Rectangular Hollow Structural Sections Research Articles

Inelastic Deformation and Local Slenderness Requirements for Rectangular HSS Braces

Rectangular hollow structural sections (HSS) are commonly used as bracing in concentrically braced frames (CBFs) designed and detailed for seismic design requirements. As the primary yielding component in CBFs, braces are expected to sustain large inelastic axial deformation during earthquake loading. It is well known that their deformation capacity depends on the width-to-thickness ratio (local slenderness). Until 2013, HSS sections were produced to meet ASTM standard A500/A500M; after 2013, the ASTM 1085 specification was implemented, and since that time, HSS sections have also been produced to meet ASTM A1085/A1085M standards. Where the ASTM A500/A500M specification requires minimum yield and tensile stress values as well as a minimum elongation and tolerances on the wall thickness, the ASTM A1085/A1085M specification also requires a minimum Charpy V-notch (CVN) toughness, a maximum yield stress of the steel, and tighter tolerances on the wall thickness and radius of curvature of the corner. These requirements offer a more reliable brace for CBFs in seismic regions. Yet there has been limited research investigating the cyclic axial response of these members. A research study was undertaken to investigate the response of ASTM A1085/A1085M tubes using the response of ASTM A500C tubes as their reference. Forty-one brace specimens were tested under cyclic inelastic axial deformation. Comparison of the data shows that most of the ASTM A500/A500 M Grade C and ASTM A1085/1085M braces meet the respective requirements of their respective ASTM standard and that the differences between the performance of ASTM A500/A500M and ASTM A1085/1085M braces are not dramatic. In addition, the study investigated the impact of width-to-thickness ratio, global slenderness, and displacement history on the response of the braces. The data show that the current AISC 341-22 high-ductility slenderness limit for special concentrically braced frame (SCBF) braces is slightly conservative. However, the data suggest that the moderate ductility slenderness limit used for ordinary concentrically braced frame (OCBF) braces is significantly more conservative than required for consistent seismic safety. Further research is required to determine appropriate limits; this paper provides some initial recommendations based on this dataset.

Prediction of the cyclic rotation capacity of steel members with cold‐formed hollow cross‐section

AbstractCold formed Hollow Structural Sections (HSS) are widely used in structural applications, especially in multi‐storey buildings located in seismic areas because of their high strength‐to‐weight ratio and torsional stiffness. However, the current version of the European seismic code provides limited rules and guidance to evaluate the ductility and the plastic rotation capacity of HSS members. The research activity carried out in this study aims to develop formulations to predict both the deformation capacity and the overstrength of cold formed HSS beams and columns at significant damage and near collapse limit states. Therefore, parametric finite element simulations have been carried out on a large set of members with different cross section (i.e., both square and rectangular HSSs), local and global slenderness, shear span and axial load ratio (from 0 to 0.5). The adopted finite element models have been calibrated against results of cyclic experimental tests available from the literature. The accuracy of the proposed equations has been statistically verified and discussion of practical applications is also provided.

Strength of transverse plate-to-rectangular HSS connection under single-concentrated compression

According to the American Institute of Steel Construction (AISC) Specification for Structural Steel Buildings (AISC 360), the transverse plate-to-HSS bearing strength of rectangular hollow structural sections (HSS) under single-concentrated compression shall be determined based on the applicable limit states in Section J10. From all the limit states, both the web local yielding (WLY) and web local crippling (WLC) are applicable for transverse plate-to-HSS concentrated compression. However, all the limit state equations in J10 were originally developed for wide-flange sections. Unlike the in-plane compression on the web of a wide-flange section, the concentrated compression on an HSS member acts like an eccentric load on the HSS web and a distributed load along the HSS flange. The eccentric load on the web and flange local bending due to the distributed load can considerably reduce the failure load as compared to the wide-flange sections. Experimental and nonlinear finite element analyses (NLFEA) carried out in this study indicate that WLY, WLC, and flange bending always simultaneously occur at failure of an HSS; hence, they are not independent limit states. While AISC WLY equation predicts a strength closer to the experimental and NLFEA results, the bearing strength of HSS members can range from 16% to 66% of that predicted by AISC WLC equations. Based on actual failure modes, 251 FE models were analyzed, and a single transverse plate-to-HSS bearing strength equation under compression for HSS members was formulated.

Overstrength and deformation capacity of steel members with cold-formed hollow cross-section

Cold formed Hollow Structural Sections (HSS) are widely used in structural applications, especially in multi-storey buildings located in seismic areas because of their high strength-to-weight ratio and torsional stiffness. However, current version of European seismic code provides limited rules and guidance to evaluate the ductility as well as the plastic rotation capacity of HSS members. Within the framework of revision of Eurocodes, still in progress, the research activity carried out in this study is aimed at developing formulations to predict both deformation capacity and overstrength of cold formed HSS beams and columns. Therefore, parametric finite element simulations were carried out on a comprehensive set of members varying the shape of cross sections (i.e. both square and rectangular HSS), local and global slenderness, shear length and axial load. The adopted finite element models were calibrated against results of cyclic experimental tests available from existing literature. The results of the parametric analysis were processed in order to derive analytical equations predicting the overstrength factor and the deformation capacity at both significant damage and near collapse limit states.

Superior design solutions of section sizes in steel buildings for different lateral frame systems and column shapes

Superior design solutions of section sizes in steel buildings for different lateral frame systems and column shapes

Computationally Efficient and Accurate Simulation of Cyclic Behavior for Rectangular HSS Braces

During earthquakes, braces behave in complex manners because of the asymmetric response nature of their responses in tension and compression. Hollow structural sections (HSS) have been popularly used for braces due to their sectional efficiency in compression. The purpose of this study is to accurately simulate the cyclic behavior of rectangular HSS braces using a computationally efficient numerical model. A conceptually efficient and simple physical theory model is used as a basis model. To improve the accuracy of the model, cyclic beam growth and buckling load, as well as the incidences of local buckling and brace fracture are estimated using empirical equations obtained from regression analyses using test data on rectangular HSS braces. The accuracy of the proposed model is verified by comparing actual and simulated cyclic curves of brace specimens with various slenderness and width-to-thickness ratios.

Weld Effective Lengths for Rectangular HSS Overlapped K-Connections

One large-scale, 33-ft-span, simply supported, Warren truss was tested to assess the performance of welds in rectangular hollow structural section (HSS) overlapped K-connections. Nine overlapped connections, within the truss, were designed to be weld-critical and sequentially failed by producing an axial force distribution with a point load, applied quasi-statically, to strategic panel points. The structural reliability (or safety index) of the existing AISC specification formulas for the effective length of welds in rectangular HSS overlapped K-connections, in Table K4.1 of the 2010 AISC Specification for Structural Steel Buildings, was determined from the tests. The results indicate that these provisions are conservative; hence, a modification to the current requirements that limits the effective width of the transverse weld elements is proposed. The proposal establishes a more economical and yet still safe weld design method for rectangular HSS overlapped K-connections.

Weld effective lengths of rectangular hollow section T-connections under branch bending

The 2010 AISC Specification for Structural Steel Buildings has expanded the scope in chapter K: design of HSS and box member connections to include a section K4: welds of plates and branches to rectangular HSS. An experimental programme was undertaken at the University of Toronto to test various unreinforced RHS-to-RHS 90° T-connections subject to branch in-plane bending moment with the objective of determining the effectiveness of the welded joint. Twelve unique test specimens were designed to be weld-critical, and the results from the full-scale tests revealed that the current equation for the effective elastic section modulus for in-plane bending, S ip, given in Table K4.1 of AISC 360-10 is very conservative. A modification to the current requirements that limits the effective width of the transverse weld elements is proposed, resulting in a safe and more economical weld design method for RHS-to-RHS T-, Y- and X- connections subject to branch axial load or bending moment. It is also concluded that the fillet weld directional strength enhancement factor, (1.00 + 0.50sin1.5 θ), should not be universally applied to all connections between square and rectangular hollow structural sections in combination with effective weld properties as it may result in an unsafe design.

Shape optimization of free-form steel space-frame roof structures with complex geometries using evolutionary computing

Recently the authors presented a two-phase genetic algorithm (GA) for minimum weight design of free-form steel space-frame roof structures consisting of discrete commercially available rectangular hollow structural sections (HSS). Subsequently the algorithm was extended to topology optimization of structures. This article presents a new methodology for simultaneous sizing, topology, and shape optimization of free-form steel space-frame roof structures with complex geometries using evolutionary computing. Two methods of altering the geometry of the structure are presented, one a simple method to be used for roof structures with relatively regular geometries, and the other for more complicated geometries. The goal is to achieve additional structural efficiencies by altering the geometry of the roof structure while simultaneously optimizing the roof member and column cross-sectional dimensions and the roof topology. Esthetics is a significant consideration in the structures of the type considered in this research. As such, preserving the general form created by the architect is considered in the proposed shape optimization algorithm. To achieve this, heuristic limits are imposed to avoid drastic or undesirable changes in their architectural form. The methodology is applied to two real-life free-form steel space-frame roof structures. They are two of the thirteen train stations making up the Ottawa Light Rail Transit (OLRT) system to be completed in Ottawa, Canada, in 2018. Efficiencies in the range of 10–16% are reported for the two examples.

Two-phase genetic algorithm for topology optimization of free-form steel space-frame roof structures with complex curvatures

A two-phase genetic algorithm is presented for simultaneous sizing and topology optimization of free-form steel space frame roof structures consisting of discrete commercially available rectangular hollow structural sections. The algorithm is applied to two real-life space roof structures intended for Ottawa Light Rail Transit (OLRT). It is shown that the algorithm is effective for topology optimization of real-life roof structures with complex curvatures in multiple planes.

Two-phase genetic algorithm for size optimization of free-form steel space-frame roof structures

A two-phase GA approach is presented for minimum weight design of free-form steel space-frame roof structures consisting of discrete commercially available rectangular hollow structural sections (HSS). The new methodology is applied to two roof structures subjected to the AISC LRFD code and ASCE-10 snow, wind, and seismic loadings. They are two of the thirteen train stations making up the Ottawa Light Rail Transit (OLRT) system to be completed in Ottawa, Canada, in 2018. Both examples have a diamond grid pattern and their members are subjected to torsion in addition to bending and axial forces. The initial design in both cases is an actual design performed in a design office by the first author iteratively using general-purpose structural analysis software over a period of days. The optimum solutions obtained using the new methodology resulted in savings of 12% and 7% for the two examples. The advantages of the two-phase GA optimization algorithm presented in this paper are three fold: a) automation of the design process of a complicated and one-of-a-kind structure; b) relieving the designer of days of iterative design process; and c) achieving a lighter and therefore more economical design.

Experimental Study of Concrete-Filled Rectangular HSS Columns Subjected to Biaxial Bending

This paper describes the experimental work on the tests of nine concrete-filled square and rectangular hollow structural section (HSS) columns subjected to axial load, uniaxial bending or biaxial bending. The experimental results suggest that the overall buckling appears accompanying with local buckling near the mid-height of column. Good agreement was found between the semi-sine wave shape and the experimental deflection shape. It is found that the cross-section remains plane before the specimen reached its load-carrying capacity. Also, the experimental results are compared with the values calculated from the AISC-LRFD, EC4 and CECS design codes, which shows that all codes provide safe bearing capacities. Compared with columns subjected to an axial load or uniaxial bending, the calculated capacities of column subjected to biaxial bending are more conservative. Among these three design codes, the capacities based on the EC4 design code yield results which are the closest to the experimental ones. The results calculated from the AISC-LRFD design code are the most conservative.

Behaviour of Filled Rectangular Steel HSS Composite Columns under Bi-Axial Bending

The purpose of this study was to investigate the behaviour of concrete-filled rectangular steel hollow structural section (HSS) columns formed by slender plates with large depth-to-width ratio subjected to bi-axial bending. As part of this study, four large concrete-filled thin-walled rib-stiffened rectangular HSS columns have been tested. Their steel tubes possess a depth-to-width ratio of 2.38 and a depth-to-thickness ratio of 175. Rib stiffeners were welded to the plate walls such that the stiffened plate width-to-thickness ratio (= 45) was less than that specified (= 60) in the Chinese design code. The results showed that local buckling of steel plate appeared after the specimen reached the ultimate capacity. Also, the fiber element analysis method is adapted to analyze the behaviour of specimen, in which the change of neutral axis position is considered. At last, the experimental results are compared with the values calculated from design codes, namely EC4, LRFD, CECS and DBJ. The results show that all codes provide safe ultimate capacities. Among them, the capacities calculated from DBJ yield results closest to the experimental ones and the other three design codes produce safety over 20%.

Fillet Weld Design for Rectangular HSS Connections

The 2010 AISC Specification for Structural Steel Buildings has expanded the scope in Chapter K ("Design of HSS and Box Member Connections"�) with a new Section K4, "Welds to Branches."� This paper describes the background to this development and examines the structural reliability of the weld effective length provisions contained therein. The latter is achieved by using a database of 31 welded square/rectangular hollow structural section (HSS) K-, T- and cross- (or X-) connections in which all test specimen failures were reached by fracture of the welded joints. The potential inclusion (or exclusion) of the sin θ effect, whereby fillet weld capacity is increased for loading not parallel to the axis of the weld, has also been investigated. In conclusion, some design examples are given to illustrate the weld design method, performed to the 2010 AISC Specification in both LRFD and ASD.

Experimental study on slotted rectangular and square hollow structural section (HSS) tension connections

An experimental study has been carried out on slotted hollow structural section (HSS) connections with and without welding at the end of the gusset plate. A total of 30 slotted square and rectangular HSS specimens, with 16 different connection configurations, were investigated for effects of weld length ratio, slot orientation, gusset plate thickness, slot opening length, and end welding. Experimental results show that the net section efficiency of the specimen with no end welding was greater than unity for a weld length ratio (L/w), where L is weld length and w is the circumferenctial distance between the longitudinal welds, as low as 0.8, and full net section efficiency was achieved with L/w ratio as low as 0.76 for a square HSS specimen with end welding. These results support findings from other research that show provisions to account for the effect of shear lag in slotted HSS connections are overly conservative in both Canadian and American design standards. Recommendations are provided to improve on provisions to account for shear lag in the Canadian design standard.

Discussion of “Shear Lag in Rectangular Hollow Structural Sections Tension Members: Comparison of Design Equations to Test Data” by Bo Dowswell and Stacey Barber

The discussers argue that the authors (Dowswell and Barber) inappropriately use data for efficiency factor (U) accuracy verification because the data, gleaned from 1999 Zhao et al. and 1995 Zhao and Hancock efforts, has a governing failure mechanism which always correponds to block shear or tear-out (TO). The discussers also argue that the authors, in calculating U, calculate weld return length (l) using a weld portion located in the weld return region which AISC definitions of l say should be neglected in calculating l. Model response validation should be done against experimental data if finite-element modeling (FEM) data is to be used. The discussers argue that the authors' inclusion of 1995 data by Girard et al. is questionable because they could not verify circumferential fracture (CF) failure mechanism reproduction capacity (and corresponding ultimate load). The discussers note, however, the authors' postulation that shear lag-induced fracture is more accurately predicted by reduced eccentricity value is correct. The discussers argue for using reduced eccentricity for connections fabricated with elliptical hollow sections and circular hollow sections for predicted capacity improvements as shown by 2006 Martinez-Saucedo et al. and 2006 Willibald et al. efforts. Shear lag reduction factor (U) influence should be assessed only by tests failing by CF. Hollow section U factor modification should be related to the latest AISC specifications.

Shear Lag in Rectangular Hollow Structural Sections Tension Members: Comparison of Design Equations to Test Data

Shear lag reduces the fracture capacity of steel tension members if some, but not all, elements of the cross section transfer force at the connection. Axially loaded rectangular hollow structural sections (HSS) are commonly connected by slotting two walls and inserting a plate into the slot. The AISC Load and resistance factor design specification for steel hollow structural sections has equations to account for shear lag in slotted HSS connections. The equations are based on tests on open structural shapes. This study compares the AISC equations to the available data from previous tests and finite element models to determine whether the equations are valid for rectangular HSS members. The results of four research projects were compared to the AISC equations. The AISC equations were found reasonably accurate and generally conservative.

Design Recommendations for Bolted Rectangular HSS Flange-Plate Connections in Axial Tension

In recent years the use of closed sections/tubes as structural members has increased significantly. Designers all around the world approve of the advantages that round as well as rectangular hollow structural sections (HSS) can offer, such as uniform strength and stiffness independent of the loading direction, high torsional and buckling strength and the aesthetic appearance. Splicing structural members is a common practice in construction to allow for long spanning trusses, changes in cross sections and transportation to site, to name but a few. The results of an experimental investigation of four bolted flange-plate connections between rectangular hollow structural sections, with bolts on all four sides, have been presented. A brief overview of different design methods for bolted flange-plate connections for square and rectangular hollow structural sections under tension load has also been given. A comparison of the load predictions of the various methods for the specimens in the experimental program supports the use of the design procedure that can be found in the AISC HSS Connections Manual (AISC, 1997).

Longitudinal Plate and Through Plate-to-Hollow Structural Section Welded Connections

A longitudinal branch plate-to-rectangular hollow structural section (HSS) member connection tends to cause excessive distortion of the HSS connecting face. Such a connection therefore results in a relatively low, deformation limit state, design resistance. A “through” branch plate connection that extends through both walls of the rectangular HSS member can be used to increase the design resistance of a standard longitudinal branch plate connection. The results of an experimental test program and a corresponding numerical study, using the finite-element method on longitudinal and corresponding through branch plate-to-HSS connections are presented in this paper. The strength and behavior of longitudinal versus through branch plate-to-HSS connections is henceforth determined and a unified limit states design (LRFD) procedure for these cognate connections is proposed.

Design of extended end-plate connections for hollow section columns

Extended end-plate connections have been widely used in moment-resisting steel frames with W-shape columns, due to their sufficient stiffness and moment capacity. In addition, such connections are easy to install and permit good quality control. Extended end-plate connections can also be employed in moment-resisting frames with hollow structural section columns by using high strength blind bolts. These bolts have been developed for installation from one side only where the rear side of the connection is inaccessible. In this study, a quantitative procedure for detailing and designing beam extended end-plate connections for rectangular hollow structural section columns using high strength blind bolts is proposed. The design procedure is consistent with the design philosophy given in limit-state codes. The proposed design is based on the results obtained from an experimental program and an analytical study. Key words: design, end plate, connection, hollow section, blind bolts, steel, frame.