Comparative Study of Linear and Geometric Nonlinear Load-Deflection Behavior of Flexural Steel Members

Background/Objectives: The proper analysis of beam is important for understanding the actual behavior and economical use of sections. The prime objective of this research paper is the comparative study of linear and geometric nonlinear load-deflection behavior of beams under vertical load. Methods/Statistical Analysis: In geometrically linear analysis, the equations of equilibrium are formulated before the deformation state and are not updated with the deformation, while in geometrical nonlinear analysis updated stiffness matrix is used at each load increment. In this study a three noded steel beam is formulated for linear and nonlinear analysis. The incremental central point load is applied to the beam. Linear and geometrically nonlinear deflection is computed for the beams. Three beams of the same length were taken for analysis, but having different thickness&support conditions. The linear and geometrical nonlinear load-deflection behavior is studied using STAAD PRO. The linear deflection is also computed by developing a finite element based code using MATLAB. Findings:The results obtained after the analysis of beams deformations are quite interesting. The percentage variation of linear and geometrical nonlinear deflection is very high for beam with lesser thickness. It was found that the support conditions also affect variation of deflection for the linear and nonlinear cases. The variation between linear and geometrical nonlinear deflection of beam is negligible when the ends are fixed. But for the same beam with simply supported end conditions the defections were found having variation up to 37 percentages. Geometrical nonlinearity is more when the load is very high and section is thin. At the initial stages of loading behavior of beam is linear only and it behaves nonlinear when we go for higher loads. Application/Improvements: Linear analysis is only an approximation, so for understanding the actual behavior of the structure and for the economical/optimized usage of sections it is suggested to go for nonlinear analysis.