Stress, strain, and elongation

Thread starter archaic
Start date Apr 22, 2020
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Elongation Strain Stress

In summary, stress and strain are two related concepts in physics, with stress being the force applied to an object and strain being the resulting deformation. Stress is typically measured in units of force per unit area, while strain is measured using Hooke's Law, which states that the amount of strain is directly proportional to the amount of stress. Elongation, the measure of the change in length of an object, is also related to stress and strain. The stress and strain of an object can be affected by various factors such as material properties, magnitude and direction of the force, and temperature.

Apr 22, 2020

archaic

Homework Statement: A vertical solid steel post of diameter d = 21 cm and length L = 2.20 m is required to support a load of mass m = 7500 kg . You can ignore the weight of the post.
What is the stress in the post?
What is the strain in the post?
What is the change in the post's length when the load is applied?

Relevant Equations: Stress is ##F/A##, and ##Y=\frac{F}{A}\frac{L}{\Delta L}##

$$\text{stress}=\frac{7500\times9.8}{0.105^2\pi}\approx2.1\times10^6\,Pa$$
##Y=20\times10^{10}\,Pa## for steel.
$$\frac{\Delta L}{L}=\frac{\text{stress}}{Y}\approx1.1\times10^{-5}$$
$$\Delta L\approx2.3\times10^{-5}\,m$$

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Apr 22, 2020

archaic

It's correct. Sorry, I get scared of the online homework platform sometimes.

Last edited: Apr 22, 2020

1. What is the difference between stress and strain?

Stress is the force applied to a material, while strain is the resulting deformation of the material. Stress is measured in force per unit area, while strain is a unitless measurement.

2. How is elongation related to stress and strain?

Elongation is the change in length of a material due to stress and strain. It is directly proportional to the applied stress and inversely proportional to the material's stiffness, or Young's modulus.

3. What factors affect the stress-strain relationship of a material?

The stress-strain relationship of a material is affected by its composition, temperature, and the rate at which stress is applied. Different materials have different stress-strain curves, which can also be affected by the material's microstructure and any defects or impurities present.

4. How is stress, strain, and elongation measured?

Stress is typically measured using a tensile or compression test, where a force is applied to a material and the resulting stress is calculated based on the cross-sectional area. Strain is measured using strain gauges or extensometers, which measure the change in length of the material. Elongation is calculated by dividing the change in length by the original length of the material.

5. What is the significance of the yield point in the stress-strain curve?

The yield point is the point on the stress-strain curve where the material begins to deform permanently, or plastically, instead of elastically. This is an important point to determine the material's strength and its ability to withstand stress without permanent deformation.