Moment Redistribution Research Articles (Page 1)

In harsh environments, steel rebars in concrete corrode; therefore, fiber-reinforced polymer (FRP) bars should be considered due to their non-corrosive nature. Moment distribution in continuous FRP-reinforced concrete beams is prohibited by the design code due to the insufficient ductility of FRP bars. However, studies have shown that FRP-reinforced concrete continuous beams exhibit considerable redistribution of moment. In this study, a nonlinear finite element model of a continuous concrete beam reinforced with basalt FRP bars is developed to numerically investigate the effect of reinforcement configuration on the redistribution of moment. The models exhibit a considerable level of moment redistribution at the internal support (hogging zone) and midspan (sagging zone). When the amount of tensile reinforcement in the sagging zone increases compared to the hogging zone, the moment redistribution at the internal support (hogging zone) increases significantly. Therefore, it is not justified to completely overlook the redistribution of moment in the design of FRP RC continuous beams.

Objective. The paper presents general equations of the moment theory of thin shallow shells with a relatively small rise above the plane of their projection taking into account creep deformation. The problem of the stress-strain state of the shell with boundary conditions is considered. At the edges, the shell is connected to diaphragms that are absolutely rigid in their plane and flexible from it. Resolving equations are obtained for calculating shallow isotropic and orthotropic shells taking into account creep deformations. The problem is reduced to a system of two fourth-order differential equations with respect to deflection and stress function. Method. The solution is given by the numerical-analytical method in the MATLAB software package. The nonlinear Maxwell-Gurevich equation is used as the equation of state between creep deformations and stresses. To determine creep deformations, a linear approximation of the first derivative with respect to time (Runge-Kutta method) was used. To verify the solution to the problem, a shell made of secondary PVC was calculated using the grid method. The method has been tested by comparing the solution with the calculations of other well-known researchers. Result. A program has been developed for calculation in the MATLAB package with the ability to vary the initial data and output a graph of the dependence of displacements and stresses on time. It has been established that stresses and internal forces in an orthotropic shell of the same shape as for an isotropic one are subject to stress redistribution: normal stresses increase, and tangential stresses decrease. Longitudinal and shear forces remain almost constant; stress changes occur mainly due to the redistribution of bending and torque moments. Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and bearing capacity of a reinforced concrete shell as well. There are no restrictions on boundary conditions and types of loading, and the beam material can be not only polymers and composites for construction purposes, but also concrete.

Abstract Due to the demand for slender and functional buildings, flat slabs are a frequently used load‐bearing element in buildings. However, the concentrated load introduction at the slab‐column connection is often the governing detail in design due to punching shear failure. Therefore, the punching shear behavior of flat slabs has been intensively studied in the past, mostly on flat slab cutouts, as the testing of flat slab systems is expensive. The investigated main characteristics of the punching shear behavior were hereby investigated and form the basis for today's design equations. However, new investigations on flat slab systems demonstrate clearly favorable influences of the system load‐bearing effect – namely compressive membrane action and moment redistributions. These phenomena lead to significant load reserves in continuous slabs and remain unconsidered in tests on flat slab cutouts. Since the design approaches are based on the available test data on cutouts, the system influences occurring in engineering practice stay disregarded. To fill the gap in experimental data deriving more advanced design approaches, a novel test setup was developed for the efficient investigation of system behavior using isolated flat slab specimens with externally applied load‐dependent loading conditions. The test program consisted of two test series with a total of 10 test specimens. The test results reveal up to 48% increased punching shear resistances going along with reduced deformations compared to isolated flat slab cutouts.

Design of hybrid steel I-girders under moment gradient: moment redistribution and cross-section behaviour

The ways in which age affects neuromuscular control in response to walking-related fatigue are poorly understood. Better understanding of the consequences of walking-related fatigue can inform the development of strategies to improve independent mobility for older adults. In this study, we measured leg muscle excitations and net joint moments in younger and older adults during a 30-min walking trial. Twelve leg muscles were monitored, and wavelet transformation and principal component analyses quantified the effects of age and time on muscle excitation patterns. Perceived exertion increased in both age groups, with higher terminal values in older adults. Over the course of prolonged walking, mean EMG frequency and amplitude decreased while EMG intensities in the slower frequency ranges increased for soleus, lateral gastrocnemius, tibialis anterior, peroneus longus, and gluteus maximus muscles. For soleus muscle, a time-dependent decrease in mean frequency was observed only for older adults. We observed a distal-to-proximal redistribution of net joint moments during prolonged walking independent of age; however, older adults walked with greater peak hip joint moments than younger adults. Our results suggest that shank muscles may exhibit higher fatigability during prolonged walking, precipitating an increased demand on proximal leg muscles to power walking. Walking in older adults is often characterized by an increased reliance on proximal leg muscles, which has in turn been implicated in their higher metabolic cost of transport. Accordingly, our collective findings point to neuromuscular changes during prolonged walking that may cause older adults to be more susceptible to walking-related fatigue than younger adults.

The design of concrete structures with embedded non-metallic composite reinforcement (FRP) is becoming more widespread. The behavior of statically determinate concrete structures reinforced by this durable material is already widely understood and known. Usage of glass and carbon fiber reinforcement is also included in the new generation of Eurocodes for concrete structures. However, in common practice, we also encounter statically indeterminate structures such as continuous beams or slabs. In the case of traditional steel reinforcement of continuous beams, it is possible to assume a certain redistribution of bending moments and to use the principle of linear elastic analysis with limited redistribution in design. According to ACI 440.1R-15 and the new generation of Eurocode a moment redistribution of internal forces on continuous beams or other statically indeterminate structures reinforced with FRP reinforcement should not be considered, given the lower material stiffness and linear elastic behavior up to failure. However, in reality, a redistribution of internal forces can occur. Based on a limited number of studies and experiments that have been carried out in this area globally, there is a premise that some degree of redistribution of bending moment may occur in FRP reinforced indeterminate structures. The objective of this work is to support this assumption through an analytical study of the behavior of a concrete cross-section reinforced with FRP bars, demonstrating its potential for internal force redistribution. The aim of this paper is to present the results of an analytical study capturing the behavior of a concrete cross-section reinforced with FRP, the determination of the deformation characteristics of such a section, and the possible application of the results to a two-span concrete beam. The main emphasis is placed on the stress-strain diagram of concrete and its influence on deformation characteristics, mainly moment-curvature relationship.

The linear analysis with limited moment redistribution is useful to reduce the maximum negative moments at support sections, bringing this way several advantages to design and execution of reinforced concrete beams and slabs. The maximum moment redistribution is not related only with the plastic rotation capacity of the critical sections, but also with the requirements at the Serviceability Limit States. The main structural concrete codes condition the maximum moment redistribution to the ductility of the sections and to the ductility of the steels used. The goal of this study is to analyze how the limitation of crack width under service conditions affects the maximum moment redistribution used in the analysis to the Ultimate Limit States. On the other hand, with the increasing use of high-strength steels, it is important to assess how this type of steels can limit the moment redistribution and how they influence the crack width. It was found that the maximum moment redistribution is significantly conditioned by the limitation of the maximum crack width and by the q SLS /q ULS ratio, which is the ratio between the load corresponding to the service conditions (q ELS ) and the load used on the verifications of the Ultimate Limit States (q ELU ). In certain situations, the maximum moment redistribution possible was lower than the values recommended by main codes, Eurocode 2 and fib Model Code. To exploit the full capacity of high strength steels, the moment redistribution must be very limited and applied only on structures located in less aggressive environments. To understand all effects of the moment redistribution, a non-linear analysis was also performed to analyze the real evolution of the moment distribution along the beam axis for different load levels. Based on the study performed, it is proposed an empirical equation to predict the maximum moment redistribution allowed, considering all key parameters.

In-service, multi-girder Steel-Concrete-Composite-Girder (SCCG) bridges may experience damage. The long-gauge Fiber-Bragg-Grating (FBG) sensor can measure macro-strain which is sensitive to damage and can be installed and distributed continuously which is impossible for traditional point-gauge strain sensors. However, it lacks application of these sensors for both model and actual SCCG bridges, especially for multi-girder SCCG bridge which has significant spatial characteristics and possible transverse load redistribution due to damages. In this study, the distributed long-gauge FBG sensors were applied to the damage identification for a multi-girder SCCG bridge. First, based on the concept of the Envelope of Macro-strain Influence Line (EMSIL), a damage indicator, RE, was proposed for the damage identification of the SCCG. To validate, experimental and numerical studies were conducted. It shows RE is sensitive to damages induced by the change of the sectional stiffness and the neutral axis position. Then, the redistribution of the bending moment due to damages was investigated for an SCCG bridge with three girders. It shows the usual damages in steel girder, transverse joint and crossbeam have little influence on the bending moment redistribution. Finally, the damage identification was conducted for individual damage in the steel girder and composite damages in both the steel girder and transverse joint (or crossbeam) of the three-girder SCCG bridge. Based on the EMSIL obtained from the quasi-static components of the macro-strain time-history under moving vehicle load using variational mode decomposition (VMD), the identification effect was satisfied using the introduced RE, which proves that RE can be utilized to identify the change of the sectional stiffness and the neutral axis position for multi-girder SCCG bridges.

Abstract The prediction of the stress increase Δσp,ULS of an unbonded tendon in a post‐tensioned continuous concrete beam at ultimate capacity is more challenging than when bonded tendons are used. Four continuous two‐span concrete beams, prestressed with unbonded tendons, were constructed and loaded up to failure in a four‐point loading arrangement at the laboratory of Civil Engineering in Tampere University. The test results from the point of moment redistribution were partially published earlier in 2024. This article presents the results of the stress increase in the unbonded tendons of the test beams. Moreover, this article presents a novel nonlinear analysis model, which was employed to examine the influence of the dilatation of the beam's axis of gravity on the magnitude of the additional tendon elongation. The comparison calculations have also been made with a simple beam model from the literature. In all test beams, the stress in the prestressing steel exhibited a significant increase at failure. The effect of beam expansion on the tendon elongation at high loading levels was approximately half of the total additional elongation of the tendon.

Moment Redistribution Effect of the Continuous Glass Fiber Reinforced Polymer-Concrete Composite Slabs Based on Static Loading Experiment

Abstract Continuous reinforced concrete (RC) beams cast in place are commonly used in construction; however, there is a notable gap in the literature regarding the performance of continuous RC beams strengthened with fiber‐reinforced polymer (FRP) sheets. Strengthening RC beams with FRP sheets typically leads to reduced ductility and moment redistribution capacity due to the linear stress–strain behavior of FRP materials compared to non‐strengthened RC beams. Addressing this gap, this study explores the feasibility of enhancing the mechanical properties and ductility of strengthened elements through a hybrid approach, combining carbon‐fiber‐reinforced polymer (CFRP) and glass‐fiber‐reinforced polymer (GFRP) sheets. An experimental program was conducted, retrofitting two continuous two‐span RC beams (250 × 150 × 6000 mm) with hybrid CFRP‐GFRP (HCG) sheets. Concentrated loads were applied at the center of each span, and comprehensive data on strains in FRP sheets, longitudinal reinforcements, and crack propagation patterns were recorded and meticulously analyzed. The outcomes demonstrated that employing HCG sheets for strengthening RC continuous beams significantly improves ductility, load‐carrying capacity, and moment redistribution, surpassing the performance of beams strengthened with either CFRP or GFRP sheets. To ensure accurate predictions of the flexural response, an analytical model was developed and rigorously verified using the experimental results. The model takes into account the strain compatibility condition and provides insights into the behavior of continuous RC beams strengthened with CFRP, GFRP, and HCG sheets. This research contributes valuable knowledge to the understanding of FRP sheet strengthening techniques, emphasizing the efficacy of HCG sheets for achieving enhanced structural performance in continuous RC beams.

Development of a novel crack-resistance technique for concrete slab in the hogging moment region of continuous composite beam

Research on Moment Redistribution of Prestressed Steel Reinforced Concrete Continuous Beams

In prestressed concrete continuous beams, building code provisions often allow for a reduction in the moment at a critical section (calculated through elastic analysis). This reduction is permitted as long as the moments in all other sections are adjusted to maintain equilibrium and support the designated loads. However, the allowable moment redistribution percentage (MRP) for prestressed concrete beams (PCBs) remains a topic of debate. Many codes currently assign a similar MRP limitation to both PCBs and reinforced concrete beams (RCBs). This approach might be over-simplistic for PCBs due to their unique behaviour. A method for identifying the maximum available MRP is proposed in this article. An in-depth study was conducted on the maximum available MRP of PCBs based on calibrated finite-element models. The results showed that parameters such as the passive reinforcement ratio, steel yield strength, slenderness ratio, eccentricity of prestressing tendons, concrete grade and load pattern, which are not considered in the codes, influence the maximum available MRP to an extent. Using the same permissible MRP as RCBs may thus be inappropriate. An equation is proposed to estimate the maximum available MRP for PCBs.

Due to their great strain capacity, high tensile strength, and ability to localize cracks, cementitious composite materials are beneficial for strengthening reinforced concrete (RC) members. This paper illustrates the application of cementitious composite materials in the form of precast thin layers to strengthen a double-spanned, full-scale RC beam. Both positive and negative zones were strengthened by the precast layer embedded into the concrete cover. The precast layers have a dimension of 20 mm in thickness and 150 mm in width as that of the substrate beam and were applied by two configurations: plain and reinforced layers. A ductile smooth steel sheet with 2 mm in thickness and 100 mm in width was used inside the reinforced precast layer. The composite action of the precast layer has mutual benefits; the embedded steel sheet localizes the cracks, while the surrounding cementitious composite materials protect the steel sheet from environmental impact. The experimental results showed that the strengthening system has a significant contribution to improve the failure mode and load-carrying capacity. The use of a plain precast layer caused a 6% increase in the ultimate load and a 33% enhancement in the moment redistribution ratio compared to the control beam (CB). Applying the strengthening system with reinforced precast layer shifted the failure mode from rupture failure in the precast layer to delamination without slippage in the embedded steel sheet and matrix, leading to the full tensile capacity of the precast layer. Besides, the yielded and ultimate loads increased by 34% and 41%, respectively, and maximum deflection increased by 36%. In addition, the beam's ductility increased by 36%, and the moment redistribution ratio was enhanced by 49% compared to the CB. Doi: 10.28991/CEJ-2024-010-09-05 Full Text: PDF

Design of cold formed C section beams with elongated circular openings based on tests

The methodology of calculation of reinforced concrete frames of buildings for a special design situation caused by initial local failures, taking into account the violation of the continuity of the concrete matrix during crack formation, is proposed. The verification of the proposed methodology is carried out by comparing it with the results of experimental data for a U-shaped reinforced concrete frame with prestressing. The bending moments in the frame, determined by the proposed calculation method, are in practically complete agreement with the values found experimentally. As a result of cracking, there was a redistribution of bending moments in the beam of the frame: the moments in the structural nodes decreased by 148 % and increased in the span by 37.5 % compared to the results obtained using the traditional finite element method approach. On the basis of the results of the calculation of the reinforced concrete 3-storey frame by the proposed method, the increase of longitudinal tensile forces in the beam support sections above the zone of local failure at failure of the middle row column is revealed in comparison with the traditional approach to modeling. The revealed effect may lead to an increase in the influence of longitudinal bending for the outermost row column to which the beam is adjacent.

To increase the starting torque of the synchronous motor, either a starting resistor or a capacitive energy storage device is turned on in the excitation winding. This will lead to a redistribution of moments and currents along the circuits of the synchronous motor. Therefore, the task of the work is to determine the component moments and currents along the engine circuits.The calculation of moments and currents is performed according to the substitution scheme according to the developed algorithm. Calculated static components of moments and currents of circuits of asynchronous start-up of SD. A summary table of extreme moments and contour currents for various schemes for turning the ENE into the excitation winding is given.

Abstract The present study deals with the semi-rigid behaviour of stainless steel structural frames due to the effect of initial voids present in the microscopic structure of stainless steel. Non-Linear Finite Element analysis of stainless steel beam-column double web-angle connections is carried out considering the effect of damage on the material behaviour. The non-linear analysis becomes useful for finding out the moment carrying capacity of a joint. Using the results of the stiffness analysis, multi-storied stainless steel structural frames are analyzed and the redistribution of moments of these joints is studied using a commercial software package. The joints are provided with the secant stiffness which is obtained from the moment-rotation curves considering the effect of ductile damage.

Национальный исследовательский Московский государственный строительный университет (НИУ МГСУ); г. Москва, Россия АННОТАЦИЯ Введение. Рассматривается актуальный вопрос перераспределения моментов в статически неопределимых железобетонных балках, подвергающихся коррозии. Статически неопределимые железобетонные балки широко используются в различных строительных приложениях, и понимание того, как коррозия влияет на перераспределение моментов в таких балках, является важным для оценки их несущей способности и безопасности. Применяются экспериментальные и аналитические методы для изучения влияния коррозии на перераспределение моментов в железобетонных балках. Материалы и методы. Использована новая техника для ускорения и контроля присутствующей коррозии, применяемой в соответствии с экспериментальной программой. Испытаны четыре двухпролетных железобетонные балки с коррозией и без при изгибающем моменте. Результаты. Экспериментальные результаты сравнили между собой. Полученные результаты свидетельствуют о том, что коррозия оказывает существенное влияние на перераспределение моментов в статически неопределимых железобетонных балках. Перераспределение моментов увеличивается с ростом процента коррозии. Предлагаемая модель позволяет в значительной степени определить коэффициент перераспределения моментов в статически неопределимых железобетонных балках. Выводы. Исследование подчеркивает существенное влияние коррозии на перераспределение моментов в статически неопределимых железобетонных балках. Полученные результаты показывают, что с увеличением процента коррозии происходит соответствующее увеличение перераспределения моментов. Полученные результаты могут стать основой для разработки будущих стратегий по снижению влияния коррозии на статически неопределимые железобетонные балки, что будет способствовать улучшению проектирования конструкций и практики их эксплуатации в строительстве.