Advanced Methods of Structural Analysis

11.2 Ancillary Diagrams 375 adbc EI, a –24° h^ =^ 0.4m a M1–0 M M3–4 M1–2 3–2 04123 b c M1–0 M1–2M3–2 M 3–4 d 1 Joint 1 3 Joint ...

376 11 Matrix Stiffness Method According to TablesA.3andA.4, the bending moments for pinned-fixed and fixed-fixed beams are M 1 ...

11.2 Ancillary Diagrams 377 a A B C b 1 2 4 A 3 5 6 Fig. 11.9 Z-Pdiagram for truss (4). All other joints of frame have two possi ...

378 11 Matrix Stiffness Method For beams we will denote thesectionswith unknown internal forces. Fig- ure11.12a shows a continuo ...

11.3 Initial Matrices 379 11.3 Initial Matrices......................................................... The first group of init ...

380 11 Matrix Stiffness Method Now we compile the vector of external forces for frame shown in Fig.11.15a. For this frame, the j ...

11.4 Resolving Equations 381 c M 2 M 3 M^5 M 4 M 1 M 6 M 10 M 7 M^9 M 8 b 1 2 3 4 5 6 7 8 10 9 a H 1 5 Fig. 11.16 Formulation of ...

382 11 Matrix Stiffness Method presented as vectorPE. Let the structure hasnunknown internal forces; these unknowns according to ...

11.4 Resolving Equations 383 a F AB c 12345 M 1 M^2 M 3 M 4 M 5 S-e b (^12) Z-P d Joint A P 1 M 2 M 3 P 1 = M 2 + M 3 Joint B P ...

384 11 Matrix Stiffness Method F 1 =16kN F 2 =10kN 3m 3m 4m a B A D C a 2 (^13) 4 Z-P b S-e 5 2 1 3 4 c d P 1 S 2 S 1 Joint B P ...

11.4 Resolving Equations 385 acb 1 2 Z-P diagram ABC^3 h M 2 M 4 M 3 M^5 M 6 M 1 S-e (^1) diagram 2 34 5 6 d ∑ hh− M 1 + M 2 M 5 ...

386 11 Matrix Stiffness Method 11.4.2 Geometrical Equations and Deformation Matrix These equations present the relationships bet ...

11.4 Resolving Equations 387 The second equation shows that if introducedconstraint 1 has angular displacement Z 1 then correspo ...

388 11 Matrix Stiffness Method 3m 3m 4m 1 2 3 4 6 5 Fig. 11.21 Construction of the internal stiffness matrix for truss Stiffness ...

11.4 Resolving Equations 389 coordinates for uniform beam with fixed ends becomes kff D EI l  42 24 (11.7a) Let us form the st ...

390 11 Matrix Stiffness Method 11.5 Set of Formulas and Procedure for Analysis.......................... The behavior of any str ...

11.5 Set of Formulas and Procedure for Analysis 391 This equation may be rewritten in the form PEDKZE: (11.13) The matrixKpresen ...

392 11 Matrix Stiffness Method 11.5.3 Matrix Procedures............................................ The following procedure for ...

11.6 Analysis of Continuous Beams 393 Notes: 1.In different textbooks the algorithm above (or slightly modified algorithm) is re ...

394 11 Matrix Stiffness Method q=2kN/m l 1 =8 m l 2 =10 m ul 2 =6 m P=12 kN ul 2 =4 m AB^1 EI a d 4.16 Joint load diagram q P M^ ...