Position Of Stiffeners Research Articles

Numerical study of slender I-girders with one longitudinal stiffener under patch loading

Slender plate I-girders are steel members widely used in bridges, viaducts and heavy industrial buildings, which are subjected to combined bending and shear, making the web panel susceptible to stability problems. Therefore, longitudinal stiffeners are sometimes placed along the web. This paper aims at investigating the load carrying capacity of girders submitted to patch loading (common in bridge launching), using finite element models. A nonlinear stability analysis was carried out considering the initial geometric imperfection as the first buckling eigenmode, with amplitude defined according to EN 1993-1-5 recommendations. The performance of girders with different stiffener locations was evaluated, discussing the structural behavior and associated failure modes. If the stiffener is effective and properly placed, the failure mode is the local buckling of the two web subpanels (which increases the patch loading resistance), although it was verified that the optimal position for patch loading is mainly governed by the web crippling resistance of the upper subpanel. The numerical results are in accordance with the experimental results available in the literature. For the studied girder configurations, the optimal stiffener position for patch loading resistance is closer to the loaded flange when compared to girders under dominant bending. Depending on the cross-sectional shape of the buckling mode, the stiffener can be unfavorable to the patch loading resistance for certain range of positions. Furthermore, the definition of positive or negative cross-sectional imperfections, i.e., the inversion of the curvature of the buckling mode shape, has impact on the load capacity for larger patch loading lengths.

Seismic behaviour of combined steel framed-tube substructure with replaceable shear links

A combined steel framed-tube structure with replaceable shear links (SFTS-links) can make plasticity isolated to links for rapid replacement of damaged links and improve the applicability of SFTS-links with enhanced ductility in high-seismic zones. In this paper, the seismic performance of thirty-storey SFTS-links and SFTS was compared by elasto-plastic time history and nonlinear static analyses. A 2/3-scale double half-storey, one-bay substructure was tested under cyclic loading in two stages. The substructure was repaired by replacing the damaged link in Stage I. Then the substructure restored to its original position was loaded to destruction in Stage II. Analysis of the substructure was conducted for two stages. The results indicate that ductility of SFTS-links is 34% higher than that of SFTS; the link can be replaced even at the story drift angle of 0.43%; replacing the damaged link can substantially improve the performance of the damaged structure; the ductile factor and the maximum viscous damping ratio of the specimen are 3.92, 0.39, respectively, and the maximum rotation angle and overstrength factor of the link are 0.147 rad, 1.54, respectively; the failure mode of the link is that expansion of the weld crack at the chamfer position of stiffeners causes tearing of link web and fracture of stiffeners. A numerical model is developed and verified with the test results. With increasing link length, initial stiffness, peak strength and cumulative energy dissipation decrease. It is recommended that the length ratio of the link should be 0.93–1.26 in SFTS-links.

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.

Flexural Behavior of Rolled Steel I Beam with Different Stiffener Position

Economy, ease and speed of construction are the main factors for using steel as a building material. In this paper conventional hot rolled steel I-beam sections are considered as the main flexural member of industrial buildings. The main goal is to increase the load carrying capacity of the beam with inverted w shape stiffener condition at centre. The initiative was to identify the maximum load behaviour and deflection of steel beams with stiffener in the web. The performance of such beams has been considered only for vertical loads. Hot rolled steel beam of ISMB 100 with stiffener were tested to failure experimentally. The beams were simply supported at the ends and subjected to a 2 equal concentrated load applied at one third of span from both ends. The deflection at centre of beam and various failure patterns are studied. All the beams were analyzed by the finite element method by using general finite element analysis software ANSYS and the results were compared with those obtained experimentally. The finite element results for deformation and ultimate strength shows good agreement with the corresponding values observed in the experiments. At last, a comparative study was carried out using finite element method to examine that which type of beam gives best performance during loading. The numerical results indicate that the use of hot rolled I section with stiffener is an economical and advantageous choice.

Low Velocity Impact Performance of Delaminated Composite Stiffened Shell

Finite element method is presented to study the low velocity impact response of delaminated composite stiffened shell. An eight noded isoparametric shell element based on first order shear deformation theory along with a three noded isoparametric beam element are employed to model the shell and the stiffener, respectively. The stiffeners are placed along the nodal lines and the properties of the stiffeners at nodes are transferred to the corresponding nodes of the shell considering its curvature and eccentricity. The formulation adopted here employs constraint technique to calculate stiffness matrices of stiffener element placed inside shell element so that there is no further increase in the total number of degrees of freedom due to the stiffener. The modified Hertzian contact law is considered to compute the contact force, while the Newmark's time integration algorithm is used to solve the time dependent equations of both impactor and shell. The multi point constraint algorithm is used to model delamination at desired location of the shell. The compatibility of deformation and equilibrium of stress resultants are ensured at the delamination crack front. The effect of stiffener position, delamination and its location, and impactor's initial velocity on dynamic response of a particular stiffened shell are presented.

Free Vibration Analysis of Eccentric and Concentric Isotropic Stiffened Plate with Orthogonal Stiffeners using ANSYS

This paper shows the study of free vibration analysis of stiffened isotropic plates with orthogonal stiffeners placed eccentrically and concentrically to the plates. In this paper finite element model is developed in ANSYS parametric design language code and discretized using 20 node structural element (SOLID 186) and convergence study of isotropic stiffened plates has been performed and compare the results with related published literature. Effects of various parameters such as boundary conditions, aspect ratios, position of stiffeners eccentrically and concentrically to the stiffened plates has been studied. The vibration analysis of stiffened plate have been studied using Block Lanczos algorithm. The results of non dimensional frequency of eccentric and concentric isotropic stiffened plate have been compare at different mode shapes, aspect ratio’s, boundary conditions using ANSYS.

Numerical analysis of influence of intermediate stiffeners setting on the stability behaviour of thin-walled steel tank shell

Cylindrical bolted steel tanks with H/D~1 can be made from very thin steel courses the thickness of which is determined by tension. The important issue is to stiffen the whole shell with intermediate stiffeners to prevent from stability loss in situations when the tank is empty and exposed to a strong wind. The FEM package Abaqus with nonlinear Riks algorithm was used for analysis. A parametric study programmed in python, internal Abaqus language was conducted to establish the influence of number and position of intermediate stiffeners on buckling resistance of the tank. After calculating nearly one thousands tasks, results were gathered with python script and compared with classic design recommendations proposed in Eurocode 3, DIN 18 800 Part 4 and AWWA D103-09. Simplified analytical approaches present in current standards are rather conservative and one may want to look for more sophisticated methods of analysis of tank shells presented in this paper for more economical design of such structures. From the comparison of the results obtained with different numerical strategies such as linear buckling analysis (LBA), geometrically nonlinear analysis of perfect (GNA) and imperfect (GNIA) structure a necessity of taking into account imperfections in GNA arises. Otherwise a capacity of the shell structure may be overestimated even over the value obtained from LBA.

Hybrid GAを用いたスティフナーを有する大型構造物の最適化に関する研究

An optimization technique using the hybrid GA for large structures in which a lot of stiffeners are attached is proposed in this paper. The object function is the mass of structure and the design variables are the number and the position of stiffeners, the shape of stiffener and the thickness of plate. These design variables make a combinational optimization problem for which genetic algorithm is effective. However, this optimization problem includes the position of stiffener and the thickness of plate which are kinds of continuous design variables. A lots of bits are needed for expressing continuous design variables by strings of genetic algorithm in order to have reasonably small increments of them, which results in a large calculation amount. In order to overcome this problem, a hybrid GA is introduced in this paper. Hybrid GA is optimization method which combines GA with another optimization technique which handles continuous design variables. The relation among the thickness of plate, the span of stiffeners attached on the plate, the deflection and the stress of plate are introduced in order to predict suitable design variables in this added optimize technique. The proposed optimization method makes it possible to optimize continuous design variables, the position of stiffeners and the thickness of plate,with small calculation amount. Several selected problems are solved to show the capacity and validity of the proposed method.

Free vibration analysis of isotropic plate with stiffeners using finite element method

This paper presents the free vibration analysis of stiffened isotropic plate by means of finite element method. Stiffeners are used in plates to increase the strength and stiffness. The effect of position of stiffeners on isotropic plate has been studied which involve the possible combination of clamped and free edge condition. The model has been discretized using a 20node solid element (SOLID186) from the ANSYS element library. The natural frequencies are calculated using Block-Lanczos algorithm. The comparisons of stiffened plate with the available results are found to be in good uniformity. The effect of different boundary conditions, stiffeners location, thickness ratio, stiffener thickness to plate thickness and aspect ratio on the vibration analysis of stiffened plates has been studied.

Innovative tooling concepts for cocured composite structures in aircraft applications

Cocuring process is a unique characteristic of composite materials wherein multiple parts like stringers, ribs and spars are simultaneously cured and bonded to a composite skin resulting in an integral structure. It has many benefits like reduction in part count, elimination of stress concentration due to fastener holes in the cocured regions and reduced assembly time and related costs. However, the application of cocuring has been limited on contoured components because of the complexities associated with the tooling. The basic requirements to be fulfilled are (a) consolidation of skins and stiffeners and (b) dimensional tolerance on position and thickness of stiffeners. Proper consolidation can be ensured through the faithful transfer of autoclave pressure by designing tools which are flexible so that they conform to desired shape whereas the positional tolerance can be achieved by using rigid tools. The resolution of such conflicting requirements requires a detailed study of the geometry of the part, design requirements and tolerances achievable on tools. This paper discusses design of tools for two types of cocured structures viz., open and closed cocured structures. The tooling technologies for realising above structures differ considerably. A few tooling concepts have been discussed based on the authors’ experience of developing cocured structures over the last two decades.

Nonlinear bending analysis of ring-stiffened functionally graded circular plates under mechanical and thermal loadings

The large deflection behaviors of ring-stiffened shear deformable functionally graded (FG) circular plates under mechanical and thermal loadings are investigated. Material properties of the FG plate are assumed to be temperature dependent, and graded through the thickness according to the power-law distribution of the volume fraction of the constituents. The nonlinear formulations are based on first-order shear deformation theory (FSDT) and the large deflection von Karman equations. In the theoretical model, the reaction of the stiffener on the plate is applied partly by means of body forces in the plate equilibrium equations. The force interaction is complemented with a set of plate–stiffener displacement compatibility equations. The dynamic relaxation (DR) method combined with the finite difference discretization technique is employed to solve the equilibrium equations. To verify the present solution, several examples are analyzed for linear/nonlinear bending of FG/isotropic circular plates with different boundary conditions. A detailed parametric study is carried out to investigate the influences of the material grading index, thickness-to-radius ratios, temperature dependency of material, temperature rise, stiffener depth, stiffener position and boundary conditions. Moreover, some linear and nonlinear analyses with different thickness-to-radius ratios are carried out to consider the effect of nonlinearity on the results.

Nonlinear Vibration Analysis of Simply Supported Stiffened Plate by a Variational Method

Large-amplitude free vibration analysis of uni-axially single stiffened rectangular plates subjected to transverse loading with simply supported boundary conditions has been presented. The mathematical formulation is based on energy principle. Geometric nonlinearity is accounted for by consideration of nonlinear strain-displacement relations. The static problem is solved through an iterative scheme and the dynamic problem is solved with the static displacement field as an initial guess. Influence of stiffener position, plate aspect ratio, and stiffener to plate thickness ratio on the large amplitude dynamic behavior has been studied. The dynamic behavior has been furnished in the form of backbone curves in a dimensionless frequency-amplitude plane.

Local and distortional buckling of cold-formed steel beams with both edge and intermediate stiffeners in their compression flanges

The true buckling behaviour of cold-formed steel beams with both edge and intermediate stiffeners in their compression flanges has been predicted with the aid of advanced numerical modelling. A series of nonlinear finite element analyses has been carried out to investigate the flexural behaviour of cold-formed Z sections with both edge and intermediate stiffeners in their flanges, when the failure is controlled by local and/or distortional buckling. The effect of the size and position of intermediate stiffeners as well as the effect of the edge stiffener/intermediate stiffener interaction on the buckling behaviour and ultimate strength of these sections has been studied. The knowledge gained from FE analyses was used to check the accuracy of the Eurocode design rules in predicting the ultimate strengths for these sections.

Asymptotic bounds on the globally optimal positions of orthogonal stiffeners for rectangular plates in elastostatic bending

The present paper treats the problem of finding the asymptotic bounds for the globally optimal locations of orthogonal stiffeners minimizing the compliance of a rectangular plate in elastostatic bending. The essence of the paper is the utilization of a method of analysis of orthogonally stiffened rectangular plates first presented by Mazurkiewicz in 1962, and obtained herein in a closed form for several special cases in the approximation of stiffeners having zero torsional rigidity. Asymptotic expansions of the expressions for the deflection field of a stiffened plate are used to derive limit-case globally optimal stiffening layouts for highly flexible and highly rigid stiffeners. A central result obtained in this work is an analytical proof of the fact that an array of flexible enough orthogonal stiffeners of any number, stiffening a simply-supported rectangular plate subjected to any lateral loading, is best to be put in the form of exactly two orthogonal stiffeners, one in each direction.

Bending analysis of stiffened composite conoidal shell roofs through finite element application

This article applies a combination of an eight-noded shell element with a three-noded beam element to solve a bending problem of a composite stiffened conoidal shell subjected to a concentrated load at the center. Benchmark problems are solved for validation of the present approach and a wide spectrum of stiffened conoidal shell problems are solved for various parametric variation of shell surfaces and positions of stiffeners. Both static deflections and force/moment resultants are examined thoroughly. The performances of the different shell options are studied by arranging them rankwise and through a typical relative performance matrix.

Bending of Composite Stiffened Hypar Shell Roofs under Point Load

The present paper applies a combination of an eight noded shell element with a three noded beam element, both curved and isoparametric to solve a bending problem of a composite stiffened hypar shell subjected to a concentrated load. Benchmark problems are solved to validate the suitability of the approach and a wide spectrum of stiffened hypar shell problems are solved by varying the lamination and curvature of simply supported and clamped shell surfaces. Different positions of stiffeners, both in plan and section, are considered together with variation of stiffener depth. Both static deflections and force/moment resultants are examined thoroughly. The performances of the different shell options are studied by arranging them rankwise and through a typical relative performance matrix, which will enable a designer to make a rational choice between a number of options.

SPSM and its application in cylindrical shells

In naval architectures, the structure of prismatic shell is used widely. But there is no suitable method to analyze this kind of structure. Stiffened prismatic shell method (SPSM) presented in this paper, is one of the harmonic semi-analytic methods. Theoretically, strong stiffened structure can be analyzed economically and accurately. SPSM is based on the analytical solution of the governing differential equations for orthotropic cylindrical shells. In these differential equations, the torsional stiffness, bending stiffness and the exact position of each stiffener are taken into account with the Heaviside singular function. An algorithm is introduced, in which the actions of stiffeners on shells are replaced by external loads at each stiffener position. Stiffened shells can be computed as non-stiffened shells. Eventually, the displacement solution of the equations is acquired by the introduction of Green function. The stresses in a corrugated transverse bulkhead without pier base of an oil tanker are computed by using SPSM.

Consideration of buckling characteristics for optimal design of stiffened punch in the blanking process of lead frame

The recent technical trend of semiconductor, chip size and high performance package technology, requires the IC lead frame to be of more multi-leads and fine pitch, and the corresponding punch thickness has been narrow. The members with high slenderness ratio such as a lead frame punch can be broken suddenly due to buckling. It is the major aim of the present work to suggest a practical optimization procedure to design the punch with the optimal number and position of stiffeners considering the maximum buckling load of punch. The various cases of punches have been also analyzed using finite element method and theoretical model, and the results have been confirmed by buckling test. It is shown that the analytical and theoretical results are in good agreement with the experimental ones. Finally, a guideline to design the punch with stiffeners is proposed through analysis of cross-section of lead frame punch such as moment of inertia and eccentricity.

Bending analysis of folded plates by the FSDT meshless method

In this paper, a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT) will be introduced to analyse the elastic bending problem of stiffened and un-stiffened folded plates under different loadings and boundary conditions. Folded plates are regarded as assemblies of plates that lie in different planes. The stiffness matrices of the plates are given by the meshfree method. Employing the element concept, which is borrowed from the finite element method, and treating every plate as a big element, the global stiffness matrix of the whole folded plate is obtained by superposing the stiffness matrices of the plates. This is about the same for the analysis of stiffened folded plates. They are considered as assemblies of stiffened plates. The stiffness matrices of the stiffened plates are also given by the meshfree method. Superior to the finite element methods, no mesh is required in determining the stiffness matrices for the plates and the stiffened plates in this paper, which means time-consuming and accuracy-suffering remeshing is entirely avoided for problems such as large deformation or crack propagation in folded plates or stiffener position changes of stiffened folded plates. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated by it and the finite element commercial software ANSYS. Good agreement is observed between the two sets of results.

Shear resistance of longitudinally stiffened panels — Part 2: Numerical parametric study

This paper presents the FE analysis of the influence of different parameters on the shear resistance of panels with different arrangements of longitudinal stiffeners. The studied parameters were the stiffener bending stiffness, the panel aspect ratio, the stiffener position, the web slenderness and the flange rigidity. Longitudinal stiffeners of trapezoidal shape were compared to open T-stiffeners. The former proved to be more efficient, since a larger panel resistance is achieved, for which in addition a smaller stiffness of trapezoidal stiffeners is needed. Different features of the new Eurocode rules were verified against the FEA results as well. Three different procedures for the determination of panel slenderness were tested and the reduction of stiffener bending stiffness, prescribed due to a better correlation with tests on open stiffeners, was verified for both closed and open stiffeners. The influence of bending moment was also considered and the verification of shear and bending interaction was discussed. Finally, the flange contribution to shear resistance was critically analysed.