Abstract

     As a key component in composite beams, the studs are prone to fatigue failure under reciprocating load. Fatigue problem is more prominent especially under circumstances of concrete cracking, stud corrosion or with initial damage. Therefore, static and fatigue tests are carried out to study the fatigue properties of push-out specimens with initial defects, including stud damage and concrete cracking. The test results show that the damage of stud has a great influence on fatigue life, while the crack of concrete has a little influence on fatigue life. The damage of stud has a greater influence on fatigue performances compared to static properties. In addition, based on the dissipative energy theory and experimental phenomenon, the roles of stud and concrete in the process of stud fatigue failure and their interaction are summarized. The dissipative energy mainly includes the shear plastic strain energy of the stud, the plastic strain energy of concrete under compression after the stud, and the heat energy generated by the friction between the stud and concrete.

Introduction

     Steel-concrete composite beams have become popular in recent years for use in bridge engineering [1,2]. Under the complicated environment and load, there may be some damage to the composite beam. There might be some damage, such as corrosion, fractures of weld leg and longitudinal or transverse cracks in the concrete deck. The static and fatigue behavior of stud connection is sophisticated and affects the design resistance and stiffness of composite beams [3,4]. The damage of the stud and concrete may have a great influence on the shear fatigue performance of the interface.

      Welding defects significantly lower the shear capacity of studs, as is widely known. There are many types of welding defects that might appear, such as inadequate penetration, absence of fusion, and gas inclusion [5]. To determine how the damage location and degree affected the static behavior and shear capacity of stud shear connections, six specimens with identical geometrical dimensions were investigated by Qi et al [6]. The test findings showed that, in comparison to the shear capacity of normal specimen, a loss of up to 36.6 % and 62.9 % of the shank area might cause a falling shear capacity of 7.9 % and 57.2 %, respectively. The push-out test was simulated using mathematics, and the results of the test were used to validate the study. It was shown that even though the area of the stud had significantly decreased, the shear capacity was not affected by the severity of the damage when the damaged part was placed 0.5d (where d is the shank diameter) from the stud root, based on the numerical model.

Conclusions

     Static and fatigue tests were carried out on studs in steel–concrete composite study the effects of initial damage in stud and concrete on fatigue performance. The following conclusions are drawn:

     1.  Compared with nondestructive specimens, the fatigue life of transverse crack and longitudinal crack specimens were reduced by 22 % and 4.9 %, respectively, which is determined by the stress characteristics of the stud. Transverse crack makes the stud easily in a state of bending and shear composite, while longitudinal crack does not

     2.  Compared with the preset cracks of concrete, the damage of stud and weld collar had more influence on fatigue performance, in which the loss of stud section of 62.9 % leaded to only about 10 % of fatigue life. The initial damage of stud accelerates the damage accumulation in the stable fatigue development stage, while the concrete cracking leads to the increase of residual slip in the early stage.

     3. The existing calculation methods of residual slip are not completely applicable to the test results of different stresses, and most of the calculation results are too small, which requires some modification of their coefficients.

Abstract

Introduction

Conclusion

Data Availability

Conflicts of Interest

Acknowledgments

References

Copyright

Abstract

A new type joint of Circular Tubed Steel-Reinforced Concrete (CTSRC) columns was designed in this paper. The structural characteristics, manufacturing process, and mechanical properties of raw materials of the new joint were introduced. In order to simulate the earthquake action, two joint specimens were subjected to low-cycle cyclic loading at the end of the column. Based on the in-depth study of the failure characteristics, load-displacement hysteretic curve, skeleton curve, ductility index, load-strain hysteretic curve in the core area of the joint, energy dissipation performance, strength and stiffness degradation performance, and shear deformation in the core area of the joint during the whole loading process, the seismic behavior of this new type of joint was investigated. The results show that the new joint has reasonable failure characteristics, high bearing capacity, good ductility, excellent seismic energy dissipation performance, and strong resistance to strength and stiffness degradation, which meets the seismic design principle of “strong joint and weak component” and is suitable for the results with special requirements for seismic performance. In addition, preliminary design recommendations were put forward. The research results of this paper can provide a theoretical basis for the application of this kind of new structure.

1. Introduction

At present, steel-concrete composite structure has been widely used in the field of civil engineering construction. Concrete-filled steel tubular column and steel-reinforced concrete column are two main forms of steel-concrete composite structure. The concrete-filled steel tubular column makes the concrete in the tube in a three-dimensional compressive stress state through the circumferential restraint effect of the outer steel tube on the concrete in the tube, so as to improve the concrete strength and the bearing capacity of the structural column [1–3]. Steel-reinforced concrete column refers to the column concrete, equipped with steel, and with a certain stress and structural reinforcement, steel-reinforced concrete column through the synergistic effect of steel and concrete gives full play to the performance of the two materials and at the same time has excellent seismic performance and good economy. At present, it is widely used in high-rise and superhigh-rise buildings [4].

But the shortcomings of the two are also very obvious. The axial load shared by the steel tube and concrete is easy to cause the buckling of steel tube plate, leading to the decline of seismic performance of columns. Steel-reinforced concrete column is not convenient for concrete pouring because of setting steel skeleton and section steel at the same time, and the steel skeleton has insufficient constraints on concrete, which leads to low axial compression ratio limit and cannot make full use of material properties.

Therefore, on the basis of long-term engineering practice, experience accumulation, and previous research results, a new type of composite structure column has emerged: Circular Tubed Steel-Reinforced Concrete (CTSRC) column. Its outer steel tube is disconnected at the beam-column joint and does not pass through the core area of the joint. Therefore, its steel tube does not directly bear the longitudinal load but only restrains the core concrete, as shown in Figure 1. Research by relevant scholars shows that [5–7] the CTSRC column has high compression and shear bearing capacity, superior seismic performance, strong interlayer deformation capacity, good fire resistance, and convenient construction and can make full use of high-strength material performance.

1. Introduction

2. Case study

3. Proposed optimization framework

4. Results of the optimization for the case study

5. Conclusions

References

Steel jacketing (SJ) of beams and columns is widely employed as retrofitting technique to provide additional deformation and strength capacity to existing reinforced concrete (RC) frame structures. The latter are many times designed without considering seismic loads, or present inadequate seismic detailing. The use of SJ is generally associated with non-negligible costs depending on the amount of structural work and non-structural manufacturing and materials. Moreover, this kind of intervention results in noticeable downtime for the building. This paper presents a new optimization framework which is aimed at obtaining minimization of retrofitting costs by optimizing the position and the amount of steel jacketing retrofitting. The proposed methodology is applied to the case study of a 3D RC frame realized in OpenSEES and handled within the framework of a genetic algorithm. The algorithm iterates geometric and mechanical parameters configurations, based on the outcomes of static pushover analysis, in order to match the optimal retrofitting solution, intended as the one minimizing the costs and, at the same time, maintaining a specified safety level. Results of the proposed framework will provide optimized location and amount of steeljacketing reinforcement. It is finally shown that the use of engineering optimization methods can be effectively used to limit retrofitting costs without a substantial modification of structural safety.

Introduction

Steel jacketing is a widely employed technique to improve strength and deformation capacity reinforced concrete (RC) elements presenting critical conditions with respect to seismic and gravity loads condition Steel jacketing of columns is arranged in two possible ways. The first provides a full connection between the steel cage and the slab. In this case, besides the confinement effect, additional flexural strength is provided. For the cases in which full connections are not simple to be realized, steel jacketing is arranged by simply providing the cages. Also in this case a some additional flexural resistance is provided because of friction [1], but the most significant effect is related to the increase of column deformation capacity as consequence of confinement. Experimental and numerical investigations have been carried out by researches for both for the first typology of arrangement (e.g. [2-4]) and for the second one (e.g. [1,6-9]). Despite the effectiveness, it must be also said that steel jacketing is an invasive strengthening technique. In fact, its application to columns provides demolition and reconstitution of portions of masonry infills and plaster. Structural optimization is widely recognized as a valuable computational tool allowing engineers identifying cost-effective design solutions controlling design parameters, and several seismic design optimization applications for steel and RC structures are available in the literature (e.g. [10-17]). At the same time, the issue of the optimization of retrofitting interventions for RC structures has not been investigated many times in the past.

1- Introduction

2- Method of strengthening

3- Numerical modeling

4- Conclusion

References

Abstract

Concrete structures that are influenced by degradation, overloading, the thawing and freezing cycles, abrasive damage, corrosion of reinforced bars, should be repaired or strengthened. Each of those mentioned influences lead to decreasing the load-carrying capacity of the structure or its member. The damaged structure stops to fulfil the serviceability limit states (SLS) and ultimate limit states (ULS). For this reason, the structure has to be strengthened to increase the load-carrying capacity and elongation of remaining lifetime. One of new method for strengthening vertical members (columns of frame structures) is the using fiber concrete layer and utilization its increased tensile strength in comparison to common concrete.

Introduction

Geometry of structures result from architectural solution. In the last decades, the structures of buildings were changing from low wall structures to higher frame structures stiffened with stiffener walls or cores. The load-bearing system consisted of massive main walls in the past, the floor slabs were supported with these massive walls and created a difficult static system. The main goal was to replace massive structures to subtle structures as skeletal structures or concrete frames, which lead to enlarging utility area (Hruban, K., 1950). The columns are very loaded on the edges of the frame structure, where is the highest bending moment and axial load. The exceeding the design values of structure´s/member´s resistance can be by reasons of the design loads exceeding, mechanical damage (due to explosion, impact load, etc.), change of the structure function and so the increasing of considering loads. Aim of this paper is to show possibility of strengthening the columns by fiber concrete. Distribution and orientation of fibers in fiber reinforced composites are essential for the structural performance of elements and structures (Vítek at all, 2017, Rehacek at all, 2014) and using this method we can achieve the optimal strengthening and technological approach.

In this work, a heat pump system in the form of vapor recompression (VRC) is introduced in the dividing wall column (DWC) to further improve its thermal efficiency performance. It is a fact that the temperature difference is reasonably large between the top and bottom of a DWC, which typically produces at least a single side product. This may lead to a very large compression ratio (CR), with which, the operation of VRC in the DWC becomes quite complicated and may not be economically so attractive. To improve this situation, the vapor recompression mechanism is further proposed between the side stream and reboiler drum of the DWC column. Utilizing the latent heat of a vapor stream from an intermediate tray in liquid reboiling of the stripper, this side vapor recompressed DWC (SVR-DWC) configuration can reduce the utility consumption and thus improves its energetic and economic potential substantially. This proposed thermally integrated scheme is finally illustrated by a ternary system.

Introduction

As climate changes and resource crisis have emerged as global threats, the capability to deal with environment and energy issues is indeed an important index in determining the future of the national economy [1]. There are a handful of policies framed at the national and international levels targeting to decrease the emissions of greenhouse gases, reduce the dependency on fossil fuels and mitigate the climate change. In this light, the European Union (EU) has set the goals through the 20-20-20 targets in 2007 with a reduction in greenhouse gas emissions of at least 20% below 1990 levels, a consumption of 20% out of renewable energy sources and an increase in energy efficiency by 20% within 2020 [2]. This work is concerned with the thermal integration that is typically used for improving the energy efficiency. Here, a century old chemical unit, namely distillation column, is selected as a potential candidate that shows a maximum thermodynamic efficiency of 20% [3]. Presently, more than 80% of the global energy demand is met by fossil fuels [4]. In the United States, distillation alone accounts for an about 10% of the total industrial energy consumption. Keeping its large energy demand and low thermal efficiency, several heat integration techniques have been scrutinized seeking lower utility consumption and better profitability. The most popular schemes include the vapor recompression (VRC) [5] heat pump system and the dividing wall column (DWC) [6]. It is observed that [7] the former configuration performs well for the separation of close-boiling mixtures because of the requirement of a low compression ratio (CR) in VRC operation. As far as DWC is concerned, it has been known for several decades since the first patent filed in 1949 [8]. Then Petlyuk et al. [9] have developed a fully thermally coupled distillation column (FTCDC) that consists of a prefractionator and a main column, which is popularly known as Petlyuk column. Actually, the DWC column follows the concept of FTCDC by accommodating both the prefractionator and the main tower in a single shell [10]. It should be noted that the first industrial application of DWC was established by BASF in 1985 [11]. Currently, more than 100 DWC units are being used in industry [11]. Compared to a conventional system with direct or indirect sequence of distillation columns, the DWC scheme can achieve up to 30% savings in capital as well as operating cost [12,13]. Interestingly, this configuration requires a single reboiler and a condenser, whereas for example, a conventional two column system (CTCS) used in separating a ternary mixture requires two reboilers and two condensers. Reducing utility consumption as well as number of equipment (i.e., heat exchangers) leads to lower the capital and operating cost of DWC. This apart, the DWC column can also reduce the installation space up to 40% compared to the conventional sequences [14]. This savings in space requirements is owing to the reduced number of heat exchangers and associated equipment such as pumps, their supports etc. Because of these potential benefits, the DWC has emerged as a promising technology in boosting the thermodynamic reversibility of distillation in the current scenario of competition and environmental concerns.

Polypropylene engineered cementitious composites (PP-ECC) exhibit superior strength and strain hardening under tensile deformation, which is expected to enhance the anti-cracking performance and self-confinement of the plastic hinge region in structural columns. However, there is still a lack of fundamental studies on the compressive behavior of a reinforcement-confined PP-ECC column. This paper presents a proof-of-concept experimental study on the confined PP-ECC column and hybrid normal strength concrete (NSC)-ECC column. Two sets of reinforcement-confined columns were designed: a pure PP-ECC column and a hybrid C30-PP-ECC column. Then, static compression tests were carried out to prove the effectiveness of the confinement in enhancing the peak strength of the hybrid column with respect to pure PP-ECC columns. However, the deformability improvement was not remarkable, with an increase of only 3.2% from samples containing no stirrups to those containing stirrups at a volumetric ratio of 1.6%. An equation was proposed to predict the peak strength of the confined PP-ECC columns. This equation considered the contribution from the tensile capacity of PP-ECC to the circumferential confining effect of the columns. The hybrid column delivered better deformability but smaller peak strength compared with the pure PP-ECC columns. Some mechanical features of the hybrid column were discussed.

Introduction

In recent years, the engineered cementitious composite (ECC) has demonstrated evident advantages for crack resistance and tensile strain hardening [1–4]. Currently, polyvinyl alcohol (PVA) and polyethylene (PE) fibers are commonly used in ECCs. With the application of PVA and PE fibers, the tensile stress and ultimate deformability of an ECC can be larger than 3 MPa and 5%, respectively [5,6]. On the basis of advances with this material, many composite components or structures were developed and investigated to improve the structural deformability and crack resistance [7–9]. Choi et al. [10] reviewed the mechanical properties of ECC and its application in different structural components, such as beam-wall connections, coupling beams in walls, shear walls, and columns. Due to the excellent strain hardening behavior and ductility of ECC materials, these composite structures exhibited better deformability and energy dissipation capacity when used as reinforced ECC columns and ECC beam-column connections. The specimen failed after the ECC was crushed but only at very large deformation. However, the high cost of PVA and PE fibers hinder the large-scale promotion of ECC in practical engineering.

Broadband environmental excitations from wind, ocean wave and earthquakes are especially dangerous for flexible tall structures such as wind turbines, towers or cable-stayed bridges. Liquid Dampers have been studied for almost thirty years in terms of their capability for suppression of vibration in such structures. The work presented in this paper focuses on the Tuned Liquid Column Damper, both open and sealed, and the identification of its time-varying properties of nonlinear damping, frequency and air pressure identification. Experimental tests are conducted on a full scale model of the damper which is subjected to both white noise and harmonic excitation by means of a hydraulic shaker. Exponential decay of the displacement of the liquid column was measured and analysed. The identification procedure was conducted step-wise, first, mode separation with the use of Continuous Wavelet Transform was carried out and then identification of the instantaneous damping ratio for the first mode of vibration was performed. Results indicate that the damping ratio is nonlinear, timevarying and depends on the level of vibration. The air pressure data in the sealed TLCD was also recorded and analysed to reveal the nonlinear nature of the pressure change and the presence of higher odd harmonics.

Introduction

Liquid dampers have been successfully utilized in practise to supress amplitudes of structural vibration under wind, wave and earthquake excitation. The concept of using fluid to stabilize the rolling of ships was developed in the 1860s [1]. This damping technology is known by the name of anti-roll-tanks and widely used in naval architecture [2]. As compared to sloshing [3] or rectangular dampers [4], Tuned Liquid Column Dampers (TLCDs), which dissipate energy by the movement of an oscillatory column of liquid through orifice(s) provided in the cross section of a U-shaped container, have attracted special attention due to their high volumetric efficiency with respect to given amount of liquid, consistent behaviour across a wide range of excitation levels and a damping mechanism that can be quantified in a definite manner. The theoretical concept of the TLCD was developed in [5] and experimentally verified in [6]. Also its nonlinear mathematical description was provided and the relationship between head-loss coefficient and liquid damping validated. Since then, considerable research work has been carried out on the characterization and performance of TLCDs [7–14] including investigations on applicability to control of short period structures, wind turbines and on the impact of soil-structure interaction. Since a TLCD is described by a relatively simple mathematical model, it is amenable for semi-active and active control. Some studies on TLCD, acting as an active vibration damper, were carried out in [15,16]. Experimental study for calculating the effectiveness of semiactive LCD for wind-induced vibration was carried out in [17]. Effectiveness of the semi-active LCD system and the hybrid viscous damper LCD control system for the suppression of wind-induced motion of highrise buildings was examined in [18]. Attempts to achieve enhanced TLCD performance by using Electro-Rheological fluid (ER fluid) or Magneto-Rheological fluid (MR fluid) were presented in [19–21]. Experimental and theoretical investigations on the equivalent viscous damping of structures with TLCD having MR-fluids was carried out in [14,22]. Some researchers considered the vertical limbs of the TLCD to be sealed and utilized the air-spring effects in the sealed U-tube to extend the applicability of the control device to the high frequency range [23]. Sealed TLCDs were also studied for the control of wind induced multi-modal lateral and torsional vibration of long span cable stayed bridges by [24] and for the seismic vibration control of steel jacket platforms by [25]. Previous research studies in the field are related mainly to the design and control aspects of TLCDs. Identification of vibration/modal parameters has attracted much less attention. This is particularly relevant to the identification and characterisation of the time-varying behaviour of these parameters. The present paper aims to model and experimentally identify nonlinear, time-varying damping in conventional TLCDs and nonlinear behaviour of air pressure in sealed TLCDs. The structure of the paper is as follows. Two simple mathematical models associated with the analysed nonlinear behaviour of the TLCD are presented in Section 2. The identification procedure, based on wavelet analysis, is briefly described in Section 3. Experimental work and results are presented in Section 4. Finally, the paper is concluded in Section 5.

1- Introduction

2- Calculation methodology

3- Worked example: design steps using a typical site from the UK

4- Conclusions

References

Abstract

A simplified design procedure for foundations of offshore wind turbines is often useful as it can provide the types and sizes of foundation required to carry out financial viability analysis of a project and can also be used for tender design. This paper presents a simplified way of carrying out the design of monopiles based on necessary data (i.e. the least amount of data), namely site characteristics (wind speed at reference height, wind turbulence intensity, water depth, wave height and wave period), turbine characteristics (rated power, rated wind speed, rotor diameter, cut-in and cut-out speed, mass of the rotor-nacelle-assembly) and ground profile (soil stiffness variation with depth and soil stiffness at one diameter depth). Other data that may be required for final detailed design are also discussed. A flowchart of the design process is also presented for visualisation of the rather complex multi-disciplinary analysis. Where possible, validation of the proposed method is carried out based on field data and references/guidance are also drawn from codes of practice and certification bodies. The calculation procedures that are required can be easily carried out either through a series of spreadsheets or simple hand calculations. An example problem emulating the design of foundations for London Array wind farm is taken to demonstrate the proposed calculation procedure. The data used for the calculations are obtained from publicly available sources and the example shows that the simplified method arrives at a similar foundation to the one actually used in the project.

Introduction

Offshore wind turbines are expected to operate for a lifetime of 20– 30 years, while foundations are often designed for a longer design life. The selection of foundation type and the design is a complex task, which strongly depends not only on the site characteristics, but also on the maturity and track record of different design concepts. As the offshore wind industry is still in an early stage of large scale development, individual projects take a longer time than the rate at which technology advances. As such, it is not uncommon to change the type of turbine and the size/type of foundations during the development phase of a project. Therefore, development consent is typically obtained for a flexible project that allows for optimised detailed design using the most recent technological advances available at the time of final design. Consequently, it is important to have a simplified design procedure that allows for quick design using only limited site and turbine data, and that can be used in the tender design and early design phases of monopile foundations. Naturally, the procedure described in this paper has to be supplemented and refined with more accurate analyses when more information and data about the site conditions (met ocean data, geotechnical conditions) and chosen turbine becomes available. Accordingly, this paper does not aim to provide a methodology for detailed design and optimisation of monopiles but aims to provide a tool for initial design. Most importantly, the paper aims to show the multidisciplinary complex nature of the task. As such, the procedure defines the monopile through a simple geometry that is described by a pile diameter, wall thickness, pile length, and embedded length. Practical issues related to installation and manufacturing are discussed and it may be noted these aspects are beyond the scope of generalised simplified design procedure. However, it is suggested that manufacturing procedures can be taken into account through S-N curves required for typical welds.

In practice various methods are used to demolish structures, ranging from simple ‘brute-force’ type approaches, to highly technical progressive demolition techniques, such as outlined by the JISF (2015). Multiple codes of practice have been produced to assist contractors during demolition [e.g. HK Bldg. Dept. (2004), Indian Standard 4130 (2002)]. Demolition associations have been formed, such as in the UK, USA and EU, to try assist demolition contractors and regulate the industry. However, these guidelines, codes and organisations typically only provide construction related guidelines without giving information to assist structural engineers who have to ensure that structures remain safe during the demolition process. Minimal research has been conducted and literature published up to this point on predicting the load capacity of weakened structures (van Jaarsveldt and Walls 2016). The techniques and analysis methods used in industry rely primarily on experience obtained from previous projects, and are less focused on strict theoretical principles, although some practitioners may use simplifed design equations. It is necessary that sound engineering and scientifc principles be applied to this problem to produce verifable and safe design techniques. Furthermore, with safety requirements becoming much stricter worldwide, contractors may now be required to show by calculation that their procedures are safe, which currently cannot easily be done. One of the most efective methods available for demolishing structures involves the pre-cutting of steel columns of a structure at a certain height, using diferent types of cuts. This weakens the columns of the structure so that the least efort can be used to demolish the structure by means of pulling out some of the columns or by using explosives (NDA 2014). The pre-cutting of the columns is done manually, which causes this method to have safety implications. If a structure has been weakened too much it could collapse during the weakening process (Walls 2017). Conversely, if a structure has not been weakened enough it will not collapse when required, leading to a partially collapsed structure, which is also a very dangerous scenario. This paper will focus on determining the capacity of weakened columns through experimental testing and fnite element modelling. 2 Background Steel structures are demolished for diferent reasons, such as: removing buildings that have been damaged by fre or other events, to make way for new developments, or because buildings are no longer safe to use (NDA 2014). The demolition video screen-shots in Fig. 1 illustrate a furnace structure that was demolished by Jet Demolition (Pty) Ltd. For a detailed description of the collapse mechanism refer to Walls (2017). The structure was weakened through applying pre-cuts to the columns and the beams, as shown in Fig. 1a. However, the furnace can be seen to remain in its original position, whilst demolition staf were operating in the area. The middle columns of the structure were then pulled out using steel cables as shown in Fig. 1b. This caused the structure to fail as seen in Fig. 1c. This process illustrates one of the current industry approaches used for the demolition of steel structures.

I-section steel columns have been widely used in steel structures due to their unique advantages of simple production process, uniform texture, light weight, high strength, perfect ductility and toughness, however steel structures are poor in resistance of fire or high temperature. In the past decades, mechanical behaviors of the steel column after fire or in fire have been extensively studied by different researchers. Tondini et al. [1] carried out a series of tests on samples of high-strength steel circular columns at elevated temperatures. Kervalishvili and Talvik [2] studied the stability of axially loaded steel columns with square hollow sections in fire and developed an alternative approach to calculate its buckling. Yang and Yang [3] used experimental methods to investigate the effect of the load ratios, weld details, and the width to thickness ratios on the fire behavior of welded steel box columns. Fan et al. [4] performed the fire test on eight square sections of stainless steel columns mainly to investigate the effects of the section dimension, load ratio, and eccentricity on the fire performance of the stainless steel column. The test results show that eccentricity and load ratio are the key factors for fire performance of the stainless steel col umn. Feng et al. [5] conducted an experimental study on 52 cold-formed thin-walled short steel channel columns at high temperatures to study the physical behavior and failure modes of this type of columns. Cheng et al. [6] presented a numerical investigation on the buckling behavior of channel-section columns. Scullion et al. [7] performed an experimental study on behavior of elliptical section steel columns in fire. Yang et al. [8] conducted a series of H steel columns under fire load. The tests results show that the slenderness ratios of steel columns and width-to-thickness ratio of steel plates are two key factors linked to global buckling of columns and local buckling, respectively. Yang and Hsu [9] conducted a series of experiments to examine the effect of the slenderness ratio of steel columns, the width-to-thickness ratio of flanges, and residual stresses on the ultimate strength of H steel column at elevated temperature. Ragheb [10] developed an inelastic stability model to investigate the local buckling performance of structural steel I-section columns at high temperatures. On the basis of this model, effects of several parameters on the local buckling capacity of steel I-section columns were also investigated. In order to study the effect of stiffness of the surrounding structure on steel I-section columns at elevated temperatures, Correia and Rodrigues [11] conducted a great many fire resistance tests. The results showed that the column’s critical temperature did not reduce with increasing of the stiffness of the surrounding structure. It was also found that the higher initial load levels in fire resulted in shorter critical temperatures of the steel columns. All these researches as above are investigating the mechanical properties of steel column in fire.

Global buckling tends to occur in compressed steel columns when they are slender. However, the buckling resistance can be drastically improved by introducing stays and crossarms. The compressed steel column, which is equipped with stays and crossarms, has been named prestressed stayed steel columns (PSSC). In the PSSC shown in Fig. 1, an additional restraint can be placed on the main column by the crossarms in conjunction with pre-tensioned stays. Research on PSSC has been conducted since the 1960s, in which Chu and Berge first investigated the critical buckling loads in PSSCs [1]. Following the work of Chu and Berge, Hafez quantitatively examined the effect of pretension on the buckling load by theoretical derivation based on the assumption of small deformations [2]. With the development of computer technology, particularly over the last twenty years, nonlinear buckling analysis in PSSCs by finite element (FE) software became possible. Thus, geometric imperfections governing nonlinear buckling [3–5], evaluate the post-buckling behaviour [6,7], and investigate the optimum design method can be conducted numerically [8,9]. Experimental studies have also been conducted in parallel with FE analyses on PSSCs [10–14]. For practical application of PSSCs, the compressed steel columns are generally stiffened by spatial crossarm systems (see Fig. 2) around the main column and multiple crossarms along the main column length (see Fig. 2(b)). Unfortunately, most of the previous studies concentrated on investigating PSSCs with crossarms only set at the mid-span of the main column (see Fig. 2(a)), which are not typically found in practice. As far as the authors are aware, references [15, 16] are the only studies aimed at investigating the stability of PSSCs with multiple crossarms. However, the interactive buckling behaviour of PSSCs with multiple crossarms has not been investigated. In fact, research on PSSCs with single-bay crossarms shows that interactive buckling may become dominant when determining the actual buckling strength. Based on the background information introduced above, this current work focuses on investigating the stability of PSSCs stiffened with multiple crossarms along the main column length. First, pretension was derived by geometric analysis, which corresponds to the maximum critical buckling load. This pretension level was used as the benchmark pretension value in the FE simulation. Subsequently, critical and nonlinear buckling analyses were conducted to explore the buckling strength of PSSCs stiffened with multiple crossarms. In addition, a discussion based on parametric analysis results was presented to quantitatively examine the effect of cross-sectional area of the stays and pretension in stays.

Cold-formed steel is an efficient, economic, and environment-friendly building material with a reasonable section shape, good mechanical properties, and high steel utilization. Cold-formed steel possesses promising application prospects in the modern construction industry [1]. Currently, considerable research has mainly focused on cold-formed steel columns with thin walls. Relative systematic standards and guidelines for cold-formed steel columns with thin walls are issued [2–7]. The demands for cold-formed steel columns with thick walls have increased gradually with the development of cold-formed technology and large engineering construction. With the development of cold -formed steels, the height and thickness of cross-section of cold-formed thin-walled rectangular steel columns has reached 800 mm and 22 mm respectively, which have been used in the Tianjin Wanhui Square Project in China (Figs. 1–2). However, few studies have referred to the mechanical properties and the design method of large-section cold-formed steel columns with thick walls. Wen conducted an experimental study on the axial bearing capacity of short cold-formed steel columns with wall thickness ranging 7.5–16 mm [8]. Li discussed the reliability of an axial compression member with 8–12 mm thick cold-formed steel columns [9–11]. Chen investigated the ultimate bearing capacity of cold-formed rectangular steel columns with 8–9 mm thick walls [12]. Liu examined the axial compression performance of cold-formed rectangular steel columns with 22 mm thick walls [13]. The previous research on cold-formed thin-walled and thick-walled section steel found that the cold hardening effect is intensified as the thickness increases; where the strength increases by 4% to 34% for thinwalled rectangular steel tube (0.4–6 mm thick) [14–16], but increases by 8% to 41% for thick-walled one (6–16 mm thick) [10,17–20]. For thin-walled cold-formed steel tube made by direct method, the yielding strength in the corner part is 30%–55% higher than that in the flat part, especially when the width-to-thickness ratio is large [10,14–16,19]; the strength of cold-formed member made by direct method is 6%–20% higher than that by indirect method [13,17]. Similar to rolled steel, the cold-formed steel also would experience different failure modes (overall buckling or local buckling) due to different slenderness ratio and width-to-thickness ratio [8,12,21,22], and the local buckling mainly occurred to the welding parts [19,11]. As the thickness grows, the material strength and the cold hardening effect increase, the yielding strength increases by 16%–41% compared to base metal [19,11]. The previous numerical studies for cold-form steel members was usually used FEM analysis, which considering the initial imperfection, material nonlinearity and geometric nonlinearity [5–7,13,14,23]; however, few research concerned about residual stress. The residual stress had some effect on the bearing capacity of cold-formed rectangular steel tube, for example the load bearing capacity would decrease by about 7% and the member would experience earlier failure [12,24–26].

Elastic buckling properties of thin-walled storage rack columns under compression, e.g., critical buckling loads, are often the input parameters for analytical design solutions (e.g., the direct strength method in AISI_S100 2016). This paper deals with the accurate estimation of the elastic buckling properties of Σ-shaped rack sections with patterned holes. The investigation of the elastic buckling behaviour of three different Σ-shaped rack sections (with and without patterned holes) under compression is presented. More than 4000 finite element simulations were performed on these rack sections using the finite element program, ANSYS 18.1. The influences of the holes, perforation pattern, number of buckling half-wavelengths, and boundary conditions on the section’ buckling behaviour were studied. An alternative method is proposed to generate signature curves for solid rack sections, and its effectiveness has been tested to generate signature curves for perforated rack sections. Multihalf-wavelengths method is proposed to determine the critical buckling loads and critical buckling half-wavelengths of perforated rack sections, which has been proved to be unbiased and accurate. The results show that by considering the holes, the critical buckling loads of the rack sections decreased while the critical buckling halfwavelengths increased. The alternative method failed to generate the signature curves of perforated rack sections accurately since the shape functions used for describing the shapes of buckling modes of perforated rack columns are significantly different from those used for solid rack sections.

Introduction

Rack columns are generally made of thin-walled steel sheets, and the steel sheets are cold-formed into the desired sections of the columns. The columns are used to form the upright frames of a storage system and serve as compression members. To simplify the assembly of the upright frames and make the intervals of shelf panels adjustable, holes are often made at webs or flanges of rack columns along the length uniformly. Most rack columns have open and singly symmetric cross-sections. It imposes difficulties on structural designers for designing such columns, especially for perforated rack columns. This is because multiple buckling modes need to be considered for rack columns in the design. The common buckling modes of Local (L), Distortional (D), Torsional + Flexural (TF), and Flexural (F) buckling are shown in Fig. 1, and their definitions are given in the AISI_S100 [1]. The flexural buckling mode around the strong principal axis of the rack section is not available since the flexural buckling modes around the strong principal axis are always accompanied by torsional buckling mode due to the singly symmetric cross-section. TF and F buckling usually jointly termed as Global (G) buckling.