Open Access Open Access  Restricted Access Subscription or Fee Access

An Improved Model for the Analysis of Plates Stiffened by Parallel Beams Including Creep and Shrinkage Effects: Application to Concrete or to Composite Steel-Concrete Structures

E. J. Sapountzakis(1*)

(1) School of Civil Engineering, National Technical University of Athens, Greece
(*) Corresponding author


DOI: https://doi.org/10.15866/irea.v6i2.15377

Abstract


In this paper, an improved model for the static analysis of reinforced concrete plates stiffened by arbitrarily placed parallel reinforced concrete or steel beams with deformable connection taking into account the influence of creep and shrinkage effects relative with the time of the casting and the time of the loading of the plate and the beams is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation (i.e. uplift neglected) and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces taking into account their relation with the interface slip through the shear connector stiffness. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account describing better in this way the actual response of the plate - beams system. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model describes better the actual response of the plate - beams system and permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The evaluated lateral deflections of the plate - beams system are found to exhibit considerable discrepancy from those of other models, which neglect inplane and axial forces and deformations. Numerical examples with great practical interest are presented.
Copyright © 2018 Praise Worthy Prize - All rights reserved.

Keywords


Bending; Ribbed Plate; Boundary Element Method; Creep; Elastic Stiffened Plate; Reinforced Plate With Beams; Shrinkage; Slab-And-Beam Structure

Full Text:

PDF


References


M.T. Huber, Die Theorie des Kreuzweise Bewehrten Eisenbetonplatte, Der Bauing., Vol.4:354-392, 1923.

Y. Guyon, Calcul des Ponts Larges a Poutres Multiples Solidarisées por les Entretoises, Ann. Ponts et Chausées, Vol. 116(Issue 5):553-612, 1946.

C. Massonet, Method of Calculations for Bridges with Several Longitudinal Beams Taking into Account their Torsional Resistance, International Association for Bridges and Structural Engineering, 147-182, 1950.

W. Cornelius, Die Berechnung der Ebener Flächentragwerke mit Hilfe der Theorie der Orthogonal Anisotropen Platten, Der Stahlbau, Vol.2:21-26, 1952.

R.P. Pama,; and A.R. Cusens, Edge Beam Stiffening of Multibeam Bridges, Journal of the Structural Division, ASCE,V, Vol. 93(ST2):141-161 April 1967.

G.H. Powell, and D.W. Ogden Analysis of Orthotropic Steel Plate Bridge Decks, Journal of the Structural Division, ASCE, Vol. 95, (ST5):909-921, May 1969.

M. Mukhopadhay, Stiffened Plates in Bending, Computers & Structures, 541-548, 1994.

A.R. Kukreti, and Y. Rajapaksa, Analysis Procedure for Ribbed and Grid Plate Systems used for Bridge Decks, Journal of Structural Engineering, ASCE, Vol. 116(Issue 2):372-391, February 1990.

A.R. Kukreti, and E. Cheraghi, Analysis Procedure for Stiffened Plate Systems Using an Energy Approach, Computers & Structures, Vol. 46(Issue 4):649-657, February 1993.

Z. A.Siddiqi, and R.A. Kukreti, Analysis of Eccentrically Stiffened Plates with Mixed Boundary Conditions Using Differential Quadrature Method, Applied Mathematical Modelling, 251-275, 1998.

Y.K. Cheung, Finite Strip Method in Analysis of Elastic Plates with Two Opposite Sides Simply Supported Ends, Proceedings of the Institution of Civil Engineers, Vol. 40:1-7, 1968.

I.P. King, and O.C. Zienkienwicz, Slab Bridges with Arbitrary Shape and Support Conditions: A General Method of Analysis Based on Finite Element Method, Proceedings of the Institution of Civil Engineers, Vol. 40:9-36, 1968.

M. Mukhopadhay, Stiffened Plate Plane Stress Elements for the Analysis of Ships’ Structures, Computers and Structures, 563-573, 1981.

A. Deb, and M. Booton, Finite Element Models for Stiffened Plates under Transverse Loading, Computers and Structures, 361-372, 1988.

G.S. Palani, N.R. Iyer, and T.V.S.R. Apa Rao, An Efficient Finite Element Model for Static and Vibration Analysis of Eccentrically Stiffened Plates/Shells, Computers and Structures, 651-661, 1992.

S. Peng-Cheng, H. Dade, and W. Zongmu, Static Vibration and Stability analysis of Stiffened Plates Using B Spline Functions, Computers and Structures, 73-78, 1993.

M.P. Rossow, and A.K. Ibrahimkhail, Constraint Method Analysis of Stiffened Plates, Computers and Structures, Vol. 51-60, 1978.

A.H. Sheikh, and M. Mukhopadhay, Analysis of Stiffened Plate with Arbitrary Planform by the General Spline Finite Strip Method, Computers and Structures, Vol. 53-67, 1992.

C. Katz, and J. Stieda, Praktische FE-Berechnungen mit Plattenbalken, Bauinformatik, Vol. 1:30-34, 1992.

W. Wunderlich, G. Kiener, and W. Ostermann, Modellierung und Berechnung von Deckenplatten mit Unterzügen, Bauingenieur, Vol. 69:381-390, 1994.

G. Rombach, Anwendung der Finite-Elemente-Methode im Betonbau, (Ernst & Sohn, Berlin, 2000).

F.Hartmann, and C.Katz, Statik mit finiten Elementen, (Springer, Berlin-Heidelberg, 2002).

C. Hu, and G.A.Hartley, Elastic Analysis of Thin Plates With Beam Supports, Engineering Analysis with Boundary Elements, Vol. 13:229-238, 1994.

J.B. de Paiva, Boundary Element Formulation of Building Slabs, Engineering Analysis with Boundary Elements, Vol. 17:105-110, 1996.

M. Tanaka, and A.N. Bercin, A Boundary Element Method Applied to the Elastic Bending Problem of Stiffened Plates, Boundary Element Method XIX, 203-212, 1997.

E.J. Sapountzakis, and J.T. Katsikadelis, Dynamic Analysis of Elastic Plates Reinforced with Beams of Doubly-Symmetrical Cross Section, Computational Mechanics, Vol. 23:430-439, 1999.

E.J. Sapountzakis, and J.T. Katsikadelis, Analysis of Plates Reinforced with Beams, Computational Mechanics, Vol. 26:66-74, 2000.

M. Tanaka, T. Matsumoto, and S.A Oida, Boundary Element Method Applied to the Elastostatic Bending Problem of Beam-Stiffened Plates, Engineering Analysis with Boundary Element, Vol, 24:751-758, 2000.

E.J. Sapountzakis, and J.T. Katsikadelis Interface Forces in Composite Steel-Concrete Structures, International Journal of Solids and Structures, Vol. 37:4455-4472, 2000.

E.J. Sapountzakis, and J.T. Katsikadelis, Creep and Shrinkage Effect on Reinforced Concrete Slab-and-Beam Structures, Journal of Engineering Mechanics, ASCE, Vol. 128(Issue 6):625-634, 2002.

P.H. Wen, M.H. Aliabadi, and A. Young, Boundary Element Analysis of Shear Deformable Stiffened Plates, Engineering Analysis with Boundary Elements, Vol. 26:511-520, 2002.

E.J. Sapountzakis, and J.T. Katsikadelis, A New Model for the Analysis of Composite Steel – Concrete Slab and Beam Structures with Deformable Connection, Computational Mechanics, Vol. 31(Issue 3-4):340-349, 2003.

F. Hartmann, BE-SLABS 8.0.0, Boundary Element Analysis of Slabs, Student Version, http://www.be-statik.de, 2003.

E.J. Sapountzakis; and J.T. Katsikadelis, Creep and Shrinkage Effect on the Dynamic Analysis of Reinforced Concrete Slab-and-Beam Structures, Journal of Sound and Vibration, Vol. 260(Issue 3):403-416, 2003.

L. Oliveira Neto, and J.B. Paiva, A special BEM for Elastostatic Analysis of Building Floor Slabs on Columns, Computers and Structures, Vol. 81:359–372, 2003.

E.J. Sapountzakis Dynamic Analysis of Composite Steel-Concrete Structures with Deformable Connection, Computers and Structures, Vol. 82(Issue 9-10):717-729, 2004.

G.R Fernandes. and W.S. Venturini Building Floor Analysis by the Boundary Element Method, Computational Mechanics, Vol. 35:277-291, 2005.

S.F. Ng, M.S. Cheung, and T.A Xu, Combined Boundary Element and Finite Element Solution of Slab and Slab-on-Girder Bridges, Computers and Structures, Vol. 37:1069-1075, 1990.

M.S. Cheung, G. Akhras, and W. Li, Combined Boundary Element / Finite Strip Analysis of Bridges, Journal of Structural Engineering, Vol. 120:716-727, 1994.

E.J. Sapountzakis, and V.G. Mokos, Analysis of Plates Stiffened by Parallel Beams, International Journal for Numerical Methods in Engineering, Vol. 70:1209-1240, 2007.

E.J. Sapountzakis, and V.G. Mokos, An Improved Model for the Analysis of Plates Stiffened by Parallel Beams with Deformable Connection, Computers and Structures, Vol. 86:2166-2181, 2008.

E.J. Sapountzakis, and V.G. Mokos, An Improved Model for the Dynamic Analysis of Plates Stiffened by Parallel Beams, Engineering Structures, Vol. 30:1720-1733, 2008.

J.T. Katsikadelis, The Analog Equation Method. A Boundary – only Integral Equation Method for Nonlinear Static and Dynamic Problems in General Bodies, Theoretical and Applied Mechanics, Vol. 27:13-38, 2002.

H. Trost, and J. Wolff, Zur Wirklichkeitsnahen Ermittlung der Beanspruchungen in Abschnittsweise Hergestellten Spannbetontragwerken, Der Bauingenieur, Vol. 45:155-1691970.

Eurocode No.2 Design of Concrete Structures, Part 1: General Rules and Rules for Buildings, Eurocode 2 Editorial Group, 1991.

E.J. Sapountzakis, and V.G. Mokos, Warping Shear Stresses in Nonuniform Torsion by BEM, Computational Mechanics, Vol. 30(Issue 2):131-142, 2003.

J.T. Katsikadelis, and M.S. Nerantzaki, Non-linear Analysis of Plates by the Analog Equation Method, Computational Mechanics, Vol. 14:154-164, 1994.

J.T. Katsikadelis, and A.E. Armenakas, A new Boundary Equation Solution to the Plate Problem, ASME, Journal of Applied Mechanics, Vol. 56:364-374, 1989.

J.T. Katsikadelis, Boundary Elements: Theory and Applications. (Elsevier, Amsterdam-London, 2002).

J.T. Katsikadelis, and G.C. Tsiatas, Large Deflection Analysis of Beams with Variable Stiffness, Acta Mechanica, Vol. 164:1-13, 2003.

L. Gaul, and C. Fiedler, Methode der Randelemente in Statik und Dynamik. (Vieweg, Braunschweig-Wiesbaden, 1997).

E. Isaacson, and H.B. Keller, Analysis of Numerical Methods, (John Wiley and Sons, New York, 1966).

E.J. Sapountzakis, and J.T. Katsikadelis, Unilaterally Supported Plates on Elastic Foundations by the Boundary Element Method, Journal of Applied Mechanics, Trans. ASME, Vol. 59:580-586, 1992.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2019 Praise Worthy Prize