Bidirectional Loading Research Articles

Energy dissipation capacity for waffle-flat-plate structures subjected to bi-directional seismic loadings

The seismic capacity of buildings is usually studied through separate analysis of two orthogonal directions, then combined using empirical rules. Nevertheless, the three-dimensional nature of seismic action gives rise to interaction among its different components, especially the two horizontal ones, which can cause substantial discrepancy between the actual 3D response and the one obtained by combining uniaxial responses. The present study addresses this problem for waffle-flat-plate (WFP) structures with an irregular layout of columns from the standpoint of energy dissipation capacity. A portion of a WFP prototype structure that was built in Laboratory was subjected, simultaneously, to two horizontal components of a far-field seismic record upon a shake-table. Several shakings of increasing intensity were applied until the collapse of the structure. Afterwards, a numerical model of the specimen was developed and validated with the experimental results. The numerical model was subjected to several sets of ground motions having diverse ratios of energy input from the horizontal components. When the total energy dissipated by the structure through cumulative plastic deformations until failure was obtained for each set of accelerograms, a fairly stable quantity was found to be concentrated within a narrow range of values. Moreover, the specimen subjected to bi-directional seismic loading showed a higher ultimate energy dissipation capacity than under uni-directional loadings.

On the response of fiber reinforced elastomeric isolators (FREIs) under bidirectional shear loads

Fiber Reinforced Elastomeric Isolators (FREIs) have been proposed as an alternative to Steel Reinforced Elastomeric Isolators (SREIs) and several studies have highlighted the advantages of this technology over conventional devices. When FREIs are unbonded to the top and bottom substructure, the bearings exhibit softening under imposed lateral deformations with or without instability depending on the aspect ratio of the device. Research studies available in literature have focused on the response of rectangular bearings when loaded in shear along their base. Very little is known on the lateral response of these devices under bidirectional shear loading. This study aims to assess the response of rectangular FREIs under combined axial and bidirectional shear loads and to show the effects of (i) the secondary shape factor of the bearing, of (ii) the axial pressure, of (iii) the horizontal loading direction on the stability of these devices. As result of a large set of analyses, stability domains have been derived which take into account all of the variables listed above. Based on the results of this work, simple to use design considerations can be derived. Results of this study contribute towards the real implementation of this technology particularly in developing regions of the world.

Substructure Modeling and Loading-Control Techniques for the Test of a Full-Scale Spatial RC Frame with Buckling-Restrained Braces Subjected to Bidirectional Loading

To investigate the performance of reinforced-concrete frames with buckling restrained braces (RCF-BRB) subjected to bidirectional earthquakes, a full-scale two-story RCF-BRB was tested using substructured pseudodynamic (PsD), quasistatic, and pushover techniques. This paper focuses on the structural modeling for the substructured PsD tests, and the control and measurement issues of the bidirectional loading system. To make a credible reproduction of the structural response using substructured PsD technique, an overlap modeling technique together with tuning the mass of the lamped-mass model and stiffness of the numerical substructure was employed to reduce errors caused by the incomplete boundary condition. The outer-loop control method based on Newton’s iteration method was introduced for the loading system, with the data from external displacement sensors as the feedback to avoid errors caused by possible gaps in the connection parts of the loading system. The redundancy issue, caused by the actuators outnumbering the degrees of freedom of the floor to be controlled, is addressed with a force-displacement mixed control technique. The three of four actuators were controlled in displacement mode, whereas the redundant one was in force mode. The force command to the redundant actuator was determined with the optimization criteria to minimize the loads relative to the capacities of the actuators. The working range of the displacement sensors is investigated using numerical and geometric approaches. Failure examples from numerical simulation and experiment were shown to emphasize the importance of proper arrangement of displacement sensors. A rearrangement of the displacement sensors was proposed for the pushover test to enlarge the working range. Time-history results of the prototype structure using the calibrated finite-element model show that the PsD substructure test results could represent seismic responses of the prototype structure. The measured mass-center displacements accurately tracked the target displacements throughout the test, indicating the effectiveness of the loading control and measuring system.

Predictive model for bidirectional shear strength of reinforced concrete columns subjected to biaxial cyclic loading

Corner columns are subjected to bidirectional lateral loading in three-dimensional framed structures during seismic events, which can deteriorate their shear strength. The majority of the design codes do not consider the effect of biaxial lateral loading in the calculation of the column shear strength, and hence an accurate formulation that can predict the bidirectional shear strength is still lacking. Gene Expression Programming (GEP) was used in this research to predict the bidirectional shear strength of columns subjected to biaxial cyclic loads based on a database collected from different experimental studies found in the literature. Based on the previous experimental studies, it is found that the biaxial shear strength of RC columns are predominantly controlled by the column axial load, cross-sectional area of the columns, column shear reinforcement area, concrete compressive strength, and the height of the column. These parameters were used to develop the GEP models in this research. The models were statistically evaluated in order to ensure their applicability, and then they were compared to the ACI-318 formulation of the uniaxial shear strength. The R2 value obtained using the ACI-318 formulations is low compared to that obtained using the GEP models, where the R2 value obtained using the ACI formulation is 0.35, and that obtained using the first and second GEP models are 0.87 and 0.73, respectively. This confirms that the GEP models are more fitting to the experimental results compared to the ACI-318 formulation.

Quasi-static testing and numerical simulation study on seismic performance of reinforced concrete core wall with embedded steel frame under sequentially bidirectional loading

A large scale quasi-static test of reinforced concrete core wall with embedded steel frame (SFRC) under bidirectional loading was conducted to study the spatial failure mechanism systematically. The coupled shear wall and the single limb shear wall were respectively set in two directions of the specimen to reflect the effect of coupling beams. Subsequently, numerical simulation was adopted for parametric analysis. It is found that, in this large scale quasi-static test, the occurrence and propagation of concrete cracks were easily and clearly captured to evaluate the damage degrees. Deformation limits summarized from the Chinese code and US standard were examined by test results, and the upper limit value of “Collapse” in the Chinese code is strict. Compared with the single limb shear wall in the y-direction, coupling beams in the x-direction were damaged firstly to protect walls. The maximum drift angle of the coupled shear wall was less than that of the single limb shear wall by 30% at the yield point. Many spatial damage phenomena were revealed by the sequentially bidirectional cyclic loading, e.g., the effect of loading in the y-direction aggravated the damage degrees of walls in the x-direction. The finite element model of the specimen was validated well by the test results. From simulation results, the effect of the embedded steel frame was demonstrated, and suggestions for the seismic design of SFRC core wall were given. This research can provide a basis for the design and evaluation of hybrid structures.

Analysis of different cross-frame placements to enhance torsional irregular buildings against structural failure under earthquake bidirectional loadings: A case study

Cross bracing frames (CFs) are employed as traditional passive energy dissipating devices, which are placed into the moment-resisting frames of the Benchmark building picked for analysis purposes. These devices are widely used, easy to construct, and inexpensive to contribute better seismic protection for existing and new buildings as compared to complex control systems like active/passive Tuned Mass Dampers (TMDs) and so on. Therefore, in this research, the best three-predetermined CFs placements are selected, and the time history analyses are made under bi-directional seismic loads such as two orthogonal excitations of El Centro in 1940, North-Ridge in 1994, and Kocaeli, Turkey in 1999. In conclusion, the obtained results show that integrating CFs into MRFs should be made by taking into consideration eliminating eccentricity in the seismic design; otherwise, they can lead to an increase in the possibility of structural damages.

Comparison of experimental approaches for seismic performance evaluation of bridge piers with high strength self-consolidating concrete towards practical engineering application

In this study, three different types of experimental approaches are carried out for the seismic evaluation of high strength self-consolidating concrete bridge columns in high seismic zone, including unidirectional quasi-static, bidirectional quasi-static and shake table tests. The 1/4-scale bridge column specimens are based on the practical engineering application of urban viaduct in high seismic region of northern China. The use of high strength self-consolidating concrete is to fulfill the demand of short construction time, high seismic resistance and harsh weather durability in the area. Based on the experimental results, it is found that similar damage progression is observed from all the tested specimens with concrete crush and longitudinal rebar buckling. Quasi-static cyclic tests tend to be more conservative but to overestimate the energy dissipation capacity and ductility, and the coupling effect from bidirectional loading cannot be ignored. In addition, nonlinear numerical models with improved bond-slip modeling approach are developed and calibrated by OpenSEES with the experimental data, where good agreement is achieved especially at early loading stage.

Calculation Formula for the Pullout Force of Uniaxial Geogrid-Reinforced Expansive Soil

To obtain the action force between the reinforcing material and filler in reinforced soil, many scholars at home and abroad have conducted pullout tests, which are limited by the testing apparatus. Most of them have studied the pullout force between a biaxial geogrid and sand. The pullout force formula is generally believed to be composed of the surface friction and lateral resistance of transverse ribs, and uniaxial geogrids have rarely been researched experimentally on the basis of the pullout force between them and the expansive soil filler due to the large distance among transverse ribs. This study draws on existing methods to determine the pullout force, conducts a preliminary analysis, proposes a formula for calculating the maximum pullout force, uses a self-developed large-scale CNC pullout test system, and utilizes its large size, bidirectional airbag loading, and ability to eliminate side wall friction. The design of the test scheme is optimized to obtain two important calculation parameters in the formula: one is to cut grids of different lengths to provide lateral resistance and then implement them to obtain the coefficient of sliding friction between grid and fill; the other is to develop different numbers of horizontal ribs in the pullout test of a grille, and the lateral resistance of the end bearing of a single transverse rib is measured. The results of the lateral resistance of the end bearing based on the analysis of the three mechanisms of shear, punching, and Prandtl failures are compared. The lateral resistance of the lateral rib end bearing measured from the test is proven reasonable. Two types of expansive soils reinforced by different types and sizes of grids are analyzed with the calculation formula of the maximum pullout force, and the coefficient of pullout friction is determined to be rational. The research results can be used to guide the design and construction of uniaxial geogrid-reinforced expansive soil and the modification and upgrading of products by grid manufacturers.

Bidirectional loading performance of gusset plates in buckling restrained braced frames

A study is conducted to evaluate the performance of gusset plates (GPs) in buckling restrained braced frames (BRBFs) subjected to bidirectional loading. It involves an experimental test, a parametric numerical study and a comparison with Thornton, AISC, Takeuchi’s and Notional Load Yield Line (NLYL) methods. The experimental test was conducted on a one-storey BRBF with pinned beam connections under both unidirectional and bidirectional cyclic loading.It was found that bidirectional loading decreases the GP axial strength by up to 18%, but there is no clear correlation with GP thickness. The parametric study indicated that greater out-of-plane (OOP) drifts reduce the GP axial strength. The methods evaluated with respect to the parametric study generally provided conservative strength predictions. The AISC method with an effective length factor of 2.0, which does not explicitly account for out-of-plane loading, was the most conservative among all methods. The strength predicted ranged from 69% to 92% of the actual strength. Similarly, both Takeuchi’s and NLYL method under bidirectional loading are conservative when the GPs have a rotational stiffness within the likely range of practical applications. However, they are non-conservative for BRBF GPs with a very low rotational stiffness. The NLYL method is less conservative than Takeuchi’s method. The NLYL method is always conservative for the limited range of CBF GP configurations investigated.

Bidirectional Loading History for Seismic Testing of 3D Frame Joints

Beam-column-joints (BCJ) in reinforced concrete (RC) frames are known to be critical against seismic actions. Hence, several researchers have conducted related investigations. The loading history used in the experimental investigations must be a sufficiently accurate and conservative representation of seismic loading on the structure and should trigger all possible critical failure mechanisms in the subassembly. Presently, there is significant diversity in the loading histories used for seismic investigation of structural subassemblies. This paper intends to propose an optimum loading history for considering bidirectional (horizontal) seismic action on 3D-RC BCJ subassemblies. To this end, the available loading histories (unidirectional and bidirectional) for simulation of seismic loads on RC joint subassemblies are reviewed in the context of the demands they impose on the joints. Finite element modeling and analyses are used as a tool for investigating the response of 3D-BCJ subassembly under different bidirectional loading states.

Mechanical Behavior and Structure Optimization of Compressed PHP Packer Rubber

One of the core tools of horizontal well-staged fracturing completion technology is the compressed packer. The sealing and stability of packer rubber are key factors affecting the safe exploitation of high temperature, high pressure, and deep, complex oil and gas resources. The phenomenon of low setting pressure and early setting failure frequently occurs due to the unreasonable sealing structure. Therefore, in this paper, the tensile test of dumbbell hydrogenated nitrile butadiene rubber (HNBR) samples is conducted, and the stress-strain data of HNBR were obtained. The finite element mechanical model (FEM) of compressed PHP packer is established with consideration of material nonlinearity, geometric nonlinearity and double contact nonlinearity by adopting large-scale finite element analysis software ANSYS Workbench, verified by measured test data. Based on the verified FEM, the mechanical behavior and sealing performance of the original rubber under different setting loads are simulated. The contact pressure and its distribution, deformation, compression stroke of rubber and the relationship between them and axial loads are obtained. The mechanical behavior and sealing performance of packer rubber under different heights, thicknesses, external bevel angles, loading modes and steel-rubber friction coefficients with and without outburst prevention devices are investigated systematically using a manual-graphical optimization trial method. Results show that the packer rubber with the height of 75 mm, external bevel angle of 45°, steel-rubber friction coefficient ranging from 0.10 to 0.15 and outburst prevention devices can achieve the largest contact pressure and best sealing performance by adopting the setting method of bidirectional loading.

Bioinspired fabrication of reconfigurable elastomeric cementitious structures using self-healing mechanical adhesives interfaces

Modern construction technologies are in high demand of new highly customizable and easy-to-assemble structural materials with enhanced mechanical performance and the capability to self-repair autonomously. This article describes the simple and cost-effective manufacturing of Self-Healing Elastomeric/Cementitious/Mechanical Adhesive Structures (SECMAS). SECMAS are comprised of cementitious bricks joined by mechanical adhesive interfaces and organized in nacre-inspired, brick-and-mortar structures. This scalable staggered design provides SECMAS with the capability to concentrate the formation and propagation of cracks along the mechanical adhesive interfaces, which efficiently distribute loading forces and accommodate deformation. The periodic distribution of elastomeric reinforcing layers inside the SECMAS facilitates its elastic self-recovery after severe deformation, restoring the interlocking of the mechanical adhesive interfaces and enabling SECMAS to autonomously recover their original mechanical properties at room temperature. Moreover, the rapid recovery of the mechanical adhesive interfaces enables repeated self-healing under cycling bidirectional loading forces. The modular structure of SECMAS and their easy-to-assemble and easy-to-disassemble mechanical adhesive interfaces facilitates the rapid exchange of damaged components for new ones, enlarging service life. Furthermore, the simple and scalable design rules derived for the construction of SECMAS facilitate their rapid reconfiguration into a variety of self-repairing structural elements, promoting sustainable construction.

Bidirectional Seismic Energy Input to an Isotropic Nonlinear One-Mass Two-Degree-of-Freedom System

The test results obtained for reinforced concrete columns by several studies have revealed that the peak displacement and cumulative hysteresis energy are important parameters for evaluating the damage of columns under horizontal bidirectional and unidirectional loading. Therefore, the seismic parameters related to the nonlinear peak displacement and cumulative hysteresis energy with regard to horizontal bidirectional seismic input should be investigated. In this study, the bidirectional seismic input to an isotropic nonlinear one-mass two-degree-of-freedom system was evaluated. First, a dimensionless parameter γ, which controls the low-cycle fatigue effect, was formulated as a function of two energy input parameters (the maximum momentary input energy and total input energy) and a nonlinear system (ductility and normalized hysteresis energy absorption during a half cycle). Then, the maximum momentary input energy and total input energy were evaluated according to the ground motion characteristics (Fourier coefficient of horizontal ground motion components) and system properties. Finally, the nonlinear peak displacement and parameter γ of the nonlinear system were evaluated on the basis of the maximum momentary input energy and total input energy. The results revealed that the nonlinear peak displacement and parameter γ can be properly evaluated using two energy parameters.

Analytic solution for buckling of rectangular isotropic plates with internal point supports

In this paper, analytical solutions for the buckling loads of thin rectangular plates with internal supports and different boundary conditions are derived. The analytical method presented herein is based on the development of a static solution for a plate. The physical meaning of buckling is the loss of stiffness, and it is found as the value of the in-plane loading intensity at which a zero force on the plate surface will generate infinite displacement. The solution is obtained in a series form, and the coefficients are solved to match the edge conditions. For every internal support in the plate domain we add one equation enforcing zero deflection at that point. By using this new method, exact buckling loads and buckling modes of many new cases of plates with various boundary conditions and several internal supports are obtained. The optimal location for placing an additional support is shown for several cases of square plates. Results are given for several cases of uni-directional and bi-directional loading.

Fragility analysis of rectangular and circular reinforced concrete columns under bidirectional multiple excitations

This paper presents a numerical investigation on seismic performance of reinforced concrete (RC) cantilever columns under unidirectional and bidirectional excitations. The influence of cross-sectional geometry and multiple excitations have been examined in this study. An advanced nonlinear finite element model is employed to model different failure modes of RC columns under seismic excitation. The model simulates degradation of materials under cyclic loading, including inelastic buckling and low-cycle fatigue degradation of longitudinal reinforcement. A series of monotonic pushover and incremental dynamic analyses (IDA) are conducted on hypothetical rectangular and circular columns. Proposing a unique algorithm, an existing inclusive damage index is implemented to quantify the different sources of damage including flexural, shear and reinforcement slippage damage under bidirectional excitation. Ground motion records are carefully selected using conditional mean spectrum (CMS) to generate as-recorded real mainshock and aftershock (MSAS) sequences. Results show that multiple bidirectional excitations significantly increase the damage that accumulates in RC columns. Moreover, inelastic buckling and low-cycle fatigue degradation of longitudinal bars have an evident contribution to the failure of RC columns. It is also found that the rectangular column is more prone to collapse under bidirectional loading in comparison to circular section. The analyses results show that the impact of bidirectional excitation on the seismic performance of the studied cantilever columns is considerable. This implies that seismic performance assessment of RC structures using unidirectional excitation can be biased.

Extended Newmark method to assess stability of slope under bidirectional seismic loading

The paper concerns the dynamic behavior of a simple slope model subjected to simultaneous horizontal and vertical excitations. The proposed method is based on Newmark's sliding block concept, however, four new features are introduced. The most important assumption is that the normal component of dynamic excitations affects the resisting force both before and after the initiation of the relative slope motion, making it time-dependent. The proposed formula and solution method is validated by experiments conducted on the shaking table and the bidirectional oscillatory device. The block displacement and acceleration time-histories are measured and analyzed. Experiments results conducted for bidirectional cyclic motion showed that the influence of vertical acceleration on the stability of the slope can be both negligible and significant (up to 57%). The numerical tests results, performed for thirty-five European seismic records, showed the underestimation of permanent displacement can reach up to 19% if the vertical excitation is neglected.

Intramedullary nailing confers an increased risk of medial migration compared to dynamic hip screw fixation in unstable intertrochanteric hip fractures

IntroductionMedial migration of the femoral neck element (FNE) superomedially against gravity with respect to the intramedullary component of the cephalomedullary nail is a complication increasingly recognized to cause femoral head cut-out in intramedullary nailing of pertrochanteric hip fractures. Although cut-outs are common to both intra- and extramedullary fixation, especially in unstable pertrochanteric hip fractures, FNE medial migration in sliding hip screws continues to remain sparse despite increased awareness of the phenomenon. This study aims to investigate whether intramedullary nailing is biomechanically predisposed to FNE medial migration compared to extramedullary fixation with sliding hip screws to account for the discrepancy in reported FNE medial migration rates. Materials and methodsTwelve fourth-generation synthetic femurs (Sawbones) with unstable intertrochanteric fractures were divided into 2 groups (n=6 per group). Fracture fixation was performed using the Proximal Femoral Nail Antirotation (PFNA, Synthes) (n=6) in the first group, and the Dynamic Hip Screw (DHS, Synthes) (n=6) in the second group. Both groups were subjected to bidirectional cyclic loading (600N compression loading, 120N tensile loading) at 2 Hz for 5000 cycles. The medial migration distance (MMD) was recorded at the end of the testing cycles. ResultsThe mean MMD in the PFNA group was 4.56mm (SD 0.69mm) with consistent reproduction of medial migration across all constructs tested. This was significantly more compared to the MMD of 1.17mm (SD 0.69mm) in the DHS group (p<0.001). ConclusionIntramedullary nailing of unstable intertrochanteric hip fractures is inherently predisposed to FNE medial migration making it more susceptible to consequent cut-out compared to fixation with the DHS.

Experimental Cyclic Test of Reduced Damage Detailed Drywall Partition Walls Integrated with a Timber Rocking Wall

ABSTRACT Bidirectional quasi-static cyclic loading was applied to a subassembly of drywall partition walls integrated with cross-laminated timber rocking walls. Details aimed to reduce seismic damage to the partition walls were investigated, such as slip connections of partition walls to the diaphragm and gap detailing for the wall intersections. Telescoping detailing eliminated damage to the framing at the wall ends compared to traditional slip-track detailing. The distributed gap wall delayed the damage to about 1% inter-story drift. In the corner gap wall, the sacrificial corner bead opened up at low drifts (0.43%), but the wall was damage-free until more than a 2% drift.

Effect of Bi-directional excitation on a curved bridge with lead rubber bearing

Abstract A continuous bridge, horizontally curved in plan and isolated with Lead Rubber Bearing (LRB), has been investigated under seismic loading conditions. Two recorded ground motions, representative of historical earthquakes along with far-field (Imperial Valley) and forward directivity effect (Turkey), respectively, have been considered. The bi-directional effect of the bearings considering interaction behavior of bearing and pier has been determined. Modeling and analysis of the bridge have been done by finite element approach. It has been noticed that there is a significant influence of bi-directional loading and the same is found to be maximum in Turkey ground motion which might be due to forward directivity effect.

Experimental Performance of a Full-Scale Spatial RC Frame with Buckling-Restrained Braces Subjected to Bidirectional Loading

To investigate the performance of a RC frame with buckling-restrained braces (RCF-BRB) subjected to bidirectional earthquakes, a full-scale two-story RCF-BRB was tested using substructural pseudodynamic, quasi-static, and pushover techniques. The test results showed that the RCF-BRB designed based on the current Chinese building codes exhibited reliable seismic performance, because the selected performance objectives were achieved in the tests. The specimen displayed an effective and stable energy-dissipating capacity even when the interstory drift exceeded 3%. The pushover test revealed excellent deformation capacity of the RCF-BRB, because the interstory drift ratio reached 5.9% in both loading directions. Compared with conventional gusset plates, the unconstrained gusset plates reduced the damage of the RC members significantly. The strut-and-tie model was confirmed to be reliable for the design of discontinuity regions (D-regions) of the RC beam ends with unconstrained gusset plates.