Beam Load Calculator
Enter your beam span, support condition, load type, and cross-section dimensions to instantly find the support reactions, maximum bending moment, maximum shear force, mid-span deflection, and maximum bending stress. Choose between metric and imperial units and switch between a simply-supported beam and a cantilever at any time.
How the beam load calculator works
This calculator applies classical elastic beam theory (Euler-Bernoulli) to find the support reactions, internal forces, and deflection of two common structural configurations. For a simply-supported beam, equilibrium of vertical forces and moments at the supports gives the reactions; for a cantilever, the fixed end must resist both the full shear and the full moment. Internal shear and bending moment are then found from equilibrium at every cross-section. Deflections use the closed-form integration of the bending moment equation (the double-integration or moment-area methods), which assume the beam is linearly elastic and that cross-sections remain plane. The bending stress at the outer fibre is found from the flexure formula: sigma = M * y / I, where y = d/2 for a rectangular section.
Simply supported vs cantilever: what changes
A simply-supported beam (pinned at A, roller at B) develops equal reactions of P/2 for a central point load, or wL/2 for a UDL. The maximum moment is at midspan. A cantilever (fixed at A, free at B) resists the entire load at the fixed end: the full force P or wL as a shear reaction, plus a moment equal to P*L (point) or wL^2/2 (UDL). Because the cantilever is only supported at one end, it deflects far more for the same span, load, and stiffness: P*L^3/(3EI) vs P*L^3/(48EI) for a central point load, a 16-fold difference. This is why cantilevered elements such as balconies and overhangs require deeper or heavier sections than equivalent simply-supported spans.
Point load vs uniform distributed load (UDL)
A point load concentrates all the force at one location, creating an abrupt change in the shear force diagram and a triangular bending moment diagram that peaks at the load. A UDL spreads the load evenly along the span, producing a parabolic bending moment diagram with a lower peak for the same total force. For example, a simply-supported 5 m beam carrying 10 kN as a central point load has a maximum moment of 12.5 kN-m, while the same 10 kN spread as a 2 kN/m UDL gives only 6.25 kN-m at midspan. Choosing the right load model matters: distributed self-weight and floor loads are best represented as UDLs, while columns, wall loads, and machinery footings are modelled as point loads.
Checking your results: deflection limits and stress
Two checks govern most beam designs. The strength check compares the calculated maximum bending stress (sigma = M*y/I) against the material allowable bending stress: 165 MPa for common structural steel (A36/S275), 138 MPa for 6061-T6 aluminium, and typically 7-15 MPa for structural timber depending on grade. The serviceability check compares L/delta_max against the code limit: L/360 for floors under live load and L/240 under total load are the most widely used thresholds. If either check fails, you need a deeper section (larger I), a shorter span, a different material, or a change in support condition. The steps panel shows the exact numbers substituted into each formula.
Typical beam deflection limits (serviceability)
| Application | Deflection limit | Span/delta ratio | Notes |
|---|---|---|---|
| Floor beams (live load) | L/360 | 360 | Typical residential and commercial floors |
| Floor beams (total load) | L/240 | 240 | Total dead + live load |
| Roof beams (live load) | L/360 | 360 | Sloped roofs |
| Roof beams (total, no ceiling) | L/180 | 180 | Flat or low-slope roofs without plaster |
| Roof beams (total, plaster ceil.) | L/240 | 240 | Ceilings susceptible to cracking |
| Cantilever beams (live load) | L/180 | 180 | Half of simply-supported limit by convention |
| Lintels and headers | L/600 | 600 | To protect brittle masonry above |
Common span-to-deflection limits from building codes and structural engineering practice. L is the beam span.
Frequently asked questions
What is a beam support reaction?
A support reaction is the upward force (and, for a fixed support, the moment) that a support must provide to keep the beam in static equilibrium. For a simply-supported beam with a central load P, each support provides P/2. For a cantilever, the fixed wall provides the entire load as a shear force plus a bending moment equal to P times the span.
What is the deflection limit for a floor beam?
Most building codes specify L/360 for live load deflection and L/240 for total (dead plus live) load deflection in floor beams, where L is the beam span. These limits prevent cracking in non-structural finishes and ensure the floor does not feel bouncy. Cantilevers use L/180 for live load by convention. This calculator shows the span/deflection ratio so you can compare it directly against whichever limit applies.
How do I calculate the bending moment in a beam?
For the standard cases covered here: simply-supported beam with a central point load, M_max = P*L/4; with a UDL, M_max = w*L^2/8. For a cantilever with a point load at the free end, M_max = P*L; with a UDL, M_max = w*L^2/2. For other load positions or multiple loads, use the principle of superposition or free-body diagrams at successive cross-sections.
What is the second moment of area and why does it matter?
The second moment of area (also called moment of inertia) I quantifies how a cross-section resists bending. For a solid rectangle, I = b*d^3/12. Doubling the depth d quadruples I, which halves the bending stress and reduces deflection by a factor of four. This is why beams are almost always oriented with the larger dimension vertical, and why I-beams and H-sections are so efficient: they place the most material as far from the neutral axis as possible.
Can I use this calculator for steel I-beams?
Yes, but you need to use the actual I value for the section (from a steel section tables, not the rectangular formula). Look up your section (e.g., W8x31 or UB203x102) in the manufacturer or code section tables to get the strong-axis I and the elastic section modulus Z = I/y_max. Then cross-check the deflection formula manually using those values. The reference table in this calculator shows the most common allowable deflection limits.
What does L/360 mean?
L/360 means the maximum allowable deflection is the beam span divided by 360. For a 5 m beam, that is 5000/360 = 13.9 mm. The ratio is a practical limit developed from observation: when deflections exceed L/360 under live load, many floor finishes crack and occupants notice the movement. Tighter limits (L/480 or L/600) apply where very stiff surfaces such as stone tile or brittle masonry are present.