Mechanical Principles Assignment 2

Higher National Certificate

Mechanical Principles

Assignment Two

Carl Jones

Table of Contents
Question 1a) 5
Q1bi) 6
Q1bii) 7
Q1biii) 10
Q1ci) 11
Q1cii) 12
Question 2a) 13
Question 3a) 15
Question 3b) 15
Question 3c) 18
Question 4a) 19
Question 4bi) 19
Question 4bii) 20
Question 4ci) 21
Question 4cii) 21
Graph 21
Question 4ciii) 22
Question 4civ) 22
Question 4d) 23

Question 1a)
Hoop Stress (circumferential stress) is simply the stress due to radial pressure.
The circumferential stress in a material of cylindrical form subjected to internal or external pressure. It is the stress felt along the circumference of a cylindrical surface because of pressure from inside the cylinder or outside the cylinder. For example, when a submarine, which is roughly cylindrical dives deeper, the sub is subjected to hoop stress because of the pressure of water surrounding it.
The hoop stress is twice as much as the longitudinal stress for the cylindrical pressure vessel.
The Equation for Hoop Stress is
Longitudinal Stress (Axial stress) is simply the stress due to Axial pressure.
When the cylinder has closed ends the internal pressure acts on them to develop a force along the axis of the cylinder.
The Equation for Longitudinal Stress is

Hoop stress can be used for both Cylinder and Spherical Pressure vessels where as Longitudinal is only used for Cylinders.

Q1bi) d=0.75m Longitudinal stress

And Hoop Stress = 2x Longitudinal Stress

Q1bii)
To find change in internal volume
Let d= internal diameter
Let c- inner circumference
Therefore c=πd

Due to internal pressure let c→c+dc
And like wise d→d+dd
Since c= πd
When pressure is excerted

Now dividing by “c” πd
=
=
We cam write these as strains i.e.

Change in Volume may be found by considering the volumetric strain (Єv) in the x,y and z direction.
So

But

The original volume

Q1biii)
The Volumetric strain is equal to the sum of the mutually