Prediction of Flexural Deformation of Reinforcement Concrete Beams with Polynomial Tension Stiffening Model

Based on an assumption of parabolic bond stress distribution,a simplified model with quartic polynomial function of the relative slip of steel bar and surrounding concrete for reinforced concrete (RC)tensile member was proposed. The post-cracking behavior as well as tension stiffening effect was considered in the new model. The relative slip of bending member could also be determined through the extension of the new model,which could be applied to obtaining the concentrated rotations at certain sections in order to predict the flexural deformation of RC beam. Several examples of four-point bending RC beams were approached to verify the new model,and the predictions of the flexural deflections of RC beams agreed well with experimental results. The new model can be extended to the application of partially corroded RC beam.

Analysis model for damage of reinforced bars in RC beams under contact explosion

The load-bearing capacity of reinforced concrete(RC) beams primarily relies on internal reinforced bars.However, limited research has been conducted on the dynamic response of these bars. To address this gap, this study has established an analytical model using dimensional analysis for calculating the deformation of reinforced bars within RC beams subjected to contact explosion. Comparison with experimental data reveals that the model has a relative error of 5.22%, effectively reflecting the deformation of reinforced bars. Additionally, based on this model, the study found that while concrete does influence the deformation of reinforced bars, this influence can be disregarded in comparison to the material properties of the bars themselves. The findings of this study have implications for calculating the residual load-bearing capacity of damaged RC beams, evaluating the extent of damage to RC beams after blast loading, and providing guidance for the blast-resistant design of RC structures.

Preparation and Reinforcement Adaptability of Jute Fiber Reinforced Magnesium Phosphate Cement Based Composite Materials

To improve the brittleness characteristics of magnesium phosphate cement-based materials(MPC)and to promote its promotion and application in the field of structural reinforcement and repair,this study aimed to increase the toughness of MPC by adding jute fiber,explore the effects of different amounts of jute fiber on the working and mechanical properties of MPC,and prepare jute fiber reinforced magnesium phosphate cement-based materials(JFRMPC)to reinforce damaged beams.The improvement effect of beam performance before and after reinforcement was compared,and the strengthening and toughening mechanisms of jute fiber on MPC were explored through microscopic analysis.The experimental results show that,as the content of jute fiber(JF)increases,the fluidity and setting time of MPC decrease continuously;When the content of jute fiber is 0.8%,the compressive strength,flexural strength,and bonding strength of MPC at 28 days reach their maximum values,which are increased by 18.0%,20.5%,and 22.6%compared to those of M0,respectively.The beam strengthened with JFRMPC can withstand greater deformation,with a deflection of 2.3 times that of the unreinforced beam at failure.The strain of the steel bar is greatly reduced,and the initial crack and failure loads of the reinforced beam are increased by 192.1%and 16.1%,respectively,compared to those of the unreinforced beam.The JF added to the MPC matrix dissipates energy through tensile fracture and debonding pull-out,slowing down stress concentration and inhibiting the free development of cracks in the matrix,enabling JFRMPC to exhibit higher strength and better toughness.The JF does not cause the hydration of MPC to generate new compounds but reduces the amount of hydration products generated.

Strengthening effects of BFRP on reinforced concrete beams

Reinforced concrete （RC） beams externally bonded with basalt fiber reinforced polymer （BFRP） are experimentally investigated by using different numbers of bonding plies, transverse anchorages as well as the initial conditions of strengthened beams. The performances of the BFRP strengthening are compared with those of the carbon fiber reinforced polymer （CFRP） and the glass fiber reinforced polymer （GFRP） under the same experimental condition. Experimental results indicate that the strength and ductility of the strengthened beam with two plies of the BFRP are improved remarkably than those with one ply. The strengthening effects of the BFRP lie between those of the CFRP and the GFRP. The BFRP strengthening is little influenced by pre-cracks of concrete. Most failures are caused by interfaciai debonding induced by flexural cracks in the experiment. Clamping of Uwraps along the whole beam is less efficient than endpoint anchorage for increasing the ultimate load of the strengthened beam. Finally, the models suggested by the five guidelines for predicting the debonding strain of the CFRP are extended to the BFRP and the conservative estimates of the debonding strain of the BFRP are given as well.

Durability of concrete beams reinforced with CFRP sheet under wet-dry cycles and loading

The test results of eight concrete beams reinforced with carbon fiber reinforced polymer （CFRP） sheets subjected to an aggressive environment under a sustained load are presented. The beams are 1 700 mm long with a rectangular cross-section of 120- mm width and 200-mm depth. The beams are precracked with a four-point flexural load, bonded CFRP sheets, and placed into wet-dry saline water（ NaCl） either in an unstressed state or loaded to about 30% or 60% of the initial ultimate load. The individual and coupled effects of wet-dry saline water and sustained bending stresses on the long term behaviour of concrete beams reinforced with the CFRP are investigated. The test results show that the coupled action of wet-dry saline water and sustained bending stresses appears to significantly affect the load capacity and the failure mode of beam strengthened with CFRP, mainly due to the degradation of the bond between CFRP and concrete. However, the stiffness is not affected by the coupled action of wet-dry cycles and a sustained load.

Behavior of interfacial stresses between RC beams and GFRP sheets

Seven reinforced concrete （RC） beams with epoxy-bonded glass fiber reinforced plastic （GFRP） sheets and two control RC beams were experimentally tested to investigate the bond behavior of the interfaces between RC beams and GFRP sheets. The variable parameters considered in test beams are the layers of GFRP sheets, the bond lengths and the reinforcement ratios. The results indicate that the flexural strength of the repaired beams is increased, but the ultimate load of beams with GFRP sheets debonding failure is reduced relatively. The bond length is the main factor that results in bonding failure of the strengthened beams. An experimental method of interfacial shear stress is proposed to analyze the distribution of shear stress according to experimental results. The analytical method of shear and normal stresses and a simple equation are proposed to predict the peeling loads. The proposed model is applied to experimental beams. The analytical results show a good agreement with the experimental results.

Flexural behaviors of FRP strengthened corroded RC beams

The flexural behavior of eight FRP （ fiber reinforced polymer） strengthened RC （reinforced concrete） beams with different steel corrosion rates are numerically studied by Ansys finite element software. The influences of the corrosion rate on crack pattern, failure mechanism, ultimate strength, ductility and deformation capacity are also analyzed. Modeling results show that the beams with low corrosion rates fail by the crushing of the concrete in the compression zone. For the beams with medium corrosion rates, the bond slip between the concrete and the longitudinal reinforcement occurs after steel yielding, and the beams finally fail by the debonding of the FRP plates. For the beams with high corrosion rates, the bond slip occurs before steel yielding, and the beams finally fail by the crushing of the concrete in the compression zone. The higher the corrosion rates of the longitudinal reinforcement, the more the carrying capacity of FRP strengthened RC beams reduces. The carrying capacity of RCB-1 （the corrosion rate is 0） is 115 kN, and the carrying capacity of RCB-7 （the corrosion rate is 20% ） is 42 kN. The deformation capacity of FRP strengthened corroded RC beams is higher than that of FRP strengthened uucorroded RC beams. The ultimate deflection of RCB-1 and RCB-7 are 20 mm and 35 nun, respectively, and the ultimate deflection of RCB-5 （the corrosion rate is 10% ） reaches 60 ilUn.

Comparison study on calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949

In order to study the calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949, tests on the mechanical performance of 66 rebars from different modem Chinese concrete buildings, the concrete compressive strength of 12 modem Chinese concrete buildings, and the concrete cover thickness of 9 modem Chinese concrete buildings are carried out; and the actual material properties and structural conformations of modem Chinese concrete buildings are obtained. Then, the comparison on calculation methods of bending behavior including the original Chinese calculation method, the present Chinese calculation method, the present American calculation method and the present European calculation method is studied. The results show that the original Chinese calculation method of bending behavior is based on the allowable stress calculation method, and the design safety factors are 3.55 to 4. 0. In term of the calculation area of longitudinal rebars of reinforced concrete beams, without considering earthquake action, the original Chinese structural calculation method is safer than the present Chinese structural calculation method, the present European structural calculation method, and the present American structural calculation method. The results can provide support for the structural safety assessments of modem Chinese reinforced concrete buildings.

Experimental study and analysis on fatigue stiffness of RC beams strengthened with CFRP and steel plate

The objective of this work is to investigate the fatigue behavior of reinforced concrete(RC) beams strengthened with externally bonded carbon fiber reinforced polymer(CFRP) and steel plate. An experimental investigation and theoretical analysis were made on the law of deflection development and stiffness degradation, as well as the influence of fatigue load ranges. Test results indicate that the law of three-stage change under fatigue loading is followed by both midspan deflection and permanent deflection, which also have positive correlation with fatigue load amplitude. Fatigue stiffness of composite strengthened beams degrades gradually with the increasing of number of cycles. Based on the experimental results, a theoretical model by effective moment of inertia method is developed for calculating the sectional stiffness of such composite strengthened beams under fatigue loading, and the calculated results are in good agreement with the experimental results.

Research on Flexural Behavior of Coral Aggregate Reinforced Concrete Beams

Through the flexural behavior test of coral aggregate reinforced concrete beams(CARCB) and ordinary Portland reinforced concrete beams(OPRCB), and based on the parameters of concrete types, concrete strength grades and reinforcement ratios, the crack development, failure mode, midspan deflection and flexural capacity were studied, the relationships of bending moment-midspan deflection, load-longitudinal tensile reinforcement strain, load-maximum crack width were established, and a calculation model for the flexural capacity of CARCB was suggested. The results showed that with the increase in the reinforcement ratio and concrete strength grade, the crack bending moment(Mcr)and ultimate bending moment(Mu) of CARCB gradually increased. The characteristics of CARCB and OPRCB are basically the same. Furthermore, through increasing the concrete strength grade and reinforcement ratio, Mcr/Mu could be increased to delay the cracking of CARCB. As the load increased, crack width(w) would also increase. At the beginning of the loading, w increased slowly. And then it increased rapidly when the load reached to the ultimate load, which then led to beam failure. Meanwhile, with a comprehensive consideration of the effects of steel corrosion on the loss of steel section and the decrease of steel yield strength, a more reasonable calculation model for the flexural capacity of CARCB was proposed.

Flexural behavior of reinforced concrete beams with high performance fiber reinforced cementitious composites

This article presents an experimental study on the flexural performance of reinforced concrete(RC)beams with fiber reinforced cementitious composites(FRCC)and hybrid fiber reinforced cementitious composites(HFRCC)in the hinge portion.Beam specimens with moderate confinement were used in the study and tested under monotonic loading.Seven diverse types of FRCC including hybrid composites using fibers in different profiles and in different volumes are employed in this study.Companion specimens such as cylindrical specimens and prism specimens are also used to study the physical properties of composites employed.The moment?curvature,stiffness behavior,ductility,crack pattern and modified flexural damage ratio are the main factors considered in this study to observe the efficacy of the employed hybrid composites.The experimental outputs demonstrate the improved post yield behavior with less rate of stiffness degradation and better damage tolerance capacity than conventional technique.

Prediction of Load Carrying Capacity of Corroded Reinforced Concrete Beam

A novel method for prediction of the load carrying capacity of a corroded reinforced concrete beam (CRCB) is presented in the paper. Nine reinforced concrete beams, which had been working in an aggressive environment for more than 10 years, were tested in the laboratory. Comprehensive tests, including flexural test, strength test for corroded concrete and rusty rebar, and pullout test for bond strength between concrete and rebar, were conducted. ne flexural test results of CRCBs reveal that the distribution of surface cracks on the beams shows a fractal behavior. The relationship between the fractal dimensions and mechanical properties of CRCBs is then studied. A prediction model based on artificial neural network (ANN) is established by the use of the fractal dimension as the corrosion index, together with the basic information of the beam. The validity of the prediction model is demonstrated through the experimental data, and satisfactory results are achieved.

Stress redistribution of simply supported reinforced concrete beams under fire conditions

This study presents experimental and numerical investigations of simply supported steel reinforced concrete(RC)beams under fire.The temperature field of cross sections,the vertical deflection at mid-span,and specifically the axial expansion displacement at beam-ends were measured during the fire tests.A novel finite element(FE)model of a RC beam under fire was developed,in which the water loss in the heat transfer analysis and the concrete transient strain in the mechanical analysis were considered.Based on the validated FE model proposed in this study,parametric studies were conducted to investigate the effects of the beam type,the protective layer thickness,and the load ratio on the thermal and mechanical behavior of simply supported RC beams.It was found that greater fire resistance and fire performance of girder beams in comparison to secondary beams contributed to the non-structural reinforcements,which effectively compensated for the reduced tensile capacities of structural reinforcements because of the degradation of the material properties.In addition,the history of normal stress distributions of concrete under fire can be divided into three phases:expansion,stress redistribution and plateau phases.

Experimental research on refractory performance of reinforced concrete beams strengthened with CFRP sheets bonded with an inorganic adhesive

To meet the requirement of fire endurance for concrete structures strengthened with CFRP sheets, this study develops an inorganic adhesive whose strength at 600 ℃ is not lower than that at normal room temperature. The inorganic adhesive is then used to bond CFRP sheets on reinforced concrete beams in order to strengthen them. The fire protection of the CFRP sheets is done using the thick-type fireproofing coatings for tunnel ( TFCT) and steel structure ( TFCSS) respectively. Four specimens are tested in the furnace together. Specimens are exposed to fire for 1. 5 h in according to the ISO834 standard fire curve,and then naturally cooled for 1 h. In the tests,the largest displacements at the mid-span positions of specimens are only from 1 /1400 to 1 /318 of actual span corresponding to the highest temperatures from 300 ℃ to 470 ℃. After the specimens are naturally cooled to the normal temperature and the fireproofing coatings are then removed,it can be seen that the CFRP sheets keep in a good state,which indicates that CFRP sheets can be tightly bonded on the concrete and work well together with the concrete beams during and after fire. Besides,the tests also verify that the fire performance of TFCT is superior to TFCSS for the strengthened beams.

Comparison on construction of strut-and-tie models for reinforced concrete deep beams

With consideration of the differences between concrete and steel,three solutions using genetic evolutionary structural optimization algorithm were presented to automatically develop optimal strut-and-tie model for deep beams.In the finite element analysis of the first method,the concrete and steel rebar are modeled by a plane element and a bar element,respectively.In the second method,the concrete and steel are assigned to two different plane elements,whereas in the third method only one kind of plane element is used with no consideration of the differences of the two materials.A simply supported beam under two point loads was presented as an example to verify the validity of the three proposed methods.The results indicates that all the three methods can generate optimal strut-and-tie models and the third algorithm has powerful capability in searching more optimal results with less computational effort.The effectiveness of the proposed algorithm III has also been demonstrated by other two examples.

Performance of Epoxy-Repaired Corroded Reinforced Concrete Beams

Reinforcement corrosion has a serious impact on the durability and safety of reinforced concrete structures.Six reinforced concrete(RC)beam specimens are constructed.After beam specimens are subjected to accelerated corrosion with the constant current,beam specimens are repaired with epoxy mortar and the flexural test of beams is investigated.Then the behaviors of repaired corroded reinforced concrete beams are evaluated.The experimental results show that cracking and ultimate loads of corroded RC beams are enhanced after being repaired.And the strain distributions measured across sections of beam specimens still obey the assumption of plane section.After being repaired,the number of cracks decreases and the crack spacing increases.

Experimental Study on the Static and Fatigue Performance of Corroded RC Beams Strengthened with AFRP Sheets

In order to research the strengthening effects of aramid fiber reinforced polymer （AFRP） sheets on the flexural performance of corroded reinforced concrete （RC） beams, the static and fatigue performance of corroded RC beams strengthened with non-prestressed AFRP sheets under different degrees of corrosion （minor： reinforcement mass loss is 2.0%, medium： reinforcement mass loss is 6.0%） have been researched experimentally in this paper, to compare with that of the control beams （un-strengthened and un-corroded） and un-strengthened corroded beams, and additionally compare with fatigue performance of those medium corroded RC beams strengthened with prestressed AFRP sheets with permanent anchors. The results show that, （1） compared with un-strengthened corroded beams under the same degrees of corrosion, the cracking, yield and ultimate monotonic loads of the minor corroded RC beam strengthened with non-prestressed AFRP sheets is respectively increased by 20%, 27% and 60%, whereas for the medium corroded RC beam strengthened with non-prestressed AFRP sheets increased by 15%, 36% and 83% respectively. The ultimate deflection of the medium corroded beam strengthened with non-prestressed AFRP sheets is 166% larger than that of the corroded un-strengthened beam under the monotonic load. （2） The fatigue life of the non-prestressed AFRP strengthened medium corroded beam is 10.4 times more than that of the un-strengthened corroded beam, but lower than that of the unstrengthened-uncorroded （virgin） beam. （3） Fatigue experiments of the beams strengthened with prestressed AFRP sheets and with those non-prestressed AFRP sheets show that the fatigue life of the retrofit RC beams increase with increasing prestress level of AFRP sheets.（4） The use of AFRP sheets for strengthening corroded RC beams is an efficient technique that can maintain the structural integrity and enhance the structural behavior of such beams.

Modeling the Flexural Carrying Capacity of Corroded RC Beam

Considering the change of bond strength between corroded steel and concrete,flexural carrying ca- pacity of corroded reinforced concrete (RC) beam was calculated.On the basis of the condition of equilibrium of forces and compatibility of deformations for the whole beam,a model for the prediction of flexural carrying capacity of the corroded RC beam was proposed.Comparison of the model's predictions with the experimental results published in the literature shows the practicality of the proposed method.

Long term behavior of self-compacting reinforced concrete beams

Tests were carried out on 8 self-compacting reinforced concrete(SCC) beams and 4 normal reinforced concrete beams. The effects of mode of consolidation,load level,reinforcing ratio and structural type on long term behavior of SCC were investigated. Under the same environmental conditions,the shrinkage-time curve of self-compacting concrete beam is very similar to that of normal concrete beam. For both self-compacting reinforced concrete beams and normal reinforced concrete beams,the rate of shrinkage at early stages is higher,the shrinkage strain at 2 months is about 60% of the maximum value at one year. The shrinkage strain of self-compacting reinforced concrete beam after one year is about 450×10-6. Creep deflection of self-compacting reinforced concrete beam decreases as the tensile reinforcing ratio increases. The deflection creep coefficient of self-compacting reinforced concrete beam after one and a half year is about 1.6,which is very close to that of normal reinforced concrete beams cast with vibration. Extra cautions considering shrinkage and creep behavior are not needed for the use of SCC in engineering practices.

Lagged strain of laminates in RC beams strengthened with fiber-reinforced polymer

Based on the theory of concrete structure, a new expression was derived for lagged strain of fiber-reinforced polymer （FLIP） laminates in reinforced concrete （RC） beams strengthened with FRP. The influence of different preloaded states and nonlinear stress-strain relationship of compressed concrete were both taken into account in this approach. Then a simplified expression was given by ignoring tensile resistance of concrete. Comparison of analytical predictions with experimental results indicates satisfactory accuracy of the procedures. The errors are less than 8% and 10% respectively when the tensile resistance of concrete is or not considered. While the maximum error of existing procedures is up to 60%.