Transcript الشريحة 1

Examples
Example 2
A thin cylinder 75 mm internal
diameter, 250 mm long with
walls 2.5 mm thick is subjected
to an internal pressure of 7
MN/m2. Determine the change
in internal diameter, the
change in length, hoop stress &
longitudinal stress (E = 200
GN/m2 &  =0.3).
Solution:
For thin cylinders:
For thin cylinders:
For thin cylenders:
For thin cylinders:
Example 3
A cylinder has an internal
diameter of 230 mm, has walls
5 mm thick and is 1 m long. It
is found to change in internal
volume by 12.0 x 10-6 m3 when
filled with a liquid at a pressure
p. If E = 200GN/m2 and  =
0.25, and assuming rigid end
plates, determine:
(a) the values of hoop and
longitudinal stresses;
(b) the modifications to these
values if joint efficiencies of
45% (hoop) and 85%
(longitudinal) are assumed;
(c) the necessary change in
pressure p to produce a further
increase in internal volume of 15
%. (The liquid may be assumed
Solution:
Check first type of
cylinder:
d / t = 230 / 5 = 46
More than 20, then the
cylinder is considered:
Thin cylinder
Second step look for the
pressure. If the pressure is
unknown then try to get it
by the available data.
 In this example the pressure
is unknown but the change
of volume is given. So that
you have to use the
available data to get the
unknown parameters.

For thin cylinders:
The original volume V is not given but
you can calculate it from the given
dimensions of the cylinder.
Calculating the original volume V:
For thin cylinders:
For thin cylinders:
b: hoop stress acting on the longitudinal
joints:
Longitudinal stress (acting on the
circumferential joints)

(c) Since the change in
volume is directly
proportional to the
pressure, the necessary
15 %, then increase in
volume is achieved by
increasing the pressure
also by 15 %.
Necessary increase in
pressure:
increase in p =
6
0.15 x 1.25 x 10
= 1.86 MN/m2



Example (4)
(a) A sphere, 1 m internal diameter
and 6 mm wall thickness, is to be
pressure-tested for safety purposes
with water as the pressure medium.
Assuming that the sphere is initially
filled with water at atmospheric
pressure, what extra volume of
water is required to be pumped in to
produce a pressure of 3 MN/m2?
For water, K = 2.1 GN/m2.
(b) The sphere is now
placed in service and filled
with gas until there is a
-6
volume change of 72 x 10
3
m
 Determine the pressure
exerted by the gas on the
walls of the sphere.

Solution
Where:
Then:
b- Change of volume of the sphere:
volume change is given of 72 x10-6 m3
The required pressure:
Problems