An interactive design algorithm for prestressed concrete girders

The primary purpose of this paper is to discuss an interactive design and analysis algorithm for prestressed concrete girders. Prestressed concrete highway bridge girder design is used for the prototype computer program to simplify the incorporation of design code requirements and loading conditions. The computer code can be extended to include other prestressed concrete girder applications. The second purpose arises from the search for the optimum prestressed concrete girder design. Linear programming is discussed as a possible method to arrive at the optimum girder cross-section and prestressing strand design. However, manufacturing standardization and techniques make selection of the optimum crosssection, prestressing force, and strand centroid eccentricity by mathematical methods rather academic. Therefore, design optimization, to be practical, must be based on standard cross-sections and prestressing strand position templates. The algorithm, guided by the engineer, selects, from tabulated standard crosssections and associated combinations of prestressing forces and eccentricities, the cross-section, prestressing force, and eccentricity to satisfy the problem constraints. The kern boundaries are calculated in the analysis portion of the algorithm. The engineer, using the kern boundaries, determines the path of the strands by specifying the strand hold-down points and associated strand centroid eccentricity. The algorithm also provides for shear reinforcement, dead load deflections at transfer and after placement of the slab, and auxiliary nonprestressed tension reinforcement at transfer.     

Optimum shape design of cold-formed thin-walled steel sections

The algorithm presented in this study obtains the optimum cross-sectional dimensions of cold-formed thin-walled steel beams subjected to general loading. It has the flexibility of considering different cross-sectional shapes such as symmetrical or unsymmetrical channel, lipped channel or Z-sections. The algorithm treats the cross-sectional dimensions such as width, depth and wall thickness as design variables and considers the displacement as well as stress limitations. The presence of torsional moments causes warping of thin-walled sections. The effect of warping in the calculation of normal stresses is included using Vlasov theorems. These theorems require the computation of sectorial properties of cross-sections. A general numerical procedure is presented for obtaining these properties. The optimum design problem of thin-walled open sections subjected to combined loading turns out to be a highly nonlinear problem. It is shown that optimality criteria method can effectively be used to obtain its solution. A number of design examples are presented to demonstrate the application of the algorithm.     

Cross-sectional properties of thin-walled multi-cellular section

A numerical procedure is applied to determine the torsional and flexural properties of multicellular cross sections which are used frequently in modern curved highway bridge girders. The shear flow in multi-cellular sections becomes indeterminate, thus requiring as many compatibility equations as the total number of cells. An algorithm to evaluate these indeterminate shear flows has been developed and incorporated into a computer program. Essentially the determination of cross-sectional properties involves various integrations. The computer program developed performs these integrations. Two hypothetical multi-cellular sections are examined and numerical results are presented along with input preparation. It is shown that any arbitrary cross section of complex geometry can be analyzed.     

Optimum weight design of steel space frames with semi-rigid connections using harmony search and genetic algorithms

In this paper, an optimization process using MATLAB-SAP2000 Open Application Programming Interface (OAPI) is presented for optimum design of space frames with semi-rigid connections. A specified list including W-profiles taken from American Institute of Steel Construction (AISC) is used in the selection of suitable sections. The stress constraints as indicated in load and resistance factor design of AISC, lateral displacement constraints being the top- and inter-storey drift and geometric constraints are considered in the optimization process. Genetic algorithm method based on biological principles and harmony search algorithm method based on the processes of musical harmony are used for optimum designs. Two different space frames are solved for the cases of rigid and semi-rigid connections, separately. A computer program is coded in MATLAB for the purpose interacting with SAP2000 OAPI. Results obtained from the analyses show that type of semi-rigid connections plays a crucial role in the optimization of steel space frames and increases the optimum weight.

     

VTOP. An improved software for design optimization of prestressed concrete beams

Optimum tendon layout of prefabricated prestressed concrete beams was an early application of design optimization methodologies. But most of the approaches found in the literature were not suitable to be implemented in real life bridge engineering. To fill the existing gap a research has been conducted in the past years by the authors to optimize prefabricated concrete beams formulating the problem in such a way that could be applied directly by bridge designers in beam and slab bridge decks. The software produced, labelled VTOP, contains the necessary capabilities for daily applications and possesses a user friendly graphical interface. This paper describes the problem formulation carried out and includes several examples to show the efficiency of the computer code implemented. Some of them are examples of single prefabricated concrete beams and also an example showing the overall analysis of a bridge deck and the subsequent optimization of the prefabricated beam subjected to the internal forces produced by the external loading is included in the paper.     

Tendon layout optimisation through configurational forces equilibration in plane stress analysis of prestressed concrete structures

The focus of this work is a novel application of configurational forces to tendon layout optimisation problems in prestressed concrete beams. To this end, the application of the method of the configurational forces is extended to two-dimensional plane stress analysis. The optimum tendon position is obtained by iteratively arriving at vanishing configurational forces. The performance of the optimisation algorithm is illustrated by means of numerical examples.     

Optimization of hybrid steel plate girders

An efficient procedure is presented for minimum weight design of unstiffened and stiffened hybrid steel plate girders subjected to arbitrary loading using the General Geometric Programming technique. The nonlinear optimization problem is formulated on the basis of the current American Institute of Steel Construction specification. Four examples are presented to show the application of the algorithm for practical optimization of hybrid steel plate girders.     

Harmony search based algorithm for the optimum design of grillage systems to LRFD-AISC

Harmony search based optimum design method is presented for the grillage systems. This numerical technique imitates the musical performance process that takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The design algorithm considers the serviceability and ultimate strength constraints which are implemented from Load and Resistance Factor Design—American Institute of Steel Construction (LRFD-AISC). It selects the appropriate W-sections for the transverse and longitudinal beams of the grillage system out of 272 discrete W-section designations given in LRFD-AISC. This selection is carried out such that the design limitations described in LRFD-AISC are satisfied and the weight of the system is the minimum. Many design examples are considered to demonstrate the efficiency of the algorithm presented.     

Optimization and sensitivity of prestressed concrete beams

This paper is concerned with the optimum design of prestressed concrete beams. Both minimum weight and minimum cost optimization formulations are given for simply supported beams having three different sections. Sensitivity of the optimum designs, with respect to various design parameters, are also discussed. The formulation is programmed for interactive use on micro-computers. An example is given and results are discussed.     

Damage assessment of prestressed concrete beams using artificial neural network (ANN) approach

An artificial neural network (ANN) based approach is presented for the assessment of damage in prestressed concrete beams from natural frequency measurements. The details of an experimental programme suitably designed and carried out to induce the desired extents of damages in the prestressed concrete beams and generate the training and test data for the ANN are presented. The analysis of the static and dynamic behavior of perfect and damaged prestressed concrete beams reveal that there exists a close relationship among the natural frequency, deflection, crack width, first crack load, ultimate load and degree of damage. Therefore, these parameters were mainly used as input data for training and testing the ANN. A feed forward ANN learning by back propagation algorithm implemented using MATLAB has been employed in this study. The main focus of this work has been to study the feasibility of using an ANN trained with only natural frequency data to assess the damage in prestressed concrete beams. This is explored by comparing the performance of an ANN trained only with natural frequency data with other ANNs trained with a mix of static and dynamic data. It has been demonstrated that an ANN trained only with dynamic data can assess the damage with less than 10% error, when the error is the difference between the actual damage in percent and predicted damage in percent. The shortcomings of this study have also been presented.     

Optimum design of prestressed concrete beams using constrained differential evolution algorithm

This paper is concerned with the cost minimization of prestressed concrete beams using a special differential evolution-based technique. The optimum design is posed as single-objective optimization problem in presence of constraints formulated in accordance with the current European building code. The design variables include geometrical dimensions that define the shape of the cross section and the amount of prestressing steel. A special (μ?+?λ)-constrained differential evolution method is performed in order to solve the optimization problem. Its search mechanism depends on several mutation strategies whereas an archiving-based adaptive tradeoff model is in charge of selecting a specific constraint-handling technique. Finally, numerical examples are included to illustrate the application of the presented approach.     

Optimum weight analysis of steel grid bridges

Bridges include different types, mainly, the truss, the plate girder, the box, the cabled systems, and the grid type. In this research work the main objective will be to analyze the grid type bridges consisting of main girders and cross girders. Optimization techniques have been utilized in order to determine the minimum weight of the steel grid bridges. The purpose of this research work is to accomplish the following: (1) To determine the ideal number of main girders supporting a reinforced concrete slab for the same geometrical dimensioning, the same conditions of live loads, the same number of cross girders, and the same type of steel. (2) To determine for the previous ideal number of main girders, whether or not the spacing between cross girders is changing, the optimum situation. (3) To determine the optimum type of steel. Three different types of steel, 37, 44, and 52, are used for both main girders and cross girders. (4) To determine to what extent the model of optimization is influenced by the restrictions of side constraints.The problem here is to find the optimum weight of steel grid bridges. Different grid bridges having two, three, four, and five main girders have been analyzed. The objective function is given by the weight of the structure and the design variables are the dimensions of the cross section. The design and side constraints are respected. The unconstrained formulation using the interior penalty function technique is selected. Powell's algorithm is chosen for the generation of the search vector and the quadratic interpolation technique is chosen for the determination of the step size.The conclusions are (1) The optimum solution for the different cases of steel types 37, 44, and 52 was the use of three main girders. (2) The use of steel type 52 with the cases of two, three, four, and five main girders would provide a saving in steel weight amounting to 20% and 25% relative to steel types 44 and 37, respectively. (3) Practically speaking, steel type 52 is more expensive than steel types 44 and 37. Nevertheless, this factor being considered, there would be a saving of 18.8% and 22% if steel type 52 is used instead of steel types 44 and 37, respectively. (4) When three main girders are used with steel types 52, 44, and 37, the weight of cross girders amounted to 10.7%, 7.1%, and 10.8%, respectively.     

Interactive computer-aided design of non-hybrid and hybrid plate girders

An interactive microcomputer program is presented for design of welded stiffened steel plate girders according to the AISC specification. The program is capable of designing hybrid girders and takes into account the tension-field action of the web. This program demonstrates the effectiveness of microcomputers in practical design of structures.     

Time- and storage-efficient implementation of an optimal planar convex hull algorithm

An implementation of an algorithm for computing the convex hull of a finite planar set of points is presented. The program is compared with an algorithm for the same purpose coded previously. Experimental results indicate that our program is superior to the other in terms of both running time and storage requirements.     

Design optimization of prestressed concrete spans for high speed ground transportation

The problem of designing stiff, lightweight, and least expensive elevated spans to support ground vehicles is investigated. A computer program using the direct search method was developed to calculate optimum geometric configurations of prestressed concrete girders with nonlinear constraint conditions involving stresses and deflections; with specified inputs on loading, unit costs and overall size; and with checks on buckling, shear and ultimate section strength. Parameters allow-for choices between stiff, expensive configurations or flexible, less expensive designs. Several numerical results for simple spans are included.     

Shear flow distribution in multi-cell girders

A computer program is described for the shear flow analysis of multi-cell girders. The basic assumption of the theory used is that the loading pattern does not cause any distortion of a transverse section of the girder. The computer routine is based on a system of defining girder cross-sectional layouts which can be applied to a wide variety of beams with a minimum of data preparation and coding. The difficulties encountered in devising the routine and the solutions adopted are described in detail. The method is demonstrated on three different beam cross-sections taken from ship structures.     

Optimum cost design of welded box beams with longitudinal stiffeners using advanced backtrack method

The use of longitudinal stiffeners in box girders loaded in bending results in savings in weight and cost. To study these savings the optimized box beams without and with stiffeners are compared to each other. The minimum cross-sectional area design can be solved analytically. A cost function is defined containing material and fabrication (welding) costs. This function is nonlinear in the structural dimensions to be optimized, therefore an advanced backtrack method is worked out and applied. An illustrative numerical example shows the savings. Received June 30, 1999     

Elastic - plastic design of unbraced frameworks

A computer program for the optimum elastic-plastic design of two-dimensional steel frameworks is described, and design examples are presented. These examples are used as a basis for comment on some of the assumptions adopted in the program. The paper also compares and contrasts the philosophy used in the program with other approaches reported in the literature.     

A program for the optimum approximation of real rational functions via linear programming

This paper presents a Turbo-Basic program that implements an algorithm for the optimum approximation of real rational functions via linear-programming. The formulation of the linear problem is based on the minimization of a minimax criterion, while its solution is derived through the dual problem. This algorithm is much faster and requires less storage than other approximation techniques. The program is implemented on an IBM-PC AT and tested by several examples. Analytical examples are presented to illustrate how the program is used and the effectiveness of the algorithm.