To transform the element matrix to the same coordinate system as the global stiffness matrix, a Transformation Matrix was used. The generated matrices now relate the displacements on their end nodes to the forces applied on them on its local coordinates. The element matrices were then generated using the material and section properties for each member. Information about the section properties needed were obtained from an online source. The matrix is dependent on the following parameters: length of the member (L), crosssectional area (A), modulus of elasticity (E), modulus of rigidity (G), Poisson’s Ratio (ν), polar moment of inertia (J), and moments of inertia about the z and y axes (Iz and Iy). Generated from each of the members using the matrix below. The global stiffness matrix is assembled from the element stiffness matrix Stiffness Matrix Method The goal of this method is to generate the global stiffness matrix which relates the displacements of each node to the forces applied on each node.
Another analysis was made using ETABS to compare the results from the manual computation with. A manual computation was done to solve for these unknowns using the stiffness matrix method using Microsoft Excel. The analysis is now left with 84 displacements and 36 support reactions to solve for. These restraints make the displacements of the nodes equal to zero. Nodes A, D, H, K, N, and R are defined as fixed supports. With 6 degrees of freedom for each node, a total of 120 degrees of freedom must be analyzed. Free body diagram of the structure The structure consists of 20 nodes labeled A to Q with 31 members using the nodes as joints as shown in Figure 1. Below is the given structure for this analysis project. Matrix structuralĪnalysis is now introduced to address this concern. As the complexity of the structure increases, the computational effort to determine all the unknowns increases exponentially. When 3-dimensional frames are considered, each node would present a total of 6 unknowns: forces and moments on each of the 3 axes. The total number of unknowns of a planar structure would then be equal to thrice the number of nodes in the structure. INTRODUCTION A planar structural element such as a beam or column element has six unknowns: two forces and a moment on each side. Frame Structural Analysis using the Stiffness Matrix Method in Microsoft Excel and ETABSĬE 155 Matrix Structural Analysis Project 2nd Semester AY 2014-2015