# Parametric Analysis of the Shear Lag Effect in Tube Structural Systems of Tall Buildings
## 2 Shear Lag Effect in Tube Structural Systems
While in [8; 11] the focus is set on the positive shear lag effect and the shear lag effect in general, in [10] the focus is set on the negative shear lag effect and the calculation methods that would best approximate it. However, this effect is quite a problem in tube structural systems of tall buildings as well. Although this effect was mostly examined in detail in box girders and bridges, the first mathematical expressions for tall buildings were set in the 1990s [12]. In [12] a mathematical model for the preliminary design of the shear lag effect in tall buildings is given. In the proposed method, independent distributions of axial displacements are used for the web and flange panels and thus the shear lag in each panel is individually allowed for. Lastly, it is deduced that the shear lag effect is dependent on the type of the horizontal load and that the positive shear lag effect is greater at the base of the building than the negative shear lag is at its top. A great advancement in theoretical knowledge is seen mostly in the complexity and preciseness of analytical methods like the one shown in [13]. In this research the shear lag effect in tall tube structures is shown regarding the axial stresses and displacements of columns. At the same time, the first computer-based models for this phenomenon are developed. According to [14] a simple model is developed for the purpose of the calculation and design of a tube structure under horizontal loads. Additionally, an expression to assess the horizontal displacement of a tall building is given with the shear lag effect considered while developing the said expression. In [5] a much more complex computer-based program is  
Figure 3: (**a**) Box section cantilever stress distribution for point load and (**b**) continuous load. developed using a 40 storey tall tube structure. It is also confirmed that the positive shear lag effect is related to the lower storeys and that the negative shear lag is related to the higher storeys of the building. Finally, it is concluded that the positive shear lag is the source of the negative shear lag. At the beginning of the 2000s the analysis of this phenomenon is expanded to more complex structural systems like tube in tube structures [15; 16; 17] where it is deduced that the negative shear lag effect is more prominent at the lower part of the interior tube than at the lower parts of the exterior tube. Furthermore in [17] exact analytical expressions are given for the calculation of the shear lag effect in this type of structural system. On the other hand, in diagrid structural systems the shear lag effect is mainly influenced by two parameters, the angle under which the exterior diagonal columns cross each other and the way the shear lag effect is taken into account in the preliminary design of structural elements [2; 18]. The next step in the research of the shear lag effect was the pursuit of ideas and ways to minimize its impact. In [6] the optimal angle under which the exterior bracings cross to minimize the shear lag effect is given. In [19] a similar analysis is conducted with the tube structural system and diagonal bracing where the shear lag effect in an ordinary tube structure is compared to its effect in a tube structure with diagonal bracing. It is deduced that the implementation of diagonal bracing has a great impact on the shear lag effect and that the angle at which the diagonals are placed is the most important factor to consider. Furthermore, according to [20] the use of two diagonals in an \"X\" like fashion is much more efficient than the use of one diagonal in any configuration regarding the decrease of the shear lag effect. The same principle of bracing can be used for tube in tube structural systems [21]. In recent years, the research conducted is mostly based on parametric analysis of different structural systems [22; 23; 24; 25]. In [22] a parametric analysis is conducted where the main parameter being varied are the layout dimensions of the building.