The ultimate goal of light steel structure design is to give an economical and reasonable design scheme. The optimization design method can better meet this requirement. The optimal design of light steel structure is of obvious significance for reducing the weight, steel consumption and structural cost of the structure. At present, the optimization design of light steel structure has been studied and applied in China, and the corresponding calculation program has been compiled, and the automatic optimization of section has been realized by computer, in order to find the design scheme with the least weight, the least material consumption or the lowest cost. This has played a certain role in improving the design quality of light steel structure and speeding up the design progress. The mathematical model of light steel structure optimization design is established as follows.

1. Design variable

The main geometric parameters of light steel structure, such as span, cornice height, roof slope and vertical column spacing, are usually determined by the owner or architect. The variables that can be optimized are mainly section parameters. Specifically, it is the width and thickness of the flange of each I-beam section and the height and thickness of the web. The thickness of steel plate is a discrete variable, and the height (width) of web and flange is generally selected from a series of regular numbers, so the design variable of light steel structure is usually a discrete variable.

2. The objective function

Structural weight is an important index in the optimal design of light steel structures, and it is easy to be written as a function of design variables, so light steel structures usually take the minimum amount of steel as the optimization goal.

Step 3 limit

The optimal design of light steel structure must meet the following constraints:

(1) strength and stability constraints.

Light steel structural members must meet the requirements of strength and stability.

(2) Stiffness constraint.

When optimizing the component size of light steel structure, the overall stiffness of the structure must meet the requirements of deformation control. Specifically, the maximum vertical displacement of the beam, the maximum horizontal displacement of the column top and the maximum horizontal displacement of the crane rail top must meet the deformation control values specified in relevant codes.

(3) Constraints of section size.

The selection of section size of light steel structure must meet the structural and service requirements of relevant codes, such as the web height of all sections must be greater than the flange width, and the flange thickness of all sections must be greater than 2mm.

(4) The overall constraints of the structure.

The optimal design of light steel structure must meet the overall constraints of the structure, that is, the selection of section size of members must ensure the continuity and rationality of beam and column sections, and meet the requirements of conventional processing and use.

(5) The upper and lower bounds of variables.