A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. (Wikipedia to the rescue!)

Pressure vessels are one of the most commonly used equipment, especially in the boilers, distilleries, compressors, vacuum chambers etc etc etc. Look around, you might have a pressure vessel at your home disguised as a fire extinguisher or your deodorant can!

The pressure vessels hold stuff under “pressure” and pose a huge danger with possibility of fatal injuries. As an engineer you provide a safe design after analyzing all the various stresses.

## 1. Recap of the theory presented in the lab

- A
**strain gage**is a sensor which changes its resistance due to deformations in the surface it is stuck on. This resistance is picked up by an amplification unit (the orange box) which spits out a final number. That number is the strain in microns. - A single strain gage provides strain and stress in just a single direction, which is more than enough for the tensile test of rod in the previous lab.
- To define a 2D stress state (stress on a surface) we need three stress components
- Normal x component $\sigma_x$
- Normal y component $\sigma_y$
- Shear xy component $\tau_{xy}$

- To get these three unknown components we need three strain gages. Usually, these three strain gages are mounted in an angular arrangement called a strain rosette. Finally by using the power of trigonometry, we can write equations to get the 2D stress state (as shown in your manual!).
**Remember, when you have shear stresses in your 2D stress state, the normal stresses are not the maximum or minimum stresses on that surface.**You need to find maximum and minimum principal(le?) stress using either the graphical method (Mohr’s Circle) or the equations provided in your lab manual.

## 2. Stresses in a *thin-walled* pressure vessel

There are two main stresses in (the cylindrical or spherical part) pressure vessels:

1. $\sigma_1$ which is the hoop stress in the circumferential direction.

2. $\sigma_2$ which is the longitudinal stress in the longer/length direction.

For your calculations, please use

Then use the various stresses to get the principal maximum and minimum stresses $\sigma_{1,2}$.

Theoretically, the different stresses for different sections of our pressure vessel are:

- For the spherical part:
- The hoop stress $\sigma_{1}$ = $\frac{p r}{2 t}$
- The longitudinal stress $\sigma_{2}$ = $\frac{p r}{2 t}$

- For the cylindrical part:
- The hoop stress $\sigma_{1}$ = $\frac{p r}{2 t}$
- The longitudinal stress $\sigma_{2}$ = $\frac{p r}{2 t}$

- For the transition part:
**Please tell me if the hoop stress and longitudinal stress for transitional zone is close to $\frac{p r}{2 t}$ or $\frac{p r}{t}$**

## 3. What do I want in the report?

Sample Calculations:

- Pick a single pressure value (say 1600 psi) and show me:
- All the strains
- All the stresses
- Principal stresses using the equation provided in the manual
- Theoretical calculations using $\frac{p r}{2 t}$ and $\frac{p r}{t}$

- Pick a single pressure value (say 1600 psi) and show me:
Graphs/Plots:

**Three**strain plots for different rosettes. The x axis should be pressure (kPa) and the y axis should be strains, each one for:- Spherical region
- Transition region
- Cylindrical region

**Three**stress plots containing both experimental and theoretical principal maximum and minimum stress for different rosettes. The x axis should be pressure (kPa) and the y axis should be stress (kPa) both experimental and theoretical stresses, each one for:- Spherical region
- Transition region
- Cylindrical region