Bending of an Aluminum beam Essay Example for Free

Bending of an Aluminum beam Essay â€Å"Beams are long straight members that are subjected to loads perpendicular to their longitudinal axis and are classified according to the way they are supported†[1]. When a beam is subjected to an external load there are unseen internal forces within the beam that one must be aware of when implementing it into any design or structure. These internal forces create stress and strain that could result in failure or deformation. This lab looked at how an aluminum cantilevered beam performed under symmetric and unsymmetrical bending as well as the stresses and strains developed as a result. Objective â€Å"To study the stress and strain induced in an I-beam under symmetric and unsymmetrical bending† [2]. Theory: ? – Normal stress (Mpa) ? – Strain (mm/mm) M – Moment (kN†¢m) I – Moment of inertia (mm^6) E – Modulus of elasticity (Mpa) G – Modulus of elasticity (Mpa) v – Poisson’s ratio. L – Length (m) *Subscripts x, y, z indicate plane of reference. The strain rosettes are orientated so that ? b = 0, ? c = -45, and ? a = 45. The strain gauge equations then simplify to ?x = ? b, ? y= ? c+ ? a- ? b, and ? xy = ? c- ? a Using Hooke’s Law: ?x= ? xE, ? y= -v ? x, ? xy=? xyG This Experiment consisted of symmetric and unsymmetrical bending. For symmetric bending the relevant theory is as follows: Because the moment about the z-axis here is zero the equation equates to: Where: My = PLA. When rotated 45 degrees: My = PLA Cos(45) and Mz = PLA Sin(45) there is compressive stress along the y-x axis The moment of inertia about the y-axis is found by determining the inertia of the shape and subtracting the imaginary parts as shown: The max normal stress with be at the furthest distance from the neutral axis which is h/2 therefore: (? x)max = The strains can be found by implementing Hooke’s Law: Since ? y and ? z are zero in symmetric loading, the two equations simplify to: Because the there is no shear stress in the x-y plane when the normal stress is at maximum the shear strain will also be zero. The vertical displacement of the end of the beam is determined by multiplying the area under the moment diagram and the distance between the end and the centroid of the diagram. This equates to: For unsymmetrical bending the theory is the same however there is a moment about the y-axis and z-axis. This will affect the calculation of the normal stress and the strain in the x and y plane. Also the moment of inertia in the z-direction will need to be determined. Procedure (a) *Mount the I-beam on to the support frame. Make sure the mounting screws are tight. (b) Measure the dimensions of the I-beam including its components. (c) Mount the magnet bases of the dial gauges at appropriate positions to permit the measurements of the deflections at the free end of the beam in the vertical and the horizontal directions. (d) *Connect properly the wires from the strain gauges to the readout unit. (e) Place weights to the hanger in increments: 4, 6, 10, 26, and 42 kg. (f) Unload the hanger in increments in the reversed order as for loading. (g) For each increment, measured the strain readings at the given locations and the vertical and horizontal deflections at the free end of the beam. (h) Repeat steps (a) to (g) by rotating the beam with the following angles: 45 °. [3] Results *Refer to appendix for sample calculation and calculated results. Part 1: I-beam at 0o Loading Loading (Kg) 4 6 10 26 42 Strain Gauge 1 (? ) 1 2 4 12 20 Strain Gauge 2 (? ) 6 10 16 43 69 Strain Gauge 3 (? ) 3 4 7 18 29 Displacement 1 (mm) 0. 09 0. 15 0. 23 0. 44 0. 5 Displacement 2 (mm) -0. 19 -0. 34 -0. 55 -1. 4 -2. 25 Load (N) 39. 2 58. 5 97. 9 255. 5 413. 1 Unloading Loading (kg) 42 26 10 6 4 Strain Gauge 1 (? ) 20 10 -3 -5 -7 Strain Gauge 2 (? ) 69 42 19 11 9 Strain Gauge 3 (? ) 29 18 6 3 2 Displacement 1 (mm) 0. 5 0. 49 0. 25 0. 16 0. 07 Displacement 2 (mm) -2. 25 -1. 46 -0. 59 -0. 37 -0. 23 Load (N) 413. 1 255. 6 96. 4 58. 7 39. 2 Part 2: I-Beam at 45o Loading Loading (kg) 4 6 10 26 42 Strain Gauge 1(? ) 1 2 2 7 13 Strain Gauge 2 (? ) 5 9 14 36 54 Strain Gauge 3 (? ) 1 1 2 8 13 Displacement 1 (mm) -0. 33 -0. 50 -0. 79 -1. 88 -2. 75 Displacement 2 (mm) -0. 66 -1. 02 -1. 69 -4. 23 -6. 40 Load (N) 39. 4 58. 7 98. 2 256. 5 413. 6 Unloading Loading (kg) 42 26 10 6 4 Strain Gauge 1 (? ) 13 4 -22 -25 -26 Strain Gauge 2 (? ) 54 38 22 20 17 Strain Gauge 3 (? ) 13 6 2 0 0 Displacement 1 (mm) -2. 75 -1. 95 -0. 92 -0. 62 0. 46 Displacement 2 (mm) -6. 40 -4. 46 -2. 17 -1. 51 -1. 15 Load (N) 413. 6 256. 3 98. 1 58. 7 39. 4 Discussion For both the symmetric and unsymmetrical bending the theoretical stresses and strains were greater than experimentally determined ones. However the experimental displacement was much higher than the theoretical displacement. These two factors can lead one to believe the I-beam has undergone this procedure many times before. Another interesting point to note is that the stresses and strains are higher at equivalent loads when unloading demonstrating that there is residual stress in the I-beam even after it has been fully unloaded. For the most part however the measured and theoretical values are very close. It is to be expected that the theoretical stresses would be higher than the experimental values. The theoretical calculations rely on a ‘perfect’ material. The modulus of elasticity and cross-sectional are said to remain the same through the length of the beam which is rarely the case. Minor imperfections in the beam would result in a weaker beam and less stress is required to deflect the beam. This is exactly what has been observed in this experiment. For the symmetric and bending theoretically there would be no horizontal displacement however some horizontal displacement was shown on the readouts. This is most likely due to the slight swaying of the weights. Since the scale of this experiment was relatively small a lot of the sources of error are pretty large. Just by not having the readout computer not calibrated properly or zeroed all the way would cause pretty large discrepancies. Even the measuring or millimeters by eye caused some error. Rounding errors would be relatively small for this experiment. Conclusion In conclusion theoretical and experimental values for stress and strain are very similar to the values observed in experimental conditions. The theoretical and experimental displacements were pretty far off and at larger scales the theoretical values would not be of much use. Closer results could have been obtained by collecting more accurate measurements or by collecting multiple sets of data using a series of strain rosettes. APPENDIX I Sample Calculations Iy= = (Mz)a =(4kg)(9. 81m/s2)(0. 77m) =30. 215 Nm (Mz)b =(4kg)(9. 81m/s2)(0. 33m) =12. 95 Nm (? x)a = = = 1. 259 Mpa (? x)b = 0. 5397 Mpa (? b)v = = = -0. 0902 mm ?xy = = = 0. 0398mm (? x)a = = =17. 22*10^-6 (? y)a = -0. 35*(? x)a = 6. 027*10^-6 Experimental Symmetric Mass (Kg) 4 6 10 26 42 26 10 6 4 ?x (E-6) 6 10 16 43 69 42 19 11 9 ?y (E-6) -2 -4 -5 -13 -20 -14 -16 -13 -14 ?xy (Mpa) 2 2 3 6 9 8 9 8 9 (? x) (Mpa) 0. 438 0. 731 1. 17 3. 14 5. 04 3. 07 1. 39 0. 804 0. 657 (? y) (Mpa) -0. 146 -0. 292 -0. 365 -0. 950 -1. 46 -1. 02 -1. 17 -0. 950 -1. 02 ?xy (Mpa) 0. 054 0. 054 0. 081 0. 162 0. 243 0. 216 0. 243 0. 216 0. 243 Theoretical – Symmetric Mass(Kg) 4 6 10 26 42 (Mz)a (N†¢m) 30. 2 45. 3 75. 5 196 317 (Mb)b (N†¢m) 12. 9 19. 4 32. 3 84. 1 135 (? x)a (Mpa) 1. 25 1. 88 3. 12 8. 13 13. 1 (? x)b (Mpa) 0. 536 0. 804 1. 34 3. 48 5. 62 ?xy (Mpa) 0. 0398 0. 0598 0. 0996 0. 258 0. 418 (? x)a (E-6) 17. 1 25. 7 42. 8 111 179 (? x)b (E-6) 7. 33 11. 0 18. 3 47. 6 77. 0 (? y)a (E-6) -5. 99 -8. 98 -14. 9 -38. 9 -62. 8 (? y)b (E-6) -2. 57 -3. 85 -6. 41 -16. 6 -26. 9 ?a (mm) 0. 0902 0. 135 0. 225 0. 586 0. 947 ?b (mm) 0. 00710 0. 0106 0. 0177 0. 0461 0. 0745 Experimental –Unsymmetrical Bending Mass (Kg) 4 6 10 26 42 26 10 6 4 (? x) (E-6) 5 9 14 36 54 38 22 20 17 (? y) (E-6) -3 -6 -10 -21 -28 -28 -42 -45 -43 ?xy (E-6) 0 -1 0 1 0 2 24 25 26 (? x) (Mpa) 0. 366 0. 658 1. 02 2. 63 3. 95 2. 78 1. 61 1. 46 1. 24 (? y) (Mpa) -0. 219 -0. 439 -0. 731 -1. 54 -2. 05 -2. 05 -3. 07 -3. 29 -3. 14 Theoretical – Unsymmetrical Bending Mass (Kg) 4 6 10 26 42 (Mz,y)a (N†¢m) 21. 3 32. 0 53. 4 138 224 (Mz,y)b (N†¢m) 9. 15 13. 7 22. 9 59. 5 96. 1 (? x) (Mpa) 0. 381 0. 572 0. 954 2. 48 4. 00 (? y) (Mpa) -1. 40 -2. 10 -3. 51 -9. 12 -14. 7 (? x) (E-6) 5. 22 7. 83 13. 1 33. 9 54. 8 (? y) (E-6) 1. 83 2. 74 4. 57 11. 9 19. 2 ?x-y (mm) 0. 0902 0. 135 0. 225 0. 586 0. 946 ?x-z (mm) 0. 391 0. 587 0. 978 2. 54 4. 11

Supernatural in Shakespeares Macbeth - Beyond the Fair and Foul Essay

More to Macbeth than Fair and Foul      Ã‚  Ã‚   The statement "Fair is foul, and foul is fair" does not thoroughly express the many themes of Shakespeare's Macbeth.   The first time this statement occurs is very early in the play, when the witches chant the exact line "Fair is foul, and foul is fair"(I.i.12) only for Macbeth to repeat it himself two scenes later.   This repetition of the lines shows that the characters themselves believe that there are many foul events taking place.   Firstly, one can watch the fair Macbeth degrading into a foul inhuman monster.   Secondly, the witches may be contrasted to Macbeth to demonstrate the real foulness in these characters.   Thirdly, it can be shown that there is simply no fairness existing in Macbeth.   Lastly, one can see that there are too many themes in Shakespeare's Macbeth to be summed up in one line.      Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Macbeth, in the beginning, is a man of valor, honor and nobility.   With his loyal traits he helps maintain Scotland's stability.   Macbeth, on the outside, seems to be the fairest man in all of Scotland; however such is not true. Under the cloaking shadows of his skin, Macbeth hides his one weakness: ambition.   His wife realizes his ambition and stirs him to act on it.   Macbeth struggles with a choice: should he let the witches' prophecies realize themselves, or should he take the steps necessary to achieve them?   Macbeth knows that the latter choice will involve the murder of his virtuous king Duncan, but even this is not enough to convince him to bide his time. After urging from his wife, he chooses the latter and murders his king.   In doing so, Macbeth disrobes himself of all that is good in the human soul: kindness, courage, honor and love.   Macbeth becomes so obses... ... Greenhaven Press, Inc., 1999. 126-35.    Cotton, N. "Witches and Magic in Macbeth." Shakespeare Quarterly. 38, 1987: 320-326.    Kinney, Arthur F. ed. William Shakpespeare: the Tragedies. Boston: Hall and Company, 1985.    Muir, Kenneth. "Introduction." In Macbeth. Ed. Kenneth Muir. New York: Routledge, 1992.    Shakespeare, William. The Tragedy of Macbeth. Elements of Literature. Sixth ed. Austin: Holt, Rinehart and Winston, 1997.    Stallybrass, Peter. "Macbeth and Witchcraft." In Focus on Macbeth. Ed. John Russell Brown. Boston: Routledge, 1982.    Wadsworth, Frank W. "Shakespeare, William." World Book Online American Edition. Online Edition. Online. Netzero. 26 Mar 2002.    "William Shakespeare." BBC Homepage. Online. Available <http://www.bbc.co.uk/history/culture/shakespeare.shtml>. 26 Mar. 2002.   

Design of Compressed Natural Gas Cylinders

Chapter 2: LITERATURE REVIEW2.1 IntroductionThis chapter [ 2 ] provides a description of the undertaking and an overview of surveies related to laminated force per unit area vas. It surveys the literature covering with the design and research work on different composite stuffs. It besides reviews the laminate analysis in the visible radiation of classical failure theories. Furthermore it tends to cover the impact of multilayered subdivisions of heterogenous stuff along with the fibre orientation on the stress distribution of force per unit area vas. It besides contain process to plan composite force per unit area vas in the visible radiation of old findings in the existing literature. This chapter besides include the methodological analysis to continue on the undertaking and behavior analysis utilizing Matlab a clip tested package.2.2 Project DescriptionThe usage of metal based CNG cylinders are popularly turning with heightening fatal hazards and menaces manifolds. In Pakistan, the usage of metal based CNG cylinder are turning really fast and therefore adding to multifaceted inadvertent hazards due to low quality criterion cylinders and their mishandling. The grounds behind these effects are use of low quality dyer's rocket and expired kits. A careful estimation shows that out of 10 metal CNG cylinders four are at hazard due to chance of blast and fatal accidents in private and public conveyance vehicles. These in fact are going beginning of serious menaces to human life and cultivate the demand to look into and convey frontward an alternate safe solution. For this intent, metal CNG cylinders may necessitate to be replaced and composite or other stuffs may be the best solution. We will research the chance of composite CNG cylinder under this undertaking. This predominating state of affairs in Pakistan emphasiss on the demand to look into the failing of metal based CNG cylinder and come up with an alternate feasible solution non merely stronger plenty than metal based CNG cylinders but besides cut down the hazard of fatal accidents and life menaces to the consumer. In other words, there is a demand to carry on empirical probe that help us to convey and alternate safe and strong beginning of CNG cylinder fabrication based on composite or other stuffs and compare its viability and strength with the bing metal based CNG cylinder. This survey seek to bridge bing spread in CNG cylinder fabrication and propose some feasible solution to get the better of by taking the restraints with an purpose to hold a feasible alternate solution of high strength, environmental friendly composite CNG cylinder. The undertaking attempt to supply a hazard free competitory merchandise. In this respect, we considered Carbon/Epoxy for the most optimized conseque nces with the high facet of strength and high weight decrease of CNG cylinder. For farther betterment optimisation of wall thickness and fiber orientation is besides be done. We will prove each bed of laminated force per unit area vas with the application of Tsai-Hill failure standards. This application will surely assist us to plan a hazard free composite CNG cylinder. The survey will continue with the specific aim enlisted in to following subdivision.2.3 Aims of the surveyThe chief aim of this survey is to look into the failings of bing metal based CNG cylinder and convey up an alternate feasible solution non merely stronger plenty than metal based CNG cylinders but besides cut down the hazard of fatal accidents and life menaces to the consumer. For this intent, we will analyze the emphasis distribution produced in thin wall metal based CNG cylinder in the visible radiation of different finite component analysis packages and place the weak parts. Hoop and longitudinal emphasiss wi ll be calculated by theoretical analysis of thin wall metal cylinder. Keeping in position the penetration obtained from theoretical and finite component analysis mistake computation will be done. As we have standardized standards, the FEA package with the least mistake will be selected for farther proceeding. We will plan a laminated CNG cylinder on the same specification as of bing metal CNG cylinder. We will further optimise the design by optimisation of angle and thickness of laminated force per unit area vas. The Matlab codification will be generated for laminate analysis of composite CNG cylinder. Subsequently on the Matlab computation will be verified by utilizing ANSYS Workbench 15. The consequences of our design for composite CNG cylinder will be justified from bing literature at domestic ( if any ) and international degree. To gauge and analyse the consequence of fibre orientation on stress distribution of composite CNG cylinder, analysis will be run on different fibre angle orientation. Before continuing on the undertaking in systematic mode we will wish to seek penetration from bing literature in the force per unit area vas context.2.4 General Overview of LiteratureThe history of semisynthetic composite stuff is spread over more than 6000 old ages. The earliest semisynthetic composite stuffs were straw and clay combined to organize bricks for edifice building. Fiber-reinforced composite stuffs besides additions popularity ( despite their by and large high cost ) in high-performance merchandises that needs to be lightweight yet strong plenty to take rough lading conditions ( Shaffer,1993 ) . After the gradual development in the field of complexs over clip it was 2006 when a fiber-reinforced complex was introduced for residential every bit good as commercial usage as a non-corrosive option to steel ( Waterman, 2007 ) . A farther development was observed in 2007 wherein a military vehicle named â€Å" Humvee † , the first all-composite military vehicle, was introduced by TPI Composites Inc and Armor Holdings Inc. It was improved in 2008 by uniting C fibre and Kevlar ( five times stronger than steel ) with enhanced thermoset rosins to do military theodolite instances by ECS Composites making 30-percent igniter instances with high strength ( Pamela J, 2009 ) . This lead to a systematic research on the topic affair which is reviewed in the following subdivision.2.5 General Overview of composite force per unit area vasAs stated in the old bomber subdivision that systematic research work on composite force per unit area vass was initiated late that is i.e. In first decennary of the new millenary ( Sheffer, 1993 ; Waterman, 2007 ; Pamela J, 2009 ; and Rayapuri Ashok and Ranjith Kumar, 2013 ) . Therefore there is utmost vestry of cognition on composite force per unit area vas. To the best of our cognition, there are merely a few surveies are available in this country but research work associating to Pakistan is farther pantie or non bing. Wang Yingjun ( 2010 ) conducted a survey in Japan and a finite component theoretical account of C fibre reinforced polymer ( CFRP ) force per unit area vas with aluminium line drive is established by ANSYS finite component package. The component utilized in the survey was Shell-99 ( 4 node ) . The outer fibril lesion fibres were overwrapped by both hoop twist and coiling twist methods. He found that safety was critical because of high working force per unit area which was more than 35MPa. He conducted the inactive analysis of the vas. The burst force per unit area was predicted farther. He found when interior force per unit area increased up to 65MPa, the maximal tensile emphasis of the first CFRP ply reached rupture strength of CFRP. So the force per unit area 65MPa was regarded as the explosion force per unit area. Rayapuri Ashok and Ranjith Kumar ( 2013 ) in their survey discussed design and analysis of multilayer high force per unit area composite vass along with their advantages over single-channel block vas. Using Abaqus FEA package for burst force per unit area analysis of CFRP composite force per unit area vass for assorted fiber orientation angles, they calculated stress concentration on dish-shaped part. They used element type Solid-46 ( 8 node ) and optimized the fibre angle orientation by analysing the fibre helically for assorted orientations such as [ +25 °/-25 ° ] s, [ +35 °/-35 ° ] s, [ +45 °/-45 ° ] s, [ +55 °/-55 ° ] s, [ +65 °/-65 ° ] s, and [ +75 °/-75 ° ] s. For this intent they utilized burst force per unit area of 35MPa along with rules specified in American Society of Mechanical Engineers ( A.S.M.E ) Sec VIII Division 1. The survey found a per centum economy in stuff of 28.48 % utilizing multilayered composite vass in the topographic point of solid walled vas of SA515 Grade 70 steel. They furthered their probe and used multilayered CFRP stuff and saved 91.62 % stuff when compared to SA515 Grade 70 steel stuff vass. The explosion force per unit areas for assorted fiber orientations are predicted utilizing the Tsai-Wu failure standards. The  ± 25 ° fiber orientation angle is obtained as the optimal fibre orientation angle for the composite force per unit area vas subjected to high internal force per unit area burden. B.Vijay Kiran ( 2012 ) developed an analytical theoretical account for anticipation of optimal fiber orientations for given bed thicknesses. He selected fiber volume fraction= 0.65 and= 0.35 which was acceptable to the present composite force per unit area vas working at 3MPa internal force per unit area. He found optimal value of fiber orientation which was  ±55 ° for glass epoxy and  ±65 ° angle for C fibre. From the finite component analysis study the maximal emphasis obtained in each lamina ( for  ±55,  ±65 degrees weaving angle ) was less than the allowable on the job strength. The factor of Safety 3 was taken for the fibre reinforced composite stuff to get the better of material design and fabrication defects. The mean critical buckling force per unit area was obtained from finite element analysis study was 4.0684N/mm2, which was more than the maximal on the job force per unit area 3N/mm2. Comparison of stiffened and unstiffened complex shell was done by both theoretically and analytically techniques and he found that the stiffened cylinder has more clasping opposition than that of the unstiffened one. Javad Marzbanrad ( 2013 ) investigated the design and analysis of high force per unit area composite vass based on â€Å" unit burden method † along with complete structural analysis and rating of weariness life-time were performed utilizing finite element commercial codification ABAQUS. He selected fiber volume fraction= 0.75 and= 0.25 and element Shell-99 ( 8 node ) . He found that the weariness life-time of vas depends on the finite component mesh size, cleft denseness and ratio in an component. K.M.Pandey ( 2014 ) investigated the clasping behaviour of reasonably thin walled filament-wound carbon–epoxy cylinders subjected to hydrostatic force per unit area. A entire 9 figure of composite laminates were considered for finite component analysis. He used Finite component package ANSYS 14.0 and three finite component plan ACOS win, MSC/NASTRAN and MSC/MARC to formalize the consequences. He besides used Element 281 ( 8 node ) to make the finite component theoretical account. The ANSYS shell component theoretical account predicted the buckling force per unit area with 1.5 % divergence from the other three finite component consequences. 2.6 Methodology We in our survey and convey for a alternate solution will analyze the emphasis distribution produced in thin wall metal based CNG cylinder in the visible radiation of different finite component analysis packages and place the weak parts. Hoop and longitudinal emphasiss will be calculated by theoretical analysis of thin wall metal cylinder.Theoretical analysis of bing metal CNG cylinder will besides be conducted in the visible radiation of insight addition from work by P.Beer and Johnson ( 2006 ) . The demand for theoretical analysis emerged as to supply a base for design of composite CNG cylinder. Keeping in position the penetration obtained from theoretical and finite component analysis mistake computation will be done. As we have standard standards the FEA package with the least mistake will be selected for farther proceeding.We will plan a laminated CNG cylinder on the same specification as of bing metal CNG cylinder. We will further optimise the design by optimisation of angle and thickness of laminated force per unit area vas. The Matlab codification will be generated for laminate analysis of composite CNG cylinder. The Matlab computation will be verified by utilizing ANSYS Workbench 15. The consequences of our design for composite CNG cylinder will be justified from bing literature at domestic and international degree. To gauge and analyse the consequence of fibre orientation on stress distribution of composite CNG cylinder, analysis will be run on different fibre angle orientation.2.7 Matlab codification for design of composite force per unit area vasclear all clc % Design of composite force per unit area vas % Properties of C fibre/epoxy with 60 % volume fraction % SI unit system fprintf ( ‘Design Of Composite Pressure Vessel ‘ ) fprintf ( ‘Properties of Carbon Fibre/Epoxy with 60 per centum Volume fraction ‘ ) fprintf ( ‘Modulus of Elasticity in Longitudinal Direction ‘ ) E1=134*10^9 % Pa fprintf ( ‘Modulus of snap in cross way ‘ ) E2=7*10^9 % Pa fprintf ( ‘Shear Modulus ‘ ) G12=4.2*10^9 % Pa fprintf ( ‘ Posion Ratio ‘ ) v12=0.25 fprintf ( ‘ Longitudinal tensile break strength ‘ ) XT=1270e6 % Pa fprintf ( ‘ Transverse tensile break strength ‘ ) YT=42e6 % Pa fprintf ( ‘ Shear Strength ‘ ) Sh=90e6 % Poision Ratio fprintf ( ‘Longitudinal compressive break strength ‘ ) XC=1130e6 % Pa fprintf ( ‘Transverse compressive break strength ‘ ) YC=141e6 % Pa fprintf ( ‘Inner radius of force per unit area vas ‘ ) r=.1335 % m % Inner radius of force per unit area vas fprintf ( ‘Burust force per unit area applied ‘ ) p=75e6 % MPa % Pressure applied fprintf ( ‘Thickness of force per unit area vas ‘ ) t1=0.01182 ; % m % Thickness of force per unit area vas fprintf ( ‘Compliance Matrix ‘ ) S= [ 1/E1 -v12/E1 0 ; -v12/E1 1/E2 0 ; 0 0 1/G12 ] fprintf ( ‘Stiffness Matrix ‘ ) Q=inv ( S ) % Stress computation fprintf ( ‘Stress calculation ‘ ) fprintf ( ‘Sigma-x ‘ ) sigmax= ( p*r ) / ( 2*t1 ) % Longitudinal emphasis ‘ fprintf ( ‘Sigma-y ‘ ) sigmay= ( p*r ) /t1 % Hoop emphasis fprintf ( ‘Txy ‘ ) Txy =0 % Shear emphasis fprintf ( ‘Optimized angle in degree ‘ ) o=54.7 % Optimized angle in grade % Stress computation at merely optimized angle fprintf ( ‘Stress computation at optimized angle ‘ ) fprintf ( ‘Longitudinal emphasis at optimized angle ‘ ) sigma1= ( sigmax* ( cosd ( o ) ^2 ) ) + ( sigmay* ( Sind ( o ) ^2 ) ) % Longitudinal emphasis at optimized angle fprintf ( ‘Transverse emphasis at optimized angle ‘ ) sigma2= ( sigmax*sind ( o ) ^2 ) + ( sigmay*cosd ( o ) ^2 ) % cross emphasis at optimized angle fprintf ( ‘Shear emphasis at optimized angle ‘ ) Taa12= – ( sigmax*sind ( o ) *cosd ( o ) ) + ( sigmay*sind ( o ) *cosd ( o ) ) +Txy* ( cosd ( o ) ^2-sind ( O ) ^2 ) % Shear Stress at Optimized angle S= [ 1/E1 -v12/E1 0 ; -v12/E1 1/E2 0 ; 0 0 1/G12 ] ; Q=inv ( S ) ; fprintf ( ‘Angle orientation ‘ ) Angles= [ 0 90 54.7 54.7 90 0 ] fprintf ( ‘Thickness distribution ‘ ) t= [ 0.59 1.18 4.13 4.13 1.18 0.59 ] *10^-3 h=0 ; n_layers=length ( T ) ; for i=1: n_layers h=h+t ( I ) ; terminal omega ( 1 ) =-h/2 ; omega ( n_layers+1 ) =h/2 ; for i=2: n_layers omega ( I ) =z ( i-1 ) +t ( i-1 ) ; terminal A=zeros ( 3,3 ) ; B=zeros ( 3,3 ) ; D=zeros ( 3,3 ) ; for i=1: n_layers A= A + ( Qbar ( Q, Angles ( I ) ) * ( omega ( i+1 ) – omega ( I ) ) ) ; B= B + ( Qbar ( Q, Angles ( I ) ) * ( omega ( i+1 ) ^2 – omega ( I ) ^2 ) /2 ) ; D= D + ( Qbar ( Q, Angles ( I ) ) * ( omega ( i+1 ) ^3 – omega ( I ) ^3 ) /3 ) ; terminal fprintf ( ‘ABD Matrix ‘ ) ABD= [ A B ; B D ] fprintf ( ‘Forces Calculation ‘ ) NM = 10^3* [ 499 ; 998 ; 500 ; 0 ; 0 ; 0 ] fprintf ( ‘Calculating Initail Strain ‘ ) strainxy = inv ( ABD ) *NM % initial strain + curvatures Qavg=zeros ( 3,3 ) ; fprintf ( ‘Calculating Q-bar for each bed ‘ ) for i=1: n_layers Qavg= Qavg + ( ( Qbar ( Q, Angles ( I ) ) * ( omega ( i+1 ) – omega ( I ) ) ) /h ) ; fprintf ( ‘layer = % vitamin D, z = % 0.1f mm ‘ , I, omega ( i+1 ) *1000 ) Q_bar=Qbar ( Q, Angles ( I ) ) terminal fprintf ( ‘Calculating Q-average ‘ ) Q_avg=Qavg fprintf ( ‘Calculating S-average ‘ ) Savg=inv ( Qavg ) fprintf ( ‘Modulus of snap in x-axis direction ‘ ) Ex=1/Savg ( 1,1 ) fprintf ( ‘Modulus of snap in y-axis direction ‘ ) Ey=1/Savg ( 2,2 ) fprintf ( ‘Shear Modulus ‘ ) Gxy=1/Savg ( 3,3 ) vxy=-Savg ( 1,2 ) *Ex fprintf ( ‘Stress computation for each bed ‘ ) for i=1: n_layers fprintf ( ‘layer = % vitamin D, z = % 0.1f mm ‘ , I, omega ( i+1 ) *1000 ) fprintf ( ‘Strain-xy Produced in the bed ‘ ) strainxyk = strainxy ( 1:3,1:1 ) + omega ( I ) *strainxy ( 4:6,1:1 ) fprintf ( ‘Stress-xy Produced in the bed ‘ ) stressxyk = Qbar ( Q, Angle ( I ) ) *strainxyk stressLT=TM ( Angles ( I ) ) *stressxyk fprintf ( ‘layer = % vitamin D, z = % 0.1f mm ‘ , I, omega ( i+1 ) *1000 ) StrainLT=S*stressLT fprintf ( ‘Longitudinal Strain ‘ ) Strain_Longitudinal=StrainLT ( 1,1 ) % Longitudinal strain fprintf ( ‘Transverse Strain ‘ ) Strain_Transverse=StrainLT ( 2,1 ) % Transverse Strain fprintf ( ‘Longitudinal Stress ‘ ) Stress_Longitudinal=stressLT ( 1,1 ) % Longitudinal Stress fprintf ( ‘Transverse Stress ‘ ) Stress_Transverse=stressLT ( 2,1 ) % Transverse Stress fprintf ( ‘Shear Stress ‘ ) Stress_Shear= stressLT ( 3,1 ) fprintf ( ‘Applying Tsai–Hill standards ‘ ) Alpha= ( stressLT ( 1,1 ) /XT ) ^2- ( stressLT ( 1,1 ) *stressLT ( 2,1 ) /XT^2 ) + ( stressLT ( 2,1 ) /YT^2 ) + ( stressLT ( 3,1 ) /Sh ) ^2 if Alpha & A ; lt ; =1 fprintf ( ‘Ok Layer is safe ‘ ) else fprintf ( ‘Not Ok Layer is non safe ‘ ) terminal terminal2.8 DrumheadThree is a scarceness of literature in this the country of composite stuffs. Most of the literature available on composite force per unit area vas is about optimisation of fiber orientation while major part of it is about Glass fiber wherein the research workers identified the emphasis distribution utilizing different fiber orientation. These surveies found the consequence curtailing weight decrease by about 29 % ( K.M.Pandey, 2014 ; Javad Marzbanrad, 2013 ; and Rayapuri Ashok, 2013 ) . For analysis purpose many of research workers benefited from ANSYS as the finite component analysis package because this to them provides more user friendly interface and extremely elaborate analysis compatibility. They selected Shell-99 and Solid-46 ( 8 node ) as component for more optimized consequences. Their most important findings were that Carbon/Epoxy had provided the highest strength consequences with a comparatively high weight decrease. They conducted their probe at 54.7 ° because they presume that it could supply the most optimized consequences but it may non be allowable practically as referred by B.Vijay Kiran ( 2012 ) . They have besides selected 4 and 8 node elements wherein 16 node component is preferred because of its more precise consequences. The other surveies under reappraisal besides used maximal shear emphasis theory while on the other manus Tsai-Hill failure theory provide more better consequences in multilayered laminate analysis. These surveies besides used Abaqus package which may give less attested consequences when compared to analysis through ANSYS Workbench. We in our survey attempt to get the better of this spread and convey a feasible alternate solution of high strength, environmental friendly composite CNG cylinder.We have utilized Matlab for numerical analysis of laminated force per unit area vas. The merchandise will travel through a battery of trial in order to conform its genuineness and cogency.

Personal Narrative My Family History - 1441 Words

I have always been mature for my age, growing up an only child kind of does that to you. I had to watch over my little cousins quite often and at that time in my life, I dreaded babysitting. The crying, the screaming, the tantrums; they annoyed me to no end. Olivia, being the youngest, would say, â€Å"your not the boss of me!† Umm, actually I am while your parents are away, so please just listen to what I ask of you. After two long years of babysitting, I had decided I really did not like kids, that I would never have any of my own. But when I turned fifteen, I regretted ever saying that, seeing as my family history was about to catch up to me. I always knew there was something â€Å"off† when it came to genetics in my family. I watched my mom go†¦show more content†¦Well, I knew all to well what my body was going through. It scared me to the core. I watched my mom go through this, now it is happening to me. I do not want surgery; I am way to young for this! The thoughts I kept having were the worst. I decided to Google some of my symptoms; which was the wrong thing to do. I have cancer? I am dying? Google, although very handy at times, was my worst enemy that night. I finally decided to talk to my mom; she had been through this, she would know what to do. She told me that she had already noticed what was going on and had scheduled an appointment at a gynecologist for me. Oh no, I am not going there. Mom, you know what they do to women there, right? Within the next couple of weeks I was sitting on a cold, hard doctors bed, wearing a paper vest, looking down at the foot stirrups, shaking to my core, just waiting for the doctor to tell me the inevitable. I know he is going to tell me I am sick that I am going through everything my mom went through. Or worst. Once he walked in, he tried to make jokes. Sorry doc, but your jokes are not helping so just please stop trying to be funny. I know what your about to do to me, those jokes are just going to make it even more awkward. And they did. During the exam, my doctor scarred me for life; he talked to me about dating his stepson, all because he knew I was a virgin. What the†¦. Are you kidding me you weirdo! When he finished, he said, â€Å"everything looks good, but lets set up anShow MoreRelatedMy Family And Education Is Important For Your Future1221 Words   |  5 Pagesin my family’s narrative. The first theme in society that contradicts the values of my family is homos exuality. As mentioned above, religion is a large part of my family, therefore, homosexuality is not part of the catholic religion. With that being said my family has a strong opinion and belief about same sex relationships. The second theme compliments my family’s values and that is getting and education. 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Most of my teachers looked atRead MoreBehavioral Intergenerational and Structural Approaches Paper1633 Words   |  7 PagesIntergenerational, and Structural Approaches Paper After assessing my nuclear and extended family using a genogram, it was apparent that a history of mental illness was a pattern within my paternal extended family. My family never went to therapy, but I truly think that it would have been beneficial throughout my childhood and teenage years. Solution-focused therapy, narrative therapy, and intergenerational therapy and three therapies that can aide families in healing processes from lack of unity, communicationRead MoreEssay on Race and Class in Alice Walkers Color Purple1622 Words   |  7 Pagesto puzzle out the markings on her first envelope from Nettie provides a concrete illustration of both Celies particular horizon of interpretation and Walkers chosen approach to the epistolary form: Saturday morning Shug put Nettie letter in my lap. Little fat queen of England stamps on it, plus stamps that got peanuts, coconuts, rubber trees and say Africa. I dont know where England at. Dont know where Africa at either. So I stir dont know where Nettie at. (102) Revealing CeliesRead MoreCase Study : Mr. Rocky Mountain 916 Words   |  4 PagesMr. Rocky Mountain is one of my patients in the radiation oncology clinic. I choose this case for the reason that later on I found out the Mr. Rocky is a father of one of my acquaintance and now my friend and the extent of his sickness. This paper will prove that illness narrative provide adequate subjective assessment and telling story of their illness allows the narrator to disclose what is important to their lives, what matter to them most. To provide effective care to the patient, understandingRead MoreExploring The Benefits And Difficulties Of Travel Accounts881 Words   |  4 Pagesworks that some may regard as genre in their own rights†¦ but it distinguishes these from other types of narrative in which travel ins narrated by a third party or is imagined.† Young’s description of travel narratives allows for accounts that were viewed as accurate in their time such as Jonathan Swift’s Gulliver’s Travels. Young and Elizabeth Bohls demonstrate the ability for travel narratives to be a combination of several literature genres, and the focus is on the aspects of the traveler ratherRead MoreThe Writing of the Long Song Essay957 Words   |  4 PagesThe writing of the long song â€Å"How can I be proud of my Jamaican roots, when my ancestors had been slaves†? This question asked by a woman with Jamaican roots followed British novelist Andrea Levy for a long time. 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