Steel Buildings in Europe

Part 4: Detailed Design 4 – 11 The basic imperfection is an out-of-verticality  of 1/200. This allowance is greater than normally specified erection tolerances, because it allows both for actual values exceeding specified limits and for effects such as lack of fit and residual stresses. The design allowance in EN 1993-1-1, § 5.3.2 is given by:  =  0  h  m = 200 1  h  m where:  h is a reduction factor for the overall height and  m is a reduction factor for the number of columns restrained by the bracing system. (For detailed definition, see EN 1993-1-1, § 5.3.2(3)). For simplicity, the value of  may conservatively be taken as 1/200, irrespective of the height and number of columns. Where, for all the storeys, the horizontal force exceeds 15% of the total vertical force, sway imperfections may be neglected (because they have little influence on sway deformation and amplification factor for such robust structures). 2.7.2 Use of equivalent horizontal forces EN 1993-1-1, § 5.3.2(7) states that vertical sway imperfections may be replaced by systems of equivalent horizontal forces, introduced for each column. It is much easier to use equivalent horizontal forces than to introduce the geometric imperfection into the model. This is because:  The imperfection must be tried in each direction to find the greater effect and it is easier to apply loads than modify geometry.  Applying forces overcomes the problems of the changes in length that would occur when considering the columns of buildings in which the column bases are at different levels. According to EN 1993-1-1, § 5.3.2(7) the equivalent horizontal forces have the design value of  N Ed at the top and bottom of each column, where N Ed is the force in each column; the forces at each end are in opposite directions. For design of the frame, it is much easier to consider the net equivalent force at each floor level. Thus an equivalent horizontal force equal to  times the total vertical design force applied at that floor level should be applied at each floor and roof level. 2.7.3 Sway imperfections over a storey The configuration of imperfections to be considered over a storey assumes a change in direction of the column at that level, as shown in Figure 2.5. The inclined columns produce a horizontal force (the horizontal component of the inclined force). This horizontal force must be transferred to the stability system (the bracing or concrete core(s)) via the floor diaphragm or via horizontal bracing designed for that purpose. Usually it is sufficient to transfer these forces via the floor diaphragm.