Yield Design of Reinforced Concrete Slabs Using a Numerical Equilibrium Formulation
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
This paper presents a numerical procedure based on equilibrium finite elements and conic programming for plastic collapse load computation of reinforced concrete slabs governed by the Nielsen yield criterion. Bending moment fields are approximated using the enhanced Morley elements with an added second-degree moment field, allowing exact equilibrium relations to be achieved when applying a uniform pressure to the slabs. Conic programming, which is robust and efficient, is incorporated into the obtained discrete equilibrium formulation to ensure solutions can be obtained rapidly. Several slabs of arbitrary geometries and boundary conditions are examined, providing accurate collapse load multipliers and distributions of moment fields at the limit state.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research has been supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 107.01-2015.41.
References
Debongnie, J., Nguyen-Xuan, H., and Nguyen-Huy, C. (2006). “Dual analysis for finite element solutions of plate bending.” Proc., 8th Int. Conf. on Computational Structures Technology, G. Montero and R. Montenegro, eds., Civil-Comp Press, Stirlingshire, Scotland.
Fox, E. N. (1974). “Limit analysis for plates: The exact solution for a clamped square plate of isotropic homogeneous material obeying the square yield criterion and loaded by uniform pressure.” Philos. Trans. R. Soc. London, Ser A, 277(1265), 121–155.
Ingerslev, A. (1923). “The strength of rectangular slabs.” Struct. Eng., 1(1), 3–14.
Johansen, K. W. (1962). Yield-line theory, Cement and Concrete Association, London.
Krabbenhoft, K., and Damkilde, L. (2003). “A general nonlinear optimization algorithm for lower bound limit analysis.” Int. J. Numer. Methods Eng., 56(2), 165–184.
Krabbenhoft, K., Lyamin, A., and Sloan, S. W. (2007). “Formulation and solution of some plasticity problems as conic programs.” Int. J. Solids Struct., 44(5), 1533–1549.
Krenk, S., Damkilde, L., and Hoyer, O. (1994). “Limit analysis and optimal design of plates with equilibrium elements.” J. Eng. Mech., 1237–1254.
Le, C. V. (2016). “Yield-stress based error indicator for adaptive quasi-static yield design of structures.” Comput. Struct., 171, 1–8.
Le, C. V., Gilbert, M., and Askes, H. (2010a). “Limit analysis of plates and slabs using a meshless equilibrium formulation.” Int. J. Numer. Methods. Eng., 83(13), 1739–1758.
Le, C. V., Nguyen-Xuan, H., and Nguyen-Dang, H. (2010b). “Upper and lower bound limit analysis of plates using fem and second-order cone programming.” Comput. Struct., 88(1–2), 65–73.
Le, C. V., Ho, P. L. H., Nguyen, P. H., and Chu, T. Q. (2015a). “Yield design of reinforced concrete slabs using a rotation-free meshfree method.” Eng. Anal. Bound. Elem., 50, 231–238.
Le, C. V., Nguyen, P. H., and Chu, T. Q. (2015b). “A curvature smoothing Hsieh-Clough-Tocher element for yield design of reinforced concrete slabs.” Comput. Struct., 152, 59–65.
Mansfield, E. H. (2000). “Collapse pressures for rhombic plates.” Int. J. Mech. Sci., 42(3), 635–643.
Maunder, E., and Ramsay, A. (2012). “Equilibrium models for lower bound limit analyses of reinforced concrete slabs.” Comput. Struct., 108, 100–109.
Mosek [Computer software]. MOSEK ApS, Denmark.
Nielsen, M. P., and Hoang, L. C. (2016). Limit analysis and concrete plasticity, CRC Press, NewYork.
Olsen, P. C. (1998). “The influence of the linearization of the yield surface on the load-bearing capacity of reinforced concrete slabs.” Comput. Mech. Appl. Mech. Eng., 162(1–4), 351–358.
Prager, W. (1952). “The general theory of limit design.” Proc., 8th Int. Congress on Applied Mechanics, Faculty of Science, Univ. of Istanbul, Istanbul, Turkey, 65–72.
Tinoco, H. A. (2017). “Numerical limit analysis of reinforced concrete slabs using a dual approach and conic programming.” Struct. Multidisc. Optim., 55(4), 1407–1423.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Oct 29, 2016
Accepted: Feb 17, 2017
Published online: May 19, 2017
Published in print: Sep 1, 2017
Discussion open until: Oct 19, 2017
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.