Every beam deflects under load. The question is whether it deflects an acceptable amount or enough to crack finishes, bind doors, or feel springy underfoot. Building codes and AISC standards limit deflection to L/240 for floors carrying live load, L/360 for floors supporting brittle finishes like plaster, and L/180 for roof members. Meeting the strength requirement does not automatically satisfy the deflection limit. Many beam selections are governed by stiffness rather than stress.
This guide covers the common loading cases, the deflection formulas that appear most often in field engineering, and how to use W-shape section properties to check a beam before ordering steel or approving a shoring plan.
Simply Supported vs Cantilever Beams
A simply supported beam rests on two supports at its ends and is free to rotate at those supports. This is the most common case: steel beams on column seats, joists on bearing walls, lintels over openings. A cantilever beam is fixed at one end (embedded in a wall or welded to a column) and free at the other. Cantilevered loading produces much larger deflections and moments for the same span and load.
For a simply supported beam with a uniform load, maximum deflection is 5wL^4 / (384EI), where w is load per unit length, L is span, E is modulus of elasticity (29,000 ksi for steel), and I is the moment of inertia. For a cantilever with a uniform load, maximum deflection is wL^4 / (8EI), about 9.6 times more deflection for the same span and load. This is why cantilever spans are typically limited to 40–60 % of the backspan length.
Beam Deflection & Load Calculator
Calculate beam deflection, bending stress, and shear for simple spans and cantilevers with W-shape lookup.
Point Loads vs Uniform Loads
A uniform load is distributed evenly across the beam length. Think of a concrete slab bearing on a steel beam or snow load on a roof purlin. The maximum moment for a simply supported beam is wL²/8 and occurs at midspan. Most floor and roof beams carry primarily uniform loads.
A concentrated (point) load acts at a single location. Equipment pads, column loads transferred through beams, and hoist pick points are common examples. A single point load P at midspan produces a moment of PL/4, lower than the uniform load moment for the same total load, but a deflection of PL³/(48EI). When both point and uniform loads act on the same beam, you can superimpose (add) the deflections from each case calculated separately. Check that the combined deflection stays within limits.
W-Shape Section Properties
Wide-flange (W-shape) beams are the workhorse of structural steel. The designation W16×40 means approximately 16 inches deep and 40 pounds per foot. Deeper beams have dramatically higher moments of inertia. A W16×40 has I = 518 in^4, while a W12×40 (same weight per foot) has only I = 310 in^4. Depth is the most efficient way to increase stiffness.
The section modulus (S = I/c, where c is the distance from neutral axis to extreme fiber) determines bending stress: f = M/S. For AISC ASD (Allowable Stress Design), the allowable bending stress for compact sections is 0.66Fy = 24 ksi for A36 steel or 33 ksi for A992 (50 ksi yield). Check both the stress (using S) and the deflection (using I) when selecting a beam size.
Beam Deflection & Load Calculator
Calculate beam deflection, bending stress, and shear for simple spans and cantilevers with W-shape lookup.
Field Checks and Practical Considerations
Before calculating, verify the actual support conditions. A beam sitting on a 4-inch bearing plate is simply supported. A beam with clip angles bolted to both flanges of a column is a shear connection and still essentially simply supported for bending. A beam with full-penetration welded flange connections to a column is a moment connection. The fixed-end condition reduces midspan deflection by about 60 % compared to simple supports.
Also check for lateral bracing. An unbraced compression flange can buckle sideways before the beam reaches its full bending capacity. Most floor beams are continuously braced by the slab or deck they support. Roof beams and crane runway girders often have the top flange in compression with no lateral restraint between purlins or bracing points. Reduce allowable stress per AISC Chapter F for unbraced length.