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

オイラーの式は柱の臨界荷重を決定するために使用され、割線の式は偏心荷重下の柱の変形と応力を計算するために使用されます。
ここでは、柱は最初は直線の均質なプリズムであり、すべての応力が比例制限内にあると仮定しました。
実際には、カラムの材料は理想的ではなく、カラムの設計は、多数の実験室実験から導き出された経験的な式に基づいています。
たとえば、多くの鉄骨柱のデータは、適用された中心荷重と破損するまで増加した荷重について記録されます。
大きな柱の場合、オイラーの公式を使用して破損を予測でき、臨界応力は弾性率に依存します。
一方、短いカラムの場合、主に降伏強度が原因で破損が発生します。
中間長のカラムの場合、破損は複雑なプロセスであり、降伏と弾性率の両方に依存します。
上記の各ケースについて、経験式をわずかに変更して鉄骨柱を設計します。

中心荷重下の柱の設計

中心荷重がかかった柱の設計は構造工学の基本的な側面であり、構造の安定性と完全性を確保するために重要です。オイラーと正割の公式は、柱の臨界荷重と変形挙動を理解して計算する上で中心的なものであり、安全で効果的な構造設計の基礎を提供します。

オイラーの公式は、柱が完全で真っ直ぐな均質な角柱であり、材料の弾性限界内で動作するという仮定の下で適用できます。オイラーの公式によれば、臨界荷重は柱の弾性率とその幾何学的特性に直接依存します。ただし、オイラーの公式は、座屈が主な破損モードである長くて細い柱に対して最も正確であることに注意することが重要です。実際の用途では、柱に使用される材料には不完全性があり、荷重下での挙動は理想的な弾性の仮定と必ずしも一致しません。実際の柱には、初期のわずかな曲がり、断面積の変化、または材料の不一致が存在する可能性があり、これらすべてが耐荷重能力と破損モードに大きな影響を与える可能性があります。したがって、広範な実験室での実験から導き出された経験式を使用して、実際の条件に耐えられる柱を設計します。これらの経験式では、降伏強度や弾性率などの材料特性に加え、柱の長さ、断面寸法、境界条件も考慮されています。

オイラーの公式で破損を正確に予測できるのに十分な長さの柱の場合、臨界応力は主に材料の弾性率に依存します。これらの柱は、材料の降伏強度を超える前に座屈によって破損します。 短い柱での破損は主に材料が降伏強度に達することが原因であり、座屈ではなく圧潰破損につながります。このような場合、設計では材料の弾性ではなく降伏強度に重点を置きます。中間の長さの柱では、降伏強度と弾性率の両方が破壊に影響を与える複雑なシナリオが示されます。これらの柱の経験式は、材料の降伏と弾性座屈の間の複雑な相互作用を考慮するために調整されています。

これらの考慮事項により、柱の長さや使用される材料に関係なく、柱の設計が頑丈で信頼性が高く、意図した荷重を故障することなく支えられることが保証されます。

オイラーの式は柱の臨界荷重を決定するために使用され、割線の式は...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Columns

カラム

KEY TERMS AND CONCEPTS

主要用語と概念

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

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 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Column Buckling and Load Design Basics

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