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

Un eje PQ se tuerce cuando se somete a pares iguales y opuestos en ambos lados.
Considere una sección perpendicular al eje del eje a través de un punto arbitrario R. El diagrama de cuerpo libre de la porción QR muestra las fuerzas de cizallamiento ejercidas por la porción PR en QR a medida que el eje gira.
Aplicando las ecuaciones de equilibrio a la porción QR, se puede demostrar que las fuerzas de corte dentro de la sección están relacionadas con el par interno. Aquí, r representa la distancia perpendicular desde el eje del eje hasta la fuerza de corte.
Ahora considere un elemento de área pequeña del eje donde la fuerza de corte se puede expresar como el producto del esfuerzo cortante y el elemento de área.
Sustituyendo esta relación, se obtiene la expresión de par en términos de esfuerzo cortante.
Esta relación debe ser satisfecha por los esfuerzos cortantes en cualquier sección transversal del eje. Sin embargo, no proporciona información sobre la distribución de estas tensiones en la sección transversal.
La distribución de los esfuerzos cortantes en un eje elástico es indeterminada solo por estática y requiere análisis de deformación.

tensiones en un eje

Stresses in a Shaft

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 El eje PQ está sujeto a una fuerza de torsión cuando se aplican pares iguales y opuestos en ambos lados. Para comprender esto, se examina una sección que corta perpendicular al eje del eje en cualquier punto arbitrario R. Cuando se analiza el diagrama de cuerpo libre del segmento QR, revela las fuerzas cortantes ejercidas por la porción PR sobre el segmento QR cuando el eje experimenta torsión.
 
 La aplicación de condiciones de equilibrio al segmento QR establece que las fuerzas cortantes internas dentro de la sección se correlacionan directamente con el torque interno. Aquí, 'r' significa la distancia perpendicular desde el eje del eje hasta la fuerza cortante. A continuación, se tiene en cuenta un elemento de área pequeña del eje. La fuerza cortante se puede expresar como la multiplicación del esfuerzo cortante y el elemento área. Al sustituir esta relación, se deriva una expresión para el momento de torsión en términos de esfuerzo cortante.
 
 <img alt="Equation 1" src="/files/ftp_upload/15612/15612_Equation_1.svg" style="text-align: center; height: 28px;">
 Esta relación derivada debe ser válida para los esfuerzos cortantes en cualquier sección transversal del eje. Sin embargo, no proporciona información sobre la distribución de estas tensiones en la sección transversal. Por último, es importante señalar que la distribución de los esfuerzos cortantes en un eje elástico no puede determinarse únicamente mediante la estática. Requiere análisis de deformación para una determinación precisa.
 
</div>

Tensiones en un eje

Un eje PQ se tuerce cuando se somete a pares iguales y opuestos en ambos lados.
Considere una sección perpendicular al eje del eje a través de un eje ...

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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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Torsional Failure and Plastic Strain in 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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