I-shaped Cross-section Research Articles

Bracing FRP I-section beams to avoid lateral-torsional buckling

This article explains as to how lateral-torsional buckling can be avoided in fiber-reinforced plastic (FRP) beams having an I-shaped cross section and subjected to major-axis bending. To enable a FRP beam to be able to develop its maximum bending moment capacity corresponding to material cracking of the extreme fibers, a number of lateral braces need to be provided. Herein, a procedure is outlined for determining the required number of lateral braces for a FRP I-section beam. It is shown that a FRP beam loaded about its major cross-sectional axis can experience a drastic reduction in its bending moment capacity if such lateral bracing is not provided, whereas it can develop its maximum load-carrying capacity up to the cracking of the extreme fibers if a sufficient number of lateral braces are provided.

The Fatigue Behavior of Built-Up Welded Beams of Commercially Pure Titanium

In this article, the results of a recent study aimed at evaluating, understanding, and rationalizing the extrinsic influence of fatigue loading on the response characteristics of built-up welded beams made from commercially pure titanium (Grade 2) are presented and discussed. The beams were made from welding plates and sheets of titanium using the pulsed gas metal arc welding technique to form a structural beam having an I-shaped cross section. The welds made for the test beams of the chosen metal were fillet welds using a matching titanium filler metal wire. The maximum and minimum load values at which the built-up beams were cyclically deformed were chosen to be within the range of 22-45% of the maximum predicted flexural static load. The beams were deformed in fatigue at a stress ratio of 0.1 and constant frequency of 5 Hz. The influence of the ratio of maximum load with respect to the ultimate failure load on fatigue performance, quantified in terms of fatigue life, was examined. The percentage of maximum load to ultimate load that resulted in run-out of one million cycles was established. The overall fracture behavior of the failed beam sample was characterized by scanning electron microscopy observations to establish the conjoint influence of load severity, intrinsic microstructural effects, and intrinsic fracture surface features in governing failure by fracture.

Vibration analysis of thin-walled composite beams with I-shaped cross-sections

A general analytical model applicable to the vibration analysis of thin-walled composite I-beams with arbitrary lay-ups is developed. Based on the classical lamination theory, this model has been applied to the investigation of load–frequency interaction curves of thin-walled composite beams under various loads. The governing differential equations are derived from the Hamilton’s principle. A finite element model with seven degrees of freedoms per node is developed to solve the problem. Numerical results are obtained for thin-walled composite I-beams under uniformly distributed load, combined axial force and bending loads. The effects of fiber orientation, location of applied load, and types of loads on the natural frequencies and load–frequency interaction curves as well as vibration mode shapes are parametrically studied.

REFINED BEAM THEORIES BASED ON A UNIFIED FORMULATION

This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.

Behavior of Prestressed Steel Beams

This paper reports on the behavior of simply supported (I-shaped cross section) steel beams prestressed by tendons. It is well known that this typology of beams has successfully been used mainly in the past. Prestressed steel beams are lighter than traditional ones that have the same length and vertical load capacity; this aspect could make them economically advantageous and a viable solution in many practical situations. This paper analyzes prestressed steel beams having a medium span ranging from 35 to 45 m and which are to be used as roof structural elements. This study focuses on two parameters that are considered two of the fundamental items for the design: the number of deviators and the value of the prestressing force. This study has been carried out with nonlinear finite-element analyses that take into account both mechanical and geometrical nonlinearities. In particular, the behavior of these beams has been investigated up to failure during tensioning and during loading (after tensioning). The effect on the structural response of bracing, which can be only at the top flange of the beams or at the top and bottom flanges of the beams, also has been considered.

Classification of I- or H-shaped cross-sections under mixed internal actions

Section classification is a key point in most of the currently available steel standards. However, several aspects of section classification need to be clarified for a proper application in the general context of three-dimensional structures. This paper presents a new method useful for classifying I-shaped cross-sections subjected to tension or compression plus biaxial bending. The method can be generalised to any kind of section and standard and could lead to design maps that are very useful for evaluating member behaviour.

Cracking in deep beams owing to shear loading. Part 1: Experimental study and assessment

In this paper, laboratory tests to failure of ten large deep beams with I-shaped cross-sections are presented. All beams had the same geometry with a shear span-to-depth ratio of 1·25 but differed in the amount of the vertical and horizontal web reinforcement. The presented results from the measurements consist of load–deformation curves, crack widths and crack patterns and strain distribution near the supports. The ultimate loads for these beams have been calculated with two strut-and-tie models and one truss model. The first strut-and-tie model calculates the tensile contribution of both reinforcement and concrete and takes into account their influence on the principal tensile stress. The second strut-and-tie model is a modification of the first one where the stress distribution along the strut is redefined. The third method is the truss model that is incorporated in a Design Code. The truss model gave the best result for the beams with a higher reinforcement ratio that exhibited in a shear compressive failure. The diagonal tensile failure that occurred in the beams with a small amount of web reinforcement was best captured with the modified strut-and-tie model.

Cracking in deep beams owing to shear loading. Part 2: Non-linear analysis

In this paper, analyses based on laboratory tests of ten large deep beams with I-shaped cross-sections loaded to failure are presented. All beams had the same geometry with a shear span-to-depth ratio of 1·25, but differed in the amount of the vertical and horizontal web reinforcement. All beam tests resulted in shear failure, either diagonal tensile failure or shear compressive failure, depending on the amount of reinforcement. The diagonal tensile failure is generally considered to be the most difficult failure to treat numerically. In this study different material models incorporated in commercial numerical analysis tools are studied. Material models based on fracture mechanics with either rotated or fixed crack directions as well as a plasticity-based model are used in the analyses. The analyses show that the plasticity-based model in Abaqus gives good agreement with the experiments regarding crack pattern, load–displacement response and estimated crack widths. The models based on fracture mechanics in Atena and Response tend to give too stiff behaviour in the load–displacement response, but generally give a good estimation of the load capacity. The analyses performed with Atena gave good estimations of the crack pattern, and the models with a fixed crack direction also gave good estimates of the crack width.

Theoretical analysis of 4-ENF tests for mode II fracturing in wood by finite element method

In this note, the four-point bend end notched flexure tests of wood of the specimen with an I-shaped cross-section were simulated by the finite element method. It was suggested that the relation between the mode II energy release rate and crack length was appropriately obtained by the data reduction method proposed in a previous work [Yoshihara H. Mode II R-curve of wood measured by 4-ENF test. Engng Fract Mech 2004;71:2065–77].

Modeling and damage detection for cracked I-shaped steel beams

This paper presents the results of a study to show how the development of a crack alters the structural behavior of I-shaped steel beams and how this can be used to evaluate nondestructive evaluation techniques. The approach is based on changes in the dynamic behavior. An approximate finite element model for a cracked beam with I-shaped cross-section is developed based on a simplified fracture model. The model is then used to review different damage cases. Damage detection techniques are studied to determine their ability to identify the existence of the crack and to identify its location. The techniques studied are the coordinate modal assurance criterion, the modal flexibility, and the state and the slope arrays.

Elastic buckling of I-beam flanges subjected to a linearly varying stress distribution

Lateral forces or torsion combined with major axis bending result in a stress gradient across the compression flanges of I-shaped flexural members. Sources that cause significant stress gradient include situations where unequal reactions come to opposite sides of a girder or beams that frame into one side of a girder, skewed bridge girder supports, wind loading on facia girders, curvature induced warping, etc. In this study, three sets of support conditions are considered for evaluating the elastic buckling capacity of flanges of I-shaped beams subjected to a stress gradient. This includes a Galerkin series solution that considers the full width of the flange plate with a variable rotational stiffness along the center of the plate. For a stress gradient leading to tension over part of the flange, equations for predicting the buckling capacity are developed using finite element analyses. Simplified equations are developed for I-shaped cross sections, and numerical examples are used to demonstrate the accuracy of the solution. A definition of the noncompact limit for flanges of I-shaped beams and girders subjected to stress gradient is presented.

Experimental and analytical investigation of tubular links for eccentrically braced frames

Eccentrically braced frames have been used as seismic load resisting systems in buildings for more than two decades. Typically, the links, which are relied upon for energy dissipation through inelastic deformation, have had a wide-flange or I-shaped cross-section that requires lateral bracing to prevent lateral torsional buckling. This has limited the use of eccentrically braced frames in bridge piers and towers, as lateral bracing is difficult to provide in those situations. This paper describes first an experimental, and then an analytical investigation into the use of members with hollow rectangular (i.e., tubular) cross-sections as eccentrically braced frame links that do not require lateral bracing. Using cross-sectional plastic analysis, the plastic shear and moment strength for a general tubular section with different web and flange yield strengths and thicknesses are derived. Equations are derived for maximum flange compactness ratio and minimum web stiffener spacing to prevent flange and web buckling. A proof-of-concept experiment involving a large scale eccentrically braced frame with a tubular link is then described. The link has a hybrid tubular cross-section composed of webs and flanges of different thicknesses, with full-penetration groove welds. Experimental results indicate that the link reached a rotation of 0.15 rad, almost twice the current 0.08 rad limit for wide-flange links, prior to suffering flange fracture. An investigation of the fracture surface indicated that flange fracture did not initiate in the full-penetration weld used to assemble the shape, but rather in the heat-affected-zone of the flange adjacent to a fillet weld used to connect a stiffener to the flange. Finally, a finite element model of the link is developed using shell elements, and reasonable agreement with the experimental results is observed.

I-section flange compactness under minor axis flexure

The present paper hopes to elucidate the problem of determining if a given I-shaped cross-section is properly proportioned to accommodate sufficient plastic hinge rotation capacity to facilitate the redistribution of moments in a structural system as needed to accommodate the formation of a collapse mechanism. It might be tempting to believe that application of the limiting flange plate slenderness value for the case of major axis flexure are applicable in this case; since the pervasive belief is that this approach ought to be conservative. However, the present research study indicates that this is not the case and thus more sophisticated analysis techniques are required to better understand this case.

Use of Fiber-Reinforced Polymer Composite Elements to Enhance Structural Steel Member Ductility

An innovative use of fiber-reinforced polymer composite materials to control the manifestation of local buckling in a steel section during plastic hinging is discussed in the present work. This discussion focuses on a technique wherein the constituent plate components in a steel I-shaped cross section are braced against local plate buckling modes through the imposition of thin longitudinal strips whose function is to enforce a nodal line along a plate element. This work demonstrates that such an approach increases the critical load for individual steel plate elements and helps to constrain plastic flow for these same elements so that the structural ductility of the overall cross section is enhanced. The research work discussed herein is analytical in nature. Detailed nonlinear finite element models are created using traditional techniques implemented on the commercially available software system ADINA. Specifics pertaining to bond-line response are not treated.

Minor Axis Moment-Thrust Response Behavior in Steel I-Shaped Members

Most current design specifications employed throughout the world prescribe the use of so-called interaction equations for the case of beam–columns. Most often these interaction equations are optimized for use with the case of I-shaped cross sections bent about the major principal centroidal axis. The current study focuses on the case wherein an I-shaped member is loaded in compression and bending about the minor principal centroidal axis. It is shown that the current AISC interaction equations can be improved on in terms of their ability to predict failure in these types of members. Alterations to the existing AISC interaction equations are suggested for improving on strength predictions relative to this case.

Behavior of cold-formed steel built-up I-sections

An experimental investigation was conducted to study the behavior of built-up cold-formed steel studs and to assess the current design provisions of the North American Specification for the Design of Cold- Formed Steel Structural Members. Typical applications include framing for windows, doorways, shear walls, and multi-story cold-formed steel framed buildings in which the lower floor utilizes built-up studs to carry the load. The built-up studs in this study consisted of two C-sections oriented back-to-back forming an I-shaped cross-section. For each specimen, the studs were connected to each other with two self-drilling screws spaced at a set interval. A cold-formed steel track section was connected running perpendicular to each end of the built-up stud with a single self-drilling screw through each flange of the C-sections. The purpose of the track section was to keep the ends of the studs together and represents a common end attachment. As a result of the investigation, the current design requirements were found to be conservative in predicting the ultimate capacity of built-up studs.

Cable-Stayed Bridge over the Guamà River, Brazil

The Guama Bridge crosses the Rio Guama in the State of Para in Brazil. It is almost 2 km in length and includes two approach viaducts and a central three-span cable stayed bridge. Decks are composed of precast prestressed concrete girders with I-shaped cross sections connected by transverse beams and supporting a top concrete slab. The girders were prefabricated at the job-site plant and transported by barges before being lifted and installed by launching gantries. Details are given of the design, the aerodynamics of the bridge and the bridge construction. The problems posed by the initial inaccessibility of the site by road and by high tides and strong currents are discussed. Details are given of the owner, designer, contractor, costs and service date.

Optimum design of prestressed concrete beams by a modified grid search method

A computer program has been developed for the optimum design of prestressed concrete beams under flexure. Optimum values of prestressing force, tendon configuration, and cross-sectional dimensions are determined subject to constraints on the design variables and stresses. 28 constraints have been used including flexural stresses, cover requirement, the aspect ratios for top and bottom flanges and web part of a beam and ultimate moment. The objective function contains cost of concrete, prestressing force and formwork. Using this function, it is possible to obtain minimum cost design, minimum weight or cross-sectional area of concrete design and minimum prestressing force design. Besides the idealized I-shaped cross-section, which is widely used in literature, a general I-shaped cross-section with eight geometrical design variables are used here. Four examples, one of which is available in the literature and the others are modified form of it, have been solved for minimum cost and minimum cross-sectional area designs and the results are compared. The computer program, which employs modified grid search optimization method, can assist a designer in producing efficient designs rapidly and easily. Considerable savings in computational work are thus made possible.

615 小型パイロンロードセルの開発

The pylon load cell are used in measuring the loads applied on the artificial leg. The compact and light-weighted PLC is desired with small interference between six components of the PLCA new PLC with I-shaped cross-section was developed where the interference was reduced by putting strain gages on the center of the web and the flange of I-shaped PLC. The static calibration test was perfomed about the PLC and the preferable result was obtained.

Elastic buckling of a centrally loaded simply supported I-section

Beams with an I-shaped cross-section (I-sections) are widely used in the building industry throughout Australia and internationally. The Australian Standard AS4100 provides guidelines for the design of such beams. Numerous failure modes are taken into account in these design rules including stability failure modes where such beams buckle out of their plane of loading. Recent failures of beams which have been designed according to the Australian Standard AS4100 have been documented and concerns have been raised that critical out-of-plane failure modes might not be included in the current version of this Australian Standard. A preliminary study on one such I-section was performed at the Centre of Construction Technology and Research (CCTR), University of Western Sydney. This preliminary study revealed that, for short beams, a failure mode exists that is not covered by the current design rules. The current paper documents these findings and proposes a simple failure model which could become the basis for the design against this failure mode.