
The Simply Supported Beam Bending Moment & Shear Calculator for Structural/Civil Engineers is a fast and accurate online tool that instantly draws shear force diagram (SFD) and bending moment diagram (BMD), calculates reactions, shear force V(x), and bending moment M(x) at any point along a simply supported beam. It handles point loads, uniform distributed loads (UDL), partial UDL, triangular loads, applied moments, and any combination using superposition — perfect for simply supported beam shear force calculator, bending moment diagram calculator, SFD BMD calculator online, RCC beam design, steel beam preliminary check, and quick statics verification.
This simply supported beam calculator includes special features like relevant visualizations (interactive SFD & BMD plots, load diagram), a dedicated section for comments, analysis and recommendations, full step-by-step calculation with every value shown, CSV export/download of results (V & M at any interval), and a Colorblind view mode for improved accessibility.
How to use Simply Supported Beam Bending Moment & Shear Calculator?
Purpose: Find support reactions, shear force V(x), bending moment M(x), maximum shear, and maximum moment so you can draw SFD/BMD and design the beam safely.
Inputs you will enter:
- Span length L (m)
- Load type(s): Point load P at distance a, UDL w (full or partial), Triangular load, Applied moment M at position
- Position x where you want V(x) and M(x) (or get values at many points)
- Multiple loads → add as many as needed (superposition is automatic)
Simply Supported Beam's Bending Moment & Shear Force Formula
Reactions (always calculate first)
\(\displaystyle R_A = \frac{\text{total moment about B}}{L}\)
\(\displaystyle R_B = \text{Total downward load} – R_A\)
Common Case: Point Load at Distance
\(\displaystyle R_A = P \frac{L – a}{L}, \quad R_B = P \frac{a}{L}\)
Shear force:
\(\displaystyle
V(x) =
\begin{cases}
R_A & x < a \\
R_A – P & x > a
\end{cases}
\)
Bending moment:
\(\displaystyle
M(x) =
\begin{cases}
R_A x & x < a \\
R_A x – P(x – a) & x > a
\end{cases}
\)
Common Case: Uniform Distributed Load over Full Span
\(\displaystyle R_A = R_B = \frac{w L}{2}\)
\(\displaystyle V(x) = R_A – w x\)
\(\displaystyle M(x) = R_A x – \frac{w x^2}{2}\)
Where:
- L = span length (m)
- x = distance from left support A (m)
- a = load position from A (m)
- P = point load (kN)
- w = UDL intensity (kN/m)
- R_A, R_B = reactions (kN)
- V(x) = shear force (kN)
- M(x) = bending moment (kNm)
How to Calculate Simply Supported Beam Shear & Moment (Step-by-Step)
- Enter span L and all loads with their positions.
- Calculator finds reactions R_A and R_B using equilibrium (ΣF_y = 0, ΣM = 0).
- For any point x, calculate V(x) = left reaction minus loads to the left of x.
- Calculate M(x) by integrating V or using direct formula (M increases where V is positive).
- For multiple loads → add the V and M from each load separately (superposition).
- Find maximum values (where V=0 for max M, or at critical points).
- Get SFD & BMD visualization + recommendations.
Examples
Example 1 – Central Point Load Span L = 6 m, Point load P = 50 kN at midspan (a = 3 m) R_A = R_B = 25 kN At x = 3 m: V jumps from +25 kN to –25 kN Max M = 25 × 3 = 75 kNm (at centre)
Example 2 – Full UDL Span L = 5 m, UDL w = 20 kN/m R_A = R_B = 50 kN V(x) = 50 – 20x Max shear = 50 kN (at ends) M(x) = 50x – 10x² Max moment = 125 kNm (at x = 2.5 m)
Simply Supported Beam Categories / Normal Range
| Load Case | Max Shear (kN) | Max Moment (kNm) | Location of Max Moment |
|---|---|---|---|
| Point load P at centre | P/2 | PL/4 | Midspan |
| Point load P at any a | max(R_A, R_B) | P a (L–a)/L | At load position |
| Full UDL w | wL/2 | wL²/8 | Midspan |
| Triangular load (0 at A, max at B) | w_max L / 3 | ≈ 0.128 w_max L² | ≈ 0.577 L |
| Triangular load (max at A, 0 at B) | w_max L / 3 | ≈ 0.128 w_max L² | ≈ 0.423 L |
Limitations
- Only for simply supported beams (no overhangs, no fixed ends).
- Assumes all loads are vertical; no axial force or torsion.
- Superposition works only for linear elastic behaviour.
- Does not calculate deflection, stress, or reinforcement — only SFD/BMD and reactions.
- For partial or complex loads, verify critical sections manually if needed.
Disclaimer
This calculator is provided for educational purposes, learning, and preliminary design checks only. All final structural designs must be reviewed and certified by a qualified professional structural engineer. The developer and platform are not liable for any errors, misinterpretations, or consequences arising from the use of these results in actual construction projects.