LARGE DEFLECTION OF DEEP BEAMS ON ELASTIC FOUNDATIONS
Adel A. Al- Azzawi and Dhiaa M. Theeban
This research deals with the geometric nonlinear behavior of beams resting on Winkler
foundation. Timoshenko’s deep beam theory is extended to include the effect of large deflection
theory. The finite difference method was used to solve the problem deep beams and the
obtained results were compared. An incremental load approach with Newton-Raphson iteration
computational technique was used for solving the nonlinear sets of node equilibrium equations
in the finite difference method.
In the finite element method (ANSYS program), the element SHELL 43 incorporated in
ANSYS 5.4 was used. The element has four nodes with six degrees of freedom at each node:
translations in the nodal x, y, and z- directions and rotations about the nodal x, y, and zdirections.
Several important parameters were incorporated in the analysis to study the effects of
vertical subgrade reaction, beam width, and beam depth to length ratio on the deflections,
bending moments and shear forces. The results obtained from this method were compared with
exact and numerical methods to check the accuracy of the solutions. Good agreements were
found, the maximum difference in deflection at midspan from the finite elements and the finite
differences was (0.79%). Also, the difference between the exact solution and the present finite
difference was found to be (0.86%).
Abstract
foundation. Timoshenko’s deep beam theory is extended to include the effect of large deflection
theory. The finite difference method was used to solve the problem deep beams and the
obtained results were compared. An incremental load approach with Newton-Raphson iteration
computational technique was used for solving the nonlinear sets of node equilibrium equations
in the finite difference method.
In the finite element method (ANSYS program), the element SHELL 43 incorporated in
ANSYS 5.4 was used. The element has four nodes with six degrees of freedom at each node:
translations in the nodal x, y, and z- directions and rotations about the nodal x, y, and zdirections.
Several important parameters were incorporated in the analysis to study the effects of
vertical subgrade reaction, beam width, and beam depth to length ratio on the deflections,
bending moments and shear forces. The results obtained from this method were compared with
exact and numerical methods to check the accuracy of the solutions. Good agreements were
found, the maximum difference in deflection at midspan from the finite elements and the finite
differences was (0.79%). Also, the difference between the exact solution and the present finite
difference was found to be (0.86%).
