Tools › Structures › Beams › Beam Deflection › Example

Simply supported beam under a uniform load: δmax = 5wL⁴/(384EI) for a W12x26

Tool	Beam Deflection
Source	American Institute of Steel Construction (2011). Steel Construction Manual, 14th ed. AISC, Chicago, IL. Table 3-23, case 1; Gere, J. M., and Goodno, B. J. (2013). Mechanics of Materials, 8th ed. Cengage, Stamford, CT. Appendix G, Table G-2.
Level	Undergraduate

Problem

A W12x26 (I = 204 in⁴, E = 29,000 ksi) spans 240 in on simple supports and carries 80 lb/in. Find the reactions, the maximum moment and deflection, the end slopes and the margin against an L/360 deflection limit.

Inputs to Enter

Case: simply supported, uniform load; L = 240 in, w = 80 lb/in, E = 29,000 ksi, I = 204 in⁴ (loaded by default)
Allowable deflection L/360

Open the Beam Deflection tool (loaded with this example)

Answers

R = wL/2 = 9,600 lb; Mmax = wL²/8 = 576,000 lb-in at mid-span
δmax = 5wL⁴/(384EI) = 0.5842 in at mid-span; θ = wL³/(24EI) = 0.007789 rad at the supports
Stiffness k = W/δ = 32,870 lb/in; δallow = L/360 = 0.6667 in → M.S. = +0.14

Notes

The tool solves every case with one singularity-function engine and prints the handbook closed form beside it; the two agree to 1e-9.