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.     

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.     

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.     

Experimental Validation of a 10-m-Span Composite UHPFRC–Carbon Fibers–Timber Bridge Concept

This paper presents the experimental study of a new structure for a 10-m-span bridge deck, which takes into account the range of possibilities offered by new and high-strength materials along with the advantages of a traditional environmental friendly material. This 10-m-span element is formed by wooden beams braced at their ends on supports, a thin (7-cm-thick) upper slab made of precast ultrahigh performance fiber-reinforced concrete (UHPFRC), and fiber-reinforced polymer at the lower chord of these beams. The test program has been aimed at identifying the major critical aspects involved in producing an initial estimate of safety margins as well as validations of the design process and its underlying assumptions. Under the first loading configuration derived from live traffic loads, both the transverse and local bending of the thin UHPFRC slab were activated and confirmed by means of a three-dimensional finite-element computation. The second loading configuration corresponds to pure global longitudinal bending, with the bearing capacity being monitored up to the theoretical ultimate limit state loading and then beyond, up to experimental failure. Critical mechanisms and safety factors have also been identified. Though concept feasibility has been demonstrated, some aspects still need to be further optimized in order to obtain greater ductility and safer control over failure modes and occurrences.     

Buckling of Multiwalled Carbon Nanotubes Using Timoshenko Beam Theory

A Timoshenko beam model is presented in this paper for the buckling of axially loaded multiwalled carbon nanotubes surrounded by an elastic medium. Unlike the Euler beam model, the Timoshenko beam model allows for the effect of transverse shear deformation which becomes significant for carbon nanotubes with small length-to-diameter ratios. These stocky tubes are normally encountered in applications such as nanoprobes or nanotweezers. The proposed model treats each of the nested and concentric nanotubes as individual Timoshenko beams interacting with adjacent nanotubes in the presence of van der Waals forces. In particular, the buckling of double-walled carbon nanotubes modeled as a pair of double Timoshenko beams is studied closely and an explicit expression for the critical axial stress is derived. The study clearly demonstrates a significant reduction in the buckling loads of the tubes with small length-to-diameter ratios when shear deformation is taken into consideration.     

Analytical Approach for Detection of Multiple Cracks in a Beam

An analytical approach for the detection of a beam with multiple cracks is presented in this article. The method is based on the bending vibration theory of Euler-Bernoulli beam and the cracks are treated as massless rotational springs, by which the cracked beam is separated into a number of segments of perfect beams. By using the nontrivial solution condition of the vibration mode of the beam elements, specially using the transfer matrix method for the multiple cracks detection, the crack identification equation of the cracked beam is obtained explicitly, which is a function of natural frequencies, the locations, and depths of the cracks. Since the natural frequencies of a cracked beam can be measured through many of the structural testing methods, then the relations of the locations and the depths of the cracks can be determined explicitly from the identification equation of a cracked beam which geometrical and physical parameters as well as the boundary conditions are given. The results of some examples are shown and the present method is validated with the existing and measured experimental data. The detection for other types of beams with different number of cracks and various boundary conditions can also be obtained by a similar procedure.     

Distortional theory of thin-walled beams

The classic thin-walled beam theory for open and closed cross-sections is generalized to include one distortional mode of deformation. Distortional cross-section parameters are introduced and the new orthogonality conditions for uncoupling of the axial displacement modes are given. A normalization technique for the distortional modes leads to unique distortional cross-section properties. The theoretical formulations for torsion and distortion are nearly similar and result in nearly identical equilibrium equations. However, for closed single- or multi-cell cross-sections the torsional and distortional shear flows may couple. A study of the order of magnitude of the governing torsional and distortional parameters shows the difference between open and closed cross-sections and the related solution types. The difference in the order of magnitude of the governing cross-section parameters also leads to approximate solution techniques. In the examples, section three cross-sections are used to illustrate variations of the theoretical parameters.