Beam Load & Bending Moment Calculator

Structural Beam Guide

What's the key thing to understand about Bending Moments and Shear Forces?

A beam supporting a load experiences bending moments (tend to curve the beam) and shear forces (tend to slice through it). For a simply supported beam (resting on two supports) with a central point load W: maximum bending moment = WL/4 (at centre). Maximum shear force = W/2 (at the supports). For a uniformly distributed load (UDL) of w kN/m: maximum bending moment = wL²/8 (at centre). Maximum shear force = wL/2 (at supports). These are the most-used structural formulas in building design.

What's the key thing to understand about Lintels and Floor Joists?

Common applications: lintels over door/window openings carry the weight of masonry above. A typical domestic lintel over a 1.2m window opening carries approximately 3-5 kN/m of load (depending on wall height above and roof). Standard steel lintels (Catnic, Birtley) have pre-tested load capacities — always check the manufacturer's span/load tables rather than calculating independently. Floor joists in C24 timber: a typical 50×200mm joist at 400mm centres over a 3.6m span can carry approximately 1.5-2 kN/m² of imposed load, which is generally sufficient for typical domestic living spaces, though always check against the specific span table for your exact timber grade and spacing.

What do I need to know about Deflection Limits?

Structural codes limit beam deflection to protect finishes and serviceability. Typical limits: floor joists: L/360 of span (a 3.6m span → maximum 10mm deflection). Lintels and beams: L/250 for most applications. For a 4.8m span: limit = 4800/250 = 19.2mm. Deflection = 5wL⁴/(384EI) for UDL on simply supported beam, where E = Young's modulus, I = second moment of area. Steel has much higher stiffness (E = 200 GPa) than timber (E = 11 GPa), which is why steel can span further for the same depth.

When You Need a Structural Engineer?

Always engage a structural engineer for: removing or modifying load-bearing walls, openings in excess of 1.2m in load-bearing walls, beams spanning more than 4m, any work near foundations, loft conversions that change the roof structure, any situation where the load path is unclear. This calculator provides educational guidance only — it does not replace structural engineering calculations. Building Regulations require structural calculations for many alterations. An RICS or ICE-registered structural engineer's calculations are typically required for building control approval on anything beyond straightforward, tabulated situations.

What do I need to know about Load Types (Dead, Live, and Point Loads)?

Structural loads on a beam are generally categorised as dead loads, live loads, or point loads, and understanding the difference matters for interpreting what this calculator's UDL and point load inputs actually represent. Dead load is the permanent, constant weight of the structure itself, such as the floor joists, decking, ceiling finish and the beam's own weight, which never changes once the building is finished. Live load is the variable, changeable weight the structure needs to support in use, such as people, furniture, and stored items on a floor, or snow loading on a roof, which fluctuates over time and is typically estimated using standard allowances for the building's use rather than measured directly. A uniformly distributed load, or UDL, represents a load spread evenly along the beam's full length, such as the combined dead and live load of a floor bearing evenly along a supporting beam beneath it, and is expressed as a load per metre of beam length. A point load, by contrast, represents a load concentrated at a single specific location along the beam, such as a column or another beam bearing down onto this beam at one point, and its position along the span, not just its magnitude, significantly affects the resulting bending moment and deflection, which is why this calculator asks for load position as well as load size.

What should I know about Material Properties (E and I) in Deflection?

Beam deflection, how much a beam physically bends or sags under load, depends on two material and shape properties working together: the modulus of elasticity, usually written as E, which describes how stiff the material itself is regardless of shape, and the second moment of area, usually written as I, which describes how effectively the beam's cross-sectional shape resists bending, independent of the material it's made from. Steel has a much higher modulus of elasticity than timber, meaning a steel beam of identical shape and size will deflect considerably less under the same load than a timber beam of the same dimensions, which is one reason steel beams or lintels are commonly specified for longer spans or heavier loads where a timber beam of practical size would deflect too much. The second moment of area depends on cross-sectional shape and, critically, on depth, since a beam's resistance to bending increases dramatically with its depth, far more than it increases with its width, which is why a beam turned on its edge, deeper than it is wide, is dramatically stiffer than the same beam lying flat, even though both orientations use the identical amount of material. This is why increasing a beam's depth is generally a far more effective way to reduce deflection and increase load capacity than increasing its width by the same amount.

What's the Difference Between Simply Supported and Cantilever Beams?

A simply supported beam rests on two supports (walls, columns, or padstones) near its ends and is free to rotate slightly at each support — this is the standard arrangement for a lintel over an opening or a floor joist spanning between two walls. Its maximum bending moment for a uniformly distributed load occurs at mid-span and equals wL²/8 (w = load per metre, L = span). A cantilever beam, by contrast, is fixed rigidly at one end and completely unsupported at the other — a balcony, a shelf bracket, or a beam projecting past its last support. Its maximum bending moment occurs at the fixed end, not mid-span, and for a uniformly distributed load equals wL²/2 — four times larger than the equivalent simply supported span for the same length and loading. This is why cantilevers feel so much more prone to sagging and deflecting than the same length of simply supported beam, and why cantilevered structures typically need a noticeably deeper or stronger section than a simply supported span of the same length.

Worked Example: Checking a Timber Floor Joist Under a UDL

Consider a timber joist spanning 4.0m, simply supported at each end, carrying a uniformly distributed load of 3.0 kN/m (a typical combined dead plus live load allowance for a domestic floor). Maximum bending moment: M = wL²/8 = 3.0 × 4.0² ÷ 8 = 3.0 × 16 ÷ 8 = 6.0 kNm. Maximum shear force (at the supports): V = wL ÷ 2 = 3.0 × 4.0 ÷ 2 = 6.0 kN. For deflection, using the standard UDL formula δ = 5wL⁴ ÷ (384EI): with a typical structural softwood joist (E ≈ 9,500 N/mm² = 9.5 kN/mm², and I for a 47×195mm joist ≈ 29.0 × 10⁶ mm⁴), converting units carefully (w in N/mm, L in mm): δ = 5 × 3.0 × 4000⁴ ÷ (384 × 9,500 × 29.0×10⁶) ≈ 12.3mm. Checking against the common serviceability limit of span/360 for floors: 4000 ÷ 360 ≈ 11.1mm. This joist is marginally over the usual deflection limit, which in practice means either reducing the span, going to a deeper joist section, reducing joist spacing, or getting an engineer to check whether a less conservative limit applies — illustrating exactly why bending strength and deflection are two separate checks that can each independently fail.

What Common Timber and Steel Section Sizes Suit Typical Domestic Spans?

These are rough, illustrative starting figures for early planning only — every real beam or joist must be checked (or specified) against the actual load, span, and timber/steel grade by the calculation above or by a structural engineer, since the figures below assume typical domestic loading and nothing unusual such as a water tank, loft conversion, or structural wall bearing on the beam.