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Analyse a simply supported beam or cantilever under a point load and a uniform load: reactions, maximum shear, bending moment and deflection, with shear force and bending moment diagrams.
Also covers: Bending moment calculator ยท Shear force diagram ยท Beam deflection calculator ยท Cantilever beam calculator ยท Simply supported beam calculator
Leave empty for none.
Distance from the left support.
Leave empty for none.
Steel โ 200 GPa, aluminium โ 69 GPa, softwood โ 10 GPa. Optional: needed for deflection.
From the section tables. Optional: needed for deflection.
Maximum bending moment
24 kNยทm
Sagging, at x = 3 m from the left support.
Left support Rโ
11 kN
Right support Rโ
11 kN
Maximum shear force
11 kN
Maximum deflection
4.712 mm
at x = 3 m ยท span/1,270
Beam and loads
Shear force diagram
Bending moment diagram
Working
Linear-elastic beam theory with small deflections and the beam's own weight ignored (add it to w). The defaults are a 6 m steel IPE 300 section (I = 8,356 cmโด). Use it to learn and check; have structural designs verified by a qualified engineer.
Simply supported (pinned at the left, roller at the right) or a cantilever fixed at the left.
A point load at any position, a uniform load over the whole span, or both. Add Young's modulus and the second moment of area to get deflection.
Reactions, maximum shear force, maximum bending moment and its position, maximum deflection, and the shear force and bending moment diagrams.
Standard elastic beam formulas: for a simply supported beam, M_max = PL/4 for a central point load and wLยฒ/8 for a uniform load; for a cantilever, M = PL and wLยฒ/2 at the wall. Combined loads are added by superposition.
A property of the cross-section's shape that measures its resistance to bending. Find it in steel section tables (e.g. 8,356 cmโด for an IPE 300 about its strong axis) or calculate it, e.g. bhยณ/12 for a rectangle.
By the usual sign convention, sagging (concave up) moments are positive and hogging (concave down) moments are negative. A cantilever hogs along its whole length.
It's for learning and checking hand calculations. Real designs need load factors, the beam's self-weight, buckling and code checks, and sign-off by a qualified engineer.
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