Technical Papers
Aug 22, 2020

Characterization of an Equivalent Coupled Flexural-Torsional Beam Model for the Analysis of Tall Buildings under Stochastic Actions

Publication: Journal of Structural Engineering
Volume 146, Issue 11

Abstract

An equivalent beam model to estimate the three-dimensional response of tall buildings to random loads is proposed in this paper. The model fully describes coupling between bending and torsion. In particular, bending behavior is described using the Timoshenko beam, while free warping is used to model torsional behavior. The beam dynamic characteristics (natural frequencies and modal shapes) are determined solving the coupled differential equations that rule the problem by means of the state variable approach. The main advantage of using such an equivalent beam is the use of a reduced-order model to estimate the response to random loads. Indeed, the proposed model can be used to reduce the computational time needed to estimate the three-dimensional elastic response of tall buildings to random loads. The influence of the mechanical characteristics of the beam on the calibration procedure and the influence of the eccentricity between centroid and center of mass on both natural frequencies and modal shapes are assessed and shown. Finally, the proposed approach is used to estimate the stochastic response of a tall building with a nonsymmetric plant to earthquake and wind loads.

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References

Ali, M. M., and K. S. Moon. 2007. “Structural developments in tall buildings: Current trends and future prospects.” Archit. Sci. Rev. 50 (3): 205–223. https://doi.org/10.3763/asre.2007.5027.
Bartoli, G., F. Cluni, V. Gusella, and L. Procino. 2006. “Dynamics of cable under wind action: Wind tunnel experimental analysis.” J. Wind Eng. Ind. Aerodyn. 94 (5): 259–273. https://doi.org/10.1016/j.jweia.2006.01.002.
Bishop, R. E. D., and W. G. Price. 1977. “Coupled bending and twisting of a timoshenko beam.” J. Sound Vib. 50 (4): 469–477. https://doi.org/10.1016/0022-460X(77)90497-7.
Cacciola, P. 2010. “A stochastic approach for generating spectrum compatible fully nonstationary earthquakes.” Comput. Struct. 88 (15–16): 889–901. https://doi.org/10.1016/j.compstruc.2010.04.009.
Carpinteri, A., and A. Carpinteri. 1985. “Lateral loading distribution between the elements of a three-dimensional civil structure.” Comput. Struct. 21 (3): 563–580. https://doi.org/10.1016/0045-7949(85)90134-8.
CEN (European Committee for Standardization). 2004. Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings. Brussels, Belgium: CEN.
Chajes, M. J., L. Zhang, and J. T. Kirby. 1996. “Dynamic analysis of tall building using reduced-order continuum model.” J. Struct. Eng. 122 (11): 1284–1291. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:11(1284).
Chakri, A., X.-S. Yang, R. Khelif, and M. Benouaret. 2018. “Reliability-based design optimization using the directional bat algorithm.” Neural Comput. Appl. 30 (8): 2381–2402. https://doi.org/10.1007/s00521-016-2797-3.
Chopra, A. 2012. Dynamics of structures. 4th ed. Upper Saddle River, NJ: Prentice Hall.
Cluni, F., M. Gioffre, and V. Gusella. 2013. “Dynamic response of tall buildings to wind loads by reduced order equivalent shear-beam models.” J. Wind Eng. Ind. Aerodyn. 123 (Dec): 339–348. https://doi.org/10.1016/j.jweia.2013.09.012.
Cluni, F., M. Gioffrè, and V. Gusella. 2014. “Analysis of coupled flexural torsional behavior of tall buildings under stochastic actions by means of equivalent beam model.” In Proc., 7th Int. Conf. (CSM-7) Computational Stochastic Mechanics, edited by G. Deodatis and P. Spanos, 15–18. Singapore: Research Publishing Services.
Cluni, F., V. Gusella, S. Spence, and G. Bartoli. 2011. “Wind action on regular and irregular tall buildings: Higher order moment statistical analysis by HFFB and SMPSS measurements.” J. Wind Eng. Ind. Aerodyn. 99 (6–7): 682–690. https://doi.org/10.1016/j.jweia.2011.01.020.
Cui, W., and L. Caracoglia. 2015. “New GPU computing algorithm for wind load uncertainty analysis on high-rise systems.” Wind Struct. Int. J. 21 (5): 461–487. https://doi.org/10.12989/was.2015.21.5.461.
Dym, C. L., and H. E. Williams. 2007. “Estimating fundamental frequencies of tall buildings.” J. Struct. Eng. 133 (10): 1479–1483. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:10(1479).
Franchin, P., F. Petrini, and F. Mollaioli. 2018. “Improved risk-targeted performance-based seismic design of reinforced concrete frame structures.” Earthquake Eng. Struct. Dyn. 47 (1): 49–67. https://doi.org/10.1002/eqe.2936.
Gioffrè, M., and V. Gusella. 2007. “Peak response of a nonlinear beam.” J. Eng. Mech. 133 (9): 963–969. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:9(963).
Heidebrecht, A. C., and B. S. Smith. 1973. “Approximate analysis of tall wall-frame structures.” J. Struct. Div. 99 (2): 199–221.
Howson, P. 2006. “Global analysis: Back to the future.” Struct. Eng. 84 (3): 18–21.
Iervolino, I., C. Galasso, and E. Cosenza. 2010. “Rexel: Computer aided record selection for code-based seismic structural analysis.” Bull. Earthquake Eng. 8 (2): 339–362. https://doi.org/10.1007/s10518-009-9146-1.
Masi, A., M. Vona, and M. Mucciarelli. 2011. “Selection of natural and synthetic accelerograms for seismic vulnerability studies on reinforced concrete frames.” J. Struct. Eng. 137 (3): 367–378. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000209.
Miranda, E. 1999. “Approximate seismic lateral deformation demands in multistory buildings.” J. Struct. Eng. 125 (4): 417–425. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:4(417).
Necib, B., and C. Sun. 1989. “Analysis of truss beams using a high order Timoshenko beam finite element.” J. Sound Vib. 130 (1): 149–159. https://doi.org/10.1016/0022-460X(89)90525-7.
Noor, A. K., and C. Andersen. 1979. “Analysis of beam-like lattice trusses.” Comput. Methods Appl. Mech. Eng. 20 (1): 53–70. https://doi.org/10.1016/0045-7825(79)90058-6.
Pekau, O., Z. Zielinski, and L. Lin. 1995. “Displacement and natural frequencies of tall building structures by finite story method.” Comput. Struct. 54 (1): 1–13. https://doi.org/10.1016/0045-7949(94)00316-U.
Piccardo, G., F. Tubino, and A. Luongo. 2014. “A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings.” Z. Angew. Math. Phys. 66 (4): 1895–1913. https://doi.org/10.1007/s00033-014-0456-z.
Piccardo, G., F. Tubino, and A. Luongo. 2016. “Equivalent nonlinear beam model for the 3-D analysis of shear-type buildings: Application to aeroelastic instability.” Int. J. Non Linear Mech. 80 (Apr): 52–65. https://doi.org/10.1016/j.ijnonlinmec.2015.07.013.
Piccardo, G., F. Tubino, and A. Luongo. 2019. “Equivalent timoshenko linear beam model for the static and dynamic analysis of tower buildings.” Appl. Math. Modell. 71 (Jul): 77–95. https://doi.org/10.1016/j.apm.2019.02.005.
Shinozuka, M., and Y. Sato. 1967. “Simulation of nonstationary random processes.” J. Eng. Mech. Div. 93 (1): 11–40.
Spence, S., and M. Gioffrè. 2011. “Efficient algorithms for the reliability optimization of tall buildings.” J. Wind Eng. Ind. Aerodyn. 99 (6–7): 691–699. https://doi.org/10.1016/j.jweia.2011.01.017.
Spence, S. M., and M. Gioffrè. 2012. “Large scale reliability-based design optimization of wind excited tall buildings.” Probab. Eng. Mech. 28 (Apr): 206–215. https://doi.org/10.1016/j.probengmech.2011.08.001.
Spence, S. M., M. Gioffrè, and A. Kareem. 2016. “An efficient framework for the reliability-based design optimization of large-scale uncertain and stochastic linear systems.” Probab. Eng. Mech. 44 (Apr): 174–182. https://doi.org/10.1016/j.probengmech.2015.09.014.
Timoshenko, S. P. 1921. “LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars.” Philos. Mag. 41 (245): 744–746. https://doi.org/10.1080/14786442108636264.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 146Issue 11November 2020

History

Received: Jun 3, 2019
Accepted: Jun 1, 2020
Published online: Aug 22, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 22, 2021

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Authors

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M. Gioffrè [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G. Duranti 93, Perugia 06125, Italy. Email: [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G. Duranti 93, Perugia 06125, Italy (corresponding author). ORCID: https://orcid.org/0000-0003-4204-2324. Email: [email protected]
Full Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G. Duranti 93, Perugia 06125, Italy. Email: [email protected]

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