Name: finding the resultant of distributed loads
Uploaded: 2023-09-22T11:49:32.000Z
Duration: 1 min 13 s
Channel: JoVE

Em aplicações de engenharia, é importante considerar a distribuição de carga ao longo da linha.
A força resultante aplicada devido à carga distribuída é representada como um único vetor, chamado de força resultante.
Considere uma placa plana de formato arbitrário sujeita a carregamento uniforme.
A força que atua em uma área infinitesimal na placa tem uma magnitude equivalente ao elemento de volume diferencial.
A força resultante que atua na placa é calculada somando todas as forças diferenciais que atuam em toda a superfície da placa.
A integração sobre a área da placa nos dá uma expressão para calcular a magnitude da força resultante, que também é igual ao volume total abaixo do diagrama de carga distribuída.
A localização da força resultante é determinada comparando os momentos da força resultante com os de todas as forças diferenciais em torno de seus respectivos eixos.
As expressões obtidas implicam que a linha de ação da força passa pelo centro geométrico ou centróide do volume sob o diagrama de carga distribuída.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica: Estática. Décima quarta edição, Nova Jersey: Pearson. Seção 9.4, pp. 511.</li>
	<li>Cerveja, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Mecânica vetorial para engenheiros. Décima primeira edição, Nova York: McGraw-Hill Education. Seção 5.3 pp. 262.</li>
</ol>

resultante de uma carga distribuída geral

Resultant of a General Distributed Loading

Ao projetar estruturas expostas a cargas não uniformes, é crucial considerar a força resultante e sua localização. Essa força resultante é um único vetor que representa a força líquida aplicada devido à carga distribuída.

Exemplos como a distribuição de carga devido ao vento e a distribuição de carga em uma ponte ilustram como esse conceito é usado para analisar e projetar estruturas seguras e confiáveis ​​sob condições variáveis de carga. A maioria das estruturas, como prédios residenciais, pontes e torres, são projetadas para resistir a cargas de vento não uniformes, que variam com a velocidade e direção do vento. Da mesma forma, as pontes são projetadas para suportar o peso dos veículos que passam por cima delas. No entanto, a distribuição de peso dos veículos não é uniforme e algumas partes da ponte podem sofrer mais estresse e deformação do que outras. É necessário calcular a força resultante atuando nos prédios ou pontes, o que é um problema de distribuição não uniforme de carga.

Para determinar essa força, a magnitude de cada força diferencial atuando em áreas infinitesimais deve ser somada e integrada sobre a área de superfície portadora de carga. A magnitude dessa força resultante é igual ao volume total sob o diagrama de carga distribuída. A localização dessa força resultante pode ser determinada comparando seus momentos com os momentos de todas as forças diferenciais em torno de seus respectivos eixos. Isso implica que a linha de ação desta força passará pelo centro geométrico ou centróide do volume considerado.

Saber onde e quanta força é aplicada a uma estrutura permite que os engenheiros garantam resistência e rigidez suficientes para que a estrutura seja adequada ao propósito. Esses valores também podem mudar com base em condições variáveis ​​de carga, portanto, é essencial considerar essas possíveis mudanças para projetar uma estrutura segura e protegida.

Resultante de uma Carga Distribuída Geral

Ao projetar estruturas expostas a cargas não uniformes, é crucial considerar a força resultante e sua localização. Esta força resultante é uma única ...

resultant-of-a-general-distributed-loading

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Center of Gravity and Centroid

Centro de Gravidade e Centroide

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

finding the resultant of distributed loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load.

This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel more stress and strain than others.

To find the resultant force, the small forces acting on tiny areas are added together with integration over the load-bearing surface. The size of the resultant force equals the total area under the distributed-loading diagram. Its location is found by comparing moments, which means the turning effects of the force about an axis.

The line of action of the resultant passes through the geometric center, or centroid, of the volume under the load diagram. Knowing both the size and location of the force helps engineers judge whether a structure has enough strength and rigidity. Because loading can change, these calculations help support safe and reliable design for buildings, bridges, and other structures.

Finding the Resultant of Distributed Loads

finding-the-resultant-of-distributed-loads

center of gravity

Center of Gravity in Balance and Design

The center of gravity is the point where an object’s weight appears to act. It is the spot used to balance the object most evenly. In mechanics, this point helps explain stability and moments of inertia. The center of gravity does not always sit inside the object’s shape. In some cases, it can lie outside the body. That is why the idea is useful for both simple and more complex shapes. Its location can be found with the principle of moments. The object is divided into very small parts, and...

center of mass

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The center of mass helps explain how an object moves through space. It is the point where the total mass of an object can be treated as concentrated. This idea applies to objects of different shapes and sizes. The center of mass is related to the center of gravity, but they are not the same. The center of gravity is the point where an object’s weight seems to be concentrated. It can be used to balance an object perfectly. Knowing the center of mass also helps predict motion. When a ball is...

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The centroid is the geometric center of a body. It is an important idea in engineering, physics, and mechanics. For many objects, it lies inside the body. A body with holes or cavities can be an exception. For a homogeneous body, the centroid matches the center of mass or the center of gravity. Homogeneous means the material has a uniform density. In that case, the centroid can often be found by balancing the moments of the body’s volume. Symmetry can also help locate the centroid. If a...

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composite bodies

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Composite bodies are made of multiple connected parts that act as one larger object. Each part still has its own weight and center of gravity. To find the center of gravity of the whole body, engineers must account for every part. When the density or specific weight is constant, the center of gravity matches the centroid. The centroid is the geometric center of a shape. This idea is useful when analyzing parts that behave as a single unit. Composite bodies are common in mechanical engineering.

theorems of pappus and guldinus

Surface Area and Volume by Centroid Paths

Pappus and Guldinus theorems help find the surface area and volume of bodies of revolution. A body of revolution is formed when a plane curve or plane area is turned around an axis that does not intersect it. For surface area, a curve is revolved around a non-intersecting axis. A small line element on the curve creates a thin ring as it moves. Adding these ring areas gives the total surface area of the solid. The first theorem says that this surface area equals the length of the generating...

theorems of pappus and guldinus: problem solving

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Pappus and Guldinus Theorems for Surface Area

Pappus and Guldinus's theorems help find the surface area and volume of composite shapes. These rules are useful when a solid is made from simple parts that are hard to measure directly. A cylindrical storage tank with a conical top is one example. The tank can be split into two simple shapes: a cylinder and a cone. To find surface area, the first theorem is used for the solid formed by revolving each generating curve around a non-intersecting axis. The calculation uses the length of the...

resultant of a general distributed loading

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

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key terms and concepts

Learn how engineers combine non-uniform loads into one resultant force, find its location with moments, and apply the idea to bridges and buildings.

Finding the Resultant of Distributed Loads | JoVE K12

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mechanical engineering

Finding the Resultant of Distributed Loads

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