The Continuous Strength Method – Review and outlook

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. Central to the method is the application of strain limits to define the resistance of a structural member or system.The method can be applied to structures formed using different materials and manufacturing processes and can be used for steel-concrete composite design and in fire scenarios. The design method enables enhancements in structural efficiency and, unlike traditional approaches, allows the assessment of both strength and ductility demands (particularly relevant for high strength steel) 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 focused 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 paper provides a review of the background and recent developments, including incorporation into design standards.

Local buckling of hot-rolled stainless steel channel section stub columns after exposure to fire

Design method for axially compressed H-sectional aluminium alloy slender column based on CSM

Hybrid welded T-section stub columns with Q690 flange and Q355 web: Testing, modelling and design

Behavior of circular stainless steel stub columns internally strengthened by longitudinal carbon steel bars

The continuous strength method for the design of aluminium alloy structural elements

An accurate and consistent approach to the out‐of‐plane stability design of steel beams and structures utilising geometrically and materially nonlinear analysis with imperfections (GMNIA) and strain limits is proposed. The method is implemented using computationally efficient beam elements, with the ultimate structural resistance defined either by (i) the ultimate load factor or (ii) the load factor at which a strain limit, determined on the basis of the continuous strength method (CSM), is attained, whichever occurs first. In the present paper, the scope of this method is extended from the in‐plane design of steel structures and structural components to scenarios in which out‐of‐plane stability effects, with a focus on lateral‐torsional buckling (LTB), govern. First, two shapes and corresponding amplitudes of equivalent imperfections, which consider the combined influence of both geometric imperfections and residual stresses, for the out‐of‐stability design of steel and stainless steel members by GMNIA are established. The existing CSM strain limits for in‐plane design are then extended to allow for the influence of shear, torsion and warping, to enable their general applicability to three‐dimensional buckling problems. It is shown that employing the proposed design method together with the proposed equivalent imperfections generally provides more accurate and consistent ultimate strength predictions than traditional Eurocode design calculations and also streamlines the design process by eliminating the need for cross‐section classification and individual member design checks.

Ultimate capacity of I-sections under combined loading – Part 2: Parametric studies and CSM design

This paper aims to develop a new continuous strength method (CSM) to more accurately predict the strain-hardening characteristics of high-strength aluminum alloy circular hollow sections (CHSs) under axial compression. A total of 11 stub column specimens made of 7A04-T6 and 6061-T6 aluminum alloys underwent testing. Additionally, 16 sets of experiment data were gathered from open sources, encompassing various aluminum alloy types such as 6082-T6, 6061-T6, and 6063-T5. Validated by experimental result, the finite element (FE) model was applied in a series of comprehensive parameter studies, supplementing the limited test result of high-strength aluminum alloy stub columns. Based on the experiment and FE results, this paper proposes a new CSM relation to determine the cross-sectional resistance of high-strength non-slender CHS aluminum alloys under compression. The cross-sectional resistance obtained from tests are compared with predicted strengths determined using the European code, as well as the solution of the CSM proposed in a previous study and in this paper. The comparison illustrates that the strength predictions in the European code and the previous study are conservative. Compared with the European code and the previous study, the strength prediction formula proposed in this paper improves accuracy by 11% and 5%, respectively, while reducing scatter by 8.4% and 2%, respectively.

This paper presents an investigation into the extension of the Continuous Strength Method (CSM) to the design of steel I-sections at elevated temperatures. Structural response of 21375 high strength and normal strength steel I-sections at elevated temperatures is considered, taking into account a very broad range of cross-section geometries and cross-section slendernesses as well as different elevated temperature levels and steel grades which include both high strength S690 and S460 steel grades and normal strength S355, S275 and S235 steel grades. The implementation of the CSM for the fire design of steel I-sections is set out. The accuracy of the CSM against that of the provisions of the European structural steel fire design standard EN 1993-1-2 and its upcoming version prEN 1993-1-2 for the ultimate resistance predictions of steel I-sections at elevated temperatures is assessed. It is shown that in comparison to the elevated temperature cross-section design provisions of EN 1993-1-2 and prEN 1993-1-2, the CSM leads to a significantly improved level of accuracy and consistency in the ultimate strength predictions of steel I-sections at elevated temperatures.

Design of stainless steel CHS-concrete infill-carbon steel CHS double-skin stub columns

Structural design of stainless steel concrete filled columns

To explore the effect of the bamboo winding angle on the axial compression properties and failure modes of bamboo winding thin‐walled tubes (BWTT), an axial compression test was conducted in this study. Seven distinct winding angles were considered. The micro‐morphology of parenchyma cells, fibers, and epoxy resin was observed based on the scanning electron microscope (SEM) and computed tomography (CT). The micro failure mechanism of BWTT was revealed. The results show that the winding angle has a significant impact on the axial compression performance of BWTT. With the increase in the winding angle, the load‐bearing capacity of BWTT declines, whereas its ductility improves. Additionally, six strength criteria were adopted to evaluate the compressive strength of BWTT, among which the Hankinson criterion ( n = 2.33) demonstrated favorable applicability. The continuous strength method (CSM) was also adopted to predict the compressive strength of BWTT, and a good correspondence was observed between the predicted and test results. An axial stress–strain model of BWTT was proposed, which was based on the Ramberg – Osgood (RO) model and considered the angle influence parameters m θ and n θ . The model results agree well with test results and can provide a theoretical foundation for the application of BWTT. Highlights Winding angle has a significant impact on the axial compression properties of BWTT. The failure mechanism of BWTT was analyzed by SEM and CT. Hankinson criterion ( n = 2.33) and CSM can predict the compressive strength of BWTT. Considering the winding angle, the compressive stress–strain model is proposed.

Ultimate response and plastic design of aluminium alloy continuous beams

A relatively new type of lean duplex stainless steel of grade EN 1.4162 with structural and economical advantages has been developed. However, investigation on columns of lean duplex stainless steel is limited. In addition, current design specifications require calculation of effective width, which is not easy to calculate for section with complicated shap. While the direct strength method (DSM) and continuous strength method (CSM) that use full area instead of effective area are gaining increasing acceptance in design.