Beam & Load Inputs

Support type

Simply supported Cantilever

Load type

Geometry

Span length L m

Load magnitude

Distributed load w kN/m

Material

Cross-section

Width b mm

Depth h mm

Consistent SI units used internally (N, mm, MPa). Results shown in kN, kN·m, mm.

Support reactions

Left / Fixed reaction R_A—

Right reaction R_B—

Fixed-end moment M_A—

Shear & moment

Max shear V_max—

Max moment M_max—

Location of M_max—

Deflection

Max deflection δ_max—

Location of δ_max—

Limit L/360 (approx.)—

Section & stress

I (moment of inertia)—

S (section modulus)—

Bending stress σ = M/S—

Allowable σ_all—

Utilization ratio—

Material used

E (modulus)—

Material—

Enter values and click Calculate.

Core formulas used by this free beam calculator

Simply supported — UDL (w over full span)

Quantity	Formula
Reactions	R_A = R_B = wL / 2
Max shear	V_max = wL / 2
Max moment	M_max = wL² / 8 (at midspan)
Max deflection	δ_max = 5wL⁴ / (384 EI)

Simply supported — point load P at midspan

Quantity	Formula
Reactions	R_A = R_B = P / 2
Max moment	M_max = PL / 4
Max deflection	δ_max = PL³ / (48 EI)

Simply supported — point load P at distance a

Quantity	Formula
Reactions	R_A = Pb/L , R_B = Pa/L (b = L−a)
Max moment	M_max = Pab / L (under the load)

Cantilever — tip load P / full UDL

Case	M_max	δ_max
Tip point load	PL	PL³ / (3EI)
Full UDL	wL² / 2	wL⁴ / (8EI)

Bending stress: σ = M / S · S = I / c · For rectangle: I = bh³/12 , S = bh²/6

How to use this beam load calculator

Choose support type (simply supported or cantilever).
Select load case and enter span + load magnitude.
Pick material (steel or wood) or enter custom E and allowable stress.
Define section: rectangle, steel W-shape preset, or custom I & S.
Click Calculate Beam — results and diagrams update instantly.
Use Print / Save PDF for a clean report.

Typical material values (approximate)

Steel A992 / S355: E ≈ 200 GPa, σ_all ≈ 165–200 MPa (service)
Douglas Fir: E ≈ 12–13 GPa, bending design values often 8–12 MPa (species/grade dependent)
Southern Pine / SPF: E ≈ 9–12 GPa
Oak: E ≈ 11–12 GPa

Important notes

This is a simple beam load calculator for educational and preliminary design use.
Assumes elastic, prismatic beam, small deflections, Euler-Bernoulli theory.
Does not replace full code checks (LRFD/ASD, LTB, shear, connection design, deflection limits per code).
Always verify with current design standards and a licensed engineer for real projects.

Free Beam Load Calculator