A copper plate of length 1 m is riveted to two steel plates of same length and same cross-secti

A copper plate of length 1 m is riveted to two steel plates...

A copper plate of length $1 \mathrm{~m}$ is riveted to two steel plates of same length and same cross-section area at $0^{\circ} \mathrm{C}$. Calculate tension (in kilo newton) generated in copper plate when heated to $20^{\circ} \mathrm{C}$. $Y_{\text {copper }}=\frac{1}{2} \times Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} Y=$ Young's modules $\alpha_{\text {copper }}=18 \times 10^{-6} \mathrm{~K}^{-1}$ $\alpha_{\text {steel }}=11 \times 10^{-6} \mathrm{~K}^{-1} \alpha=$ coefficient of linear expansion Area of each plate $=50 \mathrm{~cm}^{2}$

A copper plate of length $1 \mathrm{~m}$ is riveted to two steel plates of same length and same cross-section area at $0^{\circ} \mathrm{C}$. Calculate tension (in kilo newton) generated in copper plate when heated to $20^{\circ} \mathrm{C}$. $Y_{\text {copper }}=\frac{1}{2} \times Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} Y=$ Young's
modules $\alpha_{\text {copper }}=18 \times 10^{-6} \mathrm{~K}^{-1}$
$\alpha_{\text {steel }}=11 \times 10^{-6} \mathrm{~K}^{-1} \alpha=$ coefficient of linear expansion
Area of each plate $=50 \mathrm{~cm}^{2}$

Key Concepts

Young's Modulus

Young's modulus is a measure of the stiffness of a material, quantifying the relationship between stress and strain in a material under elastic deformation. It is an essential parameter in determining how much force is required to produce a given strain, and it plays a key role in the calculation of stresses, including those induced by thermal expansion in constrained materials.

Composite Material Interactions

This concept refers to the behavior of systems composed of different materials that are bonded or connected together, each with distinct mechanical and thermal properties. In such systems, differences in thermal expansion coefficients and stiffness can lead to complex stress distributions when the composite is subjected to temperature changes, making the understanding of material compatibility and interaction crucial.

Thermal Expansion

This concept deals with the tendency of materials to change their dimensions in response to changes in temperature. The linear expansion of an object is characterized by its coefficient of linear expansion, which quantifies how much the length of the material changes per unit temperature change. It is a critical factor when evaluating dimensional stability in materials exposed to thermal variations.

Thermal Stress

Thermal stress arises when a material is forced to expand or contract but is restrained from doing so freely. In such cases, the induced stress is a result of the conflict between the material's natural tendency to change its dimensions and the mechanical constraints imposed on it. Calculations of thermal stress often incorporate the coefficient of thermal expansion, the temperature change, and the material's stiffness.

Transcript

00:01 Here a copper plate is rotated between two silver for the same length and copper here.

00:09 So since it is being heated, so initial temperature is 0 degrees celsius and final temperature is 20 degrees of years after heating.

00:21 Now here we know that copper expands more than more than this we can also calculate we can also derive this idea from the linear extension of copper and steel because linear extension of copper is 18 and steel is 11 so here now there will be strength in the copper because copper will try to stretch more while still will try to stress will expect less so it will try to control the length of copper so copper and steel will apply force on each other laterally.

01:15 So here you can say net expansion.

01:27 So net expansion of copper will be equal to delta l which is in fact l final or i can say okay l this is about copper lc minus l0 equals to initial length l not linear coefficient of expansion of copper into changing temperature.

02:03 Delta is minor.

02:06 So that is due to the heating.

02:09 But that will not expand completely because it will apply force and it will stop it from expanding completely.

02:20 So that force it will try to stop it.

02:23 That is flyca.

02:31 That is that is in modulus of last is hitting y street.

02:36 So here f is 4 applied, l is the length, and that is for the copper, this is constant, and a is processed.

02:44 So that much length, that is deformation, this formula is for deformation...