Name: column buckling and load design basics
Uploaded: 2024-05-23T13:00:08.000Z
Duration: 1 min 17 s
Channel: JoVE

La fórmula de Euler se utiliza para determinar la carga crítica de una columna, y la fórmula de Secant se utiliza para calcular las deformaciones y tensiones de una columna bajo cargas excéntricas.
Aquí, se asumió que la columna es inicialmente un prisma recto homogéneo y todas las tensiones están dentro del límite proporcional.
En la vida real, los materiales de las columnas no son ideales, y el diseño de una columna se basa en una fórmula empírica derivada de numerosos experimentos de laboratorio.
Por ejemplo, los datos de muchas columnas de acero se registran para una carga céntrica aplicada y la aumentan hasta que fallan.
Para columnas grandes, la fórmula de Euler se puede usar para predecir la falla, y la tensión crítica depende del módulo de elasticidad.
Por otro lado, para columnas cortas, la falla ocurre principalmente debido al límite elástico.
Para las columnas de longitudes intermedias, la falla es un proceso complejo y depende tanto del rendimiento como del módulo de elasticidad.
Para cada uno de los casos anteriores, la fórmula empírica se modifica ligeramente para diseñar columnas de acero.

diseño de columnas bajo carga céntrica

El diseño de columnas bajo carga céntrica es un aspecto fundamental de la ingeniería estructural y es crítico para garantizar la estabilidad e integridad de las estructuras. Las fórmulas de Euler y Secante son fundamentales para comprender y calcular los comportamientos críticos de carga y deformación de las columnas, proporcionando una base para un diseño estructural seguro y eficaz.

La fórmula de Euler es aplicable bajo el supuesto de que la columna es un prisma perfecto, recto y homogéneo, y que opera dentro del límite elástico del material. La carga crítica, según la fórmula de Euler, depende directamente del módulo de elasticidad de la columna y de sus propiedades geométricas. Sin embargo, es esencial señalar que la fórmula de Euler es más precisa para columnas largas y delgadas donde el pandeo es el modo predominante de falla. En aplicaciones prácticas, los materiales utilizados para las columnas presentan imperfecciones y su comportamiento bajo carga no siempre se alinea con los supuestos elásticos ideales. Las columnas de la vida real pueden tener ligeras curvaturas iniciales, variaciones en el área de la sección transversal o inconsistencias de materiales, todo lo cual puede influir significativamente en su capacidad de carga y modos de falla. Por lo tanto, se utilizan fórmulas empíricas derivadas de extensos experimentos de laboratorio para diseñar columnas que puedan soportar condiciones del mundo real. Estas fórmulas empíricas tienen en cuenta las propiedades del material, como el límite elástico y el módulo de elasticidad, así como la longitud de la columna, las dimensiones de la sección transversal y las condiciones de contorno.

Para columnas que son lo suficientemente largas como para que la fórmula de Euler prediga la falla con precisión, la tensión crítica depende principalmente del módulo de elasticidad del material. Estas columnas fallan por pandeo antes de que se exceda el límite elástico del material. La falla en columnas cortas se debe predominantemente a que el material alcanza su límite elástico, lo que lleva a una falla por aplastamiento en lugar de pandeo. En estos casos, el diseño se centra en el límite elástico del material más que en su elasticidad. Las columnas de longitud intermedia presentan un escenario complejo donde tanto el límite elástico como el módulo de elasticidad influyen en la falla. Las fórmulas empíricas para estas columnas se ajustan para considerar la compleja interacción entre la fluencia del material y el pandeo elástico.

Estas consideraciones aseguran que el diseño de las columnas, independientemente de su longitud y del material utilizado, sea robusto, confiable y capaz de soportar las cargas previstas sin fallar.

Diseño de columnas bajo carga céntrica

La fórmula de Euler se utiliza para determinar la carga crítica de una columna, y la fórmula de Secant se utiliza para calcular las deformaciones y tensiones de una columna.

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Columns

Columnas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Design of Columns under a Centric Load

column buckling and load design basics

Column design under a centric load is a key part of structural engineering. It helps engineers keep buildings and other structures stable and safe. The main tools used here are Euler’s formula and Secant’s formula.

Euler’s formula is used when a column is assumed to be perfect, straight, and uniform. It also applies when the material stays within its elastic limit. The critical load from Euler’s formula depends on the material’s modulus of elasticity and the column’s shape.

This formula works best for long, slender columns, where buckling is the main failure mode. Buckling means the column bends sideways under compression before the material itself is crushed. Real columns are not ideal, so small bends, changes in cross-section, and material flaws can affect their strength.

Because of these real-world limits, engineers also use empirical formulas based on laboratory tests. These formulas include material properties such as yield strength and modulus of elasticity, along with column length, cross-sectional size, and boundary conditions. They help design columns that can handle practical loads more reliably.

The failure mode also depends on column length. Long columns usually fail by buckling before the yield strength is reached. Short columns usually fail by crushing when the material reaches yield strength instead of buckling.

Columns of intermediate length are more complicated. Their failure depends on both yield strength and modulus of elasticity. Empirical formulas for these columns account for the interaction between elastic buckling and material yielding, which supports safe design across different column types.

Column Buckling and Load Design Basics

stability of structures

Critical Load and Structure Stability

Structural stability is an important idea in mechanical engineering. It helps engineers design buildings, vehicles, and machines that stay safe and efficient under load. A simple model for studying this behavior uses two rods joined at a pivot point O with a torsional spring, which is a spring that resists twisting, at the pivot. The setup is similar to a scissor jack used to lift a car. In the example, the linkage arms are vertical, which matches the case where the vehicle has been raised as...

euler&#39;s formula for pin-ended columns

Critical Buckling Load in Pin-Ended Columns

Critical buckling load in pin-ended columns is a key idea in structural engineering. It explains when a column under compressive axial load becomes unstable and starts to buckle. A pin-connected column with a centric load F at one end has a reaction force of F' = -F at the other end. When the applied load rises above the critical load, buckling begins. To find the critical load, the column PQ can be treated like a vertical beam. Point O is chosen on the elastic curve of the beam at a distance...

euler&#39;s formula to columns with other end conditions

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Euler Buckling for Different Column Supports

Euler buckling explains how a column can fail when it is compressed. In structural engineering, it helps predict the critical load, which is the load level where a column is likely to buckle. The formula uses the modulus of elasticity, the moment of inertia of the cross-section, and the column length. The same idea also helps describe critical stress. Critical stress is found by dividing the critical load from Euler's formula by the cross-sectional area of the column. This leads to the...

euler&#39;s formula to columns: problem solving

euler-s-formula-to-columns-problem-solving

Spring-Loaded Column Buckling Analysis

Spring-loaded column buckling analysis uses static equilibrium to find the critical load in a rigid bar system. The setup has two equal-length rigid bars, AB and BC, joined at pivot point B. A tension spring with constant k is attached to B and pulls horizontally. A vertical load F is applied at point A, and the bars rotate around the pivot like a knee joint. As point B moves, the spring stretches by an amount X. The spring then pushes back against the sideways motion of B. To study the...

eccentric loading

Column Bending Under Off-Center Load

Eccentric loading shows how a column bends when a force is applied off-center. In structural engineering, this matters because the load no longer acts along the centroidal axis, so the column sees both direct compression and bending stress. The off-center force can be treated as two parts. One part is a centric load F that acts along the column’s axis. The other part is a couple moment created by the eccentricity, or distance, between the load and the centroidal axis. To study the column...

design of columns under a centric load

Column design under a centric load is a key part of structural engineering. It helps engineers keep buildings and other structures stable and safe. The main tools used here are Euler’s formula and Secant’s formula. Euler’s formula is used when a column is assumed to be perfect, straight, and uniform. It also applies when the material stays within its elastic limit. The critical load from Euler’s formula depends on the material’s modulus of elasticity and the column’s shape. This formula works...

design of columns under an eccentric load

design-of-columns-under-an-eccentric-load

Eccentric Load Stresses in Structural Columns

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure. The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part...

key terms and concepts

Learn how Euler’s and Secant’s formulas help engineers design columns under centric load, and why long, short, and intermediate columns fail differently.

Column Buckling and Load Design Basics | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Column Buckling and Load Design Basics

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