Beam Load Calculator

Beam Span (L):

Number of Point Loads (0-10):

Load 1 Magnitude (P1):

Distance from Support A (d1):

Load 2 Magnitude (P2):

Distance from Support A (d2):

Load 3 Magnitude (P3):

Distance from Support A (d3):

Load 4 Magnitude (P4):

Distance from Support A (d4):

Load 5 Magnitude (P5):

Distance from Support A (d5):

Load 6 Magnitude (P6):

Distance from Support A (d6):

Load 7 Magnitude (P7):

Distance from Support A (d7):

Load 8 Magnitude (P8):

Distance from Support A (d8):

Load 9 Magnitude (P9):

Distance from Support A (d9):

Load 10 Magnitude (P10):

Distance from Support A (d10):

1. What is the Beam Load Calculator?

Definition: This calculator determines the vertical reaction forces at the supports (A and B) of a simply-supported beam subjected to multiple point loads.

Purpose: It assists engineers and designers in analyzing the external forces acting on a beam, which is essential for structural design and ensuring stability.

2. How Does the Calculator Work?

The calculator uses equilibrium equations for a simply-supported beam:

Sum of vertical forces: $\sum F_{y} = 0 ⟹ R_{A} + R_{B} - \sum P_{i} = 0$
Sum of moments about A: $\sum M_{A} = 0 ⟹ \sum P_{i} d_{i} - R_{B} L = 0$

Solving these gives:

$R_{B} = \frac{\sum P_{i} d_{i}}{L}$
$R_{A} = \sum P_{i} - R_{B}$

Where:

$R_{A}$ : Reaction force at support A (N or lbf);
$R_{B}$ : Reaction force at support B (N or lbf);
$P_{i}$ : Point load magnitudes (N or lbf, positive downward, negative upward);
$d_{i}$ : Distances from support A (mm, cm, m, in, or ft);
$L$ : Beam span (mm, cm, m, in, or ft).

Steps:

Enter the beam span and its unit (mm, cm, m, in, or ft).
Specify the number of point loads (0 to 10).
For each load, enter the magnitude (N or lbf) and distance from support A (same units as span).
Convert all inputs to SI units (N, m).
Calculate $R_{B}$ using the moment equilibrium equation.
Calculate $R_{A}$ using the force equilibrium equation.
Convert reactions to the selected output unit (N or lbf).
Display results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Beam Load Calculation

Calculating support reactions is essential for:

Structural Analysis:

Design Safety:

Foundation Design:

Code Compliance:

4. Using the Calculator

Example 1 (Metric Units): Calculate reactions for a simply-supported beam with two point loads:

Beam Span: $L = 4 m$ ;
Loads: $P_{1} = 10 kN = 10000 N$ at $d_{1} = 2 m$ , $P_{2} = 3.5 kN = 3500 N$ at $d_{2} = 2.5 m$ ;
Output Unit: Newtons;
Moment Sum: $\sum P_{i} d_{i} = 10000 \times 2 + 3500 \times 2.5 = 20000 + 8750 = 28750 N·m$ ;
Reaction B: $R_{B} = \frac{28750}{4} = 7187.5 N$ ;
Reaction A: $R_{A} = (10000 + 3500) - 7187.5 = 6312.5 N$ ;
Result: $R_{A} = 6312.5000 N, R_{B} = 7187.5000 N$ .

Example 2 (Imperial Units): Calculate reactions with one point load:

Beam Span: $L = 10 ft$ ;
Load: $P_{1} = 2000 lbf$ at $d_{1} = 4 ft$ ;
Output Unit: Pounds-force;
Convert to SI: $L = 10 \times 0.3048 = 3.048 m$ , $P_{1} = 2000 \times 4.44822 = 8896.44 N$ , $d_{1} = 4 \times 0.3048 = 1.2192 m$ ;
Moment Sum: $\sum P_{i} d_{i} = 8896.44 \times 1.2192 \approx 10846.88 N·m$ ;
Reaction B: $R_{B} = \frac{10846.88}{3.048} \approx 3559.02 N \approx 800 lbf$ ;
Reaction A: $R_{A} = 8896.44 - 3559.02 \approx 5337.42 N \approx 1200 lbf$ ;
Result: $R_{A} = 1200.0000 lbf, R_{B} = 800.0000 lbf$ .

5. Frequently Asked Questions (FAQ)

Q: Can I include the beam’s weight?
A: Yes, enter the beam’s weight as a point load at the center (e.g., half the span length). The calculator assumes a weightless beam unless specified.

Q: What if I have distributed loads?
A: Convert distributed loads to equivalent point loads at their centroids. For example, a uniform load $w$ over length $L$ is equivalent to a point load $w L$ at $L / 2$ .

Q: Why are reactions zero when no loads are applied?
A: With no external loads, the beam is in equilibrium with zero reaction forces, assuming it’s weightless.