József Farkas

Cost calculation and optimisation of welded steel structures

Abstract The cost optimisation is important in structural design. The welding times of various welding technologies are different. Using the costcomp program we can calculate the welding times. Adding other times, like flattening plates, surface preparation, cutting, electrode changing, deslagging, painting, etc. we can form a complete cost function. Times are usually general, but costs are different in various countries. Introducing the fabrication and material specific cost ratio of k f / k m , which varies between 0 and 2 kg/min, it is possible to build the cost function from the times and to work out optimisation in different economic conditions. The investigated structures are predominantly welded from plates. Examples are shown of applications for the design of welded box beams and stiffened plates. The fabrication cost percentages for welded box beam and stiffened plate are 29–35 and 46–71% of the total costs, respectively, thus they can have a significant effect on optimum dimensions. The discrete optima depend on the manufacturers, on the k f / k m ratio and the welding technologies.

Optimum design of steel structures

Experiences with the Optimum Design of Steel Structures.- Newer Mathematical Methods in Structural.- Cost Calculations.- Beams and Columns.- Tubular Trusses.- Frames.- Stiffened Plates.- Cylindrical and Conical Shells.

2.2 – Minimum Cost Design of a Square Box Column Composed from Orthogonally Stiffened Welded Steel Plates

In the previous research the minimum cost design of the uniaxially compressed orthogonally stiffened welded steel plate has been worked out. Based on this result the cost minimization of a cantilever stub column of square box cross section with orthogonally stiffened side plates is formulated and solved. The constraints relate to the overall and stiffener torsional buckling of side plates and to the horizontal displacement of the column top due to a horizontal force. Halved rolled 1-section stiffeners are used in both directions. The cost function includes the cost of material, assembly, welding and painting. The variables are the thickness and width of the side plates as well as the dimensions and numbers of stiffeners in both directions. The optimization is performed using the particle swarm algorithm.

Mechanics and design of tubular structures

G. Davies, Static Behaviour of Welded Rectangular Hollow Section Connections.- Y. Kurobane, Static Behaviour and Earthquake Resistant Design of Welded Tubular Structures.- J. A. Packer, Behaviour and Design of Bolted and Welded Connections.- M. M. K. Lee, Fatigue, Fracture Mechanics and Defect Assessment of Tubular Structures.- K. Jarmai, Topology Optimization of Tubular Structures.- J. Farkas, Optimum Design of Tubular Structures.

Cost savings using different post-welding treatments on an I-beam subject to fatigue load

In the framework of this work, research has been carried out to obtain current data on the potential of post-weld treatment (PWT) since new PWT technologies appeared in the last years, and the older technologies have been improved. The economy of post-welding treatments is illustrated by means of a numerical example of a simply supported welded I-beam loaded in bending by a pair of pulsating forces. The vertical stiffeners are welded to the I-beam upper flange by double fillet welds, which cause a significant decrease of fatigue stress range. This low-fatigue stress range is improved by various post-welding treatments. Based on the published experimental data, it is possible to determine the measure of the increase of the fatigue stress range as well as the required treatment time for grinding, TIG dressing, hammer peening and ultrasonic impact treatment. This article provides an overview of current PWT methods and the possible improvement in fatigue strength. Furthermore, optimization of a welded I-beam has been conducted to reduce the fabrication cost. The data from the research in the form of increase in fatigue strength and application speed were included in this optimization. The treatment time is included into the cost function and the improved fatigue stress range is considered in the fatigue constraint. The comparison of costs for optimum structural versions with and without treatments shows the economy of different treatment methods. This comparison helps designers to consider the applicability of PWT and select the best available method.

Minimum Volume and Cost Design of a Welded Square Cellular Plate with Welded T-Stiffeners

Cellular plates consist of two face plates and a stiffener grid welded between them. One of their advantageous properties is that they can be calculated as isotropic ones. This property is utilized in the present study for a simply supported square plate loaded by a uniformly distributed normal load. Design constraints on normal stresses and on maximum deflection are formulated. The unknown variables are the two face plate thicknesses, the height of the welded T-section stiffeners and the number of stiffener spacing, The cost function contents the cost of material, assembly and welding. The optimum is determined by a systematic search using a Mathcad program. Welded T-stiffeners are more economic than the halved rolled I-section ones.

1.4 – Optimization of an Orthogonally Stiffened Plate Considering Fatigue Constraints

The aim of this work is the optimization of a uniaxially compressed stiffened plate subjected to static and fatigue loading. The design variables are the thickness of the base plate, the number and stiffeners of the orthogonally stiffened plate. The constraints deal with the static overall plate buckling, the stiffener failure and the fatigue strength of the welded connections between the stiffeners and the interaction of the two types of failure. The cost function includes the cost of material, assembly, welding and painting. Randomness is considered both in loading and material properties. A level II reliability method (FORM) is employed. The overall structural reliability is obtained by using Ditlevsen method of conditional bounding. The costs of the plate designed to ensure a stipulated probability of failure will be compared with the solutions obtained for a code based method, which employs partial safety factors.

A new structural version of welded cellular cylindrical shell for a cantilever column

A cantilever column is loaded by compression and bending, and the horizontal displacement of the column top as well as the outside diameter of the cylindrical shell are limited. The strengthening of the column is performed in the lower part of the column only. Three structural versions of the column are optimized and compared to each other. Firstly, the unstiffened circular shell is optimized, and it is found that the required large thickness is unsuitable for fabrication. Secondly, the stringer-stiffened circular shell is optimized. The halved rolled UC section stringers are used only in the lower part of the column; the distance of the interruption of stiffeners is also optimized. It is found that the required shell thickness is unsuitable for fabrication. Thirdly, a new structural version, the cellular shell is used. Cellular shells are constructed from two circular cylindrical shells, and a grid of stiffeners welded between them. They have similar advantages than the cellular plates, namely they can produce a large stiffness with small structural height. Their smooth surface is suitable for corrosion protection, and they are more aesthetic than the stringer-stiffened shells.

Cylindrical and Conical Shells

The problem is to find the optimum dimensions of a ring-stiffened circular cylindrical shell subject to external pressure, which minimize the structural cost. The calculation shows that the cost decreases when the shell diameter decreases. The decrease of diameter is limited by a fabrication constraint that the diameter should be minimum 2 m to make it possible the welding and painting inside of the shell.

Beams and Columns

The present study shows the difference between structures optimized for minimum volume and minimum cost. The cost function contents the cost of material, assembly, welding and painting. A simply supported welded box section beam is investigated. The design constraints are as follows: limitation of the maximum stress from the maximum bending moment, limitation of plate slendernesses to avoid local buckling of flange and web. The minimization of the volume and cost results in different beam sizes, but the cost difference between the two optima is small.