Lateral Stiffness Ratio Research Articles

First-storey height effects on the collapse performance of buildings in extreme events

Higher first-storey height could cause soft-storey irregularity due to less lateral stiffness, in which the hysteric energy dissipation is localized at the first storey of buildings. In the seismic design codes, two different approaches, based on the drift and lateral stiffness ratios, are used to determine soft-storey irregularity. In this study, four reinforced concrete models with different first-storey to typical-storey height ratios are used to show the first-storey height effects. It is shown that even if the models are regular for soft stories based on the seismic design code limits, the higher first storey considerably decreases the ductility capacity. Also, it is demonstrated that the ductility capacity is highly correlated with the storey height ratio. Although all models meet the design criteria of the Turkish Buildings and Earthquake Code (TBEC-2018), the results of the nonlinear time historey analysis reveal that the first-storey drift ratio considerably increases with the higher first-storey height. Further, the collapse performance of the four models is determined using the FEMA P695 procedure, and the results demonstrate that the collapse probability of the model with the highest first-storey height is over the ASCE 7-22 limit.

The influence of infill ALC walls on the seismic performance of prefabricated PEC T-column frames

Autoclaved lightweight concrete (ALC) is characterized by its light weight, high strength, fire resistance, and sound insulation, and has been widely used in industrial and civil construction. Partially encased concrete (PEC) columns exhibit good load-bearing performance, energy dissipation performance, and outstanding prefabrication performance. In order to study the influence of embedded prefabricated ALC wall panels on the seismic performance of assembled PEC T-shaped column frames, this study conducted low-cycle reversed loading tests on a two-story PEC T-shaped column pure frame and a two-story assembled PEC T-shaped column frame with ALC wall panels. This paper draws detailed comparisons between the failure modes and skeleton curves of the two frames. Analysis of the experimental results indicates that the stiffness contribution of infill walls is primarily affected by local compression and exhibits a negative correlation with the wall-frame lateral stiffness ratio. Furthermore, the presence of ALC walls can significantly increase the initial stiffness of the assembled frame. Therefore, based on the existing theoretical basis, a calculation model and method based on the interaction between infill wall panels and frames are proposed. The frame was numerically simulated using finite element software to study the factors affecting the initial stiffness of the frame, and a relationship formula for the wall stiffness reduction coefficient aw was obtained. The calculated lateral stiffness obtained from the formula was compared with the experimental results of this paper and other studies, proving that the model provides a safe result for the design and application of PEC T-shaped column frames filled with ALC walls, and can provide a reference for engineering practice.

Experimental Investigate on Seismic Performance of RC Hill-Side Stilted Buildings Affected by Vertical Stiffness Irregularity

ABSTRACT In this study, the ratio of lateral stiffness of the stilted story to that of the second story was proposed as the story stiffness ratio (SSR) to quantify vertical stiffness irregularities of hillside stilted buildings. A quasi-static experiment was conducted on a plane stilted frame with an SSR of 40 in the slope direction. Experimental results were compared with those of a stilted frame with an SSR of 1.01. The results show that SSR is an important factor influencing seismic failure modes of stilted buildings. As SSR decreases, structural ductility and deformation capacity improve, and stiffness degradation decelerates.

Accurate Estimation of Inter-Story Drift Ratio in Multistory Framed Buildings Using a Novel Continuous Beam Model

This study presents a novel method for accurately predicting the dynamic behavior of multistory frame buildings under earthquake ground motion. The proposed method allows approximately estimating the inter-story drift ratio, a crucial parameter strongly associated with building damage, its distribution along the building height, and its maximum value location. An equivalent continuous beam model with a rotation at the base, consisting of a combination of a shear beam and a flexural beam, is proposed to achieve this. This model derives closed-form solutions for the building’s dynamic characteristics. The lateral deformations along the height of frame buildings subjected to a given earthquake load, particularly the inter-story drift ratio profiles, and the maximum inter-story drift ratio parameter, are investigated. The proposed continuous model requires two dimensionless parameters: the lateral stiffness ratio (α) and the rotation at the base (θ), representing the drift ratio of the first story. For the expression of the lateral stiffness ratio (α) coefficient, a simple equation is also proposed using the beam-to-column stiffness ratio (ρ, or Blume coefficient) associated with the framed (discrete) system. Various building models are employed to validate the proposed method, demonstrating its applicability to both high-rise and low-rise building configurations. With the results obtained, it is shown that the proposed continuous model can be used not only for high-rise or multistory building models but also for low-rise building models.

Study of Effective Length Factor of Frame–Core Wall Structure with Cross-Layer Columns

The aim of this study was to examine the effective length factor of frame–core wall structures with cross-layer columns, which are relevant for current high-rise building construction. Using the finite element method, improved inflection point method (D-value method), and GB50017-2017, the study investigated how the height and distribution of cross-layer columns affect the lateral stiffness ratio, natural vibration period, member internal force, maximum interlayer displacement angle, and effective length factor of the column in the frame–core wall structures. However, the force acting in the frame in the weak axis direction that is considered in GB50017-2017 does not reflect the actual mechanical behavior. Therefore, when determining the effective length factor of cross-layer columns, the interaction between the remaining frames’ sub-structure and cross-layer columns is considered and the effective length factor is modified accordingly. A simplified model of a 140 m frame–core wall structure was established for analysis, and it was assumed that rigid links connect the frame and core wall hinged at both ends. The results show that increasing the height and number of cross-layer columns decreased the lateral stiffness ratio of the structure, and increased the maximum interlayer displacement angle and natural vibration period. Furthermore, the effective length factor of the structure decreased with an increase in height and the number of cross-layer columns. The modified effective length factor agrees well with the results obtained by the finite element method. These findings provide a useful reference for calculating the load-carrying capacity of cross-layer columns in engineering.

Evaluation of Criteria for Out-of-Plane Stability of Steel Arch Bridges in Major Design Codes by FE Analysis

The provisions for out-of-plane stability of steel arch bridges in three major design codes are presented in this paper. By employing an existing steel arch bridge as a model, the influence of bridge type, arch rib to lateral bracing stiffness ratio, rise-to-span ratio, arch rib spacing, and range of lateral bracing arrangements on the out-of-plane critical axial force of the arch rib is studied using FE analysis. The accuracy of the critical axial force provisions is then evaluated against the FE analysis. The results show that the influence of the rise-to-span ratio on critical axial force is generally small. The critical axial force decreases with increasing arch rib spacing when the stiffness ratio is relatively large. A smaller ratio of arch rib length provided with lateral bracing (γ-value) significantly reduces the critical axial force and normalized critical axial force decreases with increasing stiffness ratio. The critical axial force of half-through type arch bridges is lowest when the stiffness ratio is relatively small. A deck-type bridge has a larger critical axial force than a through-type bridge when the stiffness ratio is relatively large, while the results are the opposite when the ratio is small. The different assumptions made in the provisions result in the various parameters having different impacts on the out-of-plane critical axial force in each code, thus affecting code accuracy. Considering the influence of the rise-to-span ratio, ratio of lateral bracing, and arch rib spacing with different stiffness ratios, factors to improve the accuracy of the critical axial force obtained by the three codes are proposed for a practical design process.

Experimental behaviour of unreinforced and confined rat-trap bond masonry

Rat-trap bond (RTB) masonry is a fast-growing building technique owing to its thermal insulation and cost saving. While cost and energy efficiency are important parameters, structural stability and performance are as important. The aim of this study is to experimentally investigate the behaviour of unreinforced and confined RTB masonry subjected to lateral load. The experimental work consists of in-plane quasi-static cyclic load tests of two full-scale specimens; an unreinforced wall and a confined masonry wall. Key parameters such as lateral strength, stiffness, damping, force-deformation behaviour and ductility modification factor of both specimens are determined to understand the lateral load behaviour of RTB masonry. The experimental results indicate that the addition of confining elements significantly improved the behaviour of RTB masonry by enhancing the lateral strength, stiffness and ductility ratio of RTB walls by 121%, 52.8% and 23.8%, respectively.

Lateral Performance of Glulam Timber Frames with CFRP Confined Timber-Steel Buckling-Restrained Bracings

Heavy glulam timber framed structures are facing a growing inadequacy in resisting lateral actions from earthquakes and winds due to the increasing building heights. This paper presents the experimental and numerical analysis results on the hysteretic behavior of newly developed carbon fiber reinforced polymer (CFRP) confined timber-steel buckling-restrained bracings and the lateral performance of bolted glulam timber frames with such bracings. Ten timber-steel bracings and four frames with different bracing provisions were tested via reversed cyclic lateral loading. A finite-element method based model was developed, verified, and used for parametric studies. The bracing test results indicated that the design requirements for ordinary buckling restrained bracings on the confinement ratio and the transverse bulging force are adequate for the proposed timber-steel bracings. A confinement ratio no less than 4.6 is suggested. Compared to an otherwise similar bare frame, two frames with the proposed bracings were found to be 132% and 176% higher in the peak loads, more than 10 times higher in the elastic stiffness, 40% and 43% higher in ductility ratio, and on average 106% higher in the equivalent viscous damping ratio. The two frames also exhibited higher stiffness and energy dissipation than a frame braced by timber bracings, which are prone to buckling failure. Parametric studies indicated that the secant stiffness and the damping ratio of the frames at small drift can be substantially affected by the bolt slippage of the bracing-frame connections. The increased lateral stiffness ratio will lead to increase in the peak load and stiffness, but the equivalent viscous damping ratio remains nearly constant for lateral stiffness ratios larger than 2.5. The frame stiffness and peak load increase with increased rotational stiffness of the beam-column connections while the equivalent viscous damping ratio decreases.

Seismic Performance of RC Split-Foundation Frame Structures with Steel Braces in the Mountainous Area

Reinforced concrete (RC) split-foundation frame structures are widely used in mountainous areas. There are two grounding terminals with different heights in the split-foundation frame structures. Under the earthquake, the local damage phenomenon of the structures is severe due to the uneven stiffness distribution. It is one way to improve the seismic performance of the split-foundation frame structures to install steel braces in the upper embedding floor. According to the deformation characteristics of the upper embedding floor, three types of steel braces arrangement for the split-foundation frame structures were proposed: horizontal braces, V-type braces, and V-[Formula: see text] braces. Then based on the ratio of lateral stiffness of steel braces and concrete frame columns, the section of steel brace was designed. A quasi-static test was carried out to analyze the influence of steel braces on the failure mode of the RC split-foundation frame. The reasonable seismic waves were selected to carry out the nonlinear dynamic time history analysis. Then the seismic response and failure mode of the split-foundation frame structures with different braces arrangements were compared. On this basis, fragility analysis was carried out, and the earthquake-induced collapse resistance capacity of split-foundation frame structures with steel braces was preliminarily evaluated. The results show that the horizontal steel brace can improve the phenomenon of damage concentration of the split-foundation frame structures. Furthermore, setting V-shaped braces can significantly reduce the damage degree of the upper embedding end columns and change the phenomenon of locally severe damage of the split-foundation frame structures. Moreover, according to the design method proposed in this paper, setting steel braces can improve the seismic collapse resistance capacity of the split-foundation frame structures.

Seismic performance of RC frame-shear wall structures with vertical setback

The reinforced concrete (RC) frame-shear wall structure is a typical structural system for modern high-rise buildings. This paper investigates the influence of vertical setback on its seismic performance through elasto-plastic time history analysis on three groups of models under different levels of earthquakes excitation. The studied variables include setback percentage, local lateral stiffness ratio and setback position, which cause vertical irregularity to the structure. It is confirmed that existence of setback increases the inter-storey drift ratio at the setback position due to the sudden change of lateral stiffness thereby. Compared to the structure without setback but having the similar local lateral stiffness, the maximum inter-storey drift ratio is smaller due to the reduced mass associated with the existence of setback. To quantify vertical irregularity, limitation on the local lateral stiffness ratio can be relaxed to some extent for structures with setback. Considering the resulted variation of inter-storey drift ratio, setback percentage and lateral stiffness ratio are equally important. Along the height, setback at the middle height gives larger inter-storey drift ratio and seismic force.

Numerical study of seismic response of irregular multi-frame reinforced concrete bridges

In-span hinges can facilitate construction processes and diminish the adverse consequences of creep, shrinkage and thermal phenomena, but can also bring about detrimental effects such as impacts, unseating issues and large displacements. The seismic behaviour of concrete bridges has been addressed in previous studies, but it remains unclear how in-span hinges affect the seismic response of irregular bridges. The aim of this research was to determine the seismic performance of irregular multi-frame bridges. To consider a wide range of irregularity, four classes of single- and multi-frame bridges with low to high regularity indices were considered. An innovative parameter, the adjacent frame lateral stiffness ratio (AFSR), was introduced to determine the appropriate position of in-span hinges and investigate the performance of multi-frame bridges. The results showed that the beneficial or damaging effects of in-span hinges on the seismic behaviour of a bridge depend on its level of irregularity. The seismic demands of piers in multi-frame bridges are typically lower than those of single-frame bridges. The results also showed that the piers adjacent to an in-span hinge are more affected by the hinge. It is recommended that in-span hinges are located such that the AFSR approaches unity so as to avoid out-of-phase vibration of adjacent frames and unseating issues.

Unified Shear-Flexural Model for Vibration Control of Buildings Using Passive Dynamic Absorbers

A unified design model is proposed for various kinds of passive dynamic absorbers (PDAs) attached to buildings with different lateral resisting systems. A total of five different PDAs are considered in this study: (1) tuned mass damper (TMD), (2) circular tuned sloshing damper (C-TSD), (3) rectangular tuned sloshing damper (R-TSD), (4) two-way liquid damper (TWLD), and (5) pendulum tuned mass damper (PTMD). The unified model consists of a coupled shear-flexural (CSF) discrete model with equivalent tuned mass dampers (TMDs), which allows the consideration of intermediate modes of lateral deformation. By modifying the nondimensional lateral stiffness ratio, the CSF model can consider lateral deformations varying from those of a flexural cantilever beam to those of a shear cantilever beam. The unified model was applied to a 144-meter-tall building located in the Valley of Mexico, which was subjected to both seismic and along-wind loads. The building has similar fundamental periods of vibration and different nondimensional lateral stiffness ratios for both translational directions, which shows the importance of considering both bending and shear stiffness in the design of PDAs. The results show a great effectiveness of PDAs in controlling along-wind RMS accelerations of the building; on the contrary, PDAs were ineffective in controlling peak lateral displacements. For a single PDA attached at the rooftop level, the maximum possible value of the PDA mass efficiency index increases as the nondimensional lateral stiffness ratio decreases; therefore, there is an increase in the vibration control effectiveness of PDAs for lateral flexural-type deformations.

Effect of rigid connection to an asymmetric building on the random seismic response

Connection of adjacent buildings with stiff links is an efficient approach for seismic pounding mitigation. However, use of highly rigid links might alter the torsional response in asymmetric plans and although this was mentioned in the literature, no quantitative study has been done before to investigate the condition numerically. In this paper, the effect of rigid coupling on the elastic lateral-torsional response of two adjacent one-story column-type buildings has been studied by comparison to uncoupled structures. Three cases are considered, including two similar asymmetric structures, two adjacent asymmetric structures with different dynamic properties and a symmetric system adjacent to an adjacent asymmetric one. After an acceptable validation against the actual earthquake, the traditional random vibration method has been utilized for dynamic analysis under Ideal white noise input. Results demonstrate that rigid coupling may increase or decrease the rotational response, depending on eccentricities, torsional-to-lateral stiffness ratios and relative uncoupled lateral stiffness of adjacent buildings. Results are also discussed for the case of using identical cross section for all columns supporting each plan. In contrast to symmetric systems, base shear increase in the stiffer building may be avoided when the buildings lateral stiffness ratio is less than 2. However, the eccentricity increases the rotation of the plans for high rotational stiffness of the buildings.

Mitigating Inter-Story Drift Concentration of Concentrically Braced Steel Frames Using Energy-Dissipative Columns

ABSTRACT Concentrically braced steel frames (CBSF) always suffer from weak-story failure with a large inter-story drift concentrated on the weakest story. A novel system of Energy-Dissipative Column (EDC) is proposed in this paper to improve the seismic behavior of low and mid-rise CBSFs. The EDC system consists of dual hinge supported steel boundary branches and replaceable steel strip dampers between them. Nonlinear dynamic analyses are conducted on 3-story and 6-story benchmark CBSF buildings with and without EDCs. The effectiveness of EDCs with different stiffness ratios on mitigating the seismic responses of CBSFs under design based and maximum considered earthquakes are investigated. The results show that the presence of EDCs in an existing multi-story CBSF can not only dissipate seismic energy to reduce the maximum inter-story drift, but facilitate more uniform inter-story drift distribution by redistributing the seismic forces along the structural height. It is found that the maximum inter-story drift and drift concentration can be reduced by half when the lateral stiffness ratio of EDC to CBSF reaches 0.2.

Development of extended Drucker–Prager model for non-uniform FRP-confined concrete based on triaxial tests

Extended linear Drucker–Prager (DP) model has been a proper choice to capture the stress-strain of cylindrical concrete columns confined by fiber reinforced polymers (FRPs). However, most existing DP models calibrated by uniform active/passive tests are unsuitable for concrete under non-uniform passive confinement. This paper aims to calibrate the key parameters i.e., friction angle, plastic dilation angle and hardening needed for the DP model based on tri-axial test results on concrete cube subjected to non-uniform confinement. The effect of friction angle parameter is isolated from the hardening parameter within the yield function while the friction angle is defined as a function of concrete grade and hardening as a function of lateral confinement stiffness ratio. Here, the plastic lateral strains of non-uniform confined concrete, which could be obtained in cyclic tests but were usually left aside, are used to define a function for plastic dilation angle which works compatibly with the yield parameters. The resultant extended DP model could capture the stress-strain behaviour of concrete under both uniform or non-uniform passive pressure as well as the variable flow rules and different load paths occurring across the section of FRP-confined non-circular concrete.

Steel–concrete composite shear walls using precast high performance fiber reinforced concrete panels

SummaryIn this research, seismic performance of composite steel plate shear walls (CSPSWs) using high performance fiber reinforced concrete (HPFRC) panels is experimentally and numerically investigated. Three one‐story one‐bay CSPSW specimens using precast HPFRC panels were designed and fabricated for cyclic quasi‐static experiments. The HPFRC panels of composite shear wall specimens did not have any steel rebars. The main purpose of the study was to understand the effects of rigid and semirigid HPFRC panels on the seismic behavior of the system. Shear capacity, ultimate shear strength, lateral stiffness, energy dissipation, and ductility ratios of the specimens are evaluated.The experimental results demonstrate that specimens were able to resist lateral load up to at least interstory drift of 6%. Using HPFRC panels, CSPSW specimens becomes stiffer in the elastic region, and the yield displacement of the shear wall is decreased; therefore, the ductility ratio of the system is increased. It should be noted that ultimate shear strength, initial elastic stiffness, and energy absorption of specimens with an HPFRC panel on one side or both sides of the infill steel plate were approximately the same. However, using two HPFRC panels is not economical in comparison with CSPSW with an HPFRC panel on one side. Additionally, the second panel increases the seismic mass of the structure.

Comparative Analysis of Mechanical Properties in the Core Tube of frame with Transfer Layer between the Solid-Wed Beam Transfer and New Type of Inclined Column Transfer with Shaped Steel

The inclined column transfer structure has been directly applied to the engineering practice due to its direct and clear transfer force, reasonable load transfer, simple structure and convenient construction. This paper firstly introduces the application of the inclined column transfer structure in engineering practice. Aiming at the practical construction of a frame structure with a transfer layer, the three types of transfer are then used respectively, and they are ordinary transfer inclined column transfer, the addition of shaped steel to the transfer girder between the inclined column and solid-web beams transfer. Finally, a comparative analysis is carried out from the aspects of cycle, displacement, stiffness ratio, section size of transfer girders, and shear-weight ratio. The results show that the inclined column transfer structure can effectively improve the lateral stiffness ratio of the transfer layer and the connected upper layer structure with its direct transfers force, thus avoiding the form of weak layers here.

Modified plastic-damage model for passively confined concrete based on triaxial tests

Plasticity-based models are used as the constitutive relationship of concrete under passive confinement of fiber reinforced polymers (FRPs). Triaxial cube tests are needed for adjusting the parameters included in a model. Most of the existing plasticity models are developed from actively confined tests or by uniform passively confined column tests. Methods for developing a plasticity model based on non-uniform passively confined concrete tests and applied to non-uniform passive confinement are rare and needed. This study reports more than one hundred triaxial concrete cube tests under uniform and non-uniform passive confinement. Six grades of concrete were tested under monotonic and cyclic compression loads. The lateral stiffness ratio was the main parameter for designing the tests. Using the reported tests, a new approach is devised for deriving parameters of a plastic-damage model for practical application to concrete structures under non-uniform passive confinement. The lateral stiffness ratio is found to be a key factor for plasticity model parameters involving dilation angle, hardening rule, and damage variable. Based on the test results and using finite element analysis (FEA), explicit empirical models are developed for the plasticity parameters. FEA analyses using the developed plasticity-damage model performs well compared with test results.

Mitigating seismic response of RC moment resisting frames using steel energy-dissipative columns

A novel system of steel Energy-Dissipative Columns (EDCs) is proposed to mitigate seismic responses of reinforced concrete Moment Resisting Frames (MRFs). The EDC-MF dual system aims to not only dissipate seismic energy by replaceable steel strip dampers in EDCs but mitigate inter-story drift concentration to avoid soft/weak-story failure of conventional MRFs. A simplified numerical model of EDC-MF dual system is established by using lumped mass shear model for MRFs and finite element model for EDCs. Parametric studies are conducted to investigate the effect of storey number, stiffness ratio, soft story factor and seismic intensity factor on the mitigation efficiency of EDCs. The results show that the lateral stiffness ratio of EDC to MRF, the story irregularity factor of MRFs, and the ratio of story shear capacity of EDC-MF systems to seismic base shear are the most important parameters. It is found that both the maximum inter-story drift and the inter-story drift concentration can be effectively mitigated due to the presence of EDCs, compared to traditional MRFs. The mitigation efficiency of EDCs increases with increasing lateral stiffness ratio and story irregularity factor under various ground motion intensities. A rational range of lateral stiffness ratios of 0.02–0.2 is recommended for the seismic design of EDC-MF dual systems.

Pushover analysis of the reinforced concrete frames with soft first storey using a fiber hinge model

In seismic zones, the problem with the soft storey is amongst the factors that causes the formation of the rupture mechanism in reinforced concrete structures due to variation in the lateral stiffness between levels. Most seismic codes have addressed this phenomenon in realizing the admissible lateral stiffness ratio between levels, without specifying the method to be used in determining this stiffness. The current study is aiming at determining the secant stiffness of each level by using the level capacity curve obtained by nonlinear static pushover analysis, based on a fiber hinge model. The results obtained made it possible to plot a curve that represents the variation of the elastic or secant stiffness ratio between the first level and the second level of a construction as a function of a displacement at the top of the structure. This curve examines the possibility of occurrence of a first soft storey for different points of performance.