Steel Buildings in Europe

Title APPENDIX D Worked Example: Design of portal frame using elastic analysis 15 of 44 4 - 96 The non dimensional slenderness, LT  , is calculated as: LT   cr y y M W f = 6 3 909 10 355 10 2194    = 0,926 EN 1993-1-1 §6.3.2.2 For the calculation of the reduction factor,  LT , EN 1993-1-1 provides two methods. The general method, applicable to any section, is given in §6.3.2.2. §6.3.2.3 provides a method that can only be used for rolled sections or equivalent welded sections. In this example the second method is used, i.e. §6.3.2.3.  LT =     2 LT LT,0 LT LT 0,51         EN 1993-1-1 recommends the following values: LT,0   0,4   0,75 The values given in the National Annex may differ. The designer should check the National Annex of the country where the structure is to be built. EN 1993-1-1 §6.3.2.3 b h  2,5  Curve c for hot rolled I sections   LT  0,49 EN 1993-1-1 Table 6.3 Table 6.5  LT =     2 0,51 0,49 0,926 0,4 0,75 0,926     = 0,950  LT = 2 LT 2 LT LT 1        LT = 2 2 0, 75 0,926 0,950 0,950 1    = 0,685 EN 1993-1-1 §6.3.2.3 2 2 LT 0.926 1 1   = 1,17   LT = 0,685 M b,Rd = M1 pl,y y LT   f W = 6 3 10 1, 0 355 10 2194 0, 685      = 534 kNm M b,Rd = 616 kNm  534 kNm Fails Since the check for lateral torsional buckling resistance alone fails, the interaction of axial force and bending moment is not carried out. It is necessary to introduce a torsional restraint between the haunch and the base, as shown in the following figure. The bending moment is greater at the top of the column and therefore the restraint is placed closer to the maximum bending moment, rather than in the middle of the column.