Technical Papers
Mar 10, 2017

Modeling of Rocking Elastic Flexible Bodies under Static Loading Considering the Nonlinear Stress Distribution at Their Base

Publication: Journal of Structural Engineering
Volume 143, Issue 7

Abstract

In recent years, the need for resilient structural systems has led to renewed interest in the use of rocking members instead of conventional ones for the design of earthquake-resistant structures. Due to the usually constrained nature of such members, in addition to the deformability along their height, the nonlinear stress distribution at their base resulting from the partial loading of the rocking interface needs to be taken into account for an accurate estimation of the rocking motion. In this paper, a new approach is proposed for the prediction of the response of elastic rocking bodies under static loading that is able to consider such effects. The nonlinear stress distribution near the contact area results in additional displacements compared to those of the technical theory of bending, and a method to estimate them is presented and incorporated into a macroelement formulation that can be used in the context of a finite-element program. Results for typical examples are presented and compared with those of corresponding commercial software models, showing excellent agreement, while the proposed macroelement requires extremely low runtimes compared to conventional finite-element codes.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The first author would like to thank the Greek State Scholarships Foundation for its financial support through the IKY Fellowships of Excellence for Postgraduate studies in Greece—Siemens program.

References

Abaqus 6.11 [Computer software]. SIMULIA, Providence, RI.
ACI (American Concrete Institute). (2003). “Special hybrid moment frames composed of discretely jointed precast and post-tensioned concrete members.”, Farmington Hills, MI.
Avgenakis, E. (2015). “Modeling of rocking flexible bodies considering the deformability of their base.” M.S. thesis, National Technical Univ. of Athens, Athens, Greece.
Barthes, C. B. (2012). “Design of earthquake resistant bridges using rocking columns.” Ph.D. thesis, Univ. of California, Berkeley, CA.
Belleri, A., Torquati, M., and Riva, P. (2013). “Finite element modeling of rocking walls.” Proc., 4th ECCOMAS Thematic Conf. on COMPDYN, Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical Univ. of Athens, Greece.
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.
Chancellor, N. B., Eatherton, M. R., Roke, D. A., and Akbaş, T. (2014). “Self-centering seismic lateral force resisting systems: High performance structures for the city of tomorrow.” Buildings, 4(3), 520–548.
Chopra, A. K., and Yim, S. C.-S. (1985). “Simplified earthquake analysis of structures with foundation uplift.” J. Struct. Eng., 906–930.
De Borst, R., Crisfield, M. A., Remmers, J. J., and Verhoosel, C. V. (2012). Nonlinear finite element analysis of solids and structures, Wiley, Chichester, West Sussex, U.K.
Dimitrakopoulos, E. G., and DeJong, M. J. (2012). “Revisiting the rocking block: Closed-form solutions and similarity laws.” Proc. R. Soc. London, Ser. A, 468(2144), 2294–2318.
fib (International Federation for Structural Concrete). (2003). “Seismic design of precast concrete building structures.”, Lausanne, Switzerland.
Gaydon, F. (1965). “The rectangle, under general equilibrium loading, in generalized plane stress.” Proc. R. Soc. London, Ser. A, 283(1394), 356–378.
Gaydon, F., and Shepherd, W. (1964). “Generalized plane stress in a semi-infinite strip under arbitrary end-load.” Proc. R. Soc. London, Ser. A, 281(1385), 184–206.
Housner, G. W. (1963). “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am., 53(2), 403–417.
Housner, G. W., and Vreeland, T., Jr. (1965). “The analysis of stress and deformation.” California Institute of Technology, Pasadena, CA.
Kam, W. Y., Pampanin, S., Palermo, A., and Carr, A. J. (2010). “Self-centering structural systems with combination of hysteretic and viscous energy dissipations.” Earthquake Eng. Struct. Dyn., 39(10), 1083–1108.
MATLAB. [Computer software]. MathWorks, Natick, MA.
Neuenhofer, A., and Filippou, F. C. (1998). “Geometrically nonlinear flexibility-based frame finite element.” J. Struct. Eng., 704–711.
OpenSees version 2.5.0 [Computer software]. Pacific Earthquake Engineering Research Center, Berkeley, CA.
Penna, A., and Galasco, A. (2013). “A macro-element model for the nonlinear analysis of masonry members including second order effects.” Proc., 4th ECCOMAS Thematic Conf. on COMPDYN, Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical Univ. of Athens, Athens, Greece.
Penna, A., Lagomarsino, S., and Galasco, A. (2014). “A nonlinear macroelement model for the seismic analysis of masonry buildings.” Earthquake Eng. Struct. Dyn., 43(2), 159–179.
Priestley, N. M. (1991). “Overview of PRESSS research program.” PCI J., 36(4), 50–57.
Prieto, F., and Lourenço, P. B. (2005). “On the rocking behavior of rigid objects.” Meccanica, 40(2), 121–133.
Przemieniecki, J. S. (2012). Theory of matrix structural analysis, Dover Publications, New York.
Psycharis, I. N., and Jennings, P. C. (1983). “Rocking of slender rigid bodies allowed to uplift.” Earthquake Eng. Struct. Dyn., 11(1), 57–76.
Roh, H., and Reinhorn, A. M. (2009). “Analytical modeling of rocking elements.” Eng. Struct., 31(5), 1179–1189.
Roh, H., and Reinhorn, A. M. (2010a). “Modeling and seismic response of structures with concrete rocking columns and viscous dampers.” Eng. Struct., 32(8), 2096–2107.
Roh, H., and Reinhorn, A. M. (2010b). “Nonlinear static analysis of structures with rocking columns.” J. Struct. Eng., 532–542.
Skinner, R., Tyler, R., Heine, A., and Robinson, W. (1980). “Hysteretic dampers for the protection of structures from earthquakes.” Bull. New Zealand National Soc. Earthquake Eng., 13(1), 22–36.
Smith, B. J., Kurama, Y. C., and McGinnis, M. J. (2011). “Design and measured behavior of a hybrid precast concrete wall specimen for seismic regions.” J. Struct. Eng., 1052–1062.
Sritharan, S., Aaleti, S., and Thomas, D. J. (2007). “Seismic analysis and design of precast concrete jointed wall systems.”, Iowa State Univ., Ames, IA.
Standards New Zealand. (2006). “Special provisions for the seismic design of ductile jointed precast concrete structural systems.”, Wellington, New Zealand.
Vassiliou, M. F., Mackie, K. R., and Stojadinović, B. (2014). “Dynamic response analysis of solitary flexible rocking bodies: Modeling and behavior under pulse-like ground excitation.” Earthquake Eng. Struct. Dyn., 43(10), 1463–1481.
Vassiliou, M. F., Mackie, K. R., and Stojadinović, B. (2017). “A finite element model for seismic response analysis of deformable rocking frames.” Earthquake Eng. Struct. Dyn., 46(3), 447–466.
Yim, C.-S., Chopra, A. K., and Penzien, J. (1980). “Rocking response of rigid blocks to earthquakes.” Earthquake Eng. Struct. Dyn., 8(6), 565–587.
Zhang, J., and Makris, N. (2001). “Rocking response of free-standing blocks under cycloidal pulses.” J. Eng. Mech., 473–483.
Zienkiewicz, O. C., and Taylor, R. L. (2005). The finite element method for solid and structural mechanics, Butterworth-Heinemann, Burlington, MA.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 143Issue 7July 2017

History

Received: Oct 15, 2015
Accepted: Dec 20, 2016
Published online: Mar 10, 2017
Published in print: Jul 1, 2017
Discussion open until: Aug 10, 2017

Permissions

Request permissions for this article.

Authors

Affiliations

Evangelos Avgenakis [email protected]
Ph.D. Student, School of Civil Engineering, National Technical Univ. of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece. E-mail: [email protected]
Ioannis N. Psycharis, A.M.ASCE [email protected]
Professor, School of Civil Engineering, National Technical Univ. of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece (corresponding author). E-mail: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share