# Parametric Analysis of the Shear Lag Effect in Tube Structural Systems of Tall Buildings
## 5 Parametric Analysis  
The parametric analysis will be conducted with four main parameters (Figure 4):  
1. \(\mathrm{s/c}\)--the ratio of column spacing perpendicular to the horizontal load direction and column dimension, ranging from 4 to 6, in every next model variation one column is removed to maintain a constant building layout)
2. \(\mathrm{H_{1}/h}\)--the ratio of storey height and beam height (ranging from 2.9 to 4.4 with the increment of 0.1 m)
3. \(\mathrm{A/B}\)--the ratio of building layout dimensions (ranging from 0.55 to 1.0, in each step two columns are removed on the side of the building perpendicular to the horizontal load to maintain constant column spacing
4. horizontal load profile  
The parameters kept constant throughout the analysis are the column dimensions (c = 0.5 m), beam width (b = 0.5 m), storey height (H\({}_{1}\) = 3.5 m), layout dimension of the building parallel to the horizontal load (A = 24 m) and the entire height of the building (H = 126 m). The rest of the parameters are variable. The results are shown in diagrams below. The variable parameters (s/c, H\({}_{1}\)/h, A/B) are shown on the X axis, and coefficient \(\beta\) on the Y axis. Coefficient \(\beta\) is defined on Figure 8. Half of the flange panel of the tube structure is observed (Figure 8, in red) that is located on the opposite side of the horizontal load. In Figure 8 the case of the positive shear lag is shown. The number of columns in this case is N = 5.  
Figure 7: Shear lag effect on seven characteristic storeys in the flange panel (panel parallel to the panel on which the horizontal loads act).  
Coefficient \(\beta\) is defined as follows:  
\[\beta=n_{\beta}/n, \tag{1}\]  
where:  
n--actual number of columns in half of the flange panel (in the case of uneven number of columns, a half of the column is used)  
n\({}_{\beta}\)--number of columns involved in the transfer of loads calculated in Equation (2) for half of the flange panel  
\[n_{\beta}=\sum F_{i}/F_{1}, \tag{2}\]  
where:  
\(\Sigma F_{i}\)--sum of axial compressive forces in columns (F\({}_{1}\) to F\({}_{5}\))  
F\({}_{1}\)--compressive force in the edge (first or last) column of the flange panel  
Therefore, if the axial force on the edge of the flange panel (F\({}_{1}\)) is the one with maximal value, then the flange panel is under positive shear lag. On the other hand, if the same force is given with its minimal value, then the flange panel is under negative shear lag. Additionally, it is then clear that the location with the value of coefficient \(\beta=1\) is the location in which no shear lag effect exists (the positive shear lag ends and the negative one begins). Accordingly, \(\beta<1\) applies to positive shear lag and \(\beta>1\) applies to negative shear lag. Finally, as the value of \(\beta\) moves away from the value equal to 1, either less or more, the shear lag positive or negative, increases. For the positive shear lag, it means that as the value of \(\beta\) decreases (moves away from the value equal to 1), the positive shear lag increases. For the negative shear lag, it means that as the value of \(\beta\) increases (moves away from the value equal to 1) the negative shear lag increases.