How Does Thermal Expansion Cause Concrete Sidewalks to Buckle?

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Thermal expansion causes concrete sidewalks to buckle when there is no space for the slabs to expand. In this scenario, two 3-meter slabs expand from 25 to 38 degrees Celsius, leading to upward buckling due to fixed ends. The coefficient of thermal expansion is given as 12 x 10^-6 per degree Celsius. To determine the vertical displacement, one can assume the slabs maintain their integrity and apply trigonometry to calculate how high the middle ends must raise. Understanding the relationship between temperature change and slab displacement is crucial for solving this problem.
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I'm a little bit confused with this question, can any1 pls help? thanks in advance

A concrete sidewalk is constructed between two buildings on a day when the temperature is 25 degree celsius. The sidewalk is consists of two slabs each 3 meters in length and of negligible thickness. As the temperature rises to 38 degree celsius, the slabs expand but no space is provided for thermal expanson. The building do not move so the slabs buckle upward. determine the vertical displacement of the slabs due to buckling effect.

a=12 x 10^-6 / celsius degree
 
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What part is confusing? The expansion or the buckling?
 
pretty much on how to solve the vertical displacement Y_Y
 
kamakari said:
pretty much on how to solve the vertical displacement Y_Y
Lacking further details, I would just assume that the slabs maintain their integrity as they expand. Assume the far ends don't move, then figure out how high the middle ends must raise up. Use a bit of trig to find the height.
 

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