1. Introduction
Steel is an extensively used material in prefabricated buildings due to its lightweight, high strength, ease of production and processing, high construction efficiency, and strong assemblability [
1]. Furthermore, under the promotion of the Chinese policy, assembled light steel materials have emerged as a preferred option for rural housing renovation and residential construction and have been built in large numbers [
2,
3]. Currently, common low-rise assembled building structural systems include the composite insulated reinforced welded mesh concrete shear wall system (CL building structural system), the assembled composite wall structural system, the prefabricated reinforced concrete hollow mould shear wall structural system, the assembled wood structural system, the dense-column-supported frame structural system, the modular structural system, and the low-rise assembled light steel framed structural system [
4,
5,
6,
7]. Among these, the low-rise assembled light steel frame structure system is the most favored for low-rise building structures due to its advantages in modularization, standardization, environmentalization, economization, factory assembly, and informationization production.
Congenital, processing, fabrication, connection, transportation, and installation defects in steel structures significantly impact their safety and applicability. Especially in rural construction, with many unique characteristics, light steel structures’ production and installation stages are particularly susceptible to a decline in structural performance due to construction irregularities. Random defects can exacerbate this issue, potentially resulting in premature material buckling and posing a significant risk to the building’s safety. Furthermore, improving the flexural properties of materials under the effect of defects not only contributes to the structure’s safety but also helps save costs and improve construction efficiency. Therefore, the impact of structural defects on prefabricated steel materials cannot be overlooked [
8].
Currently, research on the stability and bearing capacity of steel frame materials with defects mostly focuses on large and complex structures, such as mesh frames and mesh shell structures. The defects studied are primarily initial geometrical defects and residual stresses in the structure or members [
9,
10,
11,
12,
13]. Usually, the initial geometric defects mainly refer to the buckling of the bar, increasing the perturbation and deformation of the material, and the defects’ shape can be simulated by sinusoidal waves [
14]. Residual stresses mainly refer to the stresses present in hot-rolled or welded steel members from processes such as rolling, welding, and cold forming, which may reduce the material’s fatigue life and increase the risk of fracture [
15]. Kani et al. [
16] used the tangent stiffness matrix to solve the instability mode of the structure and found that node misalignment has a more significant effect on the structure than defects in the bars. Bielewicz et al. [
17] conducted a stochastic analysis on the static response of a nonlinear model of a defective shell structure, combining the Monte Carlo method with finite element program analysis to analyze the nonlinear post-buckling behavior of shells and discuss the method’s accuracy. Lauterbach et al. [
18] used a stochastic method to simulate structural imperfections and found that the effect of geometrical imperfections can be neglected in areas where support exists in thin-walled members. Kala et al. [
19] investigated the deformation of planar trusses with stochastic imperfections subjected to vertical loading and found that asymmetric defects have a detrimental effect on the load-carrying capacity of the trusses. Roy et al. investigated the flexural behavior of back-to-back built-up cold-formed steel and the axial strength of angle columns through tests and numerical simulations [
20,
21].
Research on defects of steel frame materials started earlier and developed faster, and the current focus is on constructing a database of material defects and studying the effects of defects on structures by probabilistic methods. Arrayago et al. [
22] conducted a statistical analysis of the main parameters affecting the strength of steel based on data from the last decades. They considered factors such as steel type, cross-section geometry, defects, and residual stresses and proposed a compatible probabilistic model to provide a database for research on steel structure defects. Mirzaie [
23] measured the geometry of steel tube defects, analyzed the characteristics of the defects caused by the manufacturing process and the errors in the measurement of the defects, and demonstrated the feasibility of using probabilistic methods to generate geometric defects consistent with the measurements. Fina et al. [
24] used a probabilistic approach to establish a Gaussian random field for random defects, extending the classical probabilistic approach to the fuzzy-random approach, providing a more reasonable description of the inaccurate random defect sampling method and evaluating the simulation results of the fit.
In advanced structural analysis, there are three primary methods for considering structural defects: the direct analysis method [
25], the equivalent nominal load method [
26], and the reduced tangent modulus method [
27]. The equivalent nominal load and reduced tangential modulus methods are approximate methods proposed when computer technology was not yet mature [
28]. As hardware and software have developed, the direct analysis method of the overall structure has been adopted by design codes, and it is the most commonly used structural analysis method now. The direct analysis method involves introducing a definite defect value directly on the member in the structural analysis [
29,
30,
31]. This method recognizes that the initial state of the member is no longer ideal and considers the direct effect of the defect on the light steel materials.
Research on defects mainly focuses on traditional steel structures, with a limited investigation on the working performance of low-rise light steel materials under defective states [
32,
33,
34]. Additionally, relevant codes have not made provisions for this, and the steel structure design code is still adopted as the defect control standard in the design of light steel structures. Therefore, it is crucial to investigate the effect of initial defects on the stability performance of assembled lightweight steel buildings, given their widespread popularity [
35,
36]. To ensure the safety of light steel framed buildings and the sustainability of this material, this paper proposes an improved Monte Carlo-based method to analyze the buckling performance of low-rise assembled light steel frame materials under the separate effects of random overall geometrical defects and random component geometrical defects during the structure’s service and construction stages.
5. Conclusions
This research presents a defect simulation approach suitable for light steel materials during construction. This method is based on the prevailing design specifications for initial defects in light steel framing materials and an analysis of random defects. The Ansys finite element software is employed to evaluate the ultimate load factor and structural deformation of the structure caused by overall random defects and component unit random defects during construction. The findings of the investigation are presented as follows:
- (1)
Compared to random defects, the construction stage is identified as the primary factor affecting the ultimate load factor (nodal ultimate displacement). When considering random defects as the influencing factor, the distribution of ultimate load factors (nodal ultimate displacements) remains relatively unchanged throughout the construction stage. However, the ultimate load factors of individual construction stages may fluctuate significantly. On the other hand, when the construction stage is considered the influencing factor, the distribution of ultimate load factors (nodal ultimate displacements) varies significantly.
- (2)
The response of the light steel frame structural ultimate load factor to construction stages and random defects varies depending on the stiffness difference between the layers and the number of layers. When the stiffness difference between the layers is smaller, the ultimate load factor is more affected by overall random defects. Conversely, when the number of layers is lower, the ultimate load factor is more affected by component unit random defects.
- (3)
When the light steel frame structural integrity is better, the ultimate displacements of both random defects increase significantly, and the deformation performance of the light steel frame materials improves correspondingly. The fluctuation of nodal ultimate displacements is more significantly affected by component unit random defects than overall random defects.
- (4)
The correlation between the ultimate load factor and the ultimate displacement of the light steel frame varies for different types of defects. There is no correlation between ultimate load factors and ultimate displacements for component unit random defects, whereas a correlation exists for overall random defects. Therefore, it is necessary to differentiate between component unit random defects and overall random defects.
- (5)
The displacements of the light steel frame tend to develop more rapidly under the action of component unit random defects than under overall random defects. However, the buckling critical loads of the light steel frame are not significantly different between the two types of defects.
Our research aims to offer references and assistance for the construction process of light steel structures. We hope to promote the standardized production of light steel materials, thereby minimizing defects. Additionally, we advocate for implementing temporary bracing during construction, strict adherence to welding procedures, and including specialized analyses to ensure structural stability. In the future, we suggest further simplifying the model, expanding the calculation scale, considering the structural dynamic response, and increasing the structural layers. These measures would enable finite element analysis results to better approximate the most unfavorable limit state of the structure in actual conditions.