# Mechanic of Materials (a short lab)

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Question description

remember before u handle this work, this work is so important to me, so i will revise it many times before i turn it in and i will rate u depend on your work quality such as providing correct and full answers and meet all requirements in the attached instructions. Please avoid the Lack of depth in your response.

see the data then complete and answer the attached WORD document fully.

don't forget to graph the data report via Excel ,

Don't forget to provide me with:

1: the excel file including graphs

2: calculations via Excel for

pressure_vessel.jpg

TeacherSethGreg
School: UT Austin

Attached.

Mechanics of Materials Laboratory
Dr. M. E. Barkey
Department of Aerospace Engineering and Mechanics
The University of Alabama

Pressure Vessel Stresses

M. E. Barkey

1

04/01/18

A. Introduction and Objective
The objectives of this experiment are to compute hoop and axial stresses for a cylindrical
pressure vessel and to transform the stress state to various directions; compute strains;
and compare the strain values to measurements performed on a pressure vessel using
instrumented with strain gages.
B. Theory

1.0 Cylindrical Pressure Vessel Stress State

The state of stress on a thin-walled cylindrical pressure vessel can be found by
equilibrium equations and the assumption that the stresses in the wall thickness have
a uniform distribution. The stresses in the hoop and axial directions are derived in
the lecture.
The stresses in the hoop and axial directions are

oh =

pr
t

(1)

oa =

pr
2t

(2)

where p is the internal pressure, r is the inside radius, and t is the wall thickness of
the pressure vessel.

M. E. Barkey

2

04/01/18

H
A

When plotted on Mohr’s Circle, these points are on the horizontal diameter of the 2D circle, since there is no shearing stress in the axial-hoop coordinate system—i.e.
these stress are in-plane principal stresses.

M. E. Barkey

3

04/01/18

2-D Circle

()

( A   )

( H   )

+

2.0 Stress Transformations
Stresses can be transformed from the axial and hoop coordinate system through the
use of stress transformation equations or Mohr’s circle.

M. E. Barkey

4

04/01/18

x’y’

y’
H
y
x

y’

A

( A   )

2

x’

2-D Circle

()

x’

Y’

( y’  −x’y’ )

( H   )

X’
( x’  x’y’ )

+
M. E. Barkey

5

04/01/18

From Mohr’s Circle,

osu = oave — Rcosα
oyu = oave + Rcosα
vsuyu = Rsinα

where

oave =

oÆ +oK
2

=

3 pr
4 t

α = 28
On the surface of the pressure vessel where oz = 0 , the strains in the x’ – y’
coordinate system can be found through 3-D Hooke’s Law:

s

=

su

s

=
yu

osu
E
oyu
E

ysuyu =

M. E. Barkey

6

—...

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Anonymous
Thanks, good work

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