Current Design Rules Research Articles

Structural behaviour and design of roll-formed Aluminium Lipped Channel beams subjected to combined bending and shear

Experimental and numerical investigations were conducted in this study to explore the structural behaviour and design of Aluminium Lipped Channel (ALC) beams subjected to combined bending and shear actions. Finite element models were developed and validated using test results. The ultimate strength results obtained from the tests and parametric study were compared with those estimated using current design rules. It was found that the current design rules are too conservative to predict the ultimate capacities of ALC beams subjected to combined bending and shear. Hence new design equations were proposed in this study to accurately predict these ultimate capacities.

A novel machine learning method to investigate the web crippling behaviour of perforated roll-formed aluminium alloy unlipped channels under interior-two flange loading

This study presents a novel machine-learning model using the eXtreme Gradient Boosting (XGBoost) tool, for assessing the web crippling behaviour of perforated roll-formed aluminium alloy (RFA) unlipped channels (both fastened and unfastened) under interior-two-flange loading. A total of 1080 data points were generated for training the XGBoost model, utilizing an elastoplastic finite element (FE) model that was validated against 30 experimental results from the literature. A comparison against the numerical failure loads was conducted, and it was found that the prediction accuracy of XGBoost model was 94%. When compared with Ramdom Forest and Linear Regression methods, it was found that the proposed XGBoost model performed better than both the before mentioned methods. The web crippling strengths obtained from the XGBoost model, tests, and finite element analysis (FEA) were utilized to evaluate the performance of current design rules from the American Iron and Steel Institute (AISI), Australian/New Zealand Standards (AS/NZS 1664.1; AS/NZS 4600:2018) and Eurocode (CEN 2007). It is shown that the current design rules are not reliable to predict the web crippling strength of perforated RFA unlipped channels. As a consequence of the parametric analysis, new web crippling strength and web crippling strength reduction factor formulae for perforated RFA unlipped channels were proposed. A reliability analysis was then conducted, which confirmed that the proposed equations are capable of accurately predicting the ITF web crippling strengths of perforated RFA unlipped channels.

Experimental investigation of roll-formed aluminium lipped channel beams subjected to combined bending and web crippling

Aluminium lipped channel (ALC) beams in the construction industry are becoming more popular due to their unique mechanical characteristics of durability and high strength-to-weight ratio. However, the elastic modulus of aluminium is only one third that of steel. Hence the ALC beams can buckle easily under shear, web crippling and bending actions. In the past, the structural behaviour of ALC beams under shear, web crippling and bending actions was investigated in isolation. For practical applications, however, the structural behaviour of ALC beams under combined actions should be investigated so that rational design rules can be developed. Recently, a research study was conducted at Griffith University to investigate the structural behaviour and design of ALC beams subjected to combined bending and shear actions. In the current study, an experimental program was conducted focussing on the structural behaviour and design of ALC beams subjected to combined bending and web crippling actions. Specifically, a series of tests was performed at Griffith University using ALC beams to investigate the behaviour and strengths of such sections subjected to combined bending and web crippling under unfastened interior one flange (IOF) loading conditions. Different interaction factors were selected to study the interaction levels of the bending moment and web crippling strengths of ALC beams. The length of ALC specimens in combined actions is non-dimensionalised based on the ultimate capacities of such beams subjected to pure bending and pure web crippling. The results from the combined bending and web crippling tests were then compared with the current design rules of AS/NZS 4600, AISI S100, and Eurocode 3 Part 1.3 based on the linear interaction equations, to verify their accuracy in predicting the capacities of ALC beams under combined bending and web crippling actions.

Design of cold-formed steel wall studs subject to non-uniform elevated temperature distributions

The current design rules for cold-formed steel studs used in wall systems subject to non-uniform elevated temperature distributions are complicated with iterations and different elevated temperature section properties. This paper first investigates the accuracy of the current effective width method (EWM) and direct strength method (DSM) based design equations, and then simplifies the calculation process without compromising the accuracy in calculating the load ratios (elevated to ambient temperature capacity ratio). It also improves the accuracy of the current DSM based design equations. It then investigates the possibilities of using uniform temperature based DSM design equations for non-uniform temperature distributions and identifies the possibilities of using hot flange mechanical properties and uniform temperature based DSM design equations. Hence, it proposes a simplified uniform temperature based DSM design method with hot flange mechanical properties and a correction factor based on hot and cold flange temperatures, yield strength, length and depth of studs.

Design of cold-formed steel SHS and RHS beam–columns considering the influence of steel grade

The structural behaviour and design of cold-formed steel square and rectangular hollow section (SHS and RHS) beam–columns, made of both normal and high strength steels, are investigated in the present study through a comprehensive numerical modelling programme. Refined finite element (FE) models were first established and calibrated against a collection of existing cold-formed steel member test results from the literature. Following this, an extensive parametric study was undertaken to expand the cold-formed steel beam–column data pool, covering a wider range of steel grades, cross-section geometries, member slendernesses and loading combinations. Results from the parametric study were then used to examine the accuracy of the current codified beam–column design methods, provided in the European Standards EN 1993-1-1 (2005) and EN 1993-1-12 (2007) as well as the American Specification AISC 360-16 (2016). The comparisons revealed that the codified design rules provide varying levels of accuracy in predicting the ultimate resistances of cold-formed steel beam–columns depending on the steel grade. An improved design approach, compatible with current codified design rules in EN 1993-1-1 (2005), is proposed that features (1) recently developed column buckling curves that reflect the increasing normalised column buckling resistance with increasing steel yield strength; (2) bending moment resistances calculated using the Continuous Strength Method (CSM) and (3) new interaction curves for cold-formed steel beam–columns, which are anchored to these more accurate end points. The newly proposed design approach is shown to yield more accurate and consistent resistance predictions over current design provisions for cold-formed steel SHS and RHS beam–columns made of different steel grades, and its reliability has also been statistically verified in accordance with EN 1990.

Design of cold-formed ferritic stainless steel RHS perforated beams

Ferritic stainless steel has been increasingly used in construction industry due to its excellent mechanical properties and a relatively low price compared with other grades of stainless steel materials. Experimental and numerical investigation was performed to examine the structural behavior of ferritic stainless steel perforated beams. The experimental program consisted of twenty specimens of rectangular hollow sections subjected to four-point bending, based on which finite element model has been developed for further parametric study. The influence of hole size and section slenderness on the test and numerical specimens was evaluated. It was shown that moment capacity and curvature at ultimate moment had negligible effect for specimens with hole diameter up to 20% of web depth, but reduced when hole size beyond 20% of web depth in this study. The section slenderness of perforated beams was found to have little influence on reduction of moment capacity for the hole diameter up to 70% of web depth. The test and numerical results were also compared with design strengths predicted by the current direct strength method for cold-formed carbon steel perforated beams. It was shown that the current design rules provide conservative predictions to the cold-formed ferritic stainless steel perforated beams. In this study, modified design rules based on the direct strength method were proposed, and shown to improve the accuracy of these design rules in a reliable manner.

Effect of member orientation on static strengths of cold-formed high strength steel tubular X-joints

Rotation of brace and/or chord members has a significant effect on the static strengths of tubular joints. Brace-rotated and bird-beak tubular joints are obtained by rotating the brace and/or chord members along their respective longitudinal axes by angles corresponding to their cross-sectional diagonal planes. This paper presents an experimental investigation of 29 cold-formed high strength steel (CFHSS) brace-rotated (BR), square bird-beak (SBB) and diamond bird-beak (DBB) tubular X-joints. The tubular members were made of S960 steel, having a nominal yield strength of 960 MPa. An axial compression load was applied through the braces of brace-rotated and bird-beak tubular X-joints. The welds connecting braces and chords of brace-rotated and bird-beak tubular X-joints were laid using the automatic gas metal arc welding process. The measured values of brace-to-chord width ratio (β) ranged from 0.33 to 0.83, effective brace-to-chord width ratio (β’) ranged from 0.25 to 0.87, brace-to-chord thickness ratio (τ) ranged from 0.67 to 1.28 and chord width-to-chord thickness ratio (2γ) ranged from 25.3 to 39.1. Three failure modes were observed in this study, namely chord face failure by plastification, a combination of this with chord sidewall failure (i.e., combined failure), and chord crown failure by plastification. Nominal strength prediction methods, from prior studies on member-rotated tubular joints as well as from the prEN 1993-1-8 (2021) and CIDECT (2008, 2009), were evaluated against the static strengths obtained from the tests. Reliability analysis was also performed to check the reliability levels of the existing design rules. For the range of tests undertaken, it was found that the current design rules of RHS-to-RHS, CHS-to-RHS and CHS-to-CHS tubular X-joints given in the CIDECT (2008, 2009), when used in conjunction with a material factor of 0.80, were found suitable and reliable for the design of CFHSS BR, SBB and DBB X-joints, respectively. In addition, the effect of change of member-rotation on the joint strengths and load–deformation curves was also assessed by comparing the structural performance of member-rotated tubular X-joints with the those of corresponding identical traditional RHS-to-RHS X-joints (Pandey and Young [1]).

Experimental and numerical investigation on cold-formed steel built-up section pin-ended columns

The thorough test programme and numerical simulation were conducted to examine the buckling behaviour and loading capacity of cold-formed steel (CFS) built-up section members subjected to axial compression. In the test programme, the folded-flange channels of steel grades G500 and G550 were designed to assemble the novel built-up section compressive members. Two types of built-up sectional profiles were formed by composing channels with self-tapping screws. A total of twenty-two built-up section specimens with member lengths varied from 300 to 1500 mm were compressively loaded under pin-ended supports. The initial geometric imperfection measurements, test rig arrangement, loading procedure and test results were fully reported. In the numerical simulation, the extensive parametric study incorporating 224 CFS built-up section columns was performed to further generate numerical data covering a broad range of sectional configurations and geometric parameters. After that, the comparisons of loading capacities obtained from experiments and numerical simulation with nominal compressive strengths calculated on the basis of direct strength method (DSM) as stipulated in the Australian/New Zealand Standard and the North American Specification were conducted to assess the applicability of the current design rules for CFS built-up section members under compression. The results manifest that the codified DSM equations are generally conservative and fairly scattered to predict the resistances of the newly designed built-up section columns. The modifications of codified DSM equations are thus proposed in this study for the CFS built-up open and closed section compressive members. It is found that the modified DSM formulae reliably provide overall precise and less scattered strength predictions.

Ultimate behaviour and serviceability analysis of stainless steel reinforced concrete beams

Stainless steel reinforcement has become a very attractive option for reinforced concrete structures owing to its distinctive properties including outstanding corrosion resistance, excellent fire behaviour, long life cycle as well as low maintenance requirements. Additionally, stainless steel reinforcement offers exceptional ductility and strain hardening characteristics compared with other common materials, which are very desirable in design to avoid sudden collapse. However, most global design standards do not incorporate an appropriate design approach for reinforced concrete members with stainless steel. The substantial strain hardening characteristics of stainless steel are typically not represented in standardised material models and therefore this attractive characteristic is not exploited in design resulting in structural and economic inefficiencies. Hence, the aim of this paper is to propose and validate a new deformation-based design approach for stainless steel reinforced concrete beams based on the continuous strength method, with reference to the current design rules provided in Eurocode 2. This approach is shown to be an effective design tool that exploits the distinctive characteristics of stainless steel reinforcement in an efficient and reliable manner. It is shown to provide a more efficient design with less over-conservatism and greater accuracy, compared with other methods. A comprehensive parametric study is conducted using Abaqus software to study the influence that various geometric and material properties have on the capacity of the members. Moreover, the serviceability limit state is also explored through a detailed analysis of the deflection behaviour.

Experimental characterisation of the moment-rotation behaviour of beam-beam connections using compressed wood connectors

The widespread use of energy-intensive metallic connectors and synthetic adhesives in modern timber construction has negative implications for the end-of-life disposal or re-use of the structural timber components. Therefore, it is favourable to substitute metallic connectors and synthetic adhesives with bio-based alternatives such as wood-based connectors. Recent studies have shown that densified or compressed wood (CW) with superior mechanical properties could be suitable for the manufacture of wood-based connectors in the form of CW dowels and CW plates. This study experimentally examines the moment-rotation behaviour of semi-rigid type timber-CW beam-beam connections under pure bending. The study also assesses the suitability of current design rules to predict the moment capacity of timber-CW connections. The comparative study has shown that the moment capacity of the timber-CW connection can be conservatively predicted from the characteristic load-carrying capacity of the connections calculated using the EC 5 strength equations.

Local buckling behaviour and capacities of Cold-Formed Steel Double-I-Box stub and short column sections

This paper presents an experimental and numerical investigation on the local buckling behaviour of a new built-up Cold-Formed Steel (CFS) homogeneous and hybrid Double-I-Box Column sections (DIBCs and HDIBCs) under axial compression. In total, 24 experimental tests are conducted, out of those 12 tests are on stub columns and the remaining 12 are on short columns. The parameters considered are hybrid ratio (Φh), section’s breadth to depth ratio (B/D) and column height (H). The columns considered in this study are having an overall slenderness (λ) less than 0.20, and the flange plate slenderness (λpf) less than 1.85. Test specimens failed in either of the following three failure modes: local buckling, yielding or by the interaction of both. In all the tested specimens, typical Bottom Zone Local Buckling (BZLB) similar to the shape of Elephant’s Foot is identified. The deformation shape is recognized by expansion (outward buckling) along the major axis and contraction (inward buckling) along the minor axis at the bottom 1/4th height of the columns in opposite faces, followed by the collapse. This kind of failure mode is a clear representation of Poisson’s ratio effect at the ends causing a restraint which then creates a local imperfection under load which leads to a localized failure at bottom zones in the stub and short columns of DIBCs and HDIBCs. BZLB phenomenon is enhanced because of the tubular cross-section geometry, boundary conditions plate element slenderness, overall slenderness of these built-up sections. The ultimate capacities of both the stub and short columns are governed by their strength limits and slenderness. Nonlinear Finite Element Analysis (FEA) is performed on experimental FE models using ABAQUS software and verified against the test results and validated with the actual structural behaviour. Further FEA is performed on 96 ideal parametric FE models considering different material properties and slenderness values. Effect of the intermediate longitudinal stiffener and the influence of edge constraints on axial strengths are also reported. The axial strengths obtained from the experimental tests and FE parametric studies are compared with the predicted results using the Effective Width Method (EWM) as suggested in the Eurocode specifications to access the feasibility of the current design rules, which is found to produce reasonable predictions albeit slightly conservative. It is found that for stub columns with λ<0.1, the experimental values are found to be 1.25 times higher than the predicted values. It is also observed that for columns having λ≥0.1<0.2 with λpf>1.2 there is a reduction in local buckling resistance of around 2.5% for each increase of λpf by 10%. Hence, it is concluded that the concentric axial compression capacities of DIBCs and HDIBCs subjected to local buckling can be computed as the arithmetic summation of effective strengths of individual channel sections calculated by using the EWM design equations, as recommended in this study. The attained results prove that these sections have a considerable local inelastic reserve strength as specified in North American standards.

Post-fire behaviour of cold-formed high strength steel tubular T- and X-joints

An experimental programme to investigate the post-fire residual strengths of cold-formed high strength steel (CFHSS) tubular T- and X-joints subjected to ISO-834 standard fire [1] exposure has been presented in this study. A total of 32 joints, including 16 T-joints and 16 X-joints, was tested. The tubular members of T- and X-joints were made of S900 and S960 steel grades. The test specimens were divided into 3 sets, and subsequently, these sets were then heated up to 300 °C, 550 °C and 750 °C by generally following the ISO-834 standard fire [1] curve, respectively. Once the fire exposed tubular T- and X-joints cool down to ambient temperature, tests were then conducted. The brace members of tubular T- and X-joints were made of square, rectangular and circular hollow sections (SHS, RHS and CHS), while SHS and RHS were used as the chord members. In this study, two configurations of tubular T- and X-joints were tested, first, where SHS and RHS were used as the brace and chord members (i.e. RHS-RHS), and second, where braces were made of CHS and chords were made of SHS and RHS (i.e. CHS-RHS). The T-joints were tested by applying axial compression load through the brace members and the chord ends were supported on rollers. The X-joints were tested by applying axial compression load through the brace members without chord preload. The welding was performed using automatic gas metal arc welding process. For T- and X-joints, the nominal values of brace-to-chord width ratio (β) ranged from 0.42 to 1, brace-to-chord thickness ratio (τ) ranged from 0.75 to 1, chord width-to-thickness ratio (2γ) ranged from 25 to 35 and chord side wall slenderness ratio (h0/t0) ranged from 15 to 35. Currently, there are no specific design rules to predict the post-fire residual strengths of tubular joints. Thus, the post-fire residual joint strengths obtained in this investigation were compared with the nominal strengths calculated from the CIDECT [2] and Eurocode 3 (EC3) [3] using the measured post-fire residual mechanical properties. It is shown that the current design rules of T- and X-joints given in the CIDECT [2] and EC3 [3] could not accurately predict the post-fire residual strengths of cold-formed S900 and S960 steel grades tubular T- and X-joints.

Experimental investigations on the design and execution of shear loaded blind rivet joints in steel lightweight construction

AbstractThere is a barely manageable variety of blind rivets available on the market. This is because there is no universal product standard, which establishes the mechanical properties of blind rivets in a suitable manner. Whenever structural engineers dimension joints with blind rivets, they face a major challenge due to the lack of design values for the blind rivets themselves and the impractical application limits according to EN 1993‐1‐3. It is therefore necessary to determinate the design values of the blind rivets itself and for their applications in the field of steel lightweight construction in time and cost‐intensive experimental investigation. Furthermore, the regulations according to the ECCS, which allow the experimental‐based determination of design values for such applications, are insufficient, as they do not consider alternating stresses as well as compact joint dimensions.To close the gap of knowledge this paper presents results from systematic investigations on the shear and load‐bearing behavior of blind rivets and joints with blind rivets. Based on the investigations the authors suggest the extension of the current design and execution rules in order to allow a safe design by separate verification of the components and blind rivet.

Behaviour of Ferritic Stainless Steel Bolted T‐stubs Under Tension‐Part 1: Experimental Investigations

AbstractResearch on stainless steel structures has primarily focused on the structural response and design of individual members, whilst the response of joints has received far less attention to date. Recently, a series of experimental tests has been conducted on austenitic and duplex stainless steel moment resisting connections which highlighted both the excellent ductility and significant overstrength exhibited by such connections as well as the severe conservatism of current design rules specified in EN 1993‐1‐8 when applied to stainless steel joints. A comprehensive experimental study on the structural behaviour of stainless steel T‐stubs fabricated from EN 1.4003 ferritic stainless steel grade is reported in this paper. The tested configurations included both single and double bolt rows and have been assembled with A4‐80 stainless steel bolts. In order to determine the material characteristics of the T‐stubs and the connecting bolts, tensile coupon tests were performed and the material anisotropy exhibited by ferritic stainless steel has been quantified. The ultimate resistance, plastic deformation capacity and failure mode of each T‐stub were obtained and are reported herein. The obtained results are utilised to assess the accuracy of existing design rules and to validate the numerical model discussed in the companion paper.

Fire design proposal for members with cold‐formed lipped channel and sigma sections under compression

AbstractSteel structural elements with cold‐formed thin‐walled sections are becoming increasingly common in buildings due to their lightness and ability to support large spans. In these members, local, distortional and global instabilities are important common failure modes. At high temperatures, these instability phenomena are intensified. This paper presents a numerical study on the behaviour of columns with lipped channel and sigma sections in case of fire when subjected to compression. A parametric study, considering different steel grades, temperatures and different cross‐sections with different slendernesses, is presented. Comparisons are also made between the numerical results and analytical design rules, such as the Part 1‐2 of Eurocode 3, using its Annex E or its French National Annex, where a different constitutive law is recommended for cold‐formed profiles. It is possible to conclude that the simple calculation rules are on the safe side but sometimes too conservative. Therefore, new proposals with adjustments to the current design rules are presented for these particular cases that are very common in cold‐formed steel constructions, in order to keep the results on the safe side becoming the design rules less conservative.

Numerical study on bearing behaviour and design of aluminium sub-heads in façade systems

A sub-head refers to the horizontal member at the top of an aluminium window wall system. Under wind load, bearing failure of the aluminium sub-head (ASH) flange due to its long length is a common failure mode, being subjected to high concentrated load transferred from the vertical members (mullions). The bearing behaviour of ASH sections was previously investigated experimentally by the authors and suitable equations (DRAI) were proposed to predict the bearing capacities. These design rules were manufacturer and product specific and only applicable for sections considered in the test plan. To address these limitations, the present study further investigates the behaviour and design of ASH sections through non-linear static analyses using ABAQUS, based on implicit integration schemes. The effects of mesh size, element type, and loading plates on the bearing behaviour of ASH section under different loading and boundary conditions was addressed. The finite element models were validated against the test results in terms of ultimate loads, load–displacement curves and failure modes, and the validated model was then used to perform an extensive parametric study. A broad range of ASH sections covering flange widths ranging from 40 to 100 mm, thicknesses varying between 2 and 4 mm, bearing widths ranging from 50 to 150 mm, and six engagement lengths (5 to 30 mm) was considered in the parametric study. It should be noted that the ultimate loads obtained from the parametric study are not product nor manufacturer specific. Since no aluminium design rules exist to predict the bearing capacities of ASH sections, the accuracy of the current cold-formed steel design rules (DRSs) and that of DRAI were assessed. Both DRSs and DRAI were found not to be suitable for ASH sections in window walls, hence appropriate modifications were made in this study and the proposed design rules (DRAP) predicted accurate bearing capacities which agreed well with the numerical results.

The direct strength method for combined bending and web crippling of second-generation trapezoidal steel sheeting

Second-generation trapezoidal sheeting, characterised by longitudinal stiffeners in webs and flanges, is loaded near a support by a concentrated force and a bending moment. Currently, design codes predict related failure by: (a) determining the ultimate bending moment via the effective width approach or the Direct Strength Method (DSM); (b) finding the web crippling load via a curve-fitted formula; and (c) using an interaction rule to take into account the load combination. However, the effective width approach is quite complex to use for many longitudinal stiffeners, and the accuracy of the design codes is subject to improvement. Moreover, nowadays the DSM provides a consistent and well-established method to predict ultimate loads for cold-formed steel structures. Therefore, in this paper the application of the DSM for combined bending and web crippling of second-generation sheeting is investigated. First, to create a set of numerical experiments, an internationally representative set of second-generation trapezoidal sheeting types is found, and these types are used to design numerical three-point bending experiments with relevant span lengths and load bearing plate widths. Then, finite element models are developed and verified, and used to predict the buckling, yield, and ultimate loads for the set of numerical experiments. Additionally, all simulations are also carried out for pure bending, and (Interior One Flange) IOF and (Interior Two Flange) ITF web crippling cases. With the resulting data, an explicit DSM approach is developed, fitted to the data of the three-point bending simulations, which predicts the ultimate load for combined actions directly. Hereafter, also an interaction DSM approach is studied, which first predicts the ultimate bending moment by the DSM (by fitting the pure bending simulations), then the web crippling load by the DSM (by fitting either the IOF or ITF simulations), and then uses a classic interaction rule for the load combination. The explicit and implicit DSM approaches perform equally well, with a Coefficient of Variation (CoV) equal to 0.13. As most commercially available sheeting has been incorporated, and the DSM approaches allow for sections with an arbitrarily number of stiffeners in the web (different from the current design codes), it is recommended to include the DSM in future code revisions. The interaction DSM approach resembles the current design rules most and may therefore be preferred; however, the explicit approach is more direct and certainly deserves consideration too.

Shear resistance of austenitic and duplex stainless steel bolts

The current design rules in EN 1993-1-4 for non-preloaded stainless steel bolted connections under pure shear and tension (specified as category A and category D connections acc. to EN 1993-1-8) are essentially based on the regulations for carbon steel bolted connections. However, bolts made of stainless steels have in principle a different load bearing behaviour compared to carbon steel bolts and should be investigated systematically and considered in the design rules. For this reason, research activities have been carried out within the German research project “Load-bearing capacity of bolted connections loaded in shear and tension made of stainless steel M12 to M36” (IGF-No. 20651 N). Herein, experimental investigations and a literature review into the load bearing behaviour under pure tension and single-shear has been carried out to evaluate the resulting shear coefficients α for austenitic and duplex stainless steel bolts of property classes 50 to 12.9 as a basis for implementation in the revision of EN 1993-1-4. Furthermore, a reliability analysis according to EN 1990, Annex D has been carried out to prove the partial safety factor of γM2 = 1.25 for connections. On this basis, new shear coefficients α could be proposed which allow a more economical design of non-preloaded bolted shear connections.

Influence of rigidity of a flange ridge knot of a double hinged arch on the redistribution of efforts in its elements

The theoretical determination of the actual stiffness of the ridge knot of a steel perforated arch was carried out using the initial parameter method, which made it possible to calculate the stress in the upper reference section of the structure belt. The application of the proposed calculation method makes it possible to determine the rigidity of the bolted flange connection, taking into account its actual operation, and to change it by changing the geometrical parameters of the nodal details, that is, the diameter of the bolts or the thickness of the flanges.It is marked that in the calculation of building constructions an important value has exact determination of boundary conditions of connection of nodal elements, that substantially influences on the redistribution of efforts in the separate elements of constructions on their length and rigidity of knots. Especially it touches of flange bolted joints. Current design rules use idealized schemes of nodal joints, which, according to numerical researches, do not fully correspond to the actual operating conditions of nodal joints and constructions on the whole.&#x0D; For realization of aim of researches, that is, theoretical determination of rigidity of ridge knot of the steel preliminary tense perforated arch, the method of initial parameters is used, which allowed to define theoretical tensions in the supporting cut of fastening upper belt to the ridge knot of arch.&#x0D; Divergence in the values of actual tensions in the cuts of beam and theoretical, calculated according to the current design rules, is explained by the flexibility of the flanged bolted joints, that due to the actions in the knot of bending moment opens up, although in theoretical calculations this joint is accepted by absolutely rigid. Rigidity depends on the thickness of flanges, diameter of bolts, the distances between them, the values of the previous tension of the bolts and external loading.&#x0D; The conclusion is set forth, that the application of the offered methodology of calculation allows to define the rigidity of the bolted flanged joint taking into account its actual work, and which, according to experimental researches and theoretical calculations, differs from the idealized calculation schemes. In addition the proposed methodology allows to change the rigidity of the bolted jont, changing the diameter of the bolts or the thickness of the flanges, and also to use the additional resource of material due to some reduction of the maximum tensions in weak cuts of elements.

Nonlinear behaviour and design of stainless steel hybrid tubular K-joints with SHS-to-CHS

This paper presents a finite-element (FE) investigation on the bearing capacity of stainless steel hybrid tubular K-joints with square braces and circular chord. The nonlinear finite-element (FE) models were developed and validated against the test results available in the literature, which were then used to conduct a parametric study including 162 models. The parametric study results showed that the joint strengths of the stainless steel hybrid tubular gapped K-joints increased when the β and τ values increased and when the 2γ and e values decreased. On the other hand, the joint strengths of overlapped K-joints increased when the β, τ, and Ov values increased and when the 2γ values decreased. Furthermore, the bearing capacities obtained from the parametric study were compared with the design strengths calculated from the current design guidelines. The comparison showed that the current design rules of Chinese Code (GB 50017–2017) were generally un-conservative for stainless steel hybrid tubular K-joints. The coefficient of variations (COVs) obtained from the comparison of EC3 (2005), AS/NZS (2001) and GB 50017 (2017) were very large. However, the design strengths calculated from the International Committee for the Development and Study of Tubular Structures (CIDECT) were relatively close to the FE strengths. Therefore, modified design rules are proposed in this paper. New design formulas were developed by applying correction factors (ψg and ψo) to the current design rules of CIDECT (2008) for carbon steel CHS tubular K-joints, considering the effects of key geometric parameters of β, τ, 2γ and Ov, respectively. The proposed design rules can accurately predict the bearing capacity of stainless steel hybrid tubular K-joints with square braces and circular chord, being only 1% conservative to the FE strengths.