Keywords

1 Introduction

During the actual use of the building structure, it will be affected by the external environment. Therefore, the stability and firmness of the building itself will be affected to a certain extent, especially the reliability of the building structure. The research on the development process of foreign structural engineering shows that when the engineering construction reaches a certain degree, the reinforcement of engineering structure will become one of the main construction methods. It can be seen from relevant studies that civil engineering directly affects the process of urbanization. Drawing on the development history of developed countries, the initial stage of urbanization is the establishment of large-scale new buildings. Since then, the city has gradually matured in the process of urbanization, the scale of new buildings has continued to decline, and then the proportion of old houses has gradually increased, which are the three stages of urban development. Taking civil engineering in developed countries such as the United Kingdom and the United States as an example, the cost of building renovation in the United Kingdom in 1978 was more than three times nearly four times that in 1965. The industry of old house renovation is rising. According to a survey report of the United States, the heat of old house renovation was going to rise in the future gradually [1]. The development of civil engineering in China is relatively backward and started relatively late. After the Tangshan earthquake, the national group gradually paid more attention to the safety of buildings, especially old buildings. The group has formulated a series of standards led by the standard for seismic appraisal of industrial structures for seismic safety. To meet the gradually improved building standards, the industry of strengthening old buildings is also gradually emerging in China [2]. At present, most experts and scholars have done a lot of research on truss structure reinforcement based on actual cases. Bai [3] increased the section of a truss soffit member and achieved the goal of strengthening the connection between the upper and lower chords of the truss arch, which plays an important role in improving the overall dynamic performance of the structure after reconstruction. Yang et al. [4] adopted the expanded section method to strengthen the original lower chord members in the transformation of the truss structure of the corridor of a belt yard so that the out of the plane whole of the upper chord of the second span of the original corridor can meet the requirements. Liao et al. [5] adopted the external prestressing reinforcement method to fundamentally improve the bearing capacity of the grandstand components and narrow or close the original gap when transforming the arc grandstand structure of the Wuhan Xinhua Road stadium; it reduces the deflection of the components and is convenient for maintenance while effectively improving the rigidity of the building. Hayashi et al. [6] proposed a method combining reinforcement learning and graph embedding to optimize the binary topology of truss structures, achieving the goal of minimizing the total structure volume under stress and displacement constraints. When discussing the quality defects and reinforcement methods of an existing steel structure workshop, Guo [7] pointed out that when the steel material strength is insufficient, the reinforcement methods such as increasing the section reinforcement method and pasting steel plate reinforcement method should be adopted to make the material strength meet the requirements of the bearing capacity and stability of the truss structure. However, there is relatively few research on the reinforced truss structure in buildings worldwide. This paper discusses the application of the reinforcement method which changes the cross-sectional area of the truss in the truss structure, and the Abaqus finite element analysis and calculation software is used to establish the statically indeterminate truss simulation model to simulate the reinforcement effect. The main research contents are as follows: (1) This paper expounds on the stress characteristics of statically indeterminate truss. Then it establishes the finite element model of statically indeterminate truss by using the Abaqus. After that, the paper calculates the stress condition of the truss before reinforcement, which finds out the most unfavorable load combination, and selects the reinforcement analysis object; (2) Based on the finite element simulation model, the paper emphatically analyses the stress state of trusses strengthened by increasing section method, and the stress variation trend and reinforcement effect of each control section.

2 Finite Element Modeling

To analyze more visually the similarities and differences between the two reinforcement methods, a typical super-stationary truss model was selected for this numerical simulation. The truss model was designed to meet the requirements of the GB50017-2017 Steel Structure Design Standard [8]. The truss consists of three vertically placed square column modules (Fig. 1), which are supported by two fixed hinge supports A and B and to which three horizontal set forces F are applied at their left nodes. Specific values required are in Table 1.

Fig. 1
A diagram depicts the model of a truss which is shaped like 3 square blocks with diagonals placed one on top of another. Each of the three trusses has a force of 1.00 KN acting at the top.

Model of truss [9]

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Table 1 Specification of super-static truss members before reinforcement [9]
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The truss was modeled using Abaqus finite element software and the forces on each Rod of the truss were derived from the simulation experiments as shown in Table 2. The results obtained were also compared with two sets of accurately calculated force data for each Rod from a similar model in Rebielak [9]. Most of the experimental data differed from the literature data by less than 10%. The simulated experimental values fall within the two accurately calculated model values when the difference between the calculated results of the two sets of accurately calculated models in the paper is greater than 10%. The model is thus correctly modeled and the experimental data modeled by the Abaqus finite element software is reliable.

Table 2 Forces on each abaqus rod before reinforcement and comparison with literature (in KN)
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3 Finite Element Model Analysis and Discussion

3.1 Finite Element Model Analysis

The methods of applying prestressing reinforcement generally fall into two categories, the first being the installation of prestressing tendons within the girders and the other being the external application of prestressing. The principle is that the middle of a truss bridge is subjected to the greatest bending moment and the external application of prestressing creates an upward support force that reduces the stress of the load on the bridge mechanism [10].

The trusses mentioned in this paper cannot be reinforced using prestressing methods as they do not have anchorage points on both sides for fixing the prestressing strands, so the reinforcement method of increasing the cross-sectional area was chosen for reinforcement [11].

Analysis of the force cloud of the joist (Fig. 2) shows that the reinforcement is located at the most stressed positions, which are Rod 9 and Rod 10. When the load is too high, the modified rod will be damaged first compared to the other rods, so Rods 9 and 10 determine the ultimate load capacity of the joist structure.

Fig. 2
A force cloud diagram depicts the S mises magnitudes on the various regions of the truss. The magnitude is highest on the lowermost vertical appendages.

Force cloud diagram of the truss

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3.2 Increased Cross-Section Method

Based on the structural form and force characteristics of the joist, the Abaqus was used again to model the joist and to compare the joist before strengthening with the joist after strengthening by the increased section method. Considering the horizontal load and the steel joist forces, the calculation results were analyzed and the final retrofit reinforcement scheme adopted was determined as follows:

Welded channels were added to the left end of Rod9 and the outer end of Rod 10 [12]. The cross-sectional area after strengthening is 1413 mm2. The shape of the cross-section is shown in Fig. 3, resulting in model No. 2.

Fig. 3
The shape of a truss section reinforcement depicts a rectangular section on the left of a larger annulus.

The shape of truss section reinforcement (in mm) [12]

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3.3 Specific Research

By Abaqus simulation increasing section method, the performance of the after-reinforced joist has been analyzed. The analysis bases on the original joist shows that the force on the joist Rod 9 and Rod 10 is the largest among all the joists, as shown in Fig. 2, and in case of damage to the joist, Rod 9 and Rod 10 will be damaged before the other rods, so a sub-model is established for the ultimate bearing capacity analysis of these two rods.

Rod 9 sub-model

  1. (1)

    Original cross-sectional area model

To simulate the unilateral axial tension of the truss in the laboratory, one end of the rod is constrained and the other end is subjected to a boundary displacement of 100 mm at the reference point. The reference point is connected to the upper annular surface of the steel pipe by a “coupled” relationship, and to ensure synchronization between the reference point and the upper section when moving, the mesh is finally divided and solved to obtain a stress cloud as shown in Fig. 4.

Fig. 4
A stress nephogram of a rod depicts the magnitude of stress in its different sections by means of a spectrum. The stress is maximum on the lowest part.

Stress nephogram of rod 9

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The force and displacement relationship curve are the output for this stressed rod in the post-processing stage (Fig. 5). The support reaction force RF2 at the unique node reference point is output in the ODB field variable output. In contrast, its displacement U2 is output, and the relationship curve between U2 and RF2 is obtained with the combined command. Its highest point is the limit value of the tensile strength, as shown in Fig. 5. Its highest point value of 128.591 can be obtained by clicking on the vertical coordinate KN. After the highest point, the curve drops because the rod cross-section becomes thinner in tension, and the tensile strength slips.

Fig. 5
A line graph plots force versus displacement and the curve is linear at first and becomes curved for the maximum part.

Relation curve between output force and displacement of stressed rod 9

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  1. (2)

    Double cross-sectional area model

The same method was used to measure the ultimate load-carrying capacity after increasing the section to twice the original section and outputting a displacement versus force graph (Fig. 6). The highest value of 256.149KN was obtained.

Fig. 6
A line graph plots force versus displacement and the curve is linear at first and becomes curved for the maximum part, and has an overall decreasing trend.

Relation curve between output force and displacement of stressed rod 9 increased by twice its sectional area

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Only the cross-sectional dimensions of the member changed between the two modeling processes. The materials, analysis methods, and boundary displacements were the same. It can be seen that the maximum tensile force applied to the Rod increased after the model cross-section was increased to twice its original size, and it can be concluded that the increased cross-section method effectively raised the tensile limit.

Rod 10 flexure simulation

Rod 10 is in the compression zone, and its damage is characterized by rod instability. The characteristic value of first-order buckling is its ultimate load in buckling through buckling simulation.

  1. (1)

    Original cross-sectional area model

The rod is modeled with the same material and the same structure as rod 9, with the linear set dynamic buckling set in the analysis step, one end of the rod is fixed, and a unit load-1 is applied to its upper end at the reference point, again the reference point is linked to the upper surface using a “coupled” relationship, the mesh is divided, and a working analysis is created to obtain its cloud (Fig. 7), with an eigenvalue of 11.812KN.

Fig. 7
A stress nephrogram depicts the magnitude of stress in different regions of the rod. Maximum stress in the topmost part, and the magnitude decreases on moving down.

Stress nephogram of rod 10

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  1. (2)

    Double cross-sectional area model

The same double cross-sectional area model was constructed with the same material properties, applied loads, and other conditions, and the cross-section of the member was increased to twice its original size, and the stress cloud shown in Fig. 8 was obtained, with an increase in its characteristic value of 30.398KN.

Fig. 8
A stress nephrogram depicts the magnitude of stress in different regions of the rod. Maximum stress in the topmost part.

The stress nephogram of rod 10 increased by twice its sectional area

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It is concluded from the two modeling runs that increasing the cross-sectional area, as with the tie, results in a significant rise in the limit of force. Increasing the cross-section, whether it is a tie or a compression Rod, increases the load-carrying capacity.

3.4 Discussion

  1. (1)

    Comparison of the overall load capacity of the trusses

The test of the ultimate load-carrying capacity of the truss is carried out utilizing a trial method, which is based on the principle of continuously applying loads, the magnitude of the corresponding axial forces is close to the ultimate value measured by the sub-model.

  1. (2)

    Carrying capacity trial calculation

The modeling adopts 2D modeling, the direction of applied load and the point of action are the same as the original model, and the field outputs the S11 stress value, multiplying the stress value of the most and least stressed rod by its corresponding cross-sectional area of 706.86 mm2 to get its axial force, compared with the ultimate load of the sub-model, it can be obtained that its lateral load can be increased between 2.65 ~ 2.66 KN closest to its compressive ultimate load-bearing capacity. Meanwhile, the ultimate load-bearing capacity of the tensile rod is much greater than the ultimate load-bearing capacity of the compressive zone, so the overall force limit of the joist is determined by the rod with the greatest axial compression. The trial calculation results are shown in the Table 3.

Table 3 Trial calculation results of overall stress limit of the truss
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  1. (3)

    Double section truss model trial calculation

The modeling process properties, analysis steps, etc., remain the same, change its cross-sectional area to 1033.77 mm2, and carry out trial calculations to find the ultimate load of the truss. Its ultimate load is between 6.8 ~ 6.84 KN. The trial calculation results are shown as Table 4.

Table 4 Trial calculation results of overall stress limit of truss by twice its sectional area
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According to the experimental results, the compressed rods are damaged first. Then the limit values range from 2.65 to 2.66KN before the lateral resultant load reinforcement in the joist, From the results of compression, their limit values range from 6.8 to 6.84KN after the increase of cross-sectional area, and it can be concluded that the bearing capacity of the joist structure is very obviously improved by the method of increasing the cross-section.

4 Conclusion

In this paper, a model of a super-stationary truss is developed by using numerical simulation. The analysis of strengthening by the increased section method using the Abaqus model increases the ultimate load capacity of the truss and the ultimate load capacity of the corresponding rod has been increased. The strengthening and modification work reduces the maximum axial force of the super-static truss, reduces the maximum deformation, and improves the structural stiffness significantly, thus achieving the purpose of strengthening.

As numerical simulations are used in this paper and no experiments are carried out, a practical comparative study of the model should be carried out in the future to compensate for the limitations of this study.