Beam Load Reaction Calculator
Select beam type, load case, and input parameters, then click Calculate.
Results will appear here after calculation. This section provides practical interpretation of the calculated support reactions in real-world structural context.
Detailed analysis of the structural behavior, load distribution, and support performance will be displayed here after calculation.
Based on the calculated reactions, practical guidance for design considerations, potential issues, and optimization suggestions will be provided here.
What is Beam Load Reaction Calculator?
The Loads to Reactions Calculator instantly computes support reactions (R_A, R_B, R_C), fixed-end moments (M_A), shear forces, and bending moments for simply supported, cantilever, propped cantilever, overhanging, and continuous beams under point loads, uniform distributed loads (UDL), triangular loads, applied moments, and self-weight. It is the essential first step in drawing shear force diagrams (SFD) and bending moment diagrams (BMD) for reinforced concrete beam design and steel beam sizing.
This beam reaction forces calculator, loads to reactions calculator online, simply supported beam reactions calculator, cantilever beam reactions calculator, propped cantilever reactions calculator, and continuous beam reactions tool provides relevant visualization, a dedicated section for comments, analysis and recommendations, full step-by-step calculation with every equilibrium equation shown, CSV export/download of results (reactions, SFD & BMD values at any interval), and a Colorblind view for specially abled users.
How to use Beam Load Reaction Calculator
Calculator Use Purpose: Find all support reactions and moments under service loads so you can proceed confidently to shear, moment, deflection, and reinforcement design.
Inputs you will enter:
- Beam type (Simply Supported / Cantilever / Propped Cantilever / Overhanging / Continuous 2-span)
- Span length L (m) or spans L1, L2
- Overhang length c (if any)
- Loads: Point load P at distance a, UDL w (full or partial from start to end), triangular load w_max, applied moment M at position
- Self-weight option (auto-calculated from section or manual γ)
- Optional: horizontal loads, support settlement
Beam Loads to Reaction Formula
Simply Supported Beam – UDL
\(\displaystyle R_A = R_B = \frac{w L}{2}\)
Simply Supported Beam – Point Load at a
\(\displaystyle R_A = P \frac{L – a}{L}, \quad R_B = P \frac{a}{L}\)
Cantilever Beam – UDL
\(\displaystyle R_A = w L, \quad M_A = \frac{w L^2}{2}\)
Propped Cantilever – UDL
\(\displaystyle
R_A = \frac{5 w L}{8}, \quad
R_B = \frac{3 w L}{8}, \quad
M_A = \frac{w L^2}{8}\)
Where:
- w = UDL intensity (kN/m)
- P = point load (kN)
- L = span (m)
- a = distance from left support (m)
- R_A, R_B = vertical reactions (kN)
- M_A = fixed-end moment (kNm)
How to Calculate Beam Load Reaction (Step-by-Step)
- Select beam type and enter spans/overhangs.
- Add all loads with positions (multiple loads allowed – superposition is automatic).
- Calculator first solves equilibrium equations ΣF_y = 0 and ΣM = 0 to find reactions.
- For indeterminate cases (propped, continuous), it applies standard compatibility formulas or three-moment theorem.
- Computes shear V(x) and moment M(x) at any point using integration or direct formulas.
- Checks stability (negative reactions = uplift warning).
- Generates SFD, BMD, and recommendations (max values, critical sections, redesign suggestions if uplift occurs).
Examples
Example 1 – Simply Supported Beam with UDL + Point Load L = 7 m, UDL w = 18 kN/m, Point load P = 80 kN at 2 m from A R_A = 103 kN, R_B = 103 kN Max moment = 178.5 kNm at x ≈ 3.11 m
Example 2 – Propped Cantilever (Fixed at A, Simple at B) L = 5 m, UDL w = 30 kN/m R_A = 93.75 kN, R_B = 56.25 kN, M_A = 37.5 kNm Maximum moment now reduced from 187.5 kNm (pure cantilever) to 37.5 kNm – big saving in reinforcement.
Loads to Reactions Categories / Normal Range
| Beam Type | Typical Max Reaction | Typical Max Moment | Common Use Case |
|---|---|---|---|
| Simply Supported + UDL | wL/2 | wL²/8 | Floor beams, slabs |
| Simply Supported + Central P | P/2 | PL/4 | Bridge girders |
| Cantilever + End P | P | PL | Balconies, canopies |
| Propped Cantilever + UDL | 5wL/8 | wL²/8 | Cantilever slabs with back span |
| Continuous 2-span equal + UDL | 5wL/8 (ends), 1.25wL (middle) | wL²/8 (midspan) | Multi-span floors |
| Overhanging | Can be negative | High at support | Roof edges, signs |
Limitations
- Only for prismatic horizontal beams (no variable section or tapered beams).
- Small deflection assumption – no P-delta or second-order effects.
- Statically determinate or standard indeterminate cases only (no arbitrary multi-span with many supports).
- Self-weight must be added manually or via density option.
- Does not calculate deflection, stress, or reinforcement – only reactions, SFD & BMD.
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.