Name: sizing beams for safe bending loads
Uploaded: 2024-05-23T12:59:46.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

Design of Prismatic Beams for Bending

O processo de dimensionamento de vigas prismáticas sujeitas a flexão começa com a determinação da tensão admissível para o material escolhido.
A tensão permitida é geralmente obtida a partir de uma tabela de propriedades do material ou especificações de projeto. Alternativamente, pode ser calculado dividindo a resistência final do material por um fator de segurança adequado.
Em seguida, são desenhados os diagramas de força de corte e de momento fletor correspondentes às condições de carga especificadas.
Em seguida, o valor absoluto máximo do momento fletor é calculado usando o diagrama de força de cisalhamento.
O módulo de seção mínimo permitido é então calculado usando o valor absoluto do momento fletor da viga e a tensão permitida.
Quando uma viga de madeira é dimensionada, a relação que caracteriza a forma da sua secção é normalmente especificada. As dimensões desconhecidas são identificadas usando a relação entre as dimensões da viga e o módulo de seção.
Ao dimensionar uma viga de aço laminado, é referida uma tabela que contém as propriedades da viga de aço laminado, e apenas as secções de viga com um módulo de secção superior ou igual ao módulo de secção mínimo exigido são consideradas.

dimensionamento de vigas prismáticas para flexão

O dimensionamento de vigas prismáticas, elementos estruturais com seção transversal uniforme, tem como objetivo garantir a segurança e a integridade estrutural sob carga. O processo de projeto começa determinando a tensão admissível, seja a partir de tabelas de propriedades do material, ou dividindo a resistência última do material por um fator de segurança. Este fator de segurança é essencial para acomodar incertezas e varia dependendo do material – madeira, aço ou concreto – cada um tendo características únicas de resistência e tensão. O seu valor dependerá do material selecionado e do uso pretendido da estrutura.

A seguir, trace diagramas de força cortante e momento fletor para visualizar a distribuição de carga e identificar pontos de tensão máxima de flexão. Esta visualização é fundamental para otimizar as dimensões da viga para maximizar a segurança e a eficiência da viga.

Finalmente, calcule o módulo de seção mínimo que permitirá que a viga resista às tensões de flexão. Módulos mais altos indicam uma resistência maior. Para vigas de madeira, o projetista especifica uma relação de forma da seção transversal que produzirá o módulo desejado. Para vigas de aço, o projetista seleciona seções pré-existentes, garantindo que o módulo da viga exceda o mínimo calculado. Esta seleção garante que a viga possa suportar forças de flexão, mantendo a segurança e estabilidade estrutural.

Esta abordagem sistemática combina considerações de segurança com análise de material e carga, garantindo que a viga escolhida mantém a integridade e fiabilidade da estrutura sob cargas previstas, garantindo, em última análise, o desempenho estrutural a longo prazo.

Dimensionamento de Vigas Prismáticas para Flexão

O processo de dimensionamento de vigas prismáticas sujeitas a flexão começa com a determinação da tensão admissível para o material escolhido.
O estresse permitido é ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Analysis and Design of Beams for Bending

Análise e Dimensionamento de Vigas à Flexão

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

sizing beams for safe bending loads

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable.

The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material and the intended use of the structure.

Timber, steel, and concrete each have different strength and stress behavior, so the design method depends on the material. After selecting the material, the designer plots shear force and bending moment diagrams. These diagrams show how the load is distributed and help locate the points where bending stress is highest.

The final step is to calculate the minimum section modulus needed to resist bending stress. A higher section modulus means greater resistance to bending. For timber beams, the designer chooses a cross-section shape ratio that gives the needed modulus. For steel beams, the designer selects a standard section whose modulus is at least as large as the calculated minimum. This process helps the beam carry bending forces safely and maintain structural integrity over time.

Sizing Beams for Safe Bending Loads

design of prismatic beams for bending

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable. The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material...

prismatic beams: problem solving

Timber Beam Design Under Distributed Load

Timber beam design under a distributed load uses the beam’s size and the wood’s properties to keep the structure safe. The beam’s length and width are known at the start. The timber’s grade and species also matter because they affect the allowable stress, which is the highest stress the material can safely handle. The first step is to treat the beam as a free body. A free-body diagram shows the forces and moments acting on the beam. From this, the support reactions can be found by balancing...

singularity functions for shear

Beam Shear Diagrams with Macaulay Brackets

Beam shear diagrams can be written with singularity functions when the load changes suddenly along the beam. In structural analysis, these functions help show discontinuous shear force with one mathematical expression, even when the loading is complex. They make it easier to describe how shear changes from one point to the next. The method starts with a free-body diagram of the beam. Then the beam is cut at specific points to check the shear force in each section. For a beam with width W and...

singularity functions for bending moment

Beam Load Modeling with Singularity Functions

Singularity functions help model beam loads and bending moments when the loading changes along the beam. They make it possible to write the bending moment with one mathematical expression instead of separate equations for each section. In this method, Macaulay’s brackets are often used to show where a load starts or stops. For a simply supported beam AB, the load is uniform from the midpoint M to the right support B. To find the bending moment, the beam is cut at different points. A cut...

key terms and concepts

Learn how prismatic beams are sized for bending by finding allowable stress, using shear and moment diagrams, and choosing the right section modulus.

Sizing Beams for Safe Bending Loads | JoVE K12

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mechanical engineering

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Sizing Beams for Safe Bending Loads

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