Name: constraints in structural equilibrium
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 26 s
Channel: JoVE

El equilibrio del sistema se define no solo por sus ecuaciones, sino también con la ayuda de restricciones. Las restricciones se refieren a las restricciones en el movimiento de un sistema.
Si un sistema está sujeto a un número mínimo de restricciones para asegurar el equilibrio, se dice que está determinado estáticamente.
Para un sistema de este tipo, los soportes de reacción desconocidos se pueden estimar utilizando ecuaciones de equilibrio.
Si se añaden soportes redundantes adicionales al sistema para mantener el equilibrio, éste se vuelve estáticamente indeterminado. Esto significa que el número de restricciones que actúan sobre el sistema es mayor que el número de ecuaciones de equilibrio disponibles para su solución.
Por otro lado, considere un miembro AB conectado a dos soportes de pin en los puntos C y D, de modo que las líneas de acción de las fuerzas reactivas sean concurrentes en el punto C.
La carga aplicada tenderá a hacer que la viga esté parcialmente constreñida, ya que la ecuación de equilibrio no se cumplirá para las condiciones de carga.
Del mismo modo, cuando todas las fuerzas reactivas son paralelas entre sí, se produce una restricción inadecuada.

<ol>
	<li> Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. Págs. 251-254. </li>
</ol>

restricciones y determinación estática

Constraints and Statical Determinacy

En ingeniería estructural, el equilibrio de un sistema no solo se determina mediante sus ecuaciones de equilibrio, sino también con la ayuda de restricciones. Las restricciones se refieren a limitaciones en el movimiento de un sistema. Las combinaciones adecuadas de restricciones pueden minimizar el número total de restricciones necesarias para mantener un sistema en equilibrio mecánico. Cuando esto ocurre, se dice que el sistema es estáticamente determinado. Para estos sistemas, las reacciones de soporte desconocidas se pueden estimar utilizando las ecuaciones de equilibrio. Los sistemas estáticamente determinados son los más fáciles de analizar y diseñar, ya que todas las fuerzas que actúan sobre el sistema se pueden determinar utilizando un número específico de ecuaciones de equilibrio. Por lo general, las ecuaciones de equilibrio involucran la suma de todas las fuerzas que actúan sobre un sistema y la suma de todos los momentos igual a cero. Sin embargo, si se agregan soportes redundantes adicionales al sistema para mantener el equilibrio, este se vuelve estáticamente indeterminado. Esto significa que más restricciones están actuando sobre el sistema de las que hay ecuaciones de equilibrio disponibles para su solución. En sistemas estáticamente indeterminados, los soportes adicionales restringen el movimiento del sistema, pero también crean ecuaciones adicionales. Estas ecuaciones adicionales generalmente se obtienen mediante la deformación del sistema, que se aborda en la mecánica de los materiales. El desafío con los sistemas estáticamente indeterminados es encontrar el número correcto de soportes redundantes para agregar al sistema para que se mantenga el equilibrio sin sobre-configurar el sistema. Además, las restricciones incorrectas se refieren a una situación en la que todas las fuerzas reactivas se encuentran en un solo punto, pasan por un eje común o se vuelven paralelas. Esta condición puede causar inestabilidad en la estructura y debe evitarse en la práctica de ingeniería. Cuando las fuerzas reactivas se cruzan en un solo punto o siguen un eje común, pueden desequilibrar el cuerpo y hacer que se caiga. Del mismo modo, las fuerzas que son paralelas entre sí pueden no poder mantener el equilibrio y pueden provocar fallos estructurales. Es esencial evitar restricciones incorrectas para prevenir condiciones inestables y riesgos potenciales.

Restricciones y determinación estática

En ingeniería estructural, el equilibrio de un sistema no solo está determinado por sus ecuaciones de equilibrio, sino también con la ayuda de restricciones. ...

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

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 be solved from a fixed set of equilibrium equations.

The usual equilibrium equations include the sum of all forces equal to zero and the sum of all moments equal to zero. If extra, redundant supports are added, the system becomes statically indeterminate. That means there are more constraints than equilibrium equations, so the extra reactions cannot be found from equilibrium alone.

For statically indeterminate systems, the extra equations usually come from deformation. This topic is handled in mechanics of materials. The main challenge is choosing the correct number of redundant supports so the structure stays in equilibrium without becoming overconstrained.

Improper constraints can also create instability. This happens when all reactive forces meet at a single point, pass through a common axis, or become parallel. In those cases, the structure may topple or fail to stay balanced, so engineers avoid these conditions in practice.

Constraints in Structural 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

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

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 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 constraints affect structural equilibrium, including statically determinate and indeterminate systems, redundant supports, and unstable constraint patterns.

Constraints in Structural 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

Constraints in Structural Equilibrium

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