¿Que es el ESFUERZO de TORSION? 😎✔

Ingeniosos

13 Nov 202205:26

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

00:00

🛠️ 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.

05:02

📐 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

Torsion refers to the twisting or deformation of an object due to an applied torque. In the video, torsion is the main theme as it discusses how it occurs in mechanical systems, such as vehicle transmission systems, and its effects on a circular bar subjected to torque at its ends. The script uses the example of a bar to illustrate the concept of torsion and how it leads to the bar rotating around its longitudinal axis.

💡Torque

Torque is the rotational force that causes an object to rotate about an axis. The video script describes torque as the force applied at the ends of a bar in opposite directions, resulting in the bar's torsional deformation. It is a key concept in understanding how torsion is generated and how it affects the structural integrity of materials.

💡Moment of Torsion

The moment of torsion is the product of the torque and the distance from the point of application to the point of interest. In the script, the moment of torsion is used to explain the twisting effect on the bar, where the bar is subjected to two moments of rotation around its longitudinal axis, leading to torsional stress.

💡Circular Section

A circular section is a geometric shape that is round and symmetrical. The video script uses a bar with a circular section to demonstrate torsion, highlighting how the symmetry of the shape allows for even distribution of stress and deformation without changing the geometry of the bar.

💡Tangential Stress

Tangential stress, also known as shear stress, is the stress that acts tangentially to the surface of an object. In the context of the video, tangential stress is generated due to torsion and varies linearly from the center of the bar to its outer surface. The script explains how this stress is related to the deformation caused by the torsional force.

💡Deformation

Deformation in the video refers to the change in shape or size of an object under the influence of an external force. The script discusses how torsion causes a bar to deform, with the angle of torsion representing the amount of rotation of a section relative to its initial state. Deformation is a critical aspect of understanding the effects of torsion.

💡Shear Angle

The shear angle, denoted as Gamma in the script, is the angle formed between two initially collinear lines after the application of torsion. It represents the deformation caused by the torsional force and is used to calculate the tangential stress within the material.

💡Polar Moment of Inertia

The polar moment of inertia is a measure of a cross-sectional area's resistance to torsion. The script explains how the polar moment of inertia is integral to calculating the torsional stress and deformation within a circular bar, showing its importance in structural analysis.

💡Elastic Range

The elastic range refers to the limit within which a material deforms under stress and returns to its original shape once the stress is removed. The video script mentions that within the elastic range, Hooke's Law applies, relating the tangential stress to the material's properties and the deformation caused by torsion.

💡Hooke's Law

Hooke's Law states that the stress in a material is proportional to its strain within the elastic limit. In the context of the video, Hooke's Law is used to explain the relationship between the tangential stress and the deformation caused by torsion, assuming the material behaves elastically.

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.