Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)
92 CHAPTER 4 Virtual Work and Energy Methods mustbesmall,sothatwemayassumethatexternalandinternalforcesareunchangedinmagnitudean ...
4.2 Principle of Virtual Work 93 force,S;abendingmoment,M;andatorque,T,producedbysomeexternalloadingsystemactingon thestructureo ...
94 CHAPTER 4 Virtual Work and Energy Methods Shear Force Theshearforce,S,actingonthemembersectioninFig.4.5producesadistributiono ...
4.2 Principle of Virtual Work 95 Bending Moment The bending moment,M, acting on the member section in Fig. 4.5 produces a distri ...
96 CHAPTER 4 Virtual Work and Energy Methods sothatforastructurecomprisinganumberofmembersthetotalinternalvirtualwork,Wi,M,produ ...
4.2 Principle of Virtual Work 97 asitslineofaction.However,thevirtualworkdonebytheinternalforce,N(=P),isnegative,sincethe displa ...
98 CHAPTER 4 Virtual Work and Energy Methods Forastructurecomprisinganumberofloadpositions,thetotalexternalvirtualworkdoneisthen ...
4.3 Applications of the Principle of Virtual Work 99 4.3 ApplicationsofthePrincipleofVirtualWork................................ ...
100 CHAPTER 4 Virtual Work and Energy Methods ifweimaginethatthebeamishingedatBandthatthelengthsABandBCarerigid,avirtualdisplace ...
4.3 Applications of the Principle of Virtual Work 101 Fig.4.9 Determination of the internal force in a member of a truss using v ...
102 CHAPTER 4 Virtual Work and Energy Methods TheactualsignofFBAisthengovernedbythesignoftheexternalvirtualwork.Thus,ifthe30kN l ...
4.3 Applications of the Principle of Virtual Work 103 tookplace.Theexternalvirtualworkdonebytheunitloadis,fromFig.4.10(b),1υB.Th ...
104 CHAPTER 4 Virtual Work and Energy Methods Fig.4.11 Determination of the rotation of a simply supported beam at a support usi ...
4.3 Applications of the Principle of Virtual Work 105 Hence, θA= W 2 EIL {[ L x^2 2 − x^3 3 ]L/ 2 0 − 1 3 [ (L−x)^3 ]L L/ 2 } fr ...
106 CHAPTER 4 Virtual Work and Energy Methods These axial forces are constant along the length of each member so that for a trus ...
Problems 107 and 1 δD,h= 880 × 106 200000 × 1800 whichgives δD,h=2.44mm Both deflections are positive, which indicates that the ...
108 CHAPTER 4 Virtual Work and Energy Methods Fig. P.4.2 P.4.3 Determine the reactions at the built-in end of the cantilever bea ...
Problems 109 Fig. P.4.5 P.4.6 Usetheprincipleofvirtualworktocalculatetheverticaldisplacementsatthequarter-andmid-spanpoints inth ...
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CHAPTER 5 Energy Methods.......................................................................... In Chapter 2, we saw that the ...
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