Flexural Behavior and Deformability of Fiber Reinforced Polymer Prestressed Concrete Beams

After a brief review of the ductility and deformability indices currently used in the design of concrete beams reinforced or prestressed with steel or fiber reinforced polymer (FRP) tendons, a new definition of a deformability index (factor) for prestressed concrete beams is proposed. The new factor is defined in terms of both a deflection factor and a strength factor. The deflection factor is the ratio of the deflection at failure to the deflection at first cracking, while the strength factor is the ratio of the ultimate moment (or load) to the cracking moment (or load). The proposed deformability factor is verified not only by test results obtained by the writer, but also by other test results available in the literature and it appears to be a suitable measurement of the deformability of concrete beams prestressed with either FRP tendons or steel tendons.     

Flexural Strengthening of Reinforced Concrete Flanged Beams with Composite Laminates

Bonding composite laminates to the tension face can effectively increase the flexural strength of the reinforced-concrete flanged beams. In comparison to rectangular concrete beams, the flange provides a larger area of concrete to resist compression stresses, and considering the role of the composite in resisting tensile stresses, its addition to flanged beams can efficiently upgrade the flexural capacity. Failure of the strengthened beam may result from crushing of concrete or rupture of the plate; however, the beam must be properly detailed to avoid local shear failure at the plate cut-off point. In this paper, equations required for strengthening of the flanged beams for gravity loads will be presented. The equations have been developed based on load and resistance factor design, and have been verified through a comparison with available experimental results. Close agreement with the experimental results indicates the accuracy of the equations. Terms, definitions, and notations compatible to ordinary reinforced-concrete design codes have been used to facilitate the application of the equations.     

Observations on Higher‐Order Beam Theory

A parabolic shear‐deformation beam theory assuming a higher‐order variation for axial displacement has been recently presented. In this theory, the axial displacement variation can be selected so that it results in a suitable admissible transverse shear‐strain variation across the depth of the beam. This paper examines several transverse shear‐strain variations that can go with the aforementioned higher‐order theory. Apart from the usual simple parabolic variation, six other shear‐strain variations are considered: the sinusoidal variation, cubic, quartic, quintic, and sixth‐order polynomials. All these variations for transverse shear‐strain satisfy the requirement that the shear strain be zero at the extreme fibers (z? = ?±h/2) and nonzero elsewhere along the depth of the beam. Comparison of the results from this paper with results from others show that the simple parabolic distribution for transverse shear strain gives most accurate results. Also, Timoshenko's theory (with a shear factor of five‐sixths) and the current formulation which uses the parabolic shear‐strain distribution, give identical values for deflections.     

Robust Dynamic Sliding Mode Control of a Rotating Thin-Walled Composite Blade

This paper presents a robust control methodology for the dynamic response control of a rotating blade exposed to external excitations and modeling uncertainty. The blade is modeled as a tapered thin-walled beam with fiber-reinforced composite material. The dynamic response characteristics of a rotating composite beam are investigated; namely, ply angle, taper ratio, and various selected rotational speeds. To extend life and improve efficiency, a robust control methodology is implemented and structural tailoring composite properties are used. To this end, considering modeling uncertainties and external disturbance conditions, a sliding mode control is proposed and its performance and robustness are compared with the conventional linear quadratic Gaussian control.     

Performance of Glued-Laminated Timbers with FRP Shear and Flexural Reinforcement

Glued-laminated wood beams (glulams) have low allowable shear stresses relative to competitive engineering wood products such as parallel strand lumber and laminated veneer lumber. For heavily loaded applications such as garage door headers, the lower shear allowable stresses typically necessitate the use of larger glulam members relative to other engineered lumber. This paper reports on experimental research aimed at increasing the shear capacity of glulams. To increase the shear strength, a series of fiber-reinforced polymeric (FRP) pins are inserted into holes drilled transversely across the plies of the glulam. These pins are epoxy-bonded into place after the glulam has been produced. The test results show that the shear strength scatter in the pinned set of glulams is significantly reduced as compared to the unpinned specimens. Two- and three-parameter Weibull estimates of the service-level allowables increases between 40% and 100% for specimen sets reinforced by the FRP pins. The transverse reinforcing scheme also shows promise for aiding in engagement of composite flexural reinforcement plies into the laminate stack. Previous research has shown that the bonding between wood and FRP plies has potential long-term durability problems. Therefore, the pinning technology reported on in this work shows promise for providing a means for direct engagement (through bearing of the pins) of the FRP plies to the wood plies. This behavior has been demonstrated though the testing of larger-scale specimens with both transverse shear reinforcements and longitudinal FRP plies. The reinforcing strategies show potential structural and economic advantages, especially when the FRP is coupled with low-grade, low-value finger-jointed lumber.     

Verifications of Design Equations of Beams Externally Strengthened with FRP Composites

Based on the test information available in the literature since 1990, a comprehensive database is assembled for an extensive survey of existing studies on the flexural behavior of reinforced concrete beams externally strengthened with fiber-reinforced polymer (FRP) composites. Beam dimensions, material properties (concrete, steel reinforcement, FRP composites, etc.), and corresponding flexural responses such as failure modes, moment capacities, and so on, are collected in this database. The purpose of this database is to verify the design formulas presented in ACI 440.2R-02, Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures. The performance of some other simple strength design models is investigated based on the same database and compared with that of the ACI model, which is found to have the least scattered prediction compared to others. Finally, a modified maximum strain FRP equation is recommended.     

On the Comparison of Timoshenko and Shear Models in Beam Dynamics

The classical Timoshenko beam model and the shear beam model are often used to model shear building behavior both for stability or dynamic analysis. This technical note questions the theoretical relationship between both models for large values of bending to shear stiffness parameter. The simply supported beam is analytically studied for both models. Asymptotic solutions are obtained for large values of bending to shear stiffness parameter. In the general case, it is proven that the shear beam model cannot be deduced from the Timoshenko model, by considering large values of bending to shear stiffness parameter. This is only achieved for specific geometrical parameter in the present example. As a conclusion, the capability of the shear model to approximate Timoshenko model for large values of bending to shear stiffness parameter is firmly dependent on the material and geometrical characteristics of the beam section and on the boundary conditions.     

Spatial Stability of Shear Deformable Nonsymmetric Thin-Walled Curved Beams: A Centroid-Shear Center Formulation

An improved shear deformable curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled stability analysis of thin-walled curved beams with nonsymmetric cross sections. For this, the displacement field is introduced considering the second order terms of semitangential rotations. Next the elastic strain energy is newly derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. Then the potential energy due to initial stress resultants is consistently derived with accurate calculation of the Wagner effect. Finally, equilibrium equations and force–deformation relations are obtained using a stationary condition of total potential energy. The closed-form solutions for in-plane and out-of-plane buckling of curved beams subjected to uniform compression and pure bending are newly derived. Additionally, finite-element procedures are developed by using curved beam elements with arbitrary thin-walled sections. In order to illustrate the accuracy and the practical usefulness of this study, closed-form and numerical solutions for spatial buckling are compared with results by available references and ABAQUS’ shell elements.     

Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load

In this paper, free vibration characteristics and the dynamic behavior of a functionally graded simply-supported beam under a concentrated moving harmonic load are investigated. The system of equations of motion is derived by using Lagrange’s equations under the assumptions of the Euler–Bernoulli beam theory. Trial functions denoting the transverse and the axial deflections of the beam are expressed in polynomial forms. The constraint conditions of supports are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the exponential law and the power-law form. In this study, the effects of the different material distribution, velocity of the moving harmonic load, the excitation frequency on the dynamic responses of the beam are discussed. Numerical results show that the above-mentioned effects play very important role on the dynamic deflections of the beam.     

Performance Evaluation of Precast Posttensioned Concrete Multibeam Deck

An innovative bridge construction utilizing on-site posttensioned precast concrete beams that are compressed together with full depth grouted shear keys and transverse posttensioning is the subject of this paper. In particular, the performance of the shear keys with regard to load transfer and water tightness constitutes the main issues of investigation. This paper presents the results of a live load testing program and associated finite-element analysis results of the as-built bridge. Live truck load test results help provide insights on the lateral (transverse direction) load distribution characteristics among the interconnected beams. The measured lateral distribution of the applied truck load among adjacent beams showed that the load was transferred primarily to the beams close to the truck load position, validating the effectiveness of the shear key details in transporting loads.