¿Que es el ESFUERZO de TORSION? 😎✔
Summary
TLDRThis video script explores the concept of torsional effort, commonly found in vehicle transmission systems, electrical power generation, and various real-life applications. It explains how torsion occurs in a circular bar subjected to opposite moments at its ends, causing rotation around its longitudinal axis. The script delves into the mechanics of torsion, including the deformation it causes, the tangential stress distribution, and the calculation of torsional stress using the polar moment of inertia. It emphasizes that these principles are specific to circular geometries, noting that other shapes would complicate the analysis.
Takeaways
- 🔧 Torsion occurs in various applications, including vehicle transmission systems and electrical power generation systems.
- 📐 The script uses a circular cross-section bar as an example to explain the concept of torsion, where two opposite torques are applied at each end.
- 🔄 Torsion causes the bar to twist around its longitudinal axis without changing its geometry, thanks to the circular symmetry.
- 📏 The angle of twist is measured from the center of the section to determine how much a specific section has rotated relative to its initial state.
- 📐 Shear deformation is produced due to torsion, which is similar to the deformation explained in the video about shear stress.
- 📊 Shear deformation varies linearly from the center of the bar to the outer surface, being maximum at the surface and zero at the axis.
- 🔧 To calculate the tangential stress, the script suggests analyzing the bar by cutting it through any section and considering the equilibrium of forces.
- 📉 Tangential stress follows a linear behavior from the center to the surface, similar to shear deformation, and is maximum at the surface.
- ⚖️ The integral calculation of the tangential stress over a differential element leads to the concept of the polar moment of inertia, which describes the resistance of a section to torsion.
- 📚 The script deduces the value of the angle of twist as a function of the applied torque, bar length, transverse elasticity modulus, and polar moment of inertia.
- 🚫 The deductions made in the script are limited to bars with circular geometry; other shapes would complicate the calculations due to section deformation.
Q & A
What is torsional effort and where is it commonly found?
-Torsional effort, also known as torque, is the force that causes rotation around an axis. It is commonly found in the transmission mechanisms of vehicles, in electrical power generation systems, and in various other real-life constructions and applications.
Can you describe the example given in the script to explain torsional effort?
-The script uses the example of a circular cross-section bar that has two moments of rotation applied at its ends, in opposite directions along its longitudinal axis. This is known as a torsional moment or torque, which causes the bar to rotate or twist around its axis.
What is the term used for the angle that represents how much a section has rotated due to torsion?
-The angle that represents how much a section has rotated due to torsion is called the torsion angle.
How does the torsional effort generate deformation in the bar?
-The torsional effort generates a shearing deformation, which is defined by the angle Gamma. This results in tangential stresses, as explained in the script by referring to the video on shear stress.
What is the relationship between the torsional deformation and the bar's geometry?
-The torsional deformation is due to the bar's circular symmetry, which allows the different sections of the bar to rotate without changing their geometry.
How can the maximum shear deformation be calculated?
-The maximum shear deformation can be calculated by considering the tangent of the torsion angle, which is equal to the distance between the initial and rotated positions of a point on the bar, divided by the length of the bar.
What is the relationship between the tangential stress and the deformation in the elastic region of a material?
-In the elastic region of a material, the tangential stress is directly proportional to the deformation, following Hooke's Law, where the stress is equal to the material's transverse modulus of elasticity multiplied by the deformation.
How does the tangential stress vary across the bar's cross-section?
-The tangential stress varies linearly across the bar's cross-section, being zero at the center and maximum at the outer surface.
What is the polar moment of inertia and how is it related to torsional effort?
-The polar moment of inertia is a concept that describes a section's resistance to torsion. It is used in the calculation of the tangential stress resulting from the torsional effort, along with the applied torque, the bar's length, the transverse modulus of elasticity, and the torsion angle.
What limitations are there in the calculations and analysis presented in the script?
-The calculations and analysis presented in the script are limited to bars with circular geometry. In other cases, torsion can cause additional deformations that complicate the calculations significantly.
What is the conclusion about the tangential stress on the bar's surface due to torsional effort?
-The conclusion is that the maximum value of the tangential stress occurs on the surface of the bar due to the torsional effort, and it can be calculated using the derived equations and the polar moment of inertia.
Outlines
🛠️ Understanding Torsion Effort in Real-World Applications
This paragraph introduces the concept of torsion effort, highlighting its presence in various mechanisms such as vehicle transmission and electric generation systems. It provides an example of a circular section bar subjected to opposing torque moments at its ends. The explanation covers how torsion causes rotation without altering the bar's geometry due to its circular symmetry, leading to shear deformation and tangential stresses.
📐 Calculating Shear Deformation and Tangential Stress
The paragraph details the calculation of shear deformation by examining a specific line on the bar's surface before and after torsion. It explains how to determine the angle of torsion and the resulting tangential stress using Hooke's Law. The explanation includes the concept of linear variation of deformation from the center to the surface and the calculation of the maximum shear deformation.
📊 Analyzing Internal Stress Distribution in a Bar
This section delves into analyzing the internal stress distribution within the bar by considering a differential element at a distance from the center. It explains how tangential stress varies linearly and reaches its maximum at the surface. The paragraph introduces the concept of the polar moment of inertia and how it is used to calculate the torsion angle and tangential stress for a circular section bar.
🔍 Limitations and Future Topics
The concluding paragraph highlights the limitations of the discussed calculations, noting that they apply only to circular section bars. It mentions that torsion in non-circular sections leads to complex deformations and calculations, which will be addressed in future videos. The paragraph ends with a thank-you note, encouraging viewers to ask questions, subscribe, and continue learning.
Mindmap
Keywords
💡Torsion
💡Torque
💡Moment of Torsion
💡Circular Section
💡Tangential Stress
💡Deformation
💡Shear Angle
💡Polar Moment of Inertia
💡Elastic Range
💡Hooke's Law
Highlights
The concept of torsional effort in real-life applications like vehicle transmission mechanisms and electric generation systems.
Introduction of torsional moment or torque applied to a circular section bar, causing it to twist around its longitudinal axis.
The relationship between torsion and shear deformation, where torsion generates a shear deformation represented by the angle Gamma.
Explanation of how to calculate the shear deformation, focusing on the maximum shear deformation occurring on the surface of the bar.
Shear deformation varies linearly, being zero at the bar's axis and maximum at the external surface.
Introduction of tangential stress within the bar, balancing the applied torsional moment.
Tangential stress does not have the same value at all points, increasing linearly from the center to the exterior.
Application of Hooke's law in the elastic zone of a material, where tangential stress is proportional to shear deformation.
Calculation of tangential stress using the polar moment of inertia, describing a section's resistance to torsion.
Derivation of the angle of torsion as a function of the applied torsor, bar length, shear modulus, and polar moment of inertia.
Maximum tangential stress occurs on the bar's surface, derived from the combination of the deduced expressions.
Simplified equations for analyzing deformations and stresses generated by torsional effort.
Limitations of these deductions to circular geometry bars, with different geometries resulting in more complex calculations.
Encouragement to ask questions in the comments and subscribe to the channel for more learning.
Reminder that knowledge is limitless, inviting viewers to continue their learning journey.
Transcripts
el esfuerzo de torsión aparecen los
mecanismos de transmisión de los
vehículos en los sistemas de generación
eléctrica y en otras muchas
construcciones o aplicaciones de la vida
real en este vídeo veremos Cómo se
produce en qué consiste Y cómo
calcularlo
pongamos como ejemplo la siguiente barra
de sección circular a la que se le
aplican dos momentos de giro alrededor
de su eje longitudinal pero he sentido
contrario en cada uno de sus extremos a
este momento lo llamamos momento torsor
o torque y su aplicación genera que la
barra gire o se refuerza más
específicamente se torsione alrededor de
su eje
como veis en el dibujo las distintas
secciones de la barra rotan pero no
cambian su geometría no se deforman
gracias a su simetría circular
si dejamos fijo el extremo izquierdo lo
encontramos para que no gire podemos
analizar la deformación producida
teniendo este extremo como referencia y
fijándonos en una línea cualquiera
inicialmente esta línea une los puntos p
y q después de la torsión
q ha girado hasta colocarse en q prima
encontramos el ángulo de torsión que
representa cuanto ha girado una sección
concreta respecto del Estado inicial
medido desde el centro de la sección si
nos fijamos en cualquier elemento de la
malla que hemos dibujado sobre la
superficie de la barra ha variado su
geometría por efecto de la torsión se
produce un deslizamiento relativo de los
lados izquierdo y derecho Qué indica
esto si recordáis el vídeo sobre el
esfuerzo cortante es exactamente el
mismo sistema de deformación es decir el
esfuerzo de torsión genera una
deformación cortante que viene definida
por el ángulo Gamma por lo que también
generará tensiones tangenciales o se
animo a repasar el vídeo sobre el
esfuerzo cortante que seguro que os
aclarar algunas cosas sobre este tema
podemos saber cuánto vale la deformación
cortante sí fijándonos de nuevo en toda
la barra veremos que Gamma coincide con
el ángulo formado entre pq y p q prima
por trigonometría deducimos que la
tangente de Gamma es igual a la
distancia q prima partida de pq lo que
coincide con la longitud del Arco girado
entre la longitud de la barra como Gamma
es un ángulo pequeño podemos aproximarlo
al valor de su tangente sin embargo hay
que puntualizar que esto que hemos
calculado es la deformación cortante
máxima la que ocurre en la superficie
exterior de la barra definida por el
radio r en cualquier punto interior para
un radio menor variable que definimos
como ro La deformación cortante será
menor como conclusión la deformación
cortante variará linealmente siendo 0 en
el eje de la barra y máxima en la
superficie externa
os estaréis preguntando podemos saber
también Qué valor toma la tensión
tangencial para deducirlo necesitamos
analizar internamente la barra
cortándola por una sección cualquiera
ahora la barra solo tiene aplicada un
torsor en su extremo por lo que no está
equilibrada estáticamente para alcanzar
el equilibrio aparece una tensión
tangencial al plano de la sección con
dirección contraria al torsor sin
embargo la tensión tangencial no tiene
el mismo valor en todos los puntos ya
hemos deducido que la deformación
cortante crece linealmente desde el
centro al exterior en la zona elástica
de un material se cumple la ley de hooke
es decir la tensión tangencial es igual
al módulo de elasticidad transversal que
es una propiedad del material por la
deformación tangencial por ello la
tensión sigue el mismo comportamiento
lineal que la deformación es Cero en el
centro de la sección y máxima en la
superficie para calcular exactamente
cuánto vale fijémonos En un elemento
diferencial cualquiera de situado a una
distancia ro del centro sobre este
elemento actúa una tensión tau contraria
al momento torsor aplicado la suma de
todas las tensiones tau sobre cada
elemento diferencial por la distancia ro
hasta el centro equilibran el torsor
aplicado llegamos así a una integral
donde podemos sustituir tau por la
expresión deducida en función de la
deformación
si sacamos fuera todos los términos
constantes la integral resultante
coincide con la definición de momento
polar de Inercia concepto que ya vimos
en otro vídeo y que describe la
resistencia de una sección ante el
fenómeno de torsión
lo curioso es que con todo este cálculo
hemos deducido por el camino el valor
del ángulo de torsión como función del
torsor aplicado la longitud de la barra
el módulo de elasticidad transversal y
el momento polar de Inercia
finalmente combinando las dos
expresiones deducidas obtenemos el valor
de la tensión tangencial cuyo valor
máximo tiene lugar en la superficie de
la barra
ahora ya tenemos algunas ecuaciones
simples para poder analizar las
deformaciones y tensiones generadas por
el esfuerzo de torsión Pero cuidado
todas estas deducciones están limitadas
a barras con geometría circular en
cualquier otro caso la torsión produce
al Aveo deformando las secciones de la
barra y complicando considerablemente
los cálculos Pero esto y otras cosas ya
las dejamos para otros vídeos Muchas
gracias por elegir el canal para seguir
aprendiendo podéis dejar cualquier
pregunta en los comentarios y estáis
invitados a suscribiros Gracias y
recordad en el saber nunca cabe la
sociedad hasta otra
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