Name: statics problem-solving steps for beams
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Problem Solving in Statics

A estática é o estudo dos corpos em equilíbrio, e a resolução de problemas em estática envolve várias etapas.
O primeiro passo é formular o problema. Considere um exemplo de uma carga pontual atuando em uma viga simplesmente apoiada a uma certa distância de um dos suportes.
Aqui, as forças de reação e o momento fletor em pontos-chave precisam ser estimados.
Várias suposições são feitas para resolver esse problema. Pequenas quantidades, como a largura da viga, são negligenciadas em comparação com grandes quantidades, como seu comprimento. Convenções de sinais apropriadas são usadas para representar a direção das grandezas físicas.
Para análises posteriores, diagramas de corpo livre são desenhados. Eles ajudam a analisar as forças que atuam na viga em uma seção específica e fornecem as equações matemáticas para a força resultante e o momento fletor.
A expressão do momento fletor é usada para calcular as forças de reação substituindo todas as forças e as distâncias correspondentes.
O momento fletor no ponto c é dado pelo produto de Ra e d1.
Os resultados são relatados usando diagramas de força de flexão e cisalhamento.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 12</li>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. pág. 14, 15 e 14</li>
	<li>Oliveira, J.L.; Kraige, L.G. e Bolton, J.N. (2020). Engenharia Mecânica \u2012 Estática. Hoboken, Nova Jersey: John Wiley. pág. 14, 15 e 17</li>
</ol>

resolução de problemas na estática

A resolução de problemas na estática é um aspecto crucial da engenharia e da física que envolve a resolução de questões relacionadas a corpos em estado de equilíbrio. Geralmente, a resolução de problemas requer várias etapas para alcançar um resultado preciso. Essas etapas são cruciais para garantir que a solução seja precisa e prática.

A situação física e a modelagem matemática devem ser consideradas; no entanto, é desafiador representar todas as situações físicas usando a modelagem matemática. Com a ajuda de aproximações e suposições, os problemas podem ser formulados.

Ao fazer aproximações, distâncias muito pequenas em comparação com distâncias maiores são negligenciadas. Por exemplo, a largura de um retângulo pode ser negligenciada se ela for algumas ordens de grandeza menor que o comprimento. Aproximações de ângulos pequenos podem ser usadas quando o deslocamento angular é menor que as outras dimensões. Um exemplo de aproximação é quando a força está distribuída por todo o corpo ou objeto; isso pode ser considerado uma carga pontual. As suposições dependem puramente da precisão do resultado exigido.

O primeiro passo na resolução de problemas na estática é formular o problema. Formular o problema envolve entender o cenário físico e determinar as variáveis dentro dele. Por exemplo, considere um exemplo de uma carga pontual atuando em uma viga simplesmente apoiada à certa distância de um dos apoios. Nesse cenário, as forças de reação e os momentos fletores em pontos-chave precisam ser estimados.

Após formular o problema, diversas suposições são feitas para resolvê-lo. Suposições como negligenciar quantidades pequenas em comparação com grandes, como negligenciar a largura da viga em comparação com o comprimento da viga, são feitas. Os momentos fletores em ambas as extremidades apoiadas da viga são presumidos como zero. Outra suposição é que a viga não se deforma devido ao carregamento. Além disso, convenções de sinal apropriadas que representam a direção das grandezas físicas são usadas. Essas suposições ajudam a simplificar o problema e criar uma solução mais direta.

O próximo passo na resolução de problemas na estática é preparar diagramas de corpo livre. Diagramas de corpo livre são usados para analisar as forças atuando na viga em determinada seção e determinar equações matemáticas para a força líquida e o momento fletor. Esses diagramas ajudam a identificar a soma das forças atuando sobre o corpo e a definir a direção e a equação para o momento fletor. Eles fornecem uma imagem clara da situação em consideração e ajudam a determinar os próximos passos a serem tomados.

Uma vez que os diagramas de corpo livre são feitos, os cálculos podem ser feitos para determinar as forças de reação. O cálculo do momento fletor permite a determinação dos momentos fletores que podem então ser usados para calcular as forças de reação. Esse cálculo estima com precisão as forças de reação envolvidas no cenário.

Os diagramas de momento fletor e força cortante mostram a variação dos momentos fletores e forças cortantes ao longo do comprimento da viga. Esses diagramas auxiliam os engenheiros a entender melhor o estado do corpo em consideração e identificar possíveis áreas de preocupação.

Para representar os resultados, símbolos algébricos podem ser usados. Ao realizar cálculos numéricos, unidades consistentes precisam ser usadas em todas as equações. Outro passo fundamental é verificar a resposta. Erros nas etapas de cálculo podem ser reavaliados substituindo as soluções nas equações algébricas.

Resolução de problemas na estática

A resolução de problemas em estática é um aspecto crucial da engenharia e da física que envolve a resolução de questões associadas a corpos em estado de equilíbrio. ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

An Introduction to Statics

Uma Introdução à Estática

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

statics problem-solving steps for beams

Statics problem-solving uses a step-by-step method to analyze bodies in equilibrium, especially beams. It is an important part of physics and engineering because the goal is to find practical and accurate answers for real situations. The process usually starts with a physical situation and then turns it into a mathematical model.

That model often needs approximations and assumptions. Very small distances can be ignored when they are much smaller than the main dimensions, such as beam width compared with beam length. Small angle approximations can also be used when the angular displacement is smaller than the other dimensions. A distributed force may be treated as a point load. The exact assumptions depend on how accurate the final result needs to be.

The first major step is to formulate the problem. This means understanding the situation and identifying the variables involved. For example, a point load can act on a simply supported beam at a certain distance from one support, and the reaction forces and bending moments at key points must be estimated.

After the problem is set up, more assumptions are made to simplify the analysis. The width of the beam may be neglected compared with its length. The bending moments at both supported ends are assumed to be zero, and the beam is assumed not to deform under the loading. Sign conventions are also used so the directions of physical quantities stay consistent.

Free-body diagrams come next. A free-body diagram shows the forces acting on a beam or on a chosen section of it. These diagrams help form equations for net force and bending moment, and they give a clear picture of the situation being studied.

Once the free-body diagrams are ready, calculations can be carried out to find the reaction forces. Bending moment calculations support this step and help determine the forces at the supports. The results can then be shown with bending force diagrams and shear force diagrams, which display how bending and shear change along the beam. Algebraic symbols are used to represent the results, and consistent units must be used in every numerical calculation. The final step is to verify the answer by substituting the solution back into the algebraic equations and checking for errors.

Statics Problem-Solving Steps for Beams

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problem solving in statics

Statics problem-solving uses a step-by-step method to analyze bodies in equilibrium, especially beams. It is an important part of physics and engineering because the goal is to find practical and accurate answers for real situations. The process usually starts with a physical situation and then turns it into a mathematical model. That model often needs approximations and assumptions. Very small distances can be ignored when they are much smaller than the main dimensions, such as beam width...

key terms and concepts

Learn the step-by-step statics method for beams, including assumptions, free-body diagrams, reaction forces, bending moments, shear diagrams, and answer checks.

Statics Problem-Solving Steps for Beams | 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

Texas Essential Knowledge and Skills

Physics

PHYS.1

IPC.1.G

Chemistry and Physics

IPC.1

new-york-state-science-learning-standards

New York State Science Learning Standards

engineering-technology-and-applications-of-science

Engineering, Technology, and Applications of Science

Engineering Design

HS-ETS1-2.

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Statics Problem-Solving Steps for Beams

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