Advanced Methods of Structural Analysis

9.1 Fundamental Idea of the Mixed Method 315 A q 1 5 4 3 2 X 1 Z 2 a b 12 8m 8m 4m q=6kN/m 1 54 3 2 A stiffness 2EI stiffness ZE ...

316 9 Mixed Method 9.2 Canonical Equations of the Mixed Method........................... Compatibility conditions for structure ...

9.2 Canonical Equations of the Mixed Method 317 Thus, the character of each equation ismixedbecause it is the displacement (or r ...

318 9 Mixed Method r 210 D  kN m kN DŒm: Equilibrium condition of induced constraint 2 from bendingmoment diagramM 2 leads to ...

Problems 319 primary system of the force method and corresponding unit bending moment diagramM 1 are presented in Fig.9.2g. Ta b ...

320 9 Mixed Method P Fig. P9.1 9.2.Design diagrams of the nonsymmetrical frames are presented in Fig.P9.2a–e. Choose the best me ...

Problems 321 P 6m 4m 4m m 5m 3m Fig. P9.3 9.4.Construct the bending moment diagram for structure in Fig.P9.4. Perform the static ...

...

Chapter 10 Influence Lines Method This chapter is devoted to construction of influence lines for different statically indetermin ...

324 10 Influence Lines Method Influence line for bending moment In case offixedload, a bending moment at any sectionkequals MkDM ...

10.1 Construction of Influence Lines by the Force Method 325 In case of statically indeterminate truss of the first degree of re ...

326 10 Influence Lines Method Fig. 10.1 Design diagram of the beam and primary system a P= 1 k l l 0.4l C B A EI=constant b P= 1 ...

10.1 Construction of Influence Lines by the Force Method 327 X 1 =1 M 1 0.4 1.0 k 0.4l A RA l 1 = RC=^1 l a 0.0320.0560.0640.048 ...

328 10 Influence Lines Method Influence line for bending MomentMk Should be constructed using formula (10.4). Bending moment at ...

10.1 Construction of Influence Lines by the Force Method 329 Influence line for shear forceQk Should be constructed using formul ...

330 10 Influence Lines Method Discussion. Obtained influence lines allow calculate bending moment and shear foranysection of the ...

10.1 Construction of Influence Lines by the Force Method 331 Solution.The bending moment at the middle supportBusing correspondi ...

332 10 Influence Lines Method whereICcorresponds to the highest point of the arch (crownC); this law corre- sponds to increasing ...

10.1 Construction of Influence Lines by the Force Method 333 This arch is statically indeterminate to the third degree. Let us a ...

334 10 Influence Lines Method 10.1.2.1 Unit Coefficients ı 11 D Zl 0 MN 1 MN 1 EIx dsD Zl 0 1  1 cos'x EIC dx cos'x D Zl 0 dx ...