Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 14 3.3.2 Modified first order, for elastic frame analysis The ‘amplified sway moment method’ is the simplest method of allowing for second order effects for elastic frame analysis; the principle is given in EN 1993-1-1, § 5.2.2(5B). A first-order linear elastic analysis is first carried out; then all horizontal loads are increased by an amplification factor to allow for the second order effects. The horizontal loads comprise the externally applied loads, such as the wind load, and the equivalent horizontal forces used to allow for frame imperfections; both are amplified. Provided  cr  3,0 the amplification factor is:        cr 1 1 1  If the axial load in the rafter is significant, and  cr,est has been calculated in accordance with Appendix B, the amplifier becomes:          est cr, 1 1 1  If  cr or  cr,est is less than 3,0 second order software should be used. 3.3.3 Modified first order, for plastic frame analysis Design philosophy In the absence of elastic-plastic second order analysis software, the design philosophy is to derive loads that are amplified to account for the effects of deformed geometry (second order effects). Application of these amplified loads through a first-order analysis gives the bending moments, axial forces and shear forces that include the second order effects approximately. The amplification is calculated by a method that is sometimes known as the Merchant-Rankine method. Because, in plastic analysis, the plastic hinges limit the moments resisted by the frame, the amplification is performed on all the actions that are applied to the first-order analysis (i.e. all actions and not only the horizontal forces related to wind and imperfections). The Merchant-Rankine method places frames into one of two categories:  Category A: Regular, symmetric and mono-pitched frames  Category B: Frames that fall outside of Category A but excluding tied portals. For each of these two categories of frame, a different amplification factor should be applied to the actions. The Merchant-Rankine method has been verified for frames that satisfy the following criteria: 1. Frames in which 8  h L for any span 2. Frames in which 3 cr  