Flexural Behavior of Continuous GFRP Reinforced Concrete Beams

The results of testing two simply and three continuously supported concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars are presented. The amount of GFRP reinforcement was the main parameter investigated. Over and under GFRP reinforcements were applied for the simply supported concrete beams. Three different GFRP reinforcement combinations of over and under reinforcement ratios were used for the top and bottom layers of the continuous concrete beams tested. A concrete continuous beam reinforced with steel bars was also tested for comparison purposes. The experimental results revealed that over-reinforcing the bottom layer of either the simply or continuously supported GFRP beams is a key factor in controlling the width and propagation of cracks, enhancing the load capacity, and reducing the deflection of such beams. Comparisons between experimental results and those obtained from simplified methods proposed by the ACI 440 Committee show that ACI 440.1R-06 equations can reasonably predict the load capacity and deflection of the simply and continuously supported GFRP reinforced concrete beams tested.     

Control of Wave Propagation in Sandwich Plate Rows with Periodic Honeycomb Core

The wave propagation in sandwich plate rows with cellular core is analyzed and controlled. Honeycomb core materials of different geometry placed periodically along the structure introduce the proper impedance mismatch necessary to obstruct the propagation of waves over specified frequency bands (stop bands). The location and the extension of the stop bands can be optimized by proper selection of the geometrical and physical properties of the core. An optimal configuration of the core can be identified to design passive sandwich structures, which are stable and quiet over desired frequency bands. A theoretical model is developed to describe the wave propagation characteristics and the vibrations of a three-layered sandwich plate simply supported along its longitudinal edges. The core properties of the plate change periodically along the plate length. The wave propagation characteristics are estimated by analyzing the transfer matrix of each cell of the resulting periodic structure. The transfer matrix is also properly recast to obtain the cell’s dynamic stiffness matrix and to formulate a spectral finite element model for the periodic sandwich plate. The spectral finite element model allows predicting the dynamic behavior of the structure with a significantly reduced number of elements as compared to conventional finite elements. The numerical model is used to predict the dynamic response of the considered class of plates and to study their propagation and attenuation characteristics for various core configurations. The presented numerical results demonstrate the simplicity and the effectiveness of the proposed treatment, which reduces the transmission of waves and the plate vibrations over specified frequency bands without the need of additional passive or active control devices. Such unique characteristics can be employed to design lightweight composite panels behaving as mechanical filters. The filtering capabilities of such passive composite panels can be properly modified and optimized to fit required transmissibility levels over desired frequencies without compromising the size and the weight of the structure.     

Vibration Analysis of an Elastic Beam Subjected to a Moving Beam with Flexible Connections

The vibration problem of a simply supported beam subjected to a moving elastic structure is investigated. The model consists of two Euler-Bernoulli beams which are assumed to be connected by flexible springs at two discrete points. The dynamic response of the simply supported beam subjected to the moving elastic beam at a constant speed is studied by the modal superposition method. The elastic stiffness and the inertial effect of the moving beam are included in the analysis. By solving the ordinary differential equations governing the motion of the model, some approximate analytical results are derived and influence factors on the dynamic response of the simply supported beam are discussed in details, including the stiffness ratio, which is defined as the stiffness of the moving beam to that of the simply supported beam, the moving velocity and the connection spring stiffness between the two beams. Results of the study imply that the connection stiffness has an apparent influence on the dynamic behavior of the simply supported beam.     

Seismic Performance Assessment of Simply Supported and Continuous Multispan Concrete Girder Highway Bridges

Seismic evaluations of typical concrete girder bridges are conducted for both a multispan simply supported and a multispan continuous girder bridge common to the Central and Southeastern United States. These evaluations are performed for an approximate hazard level of 2% in 50?years by performing nonlinear time history analyses on three-dimensional analytical models. The results show significant vulnerabilities in the reinforced concrete columns, the abutments, and also in unseating of the girders. In general, the longitudinal loading of the bridges results in larger demands than the transverse loading. However, the simply supported bridge sustains bearing deformations in the transverse direction which are on the same order as their longitudinal response. These results suggest that both longitudinal and transverse loading are significant and should be considered when performing seismic hazard analyses of these bridges.     

Flexural Performance of Concrete Beams Reinforced with FRP Grids

This paper evaluates the flexural performance of simply supported concrete beams subjected to four-point monotonic loading and reinforced with a 2D fiber-reinforced plastic (FRP) grid. The main parameter of the study is the amount of longitudinal FRP reinforcement. With respect to a balanced strain condition, three underreinforced and two overreinforced FRP designs were tested with three identical beams per design. Laboratory recorded load-deflection, failure mode, cracking behavior, and reinforcement strain data are compared with theoretical predictions calculated according to traditional steel-reinforced concrete procedures. The study concludes that, with respect to ACI 318-95, flexural capacity is accurately predicted, but shear strength is not. Deflection compatibility between test results and ACI predictions employing the Branson effective moment of inertia was dependent on the percentage of longitudinal reinforcement. In general, observed flexural stiffness was less than that predicted by Branson's equation. A moment-curvature deflection procedure employing a bilinear concrete model compared very well with measured deflections. Finally, the grid configuration provides an effective force transfer mechanism. Cracking occurred at transverse bar locations only, and FRP tensile rupture was achieved with no observed deterioration in force transfer mechanics.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. II: Retrofitted

Part I of this two-part paper evaluated the seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States. The results showed that the bridges were vulnerable to damage resulting from impact between decks, and large ductility demands on nonductile columns. Furthermore, fixed and expansion bearings were likely to fail during strong ground motion. In this paper, several retrofit measures to improve the seismic performance of typical multispan simply supported and multispan continuous steel girder bridges are evaluated, including the use of elastomeric bearings, lead-rubber bearings, and restrainer cables. It is determined that lead-rubber bearings are the most effective retrofit measure for reducing the seismic vulnerability of typical bridges. While isolation provided by elastomeric bearings limits the forces into the columns, the added flexibility results in pounding between decks in the MSSS steel girder bridges. Restrainer cables, which are becoming a common retrofit measure, are effective in reducing the hinge opening in MSSS bridges with steel bearings. However, when used with elastomeric bearings, the restrainer cables negate the isolation effect of the bearings.     

Failure Mode Analyses of Reinforced Concrete Beams Strengthened in Flexure with Externally Bonded Fiber-Reinforced Polymers

As existing structures age or are required to meet the changing demands on our civil infrastructure, poststrengthening and retrofitting are inevitable. A relatively recent technique to strengthen reinforced concrete (RC) beams in flexure uses fiber-reinforced polymer (FRP) strips or sheets glued to the tension side of the beam. A number of researchers have reported that the failure mode of an FRP-strengthened RC beam can change from the desired ductile mode of an underreinforced beam to a brittle one. This paper analyzes the effects of this strengthening technique on the response and failure modes of a reference RC beam. A nonlinear RC beam element model with bond-slip between the concrete and the FRP plate is used to study how the failure mechanism of simply supported strengthened RC beams is affected by the following parameters: plate length, plate width, plate stiffness, and loading type. The beam geometry is kept constant. The parametric studies confirm the experimentally observed results according to which the most commonly observed failure modes due to loss of composite actions are affected by the plate geometric and material properties. In addition, distributed loads (difficult to apply in an experimental test) may not be as sensitive to plate debonding in the region of maximum bending moment as are beams subjected to point loads.     

Production and propagation of Hermite-sinusoidal-Gaussian laser beams

Hermite-sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the limit of large Hermite-Gaussian beam size, the sinusoidal factors are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar Hermite-Gaussian form. The propagation of these beams is examined in detail, and resonators are designed that will produce them. As an example, a special resonator is designed to produce hyperbolic-sine-Gaussian beams. This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. The beam mode has finite energy and is perturbation stable.     

Exact Solutions for Buckling of Multispan Rectangular Plates

This paper presents exact solutions for buckling of multispan rectangular plates having two opposite edges simply supported and the other two edges being either free, simply supported, or clamped. The Levy solution procedure is employed to develop an analytical approach for buckling analysis of multispan plates. The Levy solution for each span is derived and the continuity along the interface of two spans is ensured through the implementation of the essential and natural boundary conditions at the interface. Extensive buckling factors, most of which are first-known exact solutions, are given in tabular and design chart forms for two- and three-unequal-span square plates subjected to uniaxial in-plane load in the x or y directions and biaxial in-plane load. The influence of the span ratios and plate boundary conditions on the buckling factors is discussed. Buckling factors are also obtained for two-, three-, and four-equal-span rectangular plates with various edge support conditions. The exact buckling solutions presented in this paper are of benchmark values for such plates.     

Finite Beam Element Considering Shear-Lag Effect in Box Girder

A finite-element method considering the interaction of the bending and shear-lag deformation of a box girder was established. Meanwhile a shear-lag-induced stiffness matrix was defined. The stiffness matrices considering the effect of the shear lag were deduced. At each node of the beam element, two shear-lag degrees of freedom were used as boundary conditions for the box girders. The proposed formulations were then applied to analyze the effects of the shear lag on the deflection, the internal forces, and the shear-lag coefficients in the simply supported cantilever and continuous box beams under uniformly distributed and concentrated loads. The numerical results obtained using the proposed procedure were in good agreement with those using the finite-shell-element method, the finite-stringer method, the analytical method based on the variational principle, and the model tests. The proposed method is reliable and more effective for the analysis of the shear lag in the actual box-girder structures.     

Concentrations of Pressure Between an Elastically Supported Beam and a Moving Timoshenko-Beam

The present paper is concerned with the motion of an elastically supported beam that carries an elastic beam moving at constant speed. This problem provides a limiting case to the assumptions usually considered in the study of trains moving on rail tracks. In the literature, the train is commonly treated as a moving line-load with space-wise constant intensity, or as a system of moving rigid bodies supported by single springs and dampers. In extension, we study an elastically supported infinite beam, which is mounted by an elastic beam moving at a constant speed. Both beams are considered to have distributed stiffness and mass. The moving beam represents the train, while the elastically supported infinite beam models the railway track. The two beams are connected by an interface modeled as an additional continuous elastic foundation. Here, we follow a strategy by Stephen P. Timoshenko, who showed that a beam on discrete elastic supports could be modeled as a beam on a continuous elastic Winkler (one-parameter) foundation without suffering a substantial loss in accuracy. The celebrated Timoshenko theory of shear deformable beams with rotatory inertia is used to formulate the equations of motion of the two beams under consideration. The resulting system of ordinary differential equations and boundary conditions is solved by means of the powerful methods of symbolic computation. We present a nondimensional study on the influence of the train stiffness and the interface stiffness upon the pressure distribution between train and railway track. Considerable pressure concentrations are found to take place at the ends of the moving train.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. I: As Built

The seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States is evaluated. Nonlinear time history analyses are conducted using synthetic ground motion for three cities for 475 and 2,475-year return period earthquakes (10 and 2% probability of exceedance in 50 years). The results indicate that the seismic response for the 475-year return period earthquake would lead to an essentially linear response in typical bridges. However, the seismic response for a 2,475-year return period earthquake resulted in significant demands on nonductile columns, fixed and expansion bearings, and abutments. In particular, pounding between decks in the MSSS bridge would result in significant damage to steel bearings and would lead to the toppling of rocker bearings, which may result in unseating of the bridge deck.     

变截面连续梁动力特性的半解析解法

求解等跨等截面连续梁的变形和内力是土木工程领域的典型问题. 基于Euler–Bernoulli梁理论,利用位移法和辅助数列推导出任意跨数的等跨等截面连续梁梁端转动刚度的解析表达式,进而得到连续梁支点转角、弯矩在跨中集中荷载、满跨均布荷载、竖向温差作用下的通用计算公式. 研究表明：当跨数趋于无穷大时,等跨等截面连续梁的梁端转动刚度上限值为单跨梁抗弯线刚度的\t\t\t\t\t\t\t\t\t\t\t相似文献   

Impact Loading of Concrete Beams Externally Strengthened with CFRP Laminates

The quasi-static behavior of flexural members strengthened with carbon fiber reinforced polymer (CFRP) laminates has been well documented in recent years, but there is a gap in knowledge regarding the effects of dynamic and impact loading of such members. This paper presents the test results of four 8 m beams externally strengthened for flexure, two with CFRP laminates and two with steel plates. Impact loading was induced by lifting one end of the simply supported beams and dropping it from given heights. The strain rates induced in the CFRP laminates were at least three orders of magnitude greater than the strain rates used for testing CFRP laminate coupons in tension. Comparisons are made between the dynamic impact behavior of the beams strengthened with CFRP laminates and steel plates, and the behavior of both beam types is modeled using an equation of motion. The beams externally strengthened with CFRP laminates performed well under impact loading, although they could not provide the same energy absorption as the beams externally strengthened with steel plates. Additional anchoring, at least at the ends of the CFRP laminates, would improve the impact resistance of these beams. Good predictions were made with the derived equation of motion by using the flexural stiffness of the beams at their ultimate limit state.     

Second-Order Stiffness Matrix and Loading Vector of a Beam-Column with Semirigid Connections on an Elastic Foundation

The second-order stiffness matrix and corresponding loading vector of a prismatic beam–column subjected to a constant axial load and supported on a uniformly distributed elastic foundation (Winkler type) along its span with its ends connected to elastic supports are derived in a classical manner. The stiffness coefficients are expressed in terms of the ballast coefficient of the elastic foundation, applied axial load, support conditions, bending, and shear deformations. These individual parameters may be dropped when the appropriate effect is not considered; therefore, the proposed model captures all the different models of beams and beam–columns including those based on the theories of Bernoulli–Euler, Timoshenko, Rayleigh, and bending and shear.The expressions developed for the load vector are also general for any type or combinations of transverse loads including concentrated and partially nonuniform distributed loads. In addition, the transfer equations necessary to determine the transverse deflections, rotations, shear, and bending moments along the member are also developed and presented.     

子波穿过黏弹性节理的波形变化规律

将岩体和节理抽象为Kelvin黏弹性介质,建立谐波穿过黏弹性节理的传播模型,分析了谐波在黏弹性节理的透、反射系数和子波穿过节理后的波形变化规律。研究结果表明,黏弹性节理具有低通滤波特性,导致Ricker子波穿过黏弹性节理后,透射波振幅减小,主瓣不突出,波形在时域上变得更平缓;波形相关系数主要反映子波穿过黏弹性节理后发生的相位变化,而波形变化系数能综合反映子波的振幅和相位变化,因而两者描述子波波形变化时具有不同的变化规律;相对于切向刚度和切向黏性系数,节理的法向刚度和法向黏性系数对子波波形变化影响更大。     

Shear Strength of Normal Strength Concrete Beams Reinforced with Deformed GFRP Bars

This paper evaluates the shear strength, Vc, of intermediate length (2.5 < a∕d < 6) simply supported concrete beams subjected to four-point monotonic loading and reinforced with deformed, glass fiber-reinforced polymer (GFRP) reinforcement bars. Six different overreinforced GFRP designs, ρ > ρb, were tested with three replicate beams per design. All samples failed as a result of diagonal-tension shear. Measured shear strengths at failure are compared with theoretical predictions calculated according to traditional steel-reinforced concrete procedures and recently published expressions intended for beams reinforced with GFRP. Recommendations are made regarding the adequacy of shear strength prediction equations for GFRP-reinforced members. The study concludes that shear capacity is significantly overestimated by the “Building Code Requirements for Structural Concrete and Commentary” (ACI 318-99) expression for, Vc, as a result of the large crack widths, small compression block, and reduced dowel action in GFRP-reinforced flexural members. Shear strength was found to be independent of the amount of longitudinal GFRP reinforcement. A simplified empirical equation for predicting the ultimate shear strength of concrete beams reinforced with GFRP is endorsed.     

Saltatory propagation of Ca2+ waves by Ca2+ sparks

Punctate releases of Ca2+, called Ca2+ sparks, originate at the regular array of t-tubules in cardiac myocytes and skeletal muscle. During Ca2+ overload sparks serve as sites for the initiation and propagation of Ca2+ waves in myocytes. Computer simulations of spark-mediated waves are performed with model release sites that reproduce the adaptive Ca2+ release observed for the ryanodine receptor. The speed of these waves is proportional to the diffusion constant of Ca2+, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium. A simplified "fire-diffuse-fire" model that mimics the properties of Ca2+-induced Ca2+ release (CICR) from isolated sites is used to explain this saltatory mode of wave propagation. Saltatory and continuous wave propagation can be differentiated by the temperature and Ca2+ buffer dependence of wave speed.     

Comparison between Organic and Inorganic Matrices for RC Beams Strengthened with Carbon Fiber Sheets

The objective of this paper is to study and compare the performance of concrete beams strengthened with carbon fiber sheets bonded with inorganic and organic resin matrices. The experimental study consisted of testing two groups of steel-reinforced concrete beams. The first group of beams was strengthened with carbon fiber sheets bonded with an organic matrix, and the second with carbon fiber sheets bonded with an inorganic matrix. The first group of beams was strengthened with 2, 3, and 4 layers of carbon fiber sheets, while the second group was strengthened with 2, 3, 4, and 5 layers of carbon fiber sheets. Strength, stiffness, ductility, deflection, failure pattern, and cracking of beams strengthened with the two systems were compared. Results showed that the inorganic matrix system is as effective in increasing strength and stiffness of reinforced concrete beams as the organic matrix. The failure mechanism of the inorganic system, however, seems more brittle. The failure of beams strengthened with inorganic matrix showed crack formation in the composite and a minimum buildup of strain along the interface of the composite and concrete. Analytical models were proposed to predict deflection and moment capacity of the strengthened beams. The experimental values compared well with those predicted by the analytical models.