Maximum deflection of symmetric wall-frame buildings

Abstract

IntroductionThe deflection analysis of multi-storey frameworks has a long history. The mathematical problem of a cantilever composed of a number of parallel beams interconnected by cross bars (i.e., frameworks, using today's terminology) was presented and solved as early as in 1947 in a brilliant paper [Chitty, 1947]. Chitty and Wan [1948] then applied the method to tall buildings under wind load. However, the applicability of the original method was considerably restricted as they neglected the effect of the axial deformation of the columns. Numerous methods were then published, amazingly unaware of Chitty's efforts, both for individual frameworks or coupled shear walls [Csonka, 1950;Beck, 1956; Ligeti, 1974; Szmodits, 1975;Szerémi, 1984] and also for wall-frame buildings [Rosman, 1960; MacLeod, 1971; Despeyroux, 1972; Council, 1978;Stafford Smith et al., 1981; Goschy, 1981; Hoenderkamp and Stafford Smith, 1984; Taranath, 1988; Coull, 1990;Schueller, 1990;Coull and Wahab, 1993]. The most comprehensive treatment, perhaps, is to be found in the excellent textbook by Stafford Smith and Coull [1991] where a whole chapter is devoted to individual frameworks and another chapter deals with symmetric wall-frame buildings. Most of the methods, however, are too complicated, even as approximate methods, or neglect one or more significant phenomena in order to be able to offer relatively simple solutions. Furthermore, none of them are backed up with a comprehensive accuracy analysis and, as a result, their applicability is not possible to establish for practical structural engineering problems. Some are based on the equivalent column approach and use a procedure whereas the characteristic stiffnesses are simply added up for the analysis. This approach -although perfectly legitimate for stability and frequency analyses -is not acceptable for the deflection analysis, as it will be demonstrated in this paper. All the above shortcomings were addressed in a recent paper [Zalka, 2009] which offered a closed-form solution for the deflection of symmetric buildings. However, that solution is still fairly complicated and, as it will be shown later on, its accuracy can significantly be improved.

Create a Rigid and Safe Grid-Like Structure

“…Zalka presented practical results in [44][45][46] and nearly in [47][48][49], which can determine the maximum deflection of multi-story buildings. These results used the continuum method and gave a useful general practical application.…”

Maximum deflection of asymmetric wall-frame buildings under horizontal load

“…Looking at the derivations of the lateral (sway) problem [16], two possibilities may be considered. With the sway problem, two procedures were developed: the "simple" method and the "more accurate" method.…”

“…These individual bracing units (frameworks F1, F2, F3, F4, F5, F6 and F7, shear walls W2, W3, W4 and W5 and the Ucore) were all used for the accuracy analysis of the planar solution [16]. The cross-sections of the columns and beams of the frameworks were 0.4 / 0.4 (metre) unless otherwise indicated in Fig.…”

“…The case when the resultant of the external load passes through the shear centrethe planar problem -is discussed in detail in [16]. The maximum deflection of such a system of frameworks, shear walls and cores can be obtained using the ith unit of the system:…”

“…To ensure best accuracy, when the apportioners -and load shares -are determined, the co-called "more accurate" method should be used -see [16] for detailed explanation. It is only mentioned here that according to the "more accurate" method, the problem of f + m frameworks and shear walls/cores is reduced to the problem f frameworks.…”