Optimization of the cross-section of a steel welded I-beam accordingto the criterion of minimum potential strain energy

Abstract

The article considers the problem of reducing the material consumption of steel welded I-beams by optimizing their cross-section based on the criterion of minimum potential energy of elastic deformation (dU/dh = 0) accumulated in the beam during bending. Analytical differentiation of this criterion made it possible to derive a dimensionless design parameter k_A, which characterizes the optimal ratio between the wall area and the flange area of the I-beam.

Since rolled I-beam profiles were developed to ensure strength and stability while meeting criteria of economic and technological efficiency, it is advisable to use these principles to find the optimal cross-section of an I-beam. For this purpose, the shape coefficient k_F is introduced in the work, which characterizes the geometric proportions of the cross-section – the ratio of the height of the I-beam to the width of its flange. Based on the analysis of rolled profile assortments, an almost linear trend of the coefficient increase with the increase in beam height has been established.

The relationship between the coefficients k_A and k_F allows them to be used for preliminary approximate selection of an I-beam cross-section that will be close to the optimal one.

For practical implementation, a numerical iterative optimization algorithm has been developed that implements a multifactorial search for rational cross-sectional dimensions (height, wall thickness, thickness and width of flanges) under conditions of minimum beam weight and compliance with strength requirements.

Analysis of the results obtained by the algorithm showed that an increase in load leads to a decrease in kA and an increase in beam weight, which made it possible to obtain an approximate dependence k_A(q) in the form of a fifth-degree polynomial and allows the obtained dependence to be used in practical calculations.

The algorithm can be used to create software tools for automated design, build tables of optimal parameters, and develop recommendations for the standardization of welded profiles. There is a need for further improvement of the algorithm to take into account the standardized dimensions of rolled sheet metal and ensure local stability conditions.