Free Vibration of Tall Buildings using Energy Method and Hamilton’s Principle
In a framed-tube tall building, shear wall systems are the most efficient structural systems for increasing the lateral load resistance. A novel and simple mathematical model is developed herein which calculates the natural frequencies of such tall buildings. The analyses are based on a continuous model, in which a tall building structure is replaced by an idealized cantilever beam that embodies all relevant structural characteristics. Governing equations and the corresponding eigen-problem are derived based on the energy method and Hamilton’s principle. Solutions are obtained for three examples; using the separation of variables technique implemented in MATLAB. The results are compared to SAP2000 full model analysis; and they indicate reasonable accuracy. The computed natural frequencies for structures 50, 60 and 70 storey buildings were over-estimate 7, 11 and 14 percent respectively. The computed errors indicate that the proposed method has acceptable accuracy; and can be used during the initial stages of designing of tall buildings; it is fast and low cost computational process.
Alavi, Arsalan, Reza Rahgozar, Peyman Torkzadeh, and Mohamad Ali Hajabasi. “Optimal Design of High-Rise Buildings with Respect to Fundamental Eigenfrequency.” International Journal of Advanced Structural Engineering 9, no. 4 (September 25, 2017): 365–374. doi:10.1007/s40091-017-0172-y.
Alavi, Arsalan, Peyman Rahgozar, and Reza Rahgozar, “Minimum‐Weight Design of High‐Rise Structures Subjected to Flexural Vibration at a Desired Natural Frequency.” The Structural Design of Tall and Special Buildings 27, No. 15 (October 2018): e1515. doi:10.1002/tal.1515.
Davari, Seyed Mozafar, Mohsen Malekinejad, and Reza Rahgozar, “Static Analysis of Tall Buildings based on Timoshenko Beam Theory.” International Journal of Advanced Structural Engineering 11 (September 2019): 455–461.
Kwan, Albert K.H., “Simple Method for Approximate Analysis of Framed-Tube Structures.” Journal of Structural Engineering, ASCE 120, No. 4 (April 1994): 1221-1239. doi:10.1061/(ASCE)0733-9445.
Kwan, Albert K.H., “Shear Lag in Shear/Core Walls.” Journal of Structural Engineering, ASCE 122, No. 9 (1996): 1097-1104. doi:10.1061/(ASCE)0733-9445.
Tavakoli, Reihaneh, Reza Kamgar, and Reza Rahgozar. “Seismic Performance of Outrigger-Braced System Based on Finite Element and Component-Mode Synthesis Methods.” Iranian Journal of Science and Technology, Transactions of Civil Engineering (July 31, 2019). doi:10.1007/s40996-019-00299-3.
Tavakoli, Reihaneh, Reza Kamgar, and Reza Rahgozar. “Seismic Performance of Outrigger–belt Truss System Considering Soil–structure Interaction.” International Journal of Advanced Structural Engineering 11, no. 1 (February 1, 2019): 45–54. doi:10.1007/s40091-019-0215-7.
Coull, Alexander, and Bishwanath Bose, “Simplified Analysis of Frame Tube Structures.” Journal of Structural Engineering, ASCE 101, No. 11 (1975): 2223-2240.
Coull, Alexander, and Abdulla K. Ahmed, “Deflections of Framed-Tube Structures.” Journal of Structural Engineering, ASCE 104, No. 5 (1978): 857-862.
Alavi, Arsalan, and Reza Rahgozar, “Optimal Stiffness Distribution in Preliminary Design of Tubed-System Tall Buildings.” Structural Engineering and Mechanics 65, No. 6 (March 2018): 731-739. doi:10.12989/sem.2018.65.6.731.
Alavi, Arsalan, and Reza Rahgozar, “A Simple Mathematical Method for Optimal Preliminary Design of Tall Buildings with Peak Lateral Deﬂection Constraint.” International Journal of Civil Engineering 17 (July 2018): 999–1006. doi:10.1007/s40999-018-0349-1.
Poon, Dennis, Show-Song Shieh, Leonard Joseph, and Ching-Chang Chang, “Structural Design of Taipei 101, the World’s Tallest Building.” Proceedings of the CTBUH 2004, Seoul Conference, Seoul, Korea, 271-278.
Bozdogan, Kanat Burak, “A Method for Free Vibration Analysis of Stiffened Multi-Bay Coupled Shear Walls.” Asian Journal of Civil Engineering (Building and Housing) 7, No. 6 (November 2006): 639-649.
Bozdogan, Kanat Burak, “An Approximate Method for Static and Dynamic Analysis of Symmetric Wall-Frame Buildings.” The Structural Design of Tall and Special Buildings 18, No. 3 (September 2007): 279-290. doi:10.1002/tal.409.
Dym, Clive L., Harry E. Williams, “Estimating Fundamental Frequencies of Tall Buildings.” Journal of Structural Engineering, ASCE 133, No. 10 (October 2007): 1-5. doi:10.1061/(ASCE)0733-9445(2007)133:10(1479).
Kaviani, Peyman, Reza Rahgozar, and Hamed Saffari, “Approximate Analysis of Tall Buildings using Sandwich Beam Models with Variable Cross-Section.” The Structural Design of Tall and Special Buildings 17, No. 2 (August 2007): 401-418. doi:10.1002/tal.360.
Lee, Jaehong, Minsik Bang, and Jae‐Yeol Kim, “An Analytical Model for High-Rise Wall-Frame Structures with Outriggers.” The Structural Design of Tall and Special Buildings 17, No. 4 (October 2007): 839-851. doi:10.1002/tal.406.
Mohammadnejad, Mehrdad, Hasan Haji Kazemi, “Dynamic Response Analysis of Tall Buildings under Axial Force Effects.” Journal of Civil Engineering (Journal of School of Engineering) 31, No. 2 (2018): 39-53.
Mohammadnejad, Mehrdad, and Hasan Haji Kazemi, “A New and Simple Analytical Approach to Determining the Natural Frequencies of Framed Tube Structures.” Structural Engineering and Mechanics 65, No. 1 (January 2018): 111-120. doi:10.12989/sem.2018.65.1.111.
Mohammadnejad, Mehrdad, and Hasan Haji Kazemi, “Dynamic Response Analysis of a Combined System of Framed Tubed, Shear Core and Outrigger-Belt Truss.” Asian Journal of Civil Engineering (BHRC) 18, No. 8 (December 2017): 1211-1228.
Kamgar, Reza, and Reza Rahgozar, “Determination of Optimum Location for Flexible Outrigger System in Tall Buildings with Constant Cross-Section Consisting of Framed Tube, Shear Core, Belt Truss and Outrigger System using Energy Method.” International Journal of Steel Structures 17, No. 1 (2017): 1-8. doi:10.1007/s13296-014-0172-8.
Kamgar, Reza, and Reza Rahgozar, “Critical Excitation Method for Determining the Best Location of Belt Truss System in Tall Buildings.” Iranian Journal of Structures Engineering 4, No. 2 (2017): 76-88.
Tavakoli, Reihaneh, Reza Kamgar, and Reza Rahgozar. “The Best Location of Belt Truss System in Tall Buildings Using Multiple Criteria Subjected to Blast Loading.” Civil Engineering Journal 4, no. 6 (July 4, 2018): 1338. doi:10.28991/cej-0309177.
Kuang, Junshang, and S.C. Ng, “Dynamic Coupling of Asymmetric Shear Wall Structures: An Analytical Solution.” International Journal of Solids and Structures 38, No. 48-49 (November–December 2001): 8723-8733. doi:10.1016/S0020-7683(01)00052-X.
Wang, Quanfeng, L.Y. Wang, “Estimating Periods of Vibration of Buildings with Coupled Shear Walls.” Journal of Structural Engineering, ASCE 131, No. 12 (December 2005): 1931-1935. doi:10.1061/(ASCE)0733-9445(2005)131:12(1931).
Bozdogan, Kanat Burak, Duygu Öztürk, “An Approximate Method for Free Vibration Analysis of Multi-bay Coupled Shear Walls.” Mathematical and Computational Applications 12, No. 1 (2007): 41-50. doi:10.3390/mca12010041.
Kamgar, Reza, and Peyman Rahgozar. “Reducing Static Roof Displacement and Axial Forces of Columns in Tall Buildings Based on Obtaining the Best Locations for Multi-Rigid Belt Truss Outrigger Systems.” Asian Journal of Civil Engineering 20, no. 6 (April 30, 2019): 759–768. doi:10.1007/s42107-019-00142-0.
Malekinejad, Mohsen, and Reza Rahgozar, “Free Vibration Analysis of Tall Buildings with Outrigger-Belt Truss System.” International Journal of Earthquakes and Structures 2, No. 1 (March 2011): 89-107. doi:10.12989/eas.2011.2.1.089.
Meirovitch, Leonard, “Computational Methods in Structural Dynamics.” The Netherland Rockville, Maryland, USA.
Rahgozar, Reza, Zahra Mahmoudzadeh, Mohsen Malekinejad, and Peyman Rahgozar. “Dynamic Analysis of Combined System of Framed Tube and Shear Walls by Galerkin Method Using B-Spline Functions.” The Structural Design of Tall and Special Buildings 24, no. 8 (November 21, 2014): 591–606. doi:10.1002/tal.1201.
- There are currently no refbacks.
Copyright (c) 2020 Peyman Rahgozar
This work is licensed under a Creative Commons Attribution 4.0 International License.