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

欧拉公式用于确定柱的临界载荷，而割线公式用于计算偏心载荷作用下柱的变形和应力。
此处假设柱体最初为直的均质棱柱，且所有应力均在比例极限范围内。
在实际中，柱体材料并非理想状态，柱体的设计基于从大量实验室实验中得出的经验公式。
例如，许多钢柱在施加轴向荷载后，记录其数据，并逐渐增加荷载直至发生破坏。
对于大长细比柱，可采用欧拉公式预测其失稳破坏，临界应力取决于弹性模量。
另一方面，对于短柱，破坏主要由屈服强度引起。
对于中等长度的柱，其失效过程较为复杂，同时取决于屈服强度和弹性模量。
对于上述每种情况，需对经验公式进行适当调整，以设计钢柱。

中心荷载下的柱设计

Design of Columns under a Centric Load

<div>
 中心荷载下的柱设计是结构工程中的一个基本方面，这对于确保结构的稳定性和完整性是不可或缺的。欧拉和割线公式对于理解和计算柱的临界荷载和变形行为是至关重要的，这为安全有效的结构设计提供了基础。
 
 欧拉公式适用的假设是一根完美的、直的、均质的棱柱，并且它在材料的弹性极限内运行。根据欧拉公式，临界荷载直接取决于柱的弹性模量及其几何特性。然而，必须注意的是，欧拉公式对于长而细长的柱子来说是最为准确的，因为屈曲是主要能够使其失效的模式。但在实际应用中，用于柱的材料通常会表现出缺陷，并且它们在荷载下的状态并不总是符合理想的弹性假设。在现实生活中的柱可能会在初始状态时出现轻微弯曲、横截面积变化或材料不一致的情况，所有的这些因素都会显著影响到其承载能力和失效模式。因此，从大量的实验室实验中所得出的通式可以用来设计能够承受实际条件的支柱。这些通式考虑了材料的特性，例如屈服强度和弹性模量，以及柱的长度、横截面的尺寸和边界条件。
 
 对于使用欧拉公式来准确预测其长度足以失效的柱，其中的临界应力主要取决于材料的弹性模量。在超过材料的屈服强度之前，这些柱会因屈曲而导致失效。短柱的失效主要是由于材料能够达到其屈服强度，从而会导致挤压失效而不是屈曲。在这种情况下，设计的重点是材料的屈服强度而不是弹性。中等长度的柱会呈现出更为复杂的情况，其中屈服强度和弹性模量都会影响其失效。这些柱的通式经过调整，便能够分析材料屈服和弹性屈曲之间复杂的相互作用。
 
 这些因素确保了立柱的完整设计，无论其长度和使用的材料是怎样的，都会是坚固、可靠的，并且能够支撑预期的荷载而不会发生断裂。
 
</div>

欧拉公式用于确定柱的临界载荷，而割线公式用于计算柱的变形和应力……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Columns

KEY TERMS AND CONCEPTS

关键术语与概念

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

euler-s-formula-to-columns-with-other-end-conditions

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.

mechanical engineering

Column Buckling and Load Design Basics

Description

Transcript