Recent Research Advances in High-Performance Steel Tubular Members: Material Properties, Stub Columns, and Beams

Abstract

This paper presents recent advances in research on high-performance steel tubular members, including beams and columns. The term high-performance steel has been used for steels that have unparalleled characteristics such as high strength, cold formability, corrosion resistance, and ductility. Stainless steel (SS) and high-strength steel (HSS) are classified as high-performance steel. In the context of this paper, high-performance steel refers to SS and HSS, where HSS is with a nominal yield strength equal to or higher than 690 MPa. This paper initially illustrates the applications of high-performance steel as a construction material for buildings and infrastructures. Subsequently, the material properties of high-performance steel with constitutive models in response to the stress–strain curves are summarized. Furthermore, this paper reviews research on the structural performance of high-performance steel stub columns and beams and presents the associated design equations. Finally, insights into future work on the structural behavior of high-performance steel to promote its widespread use for building and infrastructure construction are provided.

1. Introduction

As a construction material, high-performance steel has distinctive characteristics, such as high strength, cold formability, corrosion resistance, ductility, and recyclability [1]. The implementation of high-performance steel in construction calls for public policies, especially in terms of enhancing engineering efficiency and sustainability, such as by reducing construction waste and minimizing the carbon footprint of buildings. This facilitates progress towards achieving several United Nations Sustainable Development Goals (SDGs), such as SDG 9—Industry, Innovation and Infrastructure and SDG 12—Responsible Production. For instance, by utilizing high-strength steel, structural member sizes can be downsized, leading to minimized resource consumption, processing time, and transportation cost. Leveraging these advantages of high-performance steel allows for minimizing the emission of embodied carbon and operational carbon and also to reducing the time and cost of material handling and erection [2].

Stainless steel (SS) and high-strength steel (HSS) are classified as high-performance steels [3]. HSS and SS have been increasingly used in iconic structures, tall buildings, bridges, and long-span structures. Recent research demonstrates the advantages of using high-performance steel in constructing steel modular buildings [4]. In this paper, high-performance steel refers to SS and HSS, in which HSS is with a nominal yield strength equal to or higher than 690 MPa. The main objective of this paper is to present the advances in research on high-performance steel (SS and HSS) structural members, including beams and columns. This study first shows the applications of SS and HSS in buildings and infrastructure construction in Section 2. Section 3 of this paper investigates the material properties of SS and HSS and elucidates the constitutive models based on the stress–strain curves. Previous research on the structural performance of high-performance steel stub columns and beams and the associated design equations are reviewed in Section 4 and Section 5. Section 6 presents the recommendations for future work on the structural behavior of high-performance steel and provides insights into promoting the use of high-performance steel for infrastructural and building construction.

2. Application of High-Performance Steel

2.1. Stainless Steel

Stainless steel, a family of corrosion-resistant alloys of iron containing a minimum of 10.5% chromium (Cr), has been increasingly used in the construction industry due to its desirable material properties, such as corrosion resistance, durability, high strength, fire resistance, low maintenance cost, and aesthetic appearance [5,6,7,8]. Commonly, three families of stainless steel—austenitic, duplex, and ferritic—are grouped based on their main chemical components [9]. Austenitic is the most common type of stainless steel used in industry, while duplex has been increasingly used in building and infrastructure construction owing to its higher strength compared with austenitic and ferritic and good ductility. Figure 1 shows the typical stress–strain curves of these three types of stainless steel.

The applications of stainless steel in building construction date back to the 1930s, when the claddings of the Chrysler Building in the USA were completed in 1930 (Figure 2a) [11]. The recent applications of stainless steel fall on a broad spectrum of civil engineering projects, including the construction of museums (Figure 2b) [12], residential buildings (Figure 2c) [13], floor systems, towers, domes, bridges, and offshore structures (Figure 2d) [14,15]. For instance,

Table 1. Stainless steel in bridges in the last two decades [15,16].

Name, Region, Year	Type of Bridge	Stainless Steel
Moreland Millennium Bridge, South Africa, 2001	Arch bridge	Austenitic 1.4301
Millennium Bridge, United Kingdom, 2001	Tilted box girder arch bridge	Duplex 1.4462
Apate Bridge, Sweden, 2002	Tied beam bridge	Duplex 1.4462
Kungalv, Sweden, 2003	Arch rail bridge	Duplex 1.4462
Pedro Arrupe Bridge, Spain, 2003	Box girder bridge	Duplex 1.4362
Likholefossen Bridge, Norway, 2004	Lightweight bridge	Lean Duplex 1.4162
Viaduct Črni Kal, Slovenia, 2004	Pre-stressed road bridge	Lean Duplex 1.4162
Cala Galdana Bridge, Spain, 2005	Arch bridge	Duplex 1.4462
Arco di Malizia, Italy, 2005	Single arch road suspension	Duplex 1.4362
New Malizia Bridge, Italy, 2005	Arch bridge	Duplex 1.4362
Corte di Piove di Sacco Bridge, Italy, 2006	Dual Arch bridge (Figure 2d)	Duplex 1.4362
Celtic Gateway Bridge, Wales, 2006	Arch bridge	Duplex 1.4362
Meads Reach, Bristol, UK, 2006	Stressed skin arc bridge	Duplex 1.4462
Zumaia Bridge, Spain, 2008	Pedestrian bridge	Duplex 1.4462
The Helix, Singapore, 2009	Tubular bridge	Duplex 1.4462
Sant Fruitos Bridge, Spain, 2009	Arch bridge	Lean Duplex 1.4162
Stonecutters Bridge, Hong Kong, 2009	Cable-stayed bridge	Duplex 1.4462
Second Gateway Bridge, Australia, 2010	Girder bridge	Lean Duplex 1.4162
Nynäshamn Road Bridge, Sweden, 2011	Beam bridge	Lean Duplex 1.4162
Nou Road Bridge, Japan, 2012	Girder bridge	Austenitic 1.4003
Hastings Bridge, USA, 2013	Tied arch bridge	Duplex 1.4362
Story Bridge, Australia, 2015	Cantilever bridge	Austenitic 1.4401/1.4404
Elizabeth Quay Pedestrian Bridge, Australia, 2016	Cable-stayed bridge	Duplex 1.4362 & 1.4462
St. Croix Crossing Bridge, USA, 2017	Cable-stayed bridge	Duplex 1.4362
Queensferry Crossing, UK, 2017	Cable-stayed bridge	Austenitic 1.4401
TRUMPF Bridge, Germany, 2018	Shell bridge	Duplex 1.4462
Hong Kong—Zhuhai—Macau Bridge, China, 2018	Cable-stayed bridge	Duplex 1.4362
Samuel De Champlain Bridge, Canada, 2019	Cable-stayed bridge	Duplex 1.4362
Sheikh Jaber Al-Ahmad Al-Sabah Causeway, Kuwait, 2019	Cable-stayed bridge	Duplex 1.4362
Saint George Bridge, Italy, 2020	Railway bridge	Austenitic 1.4307
Mississippi River Bridge, USA, 2021	Arch bridge	Duplex 1.4410

presents the details of using stainless steel for constructing bridges in the last two decades. Although the initial cost of stainless steel is higher than that of conventional structural steel, the high cost can be compensated by its long life span, low maintenance and repair costs, and corrosion resistance, particularly in adverse environmental conditions. Several studies [15,16] have presented the advantages of using stainless steel in bridge construction.

2.2. High-Strength Steel

Steel with a nominal yield strength of 460 MPa or more (or grade up to S460) has been widely used globally in the design and construction of buildings and infrastructures. The higher grades are usually associated with a higher yield strength and lower ductility (Figure 3). These material properties depend on many factors, including chemical composition, heat treatment, and steel manufacturing processes [2]. The chemical composition of steel can be modified by adding alloys, such as Manganese (Mn), Nickel (Ni), Vanadium (V), and Chromium (Cr). Mn and Ni increase the tensile strength of steel, while V and Cr enhance hardness. The brittleness of high-strength steel depends on the content of Phosphorus (P), Sulfur (S), and Nitrogen (N). Hence, HSS requires a balance between material strength, hardness, and brittleness, which controls weldability by carefully synthesizing different chemical constituents. In the last three decades, such attempts have resulted in higher steel grades (i.e., S690 with nominal yield strength equal to or higher than 690 MPa) with excellent forming and welding properties [17].

Despite the limited international codified design guidelines and long-term design experiences, HSS equal to or higher than S690 has been used worldwide for building and infrastructure construction [19]. For example, S690 was used for the roof steel trusses of the Sony Centre in Berlin, Germany, and the basement columns and roof truss in the Star City in Sydney, Australia. Other applications of HSS include the 980 m span Minato Ohashi Bridge in Osaka, Japan, with lattice girders constructed with steel with a yield strength over 690 MPa, and the 440 m span Tokyo Gate Bridge built with steel with a yield strength over 690 MPa (Figure 4a) [20]. A multi-span composite highway bridge was constructed in Germany with S690 [17]. In another design, a military steel bridge with a span of 48 m in Sweden was built with S1100 and could withstand 1000 crossings of a 65 tons weight armored tank (Figure 4b) [21].

3. Material Properties

3.1. General

Material stress–strain response is vital for understanding the structural responses of cross-sections and structural members, such as beams and columns. The stress–strain response of high-performance steel has been estimated by conducting coupon tests. The knowledge of the stress–strain responses of high-performance steel has facilitated the development of constitutive models.

3.2. Stainless Steel

A wide variety of stainless steel grades can be characterized by a rounded stress–strain response with no definite yield point [13]. Figure 1 shows typical stress–strain curves of the three main stainless steel groups—austenitic, ferritic, and duplex.

Table 2. Experimental investigations of material properties of stainless steel.

References	Family (Grade)	Thickness (mm)
Rasmussen and Hancock (1993) [23]	Austenitic (1.4301)	3
Rasmussen (2001) [24]	Austenitic (1.4301, 1.4435)	2–10
Rasmussen and Hasham (2001) [25]	Austenitic (1.4301)	3
Rasmussen and Young (2001) [26]	Austenitic (1.4301)	3
Gardner (2002) [27]	Austenitic (1.4301)	2–8
Talja (2002) [28]	Austenitic (1.4318, 1.4301)	3
Liu and Young (2003) [29]	Austenitic (1.4301)	2
Gardner and Nethercot (2004) [30]	Austenitic (1.4301)	2–8
Estrada et al. (2005) [31]	Austenitic (1.4301)	3–8
Real et al. (2007) [32]	Austenitic (1.4301)	4–8
Zhou and Young (2007) [33]	Austenitic (1.4301)	2–5
Jandera et al. (2008) [34]	Austenitic (1.4301)	2–4
Becque and Rasmussen (2009) [35]	Austenitic (1.4301)	2
Becque and Rasmussen (2009) [36]	Austenitic (1.4301)	1.2
Theofanous et al. (2009) [37]	Austenitic (1.4401)	2–3
Nip et al. (2010) [38]	Austenitic (1.4301)	3–4
Xu and Szalyga (2011) [39]	Austenitic (1.4301)	2–5
Uy et al. (2011) [40]	Austenitic (1.4301)	1.2–4.8
Afshan et al. (2013) [41]	Austenitic (1.4301, 1.4571, 1.4404)	2–8
Han et al. (2013) [42]	Austenitic (1.4301)	5
Yousuf et al. (2013) [43]	Austenitic (1.4301)	5
Fan et al. (2014) [44]	Austenitic (1.4301)	2–3
Niu et al. (2014) [45]	Austenitic (1.4301)	1.2–2
Cai and Young (2014) [46]	Austenitic (1.4301, 1.4571)	1.5
Rasmussen (2001) [24]	Ferritic (1.4003)	2–10
Lecce and Rasmussen (2006) [47]	Ferritic (1.4003, 1.4016)	1.2–2
Becque and Rasmussen (2009) [35]	Ferritic (1.4003)	1–2
Rossi (2010) [48]	Ferritic (1.4003)	1.5
Manninen (2011) [49]	Ferritic (1.4003, 1.4016, 1.4509, 1.4521)	1.5–3.5
Talja and Hradil (2011) [50]	Ferritic (1.4509)	1–3
Islam and Young (2012) [51]	Ferritic (1.4003)	3–4
Real et al. (2012) [52]	Ferritic (1.4003)	0.8
Afshan et al. (2013) [41]	Ferritic (1.4003, 1.4509)	2–8
Afshan and Gardner (2013) [53]	Ferritic (1.4003, 1.4509)	3
Tondini et al. (2013) [54]	Ferritic (1.4003)	3
Niu et al. (2014) [45]	Ferritic (1.4521)	1.2–2
Arrayago et al. (2015) [10]	Ferritic (1.4016)	3
Talja (1997) [55,56,57]	Duplex (1.4462)	2–6
Rasmussen (2001) [24]	Duplex (1.4462)	2–10
Rasmussen et al. (2003) [58]	Duplex (1.4462)	3
Ellobody and Young (2005) [59]	HSD—High-strength Duplex	1.5–3
Ellobody and Young (2006) [60]	Duplex and lean duplex (1.4462)	3–6
Young and Lui (2006) [61]	HSD—High-strength Duplex	2–3
Zhou and Young (2007) [33]	Duplex (1.4462)	2–5
Theofanous and Gardner (2010) [62]	Lean duplex (1.4162)	3–4
Huang and Young (2012) [63]	Lean duplex (1.4162)	1.5–2.5
Afshan et al. (2013) [41]	Lean duplex (1.4462)	2–8
Saliba and Gardner (2013) [64]	Lean duplex (1.4162)	4–20
Saliba and Gardner (2013) [65]	Lean duplex (1.4162)	6–12
Niu et al. (2014) [45]	Lean duplex (1.4162)	1.5
Cai and Young (2014) [46]	Lean duplex (1.4162)	1.5
Arrayago et al. (2015) [5]	Duplex (1.4462)	3
Cai and Young (2019) [66]	Lean duplex (1.4062, 1.4162)	1.5–3.0

lists the research that contributes to the understanding of the stress–strain (σ-ε) responses of different stainless steel grades achieved by conducting tensile coupon tests in the last two decades. Such extensive knowledge has paved the way for developing constitutive models for various stainless steel grades. Constitutive models are generally developed based on the Ramberg–Osgood formulation [22] (Equation (1)).

$$\epsilon =\frac{\sigma }{E}+0.002{\left(\frac{\sigma }{f_y}\right)}^n$$

(1)

where E is Young’s modulus, f_y is the 0.2% proof stress, and n is a strain hardening exponent, which defines the degree of roundedness of the curve.

An accurate representation of stainless steel comprises precise details of grade-dependent material properties, such as the degree of roundedness, strain hardening, the strain at ultimate stress, and ductility at fracture. Various constitutive models—such as Mirambell and Real (published in 2000) [67], Rasmussen (published in 2003) [68], Gardner and Ashraf (published in 2006) [69], Quach et al. (published in 2003) [70], Hradil et al. (published in 2013) [71], and Arrayago et al. (published in 2015) [10]—have captured different stages of the Ramberg–Osgood formation (Equation (1)).

For example, Mirambell and Real [67] have adopted Equation (1) up to the 0.2% proof stress (f_y) and proposed Equation (2) to predict the strain up to the ultimate tensile stress.

$$\epsilon =\frac{\sigma -f_y}{E_{0.2}}+\left({\epsilon }_u-{\epsilon }_{0.2}-\frac{f_u-f_y}{E_{0.2}}\right){\left(\frac{\sigma -f_y}{f_u-f_y}\right)}^m+{\epsilon }_{0.2} \mathrm{for} \sigma >f_y$$

(2)

where E_0.2 is the tangent modulus at f_y, f_u and ε_u are the ultimate tensile stress and ultimate strain, respectively, ε_0.2 is the total strain at f_y, and m is an exponent representing the second strain hardening effect.

Equation (2) can be simplified by noting the characteristics of excellent ductility in stainless steel materials, where it is assumed that the ultimate plastic strain in terms of the second reference system is equal to the general ultimate total strain as represented by Equation (3) [68].

$${\epsilon }_u\approx {\epsilon }_u-{\epsilon }_{0.2}-\frac{f_u-f_y}{E_{0.2}}$$

(3)

Given Equation (3), Equation (2) can be simplified to Equation (4).

$$\epsilon =\frac{\sigma -f_y}{E_{0.2}}+{\epsilon }_u{\left(\frac{\sigma -f_y}{f_u-f_y}\right)}^m+{\epsilon }_{0.2} \mathrm{for} f_y<\sigma <f_u$$

(4)

And more recently, the values of ε_u, n, and m for different grades of stainless steel were proposed by Arrayago et al. [10].

3.3. High-Strength Steel

Structural steel (hot-rolled) subjected to quasi-static tensile load generally exhibits three stages of typical stress–strain responses (Figure 3). In the elastic range, the slope is linear and is defined as the modulus of elasticity, or Young’s modulus (E). The linear path is limited by the yield stress (f_y), followed by the second stage, a region of plastic flow at approximately constant stress until the strain hardening is reached. At this point, the plateau of the plastic yield ends, and strain hardening initiates. Beyond this point is the third stage, where stress accumulation reoccurs at a reducing rate up to the ultimate tensile stress and the corresponding ultimate tensile strain [72]. Yun and Gardner [72] collected over 500 experimental stress–strain curves of structural steel from the global literature to develop a constitutive model that accurately represents structural steel’s elastic, yield plateau, and strain hardening regions. However, it should be noted that almost all the experimental data are for structural steel with a nominal yield strength of less than 460 MPa due to the limited test data for those with grades greater than S690 (nominal yield strength of 690 MPa). Some exceptions are the ten tests conducted by Wang et al. [73] using S690 and the four tests conducted by Coelho et al. [74] using S690 and S960. In contrast to hot-rolled steel, researchers have conducted tests on tubular sections made of cold-formed carbon steel with a nominal yield strength over 690 MPa, such as f_y of 1341–1405 MPa by Zhao [75], f_y of 1360–1398 MPa by Jiao and Zhao [76], f_y of 845 MPa by Sakino et al. [77], f_y of 740 MPa by Wei et al. [78], f_y of 1100 MPa by Su et al. [79], f_y of 700 and 900 MPa by Cai et al. [80], f_y of 900 and 1100 MPa by Cai et al. [81], and f_y of 1100 MPa by Cai et al. [82]. As shown in Figure 3, a higher strength is generally associated with a lower ductility of the material among different grades of steel. The ductility of high-strength steel is highly relevant in structural design. The minimum requirements of the material ductility for high-strength steel in international design specifications are summarized in

Table 3. Ductility requirements in steel materials with different specifications.

Specifications	Thickness, t (mm)	Ductility
AS/NSZ 4600 (2005) [83]	/	${\epsilon }_{50\mathrm{mm}}$ * ≥ 10%
EN 1993-1-2 (2007) [84]	/	${\epsilon }_f$ ≥ 15%
AS 3597 (2008) [85]	3 ≤ t ≤ 5	${\epsilon }_{50\mathrm{mm}}$$\ge 18\% (f_y$ ≥ 650 MPa)
	5 ≤ t ≤ 65	${\epsilon }_{50\mathrm{mm}}$$\ge 18\% (f_y$ ≥ 690 MPa)
	65 ≤ t ≤ 110	${\epsilon }_{50\mathrm{mm}}$$\ge 16\% (f_y$ ≥ 620 MPa)
	3 ≤ t ≤ 110	${\epsilon }_{50\mathrm{mm}}$$\ge 13\% (f_y$ ≥ 890 MPa)
	3 ≤ t ≤ 110	${\epsilon }_{50\mathrm{mm}}$$\ge 12\% (f_y$ ≥ 960 MPa)
EN 10025-6 (2009) [86]	/	${\epsilon }_f$ ≥ 14% (S690); ${\epsilon }_f$ ≥ 11% (S890); ${\epsilon }_f$ ≥ 10% (S960);
ASTM A514 (2013) [87]	t ≤ 65	${\epsilon }_{50\mathrm{mm}}$ ≥ 18%
	65 < t ≤ 150	${\epsilon }_{50\mathrm{mm}}$ ≥ 16%
ASTM A709 (2013) [88]	t ≤ 65	${\epsilon }_{50\mathrm{mm}}$ ≥ 18%
	65 < t ≤ 100	${\epsilon }_{50\mathrm{mm}}$ ≥ 16%
ASTM A1011 (2013) [89]	0.65 < t ≤ 2.5	${\epsilon }_{50\mathrm{mm}}$ ≥ 12%

Note: * fracture strain based on gauge length of 50 mm.

.

A recent study by Ma et al. [90] proposed a constitutive model for the stress–strain curves of cold-formed high-strength steel with nominal yield strengths of 700, 900, and 1100 MPa based on a series of coupon test results. The typical stress–strain response of cold-formed high-strength steel is similar to that of stainless steel. Thus, the proposed constitutive model closely follows the Ramberg–Osgood formation (Equation (1)), as shown in Equations (5) and (6):

$$\sigma ={\left(\frac{{\epsilon }_p}{0.002}\right)}^{\left(\frac{1}{n_0+K{\epsilon }_p{}^m}\right)}{\sigma }_{0.2}$$

(5)

$$\epsilon ={\epsilon }_p+\frac{\sigma }{E}={\epsilon }_p+\frac{{\sigma }_{0.2}}{E}{\left(\frac{{\epsilon }_p}{0.002}\right)}^{\left(\frac{1}{n_0+K{\epsilon }_p{}^m}\right)}$$

(6)

where ε_p is the plastic strain, n₀ is the original strain hardening exponent calculated as ln(0.2/0.01)/ln(σ_0.2/σ_0.01), m is the exponent for the modified Ramberg–Osgood model as proposed by Ma et al. [90], and K is the modular coefficient in the Ramberg–Osgood expression estimated by using the stress and plastic strain at the ultimate level, as shown in Equation (7), by taking ε_pu as the plastic strain at the ultimate strength, f_u.

$$K=\frac{{\log }_{\left(\frac{{\sigma }_u}{{\sigma }_{0.2}}\right)}\left(\frac{{\epsilon }_{pu}}{0.002}\right)-n_0}{{\left({\epsilon }_{pu}\right)}^m}$$

(7)

3.4. Effects of Material Properties on the Design of Structural Members

Stainless steel and carbon steel exhibit fundamentally different material responses. Stainless steel alloys typically show nonlinear stress–strain behavior at relatively low stress levels with not well-defined yielding point, and significant strain hardening strength beyond the yielding point (i.e., 0.2% proof stress), as already described in Figure 1. Regardless of these differences, most current design codes for structural stainless steel are based mainly on those for carbon steel with limited modifications [91,92,93]. It should be noted that the elastic, perfectly plastic material model has been adopted to design carbon steel structures. The suitability of such material models for designing stainless steel structures is questionable, because their fundamental material responses, such as nonlinearity and strain hardening effects, are not well considered.

In addition, the performance and design of high-strength steel structural members have become complex owing to the advents of new materials and advancements in fabrication techniques. One of the challenges is the lower material ductility associated with the higher strength of steel. As the material ductility of HSS is lower than that of conventional steel, the design rules and equations developed based on conventional steel may not be applicable to the structural design of HSS. This is an obstacle of using HSS in many civil engineering applications due to the lack of international design specifications for steel with a nominal yield strength of more than 700 MPa [84,93,94,95,96].

In the last two decades, significant investigations have been carried out that contributed to the understanding of the structural behavior of high-performance steel members, such as stub columns and beams. These studies facilitate the further development of design guidance, as discussed in the following sections.

4. High-Performance Steel Stub Columns

4.1. General

Stub columns are commonly subjected to laboratory tests to evaluate their structural performance and estimate their cross-section capacity under axial compression. Axial compression is one of the fundamental loading types of structural members. A primary concern of the cross-section classification under pure compression is the occurrence of local buckling in the elastic material range. Generally, Class 1–3 cross-sections reach the yield load, a product of the full cross-section area and material yield strength. Class 4 cross-sections cannot attain the yield load due to the local buckling of slender constituent elements. The test data on steel tubular members have been used to establish a relationship between the compressive resistance of cross-sections and slenderness. The codified cross-section slenderness and laboratory tests of high-performance steel tubular stub columns in the literature are summarized and discussed in the following sections. It should be noted that this review presents the details of rectangular hollow sections (RHSs) and square hollow sections (SHSs), but circular hollow sections of tubular stub columns are not provided due to the availability of data in the literature.

4.2. Stainless Steel

Table 4. Codified cross-section slenderness parameters and limits of stainless steel SHS and RHS.

Code	Slenderness Parameter	Slenderness Limit
ASCE-8-02 (2002) [91]	c/[t$\sqrt{\left(235/f_y\right)\left(E/210000\right)}$]	38.3
AS/NZS 4673 (2001) [92]		38.3
EN-1993-1-4 (2006) [93]		30.7
EN-1993-1-4 (2015) [9]		37.0

presents slenderness parameters and corresponding limits specified in the American Specification [91], Australian Standard [92], and European Code [93]. In Table 4, c is the critical internal compression width; t is the thickness of the tube wall; and f_y and E are the mean yield strength and Young’s modulus of steel. The American Specification (ASCE-8-02) [91] and Australian/New Zealand Standard (AS/NZS 4673) [92] provide similar design rules, with the same slenderness parameter and limit. It is worth noting that the ASCE [91] and AS/NZS [92] provide a design rule for stainless steel with 0.2% proof strength up to 450 MPa, while the design guidelines in the European Code EN-1993-1-4 cover up to 480 MPa [9]. The slenderness limit specified in the ASCE [91] and AS/NZS [92] is 38.3, whereas the limit in the European Code was increased from 30.7 in EN-1993-1-4 (2006) [93] to 37.0 in the latest EN-1993-1-4 (2015) [9].

Table 5. Experimental investigations of stainless steel tubular stub columns.

Reference	Stainless Steel Type	RHS		SHS
		Number	Sections (Depth × Width)	Number	Sections (Depth × Width)
Kuwamura (2003) [94]	Austenitic 1.4301, 1.4318	-	-	12	Min: 80 × 80 Max: 100 × 100
Liu and Young (2003) [29]	Austenitic 1.4301	-	-	4	70 × 70
Young and Liu (2003) [95]	Austenitic 1.4301	8	Min: 120 × 40 Max: 120 × 80	-	-
Gardner and Nethercot (2004) [30]	Austenitic 1.4301	16	Min: 60 × 40 Max: 150 × 100	15	Min: 80 × 80 Max: 150 × 150
Young and Lui (2005) [96]	Duplex and HAS	3	Min: 140 × 80 Max: 200 × 110	6	Min: 40 × 40 Max: 150 × 150
Gardner et al. (2006) [100]	Austenitic 1.4301	4	Min: 120 × 80 Max: 140 × 60	4	Min: 80 × 80 Max: 100 × 100
Theofanous and Gardner (2009) [101]	Lean Duplex 1.4162	2	80 × 40	6	Min: 60 × 60 Max: 100 × 100
Huang and Young (2012) [63]	Lean Duplex 1.4162	4	Min: 50 × 30 Max: 150 × 50	2	50 × 50
Afshan and Gardner (2013) [53]	Ferritic 1.4003, 1.4509	4	Min: 60 × 40 Max: 120 × 80	6	Min: 60 × 60 Max: 80 × 80
Shu et al. (2013) [102]	Austenitic 1.4301	9	Min: 75 × 45 Max: 120 × 60	10	Min: 50 × 50 Max: 100 × 100
Zhao et al. (2015) [103]	Austenitic 1.4301, 1.4307, 1.4404, 1.4571; Duplex 1.4762	2	150 × 100	3	Min: 100 × 100 Max: 150 × 150
Bock et al. (2015) [104]	Ferritic 1.4003	6	Min: 70 × 50 Max: 100 × 40	2	60 × 60

summarizes several studies conducted in the past two decades that investigated the behavior and ultimate strength of stub columns made with different stainless steel grades, cross-sections (SHSs and RHSs), and cross-section dimensions. Figure 5 shows the test setup and local buckling failure mode (as highlighted within the dashed line) of cold-formed lean duplex stainless steel RHS stub columns. The test results have been used to assess the codified slenderness limits for stainless steel SHS and RHS stub columns based on the relationship between the ratio of ultimate-strength-to-yield-strength and the cross-section slenderness parameter. A recent study conducted by Chan et al. [97] on SHS and RHS stub columns of cold-formed stainless steel with 0.2% proof stress greater than 480 MPa found that the slenderness limit specified in the ASCE [91] and AS/NZS [92] is valid, and the limit of 30.7 in EN-1993-1-4 (2006) [93] can be safely adopted. However, their research has shown that such a limit could be increased to 45.5 based on the same slenderness parameters. These are made based on the collected test results, together with the newly generated numerical results. Regarding the new design method, it is worth noting that the continuous strength method (CSM) was developed as a new design method based on a deformation-based approach that provides a constant, rational, and accurate allowance for material nonlinearity due to the spread of plasticity and strain hardening [98]. The advancement of the CSM in terms of designing stainless steel structures, including stub columns, was reviewed by Gardner et al. (2023) [99].

4.3. High-Strength Steel

The European codes, “Design of steel structures—Part 1-1: general rules and rules for buildings” (EN-1993-1-1) [105] and “Design of steel structures—Part 1-3: General rules—supplementary rules for cold-formed members and sheeting” (EN-1993-1-3) [106] suggested the same slenderness parameter and slenderness limit for steel with SHS and RHS sections. The European Code EN-1993-1-12 [84] provides supplementary rules to extend the use of steel with a nominal yield strength of 700 MPa. The American standard “Specification for structural steel buildings” (AISC-360-16) [107] allows the use of high-strength steel with a yield strength up to 690 MPa, and the “North American Specification for the design of cold-formed steel structural members” (AISI-S100-16) [108] provides provisions for the use of high-strength steel with a yield strength up to 450 MPa. The Australian Standard “Steel structures” (AS-4100) [109] was recently amended through AS-4100-A1 [110] with an increase in the nominal yield strength of steel from 450 MPa to 690 MPa.

Table 6. Codified cross-section slenderness parameters and limits of high-strength steel SHSs and RHSs.

Code	Slenderness Parameter	Slenderness Limit
AISC-360-16 (2016) [107]	c/(t$\sqrt{E/f_y}$)	1.40
AISI-S100-16 (2016) [108]	c/(t$\sqrt{E/f_y}$)	1.28
AS-4100 (1998) [109]	c/(t$\sqrt{250/f_y}$)	40.0
EN-1993-1-3 (2006) [106] EN-1993-1-1 (2005) [105]	c/(t$\sqrt{235/f_y}$)	42.0

presents the slenderness parameters and the corresponding limits specified in these design specifications, with symbols the same as those in Table 4.

Table 7. Experimental investigations of high-stength steel tubular stub columns.

Reference	Steel Grade or Yield Strength	RHS		SHS
		Number	Sections (Depth × Width)	Number	Sections (Depth × Width)
Uy (2001) [112]	fy = 750 MPa	-	-	2	110 × 110
Sakino et al. (2004) [77]	fy > 824 MPa	7	-	-	Min: 102 × 102 Max: 336 × 336
Mursi and Uy (2004) [113]	fy > 700 MPa	-	-	4	Min: 110 × 110 Max: 260 × 260
Gao et al. (2009) [114]	fy > 745 MPa	3	Min: 120 × 60 Max: 180 × 90	1	60 × 60
Ma et al. (2016) [115]	S700, S900,	4	Min: 100 × 50 Max: 200 × 120	12	Min: 80 × 80 Max: 160 × 160
Wang et al. (2017) [116]	S690QH, S700MC, S960QC	2	100 × 50	15	Min: 50 × 50 Max: 150 × 150
Cai et al. (2021) [80]	S700, S900	1	100 × 50	7	Min: 80 × 80 Max: 160 × 160

presents the details of experimental investigations of the axial behavior of HSS stub column specimens with a yield strength equal to or greater than 690 MPa. In these studies, the cross-section dimensions were in a range from 60 × 60 to 336 × 336 in mm for SHS and 100 × 50 to 200 × 120 in mm for RHS. A study by Chan et al. [97] found that the existing slenderness parameters and limits (see Table 6) can be adopted for the HSS counterparts (yield strength up to 835 MPa). However, some strength predictions were conservative. In another recent study, Ma et al. [111] concluded that the slenderness limit of 1.40, as specified in AISC-360-16 [107], is appropriate for the experimental and numerical results for HSS with a yield strength up to 1000 MPa, while the limit of 1.28, as recommended in AISI-S100-16 [108], is also safe. Based on these slenderness limits, the effective width methods described by Equation (8) in AISC-360-16 [107] and Equation (9) in AISI-S100-16 [108] can be used with a resistance factor of 0.85 to design steel stub columns. Reliability analyses have confirmed the reliability of the design values.

$$\frac{b_e}{b}=\left\{\begin{array}{c} 1 when \lambda \le 0.673\\ \frac{\lambda -0.22}{{\lambda }^2} when \lambda >0.673\end{array}\right.$$

(8)

where λ = 1.052(b/t)√(f_y/E)/√κ and κ is the plate buckling coefficient. b_e can be calculated as

$$b_e=1.92t_f\sqrt{\frac{E}{F_y}}\left(1-\frac{0.38}{b/t_f}\sqrt{\frac{E}{F_y}}\right)\le b$$

(9)

The implementation of HSS tubular members in seismic engineering is also gaining increasing attention, such as in Li and Wang [117], Li et al. [118], Ferrario et al. [119], Wang et al. [120], Shi et al. [19], and Avgerinou and Vayas [121] among others. Li and Wang [117] showed case studies of HSS structures achieving adequate ductility and energy-dissipation capacity when subjected to earthquakes. Li et al. [118] conducted a numerical simulation to study the compressive behavior of Q690 HSS columns with H- and box-sections, employing a completely numerical analysis technique with experimental verification. The buckling curves for the HSS members and the relevant design recommendations were developed. Ferrario et al. [119] performed an analytical and experimental investigation of HSS circular hollow section members designed to withstand earthquakes for better structural performance and cost reductions. Their study especially examined the performance of concentrical steel bracing as well as the whole frame under seismic loading. Results showed the applicability of using HSS tubular steel columns for non-dissipative elements in concentrical braced frames based on performance-based design approaches. Wang et al. [120] presented an experimental study on the stability capacity of circular HSS tubes (Q690) subjected to axial compression and proposed design methods and recommendations. Shi et al. [19] reviewed a series of studies on HSS advances in China and the existing investigations of the seismic behavior of HSS columns. The performance-based seismic design approach was highlighted for HSS structures. Avgerinou and Vayas [121] explored the cyclic response of seismic-resistant systems with dissipative members of HSS and carbon steel numerically and experimentally.

5. High-Performance Steel Beams

5.1. General

Structural beams are critical for the stability of steel structures. Their capacity is normally governed by their bending capacity, which depends on the beam span. The bending capacity of a beam can be estimated by using the elastic–plastic stress distribution of the beam’s cross-section. As mentioned in Section 4, a perfectly plastic material model may not be suitable for designing stainless steel structures because of the higher initial material cost and strain hardening effects beyond yielding. A stainless steel material model should consider the benefits of strain hardening and limiting deformation and, therefore, should not lead to conservative designs [122]. HSS beams behave differently from those made of mild steel due to high material strength and lower ductility, which lead to smaller rotation and deformation capacities. The following sections discuss the structural performance of SS and HSS beams subjected to bending in a typical four-point bending test (Figure 6).

5.2. Stainless Steel

Designs of stainless steel tubular beams subjected to bending are specified in international codes, such as the American Specification for the design of cold-formed stainless steel structural members ASCE [91] and the Australian/New Zealand Standard for cold-formed stainless steel structures AS/NZS [92]. These codes specify design approaches with the initiation of the yielding and inelastic reserve capacity. In the initiation of the yielding approach, the cross-section moment capacity is estimated by multiplying the effective section modulus with the yielding stress, assuming the first yield occurs at the bending capacity. Calculating the effective section modulus and effective width, accounting for local buckling, relies on an iterative calculation process. For the inelastic reserve capacity approach, moment capacity is determined by the product of equivalent force and moment arm, considering the equilibrium of stresses in the effective section. This approach assumes an ideal elastic–plastic stress–strain curve. The European Code [10] categorizes cross-sections into four classes: Class 1 and 2 sections, assumed to be fully plasticized, Class 3 sections, which first yield across the whole area, and Class 4 of slender sections accounting for local buckling and first yield across the effective area. Over the past two decades, extensive laboratory testing has been conducted on the cross-section bending capacity of stainless steel beams to assess the accuracy and reliability of the codified design rules.

The investigation conducted by Kouhi et al. [123] on austenitic stainless steel RHS beams revealed that the bending strength specified by ENV 1993-1-3 [124] could be conservative by 20–32%. Mirambell and Real [67] studied the flexural performance of stainless steel SHSs and RHSs and compared the results with the values recommended by ENV 1993-1-4 [125]. They found an overestimation of deflections in the codified designs. Zhou and Young [126] compared the experimental data of the bending behavior of different grades of stainless steel beams with predictions by design codes and found the codified strength predictions to be conservative. Ashraf et al. [127] proposed a design method using the cross-sectional deformation capacity to predict the resistance of stainless steel beams. The proposed method is more accurate and less conservative in predicting member resistance than the predictions by the American Specification [91] and EN 1993-1-4 [93]. Recent investigations focus on relatively new ferritic stainless steel and lean duplex stainless steel that are economical but have higher strength than the conventional austenitic stainless steel.

Table 8. Experimental investigations of stainless steel beams subjected to in-plane bending.

Reference	Stainless Steel	RHS		SHS
		Number	Sections (Depth × Width)	Number	Sections (Depth × Width)
Kouhi et al. (2000) [123]	Austenitic 1.4301	2	150 × 100	1	60 × 60
Gardner and Nethercot (2004) [67]	Austenitic 1.4301	4	Min: 60 × 40 Max: 100 × 50	5	Min: 80 × 80 Max: 100 × 100
Mirambell and Real (2000) [128]	Austenitic 1.4301	2	120 × 80	2	80 × 80
Zhou and Young (2005) [126]	Austenitic 1.4301; Duplex	7	Min: 100 × 50 Max: 200 × 110	8	Min: 40 × 40 Max: 150 × 150
Gardner et al. (2006) [100]	Austenitic 1.4318	4	Min: 120 × 80 Max: 140 × 60	2	100 × 100
Theofanous and Gardner (2010) [62]	Lean Duplex 1.4162	2	80 × 40	6	Min: 60 × 60 Max: 100 × 100
Afshan and Gardner (2013) [53]	Ferritic 1.4003, 1.4509	4	Min: 60 × 40 Max: 120 × 80	4	Min: 60 × 60 Max: 80 × 80
Huang and Young (2013) [129]	Lean Duplex 1.4162	8	Min: 50 × 30 Max: 150 × 50	2	50 × 50
Zhao et al. (2015) [103]	Austenitic 1.4301, 1.4307, 1.4404, 1.4571; Duplex 1.4762	2	150 × 100	3	Min: 100 × 100 Max: 150 × 150
Bock et al. (2015) [104]	Ferritic 1.4003	7	Min: 70 × 50 Max: 100 × 40	2	Min: 60 × 60 Max: 150 × 150
Arrayoga et al. (2015) [130]	Ferritic 1.4003	6	Min: 80 × 40 Max: 120 × 80	2	Min: 60 × 60 Max: 80 × 80
Zheng et al. (2016) [131]	Austenitic 1.4301	-	-	4	Min: 70 × 70 Max: 100 × 100
Zhao et al. (2016) [132]	Ferritic 1.4003	1	100 × 40	1	60 × 60

shows some important experimental investigations of stainless steel SHS and RHS tubular beams of different grades and a wide range of dimensions, for example, RHSs with a minimum and maximum of 60 × 40 (depth × width) in mm and 200 × 110 (depth × width) in mm, and SHSs with a minimum and maximum of 50 × 50 (depth × width) in mm and 150 × 150 (depth × width) in mm.

Several cross-section moment capacity models were proposed for austenitic stainless steel. For example, Real and Mirambell (published in 2005) [122] proposed a new method for calculating deflections of beams, considering the material non-linearity. Huang and Young (published in 2013) [129] modified the effective width formula for lean duplex stainless steel (Equation (10)) for internal elements that is suitable for European Code EN 1993-1-4:2006+A1: 2015 [9] and modified the direct strength method (DSM) as shown in Equation (11).

$$\rho =\frac{0.7}{\overline{{\lambda }_p}}-\frac{0.04}{{\overline{{\lambda }_p}}^2}\le 1$$

(10)

where $\rho$ is the reduction factor for local buckling, and $\overline{{\lambda }_p}$ is the element slenderness.

$$M_{DSM}=\left\{\begin{array}{c} M_y \mathrm{for} {\lambda }_t \le 0.776\\ \left(1-0.15{\left(\frac{M_{crl}}{M_y}\right)}^{0.4}\right){\left(\frac{M_{crl}}{M_y}\right)}^{0.4}{M}_y \mathrm{for} {\lambda }_t>0.776\end{array}\right.$$

(11)

where M_DSM is the nominal strength (unfactored design strength), the yield moment (M_y) is equal to S_f f_y, S_f is the gross section modulus, f_y is the yield strength, and λ_l = (M_y/M_crl)^0.5. The critical elastic local buckling moment (M_crl) of the cross-section was obtained from a rational elastic finite strip buckling analysis with a 5 mm half wavelength interval [123]. Recently, the continuous strength method was developed to calculate the bending moment capacity of cross-sections of SHSs and RHSs of different grades of stainless steel as discussed by Zhao et al. (published in 2017) [133] and summarized by Gardner et al. (published in 2023) [99].

5.3. High-Strength Steel

The structural behavior of high-strength steel is different from that of mild steel in many ways. The microstructure and alloying elements of high-strength steel result in a comparable modulus of elasticity, but larger yield and ultimate stresses than mild steel. Moreover, high-strength steel produced with cold-forming has a smaller ductility and no yield plateau (e.g., 0.2% proof stress is typically taken as the yield stress) compared with mild steel. Owing to these differences, the stress–strain relationship of high-strength steel deviates from that of mild steel; thus, high-strength steel designs require modification of the approaches in typical design codes for designing mild steel members. Jiao and Zhao [134] tested 12 high-strength steel beam specimens using the four-point bending test method. The beams were steel circular (not SHS or RHS) tubular beams with a nominal yield strength of 1350 MPa. Up to now, limited research has been available for the structural performance and design of high-strength steel SHS and RHS beams with a nominal yield strength greater than 700 MPa.

Ma et al. [135] conducted a series of four-point bending tests on cold-formed high-strength steel tubular beams in SHSs and RHSs to estimate the slenderness limits. The test results suggest the suitability of the plastic slenderness limit for flanges in BS EN 1993-1-1 [105] and the yield slenderness limit in ANSI/AISC 360-10 (AISC, 2010) [136] for SHSs and RHSs. Ma et al. [137] carried out a comprehensive parametric study using numerical simulations. Based on their findings, they proposed some improvements to the design guidelines (Equation (12)) for high-strength steel beams with yield strength ranging from 700 MPa to 1100 MPa [137].

$$\frac{M_{nl}}{M_{ne}}=\left\{\begin{array}{c}1.5 for {\lambda }_l \le 0.539\\ {\left(\frac{1}{{\lambda }_l}\right)}^{0.657} for {\lambda }_l>0.539\end{array}\right.$$

(12)

where

$$M_{nl}=M_y+\left(1-1/C_{yl}{}^2\right)\left(M_p-M_y\right)$$

(13)

$$C_{yl}=\sqrt{0.776/{\lambda }_l}\le 3$$

(14)

where λ_l is the slenderness factor for local buckling in DSM, M_nl is the nominal flexural strength for local buckling, M_ne is the nominal flexural strength for overall buckling, and it can be replaced by M_y when there is no lateral torsional buckling.

6. Outlook

The future of structural engineering is exciting, as integrated advanced analysis and design and many other developments become the main components of industrial practice [13]. High-performance steels, such as SS and HSS, with their excellent mechanical properties, are likely to become widespread in the future to respond to ever-growing interest in achieving the Sustainable Development Goals. In general, SS and HSS offer many opportunities for innovation in civil and infrastructural engineering. It is necessary to investigate the structural performance of high-performance steel under different loading conditions at the material level, component level, and even system level, to provide design guidelines for stakeholders, code writers, and engineers.

Firstly, it is necessary to investigate the effects of ductility on the structural performance of SS and HSS members (beams, columns, and beam-columns), and connections. As shown in Table 3 and illustrated in Figure 1 and Figure 3, for the ductility requirements of different codes for the different stress–strain curves, directly adopting the design criteria that were originally developed for conventional steel structures under normal design scenarios is questionable. In addition, special design guidelines may be necessary for high-performance steel (SS and HSS) due to different design scenarios, such as seismic and wind loading, impact loading, and fire conditions.

Secondly, the possibility of developing composite structural members by using high-performance steel (SS and HSS) can be explored, i.e., bimetallic steel that is combined with SS and HSS, double-skin of concrete-filled steel tubes with SS as outer skin, and HSS as inner skin and concrete in between. These opportunities can be explored for structural members subjected to axial loading, eccentric loading, pure bending, and their combinations. Furthermore, new research is essential for composite structures with a concrete strength over 100 MPa and steel yield strength over 700 MPa.

Thirdly, high-performance steel (SS and HSS) with open sections, including channel and angle sections, should be investigated as they are widely used in light gauge constructions. Open sections are easier to fabricate than closed ones (SHSs and RHSs). However, failures of these open sections are complicated. For example, members in axial compression may fail by local buckling, distortional buckling, flexural buckling, flexural-torsional buckling, and their combinations. Design rules to cover open sections of high-performance steel under these different loading conditions should be investigated and provided.

Fourthly, the cyclic performance of high-performance steel (SS and HSS) needs to be investigated to estimate its potential applications under extreme conditions, such as seismic conditions. Appropriate designs of high-performance steel structures subjected to cyclic loading conditions will mitigate economic and life losses under extreme loading conditions. Such studies should be conducted at the structural component levels of members and joints and at system levels of 2D frames and scaled frame structures.

7. Conclusions

High-performance steel has been used increasingly for building and infrastructure construction, as it significantly decreases structural member sizes, resulting in reduced resource consumption, less embodied and operational carbon emissions, as well as expedited and cost-effective transportation, material handling, and component manufacturing. Within the broad category of high-performance steel, stainless steel (SS) as well as high-strength steel (HSS) with a nominal yield strength equal to or higher than 690 MPa have been selected in this paper in order to review their applications, material properties, and the structural performance of stub columns and beams owing to their increasing use in various structures.

Duplex and austenitic are the two commonly used SSs for the construction of various types of structures, such as buildings, floor systems, towers, domes, and bridges. Duplex, particularly Duplex 1.4362 and Duplex 1.4462, has been widely used for different types of bridges (e.g., arch bridges and cable-stayed bridges) due to its high strength and good ductility. Similar to SS, HSS with carefully designed chemical compositions to achieve the required strength, hardness, and weldability has been used in various buildings and infrastructures (e.g., roofs and bridges). In the literature, tensile coupon tests have been extensively carried out for different types of SS and HSS (e.g., Austenitic 1.4301, Duplex 1.4462, S690, and S960) of various thicknesses (0.8~20 mm). The literature suggests that the constitutive model for the stress–strain response generally follows the Ramberg–Osgood formulation with specific extensions/modifications for the stages after the 0.2% proof stress.

For the design of stub columns, the slenderness of the column is the key concern, as it directly relates to the occurrence of local buckling. Thus, this paper has reviewed experiments carried out in the literature on the structural behavior of high-performance steel and the acceptable slenderness of the stub columns. It is found that the current slenderness limits adopted in American, European, and Australian standards are also applicable to high-performance steel, but with some adaptations. In the literature, four-point bending tests have been carried out for various high-performance steel tubular beams with rectangular and square hollow sections to investigate their flexural performance. It is shown that commonly used codes for the design of steel beams are conservative for SS members. Based on the existing literature, it seems that the requirements from the codes are suitable for estimating performance and designing HSS beams. Several design equations have been proposed in the literature based on experimental results of four-point bending tests of HSS beams. Finally, this study recommends conducting studies on high-performance steel structures subjected to different design scenarios at their material level, component level, and system level.