Joist Span Calculator: Allowable Span from Mechanics

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Joist Span Calculator: Allowable Span from Mechanics

Solves the allowable joist span from bending, shear and deflection directly, and tells you which limit governs. Your design values in, hand checkable spans out.

The three limits

Enter E, Fb and Fv adjusted for your species, grade, moisture and load duration, including the repetitive member factor where it applies. The tool solves the mechanics; your design standard supplies the material values, and the building official has the final say.

Diagram of floor joists at regular spacing between supports, with the allowable span governed by bending, shear or deflection
Joists at regular spacing: each carries a strip of floor set by the spacing, and the shortest of three limit spans governs.

Where joist span numbers actually come from

Every joist span table is the output of the same three limit states: bending strength, shear strength and a deflection cap. The tables package those results for standard species and loads, and they are copyrighted. The limits themselves are plain mechanics, and that is what this tool solves. It reports all three candidate spans and tells you which one governs, which the tables never show.

The load comes from your spacing: a joist at 16 in on centre carries a 16 in wide strip of floor. With 40 psf live and 10 psf dead that strip weighs 66.7 plf. From there each limit produces its own maximum span, and the shortest of the three is the answer.

A worked example you can check by hand

Take a 2 by 10 at 16 in on centre under 40 psf live plus 10 psf dead, with E of 1400000 psi, Fb of 900 psi, Fv of 135 psi and a deflection limit of L/360. Bending allows the span where wL^2/8 equals Fb times S, which solves to about 13.9 ft. The deflection limit allows about 14.5 ft, and shear would allow well over 30 ft. Bending governs, so the allowable span is 13.9 ft, and the calculator lands on exactly that.

Notice how close bending and deflection sit for this case. Drop the live load or stiffen the limit to L/480 and deflection takes over as the governing check. The table in the tool makes that swap visible the moment it happens.

Using it honestly

The design values matter as much as the mechanics. E, Fb and Fv change with species, grade, moisture and load duration, and floor joists usually earn a repetitive member increase on Fb. Pull those numbers from your own design standard or supplier literature and enter them as adjusted values. This tool checks a uniformly loaded, simply supported joist; vibration performance, cantilevers and point loads are separate questions, and the building official has the final word on all of it.

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