Name: torque and shear in a twisted shaft
Uploaded: 2024-05-23T12:59:40.000Z
Duration: 1 min 18 s
Channel: JoVE

Um eixo PQ é torcido quando submetido a torques iguais e opostos em ambos os lados.
Considere uma seção perpendicular ao eixo do eixo através de um ponto arbitrário R. O diagrama de corpo livre da porção QR mostra as forças de cisalhamento exercidas pela porção PR no QR à medida que o eixo se torce.
Aplicando as equações de equilíbrio à porção QR, pode-se mostrar que as forças de cisalhamento dentro da seção estão relacionadas ao torque interno. Aqui, r representa a distância perpendicular do eixo do eixo à força de cisalhamento.
Agora considere um elemento de pequena área do eixo onde a força de cisalhamento pode ser expressa como o produto da tensão de cisalhamento e o elemento de área.
Ao substituir essa relação, a expressão de torque é obtida em termos de tensão de cisalhamento.
Esta relação deve ser satisfeita pelas tensões de cisalhamento em qualquer seção transversal do eixo. No entanto, não fornece informações sobre a distribuição dessas tensões na secção.
A distribuição das tensões de cisalhamento em um eixo elástico é indeterminada apenas pela estática e requer análise de deformação.

tensões em um eixo

Stresses in a Shaft

O eixo PQ está sujeito a uma força de torção quando torques iguais e opostos são aplicados em ambos os lados. Uma seção que corta perpendicularmente ao eixo do eixo em qualquer ponto arbitrário R é examinada para entender isso. Quando o diagrama de corpo livre do segmento QR é analisado, ele revela as forças de cisalhamento exercidas pela porção PR sobre o segmento QR à medida que o eixo sofre torção.

A aplicação de condições de equilíbrio ao segmento QR estabelece que as forças de cisalhamento internas dentro da seção se correlacionam diretamente com o torque interno. Aqui, 'r' significa a distância perpendicular do eixo do eixo à força de cisalhamento. A seguir, é levado em consideração um elemento de pequena área do eixo. A força de cisalhamento pode ser expressa como a multiplicação da tensão de cisalhamento e do elemento de área. Ao substituir esta relação, deriva-se uma expressão para o torque em termos de tensão de cisalhamento.

<img alt="Equation 1" src="/files/ftp_upload/15612/15612_Equation_1.svg" style="height: 28px;">

Esta relação derivada deve ser verdadeira para as tensões de cisalhamento em qualquer seção transversal do eixo. No entanto, não fornece informações sobre a distribuição destas tensões ao longo da secção transversal. Por último, é importante notar que a distribuição das tensões de cisalhamento num eixo elástico não pode ser determinada apenas pela estática. Requer análise de deformação para determinação precisa.

Tensões em um Eixo

Um eixo PQ é torcido quando submetido a torques iguais e opostos em ambos os lados.
Considere uma seção perpendicular ao eixo do eixo através de um ...

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torque and shear in a twisted shaft

A shaft under torque develops internal shear forces as it twists. In this setup, equal and opposite torques act on the shaft PQ. To study the effect, a section is cut perpendicular to the shaft axis at an arbitrary point R.

The free-body diagram of the QR segment shows the shearing forces applied by the PR portion. These forces act as the shaft resists twisting. Using equilibrium on the QR segment links the internal shear forces in the cut section to the internal torque. Here, r is the perpendicular distance from the shaft axis to the shearing force.

A small area element on the cross-section is then considered. The shearing force on that element can be written as shearing stress times area. Substituting this relation gives an expression for torque in terms of shearing stress. This relation must hold for the shearing stresses in any shaft cross-section.

Even so, the relation does not show how the stress is spread across the cross-section. The distribution of shearing stress in an elastic shaft cannot be found from statics alone. It requires deformation analysis for an accurate result.

Torque and Shear in a Twisted Shaft

stresses in a shaft

A shaft under torque develops internal shear forces as it twists. In this setup, equal and opposite torques act on the shaft PQ. To study the effect, a section is cut perpendicular to the shaft axis at an arbitrary point R. The free-body diagram of the QR segment shows the shearing forces applied by the PR portion. These forces act as the shaft resists twisting. Using equilibrium on the QR segment links the internal shear forces in the cut section to the internal torque. Here, r is the...

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A transmission shaft is sized from the power it must carry and the speed it rotates at. These two design limits guide the choice of shaft material and cross-sectional size. The goal is to keep the maximum shearing stress within the elastic limit while still transmitting the needed power. Power is directly linked to torque, which is the twisting force applied to the shaft. By rearranging the power relation, the torque can be found from the required power and the shaft speed. That torque value...

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Torsional Failure and Plastic Strain in Shafts

Plastic deformation in circular shafts happens when torsional force pushes the material past its yield strength. At that point, the shaft does not return to its original shape. Instead, it keeps a permanent strain. To measure this change, the stress pattern inside the shaft must be understood. The maximum shearing stress is calculated first. Then a shearing-stress-strain diagram can be drawn to find the maximum shearing strain. Shearing strain changes linearly with the distance from the shaft...

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Shear Flow in Thin-Walled Shafts

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key terms and concepts

Explore how equal and opposite torques create internal shear forces in a shaft, and how torque relates to shearing stress in a cut section.

Torque and Shear in a Twisted Shaft | JoVE K12

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Torque and Shear in a Twisted Shaft

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