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

Considere uma placa retangular apoiada nos pontos A, B e C e sujeita a forças externas.
As forças e os momentos de casal que atuam na placa podem ser reduzidos à força resultante equivalente e ao momento de par resultante que atuam no ponto A.
Aqui, a reta que passa pelos pontos A e B não é paralela ao eixo y. As equações de equilíbrio da placa podem ser descritas usando o conjunto alternativo de equações.
A primeira equação é satisfeita se a força resultante não tiver componente x e for paralela ao eixo y.
A segunda equação é satisfeita se o momento resultante no ponto A for zero.
A terceira equação afirma que o momento no ponto B é zero, o que implica que o componente y da força resultante no sistema é zero.
Um segundo conjunto de equações de equilíbrio alternativo afirma que a soma dos momentos nos pontos A, B e C é zero. Essas equações são satisfeitas quando esses pontos não são colineares.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 220.</li>
</ol>

conjuntos de equações de equilíbrio alternativos

Alternative Sets of Equilibrium Equations

Ao analisar o comportamento de estruturas, os engenheiros frequentemente contam com o conceito de equilíbrio. Isso se refere ao estado em que todas as forças e momentos atuando em um sistema se equilibram, resultando em nenhum movimento ou rotação líquida. Em muitos casos, o equilíbrio pode ser descrito por um conjunto de equações padrão. No entanto, em algumas situações, conjuntos alternativos de equações de equilíbrio devem ser usados para descrever com precisão o comportamento do sistema.

Um exemplo de tal situação pode ser observado em uma chapa retangular apoiada nos pontos A, B e C e submetida a forças externas, conforme mostrado na figura.

<img alt="Figure 1" src="/files/ftp_upload/14272/14272_PT_Figure_1v2.svg" style="text-align: center; height: 200px;" />

Nesse caso, a força e o momento de casal atuando na chapa podem ser reduzidos à força resultante equivalente e ao momento de casal resultante atuando no ponto A. No entanto, a reta que passa pelos pontos A e B não é paralela ao eixo y. Isso significa que as equações de equilíbrio padrão não serão suficientes para descrever o comportamento da chapa. Em vez disso, conjuntos alternativos de equações de equilíbrio devem ser usados.

<img alt="Equation 1" src="/files/ftp_upload/14272/14272_Equation_1v2.svg" style="text-align: center; height: 55px;" />

A primeira equação afirma que a força resultante atuando na chapa não pode ter componente x e deve ser paralela ao eixo y. Isso garante que não haja movimento horizontal da chapa. A segunda equação afirma que o momento resultante no ponto A deve ser zero. Isso garante que não haja rotação da chapa em torno do ponto A. A terceira equação afirma que o momento no ponto B deve ser zero. Isso implica que a componente y da força resultante no sistema é zero, o que é necessário para o equilíbrio. Juntas, essas três equações descrevem com precisão o comportamento da chapa e garantem que ela permaneça em estado de equilíbrio.

Outro conjunto de equações alternativo de equilíbrio que pode ser usado em determinadas situações afirma que a soma dos momentos nos pontos A, B e C deve ser zero.

<img alt="Equation 2" src="/files/ftp_upload/14272/14272_Equation_2v2.svg" style="text-align: center; height: 55px;" />

Esse conjunto de equações é satisfeito quando esses pontos não são colineares, ou seja, não caem todos na mesma linha. Nos casos em que os pontos são colineares, as equações se reduzem ao conjunto padrão de equações de equilíbrio.

Conjuntos de Equações de Equilíbrio Alternativos

Ao analisar o comportamento das estruturas, os engenheiros geralmente confiam no conceito de equilíbrio. Isso se refere ao estado em que todas as forças e momentos ...

alternative-sets-of-equilibrium-equations

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Equilibrium of a Rigid Body

Equilíbrio de um Corpo Rígido

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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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

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Equilibrium Conditions for a Supported Plate

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