Header Sizing Calculator: Bending, Shear and Deflection Checks
Field note: this tool runs entirely in your browser. Load the page before you head out and it keeps working with no signal, and Print or save PDF gives you a clean copy for the truck.
Header Sizing Calculator: Bending, Shear and Deflection Checks
Built up lumber headers checked from mechanics: enter span, load and your own adjusted design values, get all three checks live. No copyrighted span tables, just the physics they were built from.
Adjusted design values E, Fb and Fv depend on species, grade and load duration. Enter values from your own span table or design standard. This tool checks mechanics only and the building official has the final say.
Sizing a header without a span table
A header carries everything above an opening: roof, ceiling, sometimes a floor. Span tables answer the common cases, but they are copyrighted, they hide the mechanics, and they run out the moment your load or your species is not in the table. This tool does what the table did in the first place. It takes your uniform load, your built up section and your adjusted design values, then checks bending, shear and deflection directly.
You supply three material numbers: the modulus of elasticity E, the allowable bending stress Fb and the allowable shear stress Fv, adjusted for your species, grade and load duration. Those come from your own design standard or supplier sheet. The mechanics on top of them is universal and that is what runs here.
A worked example you can check by hand
Take a 6 ft clear span carrying 400 plf, framed with two plies of 2 by 10. The section is 3 in wide and 9.25 in deep, which gives a section modulus of 42.78 in^3 and a moment of inertia of 197.86 in^4. The midspan moment is wL^2/8, which is 1800 lb ft or 21600 in lb, so the bending stress is 21600 divided by 42.78, or about 505 psi. Against an allowable of 900 psi that check passes with room to spare.
Shear at the support is wL/2, or 1200 lb. The peak shear stress in a rectangle is 1.5V/bd, about 65 psi against an allowable of 135 psi. Deflection is 5wL^4/384EI, which works out to 0.042 in against a limit of L/240, which is 0.30 in here. All three checks pass, and the calculator lands on exactly these numbers.
What governs and what to do when it fails
Short headers are almost always governed by bending or shear, long ones by deflection. When a check fails you have two levers: add a ply, which helps bending and shear in direct proportion, or go deeper, which helps bending with the square of depth and deflection with the cube. The table updates live so you can watch which lever actually moves the failing check.
One honest limit: this tool checks a uniformly loaded, simply supported header. Point loads from a girder truss or a post above need a different analysis, and bearing at the jack studs is a separate check. When the numbers are close to the line, that is precisely when the building official and a stamped design earn their keep.