Measurement of the Timoshenko Shear Stiffness. I: Effect of Warping

Fiber-reinforced polymer (FRP) composite beams are increasingly finding use in construction. Due to their lower stiffness relative to steel sections, the design of FRP structures is usually deflection controlled. Furthermore, shear deformation can be significant in FRP beams, thus, requiring the use of the Timoshenko beam theory to estimate deflections. However, the Timoshenko shear stiffness can be difficult to measure. Part of the measurement error has been attributed to shear warping effects. It has been hypothesized that warping restraints at loading points and supports increase the apparent shear stiffness to a degree that is significant at relatively short spans, e.g., L/h<10 to 15. In this study, the influence of warping on short to moderate length FRP beams under various types of loading and boundary conditions is considered using finite-element analysis. In particular, a commercially available thin-walled FRP beam was investigated. The results suggest that warping has a negligible effect for thin-walled beams at reasonable spans, i.e., L/h>5. On the contrary, the effective shear stiffness is found to decrease at shorter span lengths. This is the first of two papers in a series.     

Transverse Shear Effect on Flutter of Composite Panels

The effect of transverse shear deformation on the supersonic flutter of composite panels has been investigated using the finite element method. First‐order shear‐deformation laminated‐plate theory and quasi‐steady aerodynamic theory are employed for the analysis. The total displacement of the plate is expressed as the sum of the displacement due to bending and the displacement due to shear deformation. Thus, the aerodynamic pressure induced by the plate motion is also the sum of the pressure induced by bending deformation and the pressure induced by shear deformation. Numerical results show that the transverse shear deformation may have a significant effect on the flutter boundary if aerodynamic damping were small or neglected in the determination of flutter boundary.     

Torsional Stiffness of Prestressing Tendons in Double-T Beams

When a prestressed double-T beam is subjected to torsion, a pair of prestressing tendons resists torsional rotation because of the restoring action of the displaced prestressing tendons. A comprehensive formulation to account for the torsional restoring action of double-T beams is presented, based on Vlasov’s hypothesis of considering warping displacement in an open-section. The deformation energies of prestressing tendons and reinforcing bars are calculated based on the deformed geometry to obtain the total potential energy. A two-noded beam element with seven degrees of freedom per node approximates an axial displacement, two translations, two flexural, and one torsional rotations, and a warping displacement to derive the finite-element equilibrium equations by minimizing the potential energy function. The role of prestressing forces of the tendons on the torsional resistance and the limitations of the traditional transformed section approach are addressed when it is applied to torsional problems. As a numerical example, an existing three-span continuous double-T beam is analyzed, and the bimoment and angle of twist are compared to those calculated using conventional three-dimensional finite-element analysis and the analytical solution of governing differential equations.     

Dynamic Characteristics and Effective Stiffness Properties of Honeycomb Composite Sandwich Structures for Highway Bridge Applications

In this paper, a combined analytical and experimental study of dynamic characteristics of honeycomb composite sandwich structures in bridge systems is presented, and a relatively simple and reliable dynamic experimental procedure to estimate the beam bending and transverse shear stiffness is proposed. This procedure is especially practicable for estimating the beam transverse shear stiffness, which is primarily contributed by the core and is usually difficult to measure. The composite sandwich beams are made of E-glass fiber and polyester resins, and the core consists of the corrugated cells in a sinusoidal configuration. Based on the modeling of equivalent properties for the face laminates and core elements, analytical predictions of effective flexural and transverse shear stiffness properties of sandwich beams along the longitudinal and transverse to the sinusoidal core wave directions are first obtained. Using piezoelectric sensors, the dynamic response data are collected, and the dynamic characteristics of the sandwich structures are analyzed, from which the flexural and transverse shear stiffness properties are reduced. The experimental stiffness results are then compared to the analytical stiffness properties, and relatively good correlations are obtained. The proposed dynamic tests using piezoelectric sensors can be used effectively to evaluate the dynamic characteristics and stiffness properties of large sandwich structures suitable for highway bridge applications.     

Planar Bending of Sandwich Beams with Transverse Loads off the Centroidal Axis

Conventional analysis methods for beams do not distinguish between transverse loads that are applied at the beam centroidal axis and those acting either above or below the centroidal axis. In contrast, this paper formulates a sandwich beam finite element solution which models the effect of load height relative to the centroidal axis. Towards this goal, the governing equilibrium equations and associated boundary conditions are derived based on a Timoshenko beam formulation for the core material. Special shape functions satisfying the homogeneous form of the equilibrium equations are derived and subsequently used to formulate exact stiffness matrices. By omitting the stiffness terms related to the faces, the formulation for a homogeneous Timoshenko beam can be recovered. Also, the Euler–Bernouilli counterpart of the formulation is recovered as a limiting case of the current Timoshenko beam formulation. Effects of load height relative to the centroid are observed to have similarities with those induced by axial forces in beam-columns. For a simply supported beam, downward acting loads located below the centroidal axis are found to induce a stiffening effect while those acting above the centroidal axis are found to induce a softening effect, resulting in higher transverse displacements.     

Effect of Transverse Steel on the Response of RC Beams Strengthened in Shear by FRP: Experimental Study

The present paper shows and discusses some of the results obtained within an experimental investigation carried out on 15 reinforced concrete (RC) beams strengthened in shear by externally bonded fiber-reinforced plastics (FRP) sheets. The aim of the study is to analyze the influence that the geometrical percentage of transverse steel reinforcement could have on the FRP resisting action. In particular, the objectives of the experimental campaign are to explore the possible interaction between FRP and steel transverse reinforcement resisting actions, analyzing the deformation behavior of the shear resisting system (FRP, transverse steel, and concrete) and the modes of failure of the strengthened and not strengthened beams. The results of the tests in terms of shear capacity are compared to the design formulations provided by the American Concrete Institute and the National Research Council of Italy code-format recommendations.     

Analysis of Laminated Sandwich Plates Based on Interlaminar Shear Stress Continuous Plate Theory

The bending response of sandwich plates with stiff laminated face sheets is studied by a six-noded triangular element having seven degrees of freedom at each node. The element formulation is based on a refined higher-order plate theory having all the features for an accurate modeling of sandwich plates with affordable unknowns. The refined plate theory is quite attractive but suffers from a problem concerned with an interelement continuity requirement when it is used in finite element analysis. The problem has been dealt satisfactorily in this new element, which is applied to the analysis of sandwich plates of different kinds.     

Detection of Stiffness Reductions in Concrete Decks with Arbitrary Damage Shapes Using Incomplete Dynamic Measurements

A new refined nondestructive evaluation technique for concrete decks with arbitrary damage shapes is presented, and its utility in detecting the location and extent of the damage using only a single dynamic measurement signal is demonstrated. Six unknown parameters are considered to determine the damage distribution, which is a modified form of the bivariate Gaussian distribution function. Using a combination of the combined finite-element method (FEM) and the advanced uniform microgenetic algorithm, the various influences of different measurement locations on the damage detection are studied. In addition, the effect of noise is simulated in order to study the influence of the measurement errors and the uncertainty of the method. The sample studies demonstrate the excellence of the proposed method from the standpoints of its computation efficiency as well as its ability to investigate the complex distribution of an arbitrary stiffness reduction.     

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis, and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the direct differentiation method. The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a nonsymmetric, two-span continuous beam subjected to monotonic loading and a frame subassemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through forward finite difference analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.     

Effect of Fine Particle Migration on the Small-Strain Stiffness of Unsaturated Soils

The paper presents the results of an experimental investigation of fine particle migration from pore body to the pore throat and toward the contact between particles and its effect on skeleton stiffness of granular materials. We hypothesize that the suspended colloids in the pore fluid migrate and deposit on the contact surface between the skeleton-forming particles and change the magnitude of the soil stiffness. Three specimens were prepared using uniform spherical glass particles that were saturated with deionized water and kaolinite or silt-base slurries. The specimens were drained by evaporation which retained the fines in the soil while increasing the matric suction. Changes in soil dynamic stiffness were evaluated using piezoelectric transducers while the migration of fines and the changes of the properties of the pore fluid were monitored using synchrotron X-ray microcomputed tomography (SMCT) on identical specimens. The wave propagation experiments show that the stiffness of the tested specimens increased at different rates during the drying processes. These measurements were complemented with SMCT scanning analysis that shows an increase in mass density of the remaining slurry as the pore fluid concentrated near the particle contacts. The results indicate that the soil stiffness increase due to the alteration of the pore fluid at the particles’ contact and changes caused at the contact behavior itself. These results provide an insight about parameters that influence soil stiffness which may help in better predictions of stiffness changes in compacted soils during moisture changes.     

Dynamic Axial-Moment Buckling of Linear Beam Systems by Power Series Stiffness

The paper applies the power series method to find the dynamic stiffness for the dynamics axial-moment buckling analyses of linear framed structures. Since the formulation is exact in classical sense, one element is good enough for the entire beam. The dynamic stiffness thus obtained can be decomposed into the stiffness, mass and initial stress matrices at a particular frequency, a particular axial force and a particular initial moment. The given axial force and moment can be nonuniformly distributed. The interaction diagrams in classical loading conditions of uniform moment, moment due to concentrated and distributed lateral force are given explicitly. The effects of warping rigidity, torsion rigidity, axial tension and compression are investigated in detail. The static and dynamic interaction buckling of a two-section I-beam structure is studied. Finally, we conclude that the three dimensional interaction diagram of the dynamic biaxial moment buckling can be obtained simply by rotating the three dimensional interaction diagram of the dynamic mono-axial moment buckling about the frequency axis if the bimoments are appropriately scaled. It is shown that application for non-uniform section is not suitable due to convergent problem. The method is very efficient that many interaction diagrams are produced for the first time.     

FEA of Complex Bridge System with FRP Composite Deck

Innovative fiber-reinforced polymer (FRP) composite highway bridge deck systems are gradually gaining acceptance in replacing damaged/deteriorated concrete and timber decks. FRP bridge decks can be designed to meet the American Association of State Highway and Transportation Officials (AASHTO) HS-25 load requirements. Because a rather complex sub- and superstructure system is used to support the FRP deck, it is important to include the entire system in analyzing the deck behavior and performance. In this paper, we will present a finite-element analysis (FEA) that is able to consider the structural complexity of the entire bridge system and the material complexity of an FRP sandwich deck. The FEA is constructed using a two-step analysis approach. The first step is to analyze the global behavior of the entire bridge under the AASHTO HS-25 loading. The next step is to analyze the local behavior of the FRP deck with appropriate load and boundary conditions determined from the first step. For the latter, a layered FEA module is proposed to compute the internal stresses and deformations of the FRP sandwich deck. This approach produces predictions that are in good agreement with experimental measurements.     

In-Plane Shear Behavior of Masonry Panels Strengthened with NSM CFRP Strips. II: Finite-Element Model

A combined experimental and numerical program was conducted to study the in-plane shear behavior of clay brick masonry walls strengthened with near surface mounting carbon-fiber-reinforced polymer (CFRP) strips. This paper is focused on the numerical program. A two-dimensional finite-element (FE) model was used to simulate the behavior of FRP-strengthened wall tests. The masonry was modeled using the micromodeling approach. The FRP was attached to the masonry mesh using the shear bond-slip relationships determined from experimental pull tests. The model was designed in a way so that FRP crossing a sliding crack (perpendicularly) would prevent crack opening, normal to the direction of sliding (dilation), and increase sliding resistance. This sliding resisting mechanism was observed in the experimental tests. The FE model reproduced the key behaviors observed in the experiments, including the load-displacement response, crack development, and FRP reinforcement contribution. The FE model did not include masonry cracking adjacent to the FRP and through the wall thickness (as observed in some experiments). This type of cracking resulted in premature FRP debonding in the experiments. Debonding did not occur in the FE model because this type of masonry cracking was not modeled.     

Impact Mechanics and High-Energy Absorbing Materials: Review

In this paper a review of impact mechanics and high-energy absorbing materials is presented. We review different theoretical models (rigid-body dynamics, elastic, shock, and plastic wave propagation, and nonclassical or nonlocal models) and computational methods (finite-element, finite-difference, and mesh-free methods) used in impact mechanics. Some recent developments in numerical simulation of impact (e.g., peridynamics) and new design concepts proposed as high energy absorbing materials (lattice and truss structures, hybrid sandwich composites, metal foams, magnetorheological fluids, porous shape memory alloys) are discussed. Recent studies on experimental evaluation and constitutive modeling of strain rate-dependent polymer matrix composites are also presented. Impact damage on composite materials in aerospace engineering is discussed along with future research needs. A particular example for the design of a sandwich material as an impact mitigator is given in more detail. This brief review is intended to help the readers in identifying starting points for research in modeling and simulation of impact problems and in designing energy absorbing materials and structures.     

Performance Evaluation of Repair Technique for Damaged Fiber-Reinforced Polymer Honeycomb Bridge Deck Panels

All-composite, fiber-reinforced polymer honeycomb (FRPH) sandwich panels are an innovative application of modern composite materials in civil engineering. These panels have become increasingly popular for use as full-depth bridge decks and have been used to span both transversely between steel or concrete girders and longitudinally between abutments. Although several bridges using FRPH panels have been installed in recent years, a method to repair the panels if they are damaged has not been thoroughly investigated. This paper presents the analysis and full-scale evaluation of a 9.75 m (32 ft) long FRPH member that was subjected to severe core-face delamination damage and subsequently repaired. As such, the work presented herein is the first of its kind to be conducted for FRPH bridge members. The damaged member when repaired was shown to have approximately 65% more capacity than a similar undamaged member. The additional capacity was achieved using a single wrapping layer over the face plates and sinusoidal core. This wrapping layer is believed to have prevented a failure (at the resin bond line) between the face plates and core by engaging a shear-friction type clamping force. The contribution of the wrap layer is considered using simple calculations, rigorous finite-element models, and experimental data. Acoustic emission monitoring was used to compare the performance of the damaged and repaired specimens under sustained load.     

Evaluation of GFRP Honeycomb Beams for the O’Fallon Park Bridge

This paper presents a study on the evaluation of the static performance of a glass fiber-reinforced polymer (GFRP) bridge deck that was installed in O’Fallon Park over Bear Creek west of the City of Denver. The bridge deck has a sandwich panel configuration, consisting of two stiff faces separated by a light-weight honeycomb core. The deck was manufactured using a hand lay-up technique. To assist the preliminary design of the deck, the stiffness and load-carrying capacities of four approximately 330 mm (13 in.) wide GFRP beam specimens were evaluated. The crushing capacity of the panel was also examined by subjecting four 330×305×190?mm?(13×12×7.5?in.) specimens to compression tests. The experimental data were analyzed and compared to results obtained from analytical and finite element models, which have been used to enhance the understanding of the experimental observations. The failure of all four beams was caused by the delamination of the top faces. In spite of the scatter of the tests results, the beams showed good shear strengths at the face-to-core interface as compared to similar panels evaluated in prior studies.     

Construction of a Horizontally Curved Steel I-Girder Bridge. Part I: Erection Sequence

In the case of horizontally curved steel I-girder bridges, girder and cross-frame members are frequently detailed for erection in the no-load condition as a matter of convention. As a result, it is imperative that the erection sequence used to construct such bridges be comprehensively studied to ensure that the no-load condition can be achieved in the field and that significant superstructure component fit-up problems do not occur. The current research investigates the erection of a recently constructed horizontally curved steel I-girder bridge, in which significant difficulties were encountered during erection. The bridge erection is recreated through an analytical simulation using a detailed nonlinear finite element model. The analytical results demonstrate that a condition that closely resembles the no-load condition can be achieved in the field during construction with the proper implementation of temporary support structures; and that the difficulties encountered during the erection of the subject bridge superstructure could not be attributed to the erection scheme followed.     

Support Mechanisms of Rammed Aggregate Piers. II: Numerical Analyses

This paper is the second of a two-part series describing an investigation of the mechanical behavior of rammed aggregate piers in supporting rigid square footings. In this paper, the performances of two pier-supported footings and three isolated piers during compressive load tests were simulated using an axisymmetric finite element model and compared to experimental data. A hardening-soil constitutive model with parameters estimated from in situ and laboratory tests was used to characterize the constitutive behaviors of the pier material and the matrix soil. Pier groups were modeled as unit cells with the tributary area determined from the center-to-center spacing. Cavity expansion modeling was used to simulate the pier installation process. Verifications of the numerical model were carried out by comparing the numerical results with the data obtained from full-scale, instrumented load tests. Interpretation of the numerical results focused on the load-deformation behavior, group effect, stress concentration ratio, and the development of stresses in the matrix soil. The distributions of vertical stress underneath the pier-supported footings are also characterized.     

Effects of False Floors on Vibration Serviceability of Building Floors. II: Response to Pedestrian Excitation

This is the second of two papers that present the results of a comprehensive and systematic study into the effects of false flooring on the vibration serviceability of long-span concrete floors. In this paper, controlled pedestrian response measurements were utilized to determine the effects of the installation of false flooring on the vibration serviceability of long-span concrete floors. It was found that, in most cases, the installation of false flooring tended to reduce the measured vibration response of the floor under controlled pedestrian excitation. This was more significant for false floors with a relatively high finished floor height (FFH) than for floors with a lower finished floor height. It is tentatively proposed that the effects of false flooring be incorporated into existing design procedures by multiplying calculated responses by a vibration response reduction factor. This factor would be 0.9 for false flooring with FFH less than 500 mm or 0.8 for false flooring with FFH of 500 mm or greater.