Archibald N. Sherbourne

Differential quadrature method in the buckling analysis of beams and composite plates

Abstract This paper discusses the accuracy and convergence of the method of differential quadrature for solving a variety of differential equations with variable coefficients associated with plate and beam instability problems. The detailed solutions for buckling of rectangular, orthotropic and anisotropic, symmetric, angle-ply composite laminates under linearly varying uniaxial compression, uniaxial buckling of rectangular, isotropic plates with variable longitudinal thickness and lateral-torsional beam buckling under moment gradient are presented which highlight various computational aspects and, hopefully, contribute to a better understanding and judicious application of the method.

Behavior of eight-bolt large capacity endplate connections

Abstract Only a limited number of experimental and analytical reports exist concerning large capacity, eight-bolt, extended endplate connections. This paper describes the structural properties, both stiffness and strength, of an extended endplate connected to a column flange, with no stiffeners in either tension or compression region, using eight high strength fully and partially prestressed bolts. The case studies considered in this paper offer greater insight into the significance of endplate and column flange interaction and bolt positioning; besides the displacement and stress distributions, the prying phenomenon is also addressed. The methodology is based on a finite element modeling developed previously for the standard four-bolt array. ANSYS, version 4.4, a large-scale general purpose code is selected for equivalent three-dimensional (3D) analysis. The end-plate, beam and column flanges and web are represented as plate elements. Each bolt shank is modeled using six spar elements. 3D interface elements are used to model the boundary between column flange and back of the end-plate that may make or break contact.

Flexural-torsional stability of thin-walled composite I-section beams

Abstract An analytical study of optimal fibre direction for improving the lateral buckling strength of thin-walled composite open-section members is presented. Based on a Vlasov-type linear hypothesis, beam stiffness coefficients, which account for cross-section geometry and for the material anisotropy of the section as well as the geometrical characteristics of columns, are obtained. Uniformly distributed load, transverse concentrated load, unequal end moments, tip-loaded cantilever and columns with different types of loading, are considered. The results show that, in some cases, the web fibre angle makes a remarkable contribution to increasing the buckling load compared with the unidirectional orientation of the pultrusion process.

Computer modelling of an extended end-plate bolted connection

Abstract A methodology, based on finite element modelling, is studied to develop analytically the moment-rotation relationship for a steel bolted end-plate connection. ANSYS, a large-scale general-purpose finite element code is selected for equivalent two-dimensional (2-D) analysis. The end-plate, beam and column flanges, web and bolt shanks in the tension region are represented as plane-stress elements with their width equal to their thickness measured perpendicular to the web. Interface elements are used to model the boundary between column flange and rear of end-plate that may make or break contact. Based on deformation and stress contours of a 2-D model the contribution of beam web to the behaviour is discussed from which two types of end-plate deformation can be identified. The methodology is demonstrated for an extended end-plate connection and the results are compared against experimental data to verify the feasibility of the modelling and associated computer analyses.

3D simulation of bolted connections to unstiffened columns—I. T-stub connections

Abstract The paper presents a finite element methodology in a three-dimensional (3D) framework to study numerically the stiffness and strength of the T-stub to unstiffened column flange bolted connection as part of a comprehensive research program to investigate the behavior of endplate bolted connections. In such connections, the axes of rotation of the T-stem and column flange are at right angles; the planes containing the tensile forces are also perpendicular to each other. Therefore, they are highly interactive spatially. The main objective here is to study the applicability of the model to such a connection, so that most of the important features which are not accessible to routine experiments, like prying action and gradual plasticity of components, can be monitored. ANSYS, version 4.4, a large-scale general purpose finite element code is selected for this analysis. Initially, the simplest connection with the bolt groups in tension, which is a symmetric T-stub hanger with a single line of bolts parallel on each side of the web, is considered. Then the T-stub connection to an unstiffened column flange is discussed. Analytical results of a full-scale extended endplate connected to unstiffened column flange will be presented in Part II, a companion paper (Journal of Constructional Steel Research, 1996, 40 , 189–223) in which the structural properties of such connections will be discussed.

Optimal fibre orientation in lateral stability of laminated channel section beams

An analytical solution for predicting the lateral buckling capacity of laminated channel beams, including the influences of load form and lamination architecture, is investigated in this study. A detailed parametric study demonstrates that an improved design can be suggested which shows superior performance for optimal fibre orientation in both flanges and web in comparison with the traditional unidirected pultrusion process.

Postbuckling behaviour of optimized rectangular composite laminates

Abstract In the literature, the linear buckling load of rectangular plate elements is maximized by optimizing fibre orientation and thickness in a preselected lamination sequence. The paper considers the effects of laminate optimization on the postbuckling behaviour of biaxially compressed, specially orthotropic laminates and suggests modifications of the lamination parameters to improve postbuckling performance. Postbuckling studies, in general, involve the formal derivation of nonlinear equilibrium paths using, say, the methods of Galerkin, finite element, etc. In contrast, a simpler but effective method is proposed whereby the initial postbuckling stiffness, defined by the slope of the postbuckling load-end shortening relation at bifurcation, is adopted as a qualitative index characterizing postcritical behaviour. An explicit solution is described for simply supported plates. It is established that the postbuckling stiffness and linear buckling load are governed by completely different functions: the former depends exclusively on inplane (membrane) stiffness while the latter is a function of bending stiffness only. It has been suggested that unfavourable postbuckling performance usually follows optimization of the buckling load. A detailed parametric study substantiates this proposition by illustrating that laminates, optimal in linear buckling, do exhibit inferior postbuckling characteristics due to reduced stiffness. Improved laminate designs are suggested that exhibit superior performance in both pre- and postbuckling.

Imperfection sensitivity of optimized, laminated composite shells: A physical approach

Abstract Optimization of the axial buckling load of composite, cylindrical shells through a judicious choice of laminate configuration is often associated with increased imperfection sensitivity. Current approaches of combining postbuckling theory with an optimization program demand highly sophisticated analytical and computational methods, yet are insufficient to provide a rational theme that can be used to derive general design guidelines. The present paper is an attempt to explore the subject matter via a different avenue, such that various nonlinear effects may be understood in physical terms which require relatively little in the way of advanced mathematics and computation. The paper proposes to study the problem using a simple, but intuitively appealing, reduced stiffness analysis of cylinder buckling which recognizes the physical characteristics present in advanced postbuckling and uses them in an equivalent linear, eigenvalue analysis. This investigation highlights the specific relationship between laminate stillness parameters, efficiency of buckling resistance and imperfection sensitivity in postbuckling deformation. It is observed that the criteria lor optimality and reduced imperfection sensitivity are often opposed to each other. The reduced buckling load appears to be a useful indicator for evaluating qualitatively the relative imperfection sensitivity of various nearly optimal laminated shell designs which would be of great interest to designers. Another interesting feature is the analytical study in terms of bounded generic orthotropic constants which furnishes a general theme on the issue. A comprehensive discussion on the theoretical foundation of the reduced stiffness approach and other similar approximate methods is provided. It has been shown throughout this paper that the proposed physical approach successfully and consistently explains most of the observations reported in the literature which were based on nonlinear postbuckling analyses.

Column webs in steel beam-to-column connexions part I—Formulation and verification

Abstract A review of previous analytical and experimental work on steel beam-to-column connexions is presented. Attention is focussed on the column web behaviour for connexions in which only the column portion of the connexion fails and the formulation of a finite element analysis is outlined which is used to model connexion behaviour. Both elastic and elastic-plastic strength and initial buckling are included in the mathematical model. Numerical results are compared to known analytical values to establish the accuracy of the model. Physical experiments on interior and exterior connexions performed by others were repeated using the computer; results show the applicability of the finite element model to the investigation of these connexions.

3D simulation of bolted connections to unstiffened columns—II. Extended endplate connections

Traditionally column web stiffeners are used to increase the load carrying capacity and rigidity of extended endplate, bolted, moment connections in structural steelwork. However, elimination of these stiffeners in such connections is favored because of significant fabrication economy and simplification of connection details. Besides, the optimum analysis and design of the frame may demand joint moments other than the full plastic capacity of connecting members making column stiffening unnecessary. In this context, the principal bending planes of the column flange and endplate are orthogonal and, thus, only a three-dimensional (3D) model can address connection behavior. For this reason, there are only a limited number of experimental and analytical reports concerning this phenomenon. A description and application of such a model, using inelastic finite elements, has already been provided in Part I, a companion paper (Journal of Constructional Steel Research, 1996, 40, 169–187), in which deformation and prying action are studied for T-stub connections. This paper presents the structural properties, both stiffness and strength, of an extended endplate connected to an unstiffened column flange using high strength prestressed bolts. The case studies considered in the current paper offer more insight into the significance of endplate and column flange interaction; besides the displacement and stress distributions, the prying phenomenon, both as to value and distribution, is also discussed. ANSYS, version 4.4, a large-scale general purpose finite element code is selected for the analysis.