How to Calculate Spacing for Bridge Expansion with Linear Expansion Coefficient

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SUMMARY

The discussion focuses on calculating the necessary spacing for bridge expansion due to temperature changes, specifically using a linear expansion coefficient of 1.2 × 10-5(°C)-1. The formula used is ΔL = L0αΔT, where L0 is the original length (76 m), α is the linear expansion coefficient, and ΔT is the temperature change (69°F, converted to Celsius). The correct calculation results in a required spacing of 3.48 cm, highlighting the importance of unit conversion in engineering calculations.

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  • Understanding of linear expansion coefficients
  • Familiarity with temperature conversion between Fahrenheit and Celsius
  • Basic knowledge of algebraic manipulation
  • Experience with engineering formulas related to thermal expansion
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  • Learn about unit conversion techniques, particularly between Fahrenheit and Celsius
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Homework Statement



A bridge is made with segments of concrete 76 m long (at the original temperature). If the linear expansion coefficient is 1.2 × 10−5(◦C)−1, how much spacing is needed to allow for expansion for an increase in temperature of 69◦F? Answer in units of cm.

Homework Equations



I don't know, we never did this in lecture, so I lost as to what to do.

The Attempt at a Solution



What formula am I supposed to use?
 
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DrMcDreamy said:

Homework Statement



A bridge is made with segments of concrete 76 m long (at the original temperature). If the linear expansion coefficient is 1.2 × 10−5(◦C)−1, how much spacing is needed to allow for expansion for an increase in temperature of 69◦F? Answer in units of cm.

Homework Equations



I don't know, we never did this in lecture, so I lost as to what to do.

The Attempt at a Solution



What formula am I supposed to use?
For a formula check
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html
 
Thank you!

So it would be:

\DeltaL=Lo\alpha\DeltaT

\DeltaL= (76 m)(1.2 x 10-5)(◦C)-1(20.5◦C+17.7◦C)

\DeltaL=0.0348 m
 
^It came out to be wrong, so what did I do wrong?
 
DrMcDreamy said:
Answer in units of cm.
ΔL=0.0348 m
That's what's wrong.
 
Oh $h*t! 3.48 cm crap I didnt even realize it had asked in cm!
 

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