Name: equilibrium conditions for a supported plate
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 31 s
Channel: JoVE

Considere una placa rectangular apoyada en los puntos A, B y C y sometida a fuerzas externas.
Las fuerzas y los momentos de acoplamiento que actúan sobre la placa pueden reducirse a la fuerza resultante equivalente y al momento de acoplamiento resultante que actúan en el punto A.
Aquí, la línea que pasa por los puntos A y B no es paralela al eje y. Las ecuaciones de equilibrio de la placa se pueden describir utilizando el conjunto alternativo de ecuaciones.
La primera ecuación se cumple si la fuerza resultante no tiene componente x y es paralela al eje y.
La segunda ecuación se cumple si el momento resultante en el punto A es cero.
La tercera ecuación establece que el momento en el punto B es cero, lo que implica que la componente y de la fuerza resultante sobre el sistema es cero.
Un segundo conjunto de ecuaciones de equilibrio alternativas establece que la suma de los momentos en los puntos A, B y C es cero. Estas ecuaciones se cumplen cuando estos puntos no son colineales.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. Págs. 220.</li>
</ol>

conjuntos alternativos de ecuaciones de equilibrio

Alternative Sets of Equilibrium Equations

Cuando se analiza el comportamiento de las estructuras, los ingenieros a menudo confían en el concepto de equilibrio. Esto se refiere al estado en el que todas las fuerzas y momentos que actúan sobre un sistema se equilibran entre sí, lo que resulta en la ausencia de movimiento o rotación netos. En muchos casos, el equilibrio se puede describir mediante un conjunto de ecuaciones estándar. Sin embargo, en algunas situaciones, se deben utilizar conjuntos alternativos de ecuaciones de equilibrio para describir con precisión el comportamiento del sistema. Un ejemplo de dicha situación se puede observar en una placa rectangular soportada en los puntos A, B y C, y sometida a fuerzas externas, como se muestra en la figura. <img alt="Figure 1" src="/files/ftp_upload/14272/14272_PT_Figure_1v2.svg" style="text-align: center; height: 200px;"> En este caso, la fuerza y el momento de torsión que actúan sobre la placa se pueden reducir a la fuerza resultante equivalente y al momento de torsión resultante que actúan en el punto A. Sin embargo, la recta que pasa por los puntos A y B no es paralela al eje y. Esto significa que las ecuaciones de equilibrio estándar no serán suficientes para describir el comportamiento de la placa. En su lugar, se deben utilizar conjuntos alternativos de ecuaciones de equilibrio. <img alt="Equation 1" src="/files/ftp_upload/14272/14272_Equation_1v2.svg" style="text-align: center; height: 55px;"> La primera ecuación establece que la fuerza resultante que actúa sobre la placa no debe tener una componente en el eje x y debe ser paralela al eje y. Esto asegura que no haya movimiento horizontal de la placa. La segunda ecuación establece que el momento resultante en el punto A debe ser cero. Esto asegura que no haya rotación de la placa alrededor del punto A. La tercera ecuación establece que el momento en el punto B debe ser cero. Esto implica que la componente y de la fuerza resultante en el sistema es cero, lo cual es necesario para el equilibrio. Juntas, estas tres ecuaciones describen con precisión el comportamiento de la placa y garantizan que permanezca en un estado de equilibrio. Otro conjunto de ecuaciones alternativas de equilibrio que se pueden utilizar en ciertas situaciones establece que la suma de los momentos en los puntos A, B y C debe ser cero. <img alt="Equation 2" src="/files/ftp_upload/14272/14272_Equation_2v2.svg" style="text-align: center; height: 55px;"> Este conjunto de ecuaciones se cumple cuando estos puntos no son colineales, lo que significa que no caen todos en la misma línea. En los casos en que los puntos son colineales, las ecuaciones se reducen al conjunto estándar de ecuaciones de equilibrio.

Conjuntos Alternativos de Ecuaciones de Equilibrio

Al analizar el comportamiento de las estructuras, los ingenieros a menudo se basan en el concepto de equilibrio. Esto se refiere al estado en el que todas las fuerzas y momentos ...

alternative-sets-of-equilibrium-equations

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Equilibrium of a Rigid Body

Equilibrio de un cuerpo rígido

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 applied force and couple moment can be reduced to an equivalent resultant force and resultant couple moment at point A. However, the line through points A and B is not parallel to the y-axis. Because of that, the standard equations do not fully describe the plate’s behavior.

The alternative set requires the resultant force on the plate to have no x-component. It must be parallel to the y-axis, which prevents horizontal motion. It also requires the resultant moment at point A to be zero, so the plate does not rotate around point A. A third equation sets the moment at point B to zero, which means the y-component of the resultant force must also be zero for equilibrium.

Another alternative set states that the sum of the moments at points A, B, and C must be zero. This works when the three points are not collinear, meaning they do not lie on the same line. If the points are collinear, these equations reduce to the standard equilibrium equations.

Equilibrium Conditions for a Supported Plate

equilibrium-conditions-for-a-supported-plate

conditions of equilibrium

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alternative sets of equilibrium equations

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...

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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...

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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 supported plate can be analyzed with alternative equilibrium equations, including force balance and zero moments at points A, B, and C.

Equilibrium Conditions for a Supported Plate | 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

Equilibrium Conditions for a Supported Plate

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