Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

12 CHAPTER 1 Basic Elasticity Example 1.1 Acylindricalpressurevesselhasaninternaldiameterof2mandisfabricatedfromplates20mmthick. ...

1.6 Determination of Stresses on Inclined Planes 13 ThenegativesignforτindicatesthattheshearstressisinthedirectionBAandnotinAB. ...

14 CHAPTER 1 Basic Elasticity Fig.1.11 Stress system on two-dimensional element of the beam of Example 1.2. Thestresssystemactin ...

1.7 Principal Stresses 15 Twosolutions,θandθ+π/2,areobtainedfromEq.(1.10)sothattherearetwomutuallyperpen- dicular planes on whic ...

16 CHAPTER 1 Basic Elasticity Itfollowsthat sin2θ= −(σx−σy) √ (σx−σy)^2 + 4 τxy^2 cos2θ= 2 τxy √ (σx−σy)^2 + 4 τxy^2 sin2(θ+π/ 2 ...

1.8Mohr’s Circle of Stress 17 Fig.1.12 (a) Stresses on a triangular element; (b) Mohr’s circle of stress for stress system shown ...

18 CHAPTER 1 Basic Elasticity Hence, σn= σx+σy 2 + ( σx−σy 2 ) cos2θ+CP 1 tanβsin2θ which,onrearranging,becomes σn=σxcos^2 θ+σys ...

1.8Mohr’s Circle of Stress 19 to200N/mm^2 (tension).Calculatetheallowablevalueofshearstressatthepointonthegivenplanes. Determine ...

20 CHAPTER 1 Basic Elasticity Fig.1.14 Solution of Example 1.3 using Mohr’s circle of stress. ThenumericalsolutionsofEq.(iii)cor ...

1.9 Strain 21 ordirect strainsare associated with direct stressesσ and relate to changes in length, whileshear strainsdefinechan ...

22 CHAPTER 1 Basic Elasticity ofthelineelementis ε=lim L→ 0 L L ThechangeinlengthoftheelementOAis(O′A′−OA)sothatthedirectstraina ...

1.9 Strain 23 Now cosA′O′C′=cos(π/ 2 −γxz)=sinγxz,andasγxzis small, then cos A′O′C′=γxz. From the trigonometricalrelationshipsfo ...

24 CHAPTER 1 Basic Elasticity 1.10 CompatibilityEquations....................................................................... ...

1.12 Determination of Strains on Inclined Planes 25 SubstitutingfromEqs.(1.18)and(1.21)andrearranging, 2 ∂^2 εx ∂y∂z = ∂ ∂x ( − ...

26 CHAPTER 1 Basic Elasticity Fig.1.16 (a) Stress system on rectangular element; (b) distorted shape of element due to stress sy ...

1.13 Principal Strains 27 ThestrainεninthedirectionnormaltotheplaneEDisfoundbyreplacingtheangleθinEq.(1.30)by θ−π/2.Hence, εn=εx ...

28 CHAPTER 1 Basic Elasticity Therefore,atapointinadeformablebody,therearetwomutuallyperpendicularplanesonwhich theshearstrainγi ...

1.15 Stress–Strain Relationships 29 Sofarwehavemadenoassumptionsregardingtheforce–displacementorstress–strainrelationship intheb ...

30 CHAPTER 1 Basic Elasticity Equations(1.42)maybetransposedtoobtainexpressionsforeachstressintermsofthestrains.The procedureado ...

1.15 Stress–Strain Relationships 31 andtheshearstrainsγxy,γxz,andγyzareexpressedintermsoftheirassociatedshearstressesasfollows: ...