An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Theoretical Analysis of a New Artificial Plastic Hinge at the Frame Beam End

Opening horizontal slit in the middle web of the beam end formed a new type of artificial plastic hinge. The calculation formulas about the hinge’s interior force and bearing capacity are set up. Based on these, the condition of transfer, the location of crack and the cracking length of the artificial plastic hinge were studied further. The calculation method for the ductility factor was also presented. The calculation results and the test ones were compatible.

Influence of Confined Concrete Models on the Seismic Response of RC Frames

In this study, the influence of confined concrete models on the response of reinforced concrete structures is investigatedat member and global system levels. The commonly encountered concrete models such as Modified Kent-Park, Saatçioğlu-Razvi, and Mander are considered. Two moment-resisting frames designed according to thepre-modern code are taken into consideration to reflect the example of an RC moment-resisting frame in thecurrent building stock. The building is in an earthquake-prone zone located on Z3 Soil Type. The inelasticresponse of the building frame is modelled by considering the plastic hinges formed on each beam and columnelement for different concrete classes and stirrups spacings. The models are subjected to non-linear static analyses.The differences between confined concrete models are comparatively investigated at both reinforced concretemember and system levels. Based on the results of the comparative analysis, it is revealed that the column behaviouris mostly influenced by the choice of model, due to axial loads and confinement effects, while the beams areless affected, and also it is observed that the differences exhibited in the moment-curvature response of columncross-sections do not significantly affect the overall behaviour of the global system. This highlights the critical roleof model selection relative to the concrete strength and stirrup spacing of the member.

Theoretical and numerical study on reinforcing effect of rock-bolt through composite soft rock-mass

Anchoring mechanism and failure characteristics of composite soft rock with weak interface usually exhibit remarkable difference from those in single rock mass.In order to fully understand the reinforcement mechanism of composite soft roof in western mining area of China,a mechanical model of composite soft rock with weak interface and rock bolt which considering the transverse shear sliding between different rock layers was established firstly.The anchoring effect was quantified by a factor defined as anchoring effect coefficient and its evolution equation was further deduced based on the deformation relationship and homogenized distribution assumption of stress acting on composite structure.Meanwhile,the numerical simulation model of composite soft rock with shear joint was prompted by finite element method.Then detailed analysis were carried out for the deformation features,stress distribution and failure behavior of rock mass and rock bolt near the joint under transverse load.The theoretical result indicates that the anchoring effect of rock-bolt through weak joint changes with the working status of rock mass and closely relates with the physical and geometric parameters of rock mass and rock bolt.From the numerical results,the bending deformation of rock bolt accurately characterized by Doseresp model is mainly concentrated between two plastic hinges near the shear joint.The maximum tensile and compression stresses distribute in the plastic hinge.However,the maximum shear stress appears at the positions of joint surface.The failure zones of composite rock are produced firstly at the joint surface due to the reaction of rock bolt.The above results laid a theoretical and computational foundation for further study of anchorage failure in composite soft rock.

Mechanism of improving ductility of high strength concrete T-section beam confined by CFRP sheet subjected to flexural loading

For the purpose of inventing a new seismic retrofitting method for the reinforced high strength concrete （HSC） T-section beam using carbon fiber reinforced polymer （CFRP） sheet, three series, a total of twelve T-section beams with nine specimens confined by CFRP sheet in the plastic zone and three control beams were conducted up to failure under four-point bending test. The effectiveness of confining CFRP sheet on improving the flexural ductility of tmstrengthened T-section beams was studied. The parameters such as the width and the thickness of CFRP sheet and the type of T-section were analyzed. The experimental results show that ductility and rotation capacity of plastic hinge can be improved by the confinement of CFRP sheet, and the ductility indices increase with the increment of width and thickness of CFRP sheet. A plastic rotation model considering the width of CFRP sheet and the effect of flange of T-section beam is proposed on the basis of the model of BAKER, and the test results show a good agreement with the perdicted results. The relevant construction suggestions for seismic retrofitting design of beam-slabs system in cast-in-place framework structure are presented.

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

Since most current seismic capacity evaluations of reinforced concrete （RC） frame structures are implemented by either static pushover analysis （PA） or dynamic time history analysis, with diverse settings of the plastic hinges （PHs） on such main structural components as columns, beams and walls, the complex behavior of shear failure at beam-column joints （BCJs） during major earthquakes is commonly neglected. This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures. Based on the specifications of FEMA-356, a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established, allowing a sophisticated PA to be performed. To verify the validity of this method, the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements. By considering shear failure at BCJs, the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames, including seismic capacity and the progressive failure sequence of joints, in a precise and effective manner.

Simplified Calculation Methods for All-Vertical-Piled Wharf in Offshore Deep Water

All-vertical-piled wharf is a kind of high-piled wharf, but it is extremely different from the traditional ones in some aspects, such as the structural property, bearing characteristics, failure mechanism, and static or dynamic calculation methods. In this paper, the finite element method （FEM） and theoretical analysis method are combined to analyze the structural property, bearing behavior and failure mode of the all-vertical-piled wharf in offshore deep water, and to establish simplified calculation methods determining the horizontal static ultimate bearing capacity and the dynamic response for the all-vertical-piled wharf. Firstly, the bearing capability and failure mechanism for all-vertical-piled wharf are studied by use of FEM, and the failure criterion is put forward for all-vertical-piled wharf based on the ＇plastic hinge＇. According to the failure criterion and P-Y curve method, the simplified calculation method of the horizontal static ultimate bearing capacity for all-vertical-piled wharf is proposed, and it is verified that the simplified method is reasonable by comparison with the FEM. Secondly, the displacement dynamic magnification factor for the all-vertical-piled wharf under wave cyclic loads and ship impact loads is calculated by the FEM and the theory formula based on the single degree of freedom （SDOF） system. The results obtained by the two methods are in good agreement with each other, and the simplified calculation method of the displacement dynamic magnification factor for all-vertical-piled wharf under dynamic loads is proposed. Then the simplified calculation method determining the dynamic response for the all-vertical-piled wharf is proposed in combination with P-Y curve method. That is, the dynamic response of the structure can be obtained through the static calculation results of P-Y curve method multiplied by the displacement dynamic magnification factor. The feasibility of the simplified dynamic response method is verified by comparison with the FEM under different conditions.

Performance-based concept on seismic evaluation of existing bridges

Conventional seismic evaluation of existing bridges explores the ability of a bridge to survive under significant earthquake excitations. This approach has several major drawbacks, such as only a single structural performance of near collapse is considered, and the simplified approach of adopting strength-based concept to indirectly estimate the nonlinear behavior of a structure lacks accuracy. As a result, performance-based concepts that include a wider variety of structural performance states of a given bridge excited by different levels of earthquake intensity is needed by the engineering community. This paper introduces an improved process for the seismic evaluation of existing bridges. The relationship between the overall structural performance and earthquakes with varying levels of peak ground acceleration （PGA） can successfully be linked. A universal perspective on the seismic evaluation of bridges over their entire life-cycle can be easily obtained to investigate multiple performance objectives. The accuracy of the proposed method, based on pushover analysis, is proven in a case study that compares the results from the proposed procedure with additional nonlinear time history analyses.

Mechanical behavior of Ti-6Al-4V lattice-walled tubes under uniaxial compression

The compression behavior of the lattice-walled tubes under variable strain rates are investigated by numerical simulation,and the stress-strain relationship of the structure under quasi-static loading is theoretically analyzed.The finite element software LS-DYNA is used to simulate the structure established by the beam element,and the critical impact velocity is obtained when the structure collapses layer by layer.According to the plastic hinge theory and considering the combined action of the beam's bending moment and axial force in the structure,the stress-strain relationship of the structure under quasi-static loading is derived and compared with the experimental results.The numerical simulation results reveal that the structure of the single-layer gradient tube(SGC)does not undergo shear deformation under quasi-static and low-speed impact.The critical speed of the gradient square tube(GS)is higher than that of a cylindrical tube.The theoretical model can correctly reflect the mechanical response of the structure under uniaxial compression.

Performance Based Seismic Design of Reinforced Concrete Building

In past two decades earthquake disasters in the world have shown that significant damage occurred even when the buildings were designed as per the conventional earthquake-resistant design philosophy (force-based approach) exposing the inability of the codes to ensure minimum performance of the structures under design earthquake. The performance based seismic design (PBSD), evaluates how the buildings are likely to perform under a design earthquake. As compared to force-based approach, PBSD provides a methodology for assessing the seismic performance of a building, ensuring life safety and minimum economic losses. The non-linear static procedures also known as pushover analysis are used to analyze the performance of structure under lateral loads. Pushover analysis gives pattern of the plastic hinge formations in structural members along with other structural parameters which directly show the performance of member after an earthquake event. In this paper, a four-storey RC building is modelled and designed as per IS 456:2000 and analyzed for life safety performance level in SAP2000 v17. Analysis is carried out as per ATC 40 to find out storey drift, pushover curve, capacity spectrum curve, performance point and plastic hinges as per FEMA 273 in SAP2000 v17. From the analysis, it is checked that the performance level of the building is as per the assumption.

Investigation of mechanical failure performance of a large-diameter shield tunnel segmental ring

The control criteria for structural deformation and the evaluation of operational safety performance for large-diameter shield tunnel segments are not yet clearly defined.To address this issue,a refined 3D finite element model was established to analyze the transverse deformation response of a large-diameter segmental ring.By analyzing the stress,deformation,and crack distribution of large-diameter segments under overload conditions,the transverse deformation of the segmental ring could be divided into four stages.The main reasons for the decrease in segmental ring stiffness were found to be the extensive development of cracks and the complete formation of four plastic hinges.The deformation control value for the large-diameter shield tunnel segment is chosen as 8%o of the segment's outer diameter,representing the transverse deformation during the formation of the first semi-plastic hinge(i.e.,the first yield point)in the structure.This control value can serve as a reinforcement standard for preventing the failure of large-diameter shield tunnel segments.The flexural bearing capacity characteristic curve of segments was used to evaluate the structural strength of a large-diameter segmental ring.It was discovered that the maximum internal force combination of the segment did not exceed the segment ultimate bearing capacity curve(SUBC).However,the combination of internal force at 9°,85°,and 161°of the joints,and their symmetrical locations about the 0°-180°axis exceeded the joint ultimate bearing capacity curve(JUBC).The results indicate that the failure of the large-diameter segment lining was mainly due to insufficient joint strength,leading to an instability failure.The findings from this study can be used to develop more effective maintenance strategies for large-diameter shield tunnel segments to ensure their long-term performance.

Predetermination of potential plastic hinges on reinforced concrete frames using GFRP reinforcement

In the past,glass fiber-reinforced polymer(GFRP)-reinforcement has been successfully applied in reinforced concrete(RC)structures where corrosion resistance,electromagnetic neutrality,or cuttability were required.Previous investigations suggest that the application of GFRP in RC structures could be advantageous in areas with seismic activity due to their high deformability and strength.However,especially the low modulus of elasticity of GFRP limited its wide application as GFRP-reinforced members usually exhibit considerably larger deformations under service loads than comparable steel-reinforced elements.To overcome the aforementioned issues,the combination of steel and GFRP reinforcement in hybrid RC sections has been investigated in the past.Based on this idea,this paper presents a novel concept for the predetermination of potential plastic hinges in RC frames using GFRP reinforcement.To analyze the efficiency of the concept,nonlinear finite element simulations were performed.The results underscore the high efficiency of hybrid steel-GFRP RC sections for predetermining potential plastic hinges on RC frames.The results also indicate that the overall seismic behavior of RC structures could be improved by means of GFRP as both the column base shear force during the seismic activity as well as the plastic deformations after the earthquake were considerably less pronounced than in the steel-reinforced reference structure.

Realization of the global yield mechanism of RC frame structures by redesigning the columns using column tree method

Global failure mechanism, i.e., the strong-column weak-beam mechanism, can provide higher total energy dissipation capacity with less ductility demand on components than other failure modes, and results in a more uniform story drift distribution and higher resistance to earthquake loads at the system level. However, the current code-based elastic design method cannot guarantee the global failure mechanism of frame structures under severe earthquakes. In this paper, a simple, but practical design procedure is proposed to ensure the global failure mechanism of reinforced concrete(RC) frame structures by redesigning the columns using the column tree method(CTM). CTM considers the yield limit state of all beams and column bases. The code-based design is firstly carried out to determine the section information of all beams and base columns. Then, the internal force demands applied on the column tree can be derived. Lastly, the column moments, shear forces and axial forces are determined according to the free-body diagram of CTM to finish the column redesign. Two RC frame structures with 6 and 12 stories are illustrated to verify the design procedure. The analytical results demonstrate the proposed approach can realize the global failure mechanism.

Theoretical investigation on the energy absorption of ellipse-shaped self-locked tubes

Self-locked energy-absorbing systems have been proposed in previous studies to overcome the limitations associated with the round-tube systems because they can prevent the lateral splash of tubes from impact loadings without any constraints.In case of self-locked systems,the ellipse-shaped self-locked tube is considered to be an optimal design when compared with the ordinary circle-shaped self-locked tubes and other shaped self-locked tubes.In this study,we aim to theoretically analyze the ellipseshaped self-locked tubes.Further,a plastic hinge model is developed to predict the force-displacement relation of the tube,which is compared with the deformation process observed in the experiment and finite element method(FEM)simulation.Using this model,the effects of tuning the geometric parameters of the tube on the energy absorption performance,including the deformation efficiency,energy absorption capacity,and effective stroke ratio,are simulated and analyzed.Finally,a guideline is provided with respect to the design of the ellipse-shaped self-locked tube in engineering applications.

Effect of RC wall on the development of plastic rotation in the beams of RC frame structures

The objective of this study is, to interpret the influence of reinforced concrete walls addition in reinforced concrete frame structures considering behavior laws that reflects the actual behavior of such structures, by means of Castem2000computer code （pushover analysis）. A finite element model is proposed in this study, using the TAKEDA modified behavior model with Timoshenko beams elements. This model is validated initially on experimental model. Then the work has focused on the behavior of a RC frame with 3 levels and three bays to better visualize the behavior of plastic hinges. Once the plastic hinge control parameters are identified （plastic rotation, ultimate curvature）, a strengthening by introduction of reinforced concrete walls （RC/wall） at the ends of the reinforced concrete frame （RC/ frame） has been performed. The results show that these RC walls significantly improve the behavior, by a relocation of efforts towards the central part of the beams.

Estimation of relations among hysteretic response measures and design parameters for RC rectangular shear walls

Seismic design of RC structures requires estimation of structural member behavioral measures as functions of design parameters. In this study, the relations among cyclic behavioral measures and design parameters have been investigated for rectangular RC shear walls using numerical simulations calibrated based on the published laboratory tests. The OpenSEES numerical simulations modeling of plastic hinge hysteretic behavior of RC shear walls and estimation of empirical relations among wall hysteretic indices and design parameters are presented. The principal design parameters considered were wall dimensions, axial force, reinforcement ratios, and end-element design parameters. The estimated hysteretic response measures are wall effective stiffness, yield and ultimate curvatures, plastic moment capacity, yield and ultimate displacements, flexural shear capacity, and dissipated energy. Using results of numerous analyses, the empirical relations among wall cyclic behavioral measures and design parameters are developed and their accuracy is investigated.