176 results found
Bai L, Wadee MA, Köllner A, et al., 2021, Variational modelling of local-global mode interaction in long rectangular hollow section struts with Ramberg-Osgood type material nonlinearity, International Journal of Mechanical Sciences, Vol: 209, ISSN: 0020-7403
A variational model describing the nonlinear mode interaction in thin-walled box-section struts under pure axial compression made from a nonlinear material obeying the Ramberg–Osgood law is presented. The formulation combines continuous displacement functions and generalized coordinates, leading to the derivation of a system of differential and integral equations that describe the static equilibrium response of the strut. Solving the system of equations using numerical continuation techniques reveals the strongly unstable post-buckling response arising from combined geometrical and material nonlinearities during the interactive buckling of the global and local buckling modes—the resulting behaviour being more unstable with decreasing material hardening. A finite element (FE) model is also devised and reveals very similar post-buckling behaviour as highlighted in the variational model. The results compare very well in terms of the mechanical destabilization and the post-buckling deformation, which verifies the analytical model.
Lapira L, Wadee MA, Gardner L, 2021, Nonlinear analytical modelling of flat and hyperbolic paraboloidal panels under shear, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 477, Pages: 1-19, ISSN: 1364-5021
The hyperbolic paraboloid (hypar) form has been widely used in long-span roof structures and the subject of much research under out-of-plane loading. However, the behaviour of hypars under in-plane loading has been less keenly studied and there is no suitable guidance for their design in current codes of practice. A nonlinear analytical model treating the hypar as a deliberate imperfection applied to a flat plate is presented. A Rayleigh-Ritz formulation using appropriate shape functions is developed and the resulting equations are solved using numerical continuation techniques. The results are verified with nonlinear finite element models, showing good correlation across a range of thicknesses and degrees of initial curvature. Key moda lcontributions that influence the behaviour of the hypar are identified, providing insight into the nonlinear behaviour of hypars subject to in-plane shear. The main differences in behaviour between the flat plate and the hypar panel are shown to be most prevalent in the early stages of loading, where the influence of the initial geometry is at its greatest.
Kyvelou P, Slack H, Wadee MA, et al., 2021, Material testing and analysis of WAAM stainless steel, Sheffield, UK, Eurosteel 2020
Behzadi Sofiani B, Gardner L, Wadee MA, et al., 2021, Behaviour and design of fixed-ended steel equal-leg angle section columns, Sheffield, UK, Eurosteel 2020
Behzadi-Sofiani B, Gardner L, Wadee MA, 2021, Fixed-ended stainless steel equal-leg angle section columns - behaviour and design, 8th international conference on coupled instabilities in metal structures (CIMS 2020)
Behzadi-Sofiani B, Gardner L, Wadee MA, et al., 2021, Behaviour and design of fixed-ended steel equal-leg angle section columns, Journal of Constructional Steel Research, Vol: 182, ISSN: 0143-974X
The mechanical behaviour and design of fixed-ended steel equal-leg angle section members subjected to axial compression are addressed in this study. First, the critical buckling behaviour is described. Experimental data on steel equal-leg angle section columns collected from the literature are then used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Validation is performed by means of comparisons between test and numerical results, considering ultimate loads and failure modes, all of which are shown to be generally in good agreement. A numerical parametric study is then presented considering steel angle section columns with a wide range of slenderness values. The behaviour and load-carrying capacity of the columns is shown to be dependent on, not only the column slenderness, but also the ratio of the elastic torsional-flexural buckling load to the elastic minor-axis flexural buckling load. Finally, the collected experimental and generated numerical results are used to develop a new design approach, suitable for incorporation into future revisions of Eurocode 3, for fixed-ended steel equal-leg angle section columns, reflecting the observations made. The proposed approach offers improved accuracy and consistency in strength predictions compared to the existing codified design rules. The reliability of the new design approach, with a recommended partial safety factor γM1 = 1.0, is verified following the EN 1990 procedure.
Wu K, Wadee MA, Gardner L, 2021, Prestressed stayed beam-columns: sensitivity to prestressing levels, pre-cambering and imperfections, Engineering Structures, Vol: 226, ISSN: 0141-0296
The behaviour and structural performance of imperfect beam-columns with crossarms and externally prestressed cable stays are studied numerically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. Both doubly-symmetric and mono-symmetric systems are studied. Sensitivity of the structural response to varying prestressing levels, pre-cambering and initial imperfections is investigated. Different initial imperfection levels and combinations are considered to facilitate the exploration of interactive buckling. The optimum prestressing force in terms of ultimate resistance and two structural efficiency indicators is also studied. It is found that relatively small crossarm lengths, stay diameters and crossarm length ratios should be avoided. Moreover, mono-symmetric cases are more sensitive to the level of pre-cambering than their doubly-symmetric counterparts. Considering both load-carrying capacity and structural efficiency, doubly-symmetric cases perform best with zero pre-cambering, but mono-symmetric cases perform best with upward pre-cambering. As for the true optimum prestressing levels, these are recommended to be significantly above the linearly obtained optimum to maximize the structural efficiency.
Kyvelou P, Slack H, Daskalaki Mountanou D, et al., 2020, Mechanical and microstructural testing of wire and arc additivelymanufactured sheet material, Materials and Design, Vol: 192, ISSN: 0264-1275
Wire and arc additive manufacturing (WAAM) is a method of 3D printing that enables large elements to be built, with reasonable printing times and costs. There are, however, uncertainties relating to the structural performance of WAAM material, including the basic mechanical properties, the degree of anisotropy, the influence of the as-built geometry and the variability in response. Towards addressing this knowledge gap, a comprehensive series of tensile tests on WAAM stainless steel was conducted; the results are presented herein. As-built and machined coupons were tested to investigate the influence of the geometrical irregularity on the stress-strain characteristics, while material anisotropy was explored by testing coupons produced at different angles to the printing orientation. Non-contact measurement techniques were employed to determine the geometric properties and deformation fields of the specimens, while sophisticated analysis methods were used for post processing the test data. The material response revealed a significant degree of anisotropy, explained by the existence of a strong crystallographic texture, uncovered by means of electron backscatter diffraction. Finally, the effective mechanical properties of the as-built material were shown to be strongly dependent on the geometric variability; simple geometric measures were therefore developed to characterise the key aspects of the observed behaviour.
Wadee MA, Phillips ATM, Bekele A, 2020, Effects of disruptive inclusions in sandwich core lattices to enhance energy absorbency and structural isolation performance, Frontiers in Materials, Vol: 7, ISSN: 2296-8016
The energy absorption and structural isolation performance of axially-compressed sandwich structures constructed with stiff face plates separated with an auxetic lattice core metamaterial is studied. Advances in additive manufacturing increasingly allow bespoke, carefully designed, structures to be included within the core lattice to enhance mechanical performance. Currently, the internal structure of the lattice core is deliberately disrupted geometrically to engineer suitable post-buckling behaviour under quasi-static loading. The desirable properties of a high fundamental stiffness and a practically zero underlying stiffness in the post-buckling range ensure that energy may be absorbed within a limited displacement and that any transfer of strain to an attached structure is minimized as far as is feasible. It is demonstrated that such disruptions can be arranged to enhance the panel performance. The concept may be extended to promote cellular buckling where the internal lattice buckles with densification occurring at defined locations and in sequence to absorb energy while maintaining a low underlying mechanical stiffness.
Wu K, Wadee MA, Gardner L, 2020, Interactive buckling in prestressed stayed beam-columns, International Journal of Mechanical Sciences, Vol: 174, ISSN: 0020-7403
The instability of beam-columns with crossarms and externally prestressed cable stays is studied analytically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. A nonlinear analytical model for prestressed stayed beam-columns with doubly-symmetric and mono-symmetric configurations, based on the Rayleigh–Ritz method, is presented that captures modal interactions for perfect geometries explicitly for the first time. It is demonstrated that the theoretical compressive strength enhancements under certain configurations can only be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to severely unstable interactive post-buckling behaviour including the so-called ‘mode jumping’ phenomenon. Moreover, for mono-symmetric stayed beam-columns, it is shown that the varying levels of prestress within the stays can lead to different buckling modes which all have their own characteristic post-buckling responses. The analytical model is verified using a nonlinear finite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.
Wadee MA, Hadjipantelis N, Bazzano JB, et al., 2020, Stability of steel struts with externally anchored prestressed cables, Journal of Constructional Steel Research, Vol: 164, ISSN: 0143-974X
Externally anchored prestressed cables can be employed to enhance the stability of steeltruss compression elements significantly. To demonstrate this concept, a system comprisinga tubular strut subjected to an external compressive load and a prestressed cable anchoredindependently of the strut is studied. Energy methods are utilized to define the elasticstability of the perfect and imperfect systems, after which the first yield and rigid–plasticresponses are explored. The influence of the key controlling parameters, including thelength of the strut, the axial stiffness of the cable and the initial prestressing force, on theelastic stability, the inelastic response and the ultimate strength of the system is demon-strated using analytical and finite element (FE) models. To illustrate the application of thestudied structural concept, FE modelling is employed to simulate the structural response ofa prestressed hangar roof truss. A nearly two-fold enhancement in the load-carrying capac-ity of the truss structure is shown to be achieved owing to the addition of the prestressedcable
Wu K, Wadee MA, Gardner L, 2019, Stability and ultimate behaviour of prestressed stayed beam-columns, Engineering Structures, Vol: 201, ISSN: 0141-0296
The instability of beam-columns with crossarms and externally prestressed cable stays is studied analytically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. Three principal zones of behaviour are identified with two of these each having two sub-zones that relate the critical buckling load to the initial prestressing force applied to the stay cables. The ultimate load-carrying capacity of the beam-columns is evaluated by conducting nonlinear finite element analysis within the commercial package ABAQUS. Results show that the analytically derived critical buckling loads generally provide safe predictions of the ultimate loads due to significant post-buckling strength. It is found that releasing the geometric double symmetry of the system can make for a significantly more efficient structure due to the effect of pre-cambering against the self-weight. The strength and efficiency of stayed beam-column systems opens up a range of potential applications, including lighter alternatives to conventional props to support wide excavations, which currently utilize very heavy steelwork.
Shen J, Wadee MA, 2019, Local-global mode interaction in thin-walled inelastic rectangular hollow section struts part 2: assessment of existing design guidance and new recommendations, Thin-Walled Structures, Vol: 145, ISSN: 0263-8231
The second part of the study on the local–global mode interaction in thin-walled inelastic rectangular hollow section struts focuses on design guidance. Based on the validated finite element (FE) model from the companion paper, a framework for fully automating FE model generation, submission and post-processing for geometric and material nonlinear analysis with imperfections is first presented. The ultimate load data for specimens with different cross-section aspect ratios, cross-sectional slenderness, global slenderness and welding options are generated. The current design rules for thin-walled welded RHS struts are assessed using the numerical results and existing experimental results from the literature by means of structural reliability analysis in accordance with the methodology presented in Annex D of Eurocode EN1990. A modified Direct Strength Method (DSM) relationship is then proposed and it is demonstrated to provide superior ultimate load predictions than the current guidelines.
Shen J, Wadee MA, 2019, Local-global mode interaction in thin-walled inelastic rectangular hollow section struts part 1: nonlinear finite element analysis, Thin-Walled Structures, Vol: 145, ISSN: 0263-8231
Mass efficient thin-walled rectangular hollow section (RHS) struts have been shown to be susceptible to local–global mode interaction and exhibit sensitivity to imperfections. Material nonlinearity may increase the imperfection sensitivity of such members further and affect the final failure mode. Nonlinear finite element (FE) models for welded inelastic thin-walled RHS struts with pre-defined local and global geometric imperfections alongside residual stresses are developed within the commercial package Abaqus and validated against two independent experimental studies. Based on the validated FE model, the effects of material nonlinearity and residual stresses from welding on the ultimate load, mechanical behaviour and the imperfection sensitivity of struts are investigated. A simplified method to determine the initial geometric imperfection amplitude introduced in the FE model with residual stresses explicitly modelled within the ECCS framework is proposed for the first time. The experimental and numerical results in conjunction with existing experimental results from the literature are employed in the companion paper for the assessment of the Effective Width Method and Direct Strength Method, which also forms the basis for a new set of design recommendations.
Hadjipantelis N, Gardner L, Wadee MA, 2019, Finite-element modeling of prestressed cold-formed steel beams, Journal of Structural Engineering, Vol: 145, Pages: 04019100-1-04019100-19, ISSN: 0733-9445
The concept and structural benefits of prestressing cold-formed steel beams are explored in the present paper. In the proposed system, prestressing is applied by means of a high-strength steel cable located within the cross section of the beam at an eccentric location with respect to the strong geometric axis. The internal forces generated by the prestressing are opposite in sign to those induced under subsequent vertical loading. Hence, the development of detrimental compressive stresses within the top region of the cold-formed steel beam is delayed and thus the load-carrying capacity of the beam is enhanced. Owing to the precamber that is induced along the member during the prestressing stage, the overall deflections of the beam are also reduced significantly. In the present paper, finite-element (FE) modeling was employed to simulate the mechanical behavior of prestressed cold-formed steel beams during the prestressing and vertical loading stages. Following the validation of the FE modeling approach, a set of parametric studies was conducted, where the influence of the key controlling parameters on the structural benefits obtained from the prestressing process was investigated. The parametric results were utilized to determine how the benefits obtained from the addition of the prestressed cable can be maximized, demonstrating the significant enhancements in the performance of the cold-formed steel beam that can be achieved.
Champneys AR, Dodwell TJ, Groh RMJ, et al., 2019, Happy catastrophe: Recent progress in analysis and exploitation of elastic instability, Frontiers in Applied Mathematics and Statistics, Vol: 5, Pages: 1-30, ISSN: 2297-4687
A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and nonlinear science. The emphasis is on thin elastic structures that lose stability subcritically — without a nearby stable post-buckled state — a canonical example being a uniformly axially-loaded cylindrical shell. Such structures are hard to design and certify because imperfections or shocks trigger buckling at loads well below the threshold of linear stability. A resurgence of interest in structural instability phenomena suggests practical stability assessment require stochastic approaches and imperfection maps. This article surveys a different philosophy; the buckling process and ultimate post-buckled state are well described by the perfect problem. The significance of the Maxwell load is emphasised, where energy of the unbuckled and fully developed buckle patterns are equal, as is the energetic preference of localised states, stable and unstable versions of which connect in a snaking load-deflection path. The state of the art is presented on analytical, numerical and experimental methods. Pseudo15 arclength continuation (path-following) of a finite-element approximation computes families of complex localised states. Numerical implementation of a mountain-pass energy method then predicts the energy barrier through which the buckling process occurs. Recent developments also indicate how such procedures can be replicated experimentally; unstable states being accessed by careful control of constraints, and stability margins assessed by shock sensitivity experiments. Finally, the fact that subcritical instabilities can be robust, not being undone by reversal of the loading path, opens up potential for technological exploitation. Several examples at different length scales are discussed; a cable-stayed prestressed column, two examples of adaptive structures inspired by morphing aeroelastic surfaces, and a model for a functional auxetic material.
Hadjipantelis N, Gardner L, Wadee MA, 2019, Design of prestressed cold-formed steel beams, Thin-Walled Structures, Vol: 140, Pages: 565-578, ISSN: 0263-8231
Structural design rules for prestressed cold-formed steel beams, considering both the prestressing and imposed vertical loading stages, are presented herein. In the proposed approach, the cold-formed steel member is designed as a beam-column using linear interaction equations in conjunction with the Direct Strength Method (DSM), while the prestressed cable is designed by ensuring that its tensile capacity is not violated during the two loading stages. In the present paper, the design approach and the failure criteria, which define the permissible design zone for the prestressed system, are first introduced. The suitability of the design recommendations is then assessed by comparing a set of parametric finite element (FE) results for several combinations of prestress levels, beam geometries and cable sizes, with the corresponding design predictions. Finally, following reliability analysis, the implementation of the design recommendations is illustrated through a practical worked example.
Hadjipantelis N, Kyvelou P, Gardner L, et al., 2019, Numerical modelling of prestressed composite cold-formed steel flooring systems, Seventh International Conference in Structural Engineering, Mechanics and Computation, Publisher: CRC Press
A novel and highly-efficient prestressed composite flooring system comprising cold-formed steel joists and wood-based floorboards is introduced herein. The prestressing is applied by means of a high-strength steel cable housed within the bottom hollow flange of the steel joist, while the composite action is mobilised by making simple alterations to the currently employed fastening arrangements between the joist and the board. Geometrically and materially nonlinear finite element models with initial geometric imperfections have been developed to simulate the behaviour of the proposed system during the prestressing and vertical loading stages. The structural performance of the prestressed system is compared with that of conventional non-prestressed systems, demonstrating that substantial benefits can be achieved both in terms of load-carrying capacity and serviceability performance. Subsequently, a parametric study is conducted to investigate the effect of the steel section thickness on the ultimate moment capacity and bending stiffness of the system.
Hadjipantelis N, 2019, Prestressed cold-formed steel beams
Shen J, Wadee MA, 2019, Sensitivity to local imperfections in inelastic thin-walled rectangular hollow section struts, Structures, Vol: 17, Pages: 43-57, ISSN: 2352-0124
Mass efficient inelastic thin-walled rectangular hollow section (RHS) struts practically always fail in a combination of local–global interactive buckling and material nonlinearity while also exhibiting high sensitivity to initial imperfections. Nonlinear finite element (FE) models for inelastic thin-walled RHS struts with pre-defined local and global geometric imperfections are developed within the commercial package Abaqus. Using a unified local imperfection measurement based on equal local bending energy, the effects of imperfect cross-section profiles, imperfection wavelength and the degree of localization in the longitudinal direction on the ultimate load and the nonlinear equilibrium path are investigated for four characteristic length struts at different material yielding stress levels. The corresponding most severe imperfection profiles are determined and are found to be qualitatively different to the linear eigenmodes in all cases. Moreover, it is found that the most severe purely periodic imperfections may be used to provide a safe approximation of the ultimate load when the corresponding amplitude is constrained to the manufacturing tolerance level. An extensive parametric study on the wavelength of the most severe periodic imperfection profile is conducted and a relationship for this is proposed in terms of the normalized local slenderness, which compares excellently with the FE results.
Wadee MA, Phillips ATM, Bekele A, 2019, From buckliphobes to buckliphiles: Recent developments in exploiting positive virtues of instability, 7th International Conference on Structural Engineering, Mechanics and Computation (SEMC), Publisher: CRC PRESS-BALKEMA, Pages: 455-461
Hadjipantelis N, Gardner L, Wadee MA, 2018, Prestressed cold-formed steel beams – parametric studies and design recommendations, Hong Kong, China, Ninth International Conference on Advances in Steel Structures, Publisher: Hong Kong Institute of Steel Construction Limited
Owing to their enhanced load-carrying and serviceability performances, prestressed coldformed steel beams can potentially open up new applications within the construction industry. In theproposed concept, an eccentric prestressing force is applied to cold-formed steel beams by means of acable that is housed within a bottom hollow flange. During prestressing, tensile stresses are inducedwithin the top region of the beam, thus delaying the occurrence of local instabilities under subsequentvertical loading. Consequently, the moment capacity of the beam is enhanced. Furthermore, owing tothe prestressing, a pre-camber is also induced along the member, thus decreasing the overall verticaldeflections significantly. Following discussion of the mechanical behaviour of the proposed beams,design recommendations are developed by employing interaction equations alongside the DirectStrength Method. Subsequently, finite element (FE) analysis is employed to investigate the effects of theprestress level and the section slenderness of the steel beam on the benefits obtained from theprestressing process. The parametric FE results are then utilised to assess the design recommendations.
Zhang W, Gardner L, Wadee MA, et al., 2018, Analytical solutions for the inelastic lateral‑torsional buckling of I‑beams under pure bending via plate‑beam theory, International Journal of Steel Structures, Vol: 18, Pages: 1440-1463, ISSN: 1598-2351
The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner’s coefficient have been presented due to the limitation of Vlasov’s buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler–Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair’s formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.
Bai L, Yang J, Wadee MA, 2018, Cellular buckling from nonlinear mode interaction in unequal-leg angle struts, Thin-Walled Structures, Vol: 132, Pages: 316-331, ISSN: 0263-8231
A variational model based on total potential energy principles that describes the nonlinear mode interaction in thin-walled unequal-leg angle struts under pure axial compression is presented. The formulation, which combines continuous displacement functions and generalized coordinates, leads to the derivation of a system of differential and integral equations that describe the static equilibrium response of the strut. Solving the system of equations using numerical continuation techniques reveals, for the first time, progressive cellular buckling (or snaking) represented by a sequence of snap-back instabilities arising from the nonlinear interaction of the weak-axis flexural, strong-axis flexural and torsional buckling modes—the resulting behaviour being highly unstable. For verification purposes, a finite element (FE) model is also devised and the sequential snap-back instabilities are also captured within its framework. Moreover, once an initial geometric perturbation is incorporated within the variational model it compares very well with the FE model.
Hadjipantelis N, Gardner L, Wadee MA, 2018, Prestressed cold-formed steel beams: concept and mechanical behaviour, Engineering Structures, Vol: 172, Pages: 1057-1072, ISSN: 0141-0296
An innovative concept, whereby the load-carrying capacity and serviceability performance of cold-formed steel beams are enhanced by utilising prestressing techniques, is presented. The prestressing force is applied by means of a high-strength steel cable, which is housed at a location eccentric to the strong geometric axis within the bottom hollow flange of the cold-formed steel beam, inducing initial stresses in the beam that are opposite in sign to those introduced during the subsequent loading stage. As a consequence, the development of local instabilities during loading is delayed and thus the capacity of the beam is enhanced. Furthermore, the pre-camber induced during prestressing, as well as the contribution of the cable to the bending stiffness of the system, decrease the overall vertical deflections of the beam. The conceptual development of prestressed cold-formed steel beams and a study investigating the potential benefits are presented. The mechanical behaviour of the proposed beams in both the prestressing and imposed loading stages is described in terms of analytical expressions, while failure criteria for the design of the cold-formed steel beam and the cable are also developed by employing interaction equations in conjunction with the Direct Strength Method. Geometrically and materially nonlinear finite element analysis with imperfections is employed to simulate the behaviour of the proposed beams. Sample numerical results are presented and compared with the developed analytical expressions and failure criteria, demonstrating the substantial enhancement in moment capacity and serviceability performance offered by these beams.
Shen J, Wadee MA, 2018, Sensitivity of elastic thin-walled rectangular hollow section struts to manufacturing tolerance level imperfections., Engineering Structures, Vol: 170, Pages: 146-166, ISSN: 0141-0296
Finite element models for elastic thin-walled rectangular hollow section (RHS) struts with pre-defined local and global geometric imperfections are developed within the commercial package ABAQUS. A unified local imperfection measurement based on equal local bending energy is proposed. The effects of imperfect cross-section profiles, imperfection wavelength in the longitudinal direction and the degree of imperfection localization on the ultimate load and equilibrium path are investigated and the most severe imperfection profiles are determined. A parametric study on the wavelength of the most severe local imperfection profile is conducted and a semi-empirical equation to approximate the corresponding wavelength is proposed. Moreover, an equation to calculate the global buckling load of thin-walled RHS struts with tolerance level doubly-symmetric cross-section local imperfections is proposed.
Hadjipantelis N, Gardner L, Wadee MA, 2018, Prestressed cold-formed steel beams - conceptual development, Lisbon, Eight International Conference on Thin-Walled Structures
Shen J, Wadee MA, 2018, Length effects on interactive buckling in thin-walled rectangular hollow section struts, Thin Walled Structures, Vol: 128, Pages: 152-170, ISSN: 0263-8231
A variational model formulated using analytical techniques describing the nonlinear coupling between local and global buckling modes within an elastic thin-walled rectangular hollow section strut is presented. A system of nonlinear differential and integral equations subject to boundary conditions is derived and solved using numerical continuation techniques. The nonlinear behaviour of four representative lengths is investigated, which are characterized by the post-buckling equilibrium paths. The numerical results from the variational model are validated using a nonlinear finite element model and largely show excellent comparisons, particularly for the practically important ultimate load and the initial post-buckling behaviour. Boundaries for the four distinct length-dependent zones are identified and the most unstable zone is demonstrated to have a considerably narrower length range than previously determined for practical corner boundary conditions within the cross-section.
Fajuyitan OK, Sadowski AJ, Wadee MA, et al., 2018, Nonlinear behaviour of short elastic cylindrical shells under global bending, Thin-Walled Structures, Vol: 124, Pages: 574-587, ISSN: 0263-8231
A recent computational study identified four distinct domains of stability behaviour at different lengths in thin elastic cylindrical shells under global bending. Cylinders of sufficient length suffer from fully-developed cross-sectional ovalisation and fail by local buckling at a moment very close to the Brazier prediction. Progressively shorter cylinders experience less ovalisation owing to the increasingly strong restraint provided by the boundary at the edges. Very short thin cylinders, however, restrain the formation of even a local buckle and fail through a limit point instability at moments and curvatures significantly in excess of the classical elastic prediction. This limit point behaviour is not caused by ovalisation but by the growth of a destabilising fold on the compressed meridian.The nonlinear behaviour of very short cylinders under global bending is investigated in detail herein, covering a wide range of lengths, radius to thickness ratios and boundary conditions with both restrained and unrestrained meridional rotations corresponding to ‘clamped’ and ‘simply-supported’ conditions respectively. Two types of imperfections are investigated, the critical buckling eigenmode and a realistic manufacturing-related ‘weld depression’. A complex insensitivity to these imperfections is revealed owing to a pre-buckling stress state dominated by local compatibility bending, and the cylinder length is confirmed as playing a crucial role in governing this behaviour. The study contributes to the characterisation of multi-segment shells with very short individual cylindrical segments, often found in the aerospace and marine industries as well as in specialised civil engineering applications such as LIPP® silos.
Shen J, Wadee MA, 2018, Imperfection sensitivity of thin-walled rectangular hollow section struts susceptible to interactive buckling, International Journal of Non-Linear Mechanics, Vol: 99, Pages: 112-130, ISSN: 0020-7462
A variational model describing the interactive buckling of thin-walled rectangular hollow section struts with geometric imperfections is developed based on analytical techniques. A system of nonlinear differential and integral equilibrium equations is derived and solved using numerical continuation. Imperfection sensitivity studies focus on the cases where the global and local buckling loads are close. The equilibrium behaviour of struts with varying imperfection sizes, characterized by the equilibrium paths and the progressive change in local buckling wavelength, is highlighted and compared. The numerical results reveal that struts exhibiting mode interaction are very sensitive to both local and global imperfections. The results from the variational model are verified using the finite element method in conjunction with the static Riks method and show good comparisons. A simplified method to calculate the pitchfork bifurcation load where mode interaction is triggered for struts with a global imperfection is developed for the first time. The simplified method is calibrated to predict the ultimate load for struts with tolerance level global imperfections and combined imperfections based on the parametric study, which also reveals that local and global imperfections are relatively more significant where global and local buckling are critical respectively. Finally, the ultimate load for struts with tolerance level geometric imperfections is compared with the existing Direct Strength Method (DSM). Potential dangers of making unsafe load-carrying capacity predictions by the DSM are highlighted and an improved strength equation is proposed.
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