Steel Buildings in Europe

Part 4: Detailed Design 4 – 6 V Ed is the total design vertical load on the structure on the bottom of the storey  H,Ed is the horizontal displacement at the top of the storey, relative to the bottom of the storey, under the horizontal loads (both externally applied and equivalent horizontal forces) h is the storey height. 2.4.2 Allowance for second order effects As discussed in Section 2.3.1, horizontal flexibility influences overall structural stability and the significance of second order effects on overall design. As described in Section 2.4.1, EN 1993-1-1 § 5.2.1 introduces the concept of  cr as the basic measure of horizontal flexibility and its influence on structural stability. Depending on the value of  c , three alternative design situations are possible.  cr > 10 Where horizontal stability is provided by a concrete core, or by robust bracing, calculations will generally demonstrate that  cr > 10 for all combinations of actions. EN 1993-1-1, § 5.2.1(3) permits the use of first order analysis for such frames. When  cr > 10, second order effects are considered small enough to be ignored. It may be convenient for certain low rise frames to ensure that  cr > 10, by providing bracing of sufficient strength and stiffness. This is discussed in Section 2.6. For medium rise structures, this simple approach will usually lead to heavy triangulated bracing with large and expensive connections. 3,0 <  cr < 10 For buildings between three and ten storeys, bracing designed for strength will generally lead to 3,0 <  cr < 10. (If  cr should fall below 3,0 it is usually practical to increase bracing sizes to satisfy this lower limit). For  cr > 3,0 EN 1993-1-1, § 5.2.2(6)B permits the use of first order analysis provided that all storeys a similar:  distribution of vertical loads and  distribution of horizontal loads and  distribution of frame stiffness with respect to the applied storey shear forces. To allow for second order effects, all relevant action effects are amplified by the factor cr 1 1 1  