Quasi-static responses and associated failure mechanisms of cold-formed steel roof trusses
Introduction
Cold-formed steel (CFS) roof trusses are often used as an economical framing option in industrial and residential buildings. Unlike Open Web Steel Joists (OWSJ) and wood roofs, these light-gauge steel trusses are versatile, non-combustible, and can be fabricated into limitless ceiling profiles. The conventional design follows the American Iron and Steel Institute (AISI) document “Design Guide for Cold-Formed Steel Trusses” where information about the minimum strength and serviceability requirements are provided [1].
Past researches [2], [3], [4], [5] focused on investigating the strength and ultimate capacities of the CFS trusses under static concentrated and uniform loads. Wood [4] and Wood and Dawe [5] performed twenty-three small-scale and ten full-scale experiments to explore the ultimate capacities of CFS trusses. Results from their research showed that the predominant failure mechanism was the local buckling of the top chord adjacent to the heel plate with distortion of the heel plates in instances where the plates were inadequately stiffened. Previous research [2], [3], [4], [5] did not fully capture the inelastic behavior of CFS truss systems due to termination of experiments at the point where instability occurs or sever buckling is observed.
Investigating the performance of CFS roof systems under non-conventional loads is a challenging problem due to the limited information exist about the inelastic behavior of these systems under high levels of deformations. Such information is essential when using the Single Degree of Freedom (SDOF) technique to analyze structural members under severe load effects [6]. Another difficulty to assess the performance of CFS roof trusses is their nonstandard profiles nationally. Each manufacturing company designs unique truss systems with their standard CFS sections.
Brian et al. [7] have examined the process of analyzing CFS trusses for a case study of a DoD project that required CFS roof trusses as the best economical option for a sloped roof profile. The study showed that many assumptions were used in the process to analyze CFS roof system using the Single Degree of Freedom (SDOF) technique to eventually determine an equivalent static blast load incorporated into the delegated design performance specification for the CFS trusses. In this study [7], a finite element analysis was used to consider the global response of the roof system and to check for the localized modes of failure.
Jones et al. [8] proposed two rational design methods for designing Cold-Formed Steel Trusses (CFST) under blast loads. The first method is a simplified elastic design method that is adequate for a preliminary conservative design for higher levels of protection where inelastic deformation is minimized or not allowed. Jones et al. [8] recommended using the extraordinary events load case in Section 2.5 of ASCE7-10 [9] where the extraordinary event, in this case, will be the factored equivalent static blast load for the simplified elastic design method. The other proposed design method is the inelastic SDOF method where some levels of deformations will be accepted in the truss [8]. With the lack of blast design guidelines for CFST, reasonable assumptions related to truss stiffness, mass, and resistance were used throughout the SDOF inelastic method [8]. In 2018, Weaver et al. [10] have published the results of several field blast tests on CFS roof truss modules of 11 m by 11 m. Weaver et al. [10] recommended the careful design of CFS roof trusses to balance truss member strength and truss connection strength to ultimately obtain ductile failure modes.
To investigate the response of CFS trusses for blast analysis purposes, trusses need to be tested to ultimate failure to identify their blast resistance and be able to determine the different response limits associated with different damage levels. In general, the resistance of a structure is a quantifiable measure of the integrity of a system subjected to blast loading. It is characterized as the internal force which restores the structural member to its unloaded static position [6]. CFS members are particularly susceptible to flexural (member) buckling as well as localized buckling. When buckling occurs, a large amount of energy is released causing a drop in the resistance of the member. The progression and ultimate mode of failure of a specimen play a significant role in the resistance of the structure. While both modes of buckling result in a decline in the member’s resistance, the reduction associated with local buckling is categorically less than that of member buckling [11]. For blast analysis purposes, the post-buckling response of the specimen needs to be examined especially, if some deformations will be permitted in the design.
One of the most widely used techniques for blast analysis is the SDOF technique. One important input for this methodology is the static resistance of the analyzed structural component. More details about SDOF method can be found in [6]. The main objective of the research presented in this paper is to help provide guidance on analyzing CFS truss performance under explosions using SDOF technique by exploring the full static resistance experimentally and numerically using finite element models.
Section snippets
Quasi-static testing of CFS roof trusses to ultimate failure
Collaborating with Aegis Metal Framing to evaluate their trusses’ quasi-static performance needed as input for further blast load analysis. Two truss profiles were selected by Aegis Metal Framing. The company used their software to design the trusses under conventional loading conditions. Five small-scale 3 m (10 ft) long trusses with different profiles were built in the Remote Testing Facility (RTF) at the University of Missouri-Columbia. Specimens’ specifications are given in Table 1. Fig. 1
Quasi-static experimental results
Each truss profile was tested under a single loading point at the center and two loading points applied at top chord joints as shown in Fig. 5. The test matrix is provided in Table 1. Load-displacement relationships for the five specimens are given in Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10 where data collected from each stringpot is given for each truss specimen. Stringpots 1 and 4 are placed at 0.686 m (27″) from the end connections while stringpots 2 and 3 are placed at third points of the
Finite element simulation of quasi-static CFS truss behavior
ABAQUS [14] was used to simulate the quasi-static testing of CFS roof trusses. A previous research study was conducted on the end connections of CFS roof trusses to predict their energy absorption capacities [15]. The study included quasi-static testing and simulation of CFS trusses end connection under horizontal and vertical loads to failure. Bondok and Salim [15] investigated the use of implicit analysis to simulate the behavior of the truss end connection to failure under vertical and
Comparison of quasi-static experimental results with finite element simulations
A comparison between the mode of failure captured from the finite element simulation and the physical experiment is given in Fig. 17, which shows how closely the finite element model captured the failure mode of the physical experiment. Von Mises stress distributions at different stages of deformation are shown in Fig. 18. It can be seen from the different stages how the yield stress (light green color) sweeps all over the truss as it deforms. It can be also seen from Fig. 18 that the contact
Summary and conclusions
Five small scale CFS roof trusses were tested under quasi-static loading and the static resistance for each specimen was determined for blast response analyses using the SDOF simplified technique. Experimental results and energy comparisons show that the truss layout and the shape of loading significantly affect the performance of the truss and the failure mechanism. Generally, when the applied load is localized at a single point, the truss stiffness and the ultimate capacity will decrease. The
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors would like to thank Mike Pellock and Dave Boyd from Aegis Metal Framing for donating the materials required to build the CFST specimens.
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