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Why stress is tensor quantity? Video Lecture - Class 11

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1. Why is stress considered a tensor quantity?

Ans. Stress is considered a tensor quantity because it has both magnitude and direction. It is a measure of the internal forces within a material that develops in response to external loads or deformations. Since stress depends on both the applied force and the orientation of the material, it requires a tensor representation to fully describe its behavior.

2. What is the difference between a scalar and a tensor quantity?

Ans. A scalar quantity only has magnitude and no direction, such as temperature or mass. On the other hand, a tensor quantity has both magnitude and direction, and its values change depending on the coordinate system used. Stress is an example of a tensor quantity because it requires a full tensor representation to describe its behavior accurately.

3. How is stress represented mathematically as a tensor?

Ans. Stress is represented mathematically as a second-order symmetric tensor, known as the stress tensor. In three-dimensional space, it is typically represented as a 3x3 matrix, where each element corresponds to a component of the stress along a particular axis. The stress tensor provides a complete description of the stress state at each point within a material.

4. What are the different components of stress in a stress tensor?

Ans. The stress tensor consists of nine components, which can be divided into three groups: normal stresses, shear stresses, and the diagonal components. The normal stresses represent the forces acting perpendicular to the faces of a material, while the shear stresses represent the forces acting parallel to the faces. The diagonal components of the stress tensor capture the internal forces within the material.

5. How is stress measured experimentally?

Ans. Stress can be measured experimentally using devices such as strain gauges, load cells, or pressure transducers. These instruments are capable of converting mechanical forces or deformations into electrical signals, which can be measured and analyzed. The resulting data can then be used to determine the stress state at different points within a material.

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Jan 09, 2025 Last updated

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