Name: critical load and structure stability
Uploaded: 2024-05-23T13:00:07.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Stability of structures

点Oでピンと定数kのねじりばねで接続された2本のロッドを考えます。両方のロッドの端はピンで接続されています。
両方のロッドが完全に整列し、2つの荷重が同じ作用線に沿っている場合、システムは平衡状態を保ちます。
ここで、点Oをわずかに動かして垂直位置に対して小さな角度を作ると、2つのカップルがロッドに作用します。
最初のものは、ポイントOで作用する負荷が加わり、ロッドが垂直から離れることによるものです。
2番目のカップルは、ロッドを垂直位置に戻そうとするねじりスプリング定数によるものです。
これら 2 つのカップルのモーメントの大きさが同じ場合、臨界荷重式が定式化されます。
システムの安定性は、適用される負荷と臨界負荷の比較に依存します。
負荷が臨界負荷を超えると、システムが不安定になります。逆に、適用される負荷が臨界負荷よりも小さい場合、システムは安定しています。

構造の安定性

機械工学では、耐久性があり効率的な構造を設計するには、さまざまな力の下での装置の安定性が重要です。これらの概念を探求する基本的な方法の 1 つは、ピボット点 O で接続された 2 本の棒のような装置を分析することです。この装置には、ピボット点にバネ定数 k のねじりバネが付いています。 この装置は、車のタイヤ交換に使用されるシザージャッキに外観が似ています。この場合、リンケージのアーム (この装置の棒に相当) は完全に垂直になり、車両が可能な限り持ち上げられた場合に対応します。

これらの棒は最初は垂直に配置されており、バネの作用によって回転することができません。同じ大きさで逆方向の 2 つの外部荷重 F と F’ が、棒の長さに沿って同じ作用線を共有するように装置に加えられた場合、装置は平衡状態を保ちます。この位置合わせにより、装置を平衡状態からずらす正味モーメントや力が作用しないことが保証されます。

ただし、ピボット点 O がわずかに横に移動すると、この移動によって垂直からの棒の角度がわずかにずれます。これにより、各棒の端がピボット点に対して回転し、装置に偶力が導入されます。最初の偶力は、点 O での反力支持から生じます。この力は角度を付けて作用し、棒を最初の垂直方向からさらに変位させ、平衡状態から遠ざけようとします。 2 番目の偶力は、ねじりバネの抵抗によって生じ、復元力を発揮して棒を元の垂直位置に戻します。これら 2 つのモーメントが等しい場合、装置は臨界負荷 F_cr の点に達します。 加えられた負荷が臨界負荷を超えると、装置は不安定になります。臨界負荷未満であれば、装置は安定した状態を保ちます。

この原理は構造装置に広く適用でき、建物、車両、機械の安定化などの機械工学設計に広く使用されています。

点Oでピンと定数kのねじりばねで接続された2本のロッドを考えます。両方のロッドの端はピンで接続されています。
両方のロッドが...

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

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 far as possible. The rods are held in that vertical position by the spring. When two equal and opposite forces, F and F', act along the same line as the rods, the system stays in equilibrium because there is no net moment, or turning effect, to move it away from that state.

If point O shifts slightly sideways, the rods tilt a little from vertical. That small change makes each rod rotate about its pin connection and creates couples, which are pairs of forces that cause rotation. One couple comes from the support reaction at O, and it pushes the rod farther from the original position. The other couple comes from the torsional spring, and it acts as a restoring force that tries to bring the rods back to vertical.

The critical load Fcr is the load at which these two moments are equal. If the applied load is below this value, the system remains stable. If the load rises above it, the system becomes unstable. This idea is useful in many structural systems and helps explain why stability matters in engineering design.

Critical Load and Structure Stability

stability of structures

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...

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eccentric loading

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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 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...

design of columns under an eccentric load

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

Eccentric Load Stresses in Structural Columns

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key terms and concepts

Learn how a torsional spring, equal forces, and critical load determine whether a rod system stays stable or becomes unstable in engineering.

Critical Load and Structure Stability | 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。

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Critical Load and Structure Stability

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