Steel Beam Design Calculator: AISC 360 Flexure, Classification and Lateral Torsional Buckling

Heading to the field? Install this site from your browser menu and this tool works with no signal. See how

How to use this tool

Pick your section from the list, set the yield strength, then enter the span and the factored load. Choose whether the load is uniform or a single point load at midspan, because that changes the moment, the shear and the deflection together. Switch between LRFD and ASD with the toggle, and between kip and foot units and kN and metre units without retyping anything. The verdict banner tells you whether the section works and names the limit state that governed.

The input people get wrong is Lb. It is the distance between points where the compression flange is held sideways, not the span. If your deck braces the top flange at the third points of a 30 foot span, Lb is 10 feet, not 30. Get that one wrong and the tool will happily report a capacity three times higher than the beam really has. If you are not sure how often the flange is actually restrained, use the span. It is the conservative answer. The quick set buttons under the field cover full span, half, third points and continuous bracing.

What the calculation is doing

A steel beam in bending does something slightly counterintuitive. The compression flange behaves a bit like a column, and if nothing holds it sideways it buckles out of plane and drags the rest of the section into a twist. That is lateral torsional buckling, and for a bare steel beam it is usually what decides the capacity, not the strength of the steel.

The code handles it with two lengths. Below Lp the flange is held often enough that the section reaches its full plastic moment, so Mn equals Fy times Zx and nothing is lost. Beyond Lr the beam buckles elastically, well before the steel yields anywhere. Between them the failure is partly inelastic and AISC simply draws a straight line between the two anchor points.

The size of the effect surprises people. Take the W18x50 in the diagram. Braced every 10 feet it carries 370 kip-ft. Leave the same beam unbraced over a 30 foot span and it carries 115 kip-ft. Same steel, same section, less than a third of the capacity.

Classification, and why it is rarely the thing that gets you

Before any buckling check the section has to be classified. The flange ratio is bf over 2tf, the web ratio is h over tw, and both are compared against limits that scale with the square root of E over Fy. Compact means the element reaches yield and holds long enough to form a plastic hinge. Noncompact means it yields but buckles locally before it fully plastifies. Slender means it buckles first.

In practice almost every rolled W shape is compact in both elements at grade 50. The web limit works out near 90.6 and rolled webs do not come close. Flanges are tighter, with a limit around 9.15, and a few heavy column type sections cross it. W14x90 is the classic case: its flange ratio is 10.21, so flange local buckling pulls the design capacity from 589 kip-ft down to 574 kip-ft. Real, but small, which is exactly why classification feels like a formality right up until it is not.

A worked check you can repeat on paper

These are the tool's default values, so you can follow along and land on the same numbers. A 30 foot span, factored uniform load of 3 kip per foot, bracing at the third points so Lb is 10 feet, W18x50 in A992 grade 50.

Zx is 101 cubic inches, so Mp is 50 times 101, which is 5050 kip-inches, or 420.8 kip-ft. Lp is 1.76 times ry times the square root of E over Fy, which is 1.76 times 1.65 times 24.08, giving 69.9 inches or 5.83 feet. Lr works out at 16.97 feet. Your 10 feet sits between them, so the straight line applies. With Cb at 1.14, Mn is 410.8 kip-ft, and 0.90 times that gives a design capacity of 369.7 kip-ft.

Required moment is wL squared over 8, so 3 times 30 squared over 8, which is 337.5 kip-ft. That is 91 percent of capacity, tight but passing. Shear is nowhere near governing, at 45 kips against 192 kips.

Then you check deflection and the whole thing falls apart. At service load the beam drops 1.65 inches against an L over 360 limit of 1.00 inch. It fails serviceability while passing strength. This is ordinary on longer spans, and it is why experienced designers size shallow long span beams on stiffness first and check moment afterwards.

The fix is depth, not weight. A W24x55 is five pounds per foot lighter than the W18x50, yet its moment ratio drops to 0.767 and its deflection to 0.978 inches, so it clears all three checks. Six extra inches of depth did what more steel could not.

Cb is doing more work than you think

Cb accounts for the fact that a segment with varying moment is less prone to buckling than one held at constant peak moment. Leaving it at 1.0 is always safe and often wasteful. For that same W18x50 at 10 feet, Cb of 1.0 gives 324 kip-ft, 1.14 gives 370 kip-ft and 1.32 gives 379 kip-ft. That first step is a 14 percent gain for a number you can justify in one line.

Two values are worth memorising, both from the quarter point formula in F1-1. A simply supported beam under uniform load with no intermediate bracing gives 1.14. The same beam with a single point load at midspan gives 1.32. Both sit on the quick set buttons.

Mistakes that catch people out

Entering the span as Lb. The most common error by a distance. Lb is the spacing of lateral restraints to the compression flange. Fix: count the actual brace points, and when in doubt use the span, which is conservative.

Applying one Cb to the whole beam. Cb belongs to each unbraced segment, not to the member. A beam braced at third points has three segments, each with its own moment diagram and its own Cb. Fix: check the segment with the worst combination of moment and length, which is often not the one carrying peak moment.

Using Cb above 1.0 on a cantilever with a free end. AISC requires Cb equal to 1.0 when the free end of a cantilever is unbraced, because the quarter point logic does not hold there. Fix: set it to 1.0 and take the hit.

Forgetting the construction stage. A composite beam is well braced once the slab has cured, but bare steel carrying wet concrete is not. That temporary condition frequently governs. Fix: run the beam twice, once with the permanent bracing and once with whatever the erector actually provides.

Sizing on strength and checking deflection last. On spans past about 25 feet, stiffness usually decides the section, as the worked check above shows. Fix: start from the depth that satisfies your deflection limit, then confirm moment and shear.

Where the numbers come from, and how this was checked

The engine was verified against the AISC Steel Construction Manual Table 3-2 before this page went live. Across eight shapes from W10x22 to W30x99 the design plastic moment matched to within 0.4 percent, Lp to within 0.1 percent and Lr to within 0.3 percent. The noncompact flange case, W14x90, returned 573.6 kip-ft against the published 574. Chapter G shear matched to within 0.2 percent on four shapes, and the Cb formula reproduced the textbook values of 1.136 and 1.316 exactly.

Two properties are derived rather than read from a table. The effective radius rts comes from equation F2-7 using the warping constant for a doubly symmetric I shape. The clear web depth h is recovered by solving the tabulated area for the fillet radius, which lands within about half a percent of published h over tw values. That second one matters more than it sounds. The crude approximation of depth minus twice the flange thickness runs 3 to 6 percent high, and on a W21x44 that is enough to push the section across the boundary where the shear resistance factor drops from 1.00 to 0.90, understating shear capacity by about 10 percent.

One honest caveat. AISC rounded the constants in equation F2-6 to 1.95 and 6.76. Solve Fcr equal to 0.7Fy exactly and they come out at 1.9491 and 6.7495. The consequence is a step of roughly 0.1 percent in the capacity curve right where the inelastic and elastic branches meet at Lb equal to Lr. This tool follows the published constants, because agreeing with the Manual is more useful to you than agreeing with the algebra. If a hand check has ever disagreed with a textbook by a tenth of a percent near Lr, that is why.

Everything here assumes a doubly symmetric rolled I shape bent about its major axis with no axial load. Singly symmetric sections, built up plate girders, biaxial bending and combined axial and flexure live in other parts of the specification. Check the output against your own copy of AISC 360 before it reaches a drawing.

Related Calculators and Reference

Work the chain in order. Start with the Load Combination Generator to turn service loads into the factored load this page expects. If your section is not in the standard tables, the Section Properties Calculator gives you Ix, Sx and Zx to feed in. For the deflection side of the problem the Beam Deflection Calculator covers four standard load cases, and once the beam runs over more than one span the Continuous Beam Analyzer gives you the real moment diagram rather than a simply supported approximation. When the member carries compression instead of bending, move to the Column Design and Euler Buckling Calculator. For the concrete equivalent of this page, see the RC Beam Design Calculator. The governing document is the AISC Specification for Structural Steel Buildings, published by the American Institute of Steel Construction.