Finite element formulation for Timoshenko beams | |
| Author | Anandarajah, Arumugam |
| Call Number | AIT Thesis no.1032 |
| Subject(s) | Structural dynamics Girders--Vibration |
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering at the Asian Institute of Technology, Bangkok, Thailand . |
| Publisher | Asian Institute of Technology |
| Abstract | One method of finite element formulation for the problem of Timoshenko beams was studied. The structures considered were divided into equal length of finite number of elements. Deflected shapes for each elements were derived in terms of its nodal displacements to satisfy equilibrium equations. The equations of motion was derived by means of Lagrange equation incorporating rotatory inertia, shear deformation and axial deformation effects. Mass matrix and stiffness matrix were formulated in which nodal displacements are the variables. To verify the validity of this procedure, the frequencies and mode shapes for uniform axially stressed cantilever and for simply supported beam were compared with the results obtained by exact theories. A very good agreement was found even for higher modes. A multiflued stack was chosen to illustrate the method of finite element formulation as an example of a non uniform tall structure. It is of 242 m high and made of reinforced concrete. The outer shell with a 26 m diameter encloses and supports three elliptical reinforced concrete flues. The outer shell and the inner flues were divided into equal number of elements and the platform was considered as a spring with a dashpot. Expressing nodal dis placements in terms of modal variables, the governing equation of the latter become uncoupled, and their solution for 1940 Ei Centre earthquake was obtained from charts. |
| Year | 1977 |
| Type | Thesis |
| School | Student Research Before 1979 |
| Department | Other Field of Studies (No Department) |
| Academic Program/FoS | Thesis (Year <=1979) |
| Chairperson(s) | Karasudhi, Pisidhi |
| Scholarship Donor(s) | The United Kingdom Government |
| Degree | Thesis (M.Eng.) - Asian Institute of Techonolgy, 1977 |