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Equivalent bow imperfections for use in design by second order inelastic analysis

The stability of compression members is typically assessed through buckling curves, which include the influence of initial geometric imperfections and residual stresses. Alternatively, the capacity may be obtained more directly by carrying out either an elastic or an inelastic second order analysis using equivalent bow imperfections that account for both geometric imperfections and residual stresses. For design by second order elastic analysis, following the recommendations of EN 1993-1-1, the magnitudes of the equivalent bow imperfections can either be back-calculated for a given member to provide the same result as would be obtained from the member buckling curves or can be taken more simply as a fixed proportion of the member length. In both cases, a subsequent M–N (bending + axial) cross-section check is also required, which can be either linear elastic or linear plastic. For design by second order inelastic analysis, also referred to as design by geometrically and materially nonlinear analysis with imperfections (GMNIA) there are currently no suitable recommendations for the magnitudes of equivalent bow imperfections and, as demonstrated herein, it is not generally appropriate to use equivalent bow imperfections developed on the basis of elastic analysis. Equivalent bow imperfections suitable for use in design by second order inelastic analysis are therefore established in the present paper. The equivalent bow imperfections are calibrated against benchmark FE results, generated using geometrically and materially nonlinear analysis with geometric imperfections of L/1000 (L being the member length) and residual stresses. Based on the results obtained, an equivalent bow imperfection amplitude e0 = αL/150 (α being the traditional imperfection factor set out in EC3), is proposed for both steel and stainless steel elements and shown to yield accurate results. The reliability of the proposed approach is assessed, using the first order reliability method set out in EN 1990, against the benchmark FE ultimate loads, where it is shown that partial safety factors of 1.0 for steel and 1.1 for stainless steel can be adopted

Equivalent imperfections for the out-of-plane stability design of steel beams by second-order inelastic analysis

In current structural design specifications, such as EN 1993-1-1 for steel and EN 1993-1-4 for stainless steel, the stability of members is typically assessed through the use of buckling curves, which consider the influence of initial geometric imperfections and residual stresses. An alternative, more direct, approach is to perform either an elastic or inelastic second-order analysis of the member or structure with imperfections. For modelling convenience, so-called ‘equivalent’ imperfections are typically utilised, which consider the combined influence of both geometric imperfections and residual stresses. Equivalent imperfections for the design of columns and beams by second-order elastic analysis, also referred to as geometrically nonlinear analysis with imperfection (GNIA), are provided in the current design specifications. For columns, equivalent imperfections for design by second-order inelastic analysis, also referred to as geometrically and materially nonlinear analysis with imperfections (GMNIA), were recently developed, but for beams that are susceptible to lateral-torsional buckling (LTB), there are currently no appropriate provisions. The aim of this study is therefore to develop equivalent imperfections for use in out-of-plane stability design of steel and stainless steel members by GMNIA. The proposals are calibrated against the results of benchmark finite element (FE) simulations performed on a large number of steel and stainless steel members with geometric imperfections and residual stresses subjected to major axis bending. Two proposals for equivalent imperfection amplitudes are developed: (1) e0,mod, for use with eigenmode-affine imperfections and (2) e0,bow, for use with sinusoidal bow imperfections. The latter is applied solely in the lateral direction and as a summation of a half-sine wave and a full-sine wave. Relative to the traditional Eurocode design calculations, employing the proposed LTB imperfections in GMNIA provides generally more accurate member resistance predictions, while remaining safe-sided relative to the benchmark FE results. The reliability of the design provisions is demonstrated through statistical analysis, where it is shown that partial safety factors of 1.0 for steel and 1.1 for stainless steel can be safely adopted

Influence of geometric and material nonlinearities on the behaviour and design of stainless steel frames

Material nonlinearity affects the stiffness and consequently the distribution of internal forces and moments in indeterminate structures. This has a direct impact on their behaviour and design, particularly in the case of stainless steel, where material nonlinearity initiates at relatively low stress levels. A method for accounting for the influence of material nonlinearity in stainless steel frames, including making due allowance for the resulting amplified second order effects, is presented herein. Proposals have been developed for austenitic, duplex and ferritic stainless steels. The method was derived based on benchmark results calculated through second order inelastic analysis with strain limits, defined by the Continuous Strength Method, using beam finite element models. A comprehensive set of frames was modelled and the proposed assessment of second order effects in the plastic regime was also verified against the results of four full-scale stainless steel frame tests. The proposed method is due to be included in the upcoming revision to Eurocode 3 Part 1.

Flexural capacity and local buckling half-wavelength of high strength steel tubular beams under moment gradients: an experimental study

An experimental investigation into the effect of moment gradients on the flexural behaviour of hot-rolled high strength steel square hollow section (SHS) beams is presented in this paper. In total, 20 beam specimens in steel grades S690 and S770, and with cross-sections spanning from Class 2 to Class 4 based on the Eurocode 3 slenderness limits, were tested under three- and four-point bending. In the three-point bending tests, the beam spans were varied to achieve a range of moment gradients; the influence of different stiffening arrangements at the loading point was also considered. Local geometric imperfections were measured by means of 3D laser-scanning prior to testing and digital image correlation (DIC) was adopted to monitor the displacement and strain fields at critical regions and to assess the local buckling half-wavelengths of the test specimens for which a consistent measurement approach was proposed. The measured local buckling half-wavelengths were compared against the elastic local buckling half-wavelengths calculated using the finite strip method. It was observed that while the measured local buckling half-wavelengths remained approximately constant up to first yield, a significant reduction in half-wavelength was observed with increasing moment due to the non-uniform spread of plasticity. The comparisons also revealed that the local buckling half-wavelengths reduced with both the presence of moment gradients and intermediate stiffeners, with a new parameter proposed to quantify the local moment gradient. It was shown from the tests that the specimens subjected to moment gradients, despite the presence of shear, exhibited higher ultimate moment capacities (up to 10.5% for stiffened specimens and 3.4% for unstiffened specimens) than those subjected to uniform moments. This is attributed to the delay in the local buckling of the critical cross-section of beams under moment gradients due to the restraint provided by the less heavily stressed adjacent cross-sections

Design of stainless steel structural systems by GMNIA with strain limits

Design by GMNIA (Geometrically and Materially Nonlinear Analysis with Imperfections) allows the key behavioural features of structures to be directly captured in the analysis, improving accuracy and dramatically reducing the need for subsequent design checks. Since the analysis of frames typically employs beam elements, in which local buckling of cross-sections cannot be explicitly simulated, cross-section classification and capacity checks remain necessary. However, the step-wise and overly conservative nature of these traditional checks restricts accuracy. To resolve this, the use of strain limits, defined using the Continuous Strength Method, in place of these cross-section checks has been proposed. This design method is extended to indeterminate stainless steel structural systems herein. Ultimate load-carrying capacity predictions from the proposed design approach are compared against results obtained from benchmark shell finite element models as well as predictions using traditional stainless steel design methods. The new design framework allows for element interaction at the cross-section level, the influence of local moment gradients, the partial spread of plasticity, moment redistribution, strain hardening and the visualisation of the structural failure mechanism, resulting in more accurate and consistent resistance predictions. The method is included in AISC 370 and prEN 1993-1-14 offering a step change in efficiency for the future direction of structural stainless steel design

Elevated temperature material properties of a new high-chromium austenitic stainless steel

A testing programme was conducted to investigate the material properties of a new high-chromium grade of austenitic stainless steel - EN 1.4420 at elevated temperatures. A total of 164 tensile coupons extracted from both cold-rolled and hot-rolled sheets were tested; 80 coupons were tested isothermally with temperatures ranging from 25 °C to 1100 °C, and 84 were tested anisothermally with stress levels ranging from 10% to 90% of the material 0.2% proof stress at room temperature. The experimentally derived reduction factors for the key material properties were compared with existing design values. Design recommendations for the elevated temperature reduction factors were then proposed for this new grade, and a two-stage Ramberg–Osgood model was shown to be able to accurately represent the material stress–strain response at elevated temperature

Effects of material nonlinearity on the global analysis and stability of stainless steel frames

© 2017 Elsevier Ltd In structural frames, second order effects refer to the internal forces and moments that arise as a result of deformations under load (i.e. geometrical nonlinearity). EN 1993-1-1 states that global second order effects may be neglected if the critical load factor of the frame αcris greater than or equal to 10 for an elastic analysis, or greater than or equal to 15 when a plastic global analysis is used. No specific guidance is provided in EN 1993-1-4 for the design of stainless steel frames, for which the nonlinear stress-strain behaviour of the material will result in greater deformations as the material loses its stiffness. A study of the effects of material nonlinearity on the stability of stainless steel frames is presented herein. A series of different frame geometries and loading conditions are considered. Based on the findings, proposals for the treatment of the influence of material nonlinearity on the global analysis and design of stainless steel frames are presented

Reducing the carbon footprint of lightweight aggregate concrete

Lightweight aggregate concrete (LWAC) is a special concrete type with density of no more than 2200 kg/m³. Lower densities than normal weight concrete (2400-2500 kg/m³) are achieved using lightweight aggregates, which may originate from by-products of industrial manufacture such as fly ash, for example Lytag. Currently there is an increasing demand for LWAC for the construction of lightweight composite flooring systems, particularly in commercial buildings. Despite the well-recognized issues and challenges associated with the carbon dioxide (CO²) emissions from cement production, LWAC still contains high quantities of Portland cement (Type I or CEM I) as well as high quantities of total cementitious materials content. This has been primarily utilized to attain a certain workability and pumpability, as well as to not compromise the strength development. As such, the carbon footprint of LWAC is generally higher than that of normal weight concrete, owing also to the carbon intensive lightweight aggregates. In this work, several alternative lightweight aggregate mixes were optimized to maximize Portland cement replacement and reduce the total cementitious materials content without compromising the strength, workability and pumpability of a standard, to Eurocode 2, LC 30/33. The developed mixes contained up to 60% of ground granulated blast-furnace slag, as well as limestone powder, which resulted in a reduced carbon footprint compared to the conventional LWAC mixes. It was possible to reduce the Portland cement content by approximately 40%, the total cementitious materials content by 22% and embodied carbon (life cycle stages A1-3) by 12% compared to the initial, conventional LWAC mixes