Advanced Methods of Structural Analysis

7.6 Temperature Changes 255 ı 11 D 666:67 EI ;ı 12 Dı 21 D 275 EI ;ı 22 D 170:67 EI : (b) h = 0.6m b = 0.2m t 1 =− 10 °C 10 m 5m ...

256 7 The Force Method for portion 6-8 tavD 0 C 20 2 D 10 ı tDj 0 .C20/jDC 20 ı: These parameters for each element of the fram ...

7.6 Temperature Changes 257 Kinematical verification The summary unit bending moment diagramMN†is shown in Fig.7.20e. The expres ...

258 7 The Force Method X 1 2 ′ 1 234 5 EA 3 ′ 4 ′ d=4m h=3m 2 EA 2 EA EA Design diagram Primary system Fig. 7.21 Externally stat ...

Problems 259 In this case,  1 tD10:672 ̨t: Column 5 is used for calculation of unit displacement of the canonical equation. ...

260 7 The Force Method 7.2.A clamped-pinned beam is subjected to coupleM 0 at the roller support B(Fig.P7.2). Find the reaction ...

Problems 261 A BC ll Fig. P7.5 7.5.Calculate the reaction and bending moment at the supportB(Fig.P7.5), if the vertical settleme ...

262 7 The Force Method Ans. .7:7/ RAD P 2  3 ^2  ;MCD Plu^2  2 .3u/; MAD Pl 2   1 ^2  : .7:8/ RBD Pu^2 2 .3u/ 1 1 ...

Problems 263 7.12.The frame is subjected to uniformly distributed loadq, as shown in Fig.P7.12. Construct the internal force dia ...

264 7 The Force Method A B q EI h CD EI Fig. P7.14 Ans.X 1 D 3 16 qh; MCD 5 16 qh^2 ;MDD 3 16 qh^2 ;D qh^4 16 EI . 7.15.The po ...

Problems 265 P l A B a =ul b =ul C Fig. P7.17 Ans.RAD Pb^2 l^3 .3aCb/ ; MADPlu^2 ;MCD2P lu^2 ^2 ; fCDP a^3 b^3 3 EIl^3 . 7.18 ...

266 7 The Force Method Ans.QAD32:99kN;QBD3:02kN;QCD5:32kN; NCDD50:03kN. 7.20.Symmetrical structure is subjected to loadP, as sh ...

Problems 267 RA H MA RB H MB l=2R O q R Fig. P7.22 Ans.RADqR ; HD0:56012qR; MAD0:10658qR^2 7.23.Design diagram of a two-hinged p ...

268 7 The Force Method 7.25.A rigid horizontal beam is supported by four identical vertical rods and sup- ports a loadP, as show ...

Problems 269 7.28.The portal frame is subjected to settlementsa,b,and'of supportB.Cal- culate the free terms of canonical equati ...

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Chapter 8 The Displacement Method The displacement method is a powerful method for analysis of statically indeterminate frames s ...

272 8 The Displacement Method 8.1.1 Kinematical Indeterminacy.................................. In the case of the force method, ...

8.1 Fundamental Idea of the Displacement Method 273 ab 5 1 3 5 (^24) j 2 j 2 j 4 1 3 2 4 Hinged scheme 1 3 5 2 4 Δ 1 Δ 2 Δ 4 1 3 ...

274 8 The Displacement Method number of rigid joints is 2, hence the degree of kinematical indeterminacy of the en- tire structu ...