Beam Load Calculator
Calculate reactions, bending moment, shear force, and deflection for simply supported beams.
📖 What is a Beam Load Calculator?
A beam load calculator determines the internal forces and deformations in a beam subjected to external loads. It is a fundamental tool in structural and civil engineering, used in the design of floors, bridges, roof structures, industrial frames, and any structure where beams carry loads.
This calculator focuses on the most common scenario: a simply supported beam — one that rests on two supports and is free to rotate at each end. Two load types are supported: a point load (a concentrated force at a specific location, such as a column bearing onto a beam) and a uniformly distributed load or UDL (load spread evenly across the whole span, such as the self-weight of a slab or wind pressure).
For each load case, the calculator finds: support reactions at both ends, the maximum bending moment (and its location), the maximum shear force, and the maximum midspan deflection. These four outputs are the key quantities needed for beam selection and structural adequacy checks.
Note that this calculator provides idealised elastic results for a single span, single load. Real structures often have multiple loads, continuous spans, or non-uniform sections — consult a structural engineer and applicable design codes for complex or safety-critical designs.
📝 Beam Load Formulas
R_A = P × b / L R_B = P × a / L
M_max = P × a × b / L (at load position)
δ_max = P × a × b × (L² − a² − b²)^(3/2) / (9√3 × EI × L) [at x = √((L² − b²)/3)]
For central load (a = b = L/2): δ_max = PL³ / (48EI)
Simply Supported Beam — Uniformly Distributed Load w (kN/m):
R_A = R_B = wL / 2
M_max = wL² / 8 (at midspan)
δ_max = 5wL⁴ / (384EI)
Where: P = point load (kN) | w = distributed load (kN/m) | L = span (m) | a, b = distances from supports | EI = flexural rigidity (kN·m²)
✍️ How to Use This Calculator
- Select Point Load or Distributed Load (UDL) using the tabs above.
- Enter the beam span L in metres.
- For a point load: enter the load P in kN and its distance from the left support (a).
- For a UDL: enter the load intensity w in kN/m (total load = w × L).
- Enter EI (flexural rigidity in kN·m²) for deflection. For a standard steel I-beam, EI is typically 5,000–100,000 kN·m².
- Click Calculate to see reactions, maximum moment, shear, and deflection.
📄 Example Calculations
A 6 m simply supported beam carries a 50 kN point load at midspan. EI = 10,000 kN·m².
R_A = R_B = 50/2 = 25 kN
M_max = 50 × 3 / 4 = 37.5 kN·m (at midspan)
δ_max = (50 × 6³) / (48 × 10,000) = 10,800/480,000 = 0.0225 m = 22.5 mm
L/267 — check if this is within the allowable deflection limit (typically L/250 = 24 mm ✓)
Example 2 — Full-span UDL:
A 5 m beam carries a UDL of 15 kN/m (e.g., floor slab + finishes). EI = 8,000 kN·m².
Total load = 15 × 5 = 75 kN
R_A = R_B = 75/2 = 37.5 kN
M_max = 15 × 25 / 8 = 46.9 kN·m (at midspan)
δ_max = (5 × 15 × 5⁴) / (384 × 8,000) = 46,875/3,072,000 = 0.0153 m = 15.3 mm