Mechanic of Materials (a short lab)

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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

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Mechanic of Materials (a short lab)
pressure_vessel.jpg
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  y’ x’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 — u — u oyu E osu E vsuyu G 04/01/18 C. Lab Procedure Turn on the FL 152 strain indicator. Ensure that it is set up for the FL 130 pressure vessel experiment. Check that you and anyone else in the area are wearing safety glasses. IMPORTANT: Turn all adjustment knobs very gently to avoid damaging the pressure vessel. Check that the piston handwheel is fully out for a closed-ended pressure vessel, and the relief knob is adjusted so that there is no pressure in the system. A diagram is attached at the end of this report. Take your initial zero reading for the gages and write them down in the table. IMPORTANT: DO NOT EXCEED A MAXIMUM PRESSURE OF 30 BAR UNDER ANY CIRCUMSTANCES. Close the pressure valve and increase the pressure in the pressure vessel and note the strain gage readings according to the attached table. It will only take a fraction of a pump to increase the pressure. Note any discrepancies between the target pressure reading and the actual pressure reading. θ° bar (target) bar (actual) Raw Measurements Strain Gage Readings (micro‐strain) 0 30 45 1 2 3 60 4 90 5 0 5 10 15 20 25 30 0 IMPORTANT: DO NOT EXCEED A PRESSURE OF 30 BAR UNDER ANY CIRCUMSTANCES Release the pressure in the pressure vessel and note the reading of the strain gages. M. E. Barkey 7 04/01/18 Determine the net strain readings for each gage. θ° MPa (target) MPa (actual) Net Adjusted Strain Gage Readings (micro‐strain) (Raw ‐ Average Zero) 0 30 45 60 1 2 3 4 90 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 Note: The material of the pressure vessel is aluminum: E = 70 GPa, ν = 0.33, G = (E/2)/(1+ν). Note: wall thickness, t = 2.5 mm, outside diameter = 75 mm. M. E. Barkey 8 04/01/18 D. Lab Report Check to see is the strain readings are linear with internal pressure: plot actual pressure on the y-axis and each gage strain reading on the x-axis. All of the gages will plotted on this same plot. Fit the data for each gage with a straight line (linear regression trend line). Note any deviations from linearity in your discussion. Calculate the strain in the x’ direction for each gage direction and complete the table below for the calculated results using the highest actual pressure. Include a sample calculation for 30º and 60º. θ° MPa (actual) Calculated Strain Gage Readings (micro‐strain) (from theory) at highest pressure 0 30 45 60 90 1 2 3 4 5 Compare your calculated and experimental strain values at 3.0 MPa (or the highest actual value of pressure) and determine the percent error; complete the table below. θ° MPa (actual) Comparison of Theory and Experiment‐‐Strain readings at highest MPa (microstrain) 0 30 45 60 90 1 2 3 4 5 Theory Experiment % Error M. E. Barkey 9 04/01/18 E. Questions Why do we need to use 3-D Hooke’s Law to calculate strains for this experiment? F. Discussion M. E. Barkey 10 04/01/18 FL 130 STRESS AND STRAIN ANALYSIS ON A THIN-WALLED CYLINDER 3 Description of the device 3.1 Layout of the device The device is designed as a handy, compact benchtop device. All rights reserved, G.U.N.T. Gerätebau, Barsbüttel, Germany 09/2017 All components are mounted on a base plate, so a high degree of mobility is provided. The interface circuit for the strain gauge with auxilary resistors is placed inside the base plate. 11 10 9 8 7 6 5 4 3 2 1 12 13 Item Name Item Name 1 Relieve knob 8 Closure piston 2 Hydraulic cylinder 9 Supporting collar 3 Pump lever 10 Threaded spindle 4 Manometer 11 Handwheel for piston adjustment 5 Fixed lid 12 Base plate 6 Strain gauge application 13 Connecting socket 7 Cylinder Fig. 3.1 Device view 3 Description of the device 6 FL 130 3.3 All rights reserved, G.U.N.T. Gerätebau, Barsbüttel, Germany 09/2017 Pump lever STRESS AND STRAIN ANALYSIS ON A THIN-WALLED CYLINDER Hydraulic pump Oil filling screw The cylinder is filled with hydraulic oil. The desired Safety internal pressure is generated by way of a handvalve operated hydraulic pump and displayed on a manometer (4). NOTICE Do not exceed nominal pressure 30 bar. The membrane can be overstretched and lasting deformed. The hydraulic system may develop leaks. Fig. 3.3 Hydraulic pump The safety valve is actuated at approx. 35bar. Hydraulic oil can be refilled via the oil filling screw. 3.4 Uniaxial and biaxial stress state In the outer position of the piston (8) the pressure on the front face is supported by way of the piston and a collar (9) bolted onto the cylinder. The biaxial stress state of the closed vessel applies. Piston outside: closed In the inner position of the piston the pressure on the front face is supported by way of the base frame. No load is placed on the cylinder in longitudinal direction. The uniaxial stress state of the open pipe applies. Piston inside: open Fig. 3.4 Piston outer and inner positions 3 Description of the device 8 FL 130 3.5 STRESS AND STRAIN ANALYSIS ON A THIN-WALLED CYLINDER Cylinder with strain gauge On the surface of the cylinder strain gauges (7) are arranged around the circumference. Two diametrically opposing strain gauges form a diagonal halfbridge. All rights reserved, G.U.N.T. Gerätebau, Barsbüttel, Germany 09/2017 Fig. 3.5 Strain gauge application This prevents disturbance from overlaid bending stresses. A total of 5 half-bridges, with the varying angular positions of 0°, 30°, 45°, 60° and 90° relative to the cylinder axis, are specified. By way of the connecting socket (13) the device is connected to the G.U.N.T. multi-channel measuring amplifier FL 152. In the multi-channel measuring amplifier channels 1 - 5 are occupied. Channel Angle Colour Red The measuring channels are assigned to the strain gauges as shown in Fig. 3.6. The angle 0° corresponds to the axial direction, and the angle 90° to the tangential direction. Green Blue White Yellow Fig. 3.6 Arrangement of measuring points 3 Description of the device 9

Tutor Answer

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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