Overhanging Beam Calculator
The beam sits on two supports — A at the left end and B a distance L to the right — with a free overhang of length c projecting beyond B.
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Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the span L between the two supports and the overhang length c that projects beyond the right support.
- Enter a point load P at the overhang tip and/or a uniform load w along the overhang (fill either or both).
- Read the two support reactions and the hogging moment over the right support; a negative left reaction means that support must be tied down against uplift.
How it works
The beam sits on two supports — A at the left end and B a distance L to the right — with a free overhang of length c projecting beyond B. All loads here act on the overhang. Taking moments about A eliminates R_A and solves the right reaction directly: R_B = [P·(L+c) + W·(L + c/2)] / L, where W = w·c is the total uniform load on the overhang. Vertical equilibrium then gives R_A = P + W − R_B.
Because the load hangs beyond support B, it creates a hogging (negative) bending moment over B equal to −[P·c + W·(c/2)] — the load times its lever arm back to the support. When the overhang loads are large relative to the span, R_A can come out negative, meaning support A is being lifted rather than pushed down and needs a hold-down or tie. This is a single, clearly-defined load case for first-pass checking; a full analysis would also cover loads on the main span and the sagging moment there.
Worked example
12 kN hung off a 1.5 m overhang on a 5 m span. A beam spans L = 5 m between supports A and B, with a 1.5 m overhang past B carrying a 12 kN point load at its tip (no UDL). Moments about A: R_B × 5 = 12 × (5 + 1.5) = 78, so R_B = 15.6 kN. Vertical equilibrium: R_A = 12 − 15.6 = −3.6 kN — negative, so support A is pulled UP by 3.6 kN and needs a hold-down. Moment at support B = −(12 × 1.5) = −18 kN·m (hogging). The tool reports R_A = -3.6 kN, R_B = 15.6 kN, moment at right support = -18 kN·m.
Common mistakes
- Treating it as a plain simply-supported beam and ignoring the overhang — you miss the hogging moment over the support and the possible uplift at the far support.
- Measuring the overhang from the wrong point: c is the distance from the RIGHT support out to the free end, not from the left support or the beam centre.
- Assuming both reactions are always downward-bearing — a heavy overhang can put support A into net uplift (negative reaction), which must be resisted by anchoring, not left to gravity.
Frequently asked questions
Why is one of my support reactions negative?
A negative reaction means that support is being pulled upward rather than pushed down. When the load on the overhang is large enough, it acts like a see-saw: the overhang end goes down and the far support (A) lifts. Physically you must anchor or tie that support down — otherwise the beam would rotate off it.
Where does the overhang load go — is it carried by the near support?
Most of it is carried by the near support B, which is why R_B exceeds the total load in the worked example (15.6 kN reaction for a 12 kN load). The excess is balanced by the uplift at the far support. Moments about A give R_B directly, then vertical equilibrium gives R_A.
Does this include the bending moment in the main span?
No — this single load case focuses on loads sitting on the overhang and reports the reactions plus the hogging moment over the near support. For loads on the main span, or the maximum sagging moment along the span, use the Simply Supported Beam or Beam Reaction tools alongside this one, and superpose the effects.
Is this safe to use for final structural design?
No. It is a first-pass estimate for checking reactions and the overhang moment. Final design must account for self-weight, load combinations, deflection, buckling, connection capacity and code requirements, and be verified against AS, Eurocode or AISC by a competent structural engineer.
Related tools
- Beam Reaction Calculator
- Simply Supported Beam Calculator
- Bending Stress Calculator
- Fixed-Fixed Beam Moment Calculator
- Column Slenderness Ratio Calculator
- Fatigue Life Estimator
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