Axial Load Ratio Research Articles

Seismic Performance of Shaped Steel Reinforced High‐Strength Concrete Walls: Cyclic Loading Test and Analytical Modeling

ABSTRACTThe thickness of the bottom shear walls in tall and super‐tall structures is often designed too large to meet the limit requirements of axial compression ratios, which increases the weight and cost of the structure. To address this issue, high‐strength concrete (HSC) and shaped steel are combined to form composite shear wall members. This paper focuses on seismic performance and analytical hysteresis model of steel reinforced HSC shear walls (SRHCW) under high axial compressive load. Firstly, the reversed cyclic test was conducted to investigate the influence of concrete strength and the steel ratio on the seismic performance of SRHCWs by comparing the failure mechanism, hysteretic curves, stiffness degradation, ductility, energy dissipation, and steel bar strain variation of each specimen. Then, a hysteresis model for SRHCWs was established, and the model can be used for the nonlinear analysis and seismic performance evaluation of SRHCWs. Finally, the accuracy of the proposed hysteresis model was evaluated by the experimental data. The experimental results show that under high axial compression ratio, the interstory drift ratio capacity of SRHCWs can reach 3.03% showing excellent deformation performance. The wall specimens built with different strength concrete and shaped steel ratios exhibited similar strength, deformation, and initial stiffness, indicating that the steel ratio of the wall can be effectively reduced by upgrading the concrete strength of the wall specimens while ensuring its seismic performance. The analytical model can well predict the hysteresis force–deformation curves of SRHCWs under high axial load ratios.

EFFECT OF EARTHQUAKE DIRECTIONALITY ON THE SEISMIC RESPONSE OF RC WALL BUILDINGS

Reinforced concrete (RC) wall buildings are widely used for their proven seismic resilience, as evidenced in past earthquakes. To understand their behavior, extensive research has been conducted using both experimental and numerical methods. Despite these efforts, the impact of earthquake directionality on these structures deserves further exploration. Addressing this gap, this paper examines the effects of earthquake directionality on three RC wall buildings. Eleven ground motion records from the far-field suite of the FEMA P695 were selected, rotated, and used to perform incremental dynamic analyses of the three buildings in OpenSeesPy. The buildings seismic performance was evaluated in terms of the roof drift ratio, axial load ratio, and bending moments. Additionally, a novel performance metric, namely the MaxRotEDPpp is introduced to assess the building’s response. The results show that the direction of ground motions has a significant impact on engineering demand parameters and in the probability of exceedance for different thresholds, which can double compared to non-rotated ground motions.

Residual axial bearing capacity of square high-strength concrete-filled steel tubular columns after transverse impact loading

In recent decades, the performance of concrete-filled steel tubular (CFST) members under impact loads has received much attention. Serving as the main load-bearing components in structures, CFST members, especially those using high-strength materials, are expected to maintain their capacities in supporting the superstructures during and after potential extreme events to avoid severe consequences. The post-impact residual axial bearing capacities of square high-strength concrete-filled steel tubular columns were therefore determined to be the focus of this study. Axial loading experiments were conducted on 12 square high-strength CFST specimens with impact-induced damage, and a finite element (FE) model was developed in which both the impact loading process and the post-impact axial loading process were involved. Based on the developed FE model, parametric studies were then carried out to evaluate the influence of the material properties, the cross-sectional characteristics, the initial axial load ratio and the impact energy conditions on the post-impact residual bearing capacities of high-strength CFST columns. A total of five hundred random CFST models were modelled and analysed to ascertain the mutual relationships among the impact energy, the maximum impact deformation (support rotation) and the post-impact residual bearing capacities quantitatively, which are anticipated to facilitate both the rapid performance assessment of the impacted damaged (deformed) square CFST columns after the occurrence of impact events and the performance-based impact-resistant design in advance against such accidents.

Probabilistic modelling of steel column response to far-field detonations

Due to the deficiency of current design guidelines for blast loadings on steel structures, this research develops probabilistic models for steel wide-flange columns under axial and far-field blast loading on both their weak and strong axes. A total of 160 finite element (FE) simulations were conducted using ANSYS LS-DYNA, with columns subjected to different Axial Load Ratios (ALRs) and blast impulses. Validation against two experimental tests showed a strong correlation in displacement plots, with a material model accounting for strain rate effects. Probabilistic models for predicting maximum displacement and residual axial capacity were formulated using Bayesian inference and posterior statistics. These models were developed by incorporating dimensionless physics-based explanatory functions. The slenderness ratio of the column was identified as the most influential. The models account for uncertainties such as material and geometric properties, as well as strain rate effects. Graphical plots between the ALR and Damage Index (DI) were examined to assess the column's damage level. Furthermore, the probability of failure (fragility) of four columns for similar blast impulse was assessed w.r.t DI. These models along with ALR vs DI plots will be useful tools to know the level of building occupancy and retrofitting options.

Post-tensioned coupling beams: Mechanics, cyclic response, and damage evaluation

This study investigates the influence of axial load ratio, initial prestressing ratio, and aspect ratio on the cyclic performance of post-tensioned coupling beams. An analytical solution was derived and verified against experimental studies conducted on post-tensioned beams and a comprehensive numerical parametric analysis was conducted, examining fifty-one scenarios with varying design parameters. These scenarios incorporated three key parameters: the beams’ aspect ratio (span to height), ranging from 1.5 to 3.5; the axial load ratio, ranging from 0.04 to 0.175; and the initial prestressing ratio, ranging from 0.35 to 0.65. Increasing the axial load ratio led to more severe damage, while higher aspect and initial prestressing ratios reduced damage. The axial load ratio had the greatest effect on damage severity, while the aspect ratio mainly influenced the size and length of crushed regions at the beam corners. Deeper post-tensioned coupling beams (aspect ratio <2.5) showed higher coupling shear forces. Increasing the axial load ratio significantly boosted shear capacity, while a higher initial prestressing ratio slightly reduced it. Additionally, both a higher axial load ratio and aspect ratio increased ultimate beam chord rotation, whereas higher initial prestressing ratios decrease it. The estimated stiffness factor, ranging from 0.04 to 0.4, decreased with smaller aspect ratios. Both axial load and initial prestressing ratios had a similar influence on the stiffness factor. A smaller axial load ratio reduced beam-wall interaction and lowered the stiffness ratio, while increasing the initial prestressing ratio raised compressive stress at beam corners, leading to higher initial stiffness and a larger effective moment of inertia. These estimated stiffness factors were then used to derive a relation for the design of post-tensioned coupling beams.

Experimental study on seismic performance of bridge pier with new HRB650E high-strength steel bar

To facilitate the application of high-strength steel in reinforced concrete bridge structures, this study explores the seismic performance of full-scale HRB650E high-strength reinforced concrete bridge piers. Initially, monotonic tensile tests were conducted on HRB400 and HRB650E steel rebars with the same slenderness ratio to analyze the differences in their mechanical properties. Subsequently, quasi-static cyclic tests were carried out on four square full-scale RC bridge piers to examine the influence of new high-strength rebars, stirrup ratios, and axial load ratios on the seismic performance. Based on the experimental results, a hysteresis model suitable for HRB650E reinforced concrete columns was developed. The findings indicate that the HRB650E steel bar exhibited lower uniform elongation and fracture elongation compared to HRB400 steel bar. The displacement at which HRB650E piers reached crack damage was 36 % higher than that of HRB400 piers, and they also showed lower residual displacements at all load levels. The maximum lateral load capacity and the ductility coefficient of HRB650E piers increased significantly compared to HRB400 piers. While the initial secant stiffness of both types was comparable, HRB650E piers exhibited a slower rate of stiffness degradation, resulting in higher secant stiffness at the ultimate state. They also demonstrated 35 % higher cumulative energy dissipation at the ultimate state. When the stirrup ratio of HRB650E piers was increased from 1.1 % to 1.7 %, there was a slight reduction in residual displacement, a small increase of the yield strength, and a minor improvement in the maximum lateral load capacity. Furthermore, a higher stirrup ratio was observed to improve energy dissipation levels at all loading stages. Increasing the axial load ratio of HRB650E piers from 0.1 to 0.2 allowed the piers to withstand greater deformations at the same repairable ultimate state, with significant increases in yield strength, maximum lateral load capacity, initial secant stiffness, and secant stiffness at the ultimate state, but a small increase in the cumulative energy dissipation. The hysteresis model for HRB650E RC columns, based on experimental data, exhibited good computational accuracy.

Study on seismic response of flexure-shear critical RC columns wrapped with TRC shells

Quasi-static tests were conducted on sixteen specimens to study the seismic response of flexure-shear columns wrapped with textile reinforced concrete (TRC) shells. Two RC square columns served as controls, while the remaining columns were wrapped with TRC shells. Three types of treatment methods were applied to TRC-wrapped columns herein to study the impact of different interfacial treatments on seismic behaviours. This study also analyzed the impacts of shear span ratios, axial load ratios, and number of textile layers on the seismic response of test columns. Results revealed that the TRC confinement layers could mitigate crack development, transforming RC columns' failure modes from flexure-shear to flexure. Due to greater confinement to the concrete core, TRC-wrapped columns exhibited enhanced performances compared to control columns, with peak loads, ductility, and cumulative energy dissipation increasing by up to 49.9%, 195.3%, and 5.7 times, respectively. TRC confinement layers could mitigate the shear effects in column specimens. TRC wrapping could improve the shear capacities of flexure-shear columns, with growth rates ranging from 25.2% to 60.4%. Eventually, an equivalent viscous damping model was proposed to assess the energy dissipation capacity of flexure-shear columns wrapped with TRC shells.

Seismic Performance of Precast Drift-Hardening Concrete Walls Connected by Grout-Sheath Duct.

In order to find a suitable size of sheath duct and a reliable construction method for precast walls, a cast-in-place and five 1/2 scale precast drift-hardening concrete walls reinforced with weakly bonded ultra-high strength SBPDN rebars were fabricated and tested under reserved lateral load and constant compression. The experimental variables were the diameter of sheath ducts (45 mm, 100 mm, and 120 mm), embedded length (20d and 35d; d is the nominal diameter of SBPDN rebars), axial load ratio (0.075 and 0.15), and the construction method. The experimental observations, hysteresis behaviors, envelope curves, residual deformation, crack propagation, and energy dissipation were compared in the study. Moreover, a formula was applied to calculate the bond strength of the sheath duct. The experimental and calculated results revealed that increasing the axial load ratio and embedment length could not enhance the bond strength of the sheath ducts, and increasing the diameter decreased the bond strength significantly. Anchored the SBPDN rebars in smaller sheath ducts separately was a more stable connection method for precast concrete shear walls and provided sufficient drift-hardening capability, even at a large drift level (over 3%).

Mechanical model analysis of column-footing joints with combined socket-corrugated pipe connection

The socket connection method is widely used in precast column, particularly in seismic regions. However, reducing the socket-depth to lower costs may lead to shear failure in the socketed part of the columns. To address this issue and achieve cost objectives, a new approach combines shallow sockets with corrugated pipes for column-footing joints. Comparative tests were conducted to investigate failure in columns with socket-corrugated pipe connections (SCPC), shallow sockets (SSC), and cast-in-place (CIP). Furthermore, finite element models were employed to validate the experimental and simplified model results. The findings suggest potential shear failure in shallow socket connections, which can be mitigated by using the combined socket-corrugated pipe method that alters force transmission paths. As the axial load ratio increases, both the ultimate lateral load capacity of the specimen and the local stresses at the column base increase. In addition, the ultimate lateral load capacity of the column and the stress of the connection reinforcement are increased by increasing the strength of the longitudinal reinforcement, consequently amplifying the extent of joint area damage. Finally, a simplified strut-and-tie model of the SCPC, validated against numerical and experimental data, accurately represents force paths, ultimate lateral load capacity and failure modes in socket joints.

Numerical Study on the Retrofitting of Exterior RC Beam-column Joints with CFRP Composites Using the Grooving Method

Retrofitting seismically deficient beam-column joints (BCJs) in reinforced concrete (RC) structures is crucial to preventing collapse during high-intensity earthquakes. Fiber reinforced polymer (FRP) composites have proven effective for retrofitting these components, but debonding of the FRP from concrete surfaces remains a challenge. Recently, the grooving method (GM) has emerged as a promising solution to mitigate this issue, enhancing the bond between FRP and concrete. This paper presents a numerical investigation of BCJs retrofitted with FRP composites using the GM, focusing on various design parameters. The study utilized finite element models developed in ABAQUS, incorporating the concrete damage plasticity (CDP) model to simulate the nonlinear behavior of concrete. The interface between the concrete and FRP was modeled as a perfect bond, simulating the strong adhesion provided by the GM. The numerical results were validated against experimental data from two BCJ specimens, showing good agreement in terms of load-displacement behavior, peak loads, and failure modes. Key parameters studied include the beam longitudinal reinforcement ratio, column axial load ratio, and joint aspect ratio. The findings reveal that these parameters significantly affect the shear capacity of retrofitted joints, impacting the efficiency of the retrofitting.

Seismic in-plane behavior of composite masonry walls strengthened with cold rolled steel sheets

The seismic behavior of masonry walls strengthened by cold rolled steel sheets is numerically evaluated in this study using finite element modeling in ABAQUS. Cold-rolled steel sheets cover two sides of an unreinforced masonry wall and are bolted together to form a composite masonry wall. The behavior of the composite masonry walls is compared to that of the corresponding unreinforced masonry walls with various failure mechanisms. The finite element models of the unreinforced masonry walls are validated through experimental data in the literature. Then, cold-rolled steel sheet-strengthened walls are simulated, and variations in strength, ductility, and failure mode are investigated. A thorough sensitivity analysis is conducted on the effects of the aspect ratio, boundary condition, axial load ratio, steel sheet thickness, and connection bolt configuration on the in-plane strength and failure mode of the walls. It is observed that the steel sheets affect the local and global behavior of the masonry walls and change their failure modes. The use of through-thickness bolts to connect steel sheets to the masonry wall provides a composite action between steel sheets and the masonry wall against in-plane lateral loads. The cold-formed steel sheets not only resist a portion of the lateral load but also significantly increase the lateral strength of the masonry walls and the ductility of the whole wall system. Based on the analysis results it can be concluded that strengthening masonry walls with cold-rolled steel sheets is a promising technique for the seismic improvement of existing conventional masonry buildings and for the design of new masonry buildings.

Numerical investigation on plastic hinge behavior of hybrid steel-FRP reinforced concrete columns

This paper presents a numerical study on the plastic hinge behavior and rotation capacity of concrete columns reinforced with a combination of steel bars and fiber-reinforced polymer (FRP) bars. A meso-scale numerical model, which considers the internal heterogeneity of concrete and bond behavior between concrete and longitudinal reinforcements, was developed and validated. The failure modes, lateral load-displacement responses, and the physical plastic hinge lengths of hybrid steel-FRP reinforced concrete (SFRC) columns were investigated and compared with those of conventional steel-reinforced concrete columns. The results indicated that the steel yielding zone and curvature localization zone of SFRC columns with FRP longitudinal bars were enlarged, due to the relatively low modulus of FRP bars. After that, a parametric analysis was performed to study the plastic hinge length of SFRC columns with respect to the nominal area ratio of FRP longitudinal bars, shear span-to-depth ratio, axial load ratio, and longitudinal reinforcement ratio. A new empirical model was proposed to predict the equivalent plastic hinge length, which was subsequently integrated into an analytical method for predicting the ultimate rotation. The comparison of predictions with simulation and test results demonstrated the accuracy of both the proposed empirical model and analytical method.

Mechanics guided data-driven model for seismic shear strength of exterior beam-column joints

This study presents an enhanced predictive model for the seismic shear strength of exterior beam-column joints (BCJs). Initially, the principles of strut-and-tie mechanism and variable selection procedures were first utilized to identify the most influential parameters. Subsequently, an evolutionary algorithm, specifically multigene genetic programming (MGGP), was utilized to search for the near-optimal predictive model. The dataset used to develop, train, and test the proposed model was compiled from previously published tests, focusing specifically on cyclically loaded exterior BCJs that encountered shear and flexure -shear failures. The prediction performance of the developed model was assessed through various statistical measures, and then compared with that of other existing models. Additionally, sensitivity analyses were also performed to identify the influence and importance of each design parameter. The results demonstrated that the methodology employed in this study yielded an elegant model that adheres to the underlying mechanics and provides higher prediction accuracy compared to existing models. Furthermore, the sensitivity analyses showed that BCJ shear strength positively correlates with concrete compressive strength, beam reinforcement, joint transverse reinforcement, column intermediate vertical reinforcement, and axial load ratio, while it negatively correlates with the joint aspect ratio. Among these design parameters, beam reinforcement has the greatest influence on the model response, followed by concrete compressive strength. Conversely, column intermediate vertical reinforcement and axial load ratio have the least impact on the model response. The notable prediction capabilities and robustness demonstrated by the developed model render it an efficient design tool with promising potentials for adoption by practicing engineers and for consideration in design guidelines.

Design of improved multi-cell L-shaped CFST columns under compression and bending

In recent years, there has been a notable surge in proposals for various forms of special-shaped concrete-filled steel tubular (CFST) columns. Despite various methods developed by researchers for determining the bearing capacity of multi-cell special-shaped CFST columns under different loading conditions, these methods remain lack unified. In this study, FE models were developed to simulate performances of improved multi-cell L-shaped CFST (ML-CFST) column under compression and bending. Parametric analyses have been performed to evaluate impact of various factors, including steel yield strength fy, compressive strength of concrete fcu, steel thickness t, loading direction θ, web height c, and axial load ratio n, on performances of ML-CFST columns. The findings of study indicate that the unidirectional flexural capacity of ML-CFST member exhibits a nearly linear relationship with the variables of t, fy, and c, with a minimal impact observed from fcu on flexural capacity. The width of extended section b, fcu, fy, and t have a certain effect on flexural capacity at any angle, particularly fy, t, and b. While fcu, fy, and t exert some influence on N/Nu-M/Mu correlation curves, their influences are marginal compared to the loading direction, which is the predominant influencing factor. Additionally, Mx0/Mπ/4-My0/M3π/4 curves gradually protrude outward with the increase in n. The effects of t, fy, and fcu on the shape of Mx0/Mπ/4-My0/M3π/4 curve were relatively insignificant. Simplified unidirectional flexural capacity calculation models were proposed based on stress analysis of cross-section under ultimate states. Given that flexural capacities estimated by simplified calculation model are slightly conservative, it is recommended to increase the flexural capacities by 10 %. Furthermore, an elliptical equation was formulated to predict the flexural capacity at any angle, with the predictions being slightly conservative. Based on ultimate equilibrium theory, a simplified calculation method was presented to predict unidirectional eccentric bearing capacities of ML-CFST columns. Through regression analysis, a simplified calculation method expressed as polar coordinate form for biaxial eccentric bearing capacity was established, with calculated values aligning well with FE results.

Assessment of Ductility Demand-Based Blast Damage to Reinforced Concrete Columns under Blast Loads

This study was conducted to evaluate the influence of various structural variables on the blast damage to reinforced concrete columns. The selected primary variables were the longitudinal reinforcement ratio, transverse reinforcement ratio, and axial load ratio, with the analysis based on the ductility demand to assess the blast damage. A parametric study based on finite element analysis was performed to analyze the effects of these variables. The results revealed that an increase in the longitudinal and shear reinforcement ratios significantly decreased the level of damage sustained by the columns under blast exposure, whereas an increase in the axial load ratio resulted in a comparatively lower reduction in damage. Columns with higher transverse reinforcement ratios experienced more severe damage owing to compression-induced brittle failure as the axial load ratio increased. This study provides guidelines for the appropriate selection of design variables to mitigate blast damage in columns.

Post-earthquake fire performance of partially encased composite steel and concrete columns

Considering the potential severity of losses caused by post-earthquake fires compared to earthquakes alone, this study employed a three-dimensional Finite Element (FE) model established in ABAQUS to investigate the response of partially encased composite (PEC) steel and concrete columns under post-earthquake fire, serving as preliminary analysis for subsequent experimental studies. The validity of the FE model was verified using results from existing seismic and fire loading tests. In simulating the hysteresis behavior of PEC columns, this study evaluated the impacts of concrete discrete cracking and mechanical models on the simulation outcomes, thereby refining the modeling technique. A typical PEC column was selected as the focus of this investigation. Sequential earthquake-fire simulations were conducted using a data transfer technique to assess the fire resistance performance of different seismic damaged columns with different axial compression load ratios. The results indicate that the behavior of damaged PEC columns evolves based on initial damage, and the failure exhibits overall bending accompanied by local buckling of the steel flange. As the axial load ratio increases, the fire resistance time of seismic-damaged PEC columns significantly decreases. When the axial compression ratio is increased from 0.2 to 0.5, the fire resistance time of columns with damage factor D within 0.6 decreases by 59.07% on average. This sensitivity to axial pressure is particularly pronounced when earthquake damage is severe. Moreover, it finds that the lateral drift ratio under seismic action should be controlled within 2% to ensure that the post-earthquake fire resistance will not be significantly reduced.

Behavior of circular ultra-high-strength concrete-filled steel tube columns subjected to combined high-axial and cyclic lateral loads

The present study examined the seismic performance of circular concrete-filled steel tube (CFST) columns infilled with ultra-high-strength concrete (UHSC >100 MPa) as well as the beneficial effect of embedded spiral confining (SC) reinforcement at high axial load ratios (0.53–0.70) in order to enhance the safety and structural integrity of high-rise buildings. Seven specimens, including four CFST columns and three SC-CFST columns, were investigated under combined high axial and quasi-static cyclic lateral loads. The test parameters included axial load ratio (0.53–0.70), concrete compressive strength (64–111 MPa), embedded spiral confining reinforcement (pitch of 30 mm and 60 mm), and concrete vibration state. The test results demonstrated that adding spiral reinforcement improved the deformation capacity of CFST columns, which was reduced by the increased concrete strength. By embedding spiral confining reinforcement (volumetric ratio 3.3 %), the SC-CFST columns attained a deformation capacity comparable to that of CFST columns with normal concrete (64 MPa) for an axial load ratio of 0.53. The higher axial load ratio and concrete strength of composite columns led to a significant P-Delta moment effect, resulting in a substantial drop in columns' lateral load capacity. Composite columns with UHSC showed a larger contribution from the column base rotation to the specimen's lateral deformation when compared to composite columns with normal-strength concrete because the rigidity offered by UHSC made the column more rigid and reduced its flexural deformation. The unvibrated core concrete of the CFST column did not influence the initial stiffness and energy dissipation capacity. However, during the later stages of loading, the damage in core concrete rapidly accumulated, resulting in instant degradation of the load capacity and stiffness, considerable axial shortening, and poor deformation capacity. The experimental investigation offered a reliable reference on the performance of CFST columns constructed under high-axial load ratios (0.53–0.7) using ultra-high-strength concrete (>100 MPa) and spiral confining reinforcement so as to promote their application in practical engineering.

Investigation of plastic hinge length in high-ductility reinforced concrete shear walls

In this study, the plastic hinge lengths of reinforced concrete (R/C) cantilever shear walls were analytically determined considering various design parameters. Nonlinear static (Pushover) analyses were conducted on R/C shear wall models and their nonlinear behavior was examined using ABAQUS software. In the study, 72 shear wall models with different parameters were analyzed under the influence of vertical and horizontal loads. Parameters whose effects on plastic hinge length were investigated height/length ratio (Hw/Lw), axial load ratio (N/No), and horizontal web reinforcement ratio (ρsh). The load-displacement graphs of the modelled shear walls were obtained. The plastic hinge height of shear walls was determined according to the heights of the deformations in the concrete and longitudinal steel reinforcement in the section when the shear walls lateral load decreased by 15%. The analytical plastic hinge lengths (Lpz) were determined with respect to the location of the yield occurred at the longitudinal steel reinforcement of the shear wall. The observed plastic hinge lengths (Lp) were determined based on the height of observed the crush as of the foundation top level in the concrete shear wall model. The relationship between the findings of this study and empirical formulas in the literature was determined. It was determined that there is greater closeness between the values obtained from empirical formulas in the literature and the observed plastic hinge length values. It was observed that the plastic hinge length generally increases as the shear span increases. It was observed that the change in ρsh was not a very effective parameter in plastic hinge formation. As the N/No decreases, the plastic hinge length values ​​ generally increase. The Lp/Lpz ratio varied within the range of 0.15-0.50. In addition to ductility (μ) values were determined by using the displacements determined according to both the crushing occurred in the shear wall concrete and the yield observed in the steel reinforcement. The observed that the ductility value depends more on Hw/Lw ratio as N/No ratio decreases.

Simplified Approach for Determining Buckling Load in Portal Frames: Elastic Stability Analysis

Abstract The stability of portal frames is a critical aspect of structural engineering, significantly influencing their safety and performance. It refers to their ability to resist buckling or collapse under compressive forces, ensuring structural integrity and safety under various loading conditions. This study aims to provide design charts, created from closed-form solutions, on the probability of forming four different failure modes depending upon stiffness and axial load ratios. These charts provide a simplified and efficient method for quickly and easily assessing the elastic stability of a portal frame without the need for complex analyses or numerical simulations. The results indicate that in most cases, the governing failure mode is the sway-without-shear mode. However, upon further analysis, it is found that when the stiffness ratio (EI2/EI1) exceeds 2 and the force ratio (P2/P1) exceeds 1.33, the observed failure mode typically shifts to the symmetrical failure mode. Moreover, of the concluded results, the study discloses that the stiffer the beam, the higher the critical load ratio, and subsequently, the higher the buckling load. This is due to the fact that the beam behaves more like a rigid element, which prevents joint rotation, as in the fixed-end condition.

Blast performance of RC columns with different levels of concrete grades and reinforcing ratios

AbstractThe present article aims to study the behavior of RC columns under blast loading. A nonlinear dynamic Three‐Dimensional (3D) Finite Element FE model‐based explicit solver available in ABAQUS Software is used. A parametric study is investigated to enhance the blast resistance of RC columns under three different scaled distances z of an explosion, that is, 0.23, 0.5, and 1.07 m/kg1/3 for close, intermediate, and Far in‐distance. In addition, three levels of concrete grades are used, which are Normal Strength Concrete (NSC), High Strength Concrete (HSC), and Ultra High‐Performance Concrete (UHPC). The study also considers Three reinforcement ratios for longitudinal and transverse reinforcement ratios of (ρL = 1.28%, 2.4%, and 3.1%) and (ρs = 0.6%, 0.9%, and 1.35%), respectively. Further, three different Axial Load Ratios, ALR = 0.01, 0.2, and 0.4, are considered to examine the effect of increasing ALR on the RC column under close explosion. For more investigation, the parametric analysis considers two geometrical shapes of RC columns (square and circular). The material behaviors of concrete and reinforcing steel bars are represented using Concrete Damage Plasticity (CDP) and Johnson–Cook (J–C) models, respectively, available in ABAQUS Software. The FE model has been initially validated against experimental study. The FE‐predicted deflection and damage were observed and agreed with the practical cases. In addition, the parametric study's results demonstrate that the RC column's blast deflection is significantly reduced with increasing reinforcement ratios. However, increasing concrete grade could efficiently reduce blast damage and deflection. Furthermore, compared with NSC, UHPC significantly reduced maximum damage and deflection by around 60% for square and 55% for circular columns, respectively.