Structural
Simple Beam Deflection Calculator (Uniform Load)
For a simply supported beam carrying a uniform load, this calculator returns the maximum moment, end shear, bending stress and midspan deflection, plus the span-to-deflection ratio. It is a classic textbook check, not a design. For estimation only; a licensed PE must design.
Formula
For a simply supported beam with uniform load w: M = wL²/8, V = wL/2, Δ = 5wL⁴/(384EI). Units: w is converted from lb/ft to lb/in (÷ 12) and L from ft to in (× 12) so deflection comes out in inches with E in psi and I in in⁴. Bending stress fb = M (in-lb) ÷ S (in³).
Worked example
A 2x12 (I = 177.98 in⁴, S = 31.64 in³, E = 1,600,000 psi) spanning 14 ft with 300 lb/ft: M = 300 × 14² ÷ 8 = 7,350 ft-lb. V = 2,100 lb. fb = 7,350 × 12 ÷ 31.64 = 2,788 psi. Δ = 5 × 25 × 168⁴ ÷ (384 × 1,600,000 × 177.98) = 0.91 in, or L/184. That fails a typical L/360 live load limit and exceeds the allowable bending stress of most lumber, so a single 2x12 is not adequate here.
Assumptions and limits
- Simple supports, prismatic beam, linear elastic material, small deflections.
- Lateral torsional buckling, bearing, shear stress, notches, creep and load duration factors are not checked.
- Use E and allowable stresses from the NDS Supplement or AISC Manual for the actual material and grade.
- For estimation only. A licensed Professional Engineer (PE) must design and stamp any structural, foundation or life-safety element.
Frequently asked questions
What deflection limit should I use?
IRC Table R301.7 limits floor members to L/360 under live load and many roof members to L/240 or L/180. IBC Table 1604.3 has similar limits.
Where do I find E and I for lumber?
The American Wood Council's NDS Supplement lists section properties (I, S) for standard dressed lumber sizes and reference design values (E, Fb) by species and grade.
Can I use this to size a beam for my house?
No. It can show whether a member is obviously undersized, but a licensed engineer must design beams that carry real loads, including load combinations, connections and code adjustments.