Problem 37 - An Introduction to the Mechanics of Solids in SI Units

Question

A \(2 \mathrm{~cm}\)-outside-diameter brass tube is to be compressed \(0.1 \mathrm{~cm}\) by means of a steel screw clamp, each screw of which has 10 threads per \(\mathrm{cm}\) and an effective cross-sectional area of \(0.5 \mathrm{~cm}^{2}\). It is known that it will take \(5 \mathrm{kN}\) to compress the brass tube \(0.1 \mathrm{~cm}\). The tube is put into the clamp with the jaws parallel and just touching the tube. How many turns must be given the screw \(C\) to compress the tube \(0.1 \mathrm{~cm}\) ?

Step-by-Step Solution

Answer

One turn of the screw is needed to compress the tube by 0.1 cm.

Step 1: Determine the distance one turn moves the screw

Since there are 10 threads per centimetre, 1 turn of the screw advances it 1/10 or 0.1 cm because the distance between two successive threads is 1/10 cm.

Step 2: Calculate the total number of turns

Since each turn moves the screw 0.1 cm and the goal is to compress the tube 0.1 cm, 1 turn of the screw is needed.

Key Concepts

Strength of Materials

The field of strength of materials, also known as mechanics of materials, is a subset of materials science and mechanical engineering that deals with analyzing stresses and strains within materials. It's crucial for engineers to understand how different materials will behave under various types of forces to ensure the safety and durability of structures and machines.

For instance, when a brass tube is compressed using a screw clamp as described in the exercise, it is essential to know the capability of the material to withstand those forces without failure or excessive deformation. The problem mentioned provides insight into the practical application of these principles by calculating the force needed to compress the tube, which in this case is given as 5 kN for a 0.1 cm deformation. Understanding how materials respond to such loads allows for proper design and safety assurance in a wide array of engineering applications.

Compression of Materials

Compression of materials involves applying a force that reduces the volume of a material by pushing its molecules closer together. The resistance of a material to compression is a fundamental property that can vary widely from one material to another. In the context of the given problem, the brass tube is subjected to a compressive force distributed evenly by the clamp.

It's significant to note that the amount the material compresses depends on its compressive strength, the amount of force applied, and the nature of the force distribution. Here, we learned that a force of 5 kN will compress the brass tube by 0.1 cm. This knowledge aids engineers in predicting how much deformation will occur under given loading conditions and is critical in the design and analysis of structures and components to prevent failures due to excessive compression.

Mechanical Engineering Education

Mechanical engineering education builds a foundation in understanding the principles behind forces and the deformation of materials. It often includes problem-solving techniques similar to the exercise at hand, where students learn how the mechanics of solids applies to real-world situations. The approach to the problem engages critical thinking and applies mathematical calculations to predict outcomes.

Students are taught to assess problems step-by-step, as in calculating the number of turns of a screw necessary to achieve a desired compression of a material. This exemplifies the practical application of theoretical knowledge, grounding abstract concepts in tangible tasks. It is important for educators to clearly articulate these relationships among forces, material properties, and movement in a manner that is digestible for students. Doing so ensures a strong understanding and the ability to apply these principles innovatively in future engineering challenges.