Composite I-beams Research Articles

Static response of thin-walled composite I-beams loaded at their free-end cross-section: analytical solution

Analytical solutions for the static response of anisotropic composite I-beams loaded at their free end are presented. The analysis is accomplished within the framework of the theory of composite thin-walled beams featuring the two main coupling mechanisms, namely, circumferentially uniform stiffness (CUS) and circumferentially asymmetric stiffness (CAS) configurations. Within each of these two configurations, the implications of the directionality property of composite materials, of warping inhibition and transverse shear on the static response of I-beams are highlighted, and final conclusions are outlined.

Lateral–torsional buckling of cantilevered elastically coupled composite strip- and I-beams

The lateral–torsional buckling of composite strip- and I-beams is considered. The geometrically exact governing equations are simplified by consistently regarding certain configuration parameters as small. The assumption that these parameters are indeed small is equivalent to the assumption that the square of the maximum prebuckling cross-sectional rotation due to bending is small compared to unity. The analysis takes into account various refinements of previously published results, including the Vlasov effect, elastic coupling, the offset of the load from the centroid, and, of course, prebuckling deflections. The analysis is thereby reduced to a single fourth-order differential equation and boundary conditions, all of which are derivable from a corresponding energy expression. From the form of matched asymptotic expansions of the buckling mode when small parameters are ignored altogether, a single comparison function is found which gives the correct buckling load to within 1% for a wide range of the warping rigidity. Using this comparison function, a formula for the buckling load as a function of the small parameters of the problem is found and validated. With certain exceptions regarding the load offset parameter, the formula provides results which agree quite well with the numerical solution of the exact equations as long as all the small parameters remain small. However, the load offset parameter always appears in the governing equations as multiplied by a ratio of stiffnesses, which can become large, especially for composite I-beams. For this case, a special treatment is required.

Fabrication, Analysis, and Experimentation of a Practically Constructed Laminated Composite I-Beam Under Pure Bending

Seven I-beams constructed of AS4/3501 graphite/epoxy were tested and analyzed. The I-beams, having a layup sequence of 45/-45/03/-45/451T with various flange widths varying from ¾ to 2 ½ inches and a web height of 1 inch, were fabricated. The beams were tested under 4-point bending, producing results for the pre-buckled stiffness, buckling moment, and ultimate moment. Results indicate that wider flange beams exhibit buckling at lower moments than narrower flange beams. The flange width also affects the buckling mode. Wider flanged beams show larger edge displacements and lower mode values than narrower flanged beams. The ultimate moment capability appears to be only slightly increased by increased stiffness. Typically, increasing the flange width does not contribute significantly to the ultimate strength of the beam. For wider flanged beams, delamination occurs at the flange and then propagates to the web causing final failure. However, narrower flanged beams fail due to fiber/matrix crushing at the flange-web intersection.

Mechanical performance of carbon-fibre- and glass-fibre-reinforced epoxy I-beams: III. fatigue performance

This paper is the third in a series which describe in detail the static and fatigue mechanical behaviour and fractographic observations of the failure of composite I-beams. Experimental investigations into the fatigue response of both unnotched and web- and flange-notched continuously reinforced carbon-fibre/epoxy and glass-fibre/epoxy I-beams are discussed in the present paper. A four-point flexural configuration was used to test the I-beams, each of which had the same multidirectional stacking sequence consisting of a balanced layup of 0, +45 and −45° plies. In no cases were the beams fatigued above the loads at which buckling of the compression flange would occur under static testing. The unnotched carbon/epoxy and glass/epoxy beams did not exhibit any detectable damage within 1.2×10 6 and 8×10 6 cycles, respectively. The notched beams, on the other hand, failed as a result of the tensile and compressive stresses which were present around the web notches. Damage mechanisms, including delamination, matrix microcracking and fibre fracture, were all present at final failure around the web notches, although the extent of the different mechanisms varied during the fatigue life of the I-beams.

Damage Progression in Carbon-Fiber Reinforced Plastic I-Beams

Damage and fracture progression in carbon-fiber reinforced plastic (CFRP) composite I-beams subject to three point bending are evaluated via computational simulation. An integrated computer code that scales up constituent micromechanics level material properties to the structure level and accounts for all possible failure modes is used for the simulation of composite degradation under loading. Damage initiation, growth, accumulation, and propagation to fracture are included in the simulations. Three I-beams with different layup configurations are evaluated. Simulation results are compared with experimental data. Design implications with regard to damage tolerance and residual strength of CFRP composite beams are examined.

Rapid prototyping of composite parts using resin transfer molding and laminated object manufacturing

An expensive and time consuming aspect of a product development cycle is manufacturing the prototype of the design concept. The goal of current research is to devise a methodology for the rapid process development of resin transfer molding (RTM) in order to reduce product development cycle time and lower the cost of developing composite parts. As a first step towards this goal the feasibility of an alternative rapid prototyping technique, namely laminated object manufacturing (LOM), to fabricate molds has been investigated. The durability and dimensional stability of such a mold, as well as its economic practicality in the RTM manufacturing of a composite I-beam were considered. To keep tooling and fixturing simple, vacuum pressure was used to draw resin into the mold. However, injection at this low pressure proved difficult. To remedy the situation a high permeability layer (HPL) was incorporated into the process. The benefits and drawbacks of utilizing such a layer are also discussed in the paper. Furthermore, an RTM simulation program developed at UCLA was employed to determine optimum gate locations. Finally, the total hours to manufacture the first acceptable part were quantified for comparison with future studies.

Flexural-torsional buckling of pultruded fiber reinforced plastic composite I-beams: experimental and analytical evaluations

In this paper a comprehensive experimental and analytical approach is presented to study flexural-torsional buckling behavior of full-size pultruded fiber-reinforced plastic (FRP) I-beams. Two full-size FRP I-beams with distinct material architectures are tested under midspan-concentrated loads to evaluate their flexural-torsional buckling responses. To monitor rotations of the cross-section and the onset of critical buckling loads, transverse bars are attached to the beam crosssection and are subsequently connected to LVDTs; strain gages bonded at the edges of the top flange are also used. The analysis is based on energy principles, and the total potential energy equations for the instability of FRP I-beams are derived using nonlinear elastic theory. The equilibrium equation in terms of the total potential energy is solved by the Rayleigh-Ritz method, and simplified engineering equations for predicting the critical flexural-torsional buckling loads are formulated. A good agreement is obtained between the experimental results, proposed analytical solutions and finite-element analyses. Through the combined experimental and analytical evaluations reported in this study, it is shown that the testing setup used can be efficiently implemented in the characterization of flexural-torsional buckling of FRP shapes and the proposed analytical design equations can be adopted to predict flexural-torsional buckling loads.

Multiobjective material architecture optimization of pultruded FRP I-beams

This paper presents the application of micro/macromechanics models and optimization techniques for the optimum design of pultruded glass fiber-reinforced plastic composite I-beams with respect to material architecture: fiber orientations and fiber percentages. The beams are subjected to transverse loading, and beam deflection, buckling resistance and material failure are considered as multiple objectives (criteria) in the optimization process. Assuming a symmetrical laminated structure for the pultruded sections, experimentally verified micro/macromechanics models are used to predict ply properties, beam member response and ply strains and stresses. The Tsai-Hill failure criterion is used to determine first-ply-failure loads. Considering the coupling of lateral and distortional buckling, a stability Rayleigh-Ritz solution is used to evaluate the critical buckling loads for pultruded I-beams, and the results are verified with finite element analyses. A multiobjective design optimization formulation combined with a global approximation technique is proposed to optimize beam fiber architecture, which can greatly enhance the load carrying capacity of a section. The optimization procedure presented in this paper can serve as a practical tool to improve the performance of existing fiber-reinforced plastic without changing the current geometries.

FINITE ELEMENTS FOR THREE-MODE INTERACTION IN BUCKLING ANALYSIS

SUMMARY This paper presents a finite element formulation for the buckling mode interaction analysis of structures modelled as plate assemblies. The main assumptions are linear elasticity, a linear fundamental path, the existence of distinct critical states that.are coincident or near coincident, and a coupled path arising from a linear combination of modal displacements due to interaction. The formulation adopted is known as the W-formulation, in which the energy is written in terms of a sliding set ofincremental co-ordinates measured with respect to the fundamental path. The energy is then expressed with respect to a reduced modal co-ordinate basis and the coupled solution arising from interaction is computed. An example of a fibre­ reinforced composite I-beam subjected to axial compression illustrates the procedure. The results are compared to a simplified model developed by the authors. Also, an imperfection sensitivity analysis is performed.

Mechanical performance of carbon-fibre- and glass-fibre-reinforced epoxy I-beams: I. Mechanical behaviour

This paper is the first in a series which detail the mechanical behaviour, finite element predictions and fractographic observations of the failure of composite I-beams. Experimental investigations into the behaviour under static load of both unnotched and web- and flange-notched continuously reinforced carbon-fibre/epoxy and glass-fibre/epoxy I-beams are discussed. A four-point flexural configuration is used. The global static response and ultimate failure are described in terms of strains, compliance, buckling and final fracture. A mode of buckling that is antisymmetric across the width of the compressive flange is observed prior to failure in all cases. Failure of the unnotched I-beams is concentrated around a buckle on the compressive flange whilst failure of the notched I-beams initiates from a shear-loaded circular cutout within the web. Buckling of the unnotched beams occurs at loads that are approximately 50% of the failure loads. Failure of the notched beams occurs at loads that are approximately 75% of the failure loads of the unnotched beams. Buckling and failure of the glass/epoxy beams occur at loads that are approximately 75% of the corresponding loads in the carbon/epoxy beams.

Mechanical performance of carbon-fibre and glass-fibre-reinforced epoxy I-beams: II. Fractographic failure observations

This present paper is the second in a series which together detail the static behaviour, fractographic observations, fatigue behaviour and finite element predictions of composite I-beams subjected to mechanical loads. Fractographic observations associated with the mechanical behaviour under static load of both unnotched and web- and flange-notched continuously reinforced carbon-fibre/epoxy and E-glass-fibre/epoxy I-beams are discussed. Ultrasonic scanning, X-radiography and both optical and scanning electron microscopy have been used to elucidate the presence of different damage mechanisms and the directions of delamination growth in different regions of the beams. The principal damage mechanisms which have been identified as causing failure are delamination, matrix cracking, splitting and fibre fracture. As discussed in detail in the previous paper, a four-point flexural configuration was used. A mode of buckling that was antisymmetric across the width of the compressive flange was observed prior to failure in all cases. Failure of the unnotched I-beams initiated from a buckle on the compressive flange and the subsequent damage was predominantly in the form of delamination. The main delaminations were along the interfaces between the separate sub-components which comprise the I-beams: namely, the flange caps and C-sections and the backs of the two C-sections. These are all −45 ° + 45 ° interfaces i.e. the relative fibre angle between the adjacent plies is 90 °. Failure of the notched I-beams initiated from a shear-loaded circular cutout within the web. The critical damage mechanism was matrix cracking in local 90 ° 90 ° plies which were subject to local tensile stresses. Fibre fracture and component failure resulted from this matrix cracking.

Mechanical performance of ceramic matrix composite I-beams

Abstract Experimental studies have been performed on ceramic matrix composite (CMC) I-sections, which typify joint designs for CMC components. Axial loads and moments have been applied to activate delamination mechanisms. The maximum load bearing capacity has large variability, governed by the severity of manufacturing flaws located in the transition region of the I-section. This variability leads to an unsatisfactory design situation. Delaminations that form from these flaws arrest and behave in a stable manner, subject to a remanent load bearing capacity. This remanent capacity has minimal variability. Hence, design based on the remanent load would be robust. An expression for this design criterion is presented.

Dynamic Theory of Open Cross Section Thin-Walled Beams Composed of Advanced Composite Materials

A dynamic theory of open cross section composite thin-walled beams is presented. The theory is quite general in the sense that it is valid for any laminate stacking sequence and boundary conditions. Moreover, a number of non-classical effects such as the transverse shear flexibility and warping restraint are incorporated. As a special case, the eigenvibration problem of composite I-beams is analyzed. In this context, a powerful analytical methodology enabling one to solve the problem for a variety of boundary conditions is devised. Pertinent conclusions on the implications of the various effects are emphasized.

Optimal design of a composite I-beam

This paper describes a procedure for obtaining an optimal (minimum area) design of a uniform composite I-beam with regard to structural failure, local buckling and a central deflection constraint. The beam is subjected to a lateral point load at its midpoint, and is assumed to be simply supported at each end. An analytic procedure allows us to derive an approximate initial design. This is then modified according to some redesign heuristics so that it satisfies all the design constraints. This new design becomes the initial solution in a structural optimisation procedure known as the Complex method which eventually results in an optimal solution in terms of a set of cross-sectional dimensions. The method is extended to beams with fixed ends and results are also obtained when an aspect ratio constraint is incorporated.

Analytical-experimental investigation of free-vibration characteristics of rotating composite I-beams

This article presents a free-vibration analysis of coupled composite I-beams with couplings under rotation. A linear analysis based upon Vlasov theory was developed to obtain coupled flap-lag-torsion equations of motion for I-beams made out of general composite laminates. Constrained warping and transverse shear effects were included. Free-vibration characteristics were obtained by solving these equations using Galerkin's method. In order to validate the theory, graphite-epoxy and kevlar-epoxy I-beams with bending-torsion coupling were fabricated using an autoclave molding technique and tested in an in vacuo rotor test facility for their vibration characteristics. Induced-strain actuation by piezoceramic elements was used to excite the I-beams in the rotating frame. Strain gauges were used to measure the response of these beams over a range of rotational speeds up to 1000 rpm. Natural frequencies and strain mode shapes were determined by carrying out signal analysis using a spectrum analyzer. Good correlation between theory and experiment was achieved. About 600% increase in torsional frequency due to constrained warping occurs for graphite-epoxy beams with a slenderness ratio of 18. Nomenclature A = cross-sectional area of blade b, h = semiwidth and semiheight of I-beam Eh Et — Young's moduli in principal directions of plies of beam Glt - shear modulus of plies in principal plane Ixx, Iyy = blade cross-sectional moment of inertia about x and y axes, respectively K] - stiffness matrix for beam Kf] = flap bending stiffness matrix Kft] — flap bending-torsion coupling stiffness matrix K] = lag bending stiffness matrix K!t] - lag bending-torsion coupling stiffness matrix [Kt] = torsion stiffness matrix KA = effective polar radius of gyration of blade cross-section V(/vv + IXX)IA

Structural characteristics of wood composite I-beams

In this study, wood composite I-beams consisting of F11 slash pine flanges and either hardboard or particleboard webs were fabricated and evaluated for flexural stiffness. Prior to fabrication, both the web and flange materials were evaluated for flexural stiffness. The mean modulus of elasticity of the flange material was 16 900 MPa, while that for the particleboard and hardboard was 4250 and 4450 MPa respectively. The mean effective modulus of elasticity for the particleboard-webbed beams was 16 300 MPa and for the hardboard-webbed beams was 16 400 MPa. The implications of the findings are discussed. Key words: wood composites, I-beams, characterization.

Euler buckling of thin-walled composite columns

Pultruded composite structural members with open or closed thin-walled sections are being extensively used as columns for structural applications where buckling is the main consideration in the design. In this paper, global buckling is investigated and critical loads are experimentally determined for various fiber reinforced composite I-beams of long column length. Southwell's method is used to determine the critical buckling load about strong and weak axes. The experimentally determined buckling load is compared with theoretical predictions. A number of observations about testing methodology and data reduction techniques are presented.

Lateral-torsional buckling of thin-walled composite I-beams by the finite difference method

The finite difference method has been used to solve the differential equation for the critical loading associated with a specific lateral-torsional buckling test configuration. The linear elastic analysis is valid for thin-walled composite doubly symmetric I-beams made from mid-plane symmetric, fibre-reinforced laminated panels. Here, the test configuration has an I-beam with specially orthotropic panels. It is subjected to three-point bending, and supported at each end such that the only degree of freedom is rotation about the major axis of the beam. For the modelling case where the central load is applied at the shear centre (centroid) of the cross-section there is a favourable comparison between the finite difference results and those results presented by Timoshenko and Gere (1961, Theory of Elastic Stability 2nd edn, McGraw-Hill, New York), which were originally generated for isotropic beams. A favourable comparison has also been found between the finite difference analysis and experimental evidence using an E-glass fibre-reinforced polymeric pultruded I-beam, where the central load is now applied to the top compression flange. The various theoretical models presented in the paper are used to show that the critical loading for buckling in real composite I-beams will be strongly dependent on both the support boundary conditions and the height of the loading relative to the centroid (shear centre).

Experimental and theoretical analysis of composite I-beams with elastic couplings

This paper presents a theoretical-cum-experimental study on the static structural response of composite I-beams with elastic couplings. A Vlasov type linear theory is developed to analyze composite open section beams made out of general composite laminates, where the transverse shear deformation of the beam cross-section is included. In order to validate this analysis, graphite-epoxy and kevlar-epoxy symmetric I-beams were fabricated using an autoclave molding technique. The beams were tested under tip bending and torsional loads, and their structural response in terms of bending slope and twist measured with a laser optical system. Good correlation between theoretical and experimental results is achieved. A 630 percent increase in the torsional stiffness due to constrained warping is noticed for graphite-epoxy beams with slenderness ratio of 30. Also extension-twist coupling 'B16' of flanges of these I-beams increases the bending-torsion coupling stiffness of

Predicting the load capacity of wood composite I-beams using the tensor polynomial strenght theory

The tensor polynomial strength theory for anisotropic materials was coupled with finite-element analyses to predict the ultimate load capacity of several wood-composite I-beams. Small-specimen tests with the constituent materials provided elastic constants for the finite-element computations and ultimate strengths for development of strength tensors.