# OPTIMAL DIAGRID ANGLE TO MINIMIZE DRIFT IN HIGH-RISE STEEL BUILDINGS SUBJECTED TO WIND LOADS

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3 Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind Loads members and beams in each model type. For diagrid members, Grade 5 steel pipe with three different cross section, 7mm, 6mm, and 5mm diameter with 4mm, 3mm, and 2mm thick for 24-,48- and 72-storey building models,respectively. Grade 36, W18 76 steel section is selected for the beams in all models. ASCE/SEI 7-1 is used to estimate the lateral wind load. The building models are assumed to be in Babylon, Iraq and within category III, which implies that there is a substantial hazard to human life in the event of failure. Based on the available climatic data, the basic wind speed is assumed 1 km/hr. Based on real 3D building model with 42m 42m plan, lateral load.45 kn/m 2 was chosen, its equivalent to 3kN concentrated force in each storey level in 2D model Diagrid Inclination Angle The diagonal members in diagrid structural systems carry both gravity loads as well as lateral forces owing to their triangulated configuration. The geometry of the basic triangle model plays a major role in the internal axial force distribution, as well as in conferring global shear and bending rigidity to the building structure. Since the optimal angle of the columns for maximum bending rigidity is 9 o, (i.e. vertical columns in traditional buildings) and that of the diagonals for maximum shear rigidity is about 27 o (only one storey stacked per basic triangle model), it is expected that the optimal angle of diagonal members for diagrid structures will fall between these angles. The angle of diagrid depends on the number of stories stacked per model. In this study, 1, 2, 3, 6 and 12 stories are stacked per diagrid triangle model with typical 3.5m storey height which gives an inclination angle 27 o, 45 o, 56 o, 72 o and 81 o, respectively as shown in Figures (2) Aspect Ratio Short buildings of low aspect ratio (height/width) behave like shear beams, and tall buildings of high aspect ratio tend to behave like bending beams. Thus, it is expected that the optimal diagrid angle directly affected by the total height (or number of stories) of the building. In order to examine the effect of the aspect ratio on the optimal diagrid inclinations angle, a set of 24-storey (aspect ratio H/b = 2) buildings having various diagrid angles are analyzed using 2D finite element model. Then, the analysis is repeated for 48- and 72-storey (aspect ratio H/b = 4 and 6, respectively) as shown in Figure (3) and (4). Due to the fact that there are not strict guidelines on what is actually considered a high-rise structure, it was hoped, this range safely keeps it from being considered either a medium -rise or super-high-rise building. 4. RESULTS AND DISCUSSION Lateral displacement is studied generally in two cases, building top (roof) lateral displacement and storey drift (relative displacement between floors). The results obtained from 2D finite element analysis are tabulated as follows: 4.1. Lateral Displacement The graphs of lateral displacement versus storey number are plotted in Figure (5), (6) and (7) for 24-, 48-, and 72-storey model, respectively. It is observed that the lateral displacements are effected by the diagrid angle to largest extent especially for 24- and 48-storey building models. While the displacement is maximum for models with 27 o and 81 o diagrid angle, the displacement are reduced sequentially for models with diagrid angle between 45 o and 72 o. 3

4 Khalid K. Shadhan 24-Storey 27 O 45 O 56 O 72 O 81 O Figure 2 Diagrid angles in 24-Storey models (Aspect ratio=2) 48-Storey 27 O 45 O 56 O 72 O 81 O Figure 3 Diagrid angles in 48-Storey models (Aspect ratio=4) 72-Storey 27 O 45 O 56 O 72 O 81 O Figure 4 Diagrid angles in 72-Storey models (Aspect ratio=6) 4

5 STOREY NO. Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind Loads From Table (1), it can be observed that the minimum building top displacement value is obtained with 56 o diagrid angle in 24-storey model, and with 72 o diagrid angle for 48- and 72-storey model. Table 1 Comparison results of building top displacement (mm) Model Aspect Angle of diagrid System ratio 27 o 45 o 56 o 72 o 81 o 24-storey storey storey LATERAL DISPALACEMENT (MM) Figure 5 Lateral displacement for 24-storey models (Aspect ratio=2) 4.2. Storey Drift Ratio As per Section 11.2 in current ASCE/SEI 7-1 (21), storey drift can be defined as the lateral displacement at the top of the storey relative to the bottom of the storey, while the storey drift ratio is define as the storey drift divide by the storey height. The storey drift ratios are shown in in Figure (8), (9) and (1) for 24-, 48-, and 72- storey model, respectively. It is clear that the storey drift ratio at storey coincide with the apex of triangle is less than those in other adjacent stories. Also, the storey drift ratio is very low in bottom stories, very high at the middle stories and finally decreases towards the upper stories. 5

6 STOREY NO. STOREY NO. Khalid K. Shadhan LATERAL DISPLACEMENT (MM) Figure 6 Lateral displacement for 48-storey models (Aspect ratio=4) LATERAL DISPLACEMENT (MM) Model Figure 7 Lateral displacement for 72-storey models (Aspect ratio=6) Table 2 Comparison results of Max. Storey drift ratio (mm/mm) Aspect ratio Angle of diagrid System 27 o 45 o 56 o 72 o 81 o 24-storey storey storey

7 STOREY NO. STOREY NO. Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind Loads STOREY DRIFT RATIO (MM/MM) Figure 8 Storey drift ratios for 24-storey models (Aspect ratio=2) STOREY DRIFT RATIO (MM/MM) Figure 9 Storey drift ratios for 48-storey models (Aspect ratio=4) 4.3. Optimal Diagrid Angle In medium- and super-high-rise building, lateral displacement decreasing is an urgent criterion. Lateral displacement is studied generally in two approaches, building top lateral displacement and storey drift. In this study in order to determine optimum diagrid angle, the results for these two approaches has been used as measurable parameters. For this reason building top lateral displacement and maximum storey drift are plotted versus the diagrid angles and the results are shown in Figure (11) and (12), respectively. 7

8 Max. Lateral Displacement (mm) STOREY NO. Khalid K. Shadhan STOREY DRIFT RATIO (MM/MM) Figure 1 Storey ratios for 72-storey models (Aspect ratio=6) The optimal angle of the diagrid members for maximum bending rigidity is 9 o, (i.e. vertical traditional columns) and that of the diagonals for maximum shear rigidity is about 27 o (only one storey stacked per basic triangle model), it is expected that the optimal angle of the diagonal members of diagrid structures will fall betwee n these angles. The optimum diagrid angle is where the building top lateral displacement and storey drift ratio are minimum. It can observed that the optimum diagrid for 24-storey model is smaller than 56 o while optimum angle is 72 o for both 48- and 72-storey models Storey 48-Storey 72-Storey Diagrid angle (Degrees) Figure 11 Building top displacement vs. Diagrid angle 8

9 Max. Storey drift (mm/mm) Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind Loads Storey.1 48-Storey 72-Storey Diagrid angle (Degrees) 5. CONCLUSIONS Figure 12 Max. Storey drift ratio vs. Diagrid angle This study examined the lateral behavior of diagrid high-rise building models under lateral wind loads from which the following conclusions can be drawn based on the above results: 1. The diagrid angle has a critical influence on the lateral behavior of the high-rise building models under lateral load. The structural efficiency of diagrids can be maximized by configuring the building model to have optimum grid geometries. 2. The storey drift ratio at storey coincide with the apex of triangle is less than those in other adjacent stories. 3. Optimum diagrid angle resulted from finite element analysis for 24-storey model (aspect ratio=2) is smaller than 56 o while optimum angle is 72 o for both 48- (aspect ratio =4) and 72-storey (aspect ratio=6) models. 4. The optimal range of diagrids angle is reduced as the building aspect ratio (height/width) decreases. REFERENCES [1] ASCE/SEI 7-1; Engineers, A. S. Minimum Design Loads for Buildings and Other Structures. American Society of Civil Engineers, 21. [2] Montuori, G. M., Mele, E., Brandonisio, G. and De Luca, A. Design Criteria for Diagrid Tall Buildings: Stiffness versus Strength. The Structural Design of Tall and Special Buildings, Published online in Wiley Online Library, DOI: 1.12/tal.1144, 213. [3] Mele, E., Toreno, M., Brandonisio, G. and De Luca, A. Diagrid Structures for Tall Buildings: Case Studies and Design Considerations. The Structural Design of Tall and Special Buildings, 23, 27, pp [4] Moon, K. S., Connor J. J. and Fernandez, J. E. Diagrid Structural System for Tall Buildings: Characteristics and Methodology for Preliminary Design. The Structural Design of Tall and Special Buildings, 16(2), 27, pp

10 Khalid K. Shadhan [5] Panchal, N. B. and Patel V. R. Diagrid Structural System: Strategies to Reduce Lateral Forces on High-Rise Buildings. International Journal of Research in Engineering and Technology, 3(4), 214, pp [6] Singh, R. K., Garg, V. and Sharma, A. Analysis and Design of Concrete Diagrid Building and its Comparison with Conventional Frame Building. International Journal of Science, Engineering and Technology, 2(6), 214, pp [7] Mathew, J. and Babu, N. Topology Optimisation of Braced Frames for High-Rise Buildings. International Journal of Civil Engineering and Technology, 5(12), 214, pp

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