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

Un corpo rigido sottoposto a tre forze che agiscono in tre punti diversi è chiamato membro a tre forze.
La linea d'azione di queste forze deve essere concorrente, ad eccezione delle forze parallele in cui le linee d'azione sono parallele.
Si consideri un cassonetto collegato a un supporto per perni nel punto A e un perno attaccato a un cilindro idraulico nel punto B.
Il cilindro idraulico è un elemento a due forze in equilibrio. La forza dovuta al peso agisce attraverso il baricentro e le forze di reazione dovute al supporto agiscono nel punto A.
Il primo passo consiste nel disegnare un diagramma a corpo libero del sistema che includa tutte le forze che agiscono sul cassonetto.
Le equazioni di equilibrio della forza e del momento possono essere utilizzate per determinare le forze incognite F, A e F,CB.
Quindi, la condizione di equilibrio del momento nel punto A calcola la forza FCB.
La condizione di equilibrio della forza lungo la direzione verticale fornisce la forza di reazione verticale.
Allo stesso modo, applicando la condizione di equilibrio della forza lungo la direzione orizzontale si ottiene la forza di reazione orizzontale.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 230.</li>
	<li>Birra, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. e Self, B.P. (2019). Meccanica vettoriale per ingegneri \u2012 Statica e dinamica. New York: McGraw-Hill. Pagine 196</li>
</ol>

corpo a tre forze

Three Force Member

Un corpo rigido soggetto a tre forze che agiscono su tre punti, è conosciuto come un corpo a tre forze. Queste forze devono avere linee d'azione concorrenti, ad eccezione delle forze parallele, dove le linee d'azione sono parallele.

Ad esempio, considera un cassonetto collegato ad un supporto a perno al punto A, e ad un perno collegato a un cilindro idraulico al punto B.

<img alt="Figure 1" src="/files/ftp_upload/14274/14274_Figure_1v3.jpg" style="text-align: center; height: 300px;" />

In questo caso, il cilindro idraulico è un membro a due forze in equilibrio. La forza dovuta al peso agisce attraverso il centro di gravità e le forze di reazione dovute al supporto agiscono sul punto A.

Per risolvere le forze sconosciute FA e FCB, il primo passo consiste nel creare un diagramma di corpo libero di tutto il sistema, includendo tutte le forze che agiscono sul cassonetto.

<img alt="Figure 2" src="/files/ftp_upload/14274/14274_Figure_2v2.png" style="text-align: center; height: 250px;" />

Successivamente, possono essere utilizzate le equazioni di equilibrio delle forze e dei momenti, per determinare i valori delle forze sconosciute.

<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 condizione di equilibrio del momento al punto A fornisce il valore della forza FCB di 24,08 kN. Nel frattempo, la condizione di equilibrio delle forze lungo la direzione verticale determina la forza di reazione verticale FAy di 9,74 kN. Allo stesso modo, applicando la condizione di equilibrio delle forze lungo la direzione orizzontale si ottiene la forza di reazione orizzontale FAx di 25,74 kN.

Corpo A Tre Forze

Un corpo rigido sottoposto a tre forze che agiscono in tre punti è noto come membro a tre forze. Queste forze devono avere linee d'azione concorrenti, tranne ...

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Ingegneria Meccanica

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Equilibrium of a Rigid Body

Equilibrio di un corpo rigido

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TERMINI E CONCETTI CHIAVE

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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