Simply Supported Beam Deflection
Max deflection (in)
0.036
How it works
A simply supported beam is supported at both ends with no moment resistance at the supports — it can rotate freely. This configuration is common in floor joists, bridge girders, and shelf brackets. The Simply Supported Beam Deflection Calculator computes maximum deflection and support reactions for common load cases: point load at center, point load at any location, uniformly distributed load (UDL), and partial UDL.
**Why deflection matters** Structural codes limit deflection to prevent cracking of finishes, discomfort from floor bounce, and misalignment of doors/windows. L/360 is the standard limit for floors supporting plaster ceilings (where L is the span). L/240 applies to most other floor applications. L/480 is used for roof members supporting rigid ceilings. Exceeding the allowable deflection doesn't mean the beam fails structurally — it means occupant comfort or finish integrity is compromised.
**Key formula: midpoint deflection for UDL** δ_max = (5 × w × L⁴) / (384 × E × I), where w = load per unit length, L = span, E = modulus of elasticity, I = moment of inertia. The L⁴ exponent is significant: doubling the span increases deflection by a factor of 16. This is why long-span beams require deeper sections.
**Selecting the right beam size** If deflection exceeds allowable, increase the moment of inertia (I) by using a deeper beam. Doubling the depth increases I by a factor of 8 (for rectangular sections), dramatically reducing deflection. Adding a mid-span support cuts deflection by 80%.
All results are for linear elastic behavior under static loads. Consult a licensed engineer for structural design.
Frequently Asked Questions
- Building codes typically limit live-load deflection to L/360 for floors supporting brittle finishes (plaster, tile) and L/240 for floors with non-brittle finishes. L is the span length — a 6 m span has a limit of 6000/360 = 16.7 mm. Total load deflection (dead + live) is often limited to L/240. These are serviceability limits, not strength limits — the beam may be structurally adequate but still fail the deflection check.
- You need: span length (L), load magnitude and distribution (point load P in Newtons, or uniform load w in N/m), the beam's moment of inertia (I in mm⁴ or m⁴ from the cross-section geometry or steel table), and Young's modulus (E — 200 GPa for steel, 70 GPa for aluminum, 10–15 GPa for timber depending on species and grade). Standard steel sections have I values tabulated in AISC or equivalent national standards.
- Adding a support at the midpoint of a simply supported beam converts it to a two-span continuous beam, reducing maximum deflection by approximately 80%. The maximum moment also drops significantly. However, the support introduces a reaction force that must be carried to the foundation, and the beam is now statically indeterminate — moment distribution changes and the beam must be checked at the support location as well as at the spans.
- For a rectangular section, moment of inertia I = b×h³/12. Doubling width (b) doubles I. Doubling depth (h) increases I by 8×. Since deflection ∝ 1/I, doubling depth reduces deflection to 1/8 of the original. This is why structural engineers specify deep, narrow beams rather than wide, shallow ones — depth is far more efficient for controlling deflection. The same principle explains why I-beams concentrate material at the flanges, far from the neutral axis.