The coupling effect of axial motion and joint mass on the lateral vibrations of a rigid-jointed triangular frame

In this investigation, the coupling effects of the axial motion and other parameters on the bending eigenfrequencies and eigenmodes of laterally vibrating frames are re-examined. To this end an energy variational approach is performed on a rigid-jointed triangular frame, whose joint mass is eccentrically located with respect to its theoretical position. The governing partial differential equations subject to the appropriate boundary conditions are very conveniently formulated and successfully solved in a closed form by using generalized functions and Laplace transforms. Contrary to the usual assumptions of the standard dynamic analysis of continuous systems, herein the effect of axial contraction and extension is accounted for when establishing the translational kinematic boundary conditions. This may lead to considerable discrepancies that reveal the decisive role of the axial motion effect on the dynamic response of framed structures. Such discrepancies are clearly confirmed through a thorough numerical discussion of the governing parameters: joint mass and its rotatory inertia, joint angle, positioning of the mass, slenderness ratios, stiffness and length ratios.     

Reinforced concrete beam–column joints with crossed inclined bars under cyclic deformations

This experimental study investigates the effectiveness of crossed inclined bars (X‐bars) as joint shear reinforcement in exterior reinforced concrete beam–column connections under cyclic deformations. Test results of 20 joint subassemblages with various reinforcement ratios and arrangements including X‐bars in the joint area are presented. The X‐type, non‐conventional reinforcement is examined as the only joint reinforcement and in combination with common stirrups or vertical bars. The experimental results reported herein include full loading cycle curves, energy dissipation values and a categorization of the observed damage modes. Based on the comparisons between the overall hysteretic responses of the tested specimens, it is deduced that joints with X‐bars exhibited enhanced cyclic performance and improved damage mode since a distinct flexural hinge was developed in the beam–joint interface. Further, the combination of crossed inclined bars and stirrups in joint area resulted in enhanced hysteretic response and excellent performance capabilities of the specimens. However, in some specimens with X‐bars as the only joint shear reinforcement, the deformations of the bent anchorage of the beam's bars caused considerable damages at the back of the joint area. Discussion for a potential replacement of the joint stirrups with X‐type reinforcement in some cases of exterior joints is also included. Copyright © 2008 John Wiley & Sons, Ltd.     

Modified fish-bone model: A simplified MDOF model for simulation of seismic responses of moment resisting frames

This paper presents a simplified Multi-Degree-Of-Freedom (MDOF) model through modification of fish-bone model (or generic frame). Modified Fish-Bone (MFB) model is developed through three enhancements: (i) the moment of inertia for half-beams is reduced slightly to modify the assumption of equal rotation at each story joints, (ii) a number of truss elements are inserted to the fish-bone model to simulate flexural deformation of moment frames due to axial elongation and contraction of columns, and (iii) moment–rotation relationship of representative rotational springs is supposed to be bilinear instead of trilinear in order to consider simultaneous yielding at both ends of the beam in moment frames. The proposed model is evaluated with respect to nonlinear dynamic analysis results of three classic moment resisting frames subjected to 94 records of FEMA-440 ground motion data set. Moreover, the adequacy of this model is compared with the fish-bone model and two predictors of nonlinear seismic demand. The statistical study of predicted interstory drift demonstrates the superiority of the proposed model over the fish-bone model and both seismic demand predictors.     

Nonlinear modeling of cyclic response of RC beam–column joints reinforced by plain bars

Experience of previous earthquakes shows that a considerable portion of buildings reinforced with plain bars sustain relatively large damages especially at the beam–column joints where the damages are mostly caused by either diagonal shear cracks or intersectional cracks caused by bar slippage. While previous works mainly focus on shear failure mode, in this study, the emphasis is placed on slip based cracks as the dominant failure mode. A systematic procedure is introduced to predict the dominant failure mode at the joint which is based on the dimensional properties, reinforcement details, and axial and shear load at the joint. In addition, a relatively simple and efficient nonlinear model is proposed to simulate pre- and post-elastic behavior of the joints which fail under bar slippage mode. In this model, beam and column components are represented by linear elastic elements, dimensions of the joint panel are defined by rigid elements, and effect of slip is taken into account by a nonlinear rotational spring at the end of the beam. The proposed method is validated by experimental results for both internal and external joints .     

Study of seismic behavior of PHC piles with partial normal-strength deformed bars

Nine PHC piles with partial normal-strength deformed bars were prepared in present study, and cyclic loading tests were implemented to evaluate these piles’ seismic performance. The influence of the axial compression ratio and the amount of normal-strength deformed bars on failure modes, crack patterns, strength, stiffness, and ductility were examined. The test findings indicate that the change of axial compression ratio has a noticeable influence on the failure mode of PHC piles. A larger axial compression ratio results in a higher cracking bending resistance, ultimate bending resistance, and initial stiffness, but the propagation heights of flexural cracks decrease as the axial compression ratio increases. Furthermore, increasing the amount of normal-strength deformed bars causes a slight decrease in ductility. Finally, a calculation formula was proposed to predict the flexural capacity of PHC piles with partial normal-strength deformed bars.     

Uplift of deck or footings in bridges with distributed mass subjected to transverse earthquake

The eigenvalue problem is analytically formulated in symmetric bridges with distributed mass and moment of inertia under transverse earthquake. The piers are elastically supported on the ground. The deck is monolithically connected to one or two piers for all degrees of freedom and restrained or transversely free at the abutments. The characteristic equation, symmetric normal modes, modal participation factors, and participating mass ratios are given analytically. The problem is expressed in terms of few dimensionless parameters: (i) the radius of gyration of the deck mass divided by the pier height; (ii) the ratio of the rotational stiffness of a footing to that of the pier at the base; (iii) the ratio of flexural stiffness of the outer spans to those of the pier; (iv) the ratio of torsional stiffness of side spans to the rotational stiffness of the pier top; (v) for two piers, the side‐to‐central‐span ratio. Modal response spectrum analysis gives the moment at the base of the footings and the torque in the deck at its supports on the abutments as ratios to the values at incipient uplifting from the ground or the bearings. The peak ground acceleration of the motion at the onset of either one of these two types of nonlinearity is depicted as a function of the dimensionless parameters and the fundamental period of an elastic deck supported only at the abutments, or of a rigid deck on piers fixed against rotation at top and bottom. Copyright © 2015 John Wiley & Sons, Ltd.     

Research on seismic behavior and shear strength of SRHC frame columns

The seismic behavior of steel reinforced high strength and high performance concrete(SRHC)frame columns was investigated through pseudo-static experiments of 16 frame columns with various shear span ratios,axial compression ratios,concrete strengths,steel ratios and stirrup ratios.Three kinds of failure mechanisms are presented and the characteristics of experimental hysteretic curves and skeleton curves with different design parameters are discussed.The columns’ductility and energy dissipation were quantitatively evaluated based on seismic resistance.The research results indicate that SRHC frame columns can withstand extreme bearing capacity,but the abilities of ductility and energy dissipation are inferior because of SRHC’s natural brittleness.As a result,the axial load ratio should be restricted and some construction measures adopted,such as increasing the stirrup ratio.This research established effect factors on the bearing capacity of SPHC columns.Finally,an algorithm for obtaining ultimate bearing capacity using the flexural failure mode is established based on a modified planesection assumption.The authors also established equations to determine shearing baroclinic failure and shear bond failure based on the accumulation of the axial load force distribution ratio.The calculated results of shear bearing capacity for different failure modes were in good agreement with the experimental results.     

Modeling of rocking frames under seismic loading

A novel modeling approach for the seismic response assessment of rocking frames is presented. Rocking frames are systems with columns that are allowed to fully, or partially, uplift. Despite the apparent lack of a mechanism to resist lateral forces, they have a remarkable capacity against earthquake loading. Rocking frames are found in old structures, for example, ancient monuments, but it is also a promising design concept for modern structures such as bridges or buildings. The proposed modeling can be implemented in a general-purpose structural analysis software, avoiding the difficulties that come with the need of formulating and solving specifically tailored differential equations, or the use of detailed computational models. Different configurations of a rocking portal frame problem are examined. The model is based on rigid, or flexible, beam elements that describe the members of the frame. Negative-stiffness rotational springs are smartly positioned at the rocking interfaces in order to simulate the rocking restoring moment, while the mass and the rotational moment of inertia are considered either lumped or distributed. Both the cases of rigid and flexible piers/columns are discussed, while it is shown that frames with restrained columns can be considered in a straightforward manner. A simple alternative based on an equivalent oscillator that follows the generalized rocking equation of motion is also investigated. The efficiency and the accuracy of the proposed modeling is demonstrated with the aid of carefully chosen case studies.     

Dynamic Properties of Long Large Cross-section Underground Structures in Dynamic Seismic Analysis

Seismic safety of underground structures is one of the main concerns in underground space exploitation.As the first step for dynamic seismic response analysis,the free vibration of long large cross-section underground structures is studied in the present paper.The general free transverse vibration motion equation of long large cross-section underground structure is derived with the comprehensive consideration of internal and external damping,effects of shear,cross-sectional rotational inertia and axial forc...     

Seismic rotational displacement of gravity walls by pseudo-dynamic method: Passive case

Prediction of the seismic rotational displacements of retaining wall under passive condition is an important aspect of design in earthquake prone region. In this paper, the pseudo-dynamic method is used to compute the rotational displacements of rigid retaining wall supporting cohesionless backfill under seismic loading for the passive earth pressure condition. The proposed method considers time, phase difference and effect of amplification in shear and primary waves propagating through both the backfill and the retaining wall. The influence of ground motion characteristics on rotational displacement of the wall is evaluated. Also the effects of variation of parameters like wall friction angle, soil friction angle, amplification factor, shear wave velocity, primary wave velocity, period of lateral shaking, horizontal and vertical seismic accelerations on the rotational displacements are studied. The rotational displacement of the wall increases substantially with increase in amplification of both shear and primary waves, time of input motion, period of lateral shaking and decreases with increase in soil friction angle, wall friction angle. The rotational displacements of the wall also increase when the effect of wall inertia is taken into account. Results are provided in graphical form.     

长型大截面地下结构的横向自由振动方程

文中综合考虑了内阻尼、外阻尼、剪切变形、横截面转动惯性、轴力和地基模型参数的影响,推得了弹性地基梁的一般自由振动方程。由这一方程可以得到一系列特殊情况下地下结构的自由振动方程。这一方程不仅能从理论上扩展了Timoshenko粱理论,而且在后续的研究中,为研究上述因素对于地下结构的自由振动和强迫振动的影响奠定了理论基础。     

Estimation of monotonic behavior of reinforced concrete columns considering shear‐flexure‐axial load interaction

Reinforced concrete columns with insufficient transverse reinforcement and non‐seismic reinforcement details are vulnerable to brittle shear failure and to loss of axial load carrying capacity in the event of a strong earthquake. In this paper, a procedure is presented after examining the application of two macro models for displacement‐based analysis of reinforced concrete columns subjected to lateral loads. In the proposed model, lateral load‐deformation response of the column is simulated by estimating flexural and shear deformation components separately while considering their interaction and then combining these together according to a set of rules depending upon column's yield, flexural and shear strengths. In addition, lateral deformation caused by reinforcement slip in beam–column joint regions and buckling of compression bars are taken into account and considered in the analysis. Implementation of the proposed procedure produces satisfactory lateral load–displacement relationships, which are comparable with experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

Vibrations of timoshenko beam-columns on two-parameter elastic foundations

A finite element procedure is developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The governing matrix equation for small-amplitude, free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. Several numerical examples are provided to show the effects of axial force, foundation stiffness parameters, partial elastic foundation, shear deformation and rotatory inertia on the natural frequencies of the beam-column.     

基于能量合成法的塔式结构刚度识别研究

在Rayleigh能量法和Southwell＇s频率合成法的基础上,将结构的振动基频表示为由各变形元和惯性元组成的子系统频率的合成,其中变形元为结构的弯曲变形和剪切变形,惯性元为结构的分布质量和塔顶附加质量。通过选取满足边界条件的挠度函数,建立了底部固定、顶端带有附加质量的塔式结构基频与刚度的关系,因此可通过测量结构的振动基频识别出塔式结构的抗弯刚度和抗剪刚度。以某钢塔为计算实例,采用该算法推导出了结构振动基频与弹性模量的关系,只要知道截面的几何尺寸和材料性质,便可快速识别出各截面的刚度。有限元空间建模计算结果证明了本文提出的算法具有较高精度。该方法适合底部固定的塔式结构,可为复杂空间塔式结构使用状态的监测与评估提供参考。     

Seismic performance of steel reinforced ultra high-strength concrete composite frame joints

To investigate the seismic performance of a composite frame comprised of steel reinforced ultra high-strength concrete (SRUHSC) columns and steel reinforced concrete (SRC) beams, six interior frame joint specimens were designed and tested under low cyclically lateral load. The effects of the axial load ratio and volumetric stirrup ratio were studied on the characteristics of the frame joint performance including crack pattern, failure mode, ductility, energy dissipation capacity, strength degradation and rigidity degradation. It was found that all joint specimens behaved in a ductile manner with flexural-shear failure in the joint core region while plastic hinges appeared at the beam ends. The ductility and energy absorption capacity of joints increased as the axial load ratio decreased and the volumetric stirrup ratio increased. The displacement ductility coefficient and equivalent damping coefficient of the joints fell between the corresponding coefficients of the steel reinforced concrete (SRC) frame joint and RC frame joint. The axial load ratio and volumetric stirrup ratio have less influence on the strength degradation and more influence on the stiffness degradation. The stiffness of the joint degrades more significantly for a low volumetric stirrup ratio and high axial load ratio. The characteristics obtained from the SRUHSC composite frame joint specimens with better seismic performance may be a useful reference in future engineering applications.     

2D numerical investigation of segmental tunnel lining under seismic loading

Segmental tunnel linings are now often used for seismic areas. However, the influence of segment joints on the segmental lining behavior under seismic loading has not been thoroughly considered in the literature. This paper presents a numerical study, which has been performed under seismic circumstance, to investigate the factors that affect segmental tunnel lining behavior. Analyses have been carried out using a two-dimensional finite difference element model. The proposed model allows studying the effect of the rotational joint stiffness, radial stiffness and the axial stiffness of the longitudinal joints. The numerical results show that a segmental lining can perform better than a continuous lining during earthquake. It has been seen that the influence of the joint distribution, the joint rotational stiffness, the joint axial stiffness, Young׳s modulus of the ground surrounding the tunnel, the lateral earth pressure factor and the maximum shear strain should not be neglected. Some important differences of the segmental tunnel lining behavior under static and seismic conditions have been highlighted.     

大跨度空间网格结构多维多点随机地震反应分析

本文建立了三维正交地震动多点激励下大跨度空间网格结构的随机地震反应分析方法,依据现行抗震设计规范的有关规定,确定了平稳随机地震动功率谱密度的模型参数。数值仿真分析了一柱距80m的正方形平板网架分别在一维地震动或三维地震动的一致激励、行波激励和考虑部分相干效应的随机激励下的地震反应。结果表明:考虑地震动的空间效应会很大程度地改变结构杆件的内力,其中控制杆件的内力增幅达到30%;地震动的行波效应对结构杆件内力的影响比随机地震动的部分相干效应的影响更大;三维地震作用比一维地震作用下结构杆件的内力大。由此得出结论,对于大跨度空间网格结构,必须进行多维多点地震激励下的随机地震反应分析。     

Cyclic loading test of self-centering precast segmental unbonded posttensioned UHPFRC bridge columns

Three 1/3-scale precast segmental bridge columns, manufactured with ultrahigh-performance fiber-reinforced concrete (UHPFRC) incorporating river sand and coarse aggregate, were tested under cyclic loading. Energy dissipation (ED) bars, embedded in ultrahigh-performance concrete (UHPC) grout, maintained continuous across segment joints and unbonded at the bottom joint. Self-centering prestressing force was provided by unbonded posttensioning (PT) tendons. The research parameters included PT force level and the amount of ED bars. Test results showed that all the specimens exhibited no less than 8% drift capacities, which were remarked with the first fracture of ED bars. No obvious cracking and limited UHPFRC spalling were observed. Both PT force level and the amount of ED bars have notable effects on stiffness, lateral strength, and ductility. Increased PT force may improve ductility with the total axial loading ratio less than 0.08. All PT tendons were elastic and no yield or rupturing was found, but the stress loss was significant. The equivalent unbonded length can be evaluated with 0.007d_bf_y for ED bars embedded in UHPC grout. The rotation of the bottom joint dominated lateral deformation and the contribution of joint sliding can be neglected. The contribution λ_ED of ED bars to lateral strength should be no more than 25% to maintain self-centering capacity.     

Seismic performance of interior precast concrete beam-column connections with T-section steel inserts under cyclic loading

An experimental investigation was conducted to study the performance of precast beam-column concrete connections using T-section steel inserts into the concrete beam and joint core, under reversed cyclic loading. Six 2/3-scale interior beam-column subassemblies, one monolithic concrete specimen and five precast concrete specimens were tested. One precast specimen was a simple connection for a gravity load resistant design. Other precast specimens were developed with different attributes to improve their seismic performance. The test results showed that the performance of the monolithic specimen M1 represented ductile seismic behavior. Failure of columns and joints could be prevented, and the failure of the frame occurred at the flexural plastic hinge formation at the beam ends, close to the column faces. For the precast specimens, the splitting crack along the longitudinal lapped splice was a major failure. The precast P5 specimen with double steel T-section inserts showed better seismic performance compared to the other precast models. However, the dowel bars connected to the steel inserts were too short to develop a bond. The design of the precast concrete beams with lap splice is needed for longer lap lengths and should be done at the beam mid span or at the low flexural stress region.     

Effects of rotation motions on strong-motion data

Rotation motion and its effects on strong-motion data, in most cases, are much smaller than that of translational motion and have been ignored in most analyses of strong-motion data. However, recent observations from near-fault and/or extreme large ground motions suggest that these effects might be underestimated and quantitative analyses seem to be necessary for improving our understating of these effects. Rotation motion-related effects include centrifugal acceleration, the effects of gravity and effects of the rotation frame. Detailed analyses of these effects based on the observed data are unavailable in the literature. In this study, we develop a numerical algorithm for estimating the effects of rotational motion on the strong-motion data using a set of six-component ground motions and apply it to a set of rotation rate-strong motion velocity data. The data were recorded during a magnitude 6.9 earthquake. The peak value of the derived acceleration and rotation rate of this dataset are about 186 cm/s/s and 0.0026 rad/s. Numerical analyses of data gives time histories of these rotational motion-related effects. Our results show that all the rotation angles are less than 0.01°. The maximum centrifugal acceleration, effect from gravity and effect of the rotation frame are about 0.03 and 0.14 cm/s/s, respectively. Both these two effects are much smaller than the peak acceleration 186 cm/s/s. This result might have been expected because our data are not near-field and wave motions are expected to be nearly plane waves. However, it is worth noticing that the centrifugal acceleration is underestimated and a small rotational effect can cause large waveform difference in acceleration data. The waveform difference before and after the correction for rotational motion can reach 16 cm/s/s (about 10 %).