Optimum design of steel structures with web openings
Nikos Lagaros2008, Engineering Structures
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
The objective of this work is to perform optimum design of 3D steel structures having perforated I-section beams. The optimization problem is formulated as a combined sizing, shape and topology optimization problem. The cross-sectional dimensions of the columns and beams constitute the sizing design variables, while the number and size of the web openings of the beams constitute the topology and shape design variables, respectively. Two distinctive formulations of the optimization problem are considered depending on the finite element discretization implemented for simulating the structural elements. The two formulations, corresponding to beam and shell discretization, are compared in terms of the optimum designs achieved. A characteristic test example considered, showed that a quantifiable reduction in the weight of the structure is accomplished by allowing web openings in the beams of the structure without reducing structural strength or serviceability requirements.
Figures (9)
Key takeaways
- The shape design variables are referred to the size of the web openings, while the number of the web openings along the beams constitutes the topology design variables.
- The optimum positions for web openings along the span of the beam depend on the relative proportion of bending moment and shear force.
- In the current study, the task of topology optimization is associated with the number of web openings in each group of the beams of the structure.
- The advantages of considering perforated beams in association with the shell element discretization are demonstrated in the optimization part of this work by comparing the optimum designs achieved with and without web openings and with beam or shell element discretizations.
- The improvement achieved with shell discretization is found to be up to 20% when web openings are considered in the beams of the structure.
Related papers
Application of structural topology optimisation to perforated steel beams
Computers & Structures, 2015
This paper focuses on the application of structural topology optimisation technique to design steel perforated I-sections as a first attempt to replace the traditional cellular beams. An optimum web opening configuration is suggested based on the results of parametric studies. A FE analysis is further employed to determine the performance of the optimised beam in comparison to the conventional widely used cellular type beam. It is found that the optimised beam overperforms in terms of load carrying capacities, deformations and stress intensities. Barriers to the implementation of the topology optimisation technique to the routine design of beam web are highlighted.
Application of Topology Optimisation to the Design of Steel I-Section Webs
The 14th International Conference of Civil, Structural and Environmental Engineering Computing, 3-6 September, 2013, Cagliari, Sardinia, Italy
This research focuses on the application of structural topology optimisation the design of steel I-section beam web openings. A topology optimisation study is performed for the first time on the web of a steel I-section beam. A beam web design is then proposed based on the results of the topology optimisation study. A nonlinear finite element analysis technique is employed to determine the load carrying performance of the optimised beam in comparison to the conventional, widely used, cellular type beam. It is found that the optimised beam over performs in terms of load carrying capacities and stress intensities. Barriers to the implementation of the topology optimisation technique to the routine design of beam web are highlighted. In detail, a parametric topology optimisation study is conducted in order to determine the optimum opening topology for the wide range of beam cross sections that are found in practice. Thereafter, a generalised optimum web opening configuration is suggested based on the results of the parametric study. It is anticipated that a shape optimisation study will be required to maximise the efficiency of beams with this optimum web opening configuration.
Optimum design of steel structures
Journal of Constructional Steel Research, 1998
Optimisation of Novel Elliptically-Based Web Opening Shapes of Perforated Steel Beams.
The Journal of Constructional Steel Research, 2012
A new study was carried out and presented herein, on the optimisation of novel elliptical-based web opening shapes which enhance the structural behaviour of the perforated beams as well as lead to economic design in terms of both manufacture and usage. The finite element (FE) model used in the study was validated against experimental work conducted by the authors and the results of the comprehensive study are presented in this research paper. For ease of comparison, the yield patterns and deflected shapes of the perforated beams are presented at three characteristic load level points. Finally, shear-moment interaction FEM curves are presented for six different web opening shapes to allow for easy use of the empirical design formulas that have previously been proposed by the authors in a complementary research paper. An overall study of many standard and non-standard web opening shapes, it was shown that perforated beams with vertical and inclined elliptical web openings (3:4 width to depth ratio) behave more effectively compared to perforated beams with conventional circular and hexagonal web openings, mainly in terms of stress distribution and local deflection. Therefore, perforated steel beams with large novel elliptically-based web openings with short critical opening length at the top and bottom tee-section as well as straight-line edges are presented for first time and examined in the current research programme.
Structural Topology Optimisation in Steel Structural Applications
This study introduces applications of structural topology optimisation to buildings and civil engineering structures. Topology optimisation problems utilize the firmest mathematical basis, to account for improved weight-to-stiffness ratio and perceived aesthetic appeal of specific structural forms, enabling the solid isotropic material with penalization (SIMP) technique. Structural topology optimisation is a technique for finding the optimum number, location and shape of "openings" within a given continua subject to a series of loads and boundary conditions. Aerospace and automotive engineers routinely employ topology optimisation and have reported significant structural performance gains as a result. This paper examines two examples of where topology optimisation may be a useful design tool in civil/structural engineering in order to overcome the frontiers between civil engineers and engineers from other disciplines. The first example presents the optimised structural design of a geometrically complex high-rise structure, while the second one focuses on the optimisation and design of a perforated steel I-section beam, since such structural members are widely used nowadays in the vast majority of steel buildings.
STUDY OF STEEL BEAM WITH WEB OPENINGS: A REVIEW
The basis of this study is the serviceability requirement which arouse long after the structural erection has been completed. Beams with web openings can be competitive in such cases, even though more alternatives to solid web beams such as stub girders, trusses etc. are available and height limitation is common problem faced by designers in multistoried buildings due to economic requirements and aesthetical considerations. Substantial spaces are normally required to enable the passage for large pipes and ducts beneath steel beams which leads to uneconomic floor heights. Though web openings could lead to a significant decrease in beam’s load carrying capacity depending on the adopted openings shape, size and location but can also be very helpful and important from the point of economy. So this study is concerned with the influence of the web opening on the strength of compressive elements and web crippling strength of steel sections. And the parametric analysis to be focused on size and location of opening. The paper summarizes the relevant study of provisions as given in the corresponding design standard and software based finite element analysis carried out by different authors and review the problem to arrive at meaningful conclusion for the study. And suggestion regarding the scope of further work.
STEEL BEAMS WITH WEB OPENINGS STEEL BEAMS WITH WEB OPENINGS 1.0 INTRODUCTION
The responsibility of a Structural Engineer lies in not merely designing the structure based on safety and serviceability considerations but he also has to consider the functional requirements based on the use to which the structure is intended. While designing a power plant structure or a multi-storeyed building, the traditional structural steel framing consists of beams and girders with solid webs. These hinder the provision of pipelines and air conditioning ducts required for satisfactory functioning for which the structure is put up. Very often, the service engineer who is on the scene long after the structural erection has been completed is required to fix air conditioning ducts in place. T h e r e-r o u t i n g o f s e r v i c e s (o r i n c r e a s i n g t h e f l o o r h e i g h t a t t h e d e s i g n s t a g e f o r accommodating them) leads to additional cost and is generally unacceptable. The provision of beams with web openings has become an acceptable engineering practice, and eliminates the probability of a service engineer cutting holes subsequently in inappropriate locations. Beams with web openings can be competitive in such cases, even though other alternatives to solid web beams such as stub girders, trusses etc are available. This form of construction maintains a smaller construction depth with placement of services within the girder depth, at the most appropriate locations. The introduction of an opening in the web of the beam alters the stress distribution within the member and also influences its collapse behaviour. Thus, the efficient design of beams and plate girder sections with web openings has become one of the important considerations in modern structures. In this chapter, methods to evaluate the ultimate shear capacity of the beams and fabricated girders with circular or rectangular web openings are discussed. The methodology is based on the Von Mises yield criterion. 2.0 GUIDELINES FOR WEB OPENINGS AND STIFFENERS The shape of the web openings will depend upon the designer's choice and the purpose of the opening. There are no hard and fast rules to dictate the shapes of the openings. But, for designer's convenience, openings of regular shapes (such as circular or rectangular) are usually chosen. Introduction of openings in the web decreases stiffness of the beams resulting in larger deflections than the corresponding beams with solid webs. The strength of the beams with openings may be governed by the plastic deformations that occur due to both moment and shear at the openings.
Advanced design and optimization of steel portal frames
rmseura.tkk.fi
This study brings new insights into the advantages of using more sophisticated design methods for steel portal frames (e.g. geometrically and materially nonlinear analysis with imperfections or GMNIA, and the general method introduced in Eurocode 3), compared to the commonly used member checks with interaction formulae. The differences between the design alternatives are discussed, focusing on assessing lateral-torsional stability, and the potential benefits of using advanced shell model instead of widely used beam elements. In addition to the advanced design methods, the topic of shape optimization of frames was explored using realcoded genetic algorithm (GA). The developed optimisation tools highlight the possibility of using GA in everyday design in the future. The results of the study clearly point to the advantages of using advanced modelling, e.g. GMNIA, instead of the classical member checks. While both methods are accepted by the current steel design code EN 1993, using GMNIA can result in important savings, because it eliminates some of the conservativeness brought in by the unavoidable simplifications of the other methods. The experience shows that using complex 3D models is possible with current computational capabilities.
Topology Optimization of Beam Structures with Various End and Loading Conditions
Applied Mechanics and Materials, 2013
Topology optimization deals with optimum material (mass) distribution within a design domain to find optimal lay-out of a structure subjected to certain boundary and loading conditions. Topology optimization can be used to address conflicting requirements, such as light weight and high-strength/stiffness design. In this paper, a simulation program to analyze topology optimization of beam structures with seven different end conditions and three types of loads (single point load, two point loads and uniformly distributed load) is developed using MATLAB code adapted from Sigmunds 99 line topology optimization code. Furthermore, the program has been enhanced with a graphical user interface for ease of use. Using the developed system, it is possible to analyze the effect of different parameters.
Optimal design of a welded I-section frame using four conceptually different optimization algorithms
Structural and Multidisciplinary Optimization
The purpose of this study is to investigate the suitability of four conceptually different optimization algorithms for specifically the optimal design of welded I-section frames. The cost function to be minimized is the volume of the frame. Constraints on lateral-torsional buckling as well as local buckling of the beam and column webs and flanges are taken into consideration. The algorithms evaluated include a genetic algorithm, a novel leap-frog gradient method without line searches, as well as an orthogonal search method requiring no gradients and the differential evolution technique.
Related papers
The Effect of Optimization on the Design of Steel Structures
MultiScience - XXXIII. microCAD International Multidisciplinary Scientific Conference, 2019
In structural design, it is difficult to find the best solution. Optimization help finding these. In this paper, the basis of cost calculation is shown and some applications on welded structures like a stiffened shell, planar truss structure, stiffened plates. The objective function is the cost or mass of the structure, the constraints are static, or dynamic stresses, stabilities, size constraints. The examples describe the benefits of optimization.
DESIGN SYNTHESIS FOR SINGLE- AND MULTI-BAY STEEL FRAMES ACCORDING TO ECP’ 01
Minimum weight design of single-and multi-bay steel portal frames is presented. The design variables are the dimensions of prismatic built-up sections for beams and columns. Design constraints are considered as per ECP’ 01: shape, buckling, stresses, and deflection constraints. Both compact and non-compact sections are included in the formulation. Cases of loading comprise vertical and lateral loads. Analysis is done using Displacement Stiffness Method. An optimization technique based on the Method of Feasible Directions -through an implicit formulation– is adopted. Several examples are presented in order to assess the advantages of adopting optimization in structural steel design as compared to other classical design approaches.
Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review
2013
The type of mathematical modeling selected for the optimum design problems of steel skeletal frames affects the size and mathematical complexity of the programming problem obtained. Survey on the structural optimization literature reveals that there are basically two types of design optimization formulation. In the first type only cross sectional properties of frame members are taken as design variables.
Engineering Structures and Technologies Analysis of steel I-beams with rectangular web openings: experimental and finite element investigation ENGINEERING STRUCTURES AND TECHNOLOGIES
Steel I-shaped beams with web openings of shapes like hexagonal, circular and rectangular at regular intervals have been used since last 60-70 years. Therefore aim of this paper is to examine the behaviour of steel I-beams with rectangular web openings by performinganexperimental and parametric study. A parametric study based on finite element analysis consists of effect of fillet radius, aspect ratio of rectangular openings, stiffeners position around the openings and effect of positions of openings on load carrying capacities of steel beam with rectangular web openings was carried out by using a commercial finite element software ANSYS v.12. An overall study of such type of beam was carried out and results shows that rectangular openings having fillet radius either 2 times thickness of web or 25 mm (whichever is minimum), aspect ratio of 1.6 and reinforcement either in the form of horizontal or vertical stiffeners around the web openings found to be very effective. The fillet radius and stiffeners also affect the stress distribution around the corner regions of openings. Load carrying capacities of perforated beams are almost equal to plain-webbed beams, when openings are placed within middle two-third(neutral zone) of the span.
Design of Steel Structures
In plastic analysis and design of a structure, the ultimate load of the structure as a whole is regarded as the design criterion. The term plastic has occurred due to the fact that the ultimate load is found from the strength of steel in the plastic range. This method is rapid and provides a rational approach for the analysis of the structure. It also provides striking economy as regards the weight of steel since the sections required by this method are smaller in size than those required by the method of elastic analysis. Plastic analysis and design has its main application in the analysis and design of statically indeterminate framed structures.
Finite Element Modelling of Steel Beams with Web Openings
Engineering, 2014
Height limitations are not uncommon in multi-storey buildings due to economic requirements and esthetical considerations. Substantial spaces are normally required to enable the passage of large pipes and ducts beneath steel beams leading to uneconomic floor heights. The most adopted solution for this issue is the use of steel beam web openings to provide the required space for services. These openings could lead to a significant decrease of the beam load carrying capacity depending on the adopted openings shape, size and location. These aspects motivated the present study based on FE simulations calibrated against numerical and test results. The results accuracy enabled a comprehensive parametric analysis of beams with web openings to be made focused on the profile size, web opening location, among others. The study also investigated the efficiency of longitudinal stiffeners welded at the opening region and benefits of using an adequate edge concordance radius in beams with rectangular and square openings. The obtained results showed the need of using welded longitudinal stiffeners in order to increase the beams ultimate load carrying capacity. This adoption can double or even triple the ultimate load of beams with rectangular and square opening heights equal to 0.75 H, respectively.
Cost-Effective Design of Structural Elements through the Process of Structural Optimization
Journal of Civil Engineering Research, 2014
In the design of structural elements, there is usually more than one feasible and equally safe solution, even though not all of them may be cost-effective. Obtaining the cost-effective design out of the numerous designs is tedious, cumbersome and time-consuming. This work present the result of optimization process of a structural element carried out by using the numerical features of the Excel software. In the optimizing process, cost effectiveness in terms of area reinforcement and cross section is required, but subject to the constraints of deflection and cracking imposed by the Standard in operation. The result shows that optimal design of any structural element can be achieved by following the proposed methodology. The method also has the added advantage of reuse once it is put in operation.
Structural Design Optimization-Numerical and Simulation Approaches
2019 ASEE Annual Conference & Exposition Proceedings
is a graduate of Elizabeth City State University, acquiring a Bachelor Degree of Science in Engineering Technology, focus on Mechanics and Automation. Momen also minored in Mathematics, as he desired to be versatile and knowledgeable in the Engineering world. His research interest are in structural engineering, bridges, and aspires further education in those fields.
OPTIMUM DESIGN OF ONE-BAY PORTAL STEEL FRAMES
The paper presents optimum design of statically indeterminate two-hinged steel portal frames under multiple loadings. An explicit formulation of the analysis equations using the Virtual Work Method is developed. Loading cases include both gravity loads and wind loads. Design equations involving local buckling, lateral torsional buckling, shear buckling, combined stresses and deflection constraints, as provided by the latest Egyptian Code of Practice for Steel Construction and Bridges, are included. The objective function is chosen as the minimum weight of the structure. The design variables are the cross-sectional dimensions of the built-up sections for rafters and columns. The design constraints cover all cases of discontinuity for compact prismatic sections. Ordinary mild steel and high tensile steel cases are considered. The optimization technique adopted in this research is the Modified Method of Feasible Directions. Several examples are presented to validate the efficiency of the formulation and to prove that the designs obtained in this work are more economical than those provided by other classical design approaches. Savings up to fifty percent of the weight of the frame are achieved for some cases.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.