Advanced Methods of Structural Analysis

7.1 Fundamental Idea of the Force Method 215 Fig. 7.5 Statically indeterminate beam. Design diagram and reactions of supports A ...

216 7 The Force Method determinate beam. Analysis of this beam (calculation of all reactions, con- struction of the internal for ...

7.2 Canonical Equations of Force Method 217 Ta b l e 7. 2 Two versions of primary system and corresponding solution using princi ...

218 7 The Force Method elimination of redundant constraints andreplacing them by reactions of these con- strains. Primary unknow ...

7.2 Canonical Equations of Force Method 219 called the loaded term (loaded displacement, free term). The solution of the canoni- ...

220 7 The Force Method ıikD XZ MNiMNk EI ds; iPD XZ MNiMP^0 EI ds: (7.5) Accordingly to expression6.21, these formulas may be ...

7.2 Canonical Equations of Force Method 221 5.Calculate the unit coefficientsıik. 6.Construct the bending moment diagramMP^0 due ...

222 7 The Force Method MN†M^0 P EI D XZ  MN 1 CMN 2 CCMNn  MP^0 ds EI D1PC2PCCnP: The result of this multiplication ...

7.3 Analysis of Statically Indeterminate Structures 223 P ll a=0.4l 0 1 2 n P 02 X^1 b=0.6l EI =constant a b X 1 =1 M 1 M^0 P (^ ...

224 7 The Force Method Q 0  1 D 0:096P l l D0:096P; Q 1 nD 0:1824P l.0:096P l/ 0:4l D0:696P; Qn 2 D 0:1824P l 0:6l D0:304 ...

7.3 Analysis of Statically Indeterminate Structures 225 q Primary system X 1 1 2 3 ′^3 ′′ 4 a a EI EI q Design diagram a b Unit ...

226 7 The Force Method Displacement in the primary system due to applied load is 1PD MN 1 MP^0 EI D 1 EI  1 3  qa^2 2 a 3 ...

7.3 Analysis of Statically Indeterminate Structures 227  1 D MPMN 1 EI D a 6 EI  0  0 C 4  1 2 a 7 64 qa^2 a 1 32 qa^2  ...

228 7 The Force Method version 2 by introducing a hinge at the jointC. Therefore, the primary unknown in version 1 is reactions ...

7.3 Analysis of Statically Indeterminate Structures 229 q Primary system P X 1 X 2 1 5 4 3 2 8 7 6 6 3 4 4m 6m 5m P 3m q C B A 1 ...

230 7 The Force Method ı 22 D MN 2 MN 2 EI D 1 1 EI  1 2  8  8  2 3  8 D 170:67 EI m kN  ; (b) ı 12 Dı 21 D MN 1 MN 2 E ...

7.3 Analysis of Statically Indeterminate Structures 231 while the multiplication of the summary unit bending moment diagramMN†by ...

232 7 The Force Method  Statical verification of bending moment diagram. The free-body diagram of jointD(closed sectiona/is sho ...

7.3 Analysis of Statically Indeterminate Structures 233 Final diagram for axial forceNis presented in Fig.7.11j. Since the membe ...

234 7 The Force Method a bc Fig. 7.12 Trusses. Types of statically indeterminacy The truss (7.12a) contains one redundantsupport ...