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CONTENTS
Volume 8, Number 6, December 1999
 

Abstract
The paper presents an experimental and theoretical study on the influence of steel fibers and longitudinal tension and compression reinforcements on immediate and long-term deflections of high-strength concrete beams of 85 MPa (12,300 psi) compressive, strength. Test results of eighteen beams subjected to sustained load for 180 days show that the deflection behavior depends on the longitudinal tension and compression reinforcement ratios and fiber content; excessive amount of compression reinforcement and fibers may have an unfavorable effect on the long-term deflections. The beams having the ACI Code\'s minimum longitudinal tension reinforcement showed much higher time-dependent deflection to immediate deflection ratio, when compared with that of the beams having about 50 percent of the balanced tension reinforcement. The results of theoretical analysis of tested beams and those of a parametric study show that the influence of steel fibers in increasing the moment of inertia of cracked transformed sections is most pronounced in beams having small amount of longitudinal tension reinforcement.

Key Words
beams (supports), deflection, effective moment of inertia, flexural rigidity, high-strength concrete, immediate (instantaneous) deflection, long-term (time-dependent) deflection, reinforced concrete, steel fibers

Address
Ashour SA, King Abdulaziz Univ, Dept Civil Engn, Jeddah 21413, Saudi Arabia
King Abdulaziz Univ, Dept Civil Engn, Jeddah 21413, Saudi Arabia

Abstract
In this paper an asymptotic iteration method is adopted to analyze non-linear free vibration of reticulated circular plates composed of beam members placed in two orthogonal directions. For the resulting linear ordinary differential equations in the process of iteration, the power series with rapid convergence has been applied to obtain an analytical solution for non-linear characteristic relation between the amplitude and frequency of the structure. Numerical examples are given, and the phenomena indicating hardening of such structures have been presented for the (immovable or movable) simply-supported and clamped circular plates.

Key Words
reticulated plates, non-linear, free vibration, asymptotic iteration method

Address
Nie GH, Ruhr Univ Bochum, Inst Stat & Dynam, D-44780 Bochum, Germany
Tongji Univ, Dept Engn Mech, Shanghai 200092, Peoples R China

Abstract
The response of a reinforced concrete structure to loading is both immediate and time-dependent. Under a sustained load, the deflections caused by creep and shrinkage may be several times their instantaneous values. The paper describes a general finite element procedure, based on the so-called layered model, to analyse reinforced concrete members, and shows in particular how the simple Step by Step Method may be incorporated into this procedure. By invoking the Modified Newton Raphson Method as a solution procedure, the accuracy of the finite element method is verified against independent test results, and then applied to a variety of problems in order to demonstrate its efficacy. The method forms a general method for analysing highly indeterminate concrete structures in the time domain.

Key Words
reinforced concrete, creep, finite elements, layered method, shrinkage, Step by Step Method, time effects

Address
Bradford MA, Univ New S Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia
Univ New S Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia
SMEC, N Sydney, NSW 2060, Australia

Abstract
A new way to reduce the eigenvalue computation effort in structural dynamics is presented in this paper. The degrees of freedom of a structure may be classified into groups that are termed as sub-degrees of freedom. The eigenvalue analysis is performed with each of sub-degrees of freedom so that the computing time is much shortened. Since the dynamic coupling between sub-degrees of freedom is selected to be small and it may be considered as a perturbation, the perturbation algorithm is used to obtain an accuratae result. The accuracy of perturbation depends on the coupling between sub-degrees of freedom. The weaker the coupling is, the more accurate the result is. The procedure can be used to simplify a problem of three dimensions to that of two dimensions or from two dimensions to one dimension. The application to a truss and a space frame is shown in the paper.

Key Words
structural dynamics, eigenvalue computation, reduction, sub-degrees of freedom, perturbation

Address
Laboratorio Nacional de Engenharia Civil, Avenida do Brasil, 101. 1799 Lisboa Codex, Portugal

Abstract
An accurate and efficient shell element is presented. The stiffness of the shell element is decomposed into two parts with one part corresponding to stretching and bending deformation and the other part corresponding to shear deformation of the shell. Both parts of the stiffness are calculated with reduced integration rules, thereby improving computational efficiency. Shear strains are averaged on the reference surface such that neither locking phenomena nor any zero energy mode can occur. The satisfactory behaviour of the element is demonstrated in several numerical examples.

Key Words
shell element, locking, zero energy modes, cross reduced integration

Address
Zhong ZH, Hunan Univ, Coll Mech & Automot Engn, Changsha, Peoples R China
Hunan Univ, Coll Mech & Automot Engn, Changsha, Peoples R China
Nanyang Technol Univ, Sch Mech & Prod Engn, Singapore 639798, Singapore

Abstract
Being a significant mode of deformation, shear effect in addition to the other modes of stretching and bending have been considered to develop two finite element models for the analysis of beams on elastic foundation. The first beam model is developed utilizing the differential-equation approach; in which the complex variables obtained from the solution of the differential equations are used as interpolation functions for the displacement field in this beam element. A single element is sufficient to exactly represent a continuous part of a beam on Winkler foundation for cases involving end-loadings, thus providing a benchmark solution to validate the other model developed. The second beam model is developed utilizing the hybrid-mixed formulation, i.e., Hellinger-Reissner variational principle; in which both displacement and stress fields for the beam as well as the foundation are approxmated separately in order to eliminate the well-known phenomenon of shear locking, as well as the newly-identified problem of \"foundation-locking\" that can arise in cases involving foundations with extreme rigidities. This latter model is versatile and indented for utilization in general applications; i.e., for thin-thick beams, general loadings, and a wide variation of the underlying foundation rigidity with respect to beam stiffness. A set of numerical examples are given to demonstrate and assess the performance of the developed beam models in practical applications involving shear deformation effect.

Key Words
beams, elastic foundation, hybrid/mixed formulation, shear deformat, foundation rocking

Address
Gendy AS, Cairo Univ, Dept Struct Engn, Giza, Egypt
Cairo Univ, Dept Struct Engn, Giza, Egypt
Univ Akron, Dept Civil Engn, Akron, OH 44325 USA

Abstract
This paper presents a four-noded quadrilateral CO strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the C-1-continuity formulation, the present plate element is of C-0-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.

Key Words
laminated composite plates, Reddy-Levinson third-order plate theory, plate element, assumed strain FE formulation

Address
Shi G, Natl Univ Singapore, Inst High Performance Comp, Singapore 119260, Singapore
Natl Univ Singapore, Inst High Performance Comp, Singapore 119260, Singapore
Texas A&M Univ, Dept Mech Engn, College Stn, TX 77843 USA


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