Esfuerzo Cortante: Ejemplos y Ejercicios Resueltos ✅ [Pernos y Placas] Mecánica de Materiales Fácil

Cesar Stark

25 Sept 202009:17

Summary

TLDRThis educational video script discusses shear stress, a crucial concept in material resistance and engineering calculations for structures. It explains shear stress as the force that tends to cause a body to cut or slide relative to another part. The script illustrates this with examples, such as a load applied to two connected plates causing material to shear. It further explains the formula for shear stress, which is force per area, and applies it to practical examples like calculating the shear stress on bolts joining steel plates under a load. The video also includes exercises to help viewers practice calculating shear stress in different scenarios.

Takeaways

🔧 Shear force is a concept in material resistance that is crucial for engineering calculations involving structures.
⚙️ Shear force occurs when forces are applied to a body with the tendency to cause one part to slide or cut relative to another.
📐 The principle of shear force is demonstrated by a simple example of two plates with a load applied, causing the material to tend to cut.
📉 The formula for shear stress is force per unit area, similar to the formula for stress but applied in a different plane.
🔩 When calculating shear stress, it's important to consider how the load is distributed among multiple bolts or connectors.
📊 The example of three bolts used to join steel plates under a 12,000-pound load illustrates how shear stress is calculated per bolt.
🔢 In the example, each bolt carries one-third of the total load, which is 4,000 pounds, and is used to calculate shear stress.
📐 The area over which the force is applied is crucial in the calculation of shear stress, often involving the diameter squared of the bolt.
🔄 Different configurations of plates and bolts require adjustments in the calculation of shear stress, such as dividing the load by two in certain setups.
📝 Practice exercises are provided to apply the concept of shear stress calculation, including scenarios with varying numbers of plates and bolts.
🚫 The maximum force that can be applied without exceeding the shear stress limit is calculated by considering the given shear stress and bolt diameter.

Q & A

What is shear stress?
-Shear stress is the internal force within a material that resists forces tending to cause one part of the material to slide alongside the other. It is calculated as the force applied per unit area.
How is shear stress applied in engineering?
-Shear stress is used in engineering calculations for structures, particularly to determine the strength of materials under forces that could cause them to break or slide.
What is the formula for calculating shear stress?
-The formula for calculating shear stress is Shear Stress = Force / Area, where Force is the force causing the shear and Area is the area over which the force is applied.
What is the significance of the image with two plates and a load in the script?
-The image with two plates and a load illustrates the concept of shear stress. The load applied to the plates tends to cause one plate to slide over the other, demonstrating the principle of shear stress.
Why is it important to calculate the shear stress on bolts?
-Calculating the shear stress on bolts is important to ensure that the bolts can withstand the forces applied to them without failing, thus maintaining the structural integrity of the assembly.
In the example with three bolts and a 12,000-pound load, how is the load distributed among the bolts?
-In the example, the 12,000-pound load is evenly distributed among the three bolts, with each bolt experiencing a shear stress of 4,000 pounds.
What is the significance of the diameter of the bolt in shear stress calculations?
-The diameter of the bolt is significant because it determines the area over which the force is distributed, which in turn affects the shear stress experienced by the bolt.
How does the configuration of the plates affect the shear stress on the bolts?
-The configuration of the plates affects the shear stress on the bolts by altering the distribution of the applied force. For example, in a setup with plates above and below, the force is divided between two planes.
What is the result of the shear stress calculation for the bolt in the second example with 6,000 pounds of force?
-The result of the shear stress calculation for the bolt in the second example is 6,790 pounds per square inch, after considering that the force is divided between two planes.
How does the number of bolts affect the shear stress each bolt experiences?
-The number of bolts affects the shear stress each bolt experiences by dividing the total force among the bolts. More bolts mean each bolt experiences less shear stress.
What is the purpose of the exercises mentioned in the script?
-The exercises are designed to practice calculating shear stress in different scenarios to understand how to apply the concept and ensure the correct selection of materials and dimensions for engineering applications.

Outlines

00:00

🔩 Shear Force Basics

This paragraph introduces the concept of shear force, which is crucial in material resistance and engineering calculations. Shear force occurs when forces are applied to cause one part of a body to cut or slide relative to another. An example is given with two plates joined together, subjected to a load that tends to cause them to separate. The basic principle of shear force is explained, and a formula is introduced to calculate shear stress, which is force per unit area. The formula is applied to a scenario where three bolts are used to join two steel plates under a load of 12,000 pounds, and it's explained how the load is distributed among the bolts, resulting in a shear stress of 4,000 pounds per bolt.

05:01

📏 Calculations of Shear Stress in Different Configurations

The second paragraph elaborates on calculating shear stress in various configurations. It starts with a scenario where a bolt of three-quarters of an inch is used to join three plates under a 6,000-pound load. The load is split between two planes, and the calculation is adjusted accordingly, resulting in a shear stress of 6,790 pounds per square inch. The paragraph continues with exercises to practice calculating shear stress in different setups, such as two plates joined by two bolts under a 5,000-pound force and three plates joined by two bolts under a 12,000-pound force. The final exercise asks to determine the maximum force that can be applied without exceeding a shear stress of 10,000 pounds per square inch, given the bolt diameter.

Mindmap

Keywords

💡Shear Force

Shear force is a type of force that causes parallel layers or plates to slide over one another. In the video, shear force is central to understanding how materials resist deformation. It is exemplified by applying a force to two plates causing them to slide against each other. The script mentions that shear forces are calculated in engineering to ensure structures can withstand such forces without breaking apart.

💡Shear Stress

Shear stress is the internal resistance of a material to the effect of shear force. It is defined as the force per unit area that tends to cause deformation. In the video, shear stress is calculated using the formula force per area, and it is crucial for determining the strength of materials and the design of structures.

💡Material Resistance

Material resistance refers to a material's ability to withstand applied forces without breaking or deforming excessively. The video discusses material resistance in the context of shear forces, emphasizing the importance of understanding how materials react to such forces for engineering applications.

💡Engineering Calculations

Engineering calculations are mathematical procedures used to determine the safety and feasibility of a design. The video script mentions that shear stress is used in engineering calculations to ensure that structures can handle the forces they will experience in practice.

💡Structural Integrity

Structural integrity is the ability of a structure to maintain its shape and function under load. The video discusses how understanding shear stress helps in maintaining the structural integrity of materials and structures by preventing them from shearing or sliding apart.

💡Bolts and Connectors

Bolts and connectors are mechanical fasteners that join different parts of a structure. In the script, bolts are used as an example to illustrate how shear forces are distributed among them when joining steel plates.

💡Load Distribution

Load distribution is the process of dividing a total load among different parts of a structure or system. The video explains how the total load is distributed among bolts when they are used to join materials, which affects the calculation of shear stress.

💡Pascal

Pascal is the SI unit of pressure or stress, which is defined as one newton per square meter. In the video, pascal is used to describe the unit of shear stress when calculating forces in the metric system.

💡Pounds per Square Inch

Pounds per square inch (psi) is a unit of pressure or stress in the imperial system. The video uses psi to describe the unit of shear stress when calculating forces in the imperial system.

💡Diameter

Diameter is a term used to describe the distance across the widest part of a circle or cylinder, such as a bolt. In the video, the diameter of bolts is used to calculate the area over which shear force is applied, which is essential for determining the shear stress.

💡Area

Area is the amount of space within the boundaries of a surface. In the context of the video, calculating the area over which a force is applied is essential for determining shear stress, as it is used in the formula force per area.

Highlights

The lecture introduces the concept of shear stress, a critical topic in material resistance.

Shear stress is widely used in engineering calculations for structures.

Shear stress occurs when forces tend to make a part of a body cut or slide with respect to another part.

A simple illustration of shear stress is provided with an image of two plates under load.

The basic principle of shear stress is explained through the tendency of material to cut under force.

Shear stress is calculated using the formula of force divided by area.

The units for shear stress are pounds per square inch or newtons per square meter.

An example calculation demonstrates how to determine shear stress on bolts joining two steel plates.

The advantage of understanding shear stress is the ability to select appropriate materials for design.

A calculation shows that each bolt under a 12,000-pound load experiences 4,000 pounds of shear stress.

The distribution of load among multiple bolts is discussed, with each bolt分担着 a portion of the total load.

Different configurations of plates and bolts are presented to illustrate varying shear stress calculations.

Shear stress can fail along two planes, and the calculation assumes equal stress on both planes.

An example with a 3/4-inch bolt under a 6,000-pound load results in a shear stress of 6,790 pounds per square inch.

Exercises are provided to practice calculating shear stress in different block configurations.

A method to determine the maximum force that can be applied without exceeding shear stress limits is explained.

The final results of the exercises show calculations for shear stress in various bolt and plate setups.