Longitudinal Tensile Reinforcement Research Articles

Out-of-plane shear behavior of BFRP-reinforced geopolymer concrete one-way slabs: Experimental and numerical investigations

Sustainability and durability in construction are vital considerations that involve using environmentally friendly materials and implementing efficient design and construction techniques to minimize the environmental impact. This research study investigated the structural behavior of one-way solid slabs incorporating basalt fiber-reinforced polymer (BFRP) reinforcement and geopolymer concrete to develop an environmentally sustainable and durable structural member. Six full-scale BFRP-reinforced geopolymer concrete one-way slab specimens were prepared and subjected to four-point loading tests to assess their out-of-plane shear performances. The considered experimental parameters were compressive strength of concrete (i.e., 30, 40 and 50 MPa) and longitudinal tensile reinforcement ratios (i.e., 1.20% and 2.18%). The structural performance of the slabs was carefully investigated in terms of crack patterns, failure modes, load-deflection relationships and load-strain relationships. The obtained shear resistances from tests were compared with predicted results from the Codes of Practice and design guidelines. A two-dimensional (2D) finite element (FE) analysis was conducted, considering the bond-slip relationship between BFRP rebar and geopolymer concrete. It was found that all tested specimens were governed by shear failure and had similar shear resistance for the chosen values of considered parameters. The JSCE shear design method provided the closest prediction of shear resistance of BFRP-reinforced geopolymer concrete one-way slab. The developed FE models predicted the out-of-plane shear performance with reasonable accuracy and revealed that the slip distribution of the BFRP rebar presents a sawtooth shape owing to concrete cracking.

Experimental investigation of the effect of longitudinal tensile reinforcement ratio on ductility behaviour in GPC beams

This research first determined the strength of the cylindrical geopolymer concrete materi- als under compressive stresses. Secondly, conventional and geopolymer-reinforced concrete beams were manufactured in different reinforcement ratios, and their mechanical properties were compared under bending. The main aim of this study is to experimentally compare the effect of reinforcement ratio on the ductility behavior of an alkali-activated geopolymer con- crete (GPC) beam with that of an ordinary Portland cement (OPC) beam. First, balanced reinforcement calculations were made considering the mechanical properties obtained from the material tests. The load-displacement, moment-curvature, and crack development results obtained from beam tests are interpreted with this information. OPC and GPC beams exhibit- ed similar strength and crack development behavior. However, the behavior of GPC and OPC concretes differs regarding the ductility index. Therefore, to achieve similar ductility in the conduct of GPC and OPC beams, the balanced reinforcement ratio and section dimensions of GPC beams should be chosen to be larger than OPC.

Study on the Mechanical Performance of RC Beams under Load Reinforced by a Thin Layer of Reactive Powder Concrete on Four Sides

To repair reinforced concrete beams efficiently in a limited building space, the four-sided application of a reinforcing thin layer of reactive powder concrete (“RPCTL”) was proposed to improve the bending capacity of the members. Static flexural tests of one comparison beam and five reinforced beams were completed on a four-point centralized loading device. Changes in deflection, cracks, stresses, and damage characteristics of the specimens were measured under various levels of loading. The test results showed that the damage patterns of the reinforced specimens were dominated by the yielding of longitudinal tensile reinforcement at the bottoms of the beams and the crushing of the cementitious material in the top compression zones of the beams. The cracking load greatly increased by 1.42 to 7.12 times, and the ultimate bearing capacity increased by 0.29 to 1.41 times. The distribution characteristics and dynamic changes in the displacement, stress, and damage of the specimens were dynamically simulated by finite element software. The effects of reinforcement and initial load-holding level on the reinforcement effect were investigated. A bending capacity calculation formula for RPCTL reinforcement technology is proposed that aligns with the test results and can provide a reference for the design of RPCTL reinforcement.

Bearing capacity of UHPC‐NC connection structure in negative moment zone of PC beam bridges

AbstractA new type of UHPC‐NC (normal concrete) structure in the negative moment zone was proposed to improve the bearing capacity of the connection structure in the negative moment zone of prefabricated prestressed concrete (PC) beam bridges. First, the distribution characteristics of the crack, cracking load, ultimate moment, and ductility coefficient of the new structure were obtained by the 1:4 scale model tests. The feasibility of the connection structure is verified. Then, the value ranges of critical structural parameters affecting the bearing capacity of the connection structure based on the plane section assumption analysis, including the reasonable thickness of the UHPC layer, the reinforcement ratio of the longitudinal tensile reinforcement, and the diameter of the reinforcement, are obtained. At the same time, based on the verification of the finite element model, the influence of crucial research parameters on the bending capacity of the connection structure is obtained by using the finite element method. Finally, a theoretical method for the bending moment capacity of the connection structure of the UHPC‐NC structure is proposed, considering the high ductility characteristics of UHPC materials. The average relative error between the calculation results and the finite element method is within 7.2%, which verifies the reliability of the calculation method in this paper and provides a reference for its design and engineering application.

РАСЧЕТ ЖЕЛЕЗОБЕТОННЫХ ЭЛЕМЕНТОВ ПО ПРОЧНОСТИ НАКЛОННЫХ СЕЧЕНИЙ ПРИ ДВУХОСЕВОМ ДЕЙСТВИИ ПОПЕРЕЧНЫХ СИЛ

In the current standards for the design of reinforced concrete structures no methods for calculating inclined sections with a biaxial action of shear forces are presented. At the same time, a significant part of reinforced concrete structures is subjected to the action of shear forces in two planes. The relevance of the article is determined by the lack of standard methods for calculating of reinforced concrete elements inclined sections for the biaxial action of shear, which forces designers to use simplifications in calculations. The article reviews the Russian and foreign literature on the theory of design of reinforced concrete elements for the action of transverse forces and analyzes the design methods proposed in the current Russian and foreign design standards, as well as in the standards of past years. In the analysis of methods for calculating reinforced concrete elements for the action of transverse forces, consideration is given in various methods for calculating the factors that affect the strength of inclined sections on the action of transverse forces in normal and biaxial bending in two planes, such as the shear span, the angle of inclination of the force plane, the amount of longitudinal tensile reinforcement, the influence of longitudinal forces, size-effect.
 The main directions for further research of the issue are identified and recommendations are given that summarize domestic and foreign experience.

Application of a Nonlinear Deformation Model to the Analysis of Complete Moment-Curvature Diagrams of Reinforced Concrete Elements with Reinforcement A500

This article suggests a calculation procedure for the parameters of complete moment-curvature deformation diagrams with a down leg that can be used for the calculations of the multistorey monolithic building frameworks taking into account the specifics of reinforced concrete. To construct complete deformation diagrams for bending elements, a non-linear deformation model is used that is based on using the physical diagrams of the concrete and reinforcements to calculate the inner moments of cross-sections at all loading stages via balance and strain compatibility equations. Using this model, the authors researched complete moment-curvature deformation diagrams for the elements with different percentages of longitudinal tensile reinforcement that changes the bending properties of the structure. We used grade А500 steel as the reinforcement. The parameters of the tensile reinforcement diagram were determined in the tension testing of samples with constant deformation rates. The performed computer tests to calculate the moment-curvature diagram parameters for reinforced concrete beams reinforced with grade А500 efficiency rods and conventional grade A400 reinforcement rods with different longitudinal reinforcement congestion rates helped the authors assess the bending properties of the elements under conditions approaching their destruction and determine their efficient use in the calculations of building frameworks taking into account the redistribution of forces.

Behavior of hollow self-compacted concrete beams reinforced with aluminum sections

This paper presents a study on improving the flexural performance of self-compacting hollow concrete beams with embedded aluminum sections, both experimentally and numerically. The experimental program involved testing three specimens to illustrate the impact of the bare and aluminum-reinforced voids on the mechanical properties of the hollow beams relative to the solid reference beam. A three-dimensional (3D) non-linear finite element model (FEM) was initially developed using ABAQUS software and validated against experimental results. The validated model examined the effects of void area (16–49% of the beam cross-section), void configuration (square or circular), longitudinal tensile reinforcement ratio (0.41–1.19%), and shear reinforcement ratio (0–0.56%) on the failure patterns and load–displacement relationships of hollow reinforced concrete (RC) beams with or without reinforced internal aluminum sections. Results showed that the embedded aluminum reinforcement promoted a more uniform distribution of flexural cracks along the effective length of the hollow RC beams and delayed the formation of shear cracks compared to the bare specimens. Furthermore, the embedded aluminum reinforcement effectively restored the ultimate capacity of the hollow beams with a void area ranging from 16 to 36% of the beam cross-section. Despite having the same area, the ultimate load-carrying capacity of both bare and reinforced beams featuring circular voids was higher than those with square voids.

Calculation of the formation of normal cracks in a reinforced concrete element based on the deformation theory of plasticity of concrete by G.A. Geniev

The authors present a refined method of determining the moment of cracking in reinforced concrete bar constructions using the diagram of deformation of concrete built on the basis of the deformation theory of plasticity by G.A. Geniev in which the stress and strain invariants of concrete are linked by nonlinear dependences. In the resulting defining equations, the hypothesis of flat sections, as well as the premise of reaching the limit values of concrete deformations on the stretched fibers of the cross-section are used. Stresses in concrete are determined through deformation values in accordance with the nonlinear deformation diagram of concrete. On the basis of the assumptions accepted, analytical dependences for determining the moment of cracking in the sections of bending elements with single and double reinforcement have been acquired. The formulas obtained were used in the analysis of various factors influence on crack resistance of bendable reinforced concrete elements. It was found out that the moment of crack formation practically does not change when percentage of reinforcement of longitudinal tensile or compressed reinforcement changes. The most effective method of crack resistance improvement is the increase of concrete strength. The proposed methodology is verified by comparison with experimental results on reinforced concrete prototypes. It is concluded that the use of the diagram of nonlinear deformation of concrete on the basis of the theory of plasticity by G.A. Geniev allows to estimate more strictly the crack resistance of reinforced concrete rod elements.

Effect of the outer UHDC layer on shear and flexural behavior of RC beams produced with low binder concrete

Composite beams with a cement distribution along the cross-section more efficient can be used to increase their durability and simultaneously decrease the ecological footprint related with cement production. The higher dosages are used only on the cover layer, to provide a higher protection of the steel reinforcement, and the core of the beams is produced with a low cement concrete, using in this case 125 kg of cement per m3. In addition, the core is not subjected to such higher normal stresses as on both bottom and top of the cross section, so the mechanical performance of this concrete is not so challenging and, consequently, the cement dosage can be thus reduced.This experimental study aims to analyze how the strength capacity and stiffness of beams are affected using the ‘superskin’ concept, particularly the influence of how the external layer made with an ultra-high durability concrete (UHDC) is applied, being the core produced with a low binder concrete (LBC).Nine different beams were tested, until bending or shear-controlled failure occur, varying the longitudinal tensile reinforcement ratio and the way how the UHDC layer is applied: i) one single layer with a ‘U’ shape around cross-section and, ii) three separated thin plates, cast against the core concrete. The followings parameters were analyzed: load–displacement relation, flexural strength, shear strength, ductility, crack pattern and failure mode. The results show that this type of beams present a better structural behavior relatively to the reference beams, beyond the two benefits already identified, the durability and eco-efficiency increase. In certain beams the flexural strength increased around 70% and the shear strength almost 90%. The results also reveal the advantages of using a monolithic UHDC layer, namely, in terms of cracking.

Порівняльний аналіз несучої здатності дослідних пошкоджених залізобетонних елементів, підсилених металевими обоймами

The paper presents research results and a comparative analysis of the load-bearing deformability and crack resistance of basalt concrete beams brought to the limit state (ULS) in previous tests. The beams were reinforced with prestressed metal clips under high-level static and low-cycle alternating loads. The work performed comparative calculations of reinforced building structures using proprietary methods and existing regulatory methods. A comparison of the experimental and calculated values of the bearing capacity of damaged experimental beam samples showed their unsatisfactory convergence because the well-known regulatory and proprietary methods provide for the calculation of the bearing capacity of damaged reinforced concrete structures along a dangerous inclined crack under the predominant action of transverse force, i.e. the top of a dangerous inclined crack and clamps and vertical elements of external reinforcement. However, experimental and theoretical studies have shown that the destruction of prototype beams with large and medium shear spans under a variable low-cycle load occurs along dangerous inclined through cracks, from the overwhelming action of bending moments, in the longitudinal reinforcement elements of the frame, in the longitudinal tensile reinforcement, as well as transverse beam beams and yield stress cages. That is, the real physical picture of the operation of the system “damaged reinforced concrete beam – prestressed metal reinforcement cage” under alternating transverse load at high levels differs significantly from the physical model of previously existing regulatory and proprietary methods. All existing regulatory and proprietary methods provide for the calculation of the bearing capacity of damaged reinforced concrete structures along a dangerous inclined crack under the predominant action of transverse force, that is, the components of the bearing capacity of inclined sections on concrete above the top of a dangerous inclined crack and clamps and external elements are taken into account. Experimental and theoretical studies have shown that the destruction of prototype beams with large and medium shear spans, under alternating low-cycle loads, occurs along dangerous inclined through cracks from the overwhelming action of bending moments in the longitudinal tensile reinforcement, as well as in the transverse rods of the beam and the cage yield strength.

Effect of reinforcement on the durability of bent reinforced concrete structures under conditions of alternating freezing and thawing

The article studies the influence of the level and type of reinforcement of bending elements of reinforced concrete structures on their bearing capacity under the influence of alternating freezing and thawing. Strength and deformation characteristics for B30 concrete class were taken according to Construction Rules SP 63.13330.2018, and after exposure to alternating freezing and thawing according to Construction Rules SP 52.105.2009. The study of the stress-strain state and the assessment of the bearing capacity were carried out according to a specially developed program, in which the diagrammatic method was implemented. It is shown that the durability of bent reinforced concrete structures depends on the percentage and type of reinforcement. When reinforcing with longitudinal tensile reinforcement equal to 1%, the decrease in the bearing capacity of a reinforced concrete beam after exposure to alternating freezing and thawing will make up 5.5%, and in case of 2.5% reinforcement it will equal to 20.9%. In addition, the nature of fracture will change and the stress in the tensile reinforcement will not reach the design resistance. If it is impossible to limit the percentage of reinforcement of longitudinal tensile reinforcement, it is recommended to use double reinforcement. Installation of working reinforcement in a compressed zone in a volume of 50% of the stretched one with a reinforcement percentage of 2% will reduce the decrease in bearing capacity to 2.2% after exposure to freezing and thawing cycles and not change the nature of destruction.

Flexural performance of steel-reinforced geopolymer concrete one-way slabs: Experimental and numerical investigations

This paper investigated the out-of-plane flexural performances of ambient-cured steel-reinforced slag and fly ash-based geopolymer concrete one-way slabs, in which the activator was the blend of NaOH and sodium silicate solutions (SiO2/Na2O = 3.1–3.3). Twelve specimens were prepared and tested, which included six OPC concrete specimens. The test parameters were concrete type (i.e., geopolymer and ordinary Portland cement (OPC) concrete), concrete compressive strength (i.e., 30 MPa, 40 MPa, and 50 MPa) and longitudinal tensile reinforcement ratio (i.e., 0.82 % and 1.20 %). The failure modes, crack patterns, load–deflection relationships and load–strain relationships of all specimens were carefully studied and reported. Further, a two dimensional (2D) finite element (FE) analysis was conducted to validate the test results. The results of the study indicated that: (1) the geopolymer concrete specimens presented lesser crack width and crack spacing owing to the improved bond between rebar and geopolymer concrete; (2) the cracking load and initial stiffness of geopolymer concrete specimens were slightly lower than that of OPC concrete counterparts; (3) the current Codes of Practice GB50010-2010 and ACI 318-19 provided reasonable predictions of the cracking load and flexural load capacity of the steel-reinforced geopolymer concrete specimens; (4) the developed FE model provided a good prediction of the flexural performance of the tested slabs, and could be used for further parametric investigation.

Shear behavior of RC pile cap beams strengthened using ultra-high performance concrete reinforced with steel mesh fabric

Although pile cap bases of structures are the most significant element in the construction and one of the most difficult parts in strengthening applications, previous studies on this element, particularly strengthening, are quite limited. The most extensively utilized, highly efficient, and simple to implement solution is ultra-high performance concrete (UHPC). In this study, six-half scaled pile cap beams were prepared and experimentally tested. Three of them were strengthened with UHPC (one in shear with connectors only, one in shear with connectors and steel mesh fabric (SMF), and one in shear and punching with connectors and SMF), while the other three were not strengthened to explore the influence of side bars. The bottom bars of the all six beams were identical, consisting of main longitudinal tensile and secondary lateral reinforcement. The load-displacement response, ultimate carrying load, failure mechanisms, energy dissipation capacity, and shear ductility of pile cap beams were all thoroughly investigated. The results revealed that using side bar reinforcement and UHPC with various techniques significantly enhanced the shear strength and ductility of pile cap beams. Except for the specimen including additional internal side bars, there were no appreciable differences in the peak load of un-strengthened reinforced concrete (RC) pile cap beams. The gain in peak load was 59% due to use of side bars. The RC pile cap beam strengthened in shear and punching with connectors and SMF exhibited the highest peak load and the highest energy dissipation capacity among all tested specimens.

Research on concrete compressive strength in existing reinforced concrete elements with Schmidt hammer, ultrasonic pulse velocity method and destructive testing of cores

Concrete is a widely used material in construction. Quality control, maintenance and extending its service life are major issues after the construction stage and during the service of reinforced concrete buildings and facilities. This article presents the author’s experimental results for determining the compressive strength of concrete for tests on 12 reinforced concrete beams at the age of concrete 1926th day. In previous studies, some of the beams were loaded to a stage corresponding to the yield strength of the longitudinal tensile reinforcement, and others to a loading stage before yield, reaching a maximum crack width of 0.3 mm. The reinforced concrete elements were kept indoors for two years, and for the next more than three years they were left outdoors, exposed to external atmospheric influences. In the research was used combination of non-destructive and partially destructive techniques. The compressive strength of the concrete was determined using the method of elastic rebound (Schmidt hammer), ultrasonic pulse velocity method and partially destructive techniques - core sampling. The relative errors in the values of compressive strength obtained by the different methods were calculated. A comparative analysis of the experimentally obtained results by different methods was made. The tests were performed according to European standards for non-destructive and destructive testing of reinforced concrete structures.

Flexural performance of reinforced beams made with composite ferronickel slag concrete

Concrete containing ferronickel slag with blast furnace slag, namely composite ferronickel slag concrete or F-S concrete, is featured by low bond strength with horizontally-placed rebar compared with normal concrete of equal strength. This feature may affect the flexural capacity and deformational characteristic of F-S concrete beams, which needs to be investigated. Four under-reinforced beams were prepared and tested, including one normal concrete beam and three F-S concrete beams. The variable was the percentages of F-S powder content, i.e., 0%, 20%, 30%, and 40%. The experimental results showed that as F-S powder content increased, both the flexural capacity and ductility of RC beams decreased. For the flexural capacity analysis, directly increasing F-S powder content lowers concrete strength, thus reducing the flexural capacity. Regarding the deformational characteristic analysis, the RC beam is ideally simplified to the combination of the compressive concrete column model plus the tie bar model, and the influence of tensile rigidity effect with different bond level on the tie bar deformation is mainly studied. It is found that the lower bond stress just increases the flexural crack spacing, and changes the stress and strain distribution of rebar and concrete, but does not change the stress-mean strain relation of the rebar in the tie bar per unit length. The incorporation of F-S powder has no effect on the deformation of RC beams. Unexpectedly, the concrete strength is another important factor affecting the plastic rotation ability of RC beams. Whether increasing/decreasing the concrete strength will increase or decrease the ductility of RC beams, it is much determined by the given ratio of the longitudinal tensile reinforcement. In other words, while F-S concrete strength equals that of normal concrete, the ductility of the F-S concrete beam resembles that of normal concrete beam. F-S concrete can be applied in engineering structures, as long as it meets the design strength requirement as normal concrete does, irrespective of any F-S powder content.

Flexural Behavior of Ultra-High-Performance Fiber-Reinforced Concrete Beams after Exposure to High Temperatures.

Due to the dense structure of ultra-high-performance concrete (UHPC), it is prone to explosive spalling at high temperatures. In this paper, flexural testing of UHPC and high-strength concrete (HSC) beams was carried out at room temperature and after being subjected to different levels of thermal exposure (300–500 °C). The cross-section of the beam specimen was 150 (width) × 200 (depth) mm, and its length was 1500 mm. The flexural and shear design of the beam specimens were carried out in accordance with the ACI 318M-14 code. All of the beams were singly reinforced with two #4 rebars (minimum reinforcement ratio) as a longitudinal tensile reinforcement at the bottom of the specimen and at an effective depth of 165 mm. The flexural load was applied using the three-point load method. The results show that, at room temperature and after being subjected to different thermal exposures, compared with the HSC specimens, the stiffness of the UHPC specimens in the post-cracking stage was relatively larger and the deflection under a given load was smaller. Moreover, whether at room temperature or after exposure to different thermal exposures, the ductility of the UHPC specimens was better than that of the HSC specimens.

Bond Behaviour of Near-Surface Mounted Strips in RC Beams-Experimental Investigation and Numerical Simulations.

This paper presents an investigation of the bond mechanism between carbon fibre reinforced polymer (CFRP) laminates, concrete and steel in the near-surface mounted (NSM) CFRP-strengthened reinforced concrete (RC) beam-bond tests. The experimental program consisting of thirty modified concrete beams flexurally strengthened with NSM CFRP strips was published in. The effects of five parameters and their interactions on the ultimate load carrying capacities and the associated bond mechanisms of the beams are investigated in this paper with consideration of the following investigated parameters: beam span, beam depth, longitudinal tensile steel reinforcement ratio, the bond length of the CFRP strips and compressive concrete strength. The longitudinal steel reinforcement was cut at the beam mid-span in four beams to investigate a better assessment of the influence of the steel reinforcement ratio on the bond behaviour of CFRP to concrete bond behaviour. The numerical analysis implemented in this paper is based on a nonlinear micromechanical finite element model (FEM) that was used for investigation of the flexural behaviour of NSM CFRP-strengthened members. The 3D model based on advanced CFRP to concrete bond responses was introduced to modelling of tested specimens. The FEM procedure presents the orthotropic behaviour of the CFRP strips and the bond response between the CFRP and concrete. Comparison of the experimental and numerical results revealed an excellent agreement that confirms the suitability of the proposed FE model.

Seismic retrofit of exterior beam-column joints using steel angles connected by PT bars

A review of past earthquakes has shown that due to the lack of specific seismic details for beam-column joints, the brittle mechanisms of the structure caused by the joint behavior often lead to severe damage or even collapse of the building. Fracture of the beam-column connection is common in these mechanisms due to shear failure of connection core or reinforcement slip. The aim of this paper is to seismically retrofit the external beam-column connections without specific seismic details in existing reinforced concrete structures, considering the effect of the slab and transverse beam. For this purpose, the beam-column connections have been retrofitted using prestressed angles and bars based on the enlargement of the beam-column connection core. In this regard, seven half scale exterior beam-column connections were subjected to lateral cyclic loading with increasing amplitude. The tested specimens consist of four control specimens, one of which has special seismic details and the other three control specimens do not have special seismic details and have shortcomings such as lack of cross-sectional reinforcement of the connection core, increase of intervals for cross-sectional reinforcement of beams and columns and lack of sufficient anchorage length (with no end hook) for bottom longitudinal beam reinforcements below the beam in the connection core. The other three retrofitted specimens, like the control specimens, do not have the seismic details. Experimental results show that the use of this retrofit system has shifted the plastic hinges to the outside of the joint core and improved the bond between the concrete and the longitudinal tensile reinforcement in the joints. Moreover, the retrofit method increases loading capacity, energy dissipation, damping percentage, stiffness and ductility capacity of the members.

ЖЕСТКОСТЬ ЖЕЛЕЗОБЕТОННЫХ КОНСТРУКЦИЙ ПРИ ИЗГИБЕ ПОПЕРЕЧНОЙ И ПРОДОЛЬНОЙ СИЛАМИ

The authors developed a model for single reinforced concrete strips in block wedge and arches between inclined cracks and approximated rectangular cross-sections using small squares in matrix elements. From the analysis of the works of N.I. Karpenko and S.N. Karpenko the "nagel" forces in the longitudinal tensile reinforcement and crack slip , as a function of the opening width and concrete deformations in relation to the cosine of the angle . The experimental " nagel " forces and crack slip dependences for the connection between and in the form of an exponent for the reinforcement deformations and spacing are determined. The forces have been calculated for two to three cross-sections (single composite strips) of reinforced concrete structures. On the bases of accepted hypothesis, a new effect of reinforced concrete and a joint modulus in a strip of composite single local shear zone for the difference of mean relative linear and angular deformations of mutual displacements of concrete (or reinforcement) are developed. The hypothesis allows one to reduce the order of the system of differential equations of Rzhanitsyn and to obtain in each joint the total angular deformations of concrete and the "nagel" effect of reinforcement. The curvature of the composite bars has a relationship from the total bending moment of the bars to the sum of the rigidities. The stiffness physical characteristics of the matrix from the compressed concrete area and the working reinforcement are obtained in a system of equations of equilibrium and deformation, as well as physical equations.

Flexural capacity and ductility of lightweight concrete T‐beams

AbstractThe present study aims to estimate the flexural capacity and ductility of lightweight concrete T‐beams prepared using the expanded bottom ash and dredged soil granules (LWAC‐BS beams). Eight full‐scale beams were prepared under the main parameters including the unit weight and compressive strength of concrete and amount of longitudinal tensile reinforcement. The moment capacities and displacement ductility ratios measured for the present specimens were compared with those compiled from normal‐weight concrete (NWC) beams and lightweight concrete beams made using the expanded clay and fly ash granules (LWAC‐CF beams) with respect to the longitudinal reinforcement index (ωs). The coefficients for the equivalent rectangular stress block to assess the ultimate moment capacity of LWAC beams were formulated from the actual stress–strain curve of the concrete. The test results showed that the effect of the type of artificially expanded lightweight granules on the normalized cracking and ultimate moment capacities of LWAC beams was insignificant, whereas LWAC‐BS beams exhibited lower displacement ductility ratios than LWAC‐CF beams at the same ωs value. The maximum amount of longitudinal tensile reinforcement specified in ACI 318‐14 provision for preventing brittle failure of the beam needs to be lowered for LWAC beams. When determining the coefficients of the equivalent stress block for LWAC members, the concrete unit weight deserves consideration as a primary factor together with the compressive strength of the concrete.