Strength reduction factors for seismic analyses of buildings exposed to near-fault ground motions

To estimate the near-fault inelastic response spectra, the accuracy of six existing strength reduction factors （R） proposed by different investigators were evaluated by using a suite of near-fault earthquake records with directivity-induced pulses. In the evaluation, the force-deformation relationship is modelled by elastic-perfectly plastic, bilinear and stiffness degrading models, and two site conditions, rock and soil, are considered. The R-value ratio （ratio of the R value obtained from the existing R-expressions （or the R-p-T relationships） to that from inelastic analyses） is used as a measurement parameter. Results show that the R-expressions proposed by Ordaz ＆ Perez-Rocha are the most suitable for near-fault ground motions, followed by the Newmark ＆ Hall and the Berrill et al. relationships. Based on an analysis using the near-fault ground motion dataset, new expressions of R that consider the effects of site conditions are presented and verified.

High-Risk Rural Road Safety Study and Determining the Crash-Reduction Factors for High-Risk Rural-Road Usage

More than 32,000 motorists are killed on U.S. roads and streets annually, and approximately 54% of the accidents occur on rural roads. In an attempt to address and reduce these fatalities, the current transportation act, the Safe, Accountable, Flexible, Efficient Transportation Equality Act: A Legacy for Users (SAFETY-LU), elevated the Highway Safety Improvement Program (HSIP) to a core program and included a $90,000,000 High-Risk Rural Road Program (HRRRP) to address and significantly reduce traffic fatalities and incapacitating injuries on rural major or minor collectors, and/or rural local roads. While there were many challenges to properly implement the HRRRP in counties, this study provided important information that was needed to identify the predominant crash types on HRRRP-eligible roads and compiled a list of countermeasures for the predominant crash types that were identified on Kansas’ high-risk rural roads. For the gathered countermeasures, crash reduction factors (CRFs) were also provided from the literature review, and their values were validated by conducting interviews with Kansas county engineers/officials. This study provided valuable information for the county engineers and local government officials while they worked on improving the safety of high-risk rural roads using HRRRP funds.

Strength and stiffness reduction factors for infilled frames with openings

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence ofinfill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.

Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods

Seismic force reduction factor(SFRF) spectra of shear-type multi-degree-of-freedom(MDOF) structures are investigated. The modified Clough model, capable of considering the strength-degradation/hardening and stiffnessdegradation, is adopted. The SFRF mean spectra using 102 earthquake records on a typical site soil type(type C) are constructed with the period abscissa being divided into three period ranges to maintain the peak features at the two sitespecific characteristic periods. Based on a large number of results, it is found that the peak value of SFRF spectra may also exist for MDOF, induced by large high-mode contributions to elastic base shear, besides the mentioned two peak values. The variations of the stiffness ratio λk and the strength ratio λF of the top to bottom story are both considered. It is found that the SFRFs for λF ≤λk are smaller than those for λF > λk. A SFRF modification factor for MDOF systems is proposed with respect to SDOF. It is found that this factor is significantly affected by the story number and ductility. With a specific λF(= λk0.75), SFRF mean spectra are constructed and simple solutions are presented for MDOF systems. For frames satisfying the strong column/weak beam requirement, an approximate treatment in the MDOF shear-beam model is to assign a post-limit stiffness 15%-35% of the initial stiffness to the hysteretic curve. SFRF spectra for MDOF systems with 0.2 and 0.3 times the post-limit stiffness are remarkably larger than those without post-limit stiffness. Thus, the findings that frames with beam hinges have smaller ductility demand are explained through the large post-limit stiffness.

Study on strength reduction factors consid-ering the effect of classification of design earthquake

The strength reduction factors are not only the key factors in determining seismic action for force-based seismic design, but also the key parameters to derive the inelastic response spectra for performance-based seismic design. In this paper, with a high quality ground motion database that includes a reasonable-sized set of records from China, a statistical study on the strength reduction factors is conducted and a new expression of strength reduction factors involving classification of design earthquake, which is an important concept to determine design spectra in Chinese seismic design code, is proposed. The expression of strength reduction factors can reflect the ground motion characteristics of China to a certain extent and is particularly suitable for Chinese seismic design. Then, the influence effects of site condition, classification of design earthquake, period of vibration, ductility level, earthquake magnitude and distance to fault on strength reduction factors are investigated. It is concluded that the effect of site condition on the strength reduction factors cannot be neglected, especially for the short-period structures of higher ductility. The classification of design earthquake also has an important effect on strength reduction factors and it may be unsuitable to use the existing expressions of strength reduction factors to the design spectra of current Chinese seismic code. The earthquake magnitude has no practical effect on strength reduction factors and if the near-fault records with forward directivity effect are not taken into consideration, the effect of distance to fault on strength reduction factors can also be neglected.

Strength reduction factors for structural rubbercrete

Many researches have been carried out to study the fresh and hardened properties of concrete containing crumb rubber as replacement to fine aggregate by volume, yet there is no specific guideline has been developed on the mix design of the rubbercrete. The experimental program, which has been developed and reported in this paper, is designed and executed to provide such mix design guidelines. A total of 45 concrete mixes with three different water to cement ratio （0.41, 0.57 and 0.68） were cast and tested for fresh and mechanical properties of rubbercrete such as slump, air content, unit weight, compressive strength, flexural strength, splitting tensile strength and modulus of elasticity. Influence of mix design parameters such as percentage of crumb rubber replacement, cement content, water content, fine aggregate content, and coarse aggregate content were investigated. Three levels of slump value （for conventional concrete mixes） has been selected; low, medium and high slump. In each slump level, water content was kept constant. Equations for the reduction factors （RFs） for compressive strength, flexural strength, splitting tensile strength and modulus of elasticity have been developed. These RFs can be used to design rubbercrete mixes based on the conventional mix （0% crumb rubber content）

Response reduction factor of irregular RC buildings in Kathmandu valley

Most current seismic design includes the nonlinear response of a structure through a response reduction factor （R）. This allows the designer to use a linear elastic force-based approach while accounting for nonlinear behavior and deformation limits. In fact, the response reduction factor is used in modem seismic codes to scale down the elastic response of a structure. This study focuses on estimating the actual ＇R＇ value for engineered design/construction of reinforced concrete （RC） buildings in Kathmandu valley. The ductility and overstrength of representative RC buildings in Kathmandu are investigated. Nonlinear pushover analysis was performed on structural models in order to evaluate the seismic performance of buildings. Twelve representative engineered irregular buildings with a variety of characteristics located in the Kathmandu valley were selected and studied. Furthermore, the effects of overstrength on the ductility factor, beam column capacity ratio on the building ductility, and load path on the response reduction factor, are examined. Finally, the results are further analyzed and compared with different structural parameters of the buildings.

Crest Factor Reduction for OFDM Using Selective Subcarrier Degradation

This paper describes a crest factor reduction （CFR） method that reduces peaks in the time domain by modifying selected data subcarriers within an OFDM signal. The data subcarriers selected for modification vary with each symbol interval and are limited to those subcarriers whose aata elements are mapped onto the outer boundary of the constellation. In the proposed method, a set of peaks are identified within an OFDM symbol interval. Data subcarriers whose data element has a positive or negative correlation with the set peak are selected. For a subcarrier with an outer element and a significant positive correlation, a bit error （reversal） is intentionally introduced. This moves the data element to the opposite side of the constellation. Outer elements on negatively-correlatea subcarriers are increased in magnitude along the real or imaginary axis. Experimental results show that selecting the correct subcarriers for bit reversals and outward enhancements reduces the peak-to-average power ratio （PAPR） of the OFDM signal to a target value and limits in-band degradation measured by bit error rate （BER） and error vector magnitude （EVM）.

Effect of structural characteristics distribution on strength demand and ductility reduction factor of MDOF systems considering soil-structure interaction

It is known that structural stiffness and strength distributions have an important role in the seismic response of buildings. The effect of using different code-specified lateral load patterns on the seismic performance of fixed-base buildings has been investigated by researchers during the past two decades. However, no investigation has yet been carried out for the case of soil-structure systems. In the present study, through intensive parametric analyses of 21,600 linear and nonlinear MDOF systems and considering five different shear strength and stiffness distribution patterns, including three code-specified patterns as well as uniform and concentric patterns subjected to a group of earthquakes recorded on alluvium and soft soils, the effect of structural characteristics distribution on the strength demand and ductility reduction factor of MDOF fixed-base and soil-structure systems are parametrically investigated. The results of this study show that depending on the level of inelasticity, soil flexibility and number of degrees-of-freedoms (DOFs), structural characteristics distribution can significantly affect the strength demand and ductility reduction factor of MDOF systems. It is also found that at high levels of inelasticity, the ductility reduction factor of low-rise MDOF soil-structure systems could be significantly less than that of fixed-base structures and the reduction is less pronounced as the number of stories increases.

Properties and appropriate conditions of stress reduction factor and thermal shock resistance parameters for ceramics

Through introducing the analytical problem of the plate with convection into the solution of the transient heat conduction thermal stress field model of the elastic plate, the stress reduction factor is presented explicitly in its dimensionless form. A new stress reduction factor is introduced for the purpose of comparison. The proper- ties and appropriate conditions of the stress reduction factor, the first and second ther- mal shock resistance （TSR） parameters for the high and low Biot numbers, respectively, and the approximation formulas for the intermediate Blot number-interval are discussed. To investigate the TSR of ceramics more accurately, it is recommended to combine the heat transfer theory with the theory of thermoelasticity or fracture mechanics or use a numerical method. The critical rupture temperature difference and the critical rup- ture dimensionless time can be used to characterize the TSR of ceramics intuitively and legibly.

Effect of Inclined Tension Crack on Rock Slope Stability by SSR Technique

The tension cracks and joints in rock or soil slopes affect their failure stability.Prediction of rock or soil slope failure is one of the most challenging tasks in the earth sciences.The actual slopes consist of inhomogeneous materials,complex morphology,and erratic joints.Most studies concerning the failure of rock slopes primarily focused on determining Factor of Safety(FoS)and Critical Slip Surface(CSS).In this article,the effect of inclined tension crack on a rock slope failure is studied numerically with Shear Strength Reduction Factor(SRF)method.An inclined Tension Crack(TC)influences the magnitude and location of the rock slope’s Critical Shear Strength Reduction Factor(CSRF).Certainly,inclined cracks are more prone to cause the failure of the slope than the vertical TC.Yet,all tension cracks do not lead to failure of the slope mass.The effect of the crest distance of the tension crack is also investigated.The numerical results do not show any significant change in the magnitude of CSRF unless the tip of the TC is very near to the crest of the slope.ATC is also replaced with a joint,and the results differ from the corresponding TC.These results are discussed regarding shear stress and Critical Slip Surface(CSS).

Fatigue Characterization on a Cast Aluminum Beam of a High-Speed Train Through Numerical Simulation and Experiments

The cast aluminum beam is a key structure for carrying the body-hung traction motor of a high-speed train;its fatigue property is fundamental for predicting the residual life and service mileage of the structure.To characterize the structural fatigue property,a finite element-based method is developed to compute the stress concentration factor,which is used to obtain the structural fatigue strength reduction factors.A full-scale fatigue test on the cast aluminum beam is designed and implemented for up to ten million cycles,and the corresponding finite element model of the beam is validated using the measured data of the gauges.The results show that the maximum stress concentration occurs at the fillet of the supporting seat,where the structural fatigue strength reduction factor is 2.45 and the calculated fatigue limit is 35.4 MPa.Moreover,no surface cracks are detected using the liquid penetrant test.Both the experimental and simulation results indicate that the cast aluminum beam can satisfy the service life requirements under the designed loading conditions.

Behavior of ring footing resting on reinforced sand subjected to eccentric-inclined loading

Ring footings are suitable for the structures like tall transmission towers, chimneys, silos and oil storages.These types of structures are susceptible to horizontal loads(wind load) in addition to their dead weight.In the literature, very little or no effort has been made to study the effect of ring footing resting on reinforced sand when subjected to eccentric, inclined and/or eccentric-inclined loadings. This paper aims to study the behavior of ring footing resting on loose sand and/or compacted randomly distributed fiberreinforced sand(RDFS) when subjected to eccentric(0 B, 0.05 B and 0.1 B, where B is the outer diameter of ring footing), inclined(0°,5°,10°, 15°,-5°,-10° and-15°)and eccentric-inclined loadings by using a finite element(FE) software PLAXIS 3 D. The behavior of ring footing is studied by using a dimensionless factor called reduction factor(RF). The numerical model used in the PLAXIS 3 D has been validated by conducting model plate load tests. Moreover, an empirical expression using regression analysis has been presented which will be helpful in plotting a load-settlement curve for the ring footing.

Model-scale tests to examine water pressures acting on potentially buoyant underground structures in clay strata

Throughout the service life, underground structures are subjected to transient and sustained hydrostatic pressures. The reservoir impoundment results in an increase in water level, as well as hydraulic gradient,which can endanger the uplift performance of infrastructure. In uplift design, a reduction factor is often suggested for buoyant force acting on underground structures in clays due to the time lag effect.However, the mechanism of pore pressure generation in clays is not fully understood. This investigation presents a novel U-shaped test chamber to assess the pore pressure generation with time in the horizontal branch subjected to an increase in reservoir level in the left vertical branch. A mathematical model is developed to explain the time lag effect of pore pressure generation. The test program also involves the evaluation of uplift pressure acting on foundation model in the right vertical branch due to adjacent reservoir impoundment. It is found that the time lag effect of pore pressure generation in clays can be observed irrespective of hydraulic gradient, but a higher hydraulic gradient can lead to a faster response in pore pressure sensors. A reduction factor of 0.84-0.87 should be considered to reduce the conservatism of uplift design.

The Libration Points in Photogravitational Restricted Three-Body Problem

The phologravilational restricled three-body problem in which the mass reduclionfactors of two primaries q_1 q_2( -∞, 1] are siudied and an analytic meihod toesli,;iale the number of libralion points ana io calculate lheir hoalion is given in thispaper. The results show lhal in phologravilalional reslricled three-body problem, thenumber of librafion poinis is .from one to seven for different q_1 and q_2. As application,the motion of dust grain like comet tail in the solar syslern is also discussed.

Experimental and Numerical Investigation of Stress Condition in Unstable Soil

In unstable soils, a special erosion process termed suffusion can occur under the effect of relatively low hydraulic gradient. The critical hydraulic gradient of an unstable soil is smaller than in stable soils, which is described by a reduction factor α. According to a theory of Skempton and Brogan (1994) [1], this reduction factor is related to the stress conditions in the soil. In an unstable soil, the average stresses acting in the fine portion are believed to be smaller than the average stresses in the coarse portion. It is assumed that the stress ratio and the reduction factor for the hydraulic gradient are almost equal. In order to prove this theory, laboratory tests and discrete element modelings are carried out. Models of stable and unstable soils are established, and the stresses inside the sample are analysed. It is found that indeed in unstable soils the coarse grains are subject to larger stresses. The stress ratios in stable soils are almost unity, whereas in unstable soils smaller stress ratios, which are dependent on the soil composition and on the relative density of the soil, are obtained. A comparison between the results of erosion tests and numerical modeling shows that the stress ratios and the reduction factors are strongly related, as assumed by Skempton and Brogan (1994) [1].

Study of Bed Friction Factor for the Wu River Estuary

In this research the bed friction effect is estimated of a river estuary by use of hydrodynamic analysis. The on-site sampled data of the Wu River estuary is applied to the analysis. There are many dynamic factors that affect the flow characteristics in the estuary. The effect of tide on the generation of tidal current, bottom friction and geometry effect is the focus of this paper. The Wu River estuary is about 15 hn in length, with a small bottom slope and no physical obstruction; thus the incident wave at the estuary is considered a progressive wave with damping effect. The amplitude reduction and phase shift of the incident wave are analyzed. By the analysis of celerity reduction factor of the estuary, the estimated value of mean resistance coefficient M（μ ,κ）, damping modulus μ, and wave number κ for the sections at observation stations can be determined. Furthermore, data gathered from on-site observations are applied for validation. Finally, Manning＇ s coefficient for each section of the observation stations can be determined. It is found that the value of Manning＇ s coefficient is small downstream and increases towards upstream, and that the bed friction effect of an estuary varies largely. The estimated results of the paper are compared with the empirical formulas and the modified solution for practical application is discussed.

Static and dynamic inelastic P-Δ effect for seismic design

Seismic influence of P-Δ effect is the subject of this study.First,it is pointed out that the elastic static amplification factor shall be isolated in formulating the dynamic inelastic second order effect.An amplification factor for the static inelastic P-Δ effect is derived.Seismic force reduction factors(SFRF)for given ductility and stability coefficients are computed for one-story,one-span frames.The P-Δ amplification factors for seismic base shears are obtained by dividing SFRFs with and without P-Δ effect.Both P-Δ amplification factors and SFRFs are presented separately with two kinds of period abscissas.The P-Δ amplification factors are dependent on periods with the maximum occurring at about 0.75 s for site type C and approach to the static inelastic counterpart at long periods.Post-yield stiffness cannot fully counteract the adverse impact of the P-Δ effect.Formulas for seismic P-Δ amplification factors are proposed and compared to results of others.Collapse capacity spectra(CCS)are reviewed and their application in codes discussed.Available CCSs are compared with SFRFs with finite ductility computed for two ensembles of seismic records.A comparison reveals that the SFRFs are affected by seismic records,and available CCSs do not always provide upper limits for the SFRFs when stability coefficients are greater than 0.1 for frame models.

Experimental Study on Mechanical Properties of Q690 High-Strength Steel after High Cycle Fatigue Damage

Through the static tensile test of Q690 high-strength steel, the relevant mechanical parameters are obtained and the maximum fatigue load is determined. The fatigue life is measured by the fatigue test under the load. According to the fatigue cumulative damage method, the number of fatigue pre-damage vibration is designed in proportion. Then the fatigue pre-damage test is carried out on the high-strength steel, the stress-strain curve and the variation of residual mechanical property reduction coefficient with fatigue damage were drawn. The results show that: compared with the undamaged specimens, the yield strength and tensile strength of Q690 steel are less affected by fatigue damage, but the elongation changes more significantly, and the elastic modulus is not significantly affected. Finally, through the change of mechanical properties of Q690 high-strength steel with different fatigue damage, it provides a scientific basis for the performance evaluation of existing Q690 high-strength steel structure after fatigue damage.

A Novel Multivariate Polynomial Approximation Factorization of Big Data

In actual engineering, processing of big data sometimes requires building of mass physical models, while processing of physical model requires relevant math model, thus producing mass multivariate polynomials, the effective reduction of which is a difficult problem at present. A novel algorithm is proposed to achieve the approximation factorization of complex coefficient multivariate polynomial in light of characteristics of multivariate polynomials. At first, the multivariate polynomial is reduced to be the binary polynomial, then the approximation factorization of binary polynomial can produce irreducible duality factor, at last, the irreducible duality factor is restored to the irreducible multiple factor. As a unit root is cyclic, selecting the unit root as the reduced factor can ensure the coefficient does not expand in a reduction process. Chinese remainder theorem is adopted in the corresponding reduction process, which brought down the calculation complexity. The algorithm is based on approximation factorization of binary polynomial and calculation of approximation Greatest Common Divisor, GCD. The algorithm can solve the reduction of multivariate polynomials in massive math models, which can obtain effectively null point of multivariate polynomials, providing a new approach for further analysis and explanation of physical models. The experiment result shows that the irreducible factors from this method get close to the real factors with high efficiency.