Advanced Methods of Structural Analysis

7.3 Analysis of Statically Indeterminate Structures 235 Kinematical verification of computed internal forces may be done using t ...

236 7 The Force Method columns 2 and 3, respectively. For computation of unit displacementı 11 , the entries of the column 5 sho ...

7.3 Analysis of Statically Indeterminate Structures 237 The last result may be checked. For joint 0, the equilibrium equation P ...

238 7 The Force Method moments for the arch itself and an axial force for the tie, while the shear and axial forces for arch may ...

7.3 Analysis of Statically Indeterminate Structures 239 l=24m y x f=6m EI = const q=2kN/m q=2kN/m j Primary system (^0) X 1 1 (^ ...

240 7 The Force Method Ta b l e 7. 7 The chord length of each portion of the arch Portion 0  11  22  33  44  55  66  77  ...

7.3 Analysis of Statically Indeterminate Structures 241 MP^0 DR^0 Axq x^2 2 D24xx^2 QP^0 D  R^0 Aqx  cos'D.242x/cos' NP^0 ...

242 7 The Force Method Ta b l e 7. 1 0 Calculation of coefficient and free term of canonical equation Unit state Loaded state Po ...

7.4 Computation of Deflections of Redundant Structures 243 Corresponding axial force diagram is presented in Fig.7.15d. Knowing ...

244 7 The Force Method deflections for statically indeterminate structure becomes cumbersome. However, solution of this problem ...

7.4 Computation of Deflections of Redundant Structures 245 ql^216 8 M ql^2 P l A P= 1 l/^2 l M q A B 8 ql^2 RA ql 8 =^30 16 2 8 ...

246 7 The Force Method 7.5 Settlements of Supports................................................ If any statically indetermina ...

7.5 Settlements of Supports 247 Note that unlike the analysis of structures subjected to loads, the termMs^0 in (7.15) is absent ...

248 7 The Force Method The canonical equation and primary unknown are ı 11 X 1 C 1s D 0 , X 1 D1s=ı 11. The unit displacement ...

7.5 Settlements of Supports 249 Primary system X 1 X 2 1 5 4 3 6 8 6 3 a^4 b φ Δ1s Δ2s a b φ φ 10m 5m 3m b C B 1 2 1 a A abDesig ...

250 7 The Force Method RN'1,RN'2are reactions in direction of'-displacement due to the same primary unknowns The bending moment ...

7.6 Temperature Changes 251 Kinematical verification The summary unit bending moment diagramMN†DMN 1 C MN 2 is shown in Fig.7.18 ...

252 7 The Force Method The unit displacements should be calculated as usual. The free terms it.iD1;2;:::;n/should be calculated ...

7.6 Temperature Changes 253 2.Construct the unit bending moment and axial force diagrams 3.Calculate the unit displacements. In ...

254 7 The Force Method The negative sign means that bending moment diagram is plotted on the more cold fibers. Canonical equatio ...