Strength Reduction Factor Research Articles

Effect of Soil–Structure Interaction on Inelastic Displacement Ratios of Bridge Structures Subjected to Pulse-Like Ground Motions

This study aimed to investigate the effect of soil–structure interaction (SSI) on the inelastic displacement ratio of bridge structures subjected to near-fault pulse-like earthquake ground motions. SSI was modeled using a discrete-time recursive filter approach and frequency-dependent foundation–soil impedance functions. A total of 105 near-fault earthquake ground motion records were used for the analysis. The study also compared the soil–foundation–superstructure (SFS) system with a fixed-base system to explore the effects of spectral period normalization, strength reduction factor, earthquake magnitude, site-to-source distance, and peak ground velocity on the inelastic displacement ratio. The findings indicate that both the SFS and fixed-base systems have significant inelastic displacement demand under near-fault earthquakes, with values that can be 2–3 times higher than those predicted by ASCE-41-13, particularly in the short period range. Furthermore, as the structural period approaches the earthquake pulse period, the SFS system generally shows larger inelastic displacement ratios compared to the fixed-base system. The analytical results provide insight into the factors affecting the inelastic displacement ratio for near-fault pulse-like earthquakes.

Thermal and Structural Response of Beam-end Shear Connections During a Large Compartment Fire Experiment

The role of steel connections is essential in structural fire design and analysis for steel-framed composite structures. The current structural design provisions provide strength reduction factors of load-carrying members and their end-connection elements at elevated temperatures, based on small-scale experiments under uniform heating conditions. The realistic thermal and structural evolution in member connections, especially as part of full-scale floor assemblies exposed to a large compartment fire, has not been well characterized. A large compartment fire experiment was recently conducted on a 9.1 m by 6.1 m composite floor assembly as part of a two-story steel-framed building. The test assembly had a total of ten shear-tab (fin-plate) connections subjected to combined fire and mechanical loading. This paper presents the measured thermal response of these connections to fire and comparison with the corresponding Eurocode 3 predictions with two methods (1) incorporating the beam bottom flange temperature at midspan and (2) the section factor method. The results show that the Eurocode 3 methods conservatively predict the maximum temperature during heating and the cooling rate but overestimate the high-temperature strength of connections when estimated using the section factor method, showing that the Eurocode 3 simplified approaches are not meant to provide the details of the failure mode for connections. This study suggests that estimating the strength of connections using strength reduction factors may not guarantee a safe structural fire design. In addition, this paper estimated the total axial force (from slab and beam) at the composite connection via using the strain gauge measurements close to the column bases which were not exposed to fire. It suggests realistic axial load and rotational demand on the shear connection due to restraints to thermal elongation or contraction of supported members should be considered in future design guidance as should designing and detailing the connections for ductility to withstand the inelastic deformation demands during the heating and the cooling phases.

Seismic Performance of RC Moment Frame Buildings Considering SSI Effects: A Case Study of the New Venezuelan Seismic Code

The Soil–Structure Interaction (SSI) effect has been widely evidenced during several earthquakes around the world. In the Venezuelan context, the seismic event in Caracas in 1967 showed the significant consequences of designing buildings without considering the SSI effect. Nevertheless, limited research on the seismic performance of concrete moment frames (commonly used as structural systems in office and residential buildings in Venezuela and Latin America) considering the SSI effects has been developed, although there have been continuous updates to the Venezuelan Seismic Code. In this research, the influence of the SSI on the seismic performance of RC moment frame buildings designed according to the New Venezuelan Seismic Code was studied. An extensive numerical study of 3D buildings using concrete moment frames supported by mat foundations on sandy and clayey soils was performed. The response spectrum method, non-linear static analysis, and non-linear dynamic analysis were used to assess the seismic response of the archetypes studied. The results show that SSI effects can have a significant impact on the seismic response of RC moment frame buildings, increasing the interstory drift ratio and decreasing the shear forces. As is shown in fragility curves, the probability of collapse increases for cases with flexible bases in comparison to the cases of models with fixed bases. Additionally, in the 24-story archetype, the fixed-base model reached a maximum probability of collapse. Finally, a new proposal for the reduction of the strength-reduction factor (R) must be incorporated into the Venezuelan Seismic Code to improve the safety of the structures. Limitations in the use of RC moment frames must be incorporated for high-rise buildings since, as the present work demonstrates, for high-period structures, the normative provisions are not reached.

A Laboratory Study of Use of Crumb Rubber as Partial Replacement of Fine Aggregate in Concrete

Abstract: The aim of this study is to analyse the effect of addition of crumb rubber on the various properties of concrete. The crumb rubber is used as replacement over aggregates in the concrete mix. Crumb rubber is prepared from the scraps of tyres. In this study aggregates are replaced by 0%, 30%, 40%, 60%, 100% crumb rubber. The rubberized concrete is tested for slump and compression strength. It is found that the slump of rubberized concrete increases first but as the amount of rubber is increased the slump starts decreasing. It is observed that initial compression strength of rubberized concrete reduced significantly but the final strength is found to be more than that of ordinary concrete. Waste tyres cause tremendous pressure and ecological issues for the entire tyre industry when accumulated in cultivated land or combusted. Crumb rubber (<5 mm) grinded from waste tyres was introduced to substitute for natural fine aggregate in concrete and effectively solves the consumption challenge. This paper reviews the performance of concrete with crumb rubber as fine aggregate, providing evidence for crumb rubber concrete (CRC) materials design and application. Crumb rubber is characterized with light specific gravity, hydrophobicity and air entrapment in comparison with natural fine aggregate, inducing significant reduction in workability of fresh CRC and exhibiting poor bonding performance with cementitious matrix. By summarizing the compressive/tensile strength, elastic modulus and fracture behaviour of CRC at various rubber content, prediction models of strength reduction factors are proposed. The main reasons for strength deterioration are weak interface transition zone (ITZ) performance and non-uniform distribution of rubber particles. Water/chloride permeability, electrical/carbonation resistance and drying shrinkage of CRC are discussed for durability performance of CRC. Physical/chemical pre-treatments of rubber could alleviate the hydrophobicity and improve the mechanical and durability performance of transition zones between rubber and cement paste. Accordingly, scopes concerning the recycling of crumb rubber and its performance optimization are expected in future studies.

Axial compression performance of UHPCFCST stub columns after exposure to high temperatures

In this study, axial compression tests were performed on thirty ultra-high performance concrete-filled circular steel tube (UHPCFCST) stub columns after high-temperature exposure. Temperature, fiber type, and steel tube thickness were varied to examine the damage process, damage characteristics, load–strain curve, and load–displacement curve of the columns, as well as the effects of changing each parameter on the peak load of the UHPCFCST stub columns after high-temperature exposure. The test results reveal that the restraining effect of the steel tube prevented the core ultra-high performance concrete (UHPC) from bursting at high temperatures. The specimens remained unchanged in shape between 25 °C and 400 °C but showed significant damage at 600 °C. The ductility of specimens with either polypropylene fibers or a mix of polypropylene and steel fibers were better, and the increase in the thickness of the steel tube could prevent shear damage of the specimens. As the temperature increased, the ultimate resistance of the cross-section of the specimen tended to first increase and then decrease, with the curve gradually flattening. The ductility of the specimen was greater after 800 °C. In addition, a finite element model (FEM) of the behavior of UHPCFCST stub columns under axial compression after high-temperature exposure was established, and the stress development of the UHPC and steel tubes was analyzed. A material strength reduction factor was introduced to modify the existing method of calculating the axial compression resistance of cross-section after high-temperature exposure, and the results showed that it could be better predicted using superposition-based calculations.

The effects of strain rate on the effective yield strength of high-strength steel at elevated temperatures

PurposeThis work examines the effects of strain rate on the effective yield strength of high-strength steel at elevated temperatures, through tensile coupon tests at various strain rates, to propose appropriate reduction factors considering the strain rate effect.Design/methodology/approachThe stress–strain relationships of 385 N/mm2, 440 N/mm2 and 630 N/mm2-class steel plates at elevated temperatures are examined at three strain rate values (0.3%/min, 3.0%/min and 7.5%/min), and the reduction factors for the effective yield strength at elevated temperatures are evaluated from the results. A differential evolution-based optimization is used to produce the reduction-factor curves.FindingsThe strain rate effect enhances with an increase in the standard design value of the yield point. The effective yield strength and standard design value of the yield point exhibit high linearity between 600 and 700 °C. In addition to effectively evaluating the test results, the proposed reduction-factor curves can also help determine the ultimate strength of a steel member at collapse.Originality/valueThe novelty of this study is the quantitative evaluation of the relationship between the standard design value of yield point at ambient temperature and the strain-rate effect at elevated temperatures. It has been observed that the effect of the strain rate at elevated temperatures increases with the increase in the standard design value of the yield point for various steel strength grades.

Durability performance of RC beams strengthened with CFRP laminates and galvanized steel mesh bonded with epoxy and mortar systems

The galvanized steel mesh (GSM) systems are novel strengthening materials for the concrete structural elements, but their mechanical and long-term durability properties are needed to be investigated to enhance understanding and reliability in their use. This study investigates the behavior of reinforced concrete (RC) beams strengthened with carbon fiber reinforced polymers (CFRP) and GSM sheets under harsh climatic conditions of saline water and direct sunlight. The main focus was to recommend two important reduction factors, the bond reduction factor and the overall flexural reduction actor, when concrete beams are subjected to two said environments for a long period. These factors were compared to the ones recommended by different codes. The CFRP sheets were attached to the beams’ soffit with epoxy adhesive, whereas the GSM sheets were bonded either with epoxy (SME) or epoxy-based mortar (SMM). The specimens were weathered under saline water and direct sunlight for a period of 6, 12, and 24 months. The load-carrying capacity of CFRP, SMM, and SME strengthened specimens increased by 47%, 55%, and 55%, respectively, when compared to the unstrengthened specimens at 28 days. The bond capacity reduction factors (Rb) for CFRP, SMM, and SME strengthening systems were 0.75, 0.85, and 0.95 for saline water exposure, and 0.95, 0.85, and 0.85 for sun exposure, respectively, over a period of two years. On the other hand, the recommended overall flexure strength reduction factors (Rn) for CFRP, SMM, and SME strengthening systems were 0.85, 0.85, and 0.90 for saline water exposure, and 0.95, 0.90, and 0.90 for sun exposure, respectively. The results suggest that epoxy-based strengthening systems are more durable compared to the mortar-based systems under harsh climatic conditions.

Study on Degradation Law and the Equivalent Thickness Model of Steel Subjected to Sulfate Corrosion.

In order to study the variation of mechanical properties of steel under acid rain corrosion conditions in northern China, monotonic tensile tests were conducted on Q235 steel with a thickness of 3.0 mm and 4.5 mm using a method of artificially prepared simulated acid rain solution for indoor accelerated corrosion. The results show that the failure mode of corroded steel standard tensile coupon includes normal fault and oblique fault. The failure patterns of the test specimen show that the thickness of the steel and corrosion rate affected the corrosion resistance. Larger thicknesses and lower corrosion rates will delay the failure mode of corrosion on steel. The strength reduction factor (Ru), deformability reduction factor (Rd) and energy absorption reduction factor (Re) decrease linearly with the increasing corrosion rate from 0% to 30%. The results are interpreted also from the microstructural point of view. The number, size, and distribution of the pits are random when the steel is subjected to sulfate corrosion. The higher the corrosion rate, the clearer, denser, and more hemispherical the corrosion pits. The microstructure of steel tensile fracture can be divided into intergranular fracture and cleavage fracture. As the corrosion rate increases, the dimples at the tensile fracture gradually disappear and the cleavage surface gradually increases. An equivalent thickness reduction model is proposed based on Faraday's law and the meso-damage theory.

Effects of the Vertical Component of Ground Motion on the Maximum-Inelastic-Horizontal-Response of SDOFs

This study investigates potential effects of the vertical-component-of-ground-motion (VCGM) on the maximum-inelastic-horizontal-response (MIHR) of single-degree-of-freedom (SDOF) systems. The effects of VCGM can be considered in two categories. First, it may initiate some modes of failure, like over-compression, and second, it might adversely influence the horizontal response through altering the P-delta effect. The latter is a result of variation of the gravitational acceleration, and hence, seismic weight, upon action of the VCGM. This study uses time-history analysis to compare the response of SDOFs in presence and absence of the VCGM. In both cases, the P-delta effect is inherent in analyses and period-dependent feature of the stability-coefficient, which is essential for reliable treatment of the P-delta effect, is explicitly reflected. Since available record selection and scaling strategies use uncoupled vibrators in vertical and horizontal directions, this research follows two steps to avoid undesirable bias. The first step, which focuses on examining the influence of some important parameters, adopts an event-based record selection scheme. Results indicate that for certain combinations of the strength reduction factor and initial period of vibration the effect of the VCGM on the MIHR is significant. Specifically, the systems with initial periods between 1.0 and 2.0 s are found most vulnerable. Moreover, the mentioned effect is not limited to near source regions. The second step evaluates capability of the VCGM to initiate dynamic instability. In this step, a set of 26 records, which resembles an assumed target spectrum at a near field site, is used. Results show that under action of some of the examined records, the presence of the VCGM leads to dynamic instability; hence, this study suggests consideration of the VCGM for collapse evaluation.

Shear performance and design rules for welded stainless steel I-shaped members with web openings

The use of stainless steel I-shaped members as primary load-bearing members has become increasingly popular, particularly in acidic environments, owing to their corrosion resistance and other advantages. Openings on the web are often introduced for ease of installation. The presence of web openings can reduce the shear resistance and produce high stresses around the openings, limiting their application. However, no previous study has investigated the shear resistance and design rules of such welded stainless steel I-shaped members with web openings. This work presents a detailed numerical analysis to examine the shear performance of perforated stainless steel members. Finite element (FE) models considering material nonlinearity and initial geometric imperfections were developed and verified using corresponding test data presented by the authors and many researchers. A parametric study including 434 FE models was undertaken to analyse the influence of web openings on the shear resistance of such members. The results suggested that for members with a hole diameter–web height ratio of 0.7, web openings can reduce the shear resistance by 61.4% on average, when compared to unperforated members. The generated numerical results were used to evaluate the current design recommendations given in the Eurocode (EN 1993-1-4+A1) (2015), American standard (ANSI/AISC 370-21) (2021), and those design rules proposed by Chen et al. (2018), although they were designed only for unperforated members. The comparisons demonstrated that the current design guidelines provided non-conservative predictions for calculating the shear resistance of perforated members. New design formulas were proposed using the strength reduction factor. A reliability analysis was undertaken, which indicated that the new design formulas were reliable for predicting the shear resistance of such members.

Development of a new framework based on Gaussian regression process for rapid fragility analysis of 2-DoF base-isolated structures

This paper develops metamodels (or surrogate models) to predict the fragility parameters of structures isolated with friction pendulum (FP) isolators. An equivalent inelastic two-degree-of-freedom (2DoF) system is utilized to model the base-isolated structures.6000 system simulations are initially established based on the probability distribution of input parameters. Then, incremental dynamic analyses are carried out to achieve structural data for the fragility function generation. The developed dataset of the fragility parameters (median and dispersion) is divided into training and testing sets to train and testthe efficiency of the developed metamodels, respectively.Powerful machine learning tool, namely, Gaussian Process Regression (GPR) is utilized for mapping structural input parameters to output (or target) parameters, i.e., median and dispersion of the fragility functions. GPRs are kernel-based probabilistic models, with kernel functions constituting their core components. In this study, the predictive quality of the GPR is evaluated considering different kernel functions to obtain the most accurate and reliable predictions. The results indicate that automatic relevance determination (ARD) kernel functions are much more efficient than isotropic kernel functions. Statistical performance metrics indicate that, among the implemented kernel functions, ARD Matern 3/2 is preferable for both the superstructure and FP isolator. The proposed GPR-based prediction metamodels exhibit excellent performance in the prediction of the fragility parameters of the superstructure and isolator for all considered limit states. Using the developed metamodels, conducting a rapid seismic fragility assessment on 2DoF systems that are representative of base-isolated structures is possible. At last, metamodels are exploited in seismic reliability analysis to assess their precision for further investigations. The results of seismic reliability-based performance and relationships between the displacement ductility demand and strength reduction factor reaffirm the efficiency, sufficiency, proficiency, and practicality of the GPR-based generated metamodels.

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

Development and seismic performance evaluation of New high strength reinforced concrete column and steel beam (New-RCS) joint

Reinforced Concrete column and Steel beam (RCS) structural systems have recently become popular in Taiwan for office buildings. High seismic demand makes the size of conventional concrete columns enormous and the reinforcement over-crowded, which can be solved using high-strength materials. However, due to the lacuna of research regarding the usage of high-strength materials, existing design guidelines for the RCS systems have restricted the maximum grade of steel reinforcement to 410 MPa. Also, using high-strength materials in RCS joints necessitates innovative joint detailing and design to develop sufficient joint bearing and shear strength. Thus, a new high-strength reinforced concrete column and steel beam (New-RCS) joint was developed in this study, incorporating the use of Grade 690 MPa steel as reinforcement along with Grade 84 MPa concrete. A combination of wide flange bearing plate and flange doubler plate joint detailing was developed to improve the bearing and shear capacity of the joint. Also, a design methodology based on moment–curvature analysis was proposed to include the contribution of locked longitudinal reinforcement to bearing resistance. Subsequently, two large-scale interior beam-column subassemblies were subjected to quasi-static cyclic loading to verify the seismic behaviour of the proposed joint. One specimen was designed explicitly considering the material hardening and overstrength of steel beams. While the other was designed following the Taiwanese practice, which does not explicitly consider material hardening and overstrength but implicitly does it through strength reduction factors. Both the specimens exhibited a drift capacity of 4% with a stable and ductile hysteretic response and eventually failed through beam plastic hinging.

Ductility-strength and strength-ductility relations for a constant yield displacement seismic design procedure

The modern engineering approach to design of structures exposed to rare but intense earthquakes allows for their inelastic response. Models and tools to rapidly but accurately assess the extent of the inelastic response of the structure and control its performance are, therefore, essential. We develop a closed-form upmu -R^{*}-S_{d,y} relation between the ductility upmu and the strength reduction factor R*, as well as its approximate inverse R*-upmu -Sd,y relation, both functions of the SDOF oscillator yield displacement Sd,y, not its vibration period T. The fundamental vibration period of the structure varies during the iterative design process focused on modifying its strength. However, the yield displacement of the structure is practically invariant with respect to the strength of the structure, as it depends primarily on its geometry and material properties. We use these relations to formulate a constant yield displacement seismic design procedure and exemplify it. Noting the structure of the developed relations, we use dimensional analysis to formulate a version of the ductility-strength and strength-ductility relations that are dimensionless and independent of the seismic hazard intensity. These novel, dimensionless master relations are the upmu -R*-H/B-upkappa ductility-strength and the R*-upmu -H/B-upkappa strength-ductility relations.

Application of Machine Learning to predict the mechanical properties of high strength steel at elevated temperatures based on the chemical composition

This paper presents the results obtained using Machine Learning (ML) algorithms to predict the mechanical properties, including ultimate tensile strength, yield strength, 0.2% proof strength and elastic modulus, of high strength steel plate material at elevated temperatures. High strength steels are increasingly used in several areas of construction offering efficient structural solutions with a high strength-to-weight ratio. Safe fire design of these structures relies heavily on accurate prediction of mechanical properties of the material with temperature. The data on elevated temperature mechanical properties collected from the literature experimental tests show a high degree of scatter, implying that they are influenced significantly by various factors, most notably the testing method, manufacturing process and chemical composition. However, the current methods for predicting the mechanical properties of high strength steels at elevated temperatures by using ‘reduction factors’ as adopted by the structural design codes do not consider these effects and may lead to inaccurate predictions. To overcome these deficiencies, a ML-based prediction method that uses temperature and chemical composition as input parameters is developed in this paper. Deep Neural Networks are trained and validated on the basis of elevated temperature material data collated from the literature test programmes. The analysis of the results show that the trained algorithm gives an excellent correlation coefficient with very small error value in predicting the strength and stiffness reduction factors of HSS.

VERIFICATION OF STRENGTH REDUCTION FACTOR RELATED TO OPENING HEIGHT OF RC MUTLI-STORY SHEAR WALLS FOR THE SHORT-TERM ALLOWABLE SHEAR DESIGN

Short-term allowable shear force of RC multi-story walls for safety assurance and damage control was specified in AIJ standard. However, this allowable force for multi-story shear walls with door openings was defined by limited data. In this study, based on the experimental results of five 1/4 scale multi-story shear wall specimens with various disposition of vertically aligned door openings, several strength reduction factors related to door openings were verified for the short-term allowable force based on the observed strengths for safety assurance and the observed residual crack widths for damage control. Consequently, an optimal reduction factor was suggested.

Reliability analysis of flexural provisions of FRP-RC beams and sensitivity analysis based on FORM

A reliability analysis was conducted based on the flexural strength recommendations provided by the ACI 440.1R-15 guide concerning the glass fiber-reinforced polymer-reinforced concrete (GFRP-RC) beams. A statistical investigation was carried out by compiling the dataset of 235 specimens from the technical literature on the model uncertainty of the beams to select the best probability distribution. As such, two failure modes of concrete crushing and GFRP rupture were examined. Reliability was analyzed using the first-order reliability method (FORM) via iHLRF algorithm. Importance sampling was also employed to determine the efficiency of the FORM. Findings reveal that the flexural requirements of ACI 440.1R-15 regarding the FRP-RC beams are conservative for both failure modes, particularly the GFRP rupture failure. Subsequently, importance vector α and sensitivity vectors δ and η were conducted to rank the effect of the most important random variables and their probability distribution parameters on the reliability index. Results from the importance vector α demonstrate that the random variable d is the most significant variable in both failure modes amongst the examined design variables. Thus, uncertainty contributed with d has the greatest effect on the reliability index. Moreover, based on the results from sensitivity vectors δ and η, varying the mean and standard deviation of the random variable ML leads to maximum change in total failure probability of the problem. Finally, strength reduction factors of 0.65 and 0.75 were respectively proposed through calibration so as to reach the target reliability index for GFRP rupture and concrete crushing.

Models for Predicting Strength Reduction Factors for Concrete that Utilizes Palm Kernel Shells and Waste Automobile Tires as Aggregates

Palm kernel shells (PKS) and waste automobile tires do not only enhance the properties of concrete (e.g. damping ratio, ductility, impact resistance etc.), but also their rational utilization can significantly reduce carbon footprints and environmental pollution globally. In this study, a multivariate regression analysis was carried out to develop models for predicting the reduction factors and thereafter the strengths (compressive strength, flexural tensile strength, split tensile strength and bond strength) of concrete that utilizes PKS and waste automobile tire chips as partial to full replacement of the conventional crushed granite stones as coarse aggregates. The strength reduction factors, , were modelled as a function of the total aggregate replacement level (TAR), and the volume of PKS (P) and tire (T) particles in a given concrete mix whilst the performance of the models was assessed using the Mean Squared Error (MSE) and the Coefficient of Determination () techniques. After studying several mathematical functions, it was found that a single linear regression model can be used to predict the strength reduction factors for all the mechanical properties of the concrete tested but with different function parameters. The values of the ranged from 0 to 1 depending on the aforementioned factors. However, a of 0.53 (53%) can be achieved at the 50% optimum replacement where P50T50 for any of the mechanical properties. Furthermore, for each of the concrete properties, the was positively correlated with the volume of PKS but negatively correlated with the TAR level and volume of tire particles in the concrete matrix. Thus, an increase in the TAR level or tire content decreases the and vice versa. In conclusion, the proposed models can be used to establish the target strengths of PKS.

Strength reduction factor spectra for SDOF systems with structural fuses

Highly ductile replaceable fuses can greatly improve the performance of structures and mitigate seismic damage. A fused structure refers to a dual system that generally includes the primary structural system and the fuses acting in parallel. Few studies have thoroughly investigated the strength reduction factors of dual systems or their nonlinear response behaviors; instead, a restoring force model was adopted to represent the performance of the whole system while ignoring the interactions between the primary structure and fuses. This paper separates the two components and considers their interaction. The behavior of the primary structure and structural fuses is assumed to be similar to elastic-perfect plastic. Two parameters, the yield displacement ratio (α) and the initial stiffness ratio (β), are introduced to describe the relationship between the fuses and the primary structure. Based on a dual system, the dimensionless governing equation of motion is derived. The strength reduction factor spectra with a known displacement ductility factor (μ) are then calculated under two groups of selected ground motions. The influences of α, β, and μ are investigated statistically. The strength reduction factor spectra of the fused structure can be expressed by the four-stage predictive model developed by Newmark and Hall for traditional structures, but the spectral shape and two plateau values are closely related to α, β, and μ. These two plateaus are crucial for the spectral shape of the four-stage model. Finally, a simplified equation is proposed to estimate the strength reduction factors of dual system considering α and β with equivalent μ.

An improved analytical model for two-step corbels in a precast concrete system

Corbels are a common element in the beam–column connections of precast concrete structures. This paper analyses the failure of a two-step corbels system using computational modeling. A finite element model is developed and calibrated using the test results for two-step corbels without secondary reinforcement but with steel fiber–reinforced concrete. A database is developed from the parametric analyses of two-step corbels, varying the a/d ratio (0.34–0.76), the rate of the main reinforcement (0.19–0.50%), the compressive strength of the concrete (30–70 MPa) and the amount of steel fibers (1.0% and 1.5%). An improved analytical model, using the developed database, is proposed to design the two-step corbels. The reliability of the proposed analytical model is evaluated using a second database, developed in this paper, and a strength reduction factor of 0.66 for failure by yielding of the main reinforcement and 0.56 for failure by crushing of the concrete strut, were obtained. Therefore, the improved analytical model obtained for the design of two-step corbels represents an advance, in terms of structural safety and economy, when compared to the previous analytical models recommended in the literature.