Name: two-force body equilibrium
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 30 s
Channel: JoVE

Considérez une lampe suspendue verticalement aux bras avec son extrémité supérieure serrée.
Si l’élément du bras est isolé et que les deux forces agissent en deux points, A et B, sans charge entre les deux, on parle d’un élément à deux forces. Ici, la nature des forces est soit de traction, soit de compression.
Pour que l’élément à deux forces soit en équilibre, les forces FA et FB doivent être égales en intensité mais opposées en direction.
Pour satisfaire la condition d’équilibre du moment, FA et FB doivent avoir la même ligne d’action.
En général, un membre à deux forces peut avoir plusieurs forces agissant sur les points A et B qui sont représentées comme la force résultante aux points A et B.
Si l’intensité et la direction de la force d’un côté sont connues, la force de l’autre côté peut être calculée. Cela réduit le nombre d’inconnues de l’équation d’équilibre.
L’élément à deux forces n’est pas nécessairement droit ; il peut être plié ou courbé et est utilisé pour analyser la structure des fermes, des cadres et des machines.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. Pages 230.</li>
	<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. Pages 195.</li>
</ol>

membre à force égale

Two Force Member

L'équilibre d'un corps à deux forces est un cas particulier qui est souvent rencontré dans des applications pratiques. Un corps à deux forces est un corps rigide soumis à seulement deux forces externes. Pour que ce corps soit en équilibre, les deux forces doivent avoir la même magnitude, la même ligne d'action et des directions opposées. <img alt="Figure 2" src="/files/ftp_upload/14273/14273_PT_Figure_1v2.svg" style="text-align: center; height: 350px;"> Considérons l'une des plaques représentées soumise à deux forces, F1 et F2, qui agissent aux points A et B respectivement. Si la plaque est en équilibre, alors la somme des moments de F1 et F2 par rapport à n'importe quel axe doit être nulle. En additionnant les moments autour du point A, nous pouvons montrer que le moment de F2 doit être nul. Par conséquent, sa ligne d'action doit passer par le point A. De même, en additionnant les moments autour du point B, nous pouvons montrer que la ligne d'action de F1 doit passer par le point B. Cela signifie que les deux forces ont la même ligne d'action – la ligne joignant A et B. De plus, il peut être montré que les deux forces ont la même magnitude et des directions opposées. Cela peut être vu à partir des équations ΣFx = 0 et ΣFy = 0, où les forces s'annulent les unes les autres. Lorsque plusieurs forces agissent aux points A et B, les forces agissant à A peuvent être remplacées par leur résultante F1, et leur résultante F2 peut remplacer celles agissant à B. Un corps à deux forces peut être généralement défini comme un corps rigide soumis à des forces agissant à seulement deux points. Il est important de noter que, dans tous les cas, les résultantes F1 et F2 doivent avoir la même ligne d'action, la même magnitude et des directions opposées pour assurer l'équilibre du corps.

Membre à force égale

L’équilibre d’un corps à deux forces est un cas particulier que l’on rencontre souvent dans les applications pratiques. Un corps à deux forces est un corps rigide qui est ...

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Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Equilibrium of a Rigid Body

Équilibre d'un corps rigide

KEY TERMS AND CONCEPTS

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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 works at point B. Summing the moments about point B shows that the line of action of F1 must pass through point B. So both forces lie on the line joining A and B.

The force balance also requires ΣFx = 0 and ΣFy = 0. These equations show that the two forces have the same magnitude and opposite directions, so they cancel each other out. When several forces act at A and B, each group can be replaced by a resultant force. Those resultants must still share the same line of action, the same magnitude, and opposite directions for the body to stay in equilibrium.

Two-Force Body 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

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 a two-force body stays in equilibrium by using moment balance, force balance, and the rules for line of action, magnitude, and direction.

Two-Force Body 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

Two-Force Body Equilibrium

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