Application of graphic static method in truss optimization of building structure

The axial force line diagram and truss shape obtained from the analysis are shown in Table 1.

Scheme 3 achieves the minimum deformation under wind load.

However, recent research and engineering applications show that the graphical statics method has been well applied in the form finding optimization design of steel truss structure or high-rise structure, frame structure, structural materials and hinged support structure, and provides valuable guidance for the form finding analysis of buildings and structures.

Introduction of graphic statics method the internal force of truss can be analyzed by manual drawing method.

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9 axial force line diagram of steel truss structure.

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At present, the widely used structural analysis programs such as ETABS and yjk do not have this calculation function.

The introduction of static method as the main method of hand counting in the early stage of structural mechanics has been widely used.

The program can offset all truss nodes, calculate the axial force line diagram in real time, and calculate the virtual work representative value of the truss.

8 shape finding diagram of steel truss structure Fig.

The shape of the truss is controlled by two geometric parameters D1 and D2.

(d) the three-dimensional effect of the tower crown of scheme 3 Figure 10 the structural layout of different schemes.

For the specific method of drawing axial force line diagram, you can view the demonstration video of the author.

The program interface of the graphical static method is shown in Figure 4.

The representative values of virtual work show that when shape 1 changes to shape 4, the performance of the system improves and the total virtual work decreases.

10, Scheme 1 is the original steel truss( Φ one hundred and seventy-six × 8) , option 2 is variable depth truss( Φ one hundred and fifty × 8) , the maximum depth is 5.3m, scheme 3 is the scheme with the smallest virtual work representative value of graphical static method, and the maximum depth is 3.7m( Φ one hundred and sixty × 8)。 The steel consumption of the three schemes is equal.

Graphical statics has no advantage as a calculation method to solve the internal force.

7 Relationship between virtual work representative value and mid span node depth (a) first stage optimization (b) second stage optimization Fig.

The program for drawing axial force line diagram is compiled based on bar system finite element method, in which the function of real-time calculation of virtual work representative value is added, which can enable engineers to better carry out the shape finding analysis of truss structure.

Through the change trend of the virtual work representative value, evaluate whether the truss is optimized before and after the node offset, and the ultimate goal is to minimize the virtual work representative value of the structure.


The total steel consumption is about 7.32t.

The core of graphic statics method for solving the internal force of truss structure is the internal force balance of multiple members around the node, that is, the sum of internal force vectors is zero.

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The shape of the truss is optimized by the graphical static method, so that the top deformation of the truss can be minimized under the condition of the same amount of steel and meet the requirements of 1 / 500.

Scheme 2 shows that the deeper the truss is, the better.

The calculation of modern structural mechanics basically depends on the computer program based on finite element theory.

Through ETABS analysis, the top deformation values of the three schemes are 71.20, 44.71mm and 39.20mm.

4 program interface for solving the static mechanics method illustrates how to optimize the truss by using the graphical static method with an example: the truss span is 18m, the truss height is 3M, both ends are hinged, and all members are made of round steel pipe 200 × 20.

The program is used for the shape finding analysis of the truss.

This paper realizes this part of functions through self programming, and can be imported into ETABS / SAP2000 for structural follow-up analysis through secondary development.

In this paper, the design of steel truss is taken as an example.

The left figure is the axial force line diagram illustrating statics, and the right figure is the truss elevation.

The representative values of virtual work corresponding to the four models are shown in Table 2.

The demonstration video Figure 3 illustrates the static method to convert the truss geometry diagram into the axial force line diagram to solve the static axial force line diagram generation program.

In this paper, graphical statics is applied to engineering through programming method.

Due to the application and promotion of high-strength steel, more and more truss structures have changed from the original bearing capacity control to stiffness control, such as transfer truss and wind resistant truss, It is becoming more and more important to improve the structural efficiency of steel truss, among which the graph solution statics method, virtual work principle and topology optimization are widely used.

In the coastal area with large wind load, the section size of steel truss is controlled by deformation.

5 structural diagram of steel truss calculation example Table 1 axial force line diagram and truss shape table 2 virtual work representative values of different truss shapes diagram engineering application analysis of static method optimization more and more steel truss structural system is used to support glass to resist wind load in the tower crown of modern high-rise buildings.

The height of the truss is 24m, the depth of the truss is 1.5m, and there is a lateral support connecting the core tube at the height of 12m.

The related theories of graphic statics are described in detail.

The Android and iOS user operation is the same.

Carle published his book “graphic statics”.

Finally, an engineering example is given to show the application of the program in the form finding analysis of wind resistant truss..

6 shape finding diagram of steel truss structure (a) first stage optimization (b) second stage optimization Fig.


There is an optimal solution.

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The following results are obtained by continuously changing D1 and D2: Fig.

Truss schemes with different variable depths are modeled and analyzed through SAP2000, as shown in FIG.

Finally, the three-dimensional effect of the tower crown obtained by scheme 3 is shown in Figure 10 (d).

Figure 1 illustrates the classic works of static method Figure 2 illustrates the application of practical engineering optimization of static method.

Through secondary development, the optimized shape is imported into SAP2000 and other structural programs for subsequent analysis.


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