Abstract
A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom (MDOF) system is approximated by using the modal energy-decomposition. Energy-based base shear coefficients are verified by means of both pushover analysis and nonlinear time history (NLTH) analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.
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References
Acun B and Sucuoglu H (2010), “Performance of Reinforced Concrete Columns Designed for Flexure Under Severe Displacement Cycles,” ACI Structural Journal, 107(3): 364–371.
Adam C and Jager C (2011), “Seismic Induced Global Collapse of Non-deteriorating Frame Structures,” in Papadrakakis M., Fragiadakis M., Lagaros, N.D., editors, Computational Methods in Earthquake Engineering, Computational Methods in Applied Sciences, 21: 21–40.
Adam C and Jager C (2012), “Seismic Collapse Capacity of Basic Inelastic Structures Vulnerable to the P-Delta Effect,” Earthquake Engineering & Structural Dynamics, 41(4): 775–793.
Akbas B, Shen J and Hao H (2001), “Energy Approach in Performance-Based Seismic Design of Steel Moment Resisting Frames for Basic Safety Objective,” The Structural Design of Tall Buildings, 10(3): 193–217.
Akiyama H (1985), Earthquake-Resistant Limit-State Design for Buildings, The University of Tokyo Press, Japan.
Akiyama H (2002), “Collapse Modes of Structures Under Strong Motions of Earthquake,” Annals of Geophysics, 45(6): 791–798.
Alici FS and Sucuoglu H (2016), “Prediction of Input Energy Spectrum: Attenuation Models and Velocity Spectrum Scaling,” Earthquake Engineering & Structural Dynamics, 45(13): 2137–2161.
Asimakopoulos AV, Karabalis DL and Beskos DE (2007), “Inclusion of P-–Effect in Displacement-Based Seismic Design of Steel Moment Resisting Frames,” Earthquake Engineering & Structural Dynamics, 36(14): 2171–2188.
Bai J and Ou J (2012), “Plastic Limit-State Design of Frame Structures Based on the Strong-Column Weak-Beam Failure Mechanism,” Proceedings of the 15th World Conference on Earthquake Engineering, Lisboa, Portugal.
Bai J and Ou J (2015), “Realization of the Global Yield Mechanism of RC Frame Structures by Redesigning the Columns Using Column Tree Method”, Science China Technological Sciences, 58(10): 1627–1637.
Bayat MR, Goel SC and Chao SH (2008), “Further Refinement of Performance-Based Plastic Design of Structures for Earthquake Resistance,” 14th World Conference on Earthquake Engineering, Beijing, China.
Benavent-Climent A, Pujades LG and Lopez-Almansa F (2002), “Design Energy Input Spectra for Moderate Seismicity Regions,” Earthquake Engineering & Structural Dynamics, 31(5): 1151–1172.
Benavent-Climent A, Lopez-Almansa F and Bravo-Gonzales DA (2010), “Design Energy Input Spectra for Moderate-to-High Seismicity Regions Based on Colombian Earthquakes,” Soil Dynamics and Earthquake Engineering, 30(11): 1129–1148.
Blandon CA and Priestley MJN (2005), “Equivalent Viscous Damping Equations for Direct Displacement Based Design,” Journal of Earthquake Engineering, 9(2): 257–278.
Chao SH, Goel SC and Lee SS (2007), “A Seismic Design Lateral Force Distribution Based on Inelastic State of Structures,” Earthquake Spectra, 23(3): 547–569.
Choi H and Kim J (2006), “Energy-Based Seismic Design of Buckling-Restrained Braced Frames Using Hysteretic Energy Spectrum,” Engineering Structures, 28: 304–311.
Chopra AK (1995), Dynamics of Structures, Theory and Applications to Earthquake Engineering, Prentice Hall, Upper Saddle River, N.J.
Chou CC and Uang CM (2003), “A Procedure for Evaluating Seismic Energy Demand of Framed Structures,” Earthquake Engineering & Structural Dynamics, 32(2): 229–244.
Decanini LD and Mollaioli F (1998), “Formulation of Elastic Earthquake Input Energy Spectra,” Earthquake Engineering & Structural Dynamics, 27(12): 1503–1522.
Dindar AA, Yalçin C, Yüksel E, Özkaynak H and Büyüköztürk O (2015), “Development of Earthquake Energy Demand Spectra,” Earthquake Spectra, 31(3): 1667–1689.
Dwairi HM (2004), “Equivalent Damping in Support of Direct Displacement-Based Design with Applications to Multi-Span Bridges,” PhD Dissertation, North Carolina State University, Raleigh, North Carolina.
Dwairi HM, Kowalsky MJ and Nau JM (2007), “Equivalent Damping in Support of Direct Displacement-Based Design,” Journal of Earthquake Engineering, 11(4): 512–530.
Fajfar P and Vidic T (1994), “Consistent Inelastic Design Spectra: Hysteretic and Input Energy,” Earthquake Engineering & Structural Dynamics, 23(5): 523–537.
FEMA-356 (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington, D.C.
Fenwick RC, Davidson BJ and Chung BT (1992), “P-Delta Actions in Seismic Resistant Structures,” Bulletin of the New Zealand National Society for Earthquake Engineering, 25(1): 56–69.
Gulkan P and Sozen MA (1974), “Inelastic Responses of Reinforced Concrete Structures to Earthquakes Motions,” ACI Journal Proceedings, 71(12): 604–610.
Hernández-Montes E, Aschheim MA and Gil-Martín LM (2015), “Energy Components in Nonlinear Dynamics Response of SDOF Systems,” Nonlinear Dynamics, 82(1): 933–945.
Housner GW (1956), “Limit Design of Structures to Resist Earthquakes,” Proceedings of the World Conference on Earthquake Engineering, Berkeley, California.
Jacobsen LS (1930), “Steady Forced Vibrations as Influenced by Damping,” ASME Transactione, 52(1): 169–181.
Kalkan E and Kunnath SK (2007), “Effective Cyclic Energy as a Measure of Seismic Demand,” Journal of Earthquake Engineering, 11(5): 725–751.
Kalkan E and Kunnath SK (2008), “Relevance of Absolute and Relative Energy Content in Seismic Evaluation of Structures,” Advances in Structural Engineering, 11(1): 17–34.
Ke K, Chuan G and Ke S (2016), “Seismic Energy Factor of Self-Centering Systems Subjected to Near-Fault Earthquake Ground Motions,” Soil Dynamics and Earthquake Engineering, 84: 169–173.
Khan E, Kowlasky MJ and Nau JM (2016), “Equivalent Viscous Damping Model for Short-Period Reinforced Concrete Bridges,” Journal of Bridge Engineering, 21(2): 04015047.
Kim J, Choi H and Chung L (2004), “Energy-Based Seismic Design of Structures with Buckling-Restrained Braces,” Steel and Composite Structures, 4(6): 437–452.
Kowalsky MJ (1994), “Displacement Based Design: A Methodology for Seismic Design Applied to RC Bridge Columns,” MSc Dissertation, University of California, San Diego.
Kuwamura H and Galambos T (1989), “Earthquake Load for Structural Reliability,” Journal of Structural Engineering, 115(6): 1446–1462.
Leelataviwat S, Goel SC and Stojadinovic B (2002), “Energy-Based Seismic Design of Structures Using Yield Mechanism and Target Drift,” Journal of Structural Engineering, 128(8): 1046–1054.
Leelataviwat S, Saewon W and Goel SC (2009), “Application of Energy Balance Concept in Seismic Evaluation of Structures,” Journal of Structural Engineering, 135(2): 113–121.
Liao WC (2010), “Performance-Based Plastic Design of Earthquake Resistant Reinforced Concrete Moment Frames,” PhD Dissertation, The University of Michigan, Ann Arbor, USA.
Lopez-Almansa F, Yazgan AU and Benavent-Climent A (2013), “Design Energy Input Spectra for High Seismicity Regions Based on Turkish Registers,” Bulletin of Earthquake Engineering, 11(4): 885–912.
Okur A and Erberik MA (2012), “Adaptation of Energy Principles in Seismic Design of Turkish RC Frame Structures. Part I: Input Energy Spectrum,” Proceedings of the 15th World Conference on Earthquake Engineering, Lizbon, Portugal.
Park HG and Eom TS (2006), “A Simplified Method for Estimating the Amount of Energy Dissipated by Flexure Dominated Reinforced Concrete Members for Moderate Cyclic Deformations,” Earthquake Spectra, 22(3): 459–490.
Pettinga JD and Priestley MJN (2007), “Accounting for P-Delta Effects in Structures When Using Direct Displacement-Based Design,” Research Report ROSE 2007/02, European School for Advanced Studies in Reduction of Seismic Risk, IUSS Press, Pavia, Italy.
Pettinga JD and Priestley MJN (2008), “Accounting for P-Delta Effects in Structures When Using Direct Displacement-Based Design,” The 14th World Conference on Earthquake Engineering, Beijing, China.
PEER (2016), Pacific Earthquake Engineering Research Center Strong Ground Motion Database, http://ngawest2. berkeley.edu/.
Priestley MJN (2003), “Myths and Fallacies in Earthquake Engineering, Revisited,” The Ninth Mallet Milne Lecture, European School for Advanced Studies in Reduction of Seismic Risk, Rose School, Pavia, Italy.
Priestley MJN, Calvi GM and Kowalsky MJ (2007), Displacement-Based Seismic Design of Structures, IUSS Press, Pavia, Italy.
Rodrigues H, Varum H, Arêde A and Costa A (2012), “A Comparative Analysis of Energy Dissipation and Equivalent Viscous Damping of RC Columns Subjected to Uniaxial and Biaxial Loading,” Engineering Structures, 35: 149–164.
SAP2000 Ultimate (2016), Integrated Solution for Structural Analysis and Design, Computers and Structures Inc. (CSI), Berkeley, California, USA.
SeismoSpect (2016), Seismosoft, Earthquake Engineering Software Solutions, Pavia, Italy.
Tselentis GA, Danciu L and Sokos E (2010), “Probabilistic Seismic Hazard Assessment in Greece–Part 2: Acceleration Response Spectra and Elastic Input Energy Spectra,” Natural Hazards and Earth System Sciences, 10(1): 41–49.
TSDC (2007), Turkish Seismic Design Code, Ministry of Public Works and Settlement, Ankara, Turkey.
TS500 (2000), Requirements for Design and Construction of Reinforced Concrete Structures, Turkish Standards Institution, Ankara, Turkey.
Uang CM and Bertero VV (1990), “Evaluation of Seismic Energy in Structures,” Earthquake Engineering & Structural Dynamics, 19(1): 77–90.
Wang F, Li HN and Yi TH (2015), “Energy Spectra of Constant Ductility Factors for Orthogonal Bidirectional Earthquake Excitations,” Advances in Structural Engineering, 18(11): 1887–1899.
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Ucar, T., Merter, O. Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects. Earthq. Eng. Eng. Vib. 17, 149–163 (2018). https://doi.org/10.1007/s11803-018-0431-3
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DOI: https://doi.org/10.1007/s11803-018-0431-3