Steel Buildings in Europe

Title APPENDIX D Worked Example: Design of portal frame using elastic analysis 5 of 44 4 - 86 L cr is the developed length of the rafter pair from column to column. L cr = o cos 5 30 = 30,1 m N cr = 2 cr z 2 L EI  =   3 3 2 4 2 10 30,1 10 10 33740 210000        = 772 kN 0,09 N cr = 0,09 772  = 69 kN N R,Ed = 130 kN > 69 kN Therefore the axial compression in the rafter is significant and  cr from EN 1993-1-1 is not applicable. Following the guidance from Appendix B, frame stability is assessed based on  cr,est , in Section 5.2. 5.2. Calculation of  cr,est For a pitched roof frame:  cr,est = min(  cr,s,est ;  cr,r,est )  cr,r,est only needs to be checked for portal frames of 3 or more spans. Appendix B of this document When assessing frame stability, allowance can be made for the base stiffness. In this example, a base stiffness equal to 10% of the column stiffness has been assumed to allow for the nominally pinned bases. To calculate  cr , a notional horizontal force is applied to the frame and the horizontal deflection of the top of the columns is determined under this load. The notional horizontal force is: H NHF = 200 1 V Ed = 168 200 1  = 0,84 kN Appendix B of this document The horizontal deflection of the top of the column under this force is obtained from the elastic analysis as 1,6 mm. 1,6 mm 1,6 mm H H NHF NHF  cr,s,est is calculated as follows: