Name: solving a three-force member example
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 27 s
Channel: JoVE

Un corps rigide soumis à trois forces agissant en trois points différents est appelé un élément à trois forces.
La ligne d’action de ces forces doit être concurrente, à l’exception des forces parallèles où les lignes d’action sont parallèles.
Considérons une benne à ordures reliée à un support de goupille au point A et une goupille fixée à un cylindre hydraulique au point B.
Le vérin hydraulique est un élément à deux forces en équilibre. La force due au poids agit par le centre de gravité, et les forces de réaction dues au support agissent au point A.
La première étape consiste à dessiner un schéma du système qui comprend toutes les forces agissant sur la benne.
Les équations d’équilibre des forces et des moments peuvent être utilisées pour déterminer les forces inconnues F, A, et F, CB.
Ensuite, la condition d’équilibre de moment au point A calcule la force FCB.
La condition d’équilibre de force le long de la direction verticale donne la force de réaction verticale.
De même, l’application de la condition d’équilibre des forces le long de la direction horizontale donne la force de réaction horizontale.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 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 196</li>
</ol>

membre à trois forces

Three Force Member

Un corps rigide soumis à trois forces agissant sur trois points est connu comme un membre à trois forces. Ces forces doivent avoir des lignes d'action concourantes, à l'exception des forces parallèles, où les lignes d'action sont parallèles. Par exemple, considérons une benne reliée à un support à broche au point A et une broche attachée à un vérin hydraulique au point B. <img alt="Figure 1" src="/files/ftp_upload/14274/14274_Figure_1v3.jpg" style="text-align: center; height: 300px;"> Dans ce cas, le vérin hydraulique est un membre à deux forces en équilibre. La force due au poids agit à travers le centre de gravité et les forces de réaction dues au support agissent au point A. Pour résoudre les forces inconnues FA et FCB, la première étape consiste à créer un diagramme de corps libre de tout le système, y compris toutes les forces agissant sur la benne. <img alt="Figure 2" src="/files/ftp_upload/14274/14274_Figure_2v2.png" style="text-align: center; height: 250px;"> Ensuite, les équations d'équilibre des forces et des moments peuvent être utilisées pour déterminer les valeurs des forces inconnues. <img alt="Equation 1" src="/files/ftp_upload/14274/14274_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 2" src="/files/ftp_upload/14274/14274_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 3" p="" src="/files/ftp_upload/14274/14274_PT_Equation_3v2.svg" style="text-align: center; height: 13px;"> La condition d'équilibre des moments au point A donne la valeur de la force FCB comme étant de 24,08 kN. Pendant ce temps, la condition d'équilibre des forces le long de la direction verticale détermine la force de réaction verticale FAy comme étant de 9,74 kN. De même, en appliquant la condition d'équilibre des forces le long de la direction horizontale, on obtient la force de réaction horizontale FAx comme étant de 25,74 kN.

Membre à Trois Forces

Un corps rigide soumis à trois forces agissant en trois points est connu sous le nom d’élément à trois forces. Ces forces doivent avoir des lignes d’action concurrentes, sauf...

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Mechanical Engineering

Génie mécanique

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Equilibrium of a Rigid Body

Équilibre d'un corps rigide

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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 A.

The solution starts with a free-body diagram of the entire system. That diagram includes every force acting on the dumpster. Then the force and moment equilibrium equations are used to solve for the unknown forces.

Taking moments about point A gives the cylinder force F CB as 24.08 kN. The vertical force equilibrium condition gives the vertical reaction F Ay as 9.74 kN. The horizontal force equilibrium condition gives the horizontal reaction F Ax as 25.74 kN.

Solving a Three-Force Member Example

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...

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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...

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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

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

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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 to analyze a three-force member with a free-body diagram, equilibrium equations, and a dumpster example to find unknown reaction forces.

Solving a Three-Force Member Example | JoVE K12

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Solving a Three-Force Member Example

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