The various methods of second-order analysis for building structures are reviewed and both merits and faults of each method are stated. Especially the typical defect of simplified methods that P-δ effect can not be considered is reviewed in detail and to compensate this defect following procedures are used.
The stiffness matrix obtained from two term Taylor series expansion of $\phi_i$ of the exact stiffness matrix is compaired with the fictitious lateral load matrix obtained from the fictitious lateral load method. Ignored terms which can be considered as forces relevant to P-δ effect, are substituted by the additional shears.
Using portal method, factors arisen from the additional shears are further simplified for convenient application of the suggested method.
