# Parametric Analysis of the Shear Lag Effect in Tube Structural Systems of Tall Buildings
## 4 Computer-Based Model of the Tube Structure  
A parametric analysis was conducted in SOFiSTIK 2020 software. Based on the preliminary analysis provided in the previous chapter, dimensions of the building and construction elements are chosen for the purposes of forming a computer-based model (Figure 4):  
- Layout dimensions of the building: A/B = 24 m/24 m  
- Connecting beam dimensions: b/h = 0.5 m/1.0 m  
- Square column edge dimension: c = 0.5 m  
- Column spacing: s = 2.4 m  
- Storey height: H\({}_{1}\) = 3.5 m  
- Building height: H = 126.0 m  
- Number of storeys: 36  
The columns and beams are modelled with one dimensional finite elements (6 degrees of freedom), and assigned a corresponding cross section properties (moment of inertia for both axis, sectional area, shear deformation area, torsional moment of inertia, warping modulus and concrete material linear properties) according to column or beam member dimensions. They are connected with a fixed connection at the intersection of their axes, allowing the transfer of moment, shear force and axial force. Floor slabs are modeled as rigid diaphragms (Figure 5), by coupling of the nodes in the same storey to joint in-plane movements and rotations (flexible slab--rigid disk behavior), as allowed and recommended by Eurocode design code A linear statical analysis is performed. The building is loaded with the dead load (no additional vertical loads were considered besides the dead load) of all structural elements and wind load uniformly distributed along the height. The value of the uniformly distributed load is determined as the maximum expected value based on EN 1991-4 [26] while considering the top of the structure as a reference height. In addition, an actual wind profile will be used in the parametric analysis that is also calculated by EN 1991-1-4 [26]. The horizontal loads are concentrated at each intersection of beams and columns (Figure 6). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{**Building**} & \multicolumn{1}{c}{**Material Used**} & \multicolumn{1}{c}{**H\({}_{1}\)/H**} & \multicolumn{1}{c}{**A/B (Squared Shape)**} & \multicolumn{1}{c}{**A/B (Rectangular Shape)**} & \multicolumn{1}{c}{**s/c**} \\ \hline
1. The Plaza on Dewitt (Chicago) & Concrete & 2.8/120.4 = 0.0233 & - & 38/24 = 1.58 & 1.7/0.5 = 3.4 \\
2. World Trade Center (New York) & Steel & 3.8/417 = 0.0091 & 63.4/63.4 = 1.00 & - & 1.1/0.6 = 1.83 \\
3. Aon Center (Chicago) & Steel & 3.86/346 = 0.0112 & 59.1/59.1 = 1.00 & - & 3.0/1.0 = 3.0 \\
4. Hancock Whitney Center & Concrete/Steel & 4.15/212 = 0.0196 & - & 58.0/40.0 = 1.45 & 1.8/1.0 = 1.8 \\
4. 5. The Urban Hive (Seoul) & Concrete & 3.50/60 = 0.0583 & 24.0/24.0 = 1.00 & - & 1.6/0.5 = 3.2 \\
6. Hopewell Centre (Hong Kong) & Concrete & 3.40/222 = 0.0153 & 1.00 (circular) & - & 6.0/3.0 = 2.0 \\
7. Maya Akar business center 1 & Concrete & 3.25/110 = 0.0296 & - & 31.75/24.75 = 1.28 & 3.5/1.0 = 3.5 \\
8. Maya Akar business center 2 & Concrete & 3.25/60 = 0.0542 & - & 33.50/29.45 = 1.14 & 3.5/1.0 = 3.5 \\
1 stumb & - & 3.50/126 = 0.0276 & 1.00 & 1.36 & 2.75/1 = 2.75 \\ \hline \hline \end{tabular} H\({}_{1}\)—storey height (m). H—building height (m). A, B—floor dimensions of the building (m). s—axial distance of columns (m). c—column dimension parallel to the slab edge (m).  
\end{table} 
Table 1: Structural parameters of some well-known tall buildings with tube structural system. Figure 4: Layout of the building dimensions and the dimensions of structural elements. Figure 5: The floor layout, side view and the axonometry of the computer model (red—pinned supports at the location of columns, green—beams, yellow—rigid diaphragm, light blue—columns). The shear lag effect is observed throughout the building's height. In Figure 7 the shear lag effect is shown in seven characteristic storeys ranging from the 2 nd to the 36 th storey. On the horizontal axis from left to right eleven columns are placed and on the vertical axis the coefficient \(\alpha\) is given.