Finding Optimal Thickness for 50 MPa Pressure Vessel

[Precursor]

Homework Statement

[PLAIN]http://img714.imageshack.us/img714/7747/43416215.jpg

The attempt at a solution

I have already solved parts (a) and (b). It's part (c) that I can't get.

To get a minimum thickness at 50 MPa, I thought that the hoop stress equation would govern. Here is my calculation for it:

$$\sigma = \frac{Pr}{t}$$

Solving for t, I get:

$$t = \frac{Pr}{\sigma}$$

$$t = \frac{(1200*10^{3} Pa)(0.5m)}{50*10^{6} MPa}$$

$$t = 0.012 m$$

$$t = 12 mm$$


However, this is not the answer. The answer takes the longitudinal stress equation as the governing one. Therefore, the solution is half of mine, a thickness of 6 mm.

Why is this so?

 

[Precursor]

But you are assuming that the weld is part of the hemisphere. I believe that it is part of both the cylinder and the hemisphere. If it was only part of the hemisphere, the solution wouldn't have stated that the longitudinal stress governed.

 

[nvn]

The cylinder longitudinal force is the tensile force across the weld.

 

[Precursor]

But why would the longitudinal stress govern if the hoop stress results in a greater thickness?

 

[nvn]

Precursor: The cylinder hoop stress does not travel across the welded joint, whereas the cylinder longitudinal stress does. The longitudinal stress governs only for the weld size here. By the way, your pictures are too wide. Please see post https://www.physicsforums.com/showpost.php?p=2937012".