Required Moment of Inertia for a Deflection Limit
The inverse of the steel-camber tile: the moment of inertia a simple-span beam needs to hold the uniform-load midspan deflection to a limit, I = 5 w L^4 / (384 E delta_allow). A 1.0 kip/ft, 40 ft beam held to 1.0 in needs Ix about 1,986 in^4; pick a rolled shape with at least that Ix, then verify strength. Common limits are span/360 (LL) and span/240 (total). Sizes for stiffness only; the entered load is the service load. A design aid; the structural drawings govern.
Formula and source
I = 5 w L^4 / (384 E delta_allow), L = span x 12, the inverse of delta = 5 w L^4 / (384 E I); span_over_defl = L / delta_allow.
Simple-span uniform-load midspan deflection (AISC / mechanics of materials), solved for the moment of inertia, by name.
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