Name: rigid body force balance in equilibrium
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 28 s
Channel: JoVE

Un corps rigide ne subit aucune déformation sous l’influence de forces externes.
Considérons un manège soumis à une force externe F à une distance radiale perpendiculaire r, qui aboutit au moment d’une force autour du point O.
Si plusieurs forces agissent sur le manège, la condition d’équilibre est obtenue lorsque la somme de toutes les forces externes agissant sur lui est nulle.
L’autre condition d’équilibre stipule que la somme de tous les moments autour du point O doit être égale à zéro.
Lorsque le moment est mesuré au point A, il peut être exprimé comme la somme du moment au point O et du produit vectoriel de la distance perpendiculaire et de la force appliquée.
Ces conditions garantissent que le corps ne subit aucun mouvement de translation ou de rotation en équilibre statique.
Seules les forces externes sont considérées ici, car les forces internes à l'intérieur du corps rigide ont la même amplitude et agissent dans des directions opposées, s'annulant mutuellement en raison de la troisième loi du mouvement de Newton.

<ol>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. p. 170</li>
</ol>

conditions d'équilibre

Conditions of Equilibrium

L'équilibre fait référence à un état où un corps rigide n'est soumis à aucun mouvement de translation ou de rotation. Cet état est atteint lorsque la force et le couple agissant sur un corps rigide sont égaux à zéro. Lorsque le système des forces externes aboutit à un résultat net équivalent à zéro, le corps rigide est considéré comme étant en équilibre. Les forces internes ne sont pas prises en compte pour les conditions d'équilibre car elles se produisent sous la forme de paires égales et opposées à l'intérieur du corps, annulant ainsi leur effet mutuel. Par conséquent, ces forces internes ne contribuent pas au mouvement global ou au changement de mouvement du corps rigide. L'équilibre est déterminé par l'équilibre des forces et moments externes agissant sur le corps, car ils sont responsables de la création d'un mouvement de translation ou de rotation. Les conditions nécessaires et suffisantes d'équilibre peuvent être déterminées en établissant l'égalité de la force résultante et du moment à zéro. De plus, les équations vectorielles peuvent être remplacées par six équations scalaires en résolvant chaque force et moment en composantes rectangulaires. Cela implique que les composantes des forces externes dans les directions x, y et z sont équilibrées, et que les moments des forces externes autour des axes x, y et z sont également équilibrés. Si un corps rigide est en équilibre, le système de forces externes n'entraîne aucun mouvement de translation ou de rotation sur le corps. Pour écrire les équations d'équilibre pour un corps rigide, identifiez d'abord toutes les forces agissant sur le corps, puis tracez le diagramme de corps libre correspondant. En plus des forces appliquées à une structure, prenez en compte les réactions exercées sur la structure par ses supports. L'identification correcte de chaque réaction peut aider à résoudre les forces et réactions inconnues. La connaissance des conditions d'équilibre est cruciale pour analyser les problèmes liés aux corps rigides. En déterminant les forces et réactions inconnues et en utilisant les conditions nécessaires et suffisantes d'équilibre, il est possible de prédire le comportement des corps rigides.

Conditions d'équilibre

L’équilibre fait référence à un état dans lequel un corps rigide n’est soumis à aucun mouvement de translation ou de rotation. Cet état est atteint lorsque la force et ...

Education

Enseignement

JoVE Core

Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Equilibrium of a Rigid Body

Équilibre d'un corps rigide

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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 external forces and moments determine whether the body stays balanced. These are the forces that can cause translation or rotation. The necessary and sufficient conditions for equilibrium are found by setting the resultant force and the resultant moment equal to zero.

The vector equations for equilibrium can also be written as six scalar equations. Each force and moment is resolved into rectangular components. This means the external force components in the x, y, and z directions must balance, and the moments about the x, y, and z axes must also balance.

To write equilibrium equations for a rigid body, first identify all forces acting on it. Then draw a free-body diagram. The reactions from supports must also be included. Correctly identifying each reaction helps solve unknown forces and reactions in structures.

Rigid Body Force Balance in Equilibrium

conditions of 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 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...

key terms and concepts

Learn how rigid body equilibrium is determined by balanced external forces and moments, free-body diagrams, and support reactions in high school physics.

Rigid Body Force Balance in Equilibrium | 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

Rigid Body Force Balance in Equilibrium

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