Advanced Methods of Structural Analysis

10.3 Comparison of the Force and Displacements Methods 355 PD 1 in the right span IL.Z 1 /D 1 10i u.1u/^2 lD u 10 .1u/^2 l^2 E ...

356 10 Influence Lines Method Table 10.7 Comparison of the force and displacement methods for construction of influence linesCom ...

10.3 Comparison of the Force and Displacements Methods 357 Case of n D 1 ı^11 X C 1 ı1P D 0 r^11 Z C 1 r1P D 0 Primary unknown X ...

358 10 Influence Lines Method more preferable; if the rolled and pinned supports of this frame will be substituted by fixed ones ...

10.4 Kinematical Method for Construction of Influence Lines 359 1.Indicate the constraint or section, in which factorXarises. 2. ...

360 10 Influence Lines Method The elastic curve caused byP D 1 in the primary system is presented in Fig.10.17b;ı1Pis angle of r ...

10.4 Kinematical Method for Construction of Influence Lines 361 P= 1 1268910345 711 ll a X 1 =1 M 1 1.0 b 0.0480.0840.0960.072 0 ...

362 10 Influence Lines Method P= 1 1452 3 n k × × FL FR Inf. line R 1 R 1 (^1) + Inf. line M 3 − − Inf. line Qk 1 Qk Qk − Inf. ...

10.4 Kinematical Method for Construction of Influence Lines 363 is located within portions 2-3 and 3-4, then ordinates of influe ...

364 10 Influence Lines Method important advantage of influence lines is as follows: Influence lines for primary unknown and any ...

Problems 365 2 3 4 P= 1 (^1) k Fig. P10.2 10.3.Uniform clamped–pinned beam is shown in Fig.P10.3. (a)Construct the influence lin ...

366 10 Influence Lines Method 10.5.Analyze each design diagram in Fig.P10.5and choose the most effec- tive method for analytical ...

Problems 367 a 13452689107 11 ll 268104 ll b Fig. P10.7 Ans. (a) Ordinate of IL.Z/at point 8 is0:0274  l^2 =EI  I M 1 D5:48l; ...

368 10 Influence Lines Method l l l P= 1 0.4l k Fig. P10.9 10.10.A frame is subjected to fixed loadP(Fig.P10.10). The bending st ...

Chapter 11 Matrix Stiffness Method Matrix stiffness method (MSM) is a modern powerful method of analysis of engineering structur ...

370 11 Matrix Stiffness Method 11.1.1 Finite Elements............................................... Each structure may be subdi ...

11.1 Basic Idea and Concepts 371 X Y 1 A P x 3 y 3 2 3 x 1 y 1 x 2 y 2 D 4 a Fig. 11.2 Local and global coordinate systems The m ...

372 11 Matrix Stiffness Method The beam in Fig.11.3a has one unknown of the displacement method, i.e., the degree of kinematical ...

11.2 Ancillary Diagrams 373 q=2kN/m 1 l 1 = 8m l 2 1 q M 1 =16kNm 16kNm M^0 P 1-state 2-state (^1) J-L Mj 1 = 16kNm Fig. 11.4 Tr ...

374 11 Matrix Stiffness Method M 1  5 D ql 12  5 8 D 3  42 8 D 6 kNm M 7  2 D 3 16 P 2 l 2  7 D 18 kNm M 2  3 D P 1 l 2  ...