Beam Load & Deflection Calculator
Simply supported beam — max moment, max shear, max deflection, and bending stress under a centered point load or uniformly distributed load.
Max deflection (mid-span)
—
— L/x
Max moment
—
in-lb
Max shear
—
lb
Bending stress
—
psi
Section modulus
—
in³
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How a simply supported beam responds to load
A simply supported beam is the basic case: pinned at one end, roller at the other, free to deflect downward under load. The maximum bending moment, shear, and deflection all occur at predictable points depending on how the load is applied.
Center point load (P at mid-span)
M_max = P × L / 4 (at mid-span)
V_max = P / 2 (at supports)
δ_max = P × L³ / (48 × E × I) (at mid-span)
Uniformly distributed load (w, lb per linear inch)
M_max = w × L² / 8 (at mid-span)
V_max = w × L / 2 (at supports)
δ_max = 5 × w × L⁴ / (384 × E × I)
Bending stress
σ = M / S
S = I / c (c = distance from neutral axis to outer fiber)
For a rectangle with width b and depth h: I = bh³/12, S = bh²/6. Doubling depth multiplies I by 8 and S by 4 — depth always wins over width.
Deflection limits (IBC Table 1604.3)
- Floor live load: L/360
- Floor total load: L/240
- Roof live (no ceiling): L/180
- Roof live (plaster ceiling): L/360
- Cantilever (rule of thumb): L/180 live, L/120 total
The calculator above reports the deflection ratio so you can compare directly. δ < L/360 is generally serviceable for floor framing.
Modulus of elasticity (typical values)
- Structural steel (A36 / A992): E = 29,000,000 psi
- Aluminum 6061-T6: E = 10,000,000 psi
- Douglas-fir-larch (Select Structural): E = 1,800,000 psi
- Southern Pine #1: E = 1,700,000 psi
Frequently asked questions
Deflection formula?
Center point: PL³/(48EI). UDL: 5wL⁴/(384EI).
Max floor deflection?
L/360 live load, L/240 total per IBC Table 1604.3.
What is moment of inertia?
Stiffness in bending. Rectangle: I = bh³/12. Doubling depth multiplies I by 8.
Bending stress?
σ = M/S. Compare to material allowable: 24 ksi A36, ~1,500 psi DFL Select Structural.