Keywords: steel structures, beam-columns, structural Eurocodes, Monte-Carlo simulation, elasto-plastic FEA, interaction design equations.

Design of steel structures is specified by structural codes. The European steel building code prEN Eurocode 3 [1] is under final vote by CEN. From computational technology point of view the so-called interaction design equations are the most important phase of the code. These equations govern the design of members as well as the bracing system of the structure. The final draft of the basic code was prepared by extended developments carried out by the so-called ECCS/TC8 working group. This expert group has improved the older formula and created a `new' one. They suggested a new `three-level' specification. Level 1 formula has the priority on user- friendliness, simplicity and comprehensiveness. Level 2 formula puts the priority to accuracy, consistency and continuity with other standard checks. Level 3 is the most sophisticated technique using efficient software as well as sufficient theoretical knowledge. This approach is used extensively in the calibration of the two other levels. This paper is related to the Level 2 and 3 formulas and proposes simulation based design methodology, which keeps the principal design and safety philosophy of Eurocode 3, but uses modern computational architectures.

In the paper two approaches are introduced. The first approach is based on 3D elastic global stability analysis and generalised design equation, which is calibrated by a numerical simulation. This CAD oriented design method can replace the `hand oriented' Level 2 formula and results an automatic computer design procedure. The second approach uses the 3D global stability analysis and leads the computation of resistance back to a numerical simulation.

A CAD oriented Level 2 formula

It is important that the global analysis let response to the real stability behaviour of the whole structural model as well as its members. Using explicit stiffness matrix formula the elastic analysis for any load combination can supply the second order design stress resultants as well as the global critical load factor. However, following the above concept, a heuristic Generalised Design Equation (GDE) can be written as

where denotes the components of the longitudinal design normal stress in the most compressed cross-section point of the member using full 3D second order elastic analysis and elastic cross-section properties. In Equation (95.1) denotes the warping effect due to torsion, denotes the generalised buckling reduction factor, is the design strength (including appropriate partial safety factor) and is the generalised plasticity factor of the cross-section. The formula was verified by numerical simulation [2] for Class 1 and 2 profiles.

A Level 2 formula using parallel simulation

The numerical simulation method based on any appropriate finite element (or strip) method and appropriate design probabilistic model parameters can be applied to predict the design resistance of the structural members [2,3]. Theoretically, the methods can be extended to complex structures but there are at least two reasons why it is hardly probable: (1) the numerical simulation technique is time consumable, (2) in more complex cases the use of technique requires strong theoretical knowledge of theory of analysis and design. In the practice simulation may be restricted to determine the generalised reduction factor in Equation (95.1) on the simple beam-column models. The result can be given in term of the reduced slenderness and normal force, and it can be stored in database related to the unified object-oriented definition of cross-section [4]. From programming technology point of view the question is the following: when the reduction factor database is created. In case of standard profiles the program developers can create the database as a system component. In case of user defined cross-section the appropriate database should be created in run-time. The simulator program is the part of the design software and it can be run in the background just the cross-section has been defined. The simulation may be run parallel to the modelling. The usage of this procedure on PCs is theoretical because of the considerable running time. Advanced design systems can use distributed computation, where application server is used. While the client is working on the model, the simulation on the user-defined cross-sections can be run on the high performance application server.

1

PrEN Eurocode 3 1993-1-1:2002, "Design of steel structures. Part 1.1: General rules. European Prestandard", Stage 34 draft, 1 May, CEN 2002

2

J. Szalai, F. Papp, "Simulation of beam-column stability with automatic strain incrementation", The Sixth International Conference on Computational Structures Technology 4-6 September 2002, (to be published) doi:10.4203/ccp.75.11

3

F. Papp, "ConSteel as the Prototype of a CAD/CAM Oriented program for Concurrent Design of Beam-Column Structures", Computational Steel Structures Technology, Civil-Comp Press, pp. 1-12, Edinburgh, 2000. doi:10.4203/ccp.70.1.1

4

F. Papp, M. Iványi, K. Jármai, "Unified Object-Oriented Definition of Thin- Walled Steel Beam-Column Cross-Sections", Computer & Structures, 79, 839-852, 2001. doi:10.1016/S0045-7949(00)00183-8

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £125 +P&P)