Shear force and torsion in reinforced concrete beam elements: theoretical analysis based on Brazilian Standard Code ABNT NBR 6118:2007

Reinforced concrete beam elements are submitted to applicable loads along their life cycle that cause shear and torsion. These elements may be subject to only shear, pure torsion or both, torsion and shear combined. The Brazilian Standard Code ABNT NBR 6118:2007 [1] fixes conditions to calculate the transverse reinforcement area in beam reinforced concrete elements, using two design models, based on the strut and tie analogy model, first studied by Mörsch [2]. The strut angle θ (theta) can be considered constant and equal to 45º (Model I), or varying between 30º and 45º (Model II). In the case of transversal ties (stirrups), the variation of angle α (alpha) is between 45º and 90º. When the equilibrium torsion is required, a resistant model based on space truss with hollow section is considered. The space truss admits an inclination angle θ between 30º and 45º, in accordance with beam elements subjected to shear. This paper presents a theoretical study of models I and II for combined shear and torsion, in which ranges the geometry and intensity of action in reinforced concrete beams, aimed to verify the consumption of transverse reinforcement in accordance with the calculation model adopted As the strut angle on model II ranges from 30º to 45º, transverse reinforcement area (Asw) decreases, and total reinforcement area, which includes longitudinal torsion reinforcement (Asℓ), increases. It appears that, when considering model II with strut angle above 40º, under shear only, transverse reinforcement area increases 22% compared to values obtained using model I.

Modelling and analysis of internally BFRP reinforced beams at elevated temperatures

The aim of the work is to conduct a finite element model analysis on a small – size concrete beam and on a full size concrete beam internally reinforced with BFRP exposed at elevated temperatures. Experimental tests performed at Kingston University have been used to compare the results from the numerical analysis for the small – size concrete beam. Once the behavior of the small – size beam at room temperature is investigated and switching to the heating phase reinforced beams are tested at 100°C, 200°C and 300°C in loaded condition. The aim of the finite element analysis is to reflect the three – point bending test adopted into the oven during the exposure of the beam at room temperature and at elevated temperatures. Performance and deformability of reinforced beams are straightly correlated to the material properties and a wide analysis on elastic modulus and coefficient of thermal expansion is given in this work. Develop a good correlation between the numerical model and the experimental test is the main objective of the analysis on the small – size concrete beam, for both modelling the aim is also to estimate which is the deterioration of the material properties due to the heating process and the influence of different parameters on the final result. The focus of the full – size modelling which involved the last part of this work is to evaluate the effect of elevated temperatures, the material deterioration and the deflection trend on a reinforced beam characterized by a different size. A comparison between the results from different modelling has been developed.

Compatibility of ultra high performance concrete as repair material : bond characterization with concrete under different loading scenarios

The rehabilitation of concrete structures, especially concrete bridge decks, is a major challenge for transportation agencies in the United States. Often, the most appropriate strategy to preserve or rehabilitate these structures is to provide some form of a protective coating or barrier. These surface treatments have typically been some form of polymer, asphalt, or low-permeability concrete, but the application of UHPC has shown promise for this application mainly due to its negligible permeability, but also as a result of its excellent mechanical properties, self-consolidating nature, rapid gain strength, and minimal creep and shrinkage characteristics. However, for widespread acceptance, durability and performance of the composite system must be fully understood, specifically the bond between UHPC and NSC often used in bridge decks. It is essential that the bond offers enough strength to resist the stress due to mechanical loading or thermal effects, while also maintaining an extended service-life performance. This report attempts to assess the bond strength between UHPC and NSC under different loading configurations. Different variables, such as roughness degree of the concrete substrates, age of bond, exposure to freeze-thaw cycles and wetting conditions of the concrete substrate, were included in this study. The combination of splitting tensile test with 0, 300, 600 and 900 freeze-thaw cycles was carried out to assess the bond performance under severe ambient conditions. The slant-shear test was utilized with different interface angles to provide a wide understanding of the bond performance under different combinations of compression and shear stresses. The pull-off test is the most accepted method to evaluate the bond strength in the field. This test which studies the direct tensile strength of the bond, the most severe loading condition, was used to provide data that can be correlated with the other tests that only can be used in the laboratory. The experimental program showed that the bond performance between UHPC and NSC is successful, as the strength regardless the different degree of roughness of the concrete substrate, the age of the composite specimens, the exposure to freeze-thaw cycles and the different loading configurations, is greater than that of concrete substrate and largely satisfies with ACI 546.3R-06.

Creep and shrinkage behavior of ultra high-performance concrete under compressive loading with varying curing regimes

This Ultra High Performance Concrete research involves observing early-age creep and shrinkage under a compressive load throughout multiple thermal curing regimes. The goal was to mimic the conditions that would be expected of a precast/prestressing plant in the United States, where UHPC beams would be produced quickly to maximize a manufacturing plant’s output. The practice of steam curing green concrete to accelerate compressive strengths for early release of the prestressing tendons was utilized (140°F [60°C], 95% RH, 14 hrs), in addition to the full thermal treatment (195°F [90°C], 95% RH, 48 hrs) while the specimens were under compressive loading. Past experimental studies on creep and shrinkage characteristics of UHPC have only looked at applying a creep load after the thermal treatment had been administered to the specimens, or on ambient cured specimens. However, this research looked at mimicking current U.S. precast/prestressed plant procedures, and thus characterized the creep and shrinkage characteristics of UHPC as it is thermally treated under a compressive load. Michigan Tech has three moveable creep frames to accommodate two loading criteria per frame of 0.2f’ci and 0.6f’ci. Specimens were loaded in the creep frames and moved into a custom built curing chamber at different times, mimicking a precast plant producing several beams throughout the week and applying a thermal cure to all of the beams over the weekend. This thesis presents the effects of creep strain due to the varying curing regimes. An ambient cure regime was used as a baseline for the comparison against the varying thermal curing regimes. In all cases of thermally cured specimens, the compressive creep and shrinkage strains are accelerated to a maximum strain value, and remain consistent after the administration of the thermal cure. An average creep coefficient for specimens subjected to a thermal cure was found to be 1.12 and 0.78 for the high and low load levels, respectively. Precast/pressed plants can expect that simultaneously thermally curing UHPC elements that are produced throughout the week does not impact the post-cure creep coefficient.

Photodegradation and photostabilization of weathered wood flour filled polyethylene composites

Wood plastic composites (WPCs) have gained popularity as building materials because of their usefulness in replacing solid wood in a variety of applications. These composites are promoted as being low-maintenance, high-durability products. However, it has been shown that WPCs exposed to weathering may experience a color change and/or loss in mechanical properties. An important requirement for building materials used in outdoor applications is the retention of their aesthetic qualities and mechanical properties during service life. Therefore, it is critical to understand the photodegradation mechanisms of WPCs exposed to UV radiation and to develop approaches to stabilize these composites (both unstabilized and stabilized) as well as the effect of weathering on the color fade and the retention of mechanical properties were characterized. Since different methods of manufacturing WPCs lead to different surface characteristics, which can influence weathering, the effect of manufacturing method on the photodegradation of WPCs was investigated first. Wood flour (WF) filled high-density polyethylene (HDPE) composite samples were either injection molded, extruded, or extruded and then planed. Fourier transform infrared (FTIR) spectroscopy was used to monitor the surface chemistry of the manufactured composites. The spectra showed that the surface of planed samples had more wood component than extruded and injection molded samples, respectively. After weathering, the samples were analyzed for color fade, and loss of flexural properties. The final lightness of the composites was not dependent upon the manufacturing method. However the mechanical property loss was dependent upon manufacturing method. The samples with more wood component at the surface (planed samples) experienced a larger percentage of total loss in flexural properties after weathering due to a greater effect of moisture on the samples. The change in surface chemistry of HDPE and WF/HDPE composites after weathering was studied using spectroscopic techniques. X-ray photoelectron spectroscopy (XPS) was used to characterize the occurrence of surface oxidation whereas FTIR spectroscopy was used to monitor the development of degradation products, such as carbonyl groups and vinyl groups, and to determine changes in HDPE crystallinity. Surface oxidation occurred immediately after exposure for both the neat HDPE and WF/HDPE composites. After weathering, the surface of the WF/HDPE composites was oxidized to a greater extent than the neat HDPE after weathering. This suggests that photodegradation is exacerbated by the addition of the carbonyl functional groups of the wood fibers within the HDPE atrix during composite manufacturing. While neat HDPE may undergo cross-linking in the initial stages of accelerated weathering, the WF may physically hinder the ability of the HDPE to cross-link resulting in the potential for HDPE chain scission to dominate in the initial weathering stages of the WF/HDPE composites. To determine which photostabilizers are most effective for WF/HDPE composites, factorial experimental designes were used to determine the effects of adding two hindered amine light stabilizers, an ultraviolet absorber, and a pigment on the color made and mechanical properties of both unweathered and UV weathered samples. Both the pigment and ultraviolet absorber were more effective photostabilizers for WF/HDPE composites than hinder amine light stabilizers. The ineffectiveness of hindered amine light stabilizers in protecting WPCs against UV radiation was attribuated to the acid/base reactions occurring between the WF and hindered amine light stabilizer. The efficiency of an ultraviolet absorber and/or pigment was also examined by incorporating different concentration of an ultraviolet absorber and/or pigment into WF/HDPE composites. Color change and flexural properties were determined after accelerated UV weathering. The lightness of the composite after weathering was influenced by the concentration of both the ultraviolet absorber by masking the bleaching wood component as well as blocking UV light. Flexural MOE loss was influenced by an increase in ultraviolet absorber concentration, but increasing pigment concentration from 1 to 2% had little influence on MOE loss. However, increasing both ultraviolet absorber and pigment concentration resulted in improved strength properties over the unstabilized composites after 3000 h of weather. Finally, the change in surface chemistry due to weathering of WF/HDPE composites that were either unstabilized or stabilized with an ultraviolet absorber and/or pigment was analyzed using FTIR spectroscopy. The samples were tested for loss in modulus of elasticity, carbonyl and vinyl group formation at the surface, and change in HDPE crystallinity. It was concluded that structural changes in the samples; carbonyl group formation, terminal vinyl group formation, and crystallinity changes cannot reliably be used to predict changes in modulus of elasticity using a simple linear relationship. The effect of cross-linking, chain scission, and crystallinity changes due to ultraviolet exposure as well as the interfacial degradation due to moisture exposure are inter-related factors when weathering HDPE and WF/HDPE composites.

Discrete element methods for asphalt concrete : development and application of user-defined microstructural models and a viscoelastic micromechanical model

As an important Civil Engineering material, asphalt concrete (AC) is commonly used to build road surfaces, airports, and parking lots. With traditional laboratory tests and theoretical equations, it is a challenge to fully understand such a random composite material. Based on the discrete element method (DEM), this research seeks to develop and implement computer models as research approaches for improving understandings of AC microstructure-based mechanics. In this research, three categories of approaches were developed or employed to simulate microstructures of AC materials, namely the randomly-generated models, the idealized models, and image-based models. The image-based models were recommended for accurately predicting AC performance, while the other models were recommended as research tools to obtain deep insight into the AC microstructure-based mechanics. A viscoelastic micromechanical model was developed to capture viscoelastic interactions within the AC microstructure. Four types of constitutive models were built to address the four categories of interactions within an AC specimen. Each of the constitutive models consists of three parts which represent three different interaction behaviors: a stiffness model (force-displace relation), a bonding model (shear and tensile strengths), and a slip model (frictional property). Three techniques were developed to reduce the computational time for AC viscoelastic simulations. It was found that the computational time was significantly reduced to days or hours from years or months for typical three-dimensional models. Dynamic modulus and creep stiffness tests were simulated and methodologies were developed to determine the viscoelastic parameters. It was found that the DE models could successfully predict dynamic modulus, phase angles, and creep stiffness in a wide range of frequencies, temperatures, and time spans. Mineral aggregate morphology characteristics (sphericity, orientation, and angularity) were studied to investigate their impacts on AC creep stiffness. It was found that aggregate characteristics significantly impact creep stiffness. Pavement responses and pavement-vehicle interactions were investigated by simulating pavement sections under a rolling wheel. It was found that wheel acceleration, steadily moving, and deceleration significantly impact contact forces. Additionally, summary and recommendations were provided in the last chapter and part of computer programming codes wree provided in the appendixes.

Dynamic properties of wood using the Split-Hopkinson Pressure Bar

Strain rate significantly affects the strength of a material. The Split-Hopkinson Pressure Bar (SHPB) was initially used to study the effects of high strain rate (~103 1/s) testing of metals. Later modifications to the original technique allowed for the study of brittle materials such as ceramics, concrete, and rock. While material properties of wood for static and creep strain rates are readily available, data on the dynamic properties of wood are sparse. Previous work using the SHPB technique with wood has been limited in scope to variability of only a few conditions and tests of the applicability of the SHPB theory on wood have not been performed. Tests were conducted using a large diameter (3.0 inch (75 mm)) SHPB. The strain rate and total strain applied to a specimen are dependent on the striker bar length and velocity at impact. Pulse shapers are used to further modify the strain rate and change the shape of the strain pulse. A series of tests were used to determine test conditions necessary to produce a strain rate, total strain, and pulse shape appropriate for testing wood specimens. Hard maple, consisting of sugar maple (Acer saccharum) and black maple (Acer nigrum), and eastern white pine (Pinus strobus) specimens were used to represent a dense hardwood and a low-density soft wood. Specimens were machined to diameters of 2.5 and 3.0 inches and an assortment of lengths were tested to determine the appropriate specimen dimensions. Longitudinal specimens of 1.5 inch length and radial and tangential specimens of 0.5 inch length were found to be most applicable to SHPB testing. Stress/strain curves were generated from the SHPB data and validated with 6061-T6 aluminum and wood specimens. Stress was indirectly corroborated with gaged aluminum specimens. Specimen strain was assessed with strain gages, digital image analysis, and measurement of residual strain to confirm the strain calculated from SHPB data. The SHPB was found to be a useful tool in accurately assessing the material properties of wood under high strain rates (70 to 340 1/s) and short load durations (70 to 150 μs to compressive failure).

A study of acoustic emission technique for concrete damage detection

The Acoustic emission (AE) technique, as one of non-intrusive and nondestructive evaluation techniques, acquires and analyzes the signals emitting from deformation or fracture of materials/structures under service loading. The AE technique has been successfully applied in damage detection in various materials such as metal, alloy, concrete, polymers and other composite materials. In this study, the AE technique was used for detecting crack behavior within concrete specimens under mechanical and environmental frost loadings. The instrumentations of the AE system used in this study include a low-frequency AE sensor, a computer-based data acquisition device and a preamplifier linking the AE sensor and the data acquisition device. The AE system purchased from Mistras Group was used in this study. The AE technique was applied to detect damage with the following laboratory tests: the pencil lead test, the mechanical three-point single-edge notched beam bending (SEB) test, and the freeze-thaw damage test. Firstly, the pencil lead test was conducted to verify the attenuation phenomenon of AE signals through concrete materials. The value of attenuation was also quantified. Also, the obtained signals indicated that this AE system was properly setup to detect damage in concrete. Secondly, the SEB test with lab-prepared concrete beam was conducted by employing Mechanical Testing System (MTS) and AE system. The cumulative AE events and the measured loading curves, which both used the crack-tip open displacement (CTOD) as the horizontal coordinate, were plotted. It was found that the detected AE events were qualitatively correlated with the global force-displacement behavior of the specimen. The Weibull distribution was vii proposed to quantitatively describe the rupture probability density function. The linear regression analysis was conducted to calibrate the Weibull distribution parameters with detected AE signals and to predict the rupture probability as a function of CTOD for the specimen. Finally, the controlled concrete freeze-thaw cyclic tests were designed and the AE technique was planned to investigate the internal frost damage process of concrete specimens.

Geological Report of Conrow Wood Creek Area 8 Miles N.E. of Whitehall, Montana

Plane table and pacing methods were used in the mapping of the individual areas, but an automobile traverse was used to tie the independent areas into a composite group that would be useful for the entire zone. All land marks, section corners, roads, fence lines, drainage, and geologic features were plotted in the field and later transferred to a master map.

Pollen and non-pollen palynomorph records of the Holocene part of the composite sediment core TMD from lake Tso Moriri (NW India) and of modern surface samples from the Tso Moriri region

The high-altitude lake Tso Moriri (32°55'46'' N, 78°19'24'' E; 4522 m a.s.l.) is situated at the margin of the ISM and westerly influences in the Trans-Himalayan region of Ladakh. Human settlements are rare and domestic and wild animals are concentrating at the alpine meadows. A set of modern surface samples and fossil pollen from deep-water TMD core was evaluated with a focus on indicator types revealing human impact, grazing activities and lake system development during the last ca. 12 cal ka BP. Furthermore, the non-pollen palynomorph (NPP) record, comprising remains of limnic algae and invertebrates as well as fungal spores and charred plant tissue fragments, were examined in order to attest palaeolimnic phases and human impact, respectively. Changes in the early and middle Holocene limnic environment are mainly influenced by regional climatic conditions and glacier-fed meltwater flow in the catchment area. The NPP record indicates low lake productivity with high influx of freshwater between ca. 11.5 and 4.5 cal ka BP which is in agreement with the regional monsoon dynamics and published climate reconstructions. Geomorphologic observations suggest that during this period of enhanced precipitation the lake had a regular outflow and contributed large amounts of water to the Sutlej River, the lower reaches of which were integral part of the Indus Civilization area. The inferred minimum fresh water input and maximum lake productivity between ca. 4.5-1.8 cal ka BP coincides with the reconstruction of greatest aridity and glaciation in the Korzong valley resulting in significantly reduced or even ceased outflow. We suggest that lowered lake levels and river discharge on a larger regional scale may have caused irrigation problems and harvest losses in the Indus valley and lowlands occupied by sedentary agricultural communities. This scenario, in turn, supports the theory that, Mature Harappan urbanism (ca. 4.5-3.9 cal ka BP) emerged in order to facilitate storage, protection, administration, and redistribution of crop yields and secondly, the eventual collapse of the Harappan Culture (ca. 3.5-3 cal ka BP) was promoted by prolonged aridity. There is no clear evidence for human impact around Tso Moriri prior to ca. 3.7 cal ka BP, with a more distinct record since ca. 2.7 cal ka BP. This suggests that the sedimentary record from Tso Moriri primarily archives the regional climate history.

Análisis de envejecimiento en paneles sándwich de madera/ Ageing tests study on wood-based sandwich panels

Los paneles sándwich de madera son un producto de creciente aplicación en la edificación de nuestro país. Este ascendente uso del material debe estar acompañado de las garantías necesarias avaladas por un estudio previo de sus prestaciones. Como es preceptivo y entre otros, se evalúa su durabilidad frente a las condiciones climatológicas, clave en los productos derivados de la madera, acorde a la normativa actual definida con tal fin, la Guía ETAG 016. Sin embargo, debido a la clase de uso del material, se ha detectado que dicha normativa tal y como está concebida no es capaz de valorar su envejecimiento adecuadamente. En este trabajo se proponen ensayos alternativos al establecido tras exhaustivos aná- lisis que recrean las condiciones reales de uso y más acordes a los productos de madera. Se concluye que la incorporación de una lámina impermeable, pero permeable al vapor de agua hacia el exterior, como las utilizadas en el montaje, aportan el mejor procedimiento de ensayo. Composite lightweight wood panels are being increasingly used in construction in Spain. Their growing use should be accompanied by necessary guarantees based on studies of their properties. As it is prescriptive and in addition to others tests, in the present work is examinated the durability of these panels when exposed to the climatic conditions, a characteristic of great importance for wood products, according to Guide ETAG 016, the current standard defining the ageing tests to be used. However, due to the use class of this material, there are indications that the testing outlined in this Guide is inappropriate for assessing the ageing of wood-based sandwich panels. Alternative tests are here proposed that recreate rather better the real conditions under which these products are used. Covering the samples in a waterproof sheeting permeable to the outward movement of water vapour, which is in fact used in the installation, provided the best procedure for testing these panels.

Análisis de elementos de madera reforzados con materiales compuestos

Gran parte del patrimonio construido cuenta con edificios cuya estructura está compuesta por elementos de madera. El volumen económico que supone el mantenimiento y renovación de dicho patrimonio es considerable, por ello, es de especial interés el estudio de las diferentes técnicas de refuerzo aplicables a este tipo de estructuras. Las estructuras de madera han sido tradicionalmente reforzadas con piezas del mismo material, aumentando la sección de los elementos dañados, o con acero. La aparición de los materiales compuestos de polímeros reforzados con fibras, y su progresiva aplicación en obras de construcción, hizo que a principios de la década de los noventa se comenzara a aplicar este material en refuerzos de estructuras de madera (Puente de Sins, 1992). La madera es un material natural con una excelente relación entre sus características mecánicas y su peso. Con el uso de materiales compuestos como refuerzo ésta característica se mantiene. En cuanto a su modelo constitutivo, se admite un comportamiento elástico lineal a tracción paralela a la fibra hasta la rotura, mientras que a compresión, se considera un comportamiento lineal elástico inicial, seguido de un tramo plástico. En vigas de madera aserrada sometidas a flexión predomina el modo de fallo por tracción localizándose la fractura frecuentemente en el canto inferior. Los FRP tienen un comportamiento elástico lineal a tracción hasta la rotura y cuentan con excelentes propiedades mecánicas en relación a su peso y volumen. Si se refuerza la viga por el canto inferior se aumentará su capacidad de absorber tracciones y por tanto, es previsible que se produzca un incremento en la capacidad de carga, así como un aumento de ductilidad. En este trabajo se analizan los beneficios que aportan distintos sistemas de refuerzos de materiales compuestos. El objetivo es contribuir al conocimiento de esta técnica para la recuperación o aumento de las propiedades resistentes de elementos de madera sometidos a flexión. Se ha llevado a cabo un estudio basado en datos obtenidos experimentalmente mediante el ensayo a flexión de vigas de madera de pino silvestre reforzadas con materiales compuestos. Las fibras que componen los tejidos utilizados para la ejecución de los refuerzos son de basalto y de carbono. En el caso de los compuestos de fibra de basalto se aplican en distintos gramajes, y los de carbono en tejido unidireccional y bidireccional. Se analiza el comportamiento de las vigas según las variables de refuerzo aplicadas y se comparan con los resultados de vigas ensayadas sin reforzar. Además se comprueba el ajuste del modelo de cálculo no lineal aplicado para predecir la carga de rotura de cada viga reforzada. Con este trabajo queda demostrado el buen funcionamiento del FRP de fibra de basalto aplicado en el refuerzo de vigas de madera y de los tejidos de carbono bidireccionales con respecto a los unidireccionales. ABSTRACT Many of the buildings of the built heritage include a structure composed by timber elements. The economic volume involved in the maintenance and renewal of this built heritage is considerable, therefore, the study of the different reinforcement techniques applicable to this type of structure is of special interest. The wooden structures have traditionally been reinforced either with steel or with pieces of the same material, increasing the section of the damaged parts. The emergence of polymer composites reinforced with fibers, and their progressive use in construction, started to be applied as reinforcement in timber structures at the beginning of the nineties decade in the 20th century (Sins Bridge, 1992). Wood is a natural material with an excellent ratio between its mechanic characteristics and its weight. This feature is maintained with the use of composites as reinforcement. In terms of its constitutive model, linear elastic behavior parallel to the fiber up to fracture is admitted when subjected to tensile stress, while under compression, an initial linear elastic behavior, followed by a section plasticizing, is considered. In sawn timber beams subjected to bending, the predominant failure is mainly due to tensile stress; and frequently the fracture is located at the beam lower face. The FRP have a linear elastic behavior until fracture occurs, and have excellent mechanical properties in relation to their weight and volume. If the beam is reinforced by its lower face, its capacity to absorb tensile stresses will increase, and therefore, an increase in its carrying capacity is likely to be produced, as well as an increase in ductility. This work analyzes the benefits different reinforcement systems of composite materials provide, with the aim of contributing to the knowledge of this technique for recovering or increasing the strength properties of timber elements subjected to bending loads. It is a study based on data obtained experimentally using bending tests of pine timber beams reinforced with composite materials. Fibers used for the execution of the reinforcement are basalt and carbon. Basalt fiber composites are applied in different grammages, whereas with carbon composites, unidirectional and bidirectional fabrics are used. The behavior of the beams was analyzed regarding the reinforcement variables applied, and the results are compared with those of the tested beams without reinforcement. Furthermore it has been proved adjunting the nonlinear calculation model applied to predict the failure load of each reinforced beam. This work proves the good behavior of fiber reinforce plastic (FRP) with basalt fiber when applied to timber beams, and that of bidirectional carbon fabrics as opposed to the unidirectional ones.

Design equations for reinforced concrete members strengthened in shear with external FRP reinforcement formulated in an evolutionary multi-objective framework

Methods for predicting the shear capacity of FRP shear strengthened RC beams assume the traditional approach of superimposing the contribution of the FRP reinforcing to the contributions from the reinforcing steel and the concrete. These methods become the basis for most guides for the design of externally bonded FRP systems for strengthening concrete structures. The variations among them come from the way they account for the effect of basic shear design parameters on shear capacity. This paper presents a simple method for defining improved equations to calculate the shear capacity of reinforced concrete beams externally shear strengthened with FRP. For the first time, the equations are obtained in a multiobjective optimization framework solved by using genetic algorithms, resulting from considering simultaneously the experimental results of beams with and without FRP external reinforcement. The performance of the new proposed equations is compared to the predictions with some of the current shear design guidelines for strengthening concrete structures using FRPs. The proposed procedure is also reformulated as a constrained optimization problem to provide more conservative shear predictions.

Moment transfer and influence of transverse beams in interior waffle flat plate-column connections under lateral loading

This paper addresses two aspects of the behavior of interior reinforced concrete waffle flat plate?column connections under lateral loads: the share of the unbalanced moment between flexure and excentric shear, and the effect of the transverse beams. A non-linear finite element model (benchmark model) was developed and calibrated with the results of quasi-static cyclic tests conducted on a 3/5 scale specimen. First, from this numerical model, the portion cv of the unbalanced moment transferred by the excentricity of shear about the centroid of the critical sections defined by Eurocode 2 (EC-2) and by ACI 318-11 was calculated and compared with the share-out prescribed by these codes. It is found that while the critical section of EC-2 is consistent with the cv provided by this code, in the case of ACI 318-11, the value assigned to cv is far below (about 50% smaller) the actual one obtained with the numerical simulations. Second, from the benchmark model, seven additional models were developed by varying the depth D of the transverse beam over the thickness h of the plate. It was found that the ductility of the connection and the effective width of the plate can respectively be increased up to 50% and 10% by raising D/h to 2 and 1.5.