Advanced Methods of Structural Analysis

8.1 Fundamental Idea of the Displacement Method 275 In case 8.3a, the primary unknownsZ 1 andZ 2 are angular displacements of in ...

276 8 The Displacement Method moment arises and the second numeral isthe label of the constraint, which is rotated (in this exam ...

8.2 Canonical Equations of Displacement Method 277 introduced constraints. The canonical equations of the displacement method wi ...

278 8 The Displacement Method h l EI 1 abEI (^212) Z 2 =1 r 12 6 EI 1 /h^2 6 EI 1 /h^2 1 2 Z 2 =1 State 2 * r 22 2 EI 1 /h Z 1 = ...

8.2 Canonical Equations of Displacement Method 279 momentr 12 and unit reactive forcer 22 arise in constraints 1 and 2, respecti ...

280 8 The Displacement Method 2.According to the reciprocal reactionstheorem, the secondary reactions satisfy the symmetry condi ...

8.2 Canonical Equations of Displacement Method 281 displacementZ 1 at support 1. The primary system is obtained from a given str ...

282 8 The Displacement Method fibers, and the bending moment diagram caused by the unit primary unknown are shown in Fig.8.6b. T ...

8.2 Canonical Equations of Displacement Method 283 Inourcasewehave M1AD0:375EI 6:163 EI  16 D18:31kN m; M1BD0:3EI 6:163 EI ...

284 8 The Displacement Method ab 1 2 l=6m h=5m 6m P Design diagram 1 P^12 Primary system i=0.2EI i=0.333EI Z 1 Z^2 1 2 M 1 Z 1 = ...

8.2 Canonical Equations of Displacement Method 285 To calculate coefficients ofr 12 andr 22 it is necessary to construct the ben ...

286 8 The Displacement Method Discussion: 1.The active load acts at the level of the crossbar and the bending moments in the pri ...

8.2 Canonical Equations of Displacement Method 287 abc q 4m 6m 5m 3m 1 2 1 P i6-8 i4-5 P 1 q i1-3 2 8 q P 1 5 2 7 6 3 4 d 0.333E ...

288 8 The Displacement Method The canonical equations of the displacement method are r 11 Z 1 Cr 12 Z 2 CR1PD0; r 21 Z 1 Cr 22 Z ...

8.2 Canonical Equations of Displacement Method 289 Ta b l e 8. 1 Calculation of unit and loaded reactions at introduced constrai ...

290 8 The Displacement Method The canonical equations of the displacement method become: 2:4Z 1 C0:093Z 2  11:1933 EI D0; 0:093 ...

8.3 Comparison of the Force and Displacement Methods 291 8.3 Comparison of the Force and Displacement Methods................ Th ...

292 8 The Displacement Method Ta b l e 8. 4 (continued) Meaning of equations To t a ldisplacementin the direction ofeliminated c ...

8.3 Comparison of the Force and Displacement Methods 293 4.The determinant of the matrix of coefficients of the canonical equati ...

294 8 The Displacement Method showninFig.8.9d, then such a structure can be easily analyzed by the displacement method in canoni ...