Advanced Methods of Structural Analysis

10.1 Construction of Influence Lines by the Force Method 335 Canonical equations (10.13) become lX 1 C fl 3 X 2 D a^2 2 and l^3 ...

336 10 Influence Lines Method SinceX 3 is antisymmetrical unknown, for the right part of the arch it is necessary to change sign ...

10.1 Construction of Influence Lines by the Force Method 337 for moment of inertia of cross section may be assumed:Ixcos'x DIc.T ...

338 10 Influence Lines Method Internal forces may be defined using the corresponding influence lines by formula SDPyCq ̋,where ...

10.1 Construction of Influence Lines by the Force Method 339 The bending moment at crownCusing the influence line MCDl  P0:01 ...

340 10 Influence Lines Method P= 1 d=4m 3m a Design diagram X 1 P= 1 123 0 6 4 5 b Primary system d 1 P 1 ′ 2 ′ 3 ′ 4 ′ 5 ′ d 1 ...

10.1 Construction of Influence Lines by the Force Method 341 Unit state and corresponding internal forces in all members of the ...

342 10 Influence Lines Method Since the structure is symmetric, the elastic loadsW 4 DW 2 andW 5 DW 1. Fictitious beam presents ...

10.1 Construction of Influence Lines by the Force Method 343 In case of arbitrary external load the internal force in any member ...

344 10 Influence Lines Method 10.2 Construction of Influence Lines by the Displacement Method Let us consider a first-degree kin ...

10.2 Construction of Influence Lines by the Displacement Method 345 In case of fixed load, the shear at any sectionkis a number ...

346 10 Influence Lines Method 4.Solve the canonical equations; since the free terms are functions, the primary unknowns will be ...

10.2 Construction of Influence Lines by the Displacement Method 347 Z 1 P = 1 Primary system b P = 1 A B C ll k 0.4l a EI = cons ...

348 10 Influence Lines Method If load is located on the right spanthen angular displacement at supportBis posi- tive, i.e., this ...

10.2 Construction of Influence Lines by the Displacement Method 349 13452689107 11 k 0.081610.17280.08320.0224 + R bInfluence li ...

350 10 Influence Lines Method Table 10.5 Calculation of IL  Q^0 k  LoadPD 1 is located to the left of sectionk,.u 0:6/ LoadPD ...

10.2 Construction of Influence Lines by the Displacement Method 351 2.If a load is located in the right span, thenMk^0 andQ^0 ka ...

352 10 Influence Lines Method Solution.(a)Since a loadPis located at point 8, the internal forces at sectionkac- cording to Figs ...

10.2 Construction of Influence Lines by the Displacement Method 353 All reactions should be calculated as follows RAD X 1 l D0:0 ...

354 10 Influence Lines Method l l l a P= 1 P= 1 i=EI/l b i i Z 1 1 r 11 3 i^4 i 3 i Z 1 =1 3 i 3 i 2 i 4 i k Mk = −1.2i Qk = −^3 ...