Lip H. Teh

Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements

Abstract It has been pointed out in a previous paper by the authors [1] that conservative internal moments of a spatial beam are of the so-called fourth kind, and that the rotation variables which are energy-conjugate with these moments are vectorial rotations. Vectorial rotations of a spatial Euler–Bernoulli beam have nonlinear relationships with its transverse displacement derivatives [2] . This implies that strictly speaking, the first partial derivative of the strain energy with respect to a transverse displacement derivative is not a bending moment (even if we ignore the axial deformation), and that modifications should be introduced to the conventional Hermitian shape functions employed in the Rayleigh–Ritz method of finite element analysis. On the other hand, the neglect of the rotational behaviour of nodal moments has led to an incorrect stability matrix in the literature, and it is shown through numerical examples that this incorrect stability matrix cannot detect the flexural-torsional buckling load of spatial structures in which the members are not connected collinearly. The validity of the Wagner hypothesis on the coupling of axial and torsional deformations for a spatial beam-column is illustrated through a numerical example. Finally, one issue related to the Updated Lagrangian formulation addressed in this paper is the oft-used assumption of a straight configuration at the last known state.

Heuristic Approach for Optimum Cost and Layout Design of 3D Reinforced Concrete Frames

AbstractThis paper presents a new methodology for cost optimization of the preliminary layout design of three-dimensional (3D) reinforced concrete (RC) frames. This approach is capable of being easily employed for the optimal layout design of a realistic large RC structure that accounts for constraints imposed by design standards. The new approach considers modeling, structural analysis, concrete member design, and discrete optimization together with data on the cost of systems and materials. The methodology is comprised of two parts. First, using the cross-sectional action effects as design variables, a heuristic cost function is presented as an alternative to traditional cost functions for layout optimization of RC structures. Using the presented cost function, a structural optimization problem is formulated for column layout design of 3D RC frames. Then, an ant system algorithm, a discrete method, is proposed to solve the cost optimization problem. Two comparative design examples are included to demons...

Block Shear Capacity of Bolted Connections in Cold-Reduced Steel Sheets

AbstractThis paper examines the mechanisms for block shear failures of bolted connections in steel plates postulated in the design equations specified in the North American, European, and Australian steel structures codes. It explains that there is only one feasible mechanism for the limit state of conventional block shear failure, that which involves tensile rupture and shear yielding, regardless of the steel material ductility. It describes the fundamental shortcomings of various code equations for determining the block shear capacity of a bolted connection. Based on the tensile rupture and shear yielding mechanism, an in-plane shear lag factor, and the active shear resistance planes identified in the present work, this paper proposes a rational equation that is demonstrated to provide more accurate results than all the code equations in predicting the block shear capacities of bolted connections in G450 steel sheets subjected to concentric loading. The resistance factor of 0.8 for the proposed equation...

Cubic beam elements in practical analysis and design of steel frames

This paper discusses various issues in the use of cubic beam elements for computer structural analysis/design of steel frames. It is pointed out that the concern expressed in recent literature regarding the number of cubic elements required to model a steel member is not justified, and that the inaccuracy of one cubic element in Euler buckling analysis of a simply supported column is largely irrelevant to the second-order elastic analysis/design or advanced analysis of steel frames. The sources of inaccuracy of the cubic element are elucidated. It is also explained that the plastic-zone analysis method is not so inefficient as was previously believed. The spatial cubic element is shown to be capable of accurately accounting for the coupling between axial, flexural and torsional deformation modes. It is concluded that for the purposes of second-order elastic analysis/design and advanced analysis of 2D and 3D steel frames, the well-documented cubic element is a versatile and efficient choice.

Net Section Tension Capacity of Bolted Connections in Cold-Reduced Steel Sheets

This paper examines the accuracy of design equations specified in the North American, European and Australasian codes for cold-formed steel structures in determining the net section tension capacity of bolted connections in flat steel sheets. It points out that the shear lag factors embedded in the code equations either yield “anomalous” results or become irrelevant when they exceed unity. The “anomaly” was demonstrated through laboratory tests and is explained by using simple calculus. The configurations of specimens tested in the laboratory include single shear- and double-shear connections, with single or double bolts in a line parallel or perpendicular to the force. A proper mathematical expression for the in-plane shear lag factor, which does not suffer from the anomaly of the code equations and never implies shear lag factors greater than unity for any configuration, is presented and shown to yield improved results compared to the current specifications. The resistance factor of 0.8 for the proposed...

Geometric Design Optimization for Dynamic Response Problems of Continuous Reinforced Concrete Beams

AbstractThis paper presents a computer-aided design method for conceptual geometric layout optimization of multispan RC beams for any type of dynamic responses. A key feature of the paper is the development of a new cost-optimization method for geometric layout problems that take both cost parameters and dynamic responses into account to achieve an optimum design along with acceptable dynamic performance of RC beams. This method takes advantage of employing a new optimization formulation that considerably simplifies the preliminary layout design computations. It focuses on minimizing the structural cost subject to constraints on eigenfrequencies, modal shapes, and the static and dynamic equilibrium. The proposed structural optimization problem is solved employing an ant colony optimization (ACO) algorithm. To verify the suitability of the methodology and illustrate the performance of the algorithm, solved examples are presented.

Active Shear Planes of Bolted Connections Failing in Block Shear

AbstractIn the steel design codes worldwide, the shear area for calculating the block shear capacity of a bolted connection is either the gross or the net shear area. The authors have previously noted independent experimental evidence indicating the shear failure planes to lie midway between the gross and the net shear planes, termed the active shear planes. This paper presents the nonlinear contact finite brick element analysis results that confirm the location of the active shear planes, indicated by regions of maximum shear stresses. The finite-element analysis also found that shear stresses approach zero toward the free downstream end of the connection block. The veracity of the active shear area is further demonstrated in terms of the ability of the resulting block shear equation to predict the governing failure modes of test specimens consistently, in comparison with the equations assuming the gross and the net shear areas.

Conceptual design optimization of rectilinear building frames: A knapsack problem approach

This article presents an automated technique for preliminary layout (conceptual design) optimization of rectilinear, orthogonal building frames in which the shape of the building plan, the number of bays and the size of unsupported spans are variables. It adopts the knapsack problem as the applied combinatorial optimization problem, and describes how the conceptual design optimization problem can be generally modelled as the unbounded multi-constraint multiple knapsack problem. It discusses some special cases, which can be modelled more efficiently as the single knapsack problem, the multiple-choice knapsack problem or the multiple knapsack problem. A knapsack contains sub-rectangles that define the floor plan and the location of columns. Particular conditions or preferences for the conceptual design can be incorporated as constraints on the knapsacks and/or sub-rectangles. A bi-objective knapsack problem is defined with the aim of obtaining a conceptual design having minimum cost and maximum plan regularity (minimum structural eccentricity). A multi-objective ant colony algorithm is formulated to solve the combinatorial optimization problem. A numerical example is included to demonstrate the application of the present method and the robustness of the algorithm.

Optimum Column Layout Design of Reinforced Concrete Frames Under Wind Loading

The geometric layout optimization of a structure is a significant stage in a design process, and selecting an appropriate geometric layout can impact all the subsequent stages of the design procedure and the relevant costs. This study presents a heuristic approach for the optimum layout design of two-dimensional reinforced concrete frames in order to optimize the total cost and controls the application under wind loadings. The aim is to find the optimum column layout design for 2D frames under wind loadings considering the involved cost elements. A heuristic methodology is developed in order to achieve a new design space and an objective function for the cost and layout optimization problem. The proposed method has the capability to make use of action effects of the structure as alternative design variables in place of the commonly used cross-sectional ones. Such a feature provides the method the ability to be easily employed in large and realistic structural optimization problems, and helps the optimization algorithms to take less time, in an iterative optimization process. Then, an Ant System based algorithm is proposed to solve the presented optimization problem. Examples are included to illustrate the robustness of the methodology.

Optimum spans' lengths of multi-span reinforced concrete beams under dynamic loading

In the design of continuous beams, say bridges, achieving an economical layout is one of the primary objectives, and requires simultaneous consideration of cost and layout variables. This study aims to figure out an explicit methodology for the optimum layout design of multi-span reinforced concrete beams under dynamic loadings in order to optimize the total cost. The aim is to determine the optimum spans lengths for continuous beams under dynamic loadings considering the involved cost elements. For this purpose a new methodology is developed in order to shift from the traditional design space to a new one. Then, an objective function for the cost and layout optimization problem is formulated in the new space. The proposed method employs action effects of the beams as alternative design variables in lieu of the cross-sectional ones. This ability enables the method to be easily used in realistic structural optimization problems rather than simple models, and helps the layout design procedure to take less time, in an iterative optimization process. In order to solve the formulated optimization problem, an Ant Colony Optimization algorithm is proposed. The robustness of the methodology is illustrated through a number of examples.