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The continuous strength method (CSM) is a recently developed deformation-based design method for metallic structures. In this method, cross-section classification is replaced by a normalized deformation capacity, which defines the maximum strain that a cross-section can endure prior to failure. This limiting strain is used in conjunction with an el...
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The combined experimental and theoretical approach was applied to the study of high-speed deformation and fracture of the 1810 stainless steel. The material tests were performed using a split Hopkinson pressure bar to determine dynamic stress-strain curves, strain rate histories, plastic properties and fracture in the strain rate range of 102 ÷ 104...
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... 36 , and the model was validated against the experimental results. The test results were compared with the design strengths predicted by AS/NZS 4600:2018 33 , CSM 35,37 , and DSM [38][39][40] . The findings indicated that the calculation of bending and shear capacities based on CSM design rules more accurately reflected the web tension field effect of web-stiffened folded flange C-beam under combined bending and shear action. ...
... (36) in EN 1993-1-4+A1: 2015 29 ; η equals 1.2; and γ y , G, G sh , γ u are provided by Eqs. (37)(38)(39)(40). Figure 16a,b demonstrate that when V u is derived from DSM, regardless of whether M u is determined based on the local buckling moment capacity M ul,DSM within the DSM framework (primarily considering failure due to local buckling of the compression flange of the C-shaped beam, reinforced with angle connections near supports and load points), or through CSM, the current design rule AS/NZS 4600:2018 33 , which uses Eq. (18) for describing bending and shear interaction, is not suitable for predicting the bearing capacity of C-shaped folded flange beams with web stiffeners under combined action. Furthermore, the calculation results obtained from Eqs. (19)(20)(21) are not conservative. ...
Compared with ordinary steels, stainless steels possess advantages such as robust corrosion resistance, beautiful appearance, and excellent ductility. This article investigated the performance of a novel C-shaped folded flange section stainless steel beam with web stiffeners under bending and shear interaction, with a focus on the effect of the web tension field on its performance after transverse constraint. Stiffeners can effectively promote the bearing capacity of cold-formed thin-wall components, and folded flanges are convenient for connecting to floors, thus expanding the application range of stainless steel components. This study detailed the three-point bending tests conducted on specimens with shear span ratios of 1.5 and 2, as well as the numerical analysis methods employed. The experimental results of ultimate bearing capacity were compared with the predictions made by the Direct Strength Method (DSM) and Continuous Strength Method (CSM) adopted in current design codes. It was found that positioning the stiffeners closer to the compression flange enhanced the bearing capacity of the member, and this enhancement effect became more pronounced with an increase in the shear span ratio. Furthermore, the Continuous Strength Method (CSM) predicts the moment and shear bearing capacity more accurately. Furthermore, the Continuous Strength Method (CSM) provided more precise predictions of both the bending moment and shear capacity under the web tension field. The research results are helpful to provide theoretical basis and technical support for such members in engineering applications.
... Although some scholars have examined the structural performance of austenitic stainless steel channel sections under axial loads [25], concluding that this material exhibits excellent load-bearing properties, research on shear behavior remains limited. Previous studies have been confined to examining web shear buckling without considering the performance of the entire cross-section (including flanges) [26], lacking research on full-section buckling of thin-walled profiles under shear. Therefore, it is crucial to explore the effect of adjacent plate elements on shear buckling stress and understand the buckling patterns of thin-walled steel sections (rather than flat plate elements). ...
The failure mode of thin-walled C-channel beams typically manifests as premature local buckling of the compression flange, leading to insufficient utilization of material strength in both the flange and the web. To address this issue, this study adopts the approach of increasing the number of bends to reinforce the flange and adding V-shaped stiffeners in the middle of the web to reduce the width-to-thickness ratio of the plate elements, thereby delaying local buckling and allowing for greater plastic deformation. However, the challenge lies in the irregular cross-sectional shape and complex buckling patterns. Therefore, this paper aims to explore a suitable cross-sectional form to expand the application of stainless steel members. Subsequently, three-point bending tests were conducted on the optimally designed stainless C-channel beam with folded flanges and mid-web stiffeners. The finite element simulation results were compared and analyzed with the experimental results to validate the model’s effectiveness. After verifying the correctness of the finite element model, this study conducted numerical parameterization research to investigate the effects of the shear span ratio, complex edge stiffeners, web height–thickness ratio, and V-shaped stiffener size on the shear performance of stainless steel folded flange C-beams. The results show that changing the shear span ratio has a significant impact on the shear capacity and vertical deflection deformation of components; increasing the web height–thickness ratio can enhance the shear capacity of the component; elevating the V-shaped stiffener size can slightly improve the shear capacity of components; and for the stainless steel C-shaped beam with folded flanges and intermediate stiffening webs, adding edge stiffeners cannot remarkably promote the shear capacity of the component.
... However, the deformation obtained by the nodal displacement cloud map is actually a comprehensive out-ofplane deformation, which consists of deformations such as warping, torsion, and bending (Piana et al. 2021). In engineering, it is usually necessary to implement different reinforcement measures for different deformations (Hwang et al. 2019, Saliba andGardner 2018). Although reinforcement at large deformation locations can reduce various deformations including warping, this method is not Fig. 1 Four-node square thin plate element economical and sometimes it is difficult to achieve the desired effect. ...
... The CSM design of non-slender cross-sections has been systematically studied, while the design method for slender cross-sections, considering the influence of element interaction on post-local buckling behaviour, merits further investigation. Moreover, despite some existing research on cross-sections in shear [98], a systematic study on cross-sections under combined shear and bending is lacking. Significant work also remains to be done on extending the CSM to the design of cross-sections under concentrated transverse loads, as well as cross-sections manufactured using new techniques, such as wire arc additive manufacturing [124,125]. ...
The Continuous Strength Method (CSM) is a deformation-based approach to the design of structures that enables a continuous, rational and accurate allowance for material nonlinearity (i.e. the spread of plasticity and strain hardening). Central to the method is the application of strain limits, determined on the basis of the local slenderness of full cross-sections, to define the resistance of a structural member or system. The method can be applied to structures formed using different materials (e.g. steel, stainless steel or aluminium) and manufacturing processes (e.g. hot-rolled or cold-formed) through the assignment of suitable stress-strain relationships, and can be used for steel-concrete composite design and in fire scenarios. In composite construction, the CSM enables a more rigorous assessment to be made of the development of strength in the structural system taking due account of compatibility between the constituent materials. The design method enables enhancements in structural efficiency and, unlike traditional approaches, allows the assessment of both strength and ductility (which is particularly relevant for high strength steel) demands at the ultimate limit state. For hand calculations, a set of straightforward CSM design equations have been developed. Recognising the increasing importance and use of advanced analysis, recent research, summarised herein, has focussed on integration of the CSM strain limits into a framework of design by second order inelastic analysis, where the benefits of the method become even more substantial. This Gardner, L., Yun, X. and Walport, F. (2023). The Continuous Strength Method ̶ Review and outlook. Engineering Structures, 275, 114924. 2 paper provides a review of the background and recent developments to the CSM, including incorporation into design standards. Current and ongoing research to expand the scope of the CSM is summarised and recommendations for future work are also set out.
... Recently, the research focus moved to the investigations on welded I-section stainless steel beams and plate girders with austenitic or duplex grades, including derivation of sectional slenderness limits [14,15], prediction of shear buckling and post buckling resistances [16][17][18][19], residual stress distribution pattern [20][21][22] and moment-shear interaction curve [23]. Moreover, Saliba and Gardner [24][25][26] provided design recommendations of cross-section classification and shear resistance for lean duplex stainless steel beams, but the moment-shear interaction effect was not discussed in their studies. All previous research provided supplementary test data and contributed to the development of design methods for stainless steel structures, such as EN 1993 1-4 [8] and AISC DG 27 [9] which referred to the framework of ANSI/AISC 360-16 [27]. ...
The present study explores the flexural and shear behaviour of welded stainless steel beams with compact sections. A total of eleven specimens fabricated with austenitic, duplex and lean duplex stainless steel were tested under four-point and three-point loading strategies to obtain their failure modes, bearing capacities and ductility performance. Three-dimensional finite element models were then developed and validated with experimental results to numerically investigate the flexural and shear performance of the compact stainless steel beams. The obtained results from tests and numerical simulations were synthesised to comprehensively assess the applicability of existing codes of practice in terms of the bending, shear and moment-shear interaction design. It is found that the current design guidance for stainless steel beams adopted the elastic-perfectly plastic material model and conservatively predicted the bending, shear, as well as combined moment-shear strength. Accordingly, revised design methods considering the strain hardening effect of stainless steel beams were proposed.
... This is further aided by establishment of CSM design equations for cross-section at elevated temperature [13]. All the aforementioned developments of CSM design equation have been achieved for various loading types such as compression [14,15], bending [3,4], shear [16], combined loading [17,18] etc. Besides these studies on cross-section resistance design, CSM has also been extended to design for member buckling resistance [19,20]. ...
... CSM adopts a simple bi-linear, elastic and linear hardening, material model. Taking analogy to the CSM normal stress and normal strain model, a shear stress-strain model as given in Eq. (6) and depicted in Fig. 8 is adopted (similar to [16]). where G and G sh are shear modulus and shear strain hardening slope, calculated from Eq. (7). ...
The continuous strength method employs the deformation capacity of a cross-section and a simple material model for calculation of strength. The method allows exploitation of significant strain hardening in structural design of metallic materials like stainless steel. An initial attempt and first report of continuous strength method for torsion member is presented in this paper, using finite element analysis. Initially, a numerical parametric study was conducted on circular hollow section member with the aim of generating a database for tubular torsion member using validated finite element models. Four different grades of steel were considered for the study i.e., carbon steel (YSt 310), austenitic stainless steel (EN 1.4301), duplex stainless steel (EN 1.4162) and ferritic stainless steel (EN 1.4003). The parametric results were then used to develop CSM torsion design equations. Further, existing torsion design guidelines in EN 1993-1-1 and AISC 360-16 were also assessed. Overall, on average, CSM design equation was found to give improved, consistent and accurate prediction for all four grades of steel considered, in comparison to the existing design guidelines.
... Improved design rules for stainless steel bolted connections may thus be sought through the employment of a more suitable expression for determining the gross section resistance. The continuous strength method (CSM) [35][36][37][38][39] is a deformation-based design approach, which relates the resistance of a cross-section to its deformation capacity and utilises, for hand calculations, a bi-linear material model to take account of strain hardening. The method has been shown to lead to a high level of accuracy and consistency in predicting the resistances of stainless steel cross-sections in compression [35][36][37], bending [35][36][37][38] and shear [39]. ...
... The continuous strength method (CSM) [35][36][37][38][39] is a deformation-based design approach, which relates the resistance of a cross-section to its deformation capacity and utilises, for hand calculations, a bi-linear material model to take account of strain hardening. The method has been shown to lead to a high level of accuracy and consistency in predicting the resistances of stainless steel cross-sections in compression [35][36][37], bending [35][36][37][38] and shear [39]. The key aspects of the CSM are introduced below; extension of the method to the case of cross-sections in tension is then presented. ...
... scattered failure load predictions as well as inaccurate failure mode predictions for the stainless steel staggered bolted connection specimens. A new improved design method was then developed through the use of the CSM [35][36][37][38][39] to calculate the gross section resistances, and shown to yield substantially more accurate and consistent predictions of both failure modes and failure loads. ...
The present paper reports a thorough experimental investigation into the net section failure behaviour and capacity of stainless steel staggered bolted connections in tension. The testing programme was carried out on 31 stainless steel staggered bolted connection specimens, with 18 made of austenitic stainless steel (grade EN 1.4301), 7 made of duplex stainless steel (grade EN 1.4462) and 6 made of ferritic stainless steel (grade EN 1.4016). The geometric parameters, including the transverse and staggered pitches, and the staggered bolt hole patterns of the connection specimens, were varied. The test setup and procedures, as well as the key experimentally observed results, including the net section failure modes and loads, are reported in detail. The experimentally obtained net section failure loads and modes are analysed and discussed, and then utilised to assess the accuracy of the established design rules for stainless steel staggered bolted connections, given in the European, American and Australian/New Zealand standards. All three examined standards consider (i) net section fracture and (ii) gross section yielding in the design of stainless steel staggered bolted connections, and specify that the design failure load shall be taken as the minimum value calculated from all potential failure modes. It was found that the current design standards lead to overly conservative and scattered failure load predictions as well as inaccurate failure mode predictions. A new design approach based on the continuous strength method (CSM) is proposed, and shown to result in substantially improved predictions of both failure loads and failure modes.
... Similar to the DSM, the CSM also employs base curves as a function of the overall cross-section slenderness to take into account the element interaction within cross-sections. To date, the CSM has been successfully extended for designing cross-sections using normal strength carbon steel [9][10][11][12][13], stainless steel [13][14][15][16][17], aluminium alloy [13,18] and high strength steel [19]. The strength prediction of the CSM is demonstrated to be more accurate and consistent than that of the codified design methods. ...
... Elastic, linear strain hardening material models are adopted in the CSM design framework to rationally exploit the capacity enhancement from strain hardening. A bi-linear material model is employed for steel cross-sections with a round material response, and the CSM limiting stress (f csm ) is obtained from [10][11][12][13][14][15][16][17][18][19]: ...
... The CSM moment resistance (M csm ) of SHS, RHS and CHS with a round material response may be determined from [11][12][13][14][15][16][17][18]: ...
This paper presents an experimental investigation into concrete-filled steel tubular beams with octagonal cross-sections (OCFST) under monotonic or cyclic flexural loading. A total of eight tests, including four cyclic specimens and four monotonic counterparts, were conducted. Three concrete grades with measured compressive cylinder strength (fc′) varying from 54.5 MPa to 105.6 MPa were used to infill the OCFST specimens. The failure modes, ultimate bending moments, effective flexural stiffness, cumulative dissipated energy and deteriorations of test specimens were discussed. Test results indicate that OCFST beams exhibit a ductile plastic mode and excellent energy dissipation. Concrete grades seem to have limited influence on the ultimate strength and energy dissipation capacity. The comparison results of the ultimate bending moments and effective flexural stiffness between predictions using EN 1994-1-1 and AISC 360-16 and test results reveal their applicability to the design of OCFST beams. An energy-based hysteretic rule was adopted to assess the strength and stiffness deteriorations of the OCFST beams, and the results indicate that the predictions match well with the test observations.
... In each case, similar trends as seen for local buckling are also observed i.e. the rounded stress-strain response creates the need for modified buckling curves (and DSM strength curves) in the slender range [50][51][52][53] where failure occurs below the plastic resistance, while for stockier sections, strain hardening enables increased load-bearing capacities beyond the plastic resistance [47,49]. Tentative proposals have been made to extend the CSM to the design of cross-sections in shear [54], while extension to failure under concentrated transverse loads remains a topic for future research. ...
This paper provides a review of recent developments in research and design practice surrounding the structural use of stainless steel, with an emphasis on structural stability. The nonlinear stress-strain characteristics of stainless steel, which are discussed first, give rise to a structural response that differs somewhat from that of structural carbon steel. Depending on the type and proportions of the structural element or system, the nonlinear material response can lead to either a reduced or enhanced capacity relative to an equivalent component featuring an elastic, perfectly plastic material response. In general, in strength governed scenarios, such as the in-plane bending of stocky beams, the substantial strain hardening of stainless steel gives rise to capacity benefits, while in stability governed scenarios, the early onset of stiffness degradation results in reduced capacity. This behaviour is observed at all levels of structural response including at cross-sectional level, member level and frame level, as described in the paper. Current and emerging design approaches that capture this response are also reviewed and evaluated. Lastly, with a view to the future, the application of advanced analysis to the design of stainless steel structures and the use of 3D printing for the construction of stainless steel structures are explored.
... Similar to the DSM, the CSM also employs base curves as a function of the overall cross-section slenderness to take into account the element interaction within cross-sections. To date, the CSM has been successfully extended for designing cross-sections using normal strength carbon steel [9][10][11][12][13], stainless steel [13][14][15][16][17], aluminium alloy [13,18] and high strength steel [19]. The strength prediction of the CSM is demonstrated to be more accurate and consistent than that of the codified design methods. ...
... Elastic, linear strain hardening material models are adopted in the CSM design framework to rationally exploit the capacity enhancement from strain hardening. A bi-linear material model is employed for steel cross-sections with a round material response, and the CSM limiting stress (f csm ) is obtained from [10][11][12][13][14][15][16][17][18][19]: ...
... The CSM moment resistance (M csm ) of SHS, RHS and CHS with a round material response may be determined from [11][12][13][14][15][16][17][18]: ...
