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Designing of Steel CHS Columns Showing Maximum Compression Resistance

Marcinowski Jakub, Sadowski Mirosław

Civil and Environmental Engineering Reports

2021

Vol. 31, no. 1

79--92

The paper deals with a shape optimisation procedure of steel, compressed bars. Circular hollow sections (CHS) of variable cross sections and variable wall thickness are taken into account. The proposed procedure for designing of steel rods exhibiting maximum compression resistance is effective and possible to use in engineering practice. The advantage of the proposed shape of the bar is that it allows to increase the value of its load carrying capacity, i.e. it ensures the transfer of a higher value of compressive force than similar, solid struts of the same mass and length. The extent of the increase in the load capacity relative to the load capacity of the reference solid, cylindrical bar depends on the slenderness of the reference bar and ranges from 60% to 170%. Due to this very beneficial fact, it can be used wherever it is required to maintain a certain stiffness and an increased value of compressive force is desired, as well as in constructions where it is necessary to reduce weight while maintaining the adopted mechanical parameters, e.g. values of load bearing capacity. Final results achieved in the research were presented in the form of the flow chart allowing to design the compressed columns of optimum shape.

Using the Erfi function in the problem of the shape optimization of the compressed rod

Marcinowski J., Sadowski M.

International Journal of Applied Mechanics and Engineering

2020

Vol. 25, no. 2

75--87

The shape of the optimal rod determined in the work meets the condition of mass conservation in relation to the reference rod. At the same time, this rod shows a significant increase in resistance to axial force. In the examples presented, this increase was 80% and 117%, respectively, for rods with slenderness of 125 and 175. A practical benefit from the use of compression rods of the proposed shapes is clearly visible. The example presented in this publication shows how great the utility in the structural mechanics can be, resulting from the applications of complex analysis (complex numbers). This approach to many problems can find its solutions, while they are lacking in the real numbers domains. What is more, although these are operations on complex numbers, these solutions have often their real representations, as the numerical example shows. There are too few applications of complex numbers in the technique and science, therefore it is obvious that the use of complex analysis should have an increasing range. One of the first people to use complex numbers was Girolamo Cardano. Cardano, using complex numbers, was solving cubic equations, unsolvable to his times – as the famous Franciscan and professor of mathematics Luca Pacioli put it in his paper Summa de arithmetica, geometria, proportioni et proportionalita (1494). It is worth mentioning that history has given Cardano priority in the use of complex numbers, but most probably they were discovered by another professor of mathematics – Scipione del Ferro (cf. [1]). We can see, that already then, they were definitely important (complex numbers).