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

Consider a rectangular plate supported at points A, B, and C and subjected to external forces.
The forces and couple moments acting on the plate can be reduced to the equivalent resultant force and resultant couple moment acting at point A.
Here the line passing through points A and B is not parallel to the y-axis. The equations of equilibrium of the plate can be described using the alternative set of equations.
The first equation is satisfied if the resultant force has no x-component and is parallel to the y-axis.
The second equation is satisfied if the resultant moment at point A is zero.
The third equation states that the moment at point B is zero, which implies that the y-component of the resultant force on the system is zero.
A second set of alternative equilibrium equations states that the sum of moments at points A, B and C is zero. These equations are satisfied when these points are not collinear.

alternatieve sets van evenwichtsvergelijkingen

Alternative Sets of Equilibrium Equations

Bij het analyseren van het gedrag van structuren maken ingenieurs vaak gebruik van het concept van evenwicht. Dit verwijst naar de toestand waarin alle krachten en momenten die op een systeem werken elkaar in balans houden, waardoor er geen netto beweging of rotatie optreedt. In veel gevallen kan evenwicht worden beschreven door een set standaardvergelijkingen. Echter, in sommige situaties moeten alternatieve sets van evenwichtsvergelijkingen worden gebruikt om het gedrag van het systeem nauwkeurig te beschrijven. Een voorbeeld van zo'n situatie kan worden waargenomen bij een rechthoekige plaat die wordt ondersteund op de punten A, B en C en onderhevig is aan externe krachten, zoals weergegeven in de figuur. <img alt="Figure 1" src="/files/ftp_upload/14272/14272_PT_Figure_1v2.svg" style="text-align: center; height: 200px;"> In dit geval kunnen de kracht en het koppel dat op de plaat werken worden gereduceerd tot de equivalente resulterende kracht en het equivalente resulterende koppel dat op punt A werkt. Echter, de lijn die punten A en B verbindt is niet parallel aan de y-as. Dit betekent dat standaard evenwichtsvergelijkingen niet voldoende zijn om het gedrag van de plaat te beschrijven. In plaats daarvan moeten alternatieve sets van evenwichtsvergelijkingen worden gebruikt. <img alt="Equation 1" src="/files/ftp_upload/14272/14272_Equation_1v2.svg" style="text-align: center; height: 55px;"> De eerste vergelijking stelt dat de resulterende kracht die op de plaat werkt geen x-component mag hebben en parallel moet zijn aan de y-as. Dit zorgt ervoor dat er geen horizontale beweging van de plaat is. De tweede vergelijking stelt dat het resulterende moment op punt A nul moet zijn. Dit zorgt ervoor dat er geen rotatie van de plaat rond punt A is. De derde vergelijking stelt dat het moment op punt B nul moet zijn. Dit impliceert dat de y-component van de resulterende kracht op het systeem nul is, wat noodzakelijk is voor evenwicht. Samen beschrijven deze drie vergelijkingen nauwkeurig het gedrag van de plaat en zorgen ervoor dat deze in een toestand van evenwicht blijft. Een andere set alternatieve evenwichtsvergelijkingen die in bepaalde situaties kan worden gebruikt, stelt dat de som van de momenten op punten A, B en C nul moet zijn. <img alt="Equation 2" src="/files/ftp_upload/14272/14272_Equation_2v2.svg" style="text-align: center; height: 55px;"> Deze set vergelijkingen is voldaan wanneer deze punten niet collineair zijn, wat betekent dat ze niet allemaal op dezelfde lijn vallen. In gevallen waarin de punten collineair zijn, reduceren de vergelijkingen tot de standaard set evenwichtsvergelijkingen.

Alternatieve Sets van Evenwichtsvergelijkingen

When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments ...

alternative-sets-of-equilibrium-equations

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Mechanical Engineering

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Unit 1

Equilibrium of a Rigid Body

Evenwicht van een star lichaam

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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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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.

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Equilibrium Conditions for a Supported Plate

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