Method to Solve Bond Differential‐Equation System in Prestressed Concrete
Publication: Journal of Engineering Mechanics
Volume 119, Issue 11
Abstract
Considering the difference in the bond behavior between the ordinary reinforcement and the tendons, which are placed in grouted ducts, first a differential equation is formulated to describe the relationship between slip and strains of steels and concrete in prestressed concrete members. In the second step a numerical method is developed to solve the differential‐equation system for single cracks and stabilized crack patterns. The method is based on the application of Runge‐Kutta method for the numerical integration and on the Newton method for the optimization of the vector function. The method presented here allows the calculation of crack width, the stiffness, and the redistribution of stresses between ordinary reinforcement and tendon in prestressed concrete members. An example is provided demonstrating the practical applicability of the method. The presented method is also suitable for reinforced concrete.
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References
1.
Ciampi, E., Eligehausen, R., Bertero, V. V., and Popov, E. (1982). “Analytical model for concrete anchorages of reinforcing bar under generalized excitation.” Report No. UCE/EERC‐82/23, Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif.
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Krips, M. Rißbreitenbeschränkung im Stahlbeton und Spannbeton. Mitteilungen aus dem Institut für Massivbau, TH Darmstadt, Heft 33 (in German).
3.
Noakowski, P. (1985). “Verbundorientierte, kontinuierliche Theorie zur Ermittlung der Rißbreite.” Beton‐ und Stahlbetonbau 82, Heft. 7, 185–190, Heft 8, 215–221 (in German).
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Tue, N. (1992). “Zur Spannungsumlagerung im Spannbeton bei der Rißbildung unter statischer und wiederholter Belastung,” Dissertation, Darmstadt (in German).
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Published In
Journal of Engineering Mechanics
Volume 119 • Issue 11 • November 1993
Pages: 2194 - 2206
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Apr 8, 1992
Published online: Nov 1, 1993
Published in print: Nov 1993
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