Name: constraints in structural equilibrium
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 26 s
Channel: JoVE

システムの平衡は、その方程式だけでなく、制約の助けを借りて定義されます。制約とは、システムのモーションに対する制限を指します。
システムが平衡を確保するために最小数の制約によって保持されている場合、それは静的に決定的であると言われます。
このような系では、未知なる反応支持体を平衡方程式を用いて推定することができます。
平衡を維持するために追加の冗長サポートがシステムに追加されると、静的に不確定になります。これは、システムに作用する制約の数が、その解に使用できる平衡方程式の数よりも大きいことを意味します。
一方、点CとDで2つのピンサポートに接続されたメンバーABを考えてみて、反力の作用線が点Cで並行するようにします。
荷重条件に対して平衡方程式が満たされないため、荷重荷重はビームを部分的に拘束する傾向があります。
同様に、すべての反力が互いに平行である場合、不適切な拘束が発生します。

<ol>
	<li> ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。 ニュージャージー州ホーボーケン:ピアソンプレンティスホール。251-254ページ。 </li>
</ol>

制約と静的決定性

Constraints and Statical Determinacy

構造工学において、システムの平衡は、平衡の方程式だけでなく制約の助けも借りて決定されます。制約とは、システムの運動に対する制限を指します。適切な制約の組み合わせにより、機械的平衡を維持するために必要な制約の総数を最小限に抑えることができます。このような場合、システムは静的決定と言われます。このようなシステムでは、未知の反応力支持は平衡の方程式を使用して推定することができます。

静的決定システムは、分析と設計が最も容易であり、システムに作用するすべての力を特定の数の平衡の方程式を使用して求めることができます。通常、平衡の方程式にはシステムに作用するすべての力の総和とすべてのモーメントの総和がゼロになるという条件が含まれます。

ただし、平衡を維持するためにシステムに余分な支持が追加されると、静的不定となります。これは、解決のために利用可能な平衡の方程式よりもシステムに作用する制約の数が多いことを意味します。静的不定システムでは、追加の支持はシステムの運動を制限しますが、同時に追加の方程式も作成します。これらの追加の方程式は通常、材料力学の下で扱われるシステムの変形によって得られます。静的不定システムの課題は、システムに適切な数の余剰支持を追加して平衡を維持し、システムを過剰に制約しないことです。

さらに、不適切な制約とは、反応力がすべて一点で集まったり、共通の軸を通ったり、平行になったりする状況を指します。このような状態は構造の不安定性を引き起こす可能性があり、工学の実践では避けるべきです。反応力が一点で交差したり共通の軸に従ったりすると、体をバランスから外して転倒させることができます。同様に、互いに平行な力は平衡を保つことができず、構造の破壊につながる可能性があります。不適切な制約を回避することは、不安定な状態や潜在的な危険性を防ぐ上で重要です。

構造工学では、システムの平衡は、その平衡方程式によって決定されるだけでなく、制約の助けを借りても決定されます。...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Equilibrium of a Rigid Body

剛体のつり合い

KEY TERMS AND CONCEPTS

主要用語と概念

constraints in structural equilibrium

Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed.

A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can be solved from a fixed set of equilibrium equations.

The usual equilibrium equations include the sum of all forces equal to zero and the sum of all moments equal to zero. If extra, redundant supports are added, the system becomes statically indeterminate. That means there are more constraints than equilibrium equations, so the extra reactions cannot be found from equilibrium alone.

For statically indeterminate systems, the extra equations usually come from deformation. This topic is handled in mechanics of materials. The main challenge is choosing the correct number of redundant supports so the structure stays in equilibrium without becoming overconstrained.

Improper constraints can also create instability. This happens when all reactive forces meet at a single point, pass through a common axis, or become parallel. In those cases, the structure may topple or fail to stay balanced, so engineers avoid these conditions in practice.

Constraints in Structural Equilibrium

conditions of equilibrium

Rigid Body Force Balance in Equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero. Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body. The...

support reactions

Types of Structural Supports

Types of structural supports control how a coplanar force system moves and reacts under load. A coplanar force system is a set of forces that all lie in the same plane. The supports create reactions at the point of contact. These reactions help keep a structure stable under external forces. Supports work by stopping translation with an equal and opposite force. They can also stop rotation by applying a couple moment in the opposite direction. In structural design, these reactions are important...

internal forces and center of gravity

Forces Inside a Body and Balance

Internal forces and the center of gravity help explain how objects stay in balance. These mechanics ideas matter for structures, machines, and vehicles that must remain stable under different loads and conditions. Internal forces are created inside a body when its particles interact. They can appear as tension, compression, or shear forces. These forces act in collinear pairs with equal magnitude and opposite direction. Between connected parts, they cancel each other and help keep the body in...

alternative sets of equilibrium equations

alternative-sets-of-equilibrium-equations

Equilibrium Conditions for a Supported Plate

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads. In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example. For this plate, the...

two force member

Two-Force Body Equilibrium

A two-force body is a rigid body acted on by only two external forces. In equilibrium, those two forces must have the same magnitude, the same line of action, and opposite directions. This balance is what keeps the body at rest. For a plate with forces F1 and F2 applied at points A and B, equilibrium means the sum of moments about any axis is zero. If moments are summed about point A, the moment from F2 must be zero. That means the line of action of F2 must pass through point A. The same idea...

three force member

Solving a Three-Force Member Example

A three-force member is a rigid body acted on by three forces at three points. The forces must have concurrent lines of action. If the forces are parallel, their lines of action stay parallel instead. A dumpster provides the example used here. It is connected to a pin support at point A and to a pin on a hydraulic cylinder at point B. The hydraulic cylinder acts as a two-force member in equilibrium. The dumpster weight acts through the center of gravity, and the support reaction acts at point...

equations of equilibrium in three dimensions

equations-of-equilibrium-in-three-dimensions

Checking Force Balance in 3D Structures

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body. The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero.

support reactions in three dimensions

3D Support Types for Stability and Motion

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems. A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions. A...

constraints and statical determinacy

Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed. A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can...

key terms and concepts

Learn how constraints affect structural equilibrium, including statically determinate and indeterminate systems, redundant supports, and unstable constraint patterns.

Constraints in Structural Equilibrium | 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

Constraints in Structural Equilibrium

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