| In high-rise buildings with coupled shear walls or core tubes,coupling beams play a role in transmitting forces and dissipating seismic energy,and its stiffness,strength and ductility have an important impact on the seismic performance of structures.In the design process of practical buildings,coupling beams with small span-to-depth ratio are widely used due to the limitation of the size of the openings and the requirement of structural rigidity.The nominal shear stress of the beam is large,which is prone to brittle failure.Conventionally reinforced concrete coupling beams are susceptible to diagonal tension failure or sliding shear failure under earthquake,which are brittle and should be inhibited to satisfy the requirement of seismic performance.Diagonally reinforced concrete coupling beams have good ductility due to the shear resistance of diagonal bars,however,substantial reinforcement detailing is required in the beam,which may lead to bars congestion problems and construction difficulties.Moreover,the requirement on the width of the beam is large.In order to improve the seismic performance of coupling beam with small span-todepth ratio,engineered cementitious composites(ECC),which is a high toughness composite material with pseudo strain hardening behavior and multiple cracking characteristics,can be used to replace conventional concrete.Compared with ordinary concrete,ECC has a higher shear capacity,which can reduce the amount of diagonal bars.The end of the diagonal bars can be bent horizontally and extended into the wall pier,which is beneficial to assembly construction.The quasi-static tests of 8 ECC coupling beam and 1 ordinary concrete coupling beam specimens with small aspect ratio were carried out.Through theoretical analysis,experimental research and numerical simulation,the seismic performance and post-earthquake resilience of ECC coupling beams were investigated.This paper has made the following works:(1)A cursory method for estimating the maximum rotational demand of coupling beam under earthquake was proposed in this study.Firstly,according to the seismic fortification intensity,site classification and design seismic grouping of a building,the displacement response spectrum(DRS)can be obtained.Secondly,the formula for calculating the maximum inter-story drift was proposed combined with the earthquake response analysis of 12 buildings.Finally,42 structural models were designed according to modern Chinese codes via changing the span-to-depth ratio of the coupling beam and the height of the wall.Analysis results indicated that the relationship between the maximum rotation of coupling beam and the span-to-depth ratio shows the quadratic polynomial,while the maximum rotation with the ratio of the distance between the wall centroids to the beam span shows the linear relationship.A formula for calculating the maximum rotational demand of coupling beam is proposed.Four practical buildings were selected to verify the proposed method,calculated results showed that the proposed formula have high accuracy calculation of the rotation demand of the beam.(2)The experimental data of 41 shear-critical conventionally reinforced concrete coupling beams and 41 shear-critical diagonally reinforced concrete coupling beams were collected and the database of the coupling beams with small span-to-depth ratio was established.Based on the trussarch model and considering the compatibility between the deformation of the truss model and the arch model,as well as the influence of ductility on the shear capacity,the formulas for calculating the shear capacity of conventionally reinforced concrete coupling beams and diagonally reinforced concrete coupling beams are proposed,respectively.Based on the database,considering the influence of the longitudinal reinforcement characteristic values,the stirrup characteristic values,aspect ratio of the beam and the diagonal reinforcement characteristic values,two formulas were proposed for predicting the ultimate drift of conventionally reinforced concrete coupling beams and diagonally reinforced concrete coupling beams,respectively.Moreover,the restoring force models of the two types of coupling beams were proposed and validated,respectively,which provide a basis for seismic performance design of concrete coupling beams.(3)The pseudo-static tests of seven diagonally reinforced ECC beams,one ordinary reinforced ECC beams and one diagonal reinforced concrete coupling beams were carried out.The variable parameters were stirrup ratio,diagonal reinforcement ratio,types of layout of reinforcement,material of matrix,types of fibers and connection mode between the coupling beam and the wall pier.The seismic performance of the coupling beam,such as failure mode,hysteresis curve,displacement ductility,stiffness degradation and energy dissipation capacity were analyzed.Results showed that with the increase of stirrup ratio and diagonal reinforcement ratio,the shear capacity and ductility of the coupling beam increase gradually.Compared with the concrete coupling beam,the use of ECC in the matrix can improve the shear capacity and ductility of the beam,reduce the damage to the beam,which is easy to repair after earthquake.Compared with PVA fibers,using PE fibers as matrix materials can improve the strength,stiffness,ductility and energy dissipation capacity of coupling beam,reduce the amount of diagonal bars,and facilitate assembly construction.Diagonally reinforced ECC beams have higher shear capacity,ductility and energy dissipation capacity compared with conventionally reinforced ECC beams.The seismic performance of the coupling beam,which is connected to the wall piers with grouting sleeves,is excellent.It should be pointed out that the U-shaped reinforcement is needed to be added at the interface of the beam and the wall pier to improve the connection performance.(4)The averaged principal stress-strain relationships in the MCFT and local stress conditions at crack locations for ECC were modified based on the characteristics of ECC.When the coupling beam cracks,the fiber bridging action on the crack plane is considered.Considering the arch effect and the compatibility deformation between the truss model and the arch model,the formula for calculating the shear capacity of conventionally reinforced ECC coupling beam is proposed.Based on the softened strut-and-tie model,a theoretical model was proposed to predict the skeleton curve of restoring force model of diagonally reinforced ECC coupling beam.The proposed model is composed of the diagonal ECC strut-and-tie,diagonal reinforcement and sub-struts contributed by the longitudinal reinforcement and stirrups.Furthermore,the effects of confinement of stirrups and softening for ECC were considered.18 diagonally reinforced ECC coupling beam specimens were selected to validate the proposed model.Results indicated that the predicted results are in good agreement with the experimental results.Then,a formula for calculating the shear capacity of the diagonally reinforced ECC coupling beam was proposed.Based on the calculation results,the variation of the shear forces of diagonal ECC strut-and-tie,diagonal reinforcement and substruts with the span-to-depth ratio of the coupling beeam is given.(5)A shear hinge restoring force model of diagonally reinforced ECC coupling beam is proposed.The hysteretic curve of the beam is simulated and results indicated that the simulation results are in good agreement with the experimental results.The effects of four different types of diagonally reinforced concrete coupling beams,steel coupling beams,steel reinforced concrete coupling beams and diagonally reinforced ECC coupling beams on the seismic performance of shear wall structures under strong earthquakes were studied.Based on the test data of 40 conventionally reinforced concrete coupling beams,40 diagonally reinforced concrete coupling beams,16 diagonally reinforced ECC coupling beams and 40 concrete shear walls,the corresponding test databases are established,respectively.The vulnerability of the beams and walls were analyzed by Monte Carlo simulation.The fragility curves and repair measures corresponding to different damage states are given respectively.Based on the fragility curves,the damage state of the coupling beams and shear walls are evaluated and the repair measures are given.(6)Based on the FEMA P-58,the post-earthquake repairability of three shear wall structures with conventionally reinforced concrete coupling beams,diagonal reinforced concrete coupling beams and diagonal reinforced ECC coupling beams is quantitatively evaluated.The performance models of three structures are established,and the elastic-plastic time history analysis of three structures under strong earthquakes are carried out to obtain their seismic responses.Incremental dynamic analysis(IDA)is used to analyze the collapse resistance of the three structures,and the collapse fragility curves of the three structures are given respectively.The post-earthquake resilience of the three structures are calculated and analyzed by using the PACT software,which is a performance evaluation tool.Results showed that the damage mainly occur in the top and middle floors.The use of ECC coupling beam in the structure can greatly reduce the repair cost,repair time,and casualties.The resilience of structure can be significantly improved after earthquake.(7)A design method for the diagonally reinforced ECC coupling beam based on postearthquake repair is proposed.In the design process,the coupled shear wall is considered to be plastic.According to the fragility curve of the coupling beam,the ECC coupling beam is in the repairable state when the shear wall structure reaches the target drift.The coupling beam yields first,and then the bottom of the wall pier yields.The distribution of base shear force and lateral force are obtained by energy method,and the influence of higher modes is considered.The coupling beams and wall piers are designed in the plastic stage.According to the layout of the reinforcement,the ultimate rotational capacity of the beam can be obtained.When the rotational demand of the ECC coupling beam is less than the rotational capacity,the structural design is considered to meet the requirements.Finally,a shear wall model is selected to verify the reliability of the proposed method. |
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