## 1 Introduction  
Stainless steel is a steel alloy that contains a minimum of 10.5% chromium (Cr) content by mass. There is a wide range of stainless steels with varied levels of corrosion resistance and mechanical strength. More than 200 standardized stainless steel grades have hitherto been developed. The basic alloying elements of stainless steel grades are chromium (Cr) and nickel (Ni). According to Cr-Ni content by mass, stainless steels can be classified into five basic groups [1; 2], as shown in Figure 1.  
The five types are austenitic, ferritic, austenitic-ferritic (duplex), martensitic, and precipitation hardening stainless steels. The first three types have a wide and diverse application in the construction industry, such as building exteriors, facades, and pedestrian bridges. The last two types are for specialist applications [3]. For instance, martensitic grades are commonly used for bearings and turbine blades, and precipitation hardening grades are mostly used in the nuclear and aerospace industry. Steel hollow sections are a versatile and efficient form for construction applications [4; 5; 6; 7; 8; 9]. Buildings that use steel hollow sections have high strength-to-weight ratios. The efficient use of steel hollow sections reduces material usage, resulting in lightweight structures. It allows for large spans, and thus is a choice to achieve the optimal economic benefit. As stainless steels have excellent corrosion resistance properties, considerable long-term durability, and good mechanical strength [10; 11; 12; 13; 14], the use of cold-formed stainless steel rectangular hollow section (RHS) and square hollow section (SHS) (shown in Figure 2a) in construction industry has attracted considerable attention. For example, these sectionshave been used in the facade of the building of department of Chemistry, ETH Zurich (Switzerland), shown in Figure 2b, and the support frame of Marques de Riscal Vineyard (Spain), shown in Figure 2c. Also, they can be used for the main frame structure of residential buildings. rectangular hollow section by bending it through rollers, and welding the seam after that. In round to square forming (shown in Figure 3b), the steel strip is first formed into a circular hollow section and then it is welded. After forming the circular hollow section, square or rectangular shapes are created using profiling rollers. For the two forming methods, localized imperfection (\(\omega\)) induced by rolling and fabrication process is inevitable (shown in Figure 4). It has sufficient variability and has no definitive characterization [17]. The study of [PERSON] et al. [18] and [PERSON] et al. [19; 20] showed that both the shape and magnitude of \(\omega\) varied randomly in the longitudinal direction for cold-formed members with box section, as shown in Figure 4a. The shape of \(\omega\) in the transverse direction (cross-sectional) was convexity/concavity [21; 22], which can be modelled by a half-sine wave, as shown in Figure 4b. In numerical studies, \(\omega\) is typically modelled by local buckling mode (shown in Figure 4c) obtained from linear perturbation buckle analysis [23]. The local buckling mode gives idealized \(\omega\) and neglects uncertainty in localized imperfection. Figure 4: Localized imperfection (\(\omega\)). (**a**) Random \(\omega\) along longitudinal centerline of the surface; (**b**) \(\omega\) in transverse direction (convexity/concavity); (**c**) idealized \(\omega\) obtained from buckle analysis. Figure 3: Two forming methods for cold-formed RHS and SHS. (**a**) Direct forming [15]; (**b**) round to square forming [16]. The cross-sectional resistance of cold-formed hollow sections, which contain slender thin-walled elements, is sensitive to initial localized imperfection [24]. These sections undergo local buckling reduction in advance of failure and their ultimate capacity may be influenced by the uncertainty in localized imperfection.