STRESSES IN A THIN CYLINDER SUBJECTED TO INTERNAL PRESSURE

We were discussing the basic concept of thin cylindrical and spherical shells, bending stress in leaf spring, polar modulus of section, derivation of strain energy due to torsion and power transmitted by solid circular shaft in our previous posts.

Today we will see here the stresses in thin cylindrical shells, subjected with internal pressure, with the help of this post.

Before going ahead, we will first remind here the fundamental of a thin cylindrical shell

Thin cylindrical shell is also termed as a pressure vessel and such vessels are usually used in various engineering applications such as for storing the fluid under pressure. Boilers, LPG cylinders, Air receiver tanks are the best examples of thin cylindrical shells.

A cylindrical or spherical shell will be considered as thin cylindrical or spherical shell, if the wall thickness of shell is very small as compared to the internal diameter of the shell.

Wall thickness of a thin cylindrical and spherical shell will be equal or less than the 1/20 of the internal diameter of shell.

Stresses in a thin cylindrical shell

Let us consider one cylindrical shell, as displayed here, subjected with internal fluid pressure P.

There will be two types of stresses, which will be developed in the wall of thin cylindrical shell and these stresses are as mentioned here.

Circumferential stress or Hoop stress

Longitudinal stress

Circumferential stress or Hoop stress

Stress acting along the circumference of thin cylinder will be termed as circumferential stress or hoop stress.

If fluid is stored under pressure inside the cylindrical shell, pressure will be acting vertically upward and downward over the cylindrical wall. Pressure vessel will tend to burst as displayed here in following figure and stresses developed in such failure of cylindrical shell will be termed as circumferential stress or Hoop stress.

Circumferential stress or hoop stress developed in the wall of cylindrical shell could be easily determined with the help of following formula.

Longitudinal stress

Stress acting along the length of thin cylinder will be termed as longitudinal stress.

If fluid is stored under pressure inside the cylindrical shell, pressure force will be acting along the length of the cylindrical shell at its two ends. Cylindrical shell will tend to burst as displayed here in following figure and stresses developed in such failure of cylindrical shell will be termed as longitudinal stress. 

Longitudinal stress developed in the wall of cylindrical shell could be easily determined with the help of following formula.

Longitudinal stress = (1/2) x Circumferential stress

σ_L = 1/2 x [p x d]/2t

σ_L =  p.d/4t

Do you have suggestions? Please write in comment box.

We will now derive the expression for circumferential stress or Hoop stress developed in the wall of cylindrical shell, in the category of strength of material, in our next post.

Reference:

Strength of material, By R. K. Bansal

Image Courtesy: Google 

Bright Idea Space 

We have started another website i.e. https://brightideaspace.com/ that basically provides the new ideas, Creative prompts and challenges, Self-improvement articles, Interviews with successful creatives, Resources and tools, innovative ideas and discuss about the various thought process that will continuously improve our thought process day by day. 

Let us see here few posts of https://brightideaspace.com/  

1. The Psychology Of Facing New Challenges And How To Overcome Them

2. Green Building Materials: A Guide To Sustainable Construction

3. The Top 10 Sustainable Cities In The World And Their Clean Energy Innovations

4. The Role Of Tree Relocation In Sustainable Development 

5. How Does Laser Cleaning Work? A Comprehensive Guide

6. Living With Purpose: Finding Your Passion And Living A Meaningful Life

7. The Importance Of Living Life To The Fullest: Why Giving Your 100% Matters

8. 9 Easy Ways To Reduce Plastic Waste In Your Daily Life

9. Prioritizing What’s Important: Understanding What Truly Matters In Life And Focusing On Those Things

10. How To Implement Your Strategic Plan: A Step-By-Step Guide

11. From ‘Good’ To ‘Great’: How To Build On The Momentum Of A Good Day

12. The Power Of Positive Self-Talk: Why A Bad Day Doesn’t Mean You’re Failing

13. The Top 10 Must-Read Personal Development Books For Success

14. Kanban: A Japanese Method To Overcome Laziness And Organize Your Tasks Efficiently

15. The Importance Of A Growth Mindset In Decision-Making: How To Adopt A Positive And Open Attitude Towards Making Decisions