Displacement-Based Compatibility Strut-and-Tie Method and Application to Monotonic and Cyclic Loading
Publication: Journal of Structural Engineering
Volume 142, Issue 6
Abstract
The compatibility strut-and-tie method (C–STM) is an efficient minimalist nonlinear modeling approach for shear-critical reinforced concrete members. This paper presents two key improvements to the C–STM to better model overall behavior through failure. First, modified softened diagonal concrete struts are incorporated directly into the analysis, thereby eliminating any need for post-processing analysis, to enable accurate modeling of the failure load. Second, modeling modifications are made so that the analysis may be conducted in displacement control, thereby permitting cyclic loading and post-peak (failure) load-displacement behavior to be predicted. The modifications are implemented in SAP2000 and verified with experimental results for both monotonic and cyclic loading cases. It is observed that the C–STM predicts the overall force-deformation behavior of the structure quite well. Additionally, the C–STM also predicts the internal strain-dependent behavior of the structure and gives insights into the cause of failure of the structure.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bentz, E. C., Vecchio, F. J., and Collins, M. P. (2006). “Simplified modified compression field theory for calculating shear strength of reinforced concrete elements.” ACI Struct. J., 103(4), 614–624.
Bracci, J. M., Keating, P. B., and Hueste, M. B. D. (2000). “Cracking in RC bent-caps.”, Texas Transportation Institute, Texas A&M Univ., College Station, TX.
Chang, G. A., and Mander, J. B. (1994). “Seismic energy based fatigue damage analysis of bridge columns. I: Evaluation of seismic capacity, technical report.”, NCEER, State Univ. of New York at Buffalo, Buffalo, NY.
Collins, M. P. (1978). “Towards a rational theory for RC members in shear.” ASCE J. Struct. Div., 104(4), 649–666.
Collins, M. P., and Mitchell, D. (1991). Prestress concrete structures, Prentice Hall, Englewood Cliffs, NJ.
Collins, M. P., Mitchell, D., Adebar, P., and Vecchio, F. J. (1996). “A general shear design method.” ACI Struct. J., 93(1), 36–45.
Dilger, W. (1966). “Veränderlichkeit der Biege- und Schubsteifigkeit bei Stahlbetontragwerken und ihr Einfluβ auf Schnittkraftverteilung und Traglast bei statisch unbestimmter Lagerung.” Deutscher Ausschuss für Stahlbeton, Berlin.
Holden, T., Restrepo, J., and Mander, J. B. (2003). “Seismic performance of precast reinforced and prestressed concrete walls.” J. Struct. Eng., 286–296.
Hsu, T. T. C., Mau, S. T., and Chen, B. (1987). “Theory of transfer strength of reinforced concrete.” ACI Struct. J., 84(2), 149–160.
Hsu, T. T. C., and Zhang, L. X. (1997). “Nonlinear analysis of membrane elements by fixed-angle softened-truss model.” ACI Struct. J., 94(5), 483–492.
Karthik, M. M, and Mander, J. B. (2011). “Stress-block parameters for unconfined and confined concrete based on a unified stress-strain model.” J. Struct. Eng., 270–273.
Kim, J. H., and Mander, J. B. (1999). “Truss modeling of reinforced concrete shear-flexure behavior.”, State Univ. of New York at Buffalo, Buffalo, NY.
Kim, J. H., and Mander, J. B. (2000a). “Cyclic inelastic strut-tie modeling of shear-critical reinforced concrete members.” ACI, 193, 707–728.
Kim, J. H., and Mander, J. B. (2000b). “Seismic detailing of reinforced concrete beam-column connections.” Struct. Eng. Mech., 10(6), 589–601.
Lampert, P., and Thurlimann, B. (1968). “Torsion tests of reinforced concrete beams (Torsionsversuche an Stahlbetonbalken).” Institute fur Baustatik, ETH, Zürich, Switzerland (in German).
Li, B., and Tran, C. T. N. (2012). “Determination of inclination of strut and shear strength using variable angle truss model for shear-critical RC beams.” Struct. Eng. Mech., 41(4), 459–477.
MacGregor, J. G. (1992). Reinforced concrete mechanics and design, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.
Mander, J. B. (1983). “Seismic design of bridge piers.” Ph.D. thesis, Univ. of Canterbury, Christchurch, New Zealand.
Mander, J. B., Karthik, M. M., and Hurlebaus, S. (2014). “Structural assessment of “D” region affected by premature concrete deterioration: Technical report”, Texas Transportation Institute, Texas A&M Univ., College Station, TX.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 1804–1826.
Marti, P. (1985). “Basic tools of reinforced concrete beam design.” J. Am. Concr. Inst., 82(1), 46–56.
Mau, S. T., and Hsu, T. T. C. (1987). “Shear strength prediction for deep beams with web reinforcement.” ACI Struct. J., 84(6), 513–523.
Mitchell, D., and Collins, M. P. (1974). “Diagonal compression field theory—A rational model for structural concrete in pure torsion.” ACI Struct. J., 71(8), 396–408.
Mörsch, E. (1909). Concrete-steel construction, McGraw-Hill, New York.
Nielsen, M. P. (1967), “Am Forskydningsarmering I Jernbetonbjaelker (On shear reinforcement in reinforced concrete beams).” Bygningsstatiske Meddelelser, 38(2), 33–58.
Pan, Z., and Li, B. (2013). “Truss-arch model for shear strength of shear-critical reinforced concrete columns.” J. Struct. Eng., 548–560.
Pang, X. B. D., and Hsu, T. T. C. (1996). “Fixed-angle softened-truss model for reinforced concrete.” ACI Struct. J., 93(2), 197–207.
Paulay, T. (1969). “The coupling of shear walls.” Ph.D. thesis, Univ. of Canterbury, Christchurch, New Zealand.
Paulay, T. (1971). “Simulated seismic loading of spandrel beams.” J. Struct. Div., 97(ST9), 2407–2419.
Rausch, E. (1929). “Design of reinforced concrete in torsion (Berechnung des Eisenbetons gegen Verdrehung).” Technische Hochschule, Berlin, Germany (in German).
Ritter, W. (1899). “Construction techniques of Hennebique (Die Bauweise Hennebique).” Schweizerische Bauzeitung, 33(7), 59–61 (in German).
SAP2000 version 14.0.0 [Computer software]. Computers and Structures, Berkeley, CA.
Schlaich, J., Schaefer, K., and Jennewein, M. (1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–150.
Scott, R. M., Mander, J. B., and Bracci, J. M. (2012a). “Compatibility strut-and-tie modeling: Part I—Formulation.” ACI Struct. J., 109(5), 635–644.
Scott, R. M., Mander, J. B., and Bracci, J. M. (2012b). “Compatibility strut-and-tie modeling: Part II—Implementation.” ACI Struct. J., 109(5), 645–653.
Sritharan, S., and Ingham, J. M. (2003). “Application of strut-and-tie concepts to concrete bridge joints in seismic regions.” PCI J., 48(4), 66–90.
Sritharan, S., Ingham, J. M., and Priestley, M. J. N. (2000). “Strut-and-tie model concepts for seismic design and assessment of concrete bridge joints.” Proc., 12th World Conf. on Earthquake Engineering, New Zealand Society for Earthquake Engineering, Wellington, New Zealand.
To, N. H. T., Ingham, J. M., and Davidson, B. J. (2003). “Cyclic strut-and-tie modeling of reinforced concrete structures.” 7th Pacific Conf. on Earthquake Engineering, New Zealand Society for Earthquake Engineering, Upper Hutt, New Zealand, 102–110.
To, N. H. T., Ingham, J. M., and Sritharan, S. (2001). “Monotonic nonlinear strut-and-tie computer models.” Bull. N. Z. Soc. Earthquake Eng., 34(3), 169–190.
Vecchio, F. J. (2000). “Analysis of shear-critical reinforced concrete beams.” ACI Struct. J., 97(1), 102–110.
Vecchio, F. J., and Collins, M. P. (1986). “The modified compression-field theory for reinforced concrete elements subjected to shear.” J. ACI, 83(2), 219–231.
Vecchio, F. J., and Collins, M. P. (1993). “Compression response of cracked reinforced concrete.” J. Struct. Eng., 3590–3610.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 142 • Issue 6 • June 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 15, 2014
Accepted: Oct 15, 2015
Published online: Jan 13, 2016
Published in print: Jun 1, 2016
Discussion open until: Jun 13, 2016
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.