Advanced Methods of Structural Analysis
11.6 Analysis of Continuous Beams 395 Stiffness matrices for left and right spans are k 1 D 3 EI 1 l 1 Œ1D 3 EI 1 8 Œ1D 3 EI 1 ...
396 11 Matrix Stiffness Method 2.Computation of shear may be performed on the basis of theMPdiagram. Reac- tions of supports can ...
11.6 Analysis of Continuous Beams 397 l 1 =6m l 2 =4m l 3 =4m Δ 2 j 0 A EI 1 =1EI 0 BD2EI 0 C 2EI 0 a b M^0 Δ MBA MAB MCB MCD MB ...
398 11 Matrix Stiffness Method Stiffness matrix for structure in whole in local coordinates is kQ.55/D 2 6 6 6 6 6 4 0:667 0:33 ...
11.6 Analysis of Continuous Beams 399 The final vector of required bending moments (kNm) is ESDSE 1 CkAQ TZDEI 0 2 6 6 6 6 6 6 6 ...
400 11 Matrix Stiffness Method (^12) Z-P diagram S-e diagram 12 3 4 S 1 S 2 S 4 S 3 l 0 2 4 EI ll 6 8 10 12 14 16 18 BC a b ul l ...
11.6 Analysis of Continuous Beams 401 The stiffness matrix of all structure in global coordinates and inverse stiffness matrix a ...
402 11 Matrix Stiffness Method PD 1 at the section 2 (uD0:333; D0:667/ PD 1 at the section 4 (uD0:667;D0:333/ Matrix procedure ...
11.6 Analysis of Continuous Beams 403 They are EPDl u^2 u^2 ;SE 1 Dl 2 6 6 6 6 6 0 u^2 u^2 0 3 7 7 7 7 7 After that we ...
404 11 Matrix Stiffness Method It is possible to expand more the number of internal forces at the ends considering also the axia ...
11.7 Analysis of Redundant Frames 405 moments are zero. Therefore, the vector offixed-end moments (vector of internal forces of ...
406 11 Matrix Stiffness Method RD ac bd ;thenR^1 Ddet^1 R d c ba . In our case the inverse matrix becomes K^1 D h EI 1 4 ...
11.7 Analysis of Redundant Frames 407 q=2kN/m 4m 6m 5m 3m 1 2 1 P=8kN A B (^1) C ab 4.1667 15.36 P q MP^0 1 Z-P diagram 2 cd S-e ...
408 11 Matrix Stiffness Method The equivalent moment at joint 1 (Fig.11.27e) isM D 15:364:1667 D 11:1993kNm (clockwise); the eq ...
11.7 Analysis of Redundant Frames 409 k 2 D EI 2 l 2 Œ3D 2 EI 10 Œ3D EI 5 Œ3 ; k 3 D EI 3 l 3 Œ3D EI 3 Œ3D EI 5 Œ5 : For w ...
410 11 Matrix Stiffness Method Vector of internal unknowns bending moments isESfinDSE 1 CSE 2 ,where SE 2 DkAQ TZEDEI 5 2 6 6 4 ...
11.8 Analysis of Statically Indeterminate Trusses 411 Vector has five entries because the given structure allows five possible j ...
412 11 Matrix Stiffness Method Thus, the static matrix becomes A.56/D 2 6 6 6 6 6 6 6 4 0 10 0:707 0 0 0000:70710 1000:70700 ...
11.8 Analysis of Statically Indeterminate Trusses 413 Vector displacements ZED 2 6 6 6 6 6 6 6 6 Z 1 Z 2 Z 3 Z 4 Z 5 3 7 7 7 7 7 ...
414 11 Matrix Stiffness Method 11.9 Summary................................................................ 1.The MSM is modern ...
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