Flat Stiffeners Research Articles

Analysis of isotropic stiffened plate structure

The analysis of stiffened plate has been carried out using finite element method. The study is divided into static and dynamic analyses. Primarily, free vibration frequencies of the stiffened plate have been determined followed by determination of deflection and von Mises stress for the stiffened plate subjected to the unit uniformly distributed load (1 kN/m2). Further, deflection and von Mises stress are determined, when the plate structure is subjected to hydrostatic loading. The analyses, static and dynamic, have been done using ANSYS Workbench 15.0. A single flat stiffener is used to stiffen the plate structure and the results are evaluated by varying the stiffener geometry, keeping the volume of material almost same as the unstiffened plate. Stiffened plate structure is very popular in the structural engineering domain and has a wide range of engineering applications from ship to aerospace structures. The material used to model stiffener is extracted from the primary plate for keeping the same volume of material. The plate structure is stiffened to reduce the out-of-plane bending even if the same (approximately) amount of material is utilised. Eight-noded plate bending and two-noded beam elements are used to model the plate and stiffener, respectively. The obtained results are compared with the published results and the effect of varying stiffener geometry is further examined. It may be concluded that the response of the stiffened plates are better compared to unstiffened plate even if the same or even less quantity of material is utilised in stiffening. The present findings are useful for the designers when the plate structure is influenced by the surrounding fluid.

Buckling behavior of orthotropic steel deck stiffened by slender bulb flats for large span bridges

Slender bulb flat stiffeners with a large height-to-thickness ratio were proposed for the orthotropic steel decks (OSDs) in a large span suspension bridge. The buckling behavior of the panels stiffened with bulb stiffeners under pure compression was experimentally and numerically studied in this paper. Four specimens consisting of four longitudinal stiffeners and a top deck plate were fabricated and subjected to axial compression loading tests. Finite element models were established and validated by the result tests. A parametric analysis was conducted to study the effects of residual stresses and geometric imperfections on buckling behavior. A buckling failure of overall stiffener buckling before the yielding and ductile post-buckling behavior were observed in the tests. A buckling strength of 311∼337 MPa was obtained in the tests. The ratio of buckling stress to yield strength ranging from 0.80 to 0.86 was slightly lower than that of closed ribs, which shows a potential use of the slender bulb flat in large span suspension bridges. The numerical results showed that the residual stresses can decrease the load-bearing capacity by 10%. The residual stresses have a higher influence on the resistance than the regular geometrical imperfections. The standard vehicle load has negligible influence on the buckling resistance, but overload may cause a certain decrease.

Elastic Critical Resistance of the Simple Beam Grillage Resulting from the Lateral Torsional Buckling Condition: FEM Modelling and Analytical Considerations.

Transversely loaded beam grillages are quite often used in industrial construction. In order to produce a safe design of such structures, it is necessary to account for the lateral torsional buckling phenomenon, which reduces load-bearing capacity. To be able to calculate the relevant reduction factor, the elastic critical load must be determined. As regards the existing design practice for such structures, simplified conditions are assumed for the mutual restraint of the component beams. However, this approach does not correspond to reality. This study discusses the results of numerical investigations and analytical calculations concerning the effect of the elastic action of simple beam grillage (SBG) joints on the critical load, which results from the lateral torsional buckling (LTB) condition. The SBG was defined as a flat system of interconnected beams, unstiffened laterally and loaded perpendicularly to the grillage plane. The analysis covered H-shaped grillages with different span ratios of component beams, in which the main (coupling) beam was decisive for instability. The effectiveness of the use of closed-section stiffeners at the grillage joints was also investigated. The grillage elastic critical resistances (ECR) were determined for two variants of joint stiffening. The computations were performed by means of FEM numerical simulations. The spatial models were discretised with the following elements: (1) solid ones in Abaqus, (2) shell ones in ConSteel, and (3) thin-walled bars in ConSteel. The LTB critical moments of the weakest beam (critical beam), elastically restrained against warping and against lateral rotation (in the LTB plane), were computed using the analytical methods developed by the authors. To this end, the methods were proposed to determine the indexes of the critical beam elastic restraint in the adjacent stiffening beams. In the study, it was demonstrated that (1) taking into account the conditions of mutual elastic restraint and interaction of the component beams provides a more accurate assessment of the grillage ECR, (2) the use of closed-section stiffeners in the grillage joints increase the ECR compared with classic flat stiffeners, (3) the grillage ECR can be estimated based on the critical moment Mcr of the weakest beam (critical beam) when the conditions of its elastic restraint in joints are accounted for.

Simulations of poroelastic materials in a complex acoustic system using frequency-dependent parameters in the mid-frequency range

Efficiency requirements prompt manufacturers to develop ever lighter acoustic packages in vehicles. Poroelastic materials are essential to achieve the desired interior noise level targets and thus the simulation of their effects is of utmost importance in NVH analyses. However, it is challenging to achieve good validation between finite element method (FEM) based simulation results and measurements in the mid-frequency range (400-1000 Hz). One possible reason could be the lack of using frequency-dependent Biot-paremeters describing the poroelastic materials (PEM) characteristics of trims. The present research aims to employ frequency-dependent Biot-parameters for the PEM materials to investigate the acoustic response of a scaled car-like steel structure composed of flat plates and U-section stiffeners enclosing an air cavity. Porous acoustic material is applied to the walls of the cavity. The focus of the study is to understand the effect of applying frequency-dependent Young's modulus and damping values for the PEM parameters in the 100-1000 Hz range. Simulation results obtained from ESI VPS FEM solver are compared with measurements, with particular focus on the interior sound pressure levels. The simulation methodology, including discretization techniques, structural damping and fluid damping applications are described in detail.

Contribution of longitudinal stiffener rigidity and position to bridge girder integrity

To increase the elastic critical load of a plate, such as I-shaped cross-welded section of bridge girders, slenderness is usually reduced by dividing the web into subpanels, by means of transversal stiffeners and a longitudinal stiffener to increase flexural and torsional stiffness. The optimal solution is defined when the stiffener maximizes the buckling coefficient, with a minimal cross-section area. For this purpose, seven forms of open and closed sections of longitudinal stiffeners, with differing second moment of area, are examined in terms of buckling coefficient by theoretical solution and numerical calculation, to compare their contribution in terms of weight per linear meter of beam. The optimum value of a conventional flat stiffener position, respect panel height and an useful practical law is given to correlate the best position with respect to variations in stress gradient, from pure bending to pure compression. This practical law facilities calculation regarding where to put a stiffener with respect to compressed edge in a web panel subjected to flexural-compressive loads, in order to maximize the benefit of its action and increase the stability of bridge girders.

Strengthening of perforated walls in cable-stayed bridge pylons with double cable planes

This paper focuses on the strengthening methods used for improving the compression behaviors of perforated box-section walls as provided in the anchorage zones of steel pylons. Rectangular plates containing double-row continuous elliptical holes are investigated by employing the boundary condition of simple supporting on four edges in the out-of-plane direction of plate. Two types of strengthening stiffeners, named flat stiffener (FS) and longitudinal stiffener (LS), are considered. Uniaxial compression tests are first conducted for 18 specimens, of which 5 are unstrengthened plates and 13 are strengthened plates. The mechanical behaviors such as stress concentration, out-of-plane deformation, failure pattern, and elasto-plastic ultimate strength are experimentally investigated. Finite element (FE) models are also developed to predict the ultimate strengths of plates with various dimensions. The results of FE analysis are validated by test data. The influences of non-dimensional parameters including plate aspect ratio, hole spacing, hole width, stiffener slenderness ratio, as well as stiffener thickness on the ultimate strengths are illustrated on the basis of numerous parametric studies. Comparison of strengthening efficiency shows that the continuous longitudinal stiffener is the best strengthening method for such perforated plates. The simplified formulas used for estimating the compression strengths of strengthened plates are finally proposed.

Improving the Compression Behaviors of Perforated Plates with Slotted Holes Using Strengthening Stiffeners

AbstractThis research focuses on the strengthening methods used for improving the compression behaviors of plates perforated by slotted holes, as provided in steel bridge pylons for the purposes of access and service. The rectangular plates that were investigated each have a centric slotted hole and are simply supported on four edges in the out-of-plane direction. Three types of strengthening stiffeners, ringed stiffener (RS), flat stiffener (FS), and longitudinal stiffener (LS), are considered. Uniaxial compression tests are first conducted for 41 specimens, of which seven are unstrengthened plates and 34 are strengthened plates. Stress concentrations, failure patterns, and elasto-plastic ultimate strengths are experimentally investigated. Finite element models are further developed to predict the ultimate strengths of plates with various dimensions. The FE results are validated by the test data. The influences of nondimensional parameters including plate aspect ratio, stiffener slenderness ratio, and st...

Opening reinforcement for box-section walls containing continuous elliptical holes in steel pylons

This paper focuses on the reinforcing methods used for improving the compression behaviors of perforated box-section walls as provided in the anchorage zones of steel pylons to hold the cables. The rectangular plates investigated each have single-row continuous elliptical holes and are simply supported on four edges in the out-of-plane direction. Two types of reinforcing stiffeners named flat stiffener (FS) and longitudinal stiffener (LS) are considered. Uniaxial compression tests are first conducted for 46 specimens, of which 10 are unreinforced plates and 36 are reinforced plates. The mechanical behaviors such as stress concentration, out-of-plane deformation, failure pattern, and elasto-plastic ultimate strength are experimentally investigated. Finite element models are further developed to predict the ultimate strengths of plates with various dimensions. The FE results are validated by the test data. The influences of non-dimensional parameters including plate aspect ratio, hole spacing, hole width, stiffener slenderness ratio, as well as stiffener thickness on the ultimate strengths are illustrated on the basis of numerous parametric studies. Comparison of reinforcing efficiency shows that the continuous longitudinal stiffener is the best reinforcing method for such perforated plates. The simplified formulations used for estimating the compression strengths of reinforced plates are finally proposed.

Buckling behavior of strengthened perforated plates under shear loading

This paper is dedicated to the buckling behaviors of strengthened perforated plates under edge shear loading, which is a typical load pattern of steel plates in civil engineering, especially in plate and box girders. The square plates considered each has a centric circular hole and is simply supported on four edges in the out-of-plane direction. Three types of strengthening stiffeners named ringed stiffener (RS), flat stiffener (FSA and FSB) and strip stiffener (SSA, SSB and SSC) are mainly discussed. The finite element method (FEM) has been employed to analyse the elastic and elasto-plastic buckling behavior of unstrengthened and strengthened perforated plates. Results show that most of the strengthened perforated plates behave higher buckling strengths than the unstrengthened ones, while the enhancements in elastic buckling stress and elastoplastic ultimate strength are closely related to sti ffener types as well as plate geometric parameters including plate slenderness ratio and hole diameter to plate width ratio. The critical slenderness ratios of shear loaded strengthened perforated plates, which determine the practical buckling pattern (i.e., elastic or elasto-plastic buckling) of the plates, are also studied. Based on the contrastive analyses of strengthening efficiency considering the influence of stiffener consumption, the most efficient cutout-strengthening methods for shear loaded perforated square plates with different slenderness ratios and circular hole diameter to plate width ratios are preliminarily identified.

Strengthening of perforated plates under uniaxial compression: Buckling analysis

This paper focuses on the cutout-strengthening of perforated steel plates subjected to uniaxial compressive loads. The square plates considered each has a centrally placed circular hole and four simply supported edges in the out-of-plane direction. Four types of stiffeners named ringed stiffener ( RS), flat stiffener ( FS), longitudinal stiffener ( LS) and transverse stiffener ( TS) are mainly discussed. The finite element method (FEM) has been employed to analyse the elastic and elasto-plastic buckling behaviors of strengthened and unstrengthened perforated plates. The results show that the strengthened perforated plates have higher buckling strengths than those of the unstrengthened ones, while the elevations in elastic buckling stress and elasto-plastic ultimate strength are closely related to stiffener types (i.e., RS, FS, LS and TS) as well as plate geometric parameters (i.e., a plate slenderness ratio and a hole diameter ratio). Furthermore, comparisons of strengthening efficiency considering the variations of buckling stress with stiffener weight are carried out, and recommendations on the most efficient cutout-strengthening methods for the uniaxially compressed perforated square plates with centric circular holes are proposed.

On the design of stiffeners in steel plate shear walls

This paper describes a numerical investigation to provide a practical design method for stiffening thin steel plate shear walls. The procedure considers one-sided transverse and longitudinal flat stiffeners located in various arrangements on shear plates which effectively divides the plate into subpanels and expands tension fields across the infill walls. The results obtained from several nonlinear static analyses are employed to draw applicable empirical relationships for evaluating optimal dimensions of stiffeners. The procedure also ascertains the effects of optimised stiffeners on the postbuckling behaviour and ultimate load bearing capacity of stiffened shear walls.

Numerical Investigation on the Crack Propagation in a Flat Stiffened Panel

This work is focussed on the numerical prediction of the fracture resistance of a flat fullscale aluminium alloy 2024 T3 stiffened panel under monotonic traction loading condition. The numerical simulations are based on the micromechanical Gurson-Tvergaard (GT) model for ductile damage. The applicability of the GT model to this kind of structural problem has been studied and assessed by comparing numerical results, obtained by using the WARP 3D finite element code, with experimental data provided from literature.

Minimum cost design of a welded stiffened square plate loaded by biaxial compression

The optimized plate structure consists of a simply supported square base plate stiffened with an orthogonal grid of flat stiffeners welded to the base plate by fillet welds. The uniformly distributed compressive load acts biaxially in the plane determined by the centre of gravity of T-sections, which consist of a part of the base plate and of a stiffener. In the optimization process the number of stiffeners as well as the thicknesses of the base plate and flat stiffeners, which minimize the cost function and fulfil the design constraints, as sought. The cost function includes the cost of material, assembly, welding and painting. Constraints relate to the global buckling, local buckling of base plate parts and stiffeners as well as to the deflection due to shrinkage of welds. To illustrate the effectiveness of the mathematical methods, the problem is solved by the Rosenbrock’s hill-climb algorithm as well as by entropy-based unconstrained minimization.

Buckling of stiffened plates with bulb flat flanges

The subject of this research is the buckling behavior of a rectangular plate, with a bulb flat stiffener attached to one side of the plate. The stiffener cross section has a thin web and a bulb flat flange that extends to one side of the web. The stiffened plate structure is subjected to axial compression that increases to the buckling load. Results of the investigation include planar property formulas for the asymmetric flange geometry, an analytic expression for the Saint-Venant torsional constant of the flange cross section, and an analytic expression for the buckling stress corresponding to a tripping mode of the structure. The torsional constant for the bulb flat stiffener is 15–23% higher than understood previously. The analytic expression for the buckling stress of a bulb flat stiffened plate differs by less than 4% from finite element and experimental results.

Torsional rigidities of open stiffeners to compression flanges

A critical review of code provisions and other proposals concerning the requirements for torsional rigidities of flat stiffeners to compression flanges is made. The relevant rules are investigated by means of 65 tests on compressed, stiffened plates with various loading and supporting conditions. A new design rule for the determination of the dimensions of flat stiffeners, based on their ultimate stress and the ultimate stress of the stiffened plate, is proposed and relevant design charts are given.

Buckling and Failure of Flat Stiffened Panels

Compression panels, regardless of the local buckling of the skin, can be divided into three regions: short panels, having slenderness ratio equal to or less than 10, long panels, which are shown to fail essentially because of the long wave buckling of the skin, and panels of intermediate length in the transition region. In this paper, a comprehensive and self-sufficient analysis is presented for computing the failing stresses of stiffened panels, in particular, Z-section stiffened panels, in all possible regions of interest. The analysis not only includes the review of the methods previously proposed, but also comprises of many new results, such as the author's most recent formulas based on energy methods for the short and long wave buckling of the skin, the development of the formulas for the maximum strength of panels, and the application of the power law for determining the strength of the panels in the transition range. Since numerous types of panels and modes of failure are involved, the methods of analysis naturally are complex. Therefore, for the clarification of the various steps involved in the computations and for the removal of the confusion that may arise in the minds of the readers, adequate examples are included wherever needed. Extensive comparison of the analysis also is made with tests on 75S-T6 and 24S-T aluminum Z-stiffened panels. It is shown that the analysis is in good agreement with tests.

A finite prism element for stability analysis of bulb flat stiffeners

For the purpose of analysing the effect of the bulb on the torsional buckling stress of panels with bulb flat stiffeners, an element in the form of a triangular prism has been developed. The bulb was divided up into a mesh of such prisms, whilst the web was treated according to classical thin plate theory. The elastic and geometric stiffness matrices of a typical prism are presented in explicit form, and the procedure for enforcing compatibility between the bulb and web plate, in order to connect them together, is explained.

Critical Buckling of Some Stiffened Panels in Compression, Shear and Bending

SummaryPrevious papers by the authors and others have developed exact methods for computing the critical buckling loads of prismatic assemblies of rigidly interconnected thin flat rectangular plates. The plates may be isotropic or anisotropic and can carry uniform in-plane shear stresses and transverse stresses in addition to a longitudinal stress which varies linearly over the cross section but is longitudinally invariant. Published results obtained using these methods have only covered a few of the types of structure and loading which are of interest. This paper presents results which complement those already published. For instance, interaction curves are given for common types of panel in combined in-plane shear and longitudinal compression and bending. About half of these curves are nearly parabolic while some others differ greatly from the parabola, which errs on the safe side for all the results presented. Other results cover critical loads other than the lowest, panels with bulb flat stiffeners, as used for bridge decks, and the effects of assumptions usually made when idealising real panels before computation.