# Mechanic of Materials (a short lab)

*label*Science

*timer*Asked: Jun 24th, 2018

*account_balance_wallet*$10

**Question description**

r*emember 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__

## Tutor Answer

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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