# Column Buckling Load Calculator (Euler) Calculate the Euler critical buckling load of an axially loaded column: P_cr = π²·E·I/(K·L)². Supports pinned-pinned (K=1), fixed-free (K=2), fixed-pinned (K=0.7), fixed-fixed (K=0.5). Returns effective length, radius of gyration, slenderness ratio λ, and critical stress σ_cr. > Canonical page: https://elysiatools.com/en/tools/column-buckling-load - **Category:** Math & Numbers - **Keywords:** Euler buckling, critical load, P_cr, slenderness ratio, effective length, column buckling, elastic stability, mechanics of materials, civil engineering ## Overview The Column Buckling Load Calculator (Euler) computes the critical buckling load and critical stress for axially loaded columns using the Euler buckling formula. By inputting the column's material properties, cross-sectional geometry, length, and end support conditions, you can quickly determine key elastic stability parameters including effective length, radius of gyration, and slenderness ratio. ## Inputs - **End Condition** (select) - **Young's Modulus E (GPa)** (number): Elastic modulus (200 for steel, 70 for aluminum, 25–35 for concrete). - **Moment of Inertia I (mm⁴)** (number): Second moment of area about the buckling axis. - **Cross-Section Area A (mm²)** (number): e.g. 1000 - **Column Length L (m)** (number): e.g. 3 - **Decimal Places** (number) ## When to use - When designing structural columns or struts to ensure they do not fail due to elastic buckling under axial compressive loads. - When analyzing how different end support conditions, such as fixed-fixed or fixed-free, affect the effective length and load capacity of a column. - When calculating the slenderness ratio and critical stress of a member to verify if Euler's elastic buckling theory is applicable. ## How it works - Select the column's end support condition to determine the effective length factor (K). - Input the material's Young's Modulus (E) in GPa, the cross-section's moment of inertia (I) in mm⁴, the cross-sectional area (A) in mm², and the column length (L) in meters. - The calculator computes the effective length, radius of gyration, and slenderness ratio. - The tool applies Euler's formula to output the critical buckling load (P_cr) and the critical buckling stress (σ_cr). ## Use cases - Verifying the structural stability of steel columns in building frames under axial loads. - Comparing the load-bearing capacity of different column support configurations during preliminary structural design. - Solving mechanics of materials problems involving elastic column buckling and slenderness limits. ## Frequently asked questions ### What end conditions does this calculator support? It supports pinned-pinned (K=1.0), fixed-free (K=2.0), fixed-pinned (K=0.7), and fixed-fixed (K=0.5) boundary conditions. ### What units should I use for the inputs? Input Young's Modulus in GPa, moment of inertia in mm⁴, cross-sectional area in mm², and column length in meters. ### How is the radius of gyration calculated? It is calculated as the square root of the moment of inertia divided by the cross-sectional area. ### When is Euler's buckling formula valid? It is valid for long, slender columns where failure is governed by elastic buckling rather than material yielding. ### What outputs does the calculator provide? It outputs the effective length, radius of gyration, slenderness ratio, critical buckling load (in N and kN), and critical stress (in MPa). ## Related tools - [Active Earth Pressure (Rankine)](https://elysiatools.com/en/tools/active-earth-pressure): Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. 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