# Thermal Stress

1. Jun 23, 2013

### aaronfue

1. The problem statement, all variables and given/known data

I am having a hard time understanding the length measurement in the problem. We went over this example in class and the length, L, was something I didn't realize until now.

Question:
A 6-ft-long steam pipe is made of A-36 steel with σ=40 ksi (yield stress). It is connected directly to two turbines A and B as shown. The pipe has an outer diameter of 4 in. and a wall thickness of 0.25 in. The connection was made at T = 70°F. If the turbines’ points of attachment are assumed to have a stiffness of determine the force the pipe exerts on the turbines when the steam and thus the pipe reach a temperature of T2 =275°F.

2. Relevant equations

δT = $\alpha$*ΔT*L

3. The attempt at a solution

I thought the equation would be: δT = 6.6(10-6)*(205°F)*(72 in.)

But in my notes, it was: δT = 6.6(10-6)*(205°F)*(36 in.)

Can someone explain why the length was 36 inches and not 72 inches? I was thinking that the length was chosen arbitrarily but I wasn't sure.

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2. Jun 23, 2013

### SteamKing

Staff Emeritus
If you want to calculate the additional force imposed on the turbines by thermal expansion of the pipe, then assume that the middle of the pipe remains stationary w.r.t. the turbines. The additional length of the pipe is going to want to push both turbines off their foundations (you OP omitted the stiffness value of the turbine foundations). The amount of expansion at each end of the pipe will be proportional to the half length of the pipe, rather than the total length.

3. Jun 24, 2013

### aaronfue

I understand now. Thanks!