Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 13 3.3 First order and second order analysis For both plastic analysis and elastic analysis of frames, the choice of first-order or second order analysis may be governed by the in-plane flexibility of the frame, measured by the factor  cr (see Section 3.3.1). In practice, the choice between first and second order analysis is also dependent on the availability of software. Even if a portal frame was sufficiently stiff that second order effects were small enough to be ignored, it may be convenient still to use second order analysis software. When a second order analysis is required but is not available, modified first order methods can be useful for calculations. A modified first order approach is slightly different for elastic and plastic analysis, and is described in Sections 3.3.2 and 3.3.3. In elastic analysis, the horizontal actions are amplified; in plastic analysis, all actions are amplified. 3.3.1  cr factor Expression 5.2 of EN 1993-1-1 § 5.2.1(4)B gives  cr as:              H,Ed Ed Ed cr   h V H Note 1B and Note 2B of that clause limit the application of Expression 5.2 to roofs with shallow roof slopes and where the axial force in the rafter is not significant. Thus:  a roof slope is considered as shallow at slopes no steeper than 26°  axial force in the rafter may be assumed to be significant if Ed y 0,3 N Af   . A convenient way to express the limitation on the axial force is that the axial force is not significant if: cr Ed 0.09 N N  Where N cr is the elastic critical buckling load for the complete span of the rafter pair, i.e. 2 2 cr L EI π N  L is the developed length of the rafter pair from column to column, taken as span/Cos θ ( θ is the roof slope) If the limits are satisfied, then Expression 5.2 may be used to calculate  cr. In most practical portal frames, the axial load in the rafter will be significant and Expression 5.2 cannot be used. When the axial force in the rafter is significant, Appendix B provides an alternative, approximate method to calculate the measure of frame stability, defined as  cr,est . In many cases, this will be a conservative result. Accurate values of  cr may be obtained from software.