Dissertations / Theses on the topic 'Flexural response'

In support of crashworthiness studies of composite airframes, the present study was undertaken to understand the large deflection flexural response and failure of graphite-epoxy laminated beams. The beam specimens were subjected to eccentric axial impact loads and to static eccentric axial loads, in order to assess the damage caused by impact.

A geometrically and materially nonlinear analysis of the response and failure of the static test specimens is presented. The analysis employed an incremental, noniterative finite element model based on the Kantrovich method and a corotational solution technique. Width-wise effects are included by assuming specific forms of the displacements across the width, with length-wise variation introduced as a degree of freedom. This one-dimensional, 22 degree of freedom finite element accurately predicted the load-deflection and strain-deflection responses of the static test specimens.

Inclusion of nonlinear material behavior was found to be important in correctly predicting load-deflection response of uniaxial materials, while inclusion of width-wise effects was determined to be more important for laminates with off-axis plies due to the existence of coupling between bending and twisting curvatures (D₁₆and D₂₆). Once material nonlinearity begins to occur in flexure, even symmetric laminates exhibit bending-stretching coupling due to different material response in tension and compression.

Master of Science

The structural response of unreinforced masonry elements strengthened with hybrid elastomeric/fiber materials was investigated through material characterization and flexural experiments. Material characterization tests were performed on various unreinforced and reinforced elastomeric materials to identify those materials that were best suited for use as structural retrofits. After material characterization was completed, the three most promising material systems were selected for further investigation, including one unreinforced elastomer film and two reinforced elastomer films with fiber orientations at 0/90° and +/- 45° relative to the major axis of the masonry elements. A series of four-point bending tests were performed on the selected masonry and epoxy bonded elastomer/fiber hybrid retrofits to determine the structural response of the composite systems. The experimental load-deformation response was used, along with material characterization results, in the development of a semi-empirical model to predict the static moment capacity of the strengthened masonry system. This model will be used in the development of reliable design criteria for masonry walls strengthened with these advanced materials.

A model is presented to use normalized multi-linear tension and compression material characteristics of strain-hardening textile reinforced concrete and derive closed form expressions for predicting moment-curvature capacity. A set of design equations are derived and simplified for use in spreadsheet based applications. The model is applicable for both strain-softening and strainhardening materials. The predictability of the simplified model is checked by model calibration and development of design charts for moment capacity and stress developed throughout the cross section of a flexural member. Model is calibrated by predicting the results of Alkali Resistant Glass and Polyethylene fabrics. A case for the flexural design of Glass Fiber Reinforced Concrete (GFRC) specimen as a simply supported beam subjected to distributed load is used to demonstrate the design procedure.

Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 49).
Ultramicrotomy is the process of cutting specimens into submicron-thickness slices for subsequent imaging using a scanning electron microscope (SEM). Ultramicrotomes, devices that employ this process, have incorporated oscillations into this process to reduce the damage done on each slice. Extensive research has been made in trying to identify the appropriate settings: frequency, amplitude of cut, and feed speed, to maximize the reduction of this damage. Currently, however, there exists no research that tries to understand why the introduction of oscillations provides such a reduction in damage. To understand the mechanics behind oscillatory orthogonal cutting, specifically in ultramicrotomy, the frequency response of a compliant mechanism must be understood. The frequency response of a complaint flexural stage driven by piezoelectric actuator was measured. Using a Linear Variable Differential Transformer (LVDT) and a dynamic signal analyzer via LabView, the frequency response of the stage was measured from 100Hz to 10000Hz. A model was then fitted to the measured response. Using this model, a comparison between a simulated-reference response of the position of the stage to the output response of the model showed that a controller was required to minimize the error in the position of the stage.
by Raul Barraza.
S.B.

This paper presents results of an experimental investigation to study the structural performance and deformability of a concrete bridge deck reinforced with corrosion resistant reinforcing (CRR) bars, i.e., bars that exhibit improved corrosion resistance when embedded in concrete as compared to traditional black steel. Flexural tests of one-way slabs were conducted to simulate negative transverse flexure over a bridge girder as assumed in the commonly employed strip design method. The bar types studied were Grade 60 (uncoated), epoxy-coated reinforcing (ECR, Grade 60), Enduramet 32 stainless steel, 2304 stainless steel, MMFX2, and glass fiber reinforced polymer (GFRP). The experimental program was designed to evaluate how a one-to-one replacement of the Grade 60 with CRR, a reduction of concrete top clear cover, and a reduction in bar quantities in the bridge deck top mat influences flexural performance at service and ultimate limit states. Moment-curvature predictions from the computer-based sectional analysis program Response 2000 were consistent with the tested results, demonstrating its viability for use with high strength and non-metallic bar without a defined yield plateau.    
    Deformability of the concrete slab-strip specimens was defined with ultimate-to-service level ratios of midspan deflection and curvature. The MMFX2 and Enduramet 32 one-to-one replacement specimens had deformability consistent with the Grade 60 controls, demonstrating that bridge deck slabs employing high strength reinforcement without a defined yield plateau can still provide sufficient ductility at an ultimate limit state. A reduction in bar quantity and cover provided acceptable levels of ductility for the 2304 specimens and MMFX2 reinforced slabs.

Master of Science

Throughout the ocean basins many broad regions of anomalously shallow topography exist that do not fit the widely accepted model of conductive plate cooling and subsidence as a function of lithospheric age. These ‘swells’ often coincide with positive geoid, Free-air gravity and heat flow anomalies as well as groups of ocean islands and seamounts. Various mechanisms have been proposed to explain how this anomalous topography is isostatically supported at depth, including increased crustal buoyancy and dynamic asthenospheric support. The Cape Verde Swell is the largest oceanic mid-plate swell on Earth at ~1800 km in diameter, with a crest ~2.2 km high, and positive geoid, gravity and heat flow anomalies of 8 m, 30 mGal and 10-15 mW m-2, respectively. These characteristics and its location on the slow-to-stationary African Plate, which concentrates the volcanism and associated geophysical anomalies within a relatively small areal extent, makes the Cape Verde Swell an ideal location to test the various proposed mechanisms for swell support. Wide-angle seismic refraction data along an ~474 km profile, extending from the Cape Verde Swell crest, is analysed and modelled to produce a 2-D velocity-depth model of the crustal structure. The resulting model reveals no widespread thickening of the lower oceanic basement, despite evidence for localised thickening beneath the islands from other studies. Subsequent 3-D ‘whole plate’ lithospheric flexure modelling reveals that, on a regional scale, the plate is stronger than expected based on its age, with some evidence for localised weakening around the islands. Overall, the results of this study suggest that the anomalously shallow topography of the Cape Verde Swell is primarily maintained by a dynamic upwelling of hot, low density material impinging on the base of the lithosphere. Over time, conduction from this hot column has thermally rejuvenated the lithosphere on a local scale, leading to additional uplift, melting and volcanism associated with the islands.

Impact strength is one of the most important structural properties for a designer to consider, but is often the most difficult to quantify or measure. A constant concern in the field of composites is the effect of foreign object impact damage because it is often undetectable by visual inspection. An impact can create interlaminar damage that often results in severe reductions in strength and instability of the structure. The main objective of this study is to determine the effectiveness of a damage arrestment device (DAD) on the mechanical behavior of composite sandwiches, following a low-velocity impact. A 7.56-lbf crosshead dropped from a height of 37.5-inches was considered for the low-velocity impact testing. In this study, the experimental and numerical analysis of composite sandwiches were investigated, which included static 4-point bend and vibration testing. Composite sandwiches were constructed utilizing four-plies of Advanced Composites Group LTM45EL/CF1803 bi-directional woven carbon fiber face sheets with a General Plastics Last-A-Foam FR-6710 rigid polyurethane core. Specimens were cured in an autoclave, using the manufacturer’s specified curing cycle. In addition to the experimental and numerical analysis of composite sandwiches, developing and building a data acquisition (DAQ) system for the Dynatup 8250 drop weight impact tester was accomplished. Utilizing National Instruments signal conditioning hardware, in conjunction with LabView and MATLAB, complete testing software was developed and built to provide full data acquisition for an impact test. The testing hardware and software provide complete force vs. time history and crosshead acceleration of the impact event, as well as provide instantaneous impact velocity of the projectile. The testing hardware, software, and procedures were developed and built in the Aerospace Structures/Composites laboratory at Cal Poly for approximately 15% of the cost from the manufacturer. In the first study, static 4-point bend testing was investigated to determine the residual flexural strength of composite sandwich beams following a low-velocity impact. Four different specimen cases were investigated in the 4-point bend test, with and without being impacted: first a control beam with no delamination or DAD, second a control beam with a centrally located 1-inch long initial delamination, third a DAD key beam with two transverse DADs centrally located 1-inch apart, and finally a DAD key beam with a centrally located initial delamination between two transverse DADs. The specimens used followed the ASTM D6272 standard test method. The specimens were 1-inch wide by 11-inch long beams. The experimental results showed that the presence of DAD keys significantly improved both the residual stiffness and ultimate strength of a composite sandwich structure that had been damaged under low-velocity impact loading, even with the presence of an initial face-core delamination. In the second study, vibration testing was investigated as a means to detect a delamination in the structure and the effect of impact damage on the vibrational characteristics, such as damping, on composite sandwich plates. Four different specimen cases were investigated in the vibration test, both with and without being impacted: first a control plate with no delamination or DAD, second three control plates with varying 1-inch initial delamination locations at the 1st, 2nd, and 3rd bending-mode nodes, third a DAD key plate with one DAD running the entire length longitudinally along the center of the plate, and finally three DAD key plates with one DAD running the entire length longitudinally along the center of the plate and varying 1-inch delamination locations at the 1st, 2nd, and 3rd bending mode-nodes. The response accelerometer location was varied at 1-inch increments along the length of the plate. From the experimental results, it was determined that varying the location of the accelerometer had a significant effect on the detection of face-core delamination in a composite sandwich structure. Additionally, it was shown that damping characteristics significantly degraded in control case plates after a low-velocity impact, but they were better retained when a DAD key was added to the structure. Numerical analysis utilizing the finite element method (FEM) was employed to validate experimental testing, as well as provide a means to examine the stress distribution and impact absorption of the structure. The impact event was modeled utilizing the LS-Dyna explicit FE solver, which generated complete force vs. time history of the impact event. Static 4-point bending and vibration analysis were solved utilizing the LS-Dyna implicit solver. Finally a damaged mesh was obtained from the explicit impact solution and subjected to subsequent static 4-point bending and vibration analysis to numerically determine the residual mechanical behavior after impact. All cases showed good agreement between the numerical, analytical, and experimental results.

The focus of this research is characterizing a new material system composed of carbon and graphite foams, which has potential in a wide variety of applications encompassing aerospace, military, offshore, power production and other commercial industries. The benefits of this new material include low cost, light weight, fire-resistance, good energy absorption, and thermal insulation or conduction as desired. The objective of this research is to explore the bulk material properties and failure modes of the carbon foam through experimental and computational analysis in order to provide a better understanding and assessment of the material for successful design in future applications. Experiments are conducted according to ASTM standards to determine the mechanical properties and failure modes of the carbon foam. Sandwich beams composed of open cell carbon foam cores and carbon-epoxy laminate face sheets are tested in the flexure condition using a four point setup. The primary failure mode is shear cracks developing in the carbon foam core at a critical axial strain value of 2,262 με. In addition to flexure, the carbon foam is loaded under tensile and shear loads to determine the respective material moduli. Computational analysis is undertaken to further investigate the carbon foam's failure modes and material characteristics in the sandwich beam configuration. Initial estimates are found using classical laminated plate theory and a linear finite element model. Poor results were obtained due to violation of assumptions used in both cases. Thus, an additional computational analysis incorporating three dimensional strain-displacement relationships into the finite element analysis is used. Also, a failure behavior pattern for the carbon foam core is included to simulate the unique failure progression of the carbon foam on a microstructure level. Results indicate that displacements, strains and stresses from the flexure experiments are closely predicted by this two parameter progressive damage model. The final computational model consisted of a bond line (interface) study to determine the source of the damage initiation, and it is concluded that damage initiates in the carbon foam, not at the bond line.

A numerical and experimental investigation of the bending behavior of six eight-ply graphite-epoxy circular cylinders is presented. Bending is induced by applying a known end-rotation to each end of the cylinder, analogous to a beam in bending. The cylinders have a nominal radius of 6 inches, a length-to-radius ratio of 2 and 5, and a radius-to-thickness ratio of approximately 160. A [±45/0/90]S quasi-isotropic layup and two orthotropic layups, [±45/02]S and [±45/902]s, are studied. A geometrically nonlinear special-purpose analysis, based on Donnell's nonlinear shell equations, is developed to study the prebuckling responses and gain insight into the effects of non-ideal boundary conditions and initial geometric imperfections. A geometrically nonlinear finite element analysis is utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the buckling and postbuckling responses of both geonletrically perfect and imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. Extensive experimental data are obtained from quasistatic tests of the cylinders using a test fixture specifically designed for the present investigation. A description of the test fixture is included. The experimental data are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles. Buckling end-rotations, moments. and strains are reported, and predicted mode shapes are presented. Observed and predicted moment vs. end-rotation relations, deflection patterns. and strain profiles are illustrated for the postbuckling responses. It is found that a geometrically nonlinear boundary layer behavior characterizes the prebuckling responses. The boundary layer behavior is sensitive to laminate orthotropy, cylinder geometry, initial geometric imperfections, applied end-rotation, and non-ideal boundary conditions. Buckling end-rotations, strains, and moments are influenced by laminate orthotropy and initial geometric imperfections. Measured buckling results correlate well with predictions for the geometrically imperfect specimens. The postbuckling analyses predict equilibrium paths with a number of scallop-shaped branches that correspond to unique deflection patterns. The observed postbuckling deflection patterns and measured strain profiles show striking similarities to the predictions in some cases. Ultimate failure of the cylinders is attributed to an interlaminar shear failure mode along the nodal lines of the postbuckling deflection patterns.
Ph. D.

Thesis (M.S.)--University of Missouri-Columbia, 2007.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 24, 2008) Includes bibliographical references.

Abstract : The present study addressed the feasibility of reinforced-concrete squat walls totally reinforced with GFRP bars to attain reasonable strength and drift requirements as specified in different codes. Nine large-scale squat walls with aspect ratio (height to length ratio) of 1.33—one reinforced with steel bars (as reference specimen) and eight totally reinforced with GFRP bars—were constructed and tested to failure under quasi-static reversed cyclic lateral loading. The key studied parameters were: (1) use of bidiagonal web reinforcement; (2) use of bidiagonal sliding reinforcement; and (3) web reinforcement configuration (horizontal and/or vertical) and ratio. The reported test results clearly revealed that GFRP-reinforced concrete (RC) squat walls have a satisfactory strength and stable cyclic behavior as well as self-centering ability that assisted in avoiding sliding shear that occurred in the companion steel-reinforced wall following steel yielding. The results are promising regarding using GFRP-reinforced squat walls in areas prone to seismic risk where environmental conditions are adverse to steel reinforcement. Bidiagonal web reinforcement was shown to be more effective than conventional web reinforcement in controlling shear-cracks width. Using bidiagonal sliding reinforcement was demonstrated to be not necessary to prevent sliding shear. The horizontal web reinforcement ratio was found to have a significant effect in enhancing the ultimate strength and deformation capacity as long as the failure is dominant by diagonal tension. Existence of both horizontal and vertical web reinforcement was shown to be essential for cracks recovery. Assessment of the ultimate strengths using the available FRP-reinforced elements code and guidelines (CSA S806-12 and ACI 440.1R-15) was conducted and some recommendations were proposed to attain a reasonable estimation of ultimate strengths. Given their importance in estimating the walls’ later displacement, the effective flexural and shear stiffness of the investigated walls were evaluated. It was found that the cracked shear stiffness could be estimated based on the truss model; while the flexural stiffness can be estimated based on the available expressions in FRP-reinforced elements codes and guidelines. Based on a regression analysis, a simple model that directly correlates the flexural and shear stiffness degradation of the test walls to their top lateral drift was also proposed.
Résumé : La présente étude traite de la faisabilité de voiles courts en béton armé totalement renforcés avec des barres de polymères renforcés de fibres de verre (PRFV), obtenant une résistance et un déplacement latéral raisonnable par rapport aux exigences spécifiées dans divers codes. Neuf voiles à grande échelle ont été construits: un renforcé avec des barres d'acier (comme spécimen de référence) et huit renforcés totalement avec des barres de PRFV. Les voiles ont été testés jusqu’à la rupture sous une charge quasi-statique latérale cyclique inversée. Les voiles ont une hauteur de 2000 mm, une largeur de 1500 mm (élancement 2000 mm/1500 mm = 1,33) et une épaisseur de 200 mm. Les paramètres testés sont : 1) armature bi-diagonale dans l’âme; 2) armature bi-diagonale dans l’encastrement du mur à la fondation (zone de glissement); 3) configuration d’armature verticale et horizontale réparties dans l’âme et taux d’armature. Les résultats des essais ont clairement montré que les voiles courts en béton armé de PRFV ont une résistance satisfaisante et un comportement cyclique stable ainsi qu'une capacité d'auto-centrage qui ont aidé à éviter la rupture par glissement à l’encastrement (sliding shear). Ce mode de rupture (sliding shear) s’est produit pour le voile de référence armé d’acier après la plastification de l’armature. Les résultats sont prometteurs concernant l'utilisation de voiles en béton armé de PRFV dans les régions sismiques dans lesquelles les conditions environnementales sont défavorables à l’armature d’acier (corrosion). L’armature bi-diagonale en PRFV dans l’âme s’est avérée plus efficace pour le contrôle des largeurs de fissures de cisaillement comparativement à l’armature répartie dans l’âme. L'utilisation d'un renforcement de cisaillement bi-diagonal a été démontrée comme n'étant pas nécessaire dans les voiles courts en béton armé de PRFV pour prévenir la rupture par glissement à l’encastrement (shear sliding). Par ailleurs, les résultats d’essais ont montré que le taux d’armature horizontale répartie dans l’âme a un effet significatif sur l’augmentation de la résistance et la capacité en déformation des voiles dont la rupture par effort tranchant se fait par des fissures diagonales (tension failure). L'existence d’armature verticale et horizontale répartie dans l’âme du voile en béton armé de PRFV s'est révélée essentielle pour l’ouverture et la fermeture des fissures au cours des chargements cycliques. Les normes calcul CSA S806-12 et ACI 440.1R-15 ont été utilisées pour évaluer la résistance au cisaillement des voiles courts en béton armé de PRFV. Certaines recommandations ont été proposées pour obtenir une estimation raisonnable des forces ultimes. Compte tenu de leur importance dans l'estimation du déplacement latérale des voiles, la rigidité effective en flexion et en cisaillement des voiles étudiés a été évaluée. On a constaté que la raideur de cisaillement du béton fissuré pourrait être estimée en utilisant le modèle de treillis. La rigidité à la flexion peut être, quant à elle, estimée en fonction des expressions disponibles dans les normes et les guides de conception de membrures en béton armé avec des barres en PRFV. Sur la base d'une analyse de régression, un modèle simple qui corrèle directement la dégradation de la rigidité en flexion et en cisaillement des voiles courts en béton armé de PRFV testés avec le déplacement latérale dans la partie supérieure des voiles a également été proposé.

Reinforced concrete (RC) structures constitute a significant portion of the building inventory in earthquake-prone regions of the United States. Accurate analysis tools are necessary to allow the quantitative assessment of the performance and safety offered by RC structures. Currently available analytical approaches are not deemed adequate, because they either rely on overly simplified models or are restricted to monotonic loading. The present study is aimed to establish analytical tools for the accurate simulation of RC structures under earthquake loads. The tools are also applicable to the simulation of reinforced masonry (RM) structures. A new material model is formulated for concrete under multiaxial, cyclic loading conditions. An elastoplastic formulation, with a non-associative flow rule to capture compression-dominated response, is combined with a rotating smeared-crack model to capture the damage associated with tensile cracking. The proposed model resolves issues which characterize existing concrete material laws. Specifically, the newly proposed formulation accurately describes the crack opening/closing behavior and the effect of confinement on the strength and ductility under compressive stress states. The model formulation is validated with analyses both at the material level and at the component level. Parametric analyses on RC columns subjected to quasi-static cyclic loading are presented to demonstrate the need to regularize the softening laws due to the spurious mesh size effect and the importance of accounting for the increased ductility in confined concrete. The impact of the shape of the yield surface on the results is also investigated. Subsequently, a three-dimensional analysis framework, based on the explicit finite element method, is presented for the simulation of RC and RM components under cyclic static and dynamic loading. The triaxial constitutive model for concrete is combined with a material model for reinforcing steel which can account for the material hysteretic response and for rupture due to low-cycle fatigue. The reinforcing steel bars are represented with geometrically nonlinear beam elements to explicitly account for buckling of the reinforcement. The strain penetration effect is also accounted for in the models. The modeling scheme is validated with the results of experimental static and dynamic tests on RC columns and RC/RM walls. The analyses are supplemented with a sensitivity study and with calibration guidelines for the proposed modeling scheme. Given the computational cost and complexity of three-dimensional finite element models in the simulation of shear-dominated structures, the development of a conceptually simpler and computationally more efficient method is also pursued. Specifically, the nonlinear truss analogy is employed to capture the response of shear-dominated RC columns and RM walls subjected to cyclic loading. A step-by-step procedure to establish the truss geometry is described. The uniaxial material laws for the concrete and masonry are calibrated to account for the contribution of aggregate interlock resistance across inclined shear cracks. Validation analyses are presented, for quasi-static and dynamic tests on RC columns and RM walls.
Ph. D.

碩士
國立臺灣大學
土木工程學研究所
102
The reinforced concrete slender walls are frequently used in moderate-to-high rise buildings to resist the lateral loads induced by earthquakes and to limit the building lateral drift by their lateral strength and stiffness. Current seismic design of reinforced concrete structures in the U.S. follows the provisions of Chapter 21 of the American Concrete Institute (ACI 318-11) building code requirements (ACI 318-11, 2011). The technology of seismic retrofitting using of slender walls had already developed in NCREE handbook. In the study, a simplified analytical method to estimate force-displacement response of a structural wall, utilizing the moment-curvature relationship, was proposed and validated by the experimental results from literatures. In addition, tests of shear wall are compared with the analyses of the strength of walls. Based on the obtained base shear – top displacement curve and failure mechanism, this study proposes some recommendations for design and analysis of slender walls.

This paper presents test results and code predictions of four continuously and two simply supported concrete slabs reinforced with basalt fibre reinforced polymer (BFRP) bars. One continuously supported steel reinforced concrete slab was also tested for comparison purposes. All slabs tested were 500 mm in width and 150 mm in depth. The simply supported slabs had a span of 2000 mm, whereas the continuous slabs had two equal spans, each of 2000 mm. Different combinations of under and over BFRP reinforcement at the top and bottom layers of slabs were investigated. The continuously supported BFRP reinforced concrete slabs exhibited larger deflections and wider cracks than the counterpart reinforced with steel. Furthermore, the over reinforced BFRP reinforced concrete slab at the top and bottom layers showed the highest load capacity and the least deflection of all BFRP slabs tested. All continuous BFRP reinforced concrete slabs failed owing to combined shear and flexure at the middle support region. ISIS-M03-07 and CSA S806-06 design guidelines reasonably predicted the deflection of the BFRP slabs tested. However, ACI 440-1R-06 underestimated the BFRP slab deflections and overestimated the moment capacities at mid-span and over support sections.