Furat Younis Hameed Al-Ghalibi

The conventional Equivalent Frame Method EFM is usually used to analyzed buildings by considering each floor separately; i.e, the conventional EFM ignored the effect of axial force on column bending stiffness (linear analysis). This article introduces a modification to stiffness of compression members which calculated for EFM by considering the geometrical nonlinearity resulting from the effect of axial force on column bending stiffness (2 nd order analysis). The axial load effects from upper columns to lower columns are considered. New curves used to estimate the axial force resulting from the uniform distributed loads acting on the frame are proposed in terms of column to frame dimension ratios. Two equations are proposed to evaluate the column stiffness factor and column stiffness carry-over factor; these equations are developed for those framed columns in order to consider the effect of axial force by including the stability functions. Finally, numerical examples are provided to illustrate the effect of the proposed modified column stiffness on the analysis results using equivalent frame method. The results showed that the axial forces of columns has a significant effect on columns bending stiffness, also the proposed modified column stiffness is satisfied for theoretical and practical use.

This paper considered the effects of elastic foundation on effective length factor calculations using subassembly model for braced and unbraced frames, the girders far ends condition are modeled as rigid, fixed, or hinged. The derivation is under same assumptions of conventional effective length factor (K-factor) using two approaches. The first approach considered the effects of elastic foundation and girders far ends conditions by depending on 1 and 2 parameters, the general modified K-factor equations have been derived for braced and unbraced frame using slop-deflection method. In the second approach, formulae of stiffness modification parameter '', which modify the relative columns to beams stiffness factor 'G' are calculated with direct use of G in the US National codes alignment chart. Approximate modified K-factor formulae are proposed for braced and unbraced frames. The Approximate proposed modified K-factor equations are suitable for practical use. Numerical examples are presented to illustrate the effects of elastic foundation taken into consideration girders far ends conditions. The Results showed that the amount of elastic foundation modulus influenced the modified K-factor values and the stiffness of elastic foundation must be taken into account in K-factor calculations. Generally, modified K-factor values decrease with increasing of stiffness of the elastic foundation.