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

A rigid body subjected to three forces acting at three different points is called a three-force member.
The line of action of these forces must be concurrent, except for parallel forces where the lines of action are parallel.
Consider a dumpster connected to a pin support at point A and a pin attached to a hydraulic cylinder at point B.
The hydraulic cylinder is a two-force member in equilibrium. The force due to the weight acts through the center of gravity, and the reaction forces due to the support act at point A.
The first step involves drawing a free-body diagram of the system that includes all the forces acting on the dumpster.
The force and moment equilibrium equations can be used to determine the unknown forces FA and FCB.
Then, the moment equilibrium condition at point A calculates the force FCB.
The force equilibrium condition along the vertical direction gives the vertical reaction force.
Similarly, applying the force equilibrium condition along the horizontal direction yields the horizontal reaction force.

drie-krachtlid

Three Force Member

Een stijf lichaam dat onderworpen is aan drie krachten die werken op drie punten staat bekend als een drie-krachtlid. Deze krachten moeten samenvallende lijnen van actie hebben, behalve bij parallelle krachten, waarbij de lijnen van actie parallel zijn. Neem bijvoorbeeld een vuilnisbak die verbonden is met een pen ondersteuning op punt A en een pen die bevestigd is aan een hydraulische cilinder op punt B. <img alt="Figure 1" src="/files/ftp_upload/14274/14274_Figure_1v3.jpg" style="text-align: center; height: 300px;"> In dit geval is de hydraulische cilinder een evenwichtige twee-krachtlid. De kracht als gevolg van het gewicht werkt door het zwaartepunt, en de reactiekrachten als gevolg van de ondersteuning werken op punt A. Om de onbekende krachten FA en FCB op te lossen, omvat de eerste stap het maken van een vrijlichaamsdiagram van het volledige systeem, inclusief alle krachten die op de vuilnisbak werken. <img alt="Figure 2" src="/files/ftp_upload/14274/14274_Figure_2v2.png" style="text-align: center; height: 250px;"> Vervolgens kunnen de kracht- en moment evenwichtvergelijkingen worden gebruikt om de waarden van de onbekende krachten te bepalen. <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;"> De momentevenwichtsvoorwaarde op punt A geeft de waarde van de kracht FCB als 24.08 kN. Ondertussen bepaalt de krachtevenwichtsvoorwaarde in de verticale richting de verticale reactiekracht FAy als 9.74 kN. Op dezelfde manier levert het toepassen van de krachtevenwichtsvoorwaarde in de horizontale richting de horizontale reactiekracht FAx als 25.74 kN.

Drie-krachtlid

A rigid body subjected to three forces acting at three points is known as a three-force member. These forces must have concurrent lines of action, except ...

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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

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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...

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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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mechanical engineering

Solving a Three-Force Member Example

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