Rijitlik matrisi yöntemine dayalı kirişler için yapısal analizin geliştirilmesi

The using of beams in the form of steel or concrete materials is widely adopted in the construction projects. The conditions that coming with the design of the beams and the internal forces and moments depend on the cases of loading, the geometrical and physical properties of the beams, and the supporting states. The stiffness matrix is a general tool that take into account these parameters for evaluating the shear force and the bending moment diagram along the spans of the beams in part or all the construction body. The stiffness matrix can become more bigger when increasing the number of beam spans or that influence the overall internal stresses inside the member. In the present study, a technique based on Gaussian elimination theory was applied on the body of the stiffness matrix toward finding the required variables in less steps with same degree of accuracy. The study converted the matrix that used for two spans beam from six rows and six columns to only two rows and two columns that the magnitudes of the slope of deformation can be determined then the reactions and moments can be identified easily. The study move to more analytical steps by analyzing the relationship between the uniform loading, the length of span, and the beam stiffness condition EI with each of the four parts of the derived matrix: A1, A2, B1, and B2. The resultant of that analysis was building of new simple equations that can be used to obtained the four main parts of the matrix without the previous steps of the conventional stiffness matrix and the Gaussian elimination steps. The results of the new equations were checked by evaluation the values of the main parts according to the original steps and the derived equation. The differences were so small indicating the feasibility of the derived method to contribute in positive role for the design purpose. The study explained the variation of the shear forces and the bending moments along the beam spans by building simulation of specific case of beams under uniform loading by using of ANSYS workbench program. A full mathematical model for calculate the displacements and reactions has been made in MATLAB/Simulink from the main four parts of the stiffness matrix. In aim of making this model being used in analysis of continuous beam easily. Besides make use of it in field of understanding the analysis method.