All beam formula

Beam Deflection

δ = (W × L³) / (48 × E × I)

Load (W in kN): Length (L in m): Elastic Modulus (E in N/m²): Moment of Inertia (I in m⁴): Calculate Deflection

Bending Stress

σ = (M × y) / I

Bending Moment (M in kNm): Distance from Neutral Axis (y in m): Moment of Inertia (I in m⁴): Calculate Bending Stress

Elastic Lateral Buckling

Pcr = (π² × E × I) / (L²)

Elastic Modulus (E in N/m²): Moment of Inertia (I in m⁴): Length (L in m): Calculate Buckling Load

Torsional Stress

τ = (T × r) / J

Torque (T in Nm): Radius (r in m): Polar Moment of Inertia (J in m⁴): Calculate Torsional Stress

Safe Load

Safe Load = (σ_allow × Z) / FOS

Allowable Stress (N/m²): Section Modulus (Z in m³): Factor of Safety: Calculate Safe Load

Combined Axial & Bending Stress

σ = (P/A) ± (M*y/I)

Axial Load (P in kN): Area (A in m²): Bending Moment (M in kNm): Distance (y in m): Moment of Inertia (I in m⁴): Calculate Combined Stress

Eccentric Loading

σ = (P/A) ± (P*e*y/I)

Load (P in kN): Area (A in m²): Eccentricity (e in m): Distance (y in m): Moment of Inertia (I in m⁴): Calculate Eccentric Stress

Unsymmetrical Bending

σ = (M × y × cosθ) / I

Bending Moment (M in kNm): Distance (y in m): Moment of Inertia (I in m⁴): Angle (θ in degrees): Calculate Unsymmetrical Stress

Strain Energy

U = (M² × L) / (2 × E × I)

Bending Moment (M in kNm): Length (L in m): Elastic Modulus (E in N/m²): Moment of Inertia (I in m⁴): Calculate Strain Energy

Natural Frequency

ωₙ = √(k/m), T = 2π/ωₙ

Stiffness (k in N/m): Mass (m in kg): Calculate Natural Frequency

Fixed-End Moments

UDL: FEM = (w × L²)/12
Point Load: FEM = (P × L)/8

UDL

w (kN/m): L (m): FEM (UDL)

Point Load

P (kN): L (m): FEM (Point Load)

Rolling & Moving Loads (Animated ILD)

ILD visualization for shear and bending moment as load moves.

Beam Length (L in m): Animate ILD