Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 4 Figure 2.2 Symmetric mode deflection The practical consequence of P-  and P-  effects is to reduce the stiffness of the frames and its elements below that calculated by first-order analysis. Single-storey portals are sensitive to the effects of the axial compression forces in the rafters and columns. These axial forces are commonly of the order of 10% of the elastic critical buckling loads of the rafters and columns, around which level the reduction in effective stiffness becomes important. 2.2 Second order effects Second order effects increase not only the deflections but also the moments and forces beyond those calculated by first-order analysis. Second order analysis is the term used to describe analysis methods in which the effects of increasing deflection under increasing load are considered explicitly in the solution, so that the results include the P -  and P -  effects described in Section 2.1. The results will differ from the results of first-order analysis by an amount dependent on the magnitude of the P -  and P -  effects. The effects of the deformed geometry are assessed in EN 1993-1-1 by calculating the factor  cr , defined as: Ed cr F F cr   where: F cr is the elastic critical load vector for global instability, based on initial elastic stiffnesses F Ed is the design load vector on the structure. Second order effects can be ignored in a first order analysis when the frame is sufficiently stiff. According to § 5.2.1 (3), second order effects may be ignored when: For elastic analysis:  cr  10 For plastic analysis:  cr  15