Force Reduction Factor Research Articles

Damage Spectra of SDOF Structures Under Tsunami Actions Considering the Nonlinear Dynamic Analysis Method

This paper studies the damage spectra of single-degree-of-freedom (SDOF) systems for tsunami loading. The 2011 Tohoku tsunami wave traces are computed and obtained by adopting the Cornell Multi-grid Coupled Tsunami (COMCOT) model and are further verified by the Tohoku Tsunami Joint Survey (TTJS) data. The tsunami response analyses of SDOF systems are conducted taking into account the dynamic analysis method. The classical ductility damage is considered as the damage performance. The damage spectra are computed for five force reduction factors and 791 tsunami loadings. The effects of inundation depths, hysteretic model, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], are explored and interpreted scientifically and statistically. The results demonstrate that the effect of the hysteretic model, force reduction factor, R, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], on the damage of the structure is evident. Comparison with the static method and influence analysis of structural damping indicate the necessity for the application of the dynamic method. A simplified predictive formulation is developed for the evaluation of structural damage for tsunami loadings.

Physical model comparison of gray and green mitigation alternatives for flooding and wave force reduction in an idealized urban coastal environment

A 1:16 scaled physical model was constructed to investigate the effectiveness of a seawall, a submerged breakwater, and mangrove forests to mitigate overland flooding and forces on structures in an idealized urban coastal environment. The experiment was performed using tsunami-like waves at different water levels, wave amplitudes, and time scales to simulate long-wave dynamics. The baseline condition (no mitigation), seawall, submerged breakwater, and mangrove forest were tested individually, and the seawall and submerged breakwater were also tested in combination. Wave gauges, acoustic Doppler velocimeters, loadcells, and pressure gauges were used to measure wave elevations, velocities, forces, and pressures on coastal structures, respectively. The performance of these hard structures and mangroves was compared through their effects on wave elevation, particle velocity, and force reduction. Experimental results showed that each protecting structure reduced the horizontal wave forces and inland flow hydrodynamics in the low-water-level case, with a similar performance by the individual seawall, submerged breakwater, and four rows of mangroves. The combined configuration, when the seawall and submerged breakwater were installed simultaneously, caused the most significant maximum force percent reduction by approximately 50%, while mangrove forests arranged in eight rows resulted in a force reduction of 46% in the first building array. However, in the high-water-level cases, the impulsive force measured with the presence of the submerged breakwater was larger than in the baseline case; thus, the submerged breakwater may amplify the impulsive force on the vertical building rows for certain incident wave conditions. Generally, the combined hard structures induced the lowest force reduction factor measured in almost every building row compared to the seawall, submerged breakwater, and mangroves considered separately for all wave conditions and water levels. That means this multi-tiered configuration showed better performance than individual alternatives in reducing horizontal forces inland than the individual alternatives considered separately.

Nonlinear Dynamic Analyses Utilising Macro-Models of Reinforced Concrete Building Structures and Site-Specific Accelerograms

This paper aims to guide structural engineers on how to apply the rapid nonlinear time history analysis (RNLTHA) procedure effectively to predict seismic demand, taking into account ductility and overstrength, and effects of dynamic phenomena including cyclic degradation of strength and stiffness in structures, in a direct and expedient manner. The shortcoming of the conventional force-based approach of design involving the use of a force reduction factor to account for nonlinear effects is well recognised. Nonlinear static (pushover) analysis and dynamic nonlinear time history analysis (NLTHA) are offered as alternative methods of analysis by major codes of practices to achieve better optimisation in the use of materials. NLTHA has advantages over pushover analysis in being more direct and capable of capturing cyclic response behaviour. Despite the merits of NLTHA, its adoption in the industry has been limited, mainly because of the complexity and the higher analysis cost involved. RNLTHA proposed in this article uses a macroscopic model of the building to fulfil the purpose of NLTHA, whilst saving computational time and achieving a good degree of accuracy, as verified by comparison with results generated from SeismoStruct.

Performance-based seismic design of self-centering steel moment frames with SMA-bolted connections

This paper proposes a performance-based seismic design (PBSD) method for self-centering moment-resisting frames with shape memory alloy (SMA)-bolted endplate connections. PBSD can be used to achieve different performance objectives, resulting in several benefits, such as cost-effectiveness and customization of the design. This study develops a PBSD framework by establishing a relationship between the fundamental period, ductility demand, and seismic force reduction factor and using an energy-balanced concept. The design method is facilitated using an artificial neural network (ANN)-based predictive tool and an efficient experimentally-validated phenomenological model for SMA-bolted endplate connections. Maximum drift and ductility ratios are adopted as performance objectives. Two 3- and 6-story prototype frames are designed and evaluated to illustrate the proposed PBSD method. The seismic response and collapse safety of the prototype frames at different shaking intensities are evaluated. The results show that the prototype frames designed using the proposed PBSD framework meet the prescribed design objectives and the collapse safety requirements in FEMA P695. The illustrative examples confirm that the designed moment frames possess the intended self-centering capability with negligible residual deformations as low as 0.05% at the maximum considered earthquake (MCE) hazard level. The results also confirm that the designed frames exhibit uniform drift distribution along their height.

Analysis of steel baffle installed on footing with dowels for resisting boulder impact

Debris flow is a common geological hazard in mountainous area. The large boulders carried by debris flow can be particularly destructive to downhill facilities. Constructing steel baffle with a footing on steep slope is a cost-effective mitigation method to dissipate the impact energy of boulders. However, current design of steel baffle and its footing and structural connections is usually highly empirical which may impede the effectiveness of baffle on resisting boulder impact. In this study, full-scale pendulum impact tests were conducted to investigate 10-kJ boulder impact on baffle installed on cubic footings with side lengths of 650 mm and 1300 mm. The pendulum impact tests were used to calibrate the input parameters of a three-dimensional (3D) finite element model. Numerical parametric study was conducted to investigate the effects of footing size and application of steel dowels on baffle to resist boulder impact with an energy up to 100 kJ. The required footing size and embedded depth of steel dowels in soil are recommended to avoid the failure of a baffle and its footing subjected to dynamic boulder impact. To predict the boulder impact force on a steel baffle, a force reduction factor of 0.03 can be used for the simplified Hertzian method. The unique results presented in this study can be used by practitioners to design baffles, instead of large reinforced concrete structure, as a more sustainable alternative mitigation measure to strengthen the resilience of mountainous communities globally.

Effect of Pre-Hole Filled with High-Damping Material on the Inelastic Response Spectrum of Integral Abutment Bridges

ABSTRACT This paper estimates the effect of a pre-hole filled with high-damping material on the inelastic response spectrum of Integral Abutment Bridges (IAB) with pile foundation. The hysteretic response of the pile, described by a Winkler beam model, is obtained from the piece-wise definition of the subgrade stiffness, calibrated on experimental data. The pre-hole with damping pre-hole determines a reduction of the demand spectral acceleration. The force modification factors of the acceleration response spectrum of the bridge superstructure under a large set of strong/motion earthquakes are estimated. The force-reduction factors for the elastic design of IABs with damping pre-hole are proposed.

The Slender Rigid Block: Archetype for the Seismic Analysis of Masonry Structures

ABSTRACT The elasto-plastic oscillator, representing the basic model for reinforced concrete and steel structures, shows its inadequacy when dealing with masonry structures. The column, resting on a rigid plane with friction, is shown to be particularly appropriate to model the dynamic behaviour of masonry structures. At this aim, this paper investigates the motion of a slender rigid block (SRB), initially resting in its vertical configuration and hit by a seismic input, represented through a single impulse constituted by a rectangular or sinusoidal half-wave or a simplified sequence of horizontal acceleration pulses, having rectangular or sinusoidal shapes. An accumulation of the rotation of the SRB exists under the action of sequences of opposite acceleration pulses. The dynamic collapse is shown to take place when the column is led to its critical configuration – where the restoring moment of the weight is lost – so that the last pulse can further increase the rotation of the column. Expressing the behaviour of the SRB by means of the force reduction factor, the ratio between the magnitude of the collapse horizontal acceleration and the static strength of the column, the difference between the responses of the column decreases with increasing the number of the pulses of the sequence. A simple definition of the asymptotic failure domain can be obtained with a good approximation with a limited number of pulses. It is possible to evaluate the minimum collapse acceleration intensity of seismic sequences of pulses of any assigned duration able to produce the collapse of the rigid block, representing the seismic strength of the SRB. Finally, the results obtained in the theoretical analysis are compared with the outcomes of more accurate and time-consuming non-linear dynamic or incremental analyses (IDA).

Wave force reduction due to burial of submarine pipeline: A probability based analysis and comparison with DNVGL-RP-F109

Horizontal and vertical wave forces were assessed on submarine pipeline for different burial depths in soils of four different hydraulic conductivity in random waves of wide range of wave height and periods. Probability analysis is carried out for 99.99% and 98% probability of non-exceedance of vertical and horizontal wave forces on the pipeline. The force reduction due to burial of the pipelines are compared with the recommendations by DNVGL-RP-F109. The effect of changing the wave height, wave period and hydraulic conductivity on the wave forces and its change due to different burial depths are revealed. The wave force values and the quantitative differences due to 99.99% and 98% probability of non-exceedance can be used for risk-based design of buried pipelines. The recommended value of wave force reduction factor for different relative burial depth of the pipeline by DNVGL-RP-F109 is much smaller than the value of wave force reduction factor from the present study. Strong scope exists to revise this code for the betterment of submarine pipeline design engineers. The knowhow revealed in this study will be useful for optimal design of buried submarine pipelines.

Finite Analysis of Support Time for Tunnels in Strain-softening Rock Mass in Consideration of Fictitious Support Pressure

This study considers that the support time is quantitatively determined by the production limit of the displacement reduction factor and the support force under the extrusion conditions of the strain-softening rock mass. Therefore, the two indicators of the downlines under the support time are the displacement reduction factor of the support force and the yield limit. Based on the solution of the fictitious pressure proposed in an existing paper, the finite difference method is adopted to investigate the variations of the support force and displacement reduction factor versus the delayed distance considering different support types, initial stresses, and post-peak behaviours. The results show that on the one hand, the delay distance is suggested within 1 R0 in most tunnel cases; on the other hand, the factors have greater impact on rock-support interactions are rock mass and in-situ stress. Relatively contrast, softening and expansion behavior was not significant enough. Furthermore, it is also very important in composite support systems to assess the proportion of loads shared with the weakest part.

Experimental in-plane seismic strengthening of masonry infilled reinforced concrete frames by engineered cementitious composites (ECC)

The present study aimed to evaluate the performance of engineered cementitious composites (ECC) retrofit technique for unreinforced hollow clay brick masonry infill wall in non-ductile reinforced concrete (RC) frames subjected to in-plane cyclic loading (quasi-static loading). To this aim, the mechanical properties of ECC and masonry elements were tested. Then, four 1/3-scale, one-story, single-bay RC frames were fabricated. Among these specimens, one frame was tested without infill wall (BF), one frame with unretrofitted infill wall (IF-E0), and specimens IF-SF-E20 and IF-DF-E20-2 were retrofitted by using an overlay ECC on the masonry infill wall on one side and both sides, respectively. The retrofitted specimens provided higher lateral load capacity, stiffness, and energy dissipation capacity up to 215%, 32%, and 102%, respectively, compared to the unretrofitted specimen. Further, the proposed strengthening technique prevented brittle premature failure in the masonry infill walls and partially maintained the integrity of unreinforced infill walls. Also, the obtained backbone curves of specimens were idealized. Based on the results, the displacement ductility factor of the retrofitted specimens decreased up to 50%, but also the force reduction factor and the overstrength factor of them increased up to 19 and 68%, respectively. At the end of the paper, a simplified analytical method is proposed to calculate the peak strength of retrofitted masonry infilled RC frames. The results obtained from this method were close to the experimental results.

Study on live load reduction factors of train for long span multitrack railway suspension bridges

The reduction factor of live load of train for design of long span multitrack railway bridge is investigated as a parallel research program of design of the Wufengshan Yangtze River suspension bridge in China. Firstly, to simplify the calculation of cable force of the suspension bridge with higher geometry non-linearity, the force history curves of typical suspenders are developed in the simulation of random trains running on the railway on bridge. Secondly, the probabilities of the trains running on the multitrack railway crossing on the bridge are analyzed and the probability models of the force of key suspender is established by Monte-Carlo simulation based on the established suspender force history curves. Finally, the suspender force reduction factors for bridge with multitrack railway on it are determined in the sense of the same exceeding probability. The results indicate that the probability is small for the trains on different tracks crossing on bridge at the same time. The probability distribution of the maximum force of the key suspender within the design working life can be described by a combination of a weighted lognormal and a weighted normal distribution. For the two-, three- and four-tracks railway suspension bridge, the derived reduction factors of the suspender force or the live load of the trains are 0.90, 0.75 and 0.65, respectively. Comparing these factors with those specified in the China railway bridge design code reveals that the reduction factor for two-tracks railway bridge is the same, and somewhat smaller for the three- and four-tracks railway bridge.

Performance-based design of self-centering energy-absorbing dual rocking core system

The Self-centering Energy-absorbing Dual Rocking Core system (denoted as the SEDRC system) is a newly developed high-performance steel lateral force-resisting system that can achieve negligible residual inter-story drifts and avoid structural damage during rare earthquakes. Compared to many existing re-centering systems, the SEDRC system also has larger deformability and can obtain a more uniform inter-story drift responses when subjected to ground motions. This research focuses on developing a performance-based design procedure for the SEDRC systems. The seismic force reduction factor model and constant-ductility demand model have been derived via parametric nonlinear dynamic analyses of single-degree-of-freedom systems with the hysteretic behavior of the SEDRC system for developing the Displacement-Based Design (DBD) procedure. Following the developed DBD method, three six-story SEDRC systems with different parameters have been designed to achieve the desired performance objectives. Systematic numerical studies, including nonlinear static analyses, nonlinear dynamic analyses, and incremental dynamic analyses, have been conducted to validate whether the designed SEDRC system can obtain the prescribed performance target and investigate the effect of some design parameters on the seismic responses of the SEDRC systems. According to the results from the numerical studies, it can be observed that the three SEDRC systems designed through the proposed DBD method can successfully obtain the desired performance target. Moreover, higher inter-story drift at the bearing of the shear friction spring damper, as well as the higher enhanced yield-strength ratio of BRBs, can enhance the collapse-resistant capacity of the SEDRC system. Higher bearing inter-story drift can further reduce the residual inter-story drift leading to a lower collapse probability of the SEDRC system subjected to rare seismic events.

Evaluation of seismic response of inelastic structures considering soil-structure interaction

Structural deformations and soil displacements arising out of ground shaking are intertwined. This interplay is termed as seismic soil-structure interaction (SSI). Over last few decades, the conventionally perceived beneficial nature of SSI has been challenged with evidences of damaged sites from various earthquakes. This paper evaluates effects of SSI on seismic response of hardening single degree of freedom systems located in diverse geologies. The assessment is performed using substructure approach in terms of inelastic force reduction factor such that structure attains certain ductility levels. It is observed that soil-structure systems can afford a lesser reduction in design seismic forces compared to fixed-base structures. Components of total displacement arising out of structural deformation, footing translation and footing rotation are also evaluated. With increase in SSI effects, contribution of structural deformation is found to decline sharply. Footing rotation is observed to be very significant in structure-soil systems with larger SSI effects. The soil-structure system is modelled using a discrete physical model which enables inelastic response to be obtained in time domain while considering frequency dependence of impedance functions.

Seismic performance assessment of pre-engineered steel buildingson the west coast of Canada

This paper focuses on the seismic performance of typical pre-engineered steel buildings (PSB) on the west coast of Canada. PSB are widely adopted for commercial and industrial long span low-rise constructions. Their structural system consists of a moment resisting frame made of built-up tapered I-beam elements, which often have slender and/or non-compact sections to minimize steel consumption. Typical seismic design of PSB consists of elastic analysis with force reduction factors (FRF) that assume some ductility. However, failure mechanisms in PSB are usually governed by flange local buckling and lateral torsional buckling, which might not provide the expected ductility. This paper presents an extensive series of numerical analyses to evaluate the seismic performance of four PSB prototypes designed for the city of Victoria on the west coast of Canada. Prototypes have similar general dimensions, while members

Seismic performance of eccentrically braced frames designed to AISC341 and EC8 specifications

In the United States, steel eccentrically braced frames (EBFs) are designed according to AISC341 Specification while in Europe EC8 provisions are used. The European provisions were developed mostly based on the research works conducted in the US. While EBF design recommendations in AISC341 and EC8 have similarities, marked differences exist in the amount of lateral force reduction and distribution of member over-strength among the stories. In addition, the effect of link over-strength on non-dissipative members is treated differently in the two specifications. A study has been undertaken to evaluate the performance of EBFs designed according to AISC341 and EC8. Pursuant to this goal, EBF archetype buildings with 3, 6, and 9 stories were designed using US and European provisions taking into account different force reduction factors. The archetype buildings were subjected to 44 far-field ground motions at the maximum considered earthquake level as recommended by FEMA P695. Nonlinear time history analyses were conducted by OpenSees analysis platform to obtain the link rotation angle, residual frame drift and column axial forces. The results showed that using larger force reduction factors and disregarding the distribution of member over-strength among stories result in large residual frame drifts and non-uniform link rotation angles along the height of the building. Considering a force reduction factor of 5 and imposing a limit on link over-strength among the stories were found to improve the performance considerably. Design recommendations were developed to enhance the performance of EBFs by unifying the rules given in AISC341 and EC8. The study was complemented by investigating the behavior of EBFs subjected to near-field ground motions with pulse. The results showed that near-field ground motions with pulse produce much higher link rotation angles when compared with the demands produced by far-field ground motions.

Examination of Ductility and Seismic Diaphragm Design Force-Reduction Factors for Steel Deck and Composite Diaphragms

This paper analyzes the ductility and overstrength of steel deck diaphragms and composite concrete on steel deck diaphragms and computes associated diaphragm design force-reduction factors, Rs. First, a database of past tests on steel deck and composite diaphragms was created, and more than 750 specimens were compiled into the database. A subset of 95 cantilever diaphragm specimens with postpeak inelastic behavior was identified for which specimen ductility and overstrength were calculated. The effects of variables such as fastener type, fastener spacing, and deck thickness on diaphragm ductility are explored. A method is then developed for converting cantilever diaphragm specimen ductility to diaphragm system-level ductility. Finally, diaphragm design force-reduction factors, Rs, are calculated consistent with an accepted methodology to be Rs=2.09, Rs=1.13, and Rs=2.36 for bare deck diaphragms with mechanical fasteners, bare deck diaphragms with welds to the supports, and concrete on steel deck diaphragms, respectively, for cyclically loaded specimens and assuming a long period structure.

New formulation of ductility reduction factor of RC frame-wall dual systems for design under earthquake loadings

Any design of standard structures in keeping with seismic safety norms is usually founded on an approach characterised by force-based design. Research has proven, over the course of several decades, that such an approach has a solid basis and can easily be applied by the engineers in charge of the design project. Furthermore, when taken in conjunction with principles of capacity design, the force-based approach is effective against premature structural failures. The force-based design approach, however, suffers from a number of shortcomings, especially regarding the way it has been employed in seismic design codes of recent years. One of the weaknesses can be attributed to the way the base shear is calculated via a reduction factor that has been defined a priori and that remains constant for a certain structural system typology. The outcome of depending on the same design input shows that structures identical in type but variant in geometry undergo varying ductility demands and exhibit, therefore, a different seismic performance. In this research, a procedure for assessing force-reduction factors of RC frame-wall dual systems is developed, by combining the analytical formulations proposed by Zerbin et al. (2019) for wall and frame systems, separately. These analytical formulations make it possible to combine global and local ductility demands, thereby allowing a calculation of the factors of force ductility reduction that result in balanced local ductility demands and the predicted levels of damage. The proposed method is based on empiric expressions that merely require – as input data – the information available when starting the design process. The proposed formulation is applied to a set of frame-wall structures and tested by means of both nonlinear static and dynamic analyses. The current study has produced conclusions showing that, with respect to such dual system structures' seismic behaviour, the procedure proposed herein yields a more accurate assessment of than the approach being currently used by design guidelines; in turn this method may provide a valid contribution to the evolving guidelines of future seismic design codes.

Controlling Dynamic Response of Structures Using Hybrid Passive Energy Dissipation Device

ABSTRACT This paper presents a new hybrid passive control device, consisting of a viscoelastic and a friction damper connected in parallel, to mitigate the effects of wind and seismic events. The two components are synergized with the aid of a novel locking mechanism, which enables the action of one or both the components depending upon the device deformation. This provides an innovative two-phase energy dissipation capacity, and exploiting the individual strengths of the two dampers together. The response of a single degree of freedom (SDOF) hybrid damped system is represented in terms of a linear system using equivalent linearization technique, which includes all associated parameters such as the added stiffness, the added damping and the locking mechanism. In order to ascertain the influence of various parameters of the hybrid device, normalized force and normalized displacement are defined in terms of linear SDOF hybrid damped system and further used to obtain force reduction factor for multi degree freedom (MDOF) system with hybrid device. The proposed design methodology of controlling the structural response using the hybrid device is then applied on a six-story reinforced concrete (RC) building. The response of the conventional moment resisting frame (MRF) system and moment resisting frame system with hybrid device (MRHDF) are compared using the nonlinear time history analysis. The performance of the MRHDF system is found to be superior than the MRF system. The hybrid device can effectively reduce the dynamic response of the building, especially in terms of inter story drift, residual drift, base shear and floor acceleration. In addition the proposed design methodology is very simple as compared to the response modification factor approach. This configuration of hybrid device shows improved performance for meeting multiple objectives under wind/seismic events of real-life structures.

Static force-based seismic analysis of reinforced concrete frames having weaker beam-column joints

Shake table tests were conducted on three 1:3 reduced scale two-story RC frames having weaker beam-column joints. The models were subjected to multi-levels input acceleration time histories to understand the seismic behaviour of test models. The models incurred severe damages in beam-column joint panels, forming shear hinging in joint panels, and were found in the incipient collapse state under input excitation below the design level excitation. Elastic hypothetical structures were considered having fundamental frequency that of test structures, which were subjected to actually recorded input excitation, in order to assess the seismic demands (base shear force and lateral roof displacement) using simplified analytical static procedure. The analytically predicted demands were correlated with the measured inelastic response, in order to calculate seismic response parameters (force reduction factor R and displacement modification factors Cd ). On average, R = 2.0 and Cd = 1.86 were obtained for the considered structures. The derived seismic response parameters can be employed in the analytical static force-based procedure for the seismic vulnerability assessment of RC frame structures having weaker beam-column joints. Example study is presented for the vulnerability assessment of considered structure using the proposed analytical static force procedure and the derived seismic response parameters.

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 stiffness-degradation, 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 site-specific 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.