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Fundamentals of Structural Analysis Episode 1 Part 2

Tham khảo tài liệu 'fundamentals of structural analysis episode 1 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Truss Analysis Matrix Displacement Method by S. T. Mau F1 Fx1 0 1 Fx1 Py1 Fy1 0 Fy1 P J Px2 . J Fx 2 . . Fx 2 . 0 Py 2 Fy 2 Fy 2 0 p 0 Fx3 Fx3 Py3 . 0 1 Fy 3 2 Fy3 14 where the subscript outside of each vector on the RHS indicates the member number. Each of the vectors at the RHS however can be expressed in terms of their respective nodal displacement vector using Eq.12 with the nodal forces and displacements referring to the global nodal force and displacement representation Fx1 k11 k12 k13 k14 u1 FyX - k 21 22 k __ 23 F . 24 V1 Fx 2 . k 31 Jr _ 32 F_ 33 F . 34 J u 2 Fy 2 k 41 k42 k43 k44 . 1 v2 Fx 2 k11 k12 k13 k14 u 2 F y 2 k 21 Ir_ 22 Ir_ 23 k 24 v2 Fx3 . k 31 Ir 32 Ir _ 33 k 34 u3 . Fy3 k 41 k42 k43 k 44 2 V3 Fx1 1 -k11 k12 k13 k14 u1 Fy1 k21 k - - 22 Ir_ 23 k 24 V1 Fx3 k31 Ir 32 Ir _ 33 k 34 J u3 Fy 3 k 41 k42 k43 k 44. 3 v3 Each of the above equations can be expanded to fit the form of Eq. 14 Fx11 k11 k12 k13 k14 0 0 u1 Fy1 k 21 k22 k23 k24 0 0 v1 J Fx 2 . k 31 k32 k33 k34 0 0 u 2 Fy 2 k 41 k42 k43 k44 0 0 J v2 0 0 0 0 0 0 0 u3 0 1 . 0 0 0 0 0 0. 1 v3 15 Truss Analysis Matrix Displacement Method by S. T. Mau 0 0 0 0 0 0 0 u1 0 0 0 0 0 0 0 V1 F 2 0 0 k11 k12 k13 k14 u 2 Fy 2 i 0 0 k21 k._ 22 k __ 23 k. 24 V2 Fx3 0 0 k31 32 k. _ 33 k. 34 u3 . Fy 3 2 0 0 k41 k42 k43 k 44 2 . v3 FX1 -k11 k12 0 0 k13 k14 u1 Fy1 k 21 k 22 0 0 23 k 24 V1 0 0 0 0 0 0 0 u 2 0 5 0 0 0 0 0 0 V2 Fx3 k 31 k _ 32 0 0 k. _ 33 k34 u3 . Fy3 3 k 41 k42 0 0 k43 k 44 _ 3 v3 When each of the RHS vectors in Eq. 14 is replaced by the RHS of the above three equations the resulting equation is the unconstrained global stiffness equation - K11 K12 K13 K14 K15 K16 u1 Px1 1 K 21 K22 K23 K24 K 25 K26 V1 Py1 K 31 K32 K33 K34 K35 K36 u 2 Px 2 K 41 K42 K43 K44 K45 K46 V2 Py 2 K 51 K52 K53 K54 K55 K 56 u3 Px3 K 61 K62 K63 K64 K65 K66 . v3 Py3 15 where the components of the unconstrained global stiffness matrix Kjj is the superposition of the corresponding components in each of the three expanded stiffness .