Internal Force Identification And Stability Analysis Of Long Compressed Bar

Internal force identification and critical pressure are two most important aspects to determine the stability safety factor of a compressed bar in engineering project. Today frequency method has been widely used in force identification of structures such as cables and tie rods, but less used in compressed bar. Actually, based on frequency method, not only the pressure force can be identified, but also the critical pressure can be gained according to dynamic criterion. Doing research in vibration frequency method in safety coefficient evaluation of compressed bar has important meanings.Combined with the vibration frequency method and finite element method, several research is done in this thesis about pressure force identification and critical pressure analysis. It is suitable for variable section roll and inhomogeneous slender pressure roll as well.1) Use the appropriate function to be the displacement function, then base on the energy variation principle, the frequency equation is derived, which considers the pressure force and the boundary conditions of the compressed bar. This method can take the influence of arbitrary boundary and variable cross-section into account. As the corresponding relation between the pressure and frequencies is obtained, the critical force can get by ? ? 0 according to dynamic criterion.2) According to the finite element method, the computer executable procedure is setted up. Programmed with MATLAB, several programmes are designed, including solving of stiffness matrix, mass matrix, frequencies, pressure force, critical pressure and so on. Then, an example is given to testify this method.3) Effective length factor ? in Euler's Formula is calculated accurately according to different kinds of elastic boundary. The effective length factor can be looked up or interpolation calculation through the tables made. It is convenient to use ? in these tables to calculate the critical pressure of compressed bar with arbitrary elastic boundary.4) With the programs, stability analysis is done to the slender pressured bar of Dongjiang river. What is more, the influence of boundary condition, effective length, hole ratio in section and internal force to frequencies are analyzed. The result shows that, hole ratio has no obvious influence on critical pressure. However, boundary condition, effective length, and hole ratio in section all have significant influence on frequency of compressed bar. The internal force has little influence on frequency when the it is much less than critical pressure.