Coefficient of linear thermal expansion of a composite bar

In summary, the conversation discusses the effective coefficient of linear thermal expansion for a composite bar made of two different materials. The equation for the effective coefficient is given as alpha=(a1L1+a2L2)/L, where alpha is the coefficient of linear thermal expansion, a1 and a2 are the coefficients for each material, and L is the total length of the composite bar. The conversation also mentions the individual equation for the coefficient of linear thermal expansion for one material, alpha=(delta L)/Lo(delta T). The hint provided is to consider the sum of the expansions of each segment of the composite bar.
  • #1
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question: a composite bar of length L=L1+L2 is made from a bar of material 1 and length L1 attached to a bar of material 2 and length L2.

show that the effective coefficient of linear thermal expansion is :

alpha= (a1L1+a2L2)/L

[- alpha/a=coefficient of linear thermal expansion]

i have no idea how to derive that equation, the only thing i no/learned from reading the book is that the equation for the coefficient of linear thermal expansion for one material is alpha=(delta L)/Lo(delta T)

anyone who can show me/drop some hints would be greatly appreciated.

thanks in advance
 
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  • #2
Hint: The expansion ([itex]\Delta L[/itex]) of the composite bar is the sum of the expansions of each segment.
 
  • #3
ahhh...that clearified me...i think i get it...thanks alot.
 

FAQ: Coefficient of linear thermal expansion of a composite bar

1. What is the coefficient of linear thermal expansion?

The coefficient of linear thermal expansion refers to the amount of change in length that a material will experience when subjected to a change in temperature. It is a measure of how much a material will expand or contract in length per unit of temperature change.

2. How is the coefficient of linear thermal expansion measured?

The coefficient of linear thermal expansion is typically measured by subjecting a material to a known change in temperature and measuring the resulting change in length. This is usually done using specialized equipment such as a dilatometer or thermal expansion probe.

3. What is a composite bar?

A composite bar is a material made up of two or more different materials that are bonded together. This type of material is often used to combine the desirable properties of different materials, such as strength and flexibility, into one product.

4. How does the coefficient of linear thermal expansion of a composite bar differ from that of a single material?

The coefficient of linear thermal expansion of a composite bar is typically a weighted average of the coefficients of each individual material in the bar. This means that the overall expansion or contraction of the composite bar will be influenced by the properties of each individual material.

5. Why is the coefficient of linear thermal expansion important to consider in composite bars?

The coefficient of linear thermal expansion is important to consider in composite bars because it can affect the overall dimensional stability of the material. If the coefficients of the individual materials in the composite bar are significantly different, it can lead to warping, cracking, or other structural issues when the bar is subjected to temperature changes.

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