Time history comparative analyses of a thin-walled cold-formed steel structure considering P-D effect

The paper presents a comparative time history analysis based on the 1D-beam Finite Element Method (FEM) for a thin-walled cold-formed steel structure previously investigated both theoretically and experimentally. The recent earthquake which occurred in Turkey with 7.8Mw and a Peak Ground Acceleration (PGA) of almost 0.5g showed numerous collapses of different types of buildings. Romania has an active seismic area located in the Vrancea region where, in 1977 a 7.5Mw earthquake also occurred. In this context, this paper presents a comparative analysis with time history accelerograms of the recorded earthquake in North – South and East - West directions. The structural model was analyzed in Robot Structural Analysis software in two scenarios of the time history accelerograms considering also the P-Δ effect. The finite elements of the structure were defined as 1-D beam elements with hinged joints and limited axial stiffness previously obtained in past studies. The results showed a substantial increase in terms of displacements and stresses.


Introduction
Researchers worldwide are continuously studying how civil engineering structures respond to seismic movements.In addition to ensuring safety and minimizing damage, buildings must also become sustainable, meaning they should achieve maximum performance with minimal material consumption.Although seismic design codes such as EN 1998-1 [1] and the Romanian code [2] provide extensive guidance on the seismic design of steel structures, they categorize cold-formed steel structures (CFSS) as having limited ability to dissipate seismic energy.As a result, further research is needed to fill the informational gap and provide accurate information on CFSS.
Some researchers [3][4][5][6][7][8] have explored different methods to enhance the seismic performance of thinwalled steel structures.For example, adding supplemental damping devices or using special shapes and configurations have been explored to improve the seismic performance of these structures.Additionally, various numerical simulations [9] and experimental studies [10][11][12][13] have been organized to better understand the behaviour of thin-walled steel structures under seismic loads and to develop reliable analytical models to predict their response to earthquakes.Overall, research in this field aims to improve the design and construction of steel structures to ensure their safety and sustainability in earthquakeprone regions.
Based on previous work [14][15][16] the research presented in this paper focus on the structural response of a structural skeleton made of C shape thin-walled steel profile.The structural system depicted in Figure 1 utilizes a framing approach with truss-like diagonal elements situated in the peripheral panels.The structure was tested in the past on the shaking table in two scenarios of gravitational loading.The model was numerically analysed and calibrated using experimental data.In the context of the recent catastrophic earthquake which has produced in Turkey in 2023, a time history linear and nonlinear analysis was conducted in comparison with the 1977 Vrancea earthquake that occurred in Romania.Both analyses consider an additional P-D effect so the obtained results show an important influence of the model approach.

. Materials and methodology
Table 1 provides information on the material properties of the steel sheet and connectors.The steel sheet used to create the steel profiles through cold-forming was DX51D+Z.The framing elements were connected using Self Tapping Screws (STS) measuring 4.8×22mm, while the wall frames were connected to each other using Self Drilling Screws (SDS) measuring 5.5×25mm.Additionally, diagonal elements were connected using 4.8×16mm SDS.The material properties of the steel sheet were determined experimentally by performing direct tensile tests on specimens taken from the profile web.[17] 4.8x16 mm 210 300 [18] 500 [18] SDS -for panel joints ISO 15481 class (5.6) [17] 5.5x25 mm 210 300 [18] 500 [18] STS -for profile joints ISO 7049 class (5.6) [19] 4.8x22 mm 210 300 [18] 500 [18] Cold forming is a metalworking process in which steel is shaped at room temperature, rather than heated and then shaped as in traditional hot forming processes.Thin-walled steel profiles are frequently used in construction and manufacturing because of their high strength-to-weight ratio, and cold forming is often used to shape these profiles due to their efficiency and cost-effectiveness [20][21][22].The process of cold-forming C shape thin-walled steel profiles typically involves feeding a coil of steel through a series of rollers that gradually shape the steel into the desired profile.This process is also known as roll forming.The rollers are often custom-designed to produce the specific profile required, and the process can be highly automated to increase efficiency and reduce labour costs [23,24].
Cold-formed steel profiles have a number of advantages over hot-rolled profiles, including better dimensional accuracy, lower material cost, and improved consistency of properties [25,26].However, there are also some limitations to cold-formed steel, including a reduced capacity to resist lateral torsional buckling and lower ductility at low temperatures.In order to ensure the quality and high structural performance of cold-formed steel profiles, it is important to follow appropriate design and manufacturing guidelines.These guidelines may include specific tolerances for dimensions, recommendations for the use of stiffeners or other reinforcement, and guidelines for the use of appropriate fasteners and connections.
The manufacturer of these type of structures [27] can produce light steel structures made of galvanized steel.Prefabricated "U" and "C" profiles for steel structure houses, steel structure industrial buildings.

Numerical modelling of the building
There are two commonly used approaches to numerically model Cold-Formed Steel (CFS) structures that aim to replicate the actual behaviour of the structure with precision.The first approach, which is commonly referenced in scientific literature, involves employing 2D or even 3D elements with nonlinear material behaviour.While this method produces very accurate results, it is costly in terms of hardware and simulation time, particularly for intricate structures.[28][29][30][31][32][33][34].
The second approach, as presented in design codes, considers that the joints in CFS structures are the most susceptible components.Hence, numerical investigations must account for the second-order effect and actual stiffness of the joints, which can be determined through laboratory testing.In this paper, the numerical models consist of linear and non-linear models with joints that are either infinitely rigid or semi-rigid, where the latter's rigidity may either be constant or exhibit a parabolic variation.
By utilizing previously published findings and incorporating results from cyclic tests conducted on T-joints, a finite element structural model based on 1D-beam pin-connected elements presented in Figure 2 and 3 were employed to simulate the behaviour of the structure when subjected to time history accelerograms in the Robot Structural Analysis software [35].The connections of the beam elements are considered linear with joints defined with axial elastic stiffness kx=2300 N/mm.The model rests at the base on pinned and simple supports.The load cases and load values selected according to Romanian design codes are presented in Table 2.These were combined also according to CR 0-2012 Romanian code [36].

Case
Name Uniformly surface-distributed load q (kPa) According to code A time-history analysis is one of the methods used to evaluate the seismic response of cold-formed steel buildings.The time-history investigation involves the use of a ground motion record for a building model to determine the response of the building to seismic forces.Assessing the seismic response of cold-formed steel buildings using time-history analysis is a challenging process that encompasses various factors, such as the seismic hazard present at the site, the building's design, the steel's material properties, and the modelling techniques employed to simulate the building's behaviour.The precision of the analysis relies on the quality of the input data, including the ground motion record and building properties.Moreover, modelling techniques employed to replicate the building's behaviour should be authenticated against experimental data to verify the credibility of the results [38][39][40][41][42][43][44][45].
The input data used for the time history comparative analysis presented in Figure 4 of this paper were sourced from the Engineering Strong Motion database (ESM), a compilation of accelerometric data recorded in Europe and the Middle East since 1969 [46,47].The accelerograms used were defined as follows in Table 3.

Results and discussion
From the numerical analyses, the following results were observed and compared.Table 4 presents: modal analyses result with fundamental frequencies, mass participation factor, total mass, pulsation, and damping.The first two modes of vibration are translational in X and Y directions.The deformed shapes of vibration are presented in Figure 5. Figure 6 presents de maximum absolute displacement in the case of Vrancea 77 -time history analysis and Figure 7 the maximum absolute displacement in the case of Vrancea 77 considering the P-∆ effect.Also, the maximum absolute displacements for Turkey 2023 accelerograms are presented in Figures 8 and 9 with P-∆ effect.In terms of stress in structural elements, figures 10-13 present maximum and minimum principal stress for the mentioned time history analyses.In figure 14 are presented the comparative graphs for the absolute maximum displacements and maximum principal stresses attained from the analyses.In the case of Vrancea _77 seismic action the maximum absolute displacement is approximately 13 mm and is very close to the maximum acceptable displacement as per seismic design codes [2].In the case of the same action but considering the P-∆ effect, the maximum displacement was 21.79 mm which means an increase of displacement by 59%.In the case of Turkey_2023 seismic action, the maximum displacement was 33.63mm while the P-∆ effect led to an increase of 151% the maximum absolute displacement being 84.41mm.In terms of stress, the maximum principal stress obtained from the analyses, are compared and graphically presented in figure 14 b.The comparative graphs show that the maximum principal stress have a value of 105 MPa being smaller than the yielding strength of the material which is 120 MPa.Considering the P-∆ effect for the same seismic action the maximum principal stress increase by 57% resulting in a value of 165 MPa, greater than the yielding strength of the material but smaller than the ultimate strength which is 250 MPa.In the case of Turkey_ 2023 seismic action, the maximum principal stress was located in the same element but with a value of 264 MPa, while the P-∆ effect leads to an increase of the maximum principal stress by 100% than the model without a second-order effect.

Conclusions
The paper presents a comparative Time-History numerical analysis of a structural skeleton system made of thin-walled steel profiles with DX51D+Z steel.The structure was previously tested on the shaking table and the numerical model was calibrated using experimental data.The numerical model considers the limited axial stiffness of the 1-D beam elements in joints.The recorded actions of the earthquakes were chosen as a reference for the seismic areas of Romania and Turkey.
The analyses were completed considering the P-∆ effect as separate cases.So, it was observed that in the case of Vrancea_77 seismic action combined accelerograms for N-S and E-W direction, the maximum displacement and maximum principal stress are acceptable in comparison with the design code allowable values.In the case of Turkey_2023 seismic action the maximum allowable values for displacements and strength were considerably exceeded.The P-D effect leads also to a greater value of displacements and stresses for both seismic actions Vrancea_77 and Turkey_2023.
To reduce the displacements values and stress distribution for the structural skeleton there are two possibilities that can be verified in future numerical analyses: the first one consists in adding additional diagonal and other vertical profiles, and the second one consists in adding additional connectors in joints to increase the overall stiffness.These analyses must be followed by a future study where the structural steel profile skeleton will have also claddings that are basically made of OSB panels.The presence of the OSB panels influences both the overall rigidity and the stress distribution in the structural skeleton.

Figure 1 .
Figure 1.The structural skeleton made of C shape thin-walled steel profile was experimentally tested on the shaking table 2. Materials and methodology

Figure 4 .
Figure 4. Recorded and processed accelerogram of the North -South and East -West direction of the Vrancea 7.5 Mw, Romania 1977 earthquake and 7.8 Mw Turkey 2023.

Figure 14 .
Figure 14.Comparative graphs: a -maximum absolute displacements; b-maximum principal stress .1088/1757-899X/1304/1/012014 13 design code.The basics of construction design [37] European Committee for Standardization 2002 Eurocode 1: Actions on structures -Part 1-1: General actions -Densities, self-weight, imposed loads for buildings EN 1991-1-1 [38] di Lorenzo G and de Martino A 2019 Earthquake response of cold-formed steel-based building systems: An overview of the current state of the art Buildings 9 [39] Schafer B W, Ayhan D, Leng J, Liu P, Padilla-Llano D, Peterman K D, Stehman M, Buonopane S G, Eatherton M, Madsen R, Manley B, Moen C D, Nakata N, Rogers C and Yu C 2016 Seismic Response and Engineering of Cold-Formed Steel Framed Buildings [40] Abhishek C and Shelke N 2019 Comparative study of time history analysis of cold formed steel frame International Journal of Advance Research, Ideas and Innovations in Technology 5 236-40 [41] Leng J, Buonopane S G and Schafer B W Seismic Modeling and Incremental Dynamic Analysis of the Cold-Formed Steel Framed CFS-NEES Building [42] Hancock G J 2016 Cold-formed steel structures: Research review 2013-2014 http://dx.doi.org/10.1177/136943321663014519 393-408 [43] Dubina D 2008 Behavior and performance of cold-formed steel-framed houses under seismic action J Constr Steel Res 64 896-913 [44] Dubina D 2008 Structural analysis and design assisted by testing of cold-formed steel structures Thin-Walled Structures 46 741-64 [45] Leng J, Schafer B W and Buonopane S G Modeling the seismic response of cold-formed steel framed buildings: model development for the CFS-NEES building [46] Puglia R, Russo E, Luzi L, D'Amico M, Felicetta C, Pacor F and Lanzano G 2018 Strong-motion processing service: a tool to access and analyse earthquakes strong-motion waveforms Bulletin of Earthquake Engineering 16 2641-51 [47] Engineering Strong Motion Database ESM

Table 4 .
Modal analysis results