What is the height of the spans when they buckle due to a temperature increase?

[parwana]

Homework Statement

Two concrete spans of a L = 270 m long bridge are placed end to end so that no room is allowed for expansion (Fig. P10.55a). If the temperature increases by T = 21.0°C, what is the height y to which the spans rise when they buckle (Fig. P10.55b)

Homework Equations

change in L/L= average coefficient of expansion(change in T)

average coefficient of concrete= 12 X 10^-6

The Attempt at a Solution

I tried doing

change in L/270= 12 X 10^-6 (21)

I got change in L, and now I don't know what to do. HELP

 

[Kurdt]

Once you work out how much the concrete expands by its really just a case of pythagoras theorem to work out the height they raise when they buckle.

 

[parwana]

how?

I got change in L as 0.06804

 

[parwana]

This is so frustrating

 

[parwana]

anyone care to help?

 

[FredGarvin]

If you assume that the break is in the middle as the picture points out, you have the original length and the new length which is the original plus the change in length. Divide each number in half and that will give you the hypotenuse and the base sides of a right triangle. You need to find the opposite side's length, which I am assuming you can do.

 

[parwana]

^ the height should be around 3.0, I am not getting that number

 

[OlderDan]

^ the height should be around 3.0, I am not getting that number

What calculation have you done and what is your result?

 

[parwana]

L= 270
change in L/270= 12 X 10^-6 (21)= 0.06804
270+0.06804= 270.06804

270/2= 135
270.06804/2= 135.03402

now according to u I should do pythagorean theorum, which I did and got 190.9

thats not right

I got it though finally, when I do L/2, which is 270/2= 135, take the change in L, which is .06804

135 X .06804 and take its square root, I get 3.03, which is the answer

 

[OlderDan]

L= 270
change in L/270= 12 X 10^-6 (21)= 0.06804
270+0.06804= 270.06804

270/2= 135
270.06804/2= 135.03402

now according to u I should do pythagorean theorum, which I did and got 190.9

thats not right

I got it though finally, when I do L/2, which is 270/2= 135, take the change in L, which is .06804

135 X .06804 and take its square root, I get 3.03, which is the answer

Your Pythagorean calculation is incorrect. You added the square of the long leg (135) to the square of the hypotenuse. You need to subtract the square of the long leg from the square of the hypotenuse and take the square root to find the short leg.