tailieunhanh - Fundamentals of Structural Analysis Episode 2 Part 4

Tham khảo tài liệu 'fundamentals of structural analysis episode 2 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Beam and Frame Analysis Displacement Method Part II by S. T. Mau displacements and the corresponding nodal forces of the frame without the support and loading conditions. Since each node has three DOFs the frame has a total of nine nodal displacements and nine corresponding nodal forces as shown in the figure below. The nine nodal displacements and the corresponding nodal forces. It should be emphasized that the nine nodal displacements completely define the deformation of each member and the entire frame. In the matrix displacement formulation we seek to find the matrix equation that links the nine nodal forces to the nine nodal displacements in the following form Kg Ag Fg 18 where Kg Ag and Fg are the global unconstrained stiffness matrix global nodal displacement vector and global nodal force vector respectively. Eq. 18 in its expanded form is shown below which helps identify the nodal displacement and force vectors. Member 1-2 Member 2-3 i Ax1 1 i F 1 1 Fy 1 01 M1 2 Fx 2 1 Ay 2 k 1 Fy 2 02 M 2 Ax 3 Fx 3 Ay 3 Fx 3 03 M 3 18 235 Beam and Frame Analysis Displacement Method Part II by S. T. Mau According to the direct stiffness method the contribution of member 1-2 to the global stiffness matrix will be at the locations indicated in the above figure . corresponding to the DOFs of the first and the second nodes while the contribution of member 2-3 will be associated with the DOFs at nodes 2 and 3. Before we assemble the global stiffness matrix we need to formulate the member stiffness matrix. Member stiffness matrix in local coordinates. For a frame member both axial and flexural deformations must be considered. As long as the deflections associated with these deformations are small relative to the transverse dimension of the member say depth of the member the axial and flexural deformations are independent from each other thus allowing us to consider them separately. To characterize the deformations of a frame member i-j we need only four independent variables .