Effective Moment Of Inertia Research Articles

Analysis of R/C frames considering cracking effect and plastic hinge formation

The design of reinforced concrete buildings must satisfy the serviceability stiffness criteria in terms of maximum lateral deflections and inter story drift in order to prevent both structural and non-structural damages. Consideration of plastic hinge formation is also important to obtain accurate failure mechanism and ultimate strength of reinforced concrete frames. In the present study, an iterative procedure has been developed for the analysis of reinforced concrete frames with cracked elements and consideration of plastic hinge formation. The ACI and probability-based effective stiffness models are used for the effective moment of inertia of cracked members. Shear deformation effect is also considered, and the variation of shear stiffness due to cracking is evaluated by reduced shear stiffness models available in the literature. The analytical procedure has been demonstrated through the application to three reinforced concrete frame examples available in the literature. It has been shown that the iterative analytical procedure can provide accurate and efficient predictions of deflections and ultimate strength of the frames studied under lateral and vertical loads. The proposed procedure is also efficient from the viewpoint of computational time and convergence rate. The developed technique was able to accurately predict the locations and sequential development of plastic hinges in frames. The results also show that shear deformation can contribute significantly to frame deflections.

EC-2의 콘크리트 응력-변형률 곡선에 기반한 휨부재의 유효단면2차모멘트

EC-2의 콘크리트 응력-변형률 곡선에 기반한 휨부재의 유효단면2차모멘트

Experimental and Analytical Modeling of Shield Segment under Cyclic Loading

AbstractBecause of the lack of adequate monitoring performance data for shield tunnel segments from either laboratory testing or in situ measurement, it is difficult to improve the current segment design codes. As a result, overdesign or excessive use of reinforcement in tunnel linings is common. To overcome these segment design inadequacies, this study aimed to investigate the bending behavior of RC members based on measured strain data and the modeling results from a proposed analytical model, which takes into account section nonlinearity resulting from concrete tensile cracking and the actual effective moment of inertia. The cyclic four-point loading test was performed on a RC beam with an embedded optical fiber sensor and on a smart tunnel lining segment, in which two vibrating wire strain gauges with thermistors were welded into a rebar cage on either side of the neutral axis. The measured strain data for the rectangular beam subject to concrete curing and subsequent four-point loading justify the ap...

Deflection of prestressed concrete beam using fiber reinforced polymer (FRP) tendon

Numerical model analysis was carried out to study the deflection behaviour of FRP-based prestressed concrete (PSC) beam, because it does not resemble the existing deflection model of steel tendon-based PSC beam due to its non-ductile property. Deflection model by various researchers for the FRP-based PSC beams are underestimating as compared to experimental results which lead to unsafe design. There were 51 numbers of experimental results which were collected from various research articles for the numerical model analysis. Lagrange dual function convex optimisation used to predict the effective moment of inertia and shift of neutral axis distance. It reveals that the deflection of FRP tendon beam depends on deformability of material, degree of prestressing and bond strength. Design chart suggested for calculation of effective moment of inertia and effective neutral axis distance with respect to deformability index. The maximum deflection error by the proposed method is less than 5% as compared to experimental results.

Modeling the tensile steel reinforcement strain in RC-beams subjected to cycles of loading and unloading

Tension stiffening affects the strain distribution along the tensile reinforcement in a cracked reinforced concrete beam and in the tensile concrete between cracks. It also affects the overall stiffness and hence the deflection of the beam. In this paper, the results of experiments on eleven reinforced concrete beams with reinforcement ratios between 0.56% and 0.88% are reported. The overall strain in the reinforcement and the load-deflection response under both monotonic loading and cycles of loading and unloading were measured for each beam. Based on the experimental results, a model of the effective strain in the reinforcement is presented and is used to assess the effective moment of inertia of reinforced concrete beams subjected to in-service monotonic loading. Measurements from the test beams were used to calibrate a model of the steel-concrete interface damage caused by cycles of loading and unloading. The comparisons between predicted and measured overall stiffness and load-deflection responses show the validity of the present model.

DEĞİŞİK YÜKLEMELER ETKİSİ ALTINDA FARKLI DONATI ORANLARINA SAHİP BETONARME KİRİŞLERDE OLUŞAN DEPLASMANLARIN DENEYSEL OLARAK İNCELENMESİ

In the present study, the reinforced concrete beams with various reinforcement ratios, subjected to different load types such as midspan and two point loads, have been tested and the effects of the loading types and the reinforcement ratio on the deflections of beams have been investigated. The tested beams have been analysed by using the computer program developed for the analysis of reinforced concrete frames with members in cracked state, and the theoretical results have been compared with the experimental results. The deflections of beams subjected to midspan load were observed to be higher than the beams with two point loads. The effect of shear deformation on the total deflection of reinforced concrete beams has found to be important with increasing in reinforcement ratio in the beams. Keywords: Effective moment of inertia, effective shear modulus, displacements, reinforcement ratio, loading type

An effective stiffness model for GFRP RC cracked flexural members

Abstract There is no complete consensus of researchers on the problem of evaluating tension stiffening phenomena in cracked flexural glass fibre-reinforced polymer reinforced concrete members and, therefore, various empirical correction factors are used in the existing weighted averaging techniques for obtaining consistent estimates of experimental deflection of traditional steel bars reinforced concrete cross-sections. This paper presents an alternative method for deformational analysis of cracked GFRP RC flexural members based on constitutive modeling, taking into account the direct or inverse approach to evaluating the post-cracking stress-strain response of concrete in tension. The effect of tension stiffening is defined analytically by the derived formula for the effective moment of inertia, omitting the empirical correction of the moments of inertia of the uncracked or fully cracked RC cross-sections. Analytical formulae are also proposed to derive the parameters of tension stiffening based on the test data of GFRP RC beams subjected to bending. The relative systematic and random errors of the method are considered in the statistical analysis, involving the experimental sample of deflections for 42 beams. The case studies of manual calculation of the mid-span deflection of the beams by using the proposed technique and the inverse analysis for deriving tension stiffening parameters based on of the experimental data are also provided.

DEFLECTION PREDICTION OF TWO-SPAN CONTINUOUS CONCRETE BEAMS REINFORCED WITH GFRP BARS

Continuous beams are main structural members in many reinforced concrete (RC) applications such as parking garages and bridges, which are vulnerable to harsh environments. The use of glass fiber-reinforced polymers (GFRP) bars in such structures has proven to be a good solution to overcome the steel corrosion problem. In GFRP-RC beams, deflection is a concern and may govern the design; thus, attempts have been made to propose models to predict the effective moment of inertia and consequently the deflection. The current prediction models were verified against deflection of simply-supported beams. In this paper, available predictions models are compared to the experimental deflections of two-span continuous beams. Eight rectangular beams (200×300 mm) continuous over two equal spans of 2,800 mm each were constructed and tested to failure. All beams were reinforced with GFRP bars and stirrups. The test variables included concrete strength, longitudinal reinforcement ratio and transverse reinforcement ratio. The comparison revealed that the investigated models reasonably predicted the deflection at service load level while they underestimated the deflection at higher load levels. These models require to be modified in order to yield better predictions of the deflection at lower and higher load levels than service load.

Deflection of unbonded partially prestressed concrete continuous beams

Continuous beams are preferred to simply supported beams because of economy, fewer expansion/contraction joints and possible benefits from moment redistribution. In the design of unbonded partially prestressed concrete (UPPC) continuous beams, it is necessary to estimate their deflections under service loads in order to satisfy the requirements of serviceability limit state. A method is developed to convert the cross sectional area of unbonded prestressed tendons to the equivalent cross sectional area of non-prestressed steel. Then the moment of inertia of cracked section as well as Branson’s effective moment of inertia in a UPPC continuous beam can be easily determined. The computed deflections are compared with some available experimental results, including beams with external unbonded steel tendons and those with external unbonded aramid fibre reinforced polymer tendons. The proposed method gives satisfactory predictions of deflection till the yielding of non-prestressed steel. Another equation for moment of inertia of cracked section, which was originally suggested by the precast/prestressed concrete institute (PCI) Design Handbook for bonded partially prestressed concrete beams, is also evaluated in the study. In most cases the PCI equation can also give satisfactory results but in some cases its discrepancy of deflections is larger than that of the proposed method. Compared with the method recommended in the current Chinese Code, the proposed method is applicable not only to members with the conventional high-strength steel prestressing tendons, but also to those with tendons made of other materials such as fibre-reinforced polymer.

Deflection Behavior of Prestressed Concrete Beam using Fiber Reinforced Polymer (FRP) Tendon

The application of prestressing steel is restricted in highly corrosive environment area. The behavior of structure changes due to corrosion of prestressing steel, which leads to reduction in strength and it may cause sudden failure. There are many research recommendations to resist corrosion of steel, however the durability of structure shall not be ensured during service life of structure. Fiber Reinforced Polymer (FRP) Tendon is considered as an alternate material due to its corrosive resistance property and high strength. An experimental and numerical analysis carried out to study the deflection behavior of FRP tendon prestressed beam and recommended design guidelines. There are four beam specimens casted and tested in laboratory and 51 experimental results collected from research article to carry out numerical study. The ACI, 2011 [1] recommended generalized deflection calculation for beam by softening the effective moment of inertia curve and also introduced the effect of shift of neutral axis once the member exceeds cracking stress of concrete. Based on experimental and numerical analysis study it is concluded that, the deflection behavior of FRP tendon beam depends on deformability of material, degree of prestressing and bond strength. Design chart proposed for calculation of effective moment of inertia and effective neutral axis distance with respect to deformability index. The error percentage of deflec-tion values as per ACI 2011, is about 10 to 20% has reduced to less than 5% in the proposed method.

A Modified Model for Deflection Calculation of Reinforced Concrete Beam with Deformed GFRP Rebar

The authors carried out experimental and analytical research to evaluate the flexural capacity and the moment-deflection relationship of concrete beams reinforced with GFRP bars. The proposed model to predict the effective moment of inertia for R/C beam with GFRP bars was developed empirically, based on Branson’s equation to have better accuracy and a familiar approach to a structural engineer. For better prediction of the moment-deflection relationship until the ultimate strength is reached, a nonlinear parameter (k) was also considered. This parameter was introduced to reduce the effect of the cracked moment of inertia for the reinforced concrete member, including a lower reinforcement ratio and modulus of elasticity of the GFRP bar. In a comparative study using six equations suggested by others, the proposed model showed better agreement with the experimental test results. It was confirmed that the empirical modification based on Branson’s equation was valid for predicting the effective moment of inertia of R/C beams with GFRP bar in this study. To evaluate the generality of the proposed model, a comparative study using previous test results from the literature and the results from this study was carried out. It was found that the proposed model had better accuracy and was a familiar approach to structural engineers to predict and evaluate the deflection behavior.

반복하중을 받는 모듈러 슬래브의 거동 및 단면2차모멘트 평가

Recently, the maintenance activity for aging of bridge structures was difficult because of traffic jam, environment pollution and increasing cost. And to solve these problems, modular bridge research has been studied. After static and cyclic loading test was conducted for serviceability and bending performance with one way slab, effective moment of inertia of modular specimen was analyzed to estimate the deflection by KCI(2012). To conduct the test, one integral slab and three modular slabs were made for static loading and one integral and modular slab were made for cyclic. As a result of the test, the modular slab had the similar bending performance of the integral. But the ultimate deflection showed the insufficient which was smaller than 20%. In the cyclic loading test, the modular slab has different behavior of deflection with the integral, so it was evaluated difficult for serviceability. In addition, effective moment of inertia by KCI(2012) was not estimated for modular slab with connection. The new value of m which was ratio between moments is 4.53 based on result of test for predicting deflection of modular.

Characteristics of the deflection behaviour of a slab reinforced by an externally bonded fibre-reinforced polymer

In this study, the deflection test was conducted on a non-strengthened specimen and six reinforced concrete slabs reinforced with a fibre-reinforced polymer adhesion, and the behavioural characteristics owing to the differences in the material properties were determined. The experimental variables were the reinforcing materials, the pre-loading and the level of reinforcement. After the test, the effective moment of inertia suggested by ACI-318 and the moment of inertia computed from the experimental results were compared. As the level of reinforcement increased, the strength of slab also increased. From the analysis of the application of pre-loading, the pre-loaded slab exhibited a higher yield load and ultimate load than the non-pre-loaded slab. It was found that the effective moment of inertia suggested by ACI-318 underestimates the moment of inertia of the slab reinforced with the fibre-reinforced polymer.

Normal and shear resistance of longitudinal contact surfaces of segmental tunnel linings

Stiffness of contact points has a significant effect on the internal forces and structural design of segmental lining of mechanically bored tunnels. Recent research on the effect of contact points in the structural analysis of segmental lining can be categorized into: (1) using hinges at contact points (HL model), (2) reducing liner rigidity (RR model), (3) using effective moment of inertia for liners (EMI model), (4) using rotational springs at contact points (BRS model), and (5) developing a comprehensive 3D model for segmenting contact locations. The present study tried to develop a precise contact model based on experimental direct shear tests (DST) on the concrete samples of contact points in segments. By selecting the normal stress between 0.25 and 2MPa, about 90 tests were performed on the grooved cubic samples with and without gasket. As the practical outcome of this study, the contact shear and normal reaction moduli ks and kn were related to contact normal stress via two linear regression equations considering R2 of 99%. For evaluating the proposed method, finite element models of an urban tunnel liner were developed using the concept of beam on elastic foundation considering the proposed contact model of the present study (beam-contact springs (BCS)), the results of which were compared with those of the conventional contact models. Results demonstrated that the proposed model of this research had the highest correspondence with reduced RR, HL, EMI, BRS, and comprehensive coverage, respectively.

Analytical and experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars

This paper presents an experimental, numerical and analytical study of the flexural behavior of concrete beams reinforced with locally produced glass fiber reinforced polymers (GFRP) bars. Glass fiber reinforced polymers (GFRP) reinforcement bars has a lower stiffness than steel reinforcement, which should be accounted for the ultimate and serviceability conditions, including the impact on member deflection and crack widths. The bars are locally produced by double parts die mold using local resources raw materials. A total of ten beams, measuring 120mm wide×300mm deep×2800mm long, were cast and tested up to failure under four-point bending. The main parameters were reinforcement material type (GFRP and steel), concrete compressive strength and reinforcement ratio (μb, 1.7μb and 2.7μb; where μb is the reinforcement ratio at balanced condition). The mid-span deflection, crack width and GFRP reinforcement strains of the tested beams were recorded and compared. The test results revealed that the crack widths and mid-span deflection were significantly decreased by increasing the reinforcement ratio. The ultimate load increased by 47% and 97% as the reinforcement ratio increased from μb to 2.7μb. Specimens reinforced by 2.7μb can produce some amount of ductility provided by the concrete. The recorded strain of GFRP reinforcement reached to 90% of the ultimate strains. A non-linear finite element analysis (NLFEA) was constructed to simulate the flexural behavior of tested beams, in terms of crack pattern and load deflection behavior. It can be considered a good agreement between the experimental and numerical results was achieved. Modifications to ACI 440.1R-06 equation for estimating the effective moment of inertia (Ie) of FRP-reinforced concrete beams, using regression analysis of experimental results, is proposed by introducing empirical factors that effectively decrease the Ie at high load level. The proposed equation is compared with different code provisions and previous models for predicting the deflection. It can proved that the proposed factors gives good estimation for the effective moment of inertia (Ie) works well for FRP-reinforced concrete beams at high load level.

Explicit expression for effective moment of inertia of RC beams

Deflection is an important design parameter for structures subjected to service load. This paper provides an explicit expression for effective moment of inertia considering cracking, for uniformly distributed loaded reinforced concrete (RC) beams. The proposed explicit expression can be used for rapid prediction of short-term deflection at service load. The explicit expression has been obtained from the trained neural network considering concrete cracking, tension stiffening and entire practical range of reinforcement. Three significant structural parameters have been identified that govern the change in effective moment of inertia and therefore deflection. These three parameters are chosen as inputs to train neural network. The training data sets for neural network are generated using finite element software ABAQUS. The explicit expression has been validated for a number of simply supported and continuous beams and it is shown that the predicted deflections have reasonable accuracy for practical purpose. A sensitivity analysis has been performed, which indicates substantial dependence of effective moment of inertia on the selected input parameters.

Hybrid FRP–UHPFRC composite girders: Part 2 – Analytical approach

A companion paper shows the experimental testing and numerical analysis of composite girders consisting of hybrid carbon/glass fiber-reinforced polymer (HFRP) I-girders topped with precast ultra-high-performance fiber-reinforced concrete (UHPFRC) slabs. This paper presents derivations of analytical equations to examine the composite behavior of the HFRP–UHPFRC girders with varying levels of interaction at the slab/girder interface. The derived equations to predict interfacial slip strain, curvature, and deflection of the composite girders were validated by the experimental data. An equation to determine the effective moment of inertia of the HFRP–UHPFRC composite girders with partial interaction is proposed and compared against the experiment. A fairly good agreement between the experimental and analytical results was found. The derived/proposed equations can simply and reliably evaluate the composite behavior between the HFRP I-girder and the UHPFRC slab.

Force transfer mechanism in positive moment continuity details for prestressed concrete girder bridges

The force transfer mechanism in positive moment continuity details for prestressed concrete girder bridges is investigated in this paper using a three-dimensional detailed finite element model. Positive moment reinforcement in the form of hairpin bars as recommended by the National Cooperative Highway Research Program Report No 519 is incorporated in the model. The cold construction joint that develops at the interface between girder ends and continuity diaphragms is also simulated via contact elements. The model is then subjected to the positive moment and corresponding shear forces that would develop over the service life of the bridge. The stress distribution in the continuity diaphragm and the axial force distribution in the hairpin bars are presented. It was found that due to the asymmetric configuration of the hairpin bars, asymmetric stress distribution develops at the continuity diaphragm, which can be exacerbated by other asymmetric factors such as skewed bridge configurations. It was also observed that when the joint is subjected to a positive moment, the tensile force is transferred from the girder end to the continuity diaphragm only through the hairpin bars due to the lack of contact between the both members at the construction joint. As a result, the stress distribution at girder ends was found to be concentrated around the hairpin bars influence area, rather than be resisted by the entire girder composite section. Finally, the results are used to develop an approach for estimating the cracking moment capacity at girder ends based on a proposed effective moment of inertia.

Stiffness properties of the trunk in people with low back pain

The purpose of this study was to examine the dynamic properties of the trunk during unstable sitting and to determine differences between healthy and low back pain (LBP) participants.Participants sat on a custom-made chair that was able to swing freely in the sagittal plane. The chair was mounted on a force platform to measure loads acting at the trunk. Each participant was asked to find a balanced position after the chair was tilted backward and released. Movements of the trunk and chair were recorded. Effective moment of inertia, stiffness and damping coefficients were derived using a second order linear model. 10 participants were re-tested to assess reliability.Trunk stiffness was found increased for LBP subjects (p<.05) while no difference was found for damping coefficient. Gender and initial tilt angle did not affect viscoelastic properties of the spine.A second order linear model adequately described the biomechanical response of the trunk. It was shown that the trunk response was mainly elastic for all participants. The increase in trunk stiffness in LBP subjects could be a compensatory strategy to decrease pain and the risk of further injuries, but further investigations are needed to understand the nature of the viscoelastic alterations.

Correlation Between Hydroxide ion Dynamics and Transport Properties of Hydroxide/Chloride Melts According to Raman Spectroscopy Data

UDC 541.454;543.42;535.375.5 Using data obtained in analysis of the band contour for the totally symmetric stretching vibration of the OH - anion in Raman spectra of hydroxide/chloride ionic melts, a correlation has been established between the orientational relaxation time and effective moment of inertia of the hydroxide ion and the transport properties of the electrolyte. Study of the structure of ionic compounds and its controlling infl uence on physical and chemical properties is one of the fundamental scientifi c problems in physical chemistry. Today the appearance of new and improvement of conventional experimental methods for studying the structure of matter and also creation of high-tech device components has permitted considerable expansion of the range of systems that can be studied, including high-temperature ionic melts. Development of methodological approaches has led to a signifi cant increase in the amount of information that can be extracted and an increase in the reliability of this information. Raman spectroscopy is a physical method for investigation of matter which, based on recorded vibrational spectra of the analyte system, allows us to carry out structural analysis, to determine the vibrational frequencies, and to calculate force constants and the moment of inertia of a molecule and the rates of relaxation processes. In contrast to x-ray diffraction and neutron diffraction methods, determining the structure of materials (the symmetry type, the interatomic distances, the coordination numbers), the Raman spectroscopy method allows us to obtain a much greater amount of information: the recorded vibrational frequencies correspond to the position of the vibrational levels in the molecule, the width of the vibrational bands contain information about its rotational motion, and the intensity of the Raman spectra directly determines the bond ionicity or covalency (1, 2). Today a methodological approach has been developed that allows us, from analysis of the contour of the vibrational bands and the width of their isotropic and anisotropic components, to obtain important information about the dynamics of the particles in the picosecond time range (1-4). It has been shown (4) that information about relaxation processes can be obtained by calculating the temporal correlation functions, the vibrational and orientational relaxation times for the structural units. Unique information on estimation of the moments of inertia of particles, which is practically inaccessible by other methods for studying the condensed state of matter and which can be obtained only using high-resolution rotational spectra of gas molecules, can be extracted by analyzing the shape of the contour of vibrational bands using the spectral moments method (4). According to this method, the moment of inertia can be calculated from the equation (3): I = 6kT/4π 2 c 2 Mor(2),