Buckling Of Stiffeners Research Articles

Plate and stiffener buckling in transversely loaded steel panels

AbstractStiffened plates may be loaded by axial forces in two directions, i.e., along and transverse to the stiffeners, by in‐plane shear force, and by out‐of‐plane loads as from traffic or water pressure. Special care must be taken for buckling effects caused by the compressive in‐plane forces.The buckling behaviour of plates stiffened with four trapezoidal stiffeners was investigated for the case of compressive axial force directed transverse to the stiffener direction. The width and length of the stiffened plate and the ratio between the plate‐ and stiffener stiffnesses were varied. The investigation aimed to determine criteria to ensure that the dominating buckling mode was either buckling of the plate between the stiffeners, or a predictable buckling pattern of the stiffeners. For this, two formulas are presented, giving the necessary plate‐to‐stiffener stiffness ratio or the maximum length of the panel. Furthermore, capacity approaches for the axial resistance for transverse axial loading are studied, applying the Effective Width Method (EWM) and the Reduced Stress Method (RSM). Comparisons with nonlinear FE‐simulations show that the predictions range from 45% to 99% of the FE‐results.

Postbuckling Strengths of Composite Laminates with a Central Circular/Elliptical Cutout Under In-Plane Combined Loads

This paper deals with the effect of cutouts (i.e., circular and elliptical) aspect ratio on the buckling and postbuckling strengths, and failure characteristics of a simply-supported quasi-isotropic composite laminate subjected to in-plane shear and uni-axial compression combined with in-plane shear loads. The present study is carried out using self developed finite element program. The finite element formulation is based on the first order shear deformation theory and von Karmans assumptions to incorporate geometric nonlinearity. The resulting nonlinear algebraic equations are solved by Newton-Raphson method. The postbuckling strength of the laminate is defined in terms of the first-ply failure load of the lamina predicted by tensor polynomial form of the 3-D Tsai-Hill criterion. It is observed that for maximum buckling and first-ply failure strengths of the laminate with a cutout, it is preferred to have elliptical shape of the cutout as compared to the circular shape of the same area. It is also found that irrespective of load conditions and cutout shapes and sizes, shear load direction has significant effects on buckling and postbuckling stiffness of the laminate; although buckling stiffness is greater under negative shear, but the laminate shows stiffer postbuckling response under positive shear load.

The Width-Thickness Ratio Limits of Thin-Walled Steel Elements with Complex Edge Stiffeners

Complex edge stiffeners are widely used because of their superior performance over simple edge stiffeners in limiting flange buckling and improving local stability. However, most of the studies on complex edge stiffeners are qualitative. In this paper, the criterion to judge the stiffening adequacy based on the buckling half-wavelength and buckling coefficient is proposed. It is considered as the criterion that the edge stiffeners’ stiffness is not less than the minimum stiffening stiffness or the half-wavelength of buckling is not more than the width of the flange. The criterion is followed for the minimum limits of the edge stiffener width−thickness ratios; whether the flange buckling occurs before the edge stiffener buckling and the economic implications are the criteria that should be followed for the maximum limits of the edge stiffener width−thickness ratios. Using the finite strip method, the feasibility of the criteria was verified by comparing them with the rules of simple edge stiffeners. The detailed design requirements for the width−thickness ratio limits of thin-walled steel elements with complex edge stiffeners were first given from an extensive parametric analysis. Based on the optimization algorithm, the suggestions and optimum sizes of complex edge stiffeners for thin-walled steel elements are provided, considering the sections’ economy and performance. It is considered that a ratio of 1:1 between the primary and the secondary edge stiffeners’ widths is the best configuration for elements with complex edge stiffeners.

Study on Seismic Behavior and Influencing Factors of Composite Connection in Moment-resisting Steel Frame

To study the seismic behavior and influencing factors of prefabricated steel frame composite joints, cyclic loading tests of two groups of scaled specimens were carried out, and the refined numerical model was established and its validity was verified. The failure mode, hysteretic behavior and moment-rotation curve of composite joints and pure steel joints were compared, and the influence of composite slab on the mechanical properties of joints was summarized. At the same time, the parameters of the key components were selected as variables to study the changing law of the stress properties of the joints. The results indicate that the main failure modes of the overhanging end plate connection are end plate yield, bolt breakage and stiffener buckling, and the composite joints will also have local crushing of composite slab. The factors that significantly affect the bearing capacity and initial rotational stiffness of joints include the thickness of end plate, the setting of end plate stiffener, the extension of end plate, the strength of steel, the thickness of slab and the diameter of steel bars. In addition, the shape of end plate stiffeners has obvious influence on the stress distribution of joints. Finally, the calculation model of the overhanging end plate connection composite joint's initial rotational stiffness was proposed, and the stiffness superposition method was used to consider the bending stiffness of the end plate. At the same time, its reliability and high accuracy were verified, which was of great significance to engineering application.

Nonlinear thermal buckling instability analysis of a rotating nanocomposite beam reinforced with graphene platelet via the Chebyshev–Ritz scheme

Resorting to the Chebyshev–Ritz scheme instability as well as post-instability response as a consequence of the buckling occurrence for a rotating nanocomposite beam in a uniform thermal environment is studied. The beam has been reinforced with graphene platelet. The Halpin–Tsai theory is utilized for the sake of specifying the elasticity modulus of the reinforced nanocomposite beam. The Chebyshev set of polynomial functions has been used to serve as a required independent set for the Ritz method. The static displacement field owing to the rotation of the beam and the thermal load is acquired by employing a potent algorithm. The outcomes indicate that for nanocomposite beams with the graphene platelet patterns in the model of O- and U-patterns rotating, respectively, below 9,326, and 7,420 rpm, the graphene reinforcing phase should not be used since it leads to a thermal buckling stiffness for the nanocomposite rotating beam smaller than the thermal buckling stiffness of the associated original rotating beam that just made of a host matrix. Moreover, developing the weight fraction of the graphene platelet for a U-type beam rotating below 9,628 rpm lessens the corresponding thermal buckling stiffness while an X-type beam always strengthens in a similar conditions.

Local/distortional and overall interactive buckling of thin-walled cold-formed steel columns with open cross-section

The difference between local and distortional buckling of thin-walled cold-formed steel sections with stiffened elements, of members in both compression and bending are taken into consideration applying relevant design formulas available in the codes. However, for unstiffened elements, or for those unstiffened enough, the difference between distortional and local buckling modes, in some cases, and particularly for U-, Z- and L-sections, might be unclear. When these sections are edge stiffened, in the case of lipped flanges, it is not always easy to identify which of the two are dominant, while in the case of interaction with an overall buckling mode, the situation might be even more difficult. Local buckling modes involve the buckling of cross-sectional walls, while distortional buckling, also known as “stiffener buckling” or “local-torsional buckling”, is characterised by the rotation of the flange at the flange/web junction in members with edge stiffened elements. Both types of buckling are also known as “sectional” buckling modes. For interactive local/distortional buckling with the overall one, the correct evaluation of the “short” member capacity might play a significant role when checking the design capacity of a slender thin-walled member prone to interactive sectional-overall buckling mode. In the case of a stiffened flange, the effectiveness of the stiffeners can make the difference between local and distortion buckling. A boundary between local and distortional bucking of a given open section can be established to be considered in the design. To correctly apply the Ayrton–Perry formula, in order to get the ultimate capacity of a thin-walled cold-formed steel slender member, prone to interactive local or distortional buckling with the overall one, the strength of the short member has to be identified. This paper summarises the study of this problem, including the main results and conclusions, emphasising that it is difficult to separate the local and distortional modes in the case of cold-formed steel open sections used in practice, and there is some interaction between these two modes.

Elastic design of skid beams in offshore load-out systems

Skid beams are essential components in skidded load-out systems, widely used in offshore operations, and are usually made in plate or box girder forms. They are continued from the jetty to the barge for a relatively long length and are the foundation of portable superstructures to transfer the distributed vertical load to the jetty/barge. Finite element analysis is usually used to verify the strength and stability of the skid beams' components, including flange, web, and stiffener. As FEM usually includes many analyses with a trial-and-error process, this study presents a general and explicit design procedure for skid beams in load-out operations. The main design criteria are the flange's bending capacity as well as the web and stiffener's buckling capacity. The generalized integral transform technique (GITT) is applied to solve the bending equation of the flange and the buckling equations of the web and stiffener with hinged and rigid connections. An algorithm is suggested by which some design curves (concise formulas) are obtained to find the maximum slenderness ratios of the skid beam's components. Accordingly, a step-by-step design procedure is presented, which can be easily used for practical purposes and can be a better replacement for finite element analysis. Comparing the analytical method with FE modeling, there is acceptable agreement and excellent convergence. A realistic design shows that the reduction of skid beam weight is not more than 10% due to rigid connections. In addition, the weight is reduced by increasing the web and decreasing the stiffener aspect ratios.

Interactive buckling of wide plates made of Functionally Graded Materials with rectangular stiffeners

A phenomenon of multimodal buckling of wide stiffened plates made of Functionally Graded Materials (FGM) subject to uniform compression in the elastic range is considered. This phenomenon occurs only when the eigenvalues corresponding to the global mode and the lowest local mode are comparable. Dimensions of wide plates with rectangular stiffeners were selected to make the eigenvalues close to one another. All simulations were conducted with the finite element method, where the behavior of a single segment of the stiffened plate was modeled.​ Symmetry conditions were assumed along the edges connecting the segments, whereas modified boundary conditions were assumed at both the ends to fulfill strictly the conditions of free support of the plate. A nonlinear problem was solved with the Riks algorithm to trace stable and unstable equilibrium paths. Values of the ultimate load-carrying capacity determined in ultimate points, plate modes in the ultimate state and under considerable overloading were analyzed. It was found that the cases of plates with stiffeners of the stiffness comparable to the stiffness of the skin were dangerous in particular, as the stiffener stability loss decreased significantly the ultimate load-carrying capacity of the whole structure. If the local mode of “stiffener buckling” is neglected by considering the corresponding imperfection, a considerable overestimation of the load-carrying capacity of the structure can take place, regardless of the fact if it is the lowest eigenmode. Strong over-rigidity of the stiffener causes that only the plate skin is subject to buckling and, thus, the load-carrying capacity of the whole structure improves. In the extreme situation, it leads to one-mode buckling. Thermal loads are neglected in this study.

Theoretical study on the rotation angle and bearing capacity of beam-to-column composite connections in prefabricated steel frames

To study the rotation mechanisms of the steel column, end-plate, and end-plate stiffener of extended end-plate joints, cyclic loading tests were carried out on two extended end-plate joints, one of which contained a composite slab. The deformations of these three components during test loading were described using digital images, and their bearing capacities and rotation angles in the elastic stage, yield stage, and strengthening stage were deduced by the component method. The results showed that the failure modes of the extended end-plate joints were yielding of the end-plate, bolt fracture, and end-plate stiffener buckling, and the composite joint experienced local crushing of the composite slab. The composite slab improved the initial rotational stiffness and bearing capacity of the composite joint. The joint rotation angle of the extended end-plate connection was mainly composed of three parts: shear deformation of the panel zone, relative deformation between the end-plate and the column flange, and yield deformation of the end-plate stiffener. The composite slab had a constraining effect on the deformation of these three parts. In addition, by defining the moment–rotation curves of three components, a simplified three-rotation spring model was established to simulate the joint-loading process. The results showed that the model could simulate the test joint-loading process accurately, and is conducive to promoting seismic performance analyses of prefabricated steel frames.

Buckling behaviour of laminated viscoelastic composites under axial loads

This study investigates the buckling response of viscoelastic composite laminates under compression with the objective of better understanding the ply wrinkling behaviour at the early stage of thermoset composite manufacturing. The composite laminate is modelled as a 3-D viscoelastic solid using two different approaches in Abaqus©. As the application of the built-in viscoelastic model of Abaqus© is limited to isotropic materials, a more versatile orthotropic viscoelastic constitutive model based on differential form (DF) of viscoelasticity implemented as a user material subroutine (UMAT) is employed to elucidate the effect of ply anisotropy on the buckling response of uncured/partially cured unidirectional laminates. Numerical results are compared with the experimental data available in the literature to evaluate the accuracy of the proposed approach. Using the numerical model, the influence of various parameters including loading rates, the instantaneous elastic modulus, and in particular the effects of the ply anisotropy on the buckling behaviour of composite laminates are analysed. It has been found that unlike cured composites, the compressive stiffness of uncured prepregs is mainly dominated by the resin modulus rather than the fibre modulus. Additionally, it is shown that the waviness of fibres (fibre-bed effect) which stiffens the prepreg's transverse and shear properties increases its compressive stiffness slightly while the waviness effect on the post buckling stiffness is relatively significant. Hence, conducting compressive tests on uncured and partially cured prepregs as well as partially cured resin films with different thicknesses is suggested to validate the proposed modelling approach more rigorously.

Experimental and numerical study on the ultimate strength of stiffened plates subjected to combined biaxial compression and lateral loads

The ultimate strength of stiffened plates subjected to combined biaxial compression and lateral loads has not been widely investigated yet by experiments. In this study, both experimental and numerical analyses were performed to study the ultimate strength and collapse behaviors of stiffened plates under the combined biaxial compression and lateral loads. And the experimental set-up provides reference for combined loads experiments. The initial deformation of the experimental specimens has been measured by laser scanning technique and taken account in the nonlinear finite element analysis. Collapse modes have also been analyzed and compared, and influences of the interaction of lateral and transverse loads on the ultimate strength have been investigated. Results show that lateral pressure would enhance the ultimate load-carrying capacity when the lateral pressure restrained deformation. And the collapse mode was the combination of local web buckling and lateral-torsional buckling of stiffeners when transverse loads were dominant load components.

Estimation of ultimate strength of ring-stiffened cylindrical shells under external pressure with local shell buckling or torsional buckling of stiffeners

This study discusses the ultimate strength and collapse behavior of ring-stiffened cylindrical shells under external pressure with local shell buckling or torsional buckling of stiffeners. In past studies, the effect of initial deflection shape on the ultimate strength has not been completely elucidated. Additionally, a clarification of the collapse behavior and theoretical formulation based on it has not yet been reached. Therefore, in this study, the influence of the initial deflection shape is investigated using eigenmodes obtained from the elastic buckling eigenvalue analysis and the hungry-horse mode described by a simple equation. Then, the ultimate strength analyses of 432 models of ring-stiffened cylindrical shells with various dimensions are carried out using the nonlinear finite element method. From the analysis, the collapse modes are classified into five categories, namely, the shell buckling (SB) collapse (localized mode SB-1 and uniform deformation mode SB-2), the torsional buckling (TB) collapse (localized mode TB-1 and uniform deformation mode TB-2), and the combined shell-torsional buckling collapse. A new slenderness ratio is proposed using the formula for strength when the circumferential stress reaches yield stress, and the formula for the elastic buckling strength developed previously by the authors. Then, theoretical formulas for the ultimate strength are developed using the slenderness ratio, which can rationally estimate the strength.

Performance of bolted steel-beam to CFST-column joints using stiffened angles in column-removal scenario

This paper presents three experimental investigations on the performance of steel-beam to CFST-column joints using stiffened angle, long bolts and fin plate under a middle column removal scenario. Three specimens were designed and tested. The failure modes and catenary action are investigated in detail. The test results show that increasing the angle plate thickness at the joint could not only improve its performance significantly, but also trigger an early formation of catenary action. Increasing the length of short-limb had influence on the deformation ability of the proposed joint, rather than the load capacity. The buckling of stiffeners could prevent the brittle failure of the joints. With the contribution of catenary action, the joint shows much higher rotation capacities than that required in DoD design guidance. The initial stiffness of the joint was calculated using an analytical model with consideration of bolt pretension. Good agreement to the test results is achieved. A numerical analysis is also carried out, whose results show that adding additional row of bolts would improve the redundancy of the joint under column loss. An equivalent dynamic response evaluation of the joints was also performed. The results show that dynamic amplification coefficient should be worked out considering catenary action under large deformation.

Effects of non-welded multi-rib stiffeners on the performance of steel plate shear walls

This paper presents a numerical investigation of the dynamic performance of steel plate shear walls (SPSWs) stiffened by non-welded multi-rib stiffeners. Multi-rib stiffeners are installed on both sides of the steel plate and connected by threaded bolts through the plate, rather than direct welding as conventionally being done. The influence of constraints between multi-rib stiffeners and steel plate on the performance of SPSWs is first examined by finite element analysis. Afterwards, a numerical model for SPSW structure is developed and validated by the test results. The dynamic performance of SPSW structures with and without non-welded stiffeners is compared in terms of inter-story drift, acceleration response and out-of-plane deformation. Test results indicate that constraints between multi-rib stiffeners and steel plate slightly affect the loading capacity of SPSWs. The loading capacity of the SPSWs with non-welded multi-rib stiffeners is 5.8% lower than that with welded stiffeners. However, buckling of stiffeners can be avoided in the non-welded multi-rib stiffened SPSWs. For the dynamic performance of SPSW structures, use of non-welded multi-rib stiffeners is effective in reducing the inter-story drift, acceleration and out-of-plane deformation of SPSW structures under earthquake attacks, particularly for those subjected to main shocks followed with aftershocks. The use of non-welded stiffeners decreases the maximum inter-story drift and the maximum out-of-plane deformation of SPSW structures by 14.7% and 57.0%, respectively. In addition, non-welded multi-rib stiffeners can uniformly distribute the stiffness of SPSWs along the floors. In general, the proposed non-welded multi-rib stiffeners are effective in enhancing the dynamic performance of SPSWs.

Large inelastic deformation resistance of stiffened panels subjected to lateral loading

This paper presents a simplified formulation for the assessment of large deformation resistance of stiffened panels subjected to lateral loading. The method is based on rigid plastic material assumptions and the use of yield functions formulated in terms of stress resultants. The method considers the flexibility of the panel ends with respect to inward motion, while the rotational boundary conditions are free or clamped. Concentrated and distributed loads are considered, as is patch loading. The resistance-deformation curves predicted by the proposed method are compared with results from experiments and using LS-DYNA, and good agreement is obtained for panels that are not dominated by shear failure and tripping or local buckling of stiffeners at the early stage of deformation. The formulation provides a useful tool for quick estimates of panels subjected to abnormal or accidental static and transient lateral loads such as ship collisions, dropped objects, explosions, slamming, hydrostatic pressure and ice actions.

Prediction of stiffener buckling in press bend forming of integral panels

In order to predict the buckling of stiffeners in the press bend forming of the integral panel, a method for solving the critical buckling load of the stiffeners in press bend forming process was proposed based on energy method, elastic-plastic mechanics and numerical analysis. Bend to buckle experiments were carried out on the designed press bend dies. It is found that the predicted results based on the proposed method agree well with the experimental results. With the proposed method, the buckling of the stiffeners in press bend forming of the aluminum alloy integral panels with high-stiffener can be predicted reasonably.

Assessment of IACS-CSR implicit safety levels for buckling strength of stiffened panels for double hull tankers

The present study aims at applying structural reliability methods to assess the implicit safety levels of the buckling strength requirements for longitudinal stiffened panels implemented in the IACS Common Structural Rules (CSR) for double hull oil tankers. The buckling strength requirements considered are used in the initial stage of the hull girder scantlings’ design to control the buckling capacity of longitudinal stiffened panels subjected to the compressive loads induced by the hull girder vertical bending. The following buckling collapse failure modes are explicitly considered in the design formulation: uniaxial buckling of the plating between stiffeners, column buckling of stiffeners with attached plating and lateral-torsional buckling or tripping of stiffeners. The paper presents the procedure used to assess the implicit safety levels of the strength requirements for the three buckling collapse failure modes above mentioned, which includes the optimization of the scantlings of the plate panels and longitudinal stiffeners in order to reflect the minimum strength required by the formulation. A first order reliability formulation is adopted, and stochastic models proposed in the literature are used to quantify the uncertainty in the relevant design variables. A sample of five oil tankers representative of the range of application of the IACS-CSR design rules is considered. The effect of corrosion in the implicit safety levels is quantified based on the three corrosion levels of the Net Thickness Approach (NTA) adopted in the design rules. Sensitivity analyses are also performed to quantify the relative contribution or importance of each design random variable to the implicit safety levels.

Determination of optimum diameter of a welded stiffened cylindrical shell

In this overview of loaded a longitudinally stiffened welded circular cylindrical steel shell is investigated. The halved rolled I-section stringers are welded outside to the shell. The simply supported belt-conveyor bridge is loaded by bending with a uniformly distributed normal load. The design constraints are related to the shell buckling, panel stiffener buckling and the maximum deflection of the bridge. The optimum shell thickness as well as the dimensions and number of stringers are sought, which minimize the cost function. The cost function includes the material, fabrication and painting costs. For the comparison an unstiffened shell is also optimized. The cost comparison shows that the cost of stiffened version is smaller than that of the unstiffened one only in those cases when the allowable deflection is strict enough.

Stability of web plates in W-shape columns accounting for flange/web interaction

North American, British and European codes of practice provide design equations for local buckling limit state of W-shape columns, by assuming the web and the flanges are either simply supported or clamped along their lines of junctions. In doing so, the geometric interactions between the web and flange are ignored. In practice, the column webs rarely have simply supported or clamped edges but are rather elastically restrained against rotation. In addition, the in-plane boundary conditions of the web, which is dictated by geometric properties of the flanges, have a great influence on its buckling and post-buckling stiffness. The paper highlights the influence of the flange/web geometric proportions on the stability of web plates in W-shape columns under uniform compression. Results are obtained showing the influence of the flange/web thickness ( t f/ t w) on the buckling and post buckling stiffness of the web. Also, the influence of the flange/web width ( b f/ b w) on the web stability is highlighted. Graphs are presented showing the transitions between various “theoretical” boundary conditions by adjusting the flange/web geometric proportions. These graphs are useful to use in practice in order to achieve economical design of column section.

理想化構造要素法による船体の縦曲げ逐次崩壊解析

An application of the Idealized Structural Unit Method (ISUM) to analyze the progressive collapse behavior of ship's hull girder in longitudinal bending is developed. A new ISUM stiffened plate model that can cope with local panel buckling, overall stiffener buckling and localization of plastic deformation in local plate panel is employed. Stiffeners and panels are modeled individually by beam-column elements and ISUM plate elements with consideration of their interaction effect. A lateral shape function for plate panels based on their collapse mode is assumed. In the present paper, the effects of welding residual stresses are considered both in plate and in stiffeners. The progressive collapse analyses of a 1/3-scale welded steel frigate model and a single-hull VLCC are performed. High computational efficiency and sufficient accuracy of ISUM are demonstrated through a comparison with test results and large-scale nonlinear FEA.