Tham khảo tài liệu 'aircraft structures 3e episode 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 506 Matrix methods of structural analysis Xi Fx 2 3 . 3 AE L 1 1 0 -1 0 0 0 0 1 0 0 0 -1 2 -1 v2 0 u3 0 v3 0 0 0 0 -1 1 _L 1 1 1 1 0 272 2y 2 2 2 272 Vi 0 1 1 1 1 2 2y 2 2V2 2V2 272 V2 1 1 1 1 3 0 2 2 272 275 272 v3 0 1 2V2 1 272 1 2y 2 7 272. If we now delete rows and columns in the stiffness matrix corresponding to zero displacements we obtain the unknown nodal displacements 2 and v2 in terms of the applied loads FXị2 0 and Fyj w . Thus from which V vi A F F M vỉi V2 7t 2x 2 1 2 2jFk2 --772 1 2y 2 viii An The reactions at nodes 1 and 3 are now obtained by substituting for u2 and v2 from Eq. vi into Eq. iv . Thus -1 0 1 0 0 1 1 272 Fx ĩ 2 2 1 1 . 272 272. 1 1 272 Matrix analysis of space frames 507 giving .1 - - - 0 Fx 3 F 2 - w w Finally the forces in the members are found from Eqs vii and viii 12 Si 3 Sj3 AE L AE u2 111 l 2 U ỉ - I ĩ - i l w compression 0 as expected V2L . Application to statically indeterminate frameworks The matrix method of solution described in the previous sections for spring and pin-jointed framework assemblies is completely general and is therefore applicable to any structural problem. We observe that at no stage in Example did the question of the degree of indeterminacy of the framework arise. It follows that problems involving statically indeterminate frameworks and other structures are solved in an identical manner to that presented in Example the stiffness matrices for the redundant members being included in the complete stiffness matrix as before. Matrix analysis of space frames The procedure for the matrix analysis of space frames is similar to that for plane pin-jointed frameworks. The main difference lies in the transformation of the member stiffness matrices from local to global coordinates since as we see from Fig. axial nodal forces Fxi and Fx j have each now three global components FxFv j F i and Fx j Fy j F-j respectively. The member stiffness matrix referred to .
