Nonlinear Static Analysis of Structures with Rocking Columns
Publication: Journal of Structural Engineering
Volume 136, Issue 5
Abstract
In simple inelastic structures subjected to severe base motions, the maximum acceleration response is bound by the yield strength and is inversely proportional to its mass. It can be demonstrated that a similar effect is approximately produced in structures with multidegrees of freedom. In strong structures, the maximum acceleration response is dependent on the intensity of the earthquake. However, if the strength of the structure is reduced, the maximum acceleration response and associated forces in its structural and nonstructural components can be substantially reduced. If some of the structural columns (carrying gravity loads) are allowed to rock, providing very small resistance to lateral loads, it is possible to reduce the strength of the global structural system and limit the global accelerations in seismic events. However, before overturning such columns may have substantial resistance which may void the effectiveness of weakening. The objective of this study is to (1) develop a simplified analytical model for rocking columns from fixity to overturning; (2) build the computational tools to simulate the behavior of structures including such rocking columns; and (3) examine the global nonlinear static response of a weakened structure. An analytical model is developed using an equivalent flexibility approach, which considers rigid body rotations and flexural deformations. Physical experiments of rocking columns were performed, and the results are used for the calibration and validation of analytical models. An analytical model of a 1:3 scaled structure is developed using IDARC2D modified in this study to evaluate several alternatives of weakening using rocking columns.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Support for this research was provided by (1) the National Science Foundation under Grant No. NSFEEC-9701471 [to the Multidisciplinary Center for Earthquake Engineering Research (MCEER)] and (2) the State of New York (NYS). The financial support is gratefully appreciated.UNSPECIFIED
References
Bracci, J. M., Reinhorn, A. M., and Mander, J. B. (1992a). “Seismic resistance of reinforced concrete frame structure designed only for gravity loads: Part I–Design and properties of a one-third scale model structure.” Technical Rep. No. NCEER-92-0027, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
Bracci, J. M., Reinhorn, A. M., and Mander, J. B. (1992b). “Seismic resistance of reinforced concrete frame structure designed only for gravity loads: Part III—Experimental performance and analytical study of a structural model.” Technical Rep. No. NCEER-92-0029, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
Chou, C. C., and Chen, Y. C. (2005). “Cyclic tests of post-tensioned precast CFT segmental bridge columns with unbonded strands.” Earthquake Eng. Struct. Dyn., 35(2), 159–175.
Christopoulos, C and Filiatrault, A. (2006). Principles of passive supplemental damping and seismic isolation, IUSS, Institute of Advanced Study of Pavia, Pavia, Italy.
Constantinou, M. C., Soong, T. T., and Dargush, G. F. (1998). “Passive energy dissipation systems for structural design and retrofit.” MCEER Monograph Series No. 1, MCEER-98-MN01, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
El-Tawil, S., and Kuenzli, C. (2002). “Pushover of hybrid coupled walls II: Analysis and behavior.” J. Struct. Eng., 128(10), 1282–1289.
Gajan, S., Kutter, B. L., Phalen, J., Hutchinson, T. C., and Martin, G. R. (2005). “Centrifuge modeling of load-deformation behaviour of rocking shallow foundations.” Soil. Dyn. Earthquake Eng., 25, 773–783.
Hewes, J. T., and Priestley, M. J. N. (2002). “Seismic design and performance of precast concrete segmental bridge columns.” Structural Systems Research Project, Rep. No. SSRP-2001/25, Univ. of California at San Diego.
Holden, T., Restrepo, J., and Mander, J. B. (2003). “Seismic performance of precast reinforced and prestressed concrete walls.” J. Struct. Eng., 129(3), 286–296.
Kasalanati, A., and Constantinou, M. C. (1999). “Experimental study of bridge elastometric and other isolation and energy dissipation systems with emphasis on uplift prevention and high velocity near-source seismic excitation.” Technical Rep. No. MCEER-99-0004, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
Kunnath, S. K., and Reinhorn, A. M. (1989). “Seismic evaluation of r/c frame wall buildings.” Concr. Int.: Des. Constr., 11(8), 57–61.
Kurama, Y. C., and Shen, Q. (2004). “Postensioned hybrid coupled walls under lateral loads.” J. Struct. Eng., 130(2), 297–309.
Kwan, W. -P., and Billington, S. L. (2003). “Unbonded post-tensioned concrete bridge piers. I: Monotonic and cyclic analyses.” J. Bridge Eng., 8(2), 92–101.
Lavan, O., Cimellaro, G. P., and Reinhorn, A. M. (2008). “A non-iterative optimization procedure for seismic weakening and damping of inelastic structures.” J. Struct. Eng., 134(10), 1638–1648.
Madan, A., Reinhorn, A. M., and Mander, J. B. (2000). “Hysteretic behavior of concrete masonry shear walls with unbonded reinforcement.” TMS Journal—Professional J. American Masonry Society, 18(1), 31–44.
Mander, J. B., and Cheng, C. -T. (1997). “Seismic resistance of bridge pier based on damage avoidance design.” Technical Rep. No. NCEER-97-0014, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
Ou, Y. C., Chiewanichakorn, M., Aref, A. J., and Lee, G. C. (2007). “Seismic performance of segmental precast unbonded post-tensioned concrete bridge columns.” J. Struct. Eng., 133(11), 1636–1647.
Palermo, A., Pampanin, S., and Calvi, G. M. (2005). “Concept and development of hybrid solutions for seismic resistant bridge systems.” J. Earthquake Eng., 9(6), 899–921.
Park, R., and Paulay, T. (1975). Reinforced concrete structures, Wiley, New York.
Priestley, M. J. N., Seible, F., and Calvi, G. M. (1996). Seismic design and retrofit of bridges, Wiley, New York.
Reinhorn, A. M., et al. (2009). “IDARC2D Version 7.0: A program for the inelastic damage analysis of structures.” Technical Rep. No. MCEER-09-0006, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
Roh, H. (2007). “Seismic behavior of structures using rocking columns and viscous dampers.” Ph.D. dissertation, Univ. at Buffalo—State Univ. of New York, Buffalo, N.Y.
Roh, H., and Reinhorn, A. M. (2006). “Nonlinear behavior of rocking beam-columns with confined ends.” Proc., 8th U.S. National Conf. on Earthquake Engineering, Paper No. 1627, EERI CD, San Francisco.
Roh, H., and Reinhorn, A. M. (2008). “Dynamic response of weakened structures using rocking columns.” Proc., 14th World Conf. on Earthquake Engineering, Beijing, Paper No. 05–01–0021, 14WCEE-CD.
Roh, H., and Reinhorn, A. M. (2009). “Analytical modeling of rocking elements.” Eng. Struct., 31(5), 1179–1189.
Soong, T. T., and Dargush, G. F. (1997). Passive energy dissipation systems in structural engineering, Wiley, New York.
Stanton, J., and Nakaki, S. (2002). “Design guideline for precast concrete seismic structural systems.” PRESSS Rep. Nos. 01/03-09 and UW SM 02-02, Univ. of Washington, Seattle, Wash.
Toranzo-Dianderas, L. A., Retrepo, J. I., Carr, A. J., and Mander, J. B. (2004). “Rocking confined masonry walls with hysteretic energy dissipaters and shake-table validation.” Proc., 13th World Conf. on Earthquake Engineering (CD-ROM), Vancouver, Paper No. 248, 13WCEE.
Viti, S., Cimellaro, G. P., and Reinhorn, A. M. (2006). “Retrofit of a hospital through strength reduction and enhanced damping.” Smart Structures and Systems, 2(4), 339–355.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Aug 25, 2008
Accepted: Nov 4, 2009
Published online: Nov 14, 2009
Published in print: May 2010
Authors
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.