Finite Element Analysis of Concrete Beam using MATLAB

Finite element analysis generally refers to the process of determining the behavior of the physical phenomena. In case of beams, the displacements and rotations that are determined by using the finite element analysis involves in creating the mesh of the very finite elements that are combined to form the shape or outline of the structure that is being under consideration. It involves in solving of differential equation generally of the fourth order. In case of beams, Euler Bernoulli theory is used to determine the behavior of the beams which involves in the determination of stiffness matrix and force matrix which are used to compute the unknown rotations and displacements. With increase in the number of elements or discretized parts the order of the global matrix gets increased (for example, when the number of elements considered are one the order of global matrix is 4x4, when the number of elements considered are two the order of global matrix is 6x6 and so on...), and the calculations gets complicated. Hence for the easier computations MATLAB software is used which involves in use of loops like for loop, if loop etc. In the current work, the concrete beam of various dimensions is analyzed using the finite element method with the MATLAB software. The unknown displacements and the rotations are determined by forming the global stiffness and global force matrix with the help of element stiffness and element force matrix. To find the unknown displacements and the rotations using MATLAB an error free, executable program is coded using the command line present in the MATLAB. This executable program is developed using the loops. The obtained results are then compared with that of the manual method.