Guide · Pin + roller
Simply supported beam deflection
The default for floor joists, rafters and lintels sitting on two walls: pin one end, roller the other, both free to rotate. Peak deflection sits at (or near) midspan; peak moment too.
Formulas
Center P: δ = PL³/48EI · R = P/2 · M = PL/4
P at a (b = L−a): RA = Pb/L · M = Pab/L @ a
Full UDL: δ = 5wL⁴/384EI · R = wL/2 · M = wL²/8
P at a (b = L−a): RA = Pb/L · M = Pab/L @ a
Full UDL: δ = 5wL⁴/384EI · R = wL/2 · M = wL²/8
Off-center loads
The peak follows the load: δat P = Pa²b²/3EIL, and the true maximum sits between the load and center at Pb(L²−b²)3/2/9√3LEI. The calculator finds the exact station — no need to guess midspan.
Floor check shortcut
Convert area load to line load first: w = psf × tributary width. A 40 psf live load on joists at 16 in centers is 53 plf per joist — then δ = 5wL⁴/384EI against L/360.