Beam Deflection Calculator

Frequently Asked Questions

How much will a 4x10 Douglas Fir beam deflect under a 500 lb/ft UDL over a 12-foot span?

w = 500/12 = 41.67 lb/in, L = 144 in, E = 1,600,000 psi, I = 98.9 in^4. delta = 5*41.67*144^4/(384*1600000*98.9) = 0.46 in. L/360 = 0.40 in - fails; L/240 = 0.60 in - passes.

What is the L/360 allowable deflection for a 16-foot span?

L/360 = (16*12)/360 = 192/360 = 0.533 inches.

Does load type affect deflection significantly?

Yes. A center point load produces about 60% more deflection than the same total load uniformly distributed over the same span. Third-point loads fall between the two.

What E value should I use for LVL?

Most LVL manufacturers specify E = 1,700,000 to 2,000,000 psi. Use the value from the product's engineering data sheet. A common default is 1,900,000 psi.

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How This Calculator Works

Deflection is the downward bowing of a beam under load. Too much deflection causes floors to feel springy, cracks plaster ceilings, and misaligns doors. This calculator computes mid-span deflection for a simply supported beam (pinned at both ends) under three common load patterns.

Formulas use span L in inches: Uniform distributed load (UDL): delta = 5*w*L^4 / (384*E*I), where w is load in lb/in. Center point load: delta = P*L^3 / (48*E*I). Two equal point loads at third-points: delta = 23*P*L^3 / (648*E*I). Allowable deflection = L_in / 360 for floor beams and L_in / 240 for roof members.

Deflection Limits Explained

Building codes set deflection limits relative to span length:

L/360: required for floor beams supporting plaster or gypsum board ceilings. At a 12-ft span, this is 12*12/360 = 0.40 inches maximum.

L/240: minimum for roof members and some floor applications without brittle ceilings. At 12 ft: 12*12/240 = 0.60 inches.

L/180: minimum for roof rafters in some codes (non-critical finish).

These limits are serviceability checks only. A beam can satisfy deflection and still need a larger size to meet bending stress. Always check both strength and serviceability.

Practical Tips

Deflection is extremely sensitive to span: doubling the span increases deflection by a factor of 8 for point loads and 16 for UDL (because L appears to the 3rd or 4th power). Increasing the beam depth is the most cost-effective way to reduce deflection because I scales with d^3.

The modulus of elasticity E for common sawn lumber: Douglas Fir-Larch #2: 1,600,000 psi; Southern Pine #2: 1,600,000 psi; Hem-Fir #2: 1,400,000 psi; SPF #2: 1,500,000 psi. LVL typically uses E = 1,700,000 to 2,000,000 psi. Enter a custom E if you have manufacturer data for engineered lumber.

FAQ

Which load type should I use?

Use uniform distributed load for joists and beams carrying a uniformly loaded floor or roof. Use center point load for a beam carrying a concentrated load such as a post. Third-point loads model two-point loads such as a beam supporting another beam at each third of the span.

Can I enter a custom beam size?

Select any listed beam size to auto-fill the moment of inertia I. The I values used are: 4x6=20.8 in^4, 4x8=47.6 in^4, 4x10=98.9 in^4, 4x12=177.9 in^4, 6x8=70.7 in^4, 6x10=147.0 in^4, 6x12=263.7 in^4 (calculated from actual dimensions).

What if my beam is continuous over multiple spans?

Continuous beams deflect less than simply supported beams (roughly 4x less for two equal spans). This calculator is for simply supported single-span beams only.

Is this for structural design?

This is a planning and learning tool. Structural design for permitted construction must be performed or reviewed by a licensed engineer.

Beam Deflection Calculator

Frequently Asked Questions

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