Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)
32 CHAPTER 1 Basic Elasticity An examination of Eq. (1.54) shows thatν≤0.5, since a body cannot increase in volume under pressur ...
1.15 Stress–Strain Relationships 33 FromEqs.(1.52), εx= 1 200000 ( 60 +0.3× 40 )= 360 × 10 −^6 εy= 1 200000 (− 40 −0.3× 60 )=− 2 ...
34 CHAPTER 1 Basic Elasticity Fig.1.17 Mohr’s circle of strain for Example 1.5. arelocated.ThecenterCofthecircleistheintersectio ...
1.15 Stress–Strain Relationships 35 Inthecasewherethebarisreturnedtoitsoriginallengthorifthebarhadnotbeenallowedtoexpand atall,t ...
36 CHAPTER 1 Basic Elasticity thatthisstressisσx.TheninEqs.(1.58),σx=σcorσsandσy=σz=0;thetotalstraininthecopperand steelisthen,r ...
1.16 Experimental Measurement of Surface Strains 37 1.16 ExperimentalMeasurementofSurfaceStrains................................ ...
38 CHAPTER 1 Basic Elasticity TheprincipalstressesarenowobtainedbysubstitutionofεIandεIIinEqs.(1.52).Thus, εI= 1 E (σI−νσII) (1. ...
1.16 Experimental Measurement of Surface Strains 39 TheradiusofthecircleisCQand CQ= √ CN^2 +QN^2 Hence, CQ= √[ 1 2 (εa−εc) ] 2 + ...
40 CHAPTER 1 Basic Elasticity Substitutingthevaluesofεa,εb,andεcinEq.(1.69), εI= 10 −^6 2 ( 1000 − 300 )+ 10 −^6 √ 2 √ ( 1000 + ...
Problems 41 Fromthetheoryofthetorsionofcircularsectionbars(seeEq.(iv)inExample3.1), τxy=29.7N/mm^2 = Tr J = T× 25 π× 504 / 32 fr ...
42 CHAPTER 1 Basic Elasticity σx(N/mm^2 ) σy(N/mm^2 ) τxy(N/mm^2 ) (i) + 54 + 30 + 5 (ii) + 30 + 54 − 5 (iii) − 60 − 36 + 5 (iv) ...
Problems 43 P.1.7 Anelementofanelasticbodyissubjectedtoathree-dimensionalstresssystemσx,σy,andσz.Showthat ifthedirectstrainsinth ...
44 CHAPTER 1 Basic Elasticity P.1.11 The simply supported rectangular beam shown in Fig. P.1.11 is subjected to two symmetricall ...
CHAPTER 2 Two-Dimensional Problems in Elasticity.............................................. Theoretically, we are now in a po ...
46 CHAPTER 2 Two-Dimensional Problems in Elasticity byEqs.(1.6): ∂σx ∂x + ∂τxy ∂y +X= 0 ∂σy ∂y + ∂τyx ∂y +Y= 0 andtherequiredstr ...
2.2 Stress Functions 47 sothat εx= 1 E [( 1 −ν^2 )σx−ν( 1 +ν)σy] and εy= 1 E [( 1 −ν^2 )σy−ν( 1 +ν)σx] Also, γxy= 2 ( 1 +ν) E τx ...
48 CHAPTER 2 Two-Dimensional Problems in Elasticity TheEnglishmathematicianAiryproposedastressfunctionφdefinedbytheequations σx= ...
2.3 Inverse and Semi-Inverse Methods 49 Fig.2.1 Required loading conditions on rectangular sheet in Example 2.1. Example 2.2 Amo ...
50 CHAPTER 2 Two-Dimensional Problems in Elasticity Fig.2.2 (a) Required loading conditions on rectangular sheet in Example 2.2 ...
2.3 Inverse and Semi-Inverse Methods 51 Example 2.3 AcantileveroflengthLanddepth2hisinastateofplanestress.Thecantileverisofunitt ...
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