Moment Magnification Research Articles

Behavior and design approach of ultra-high-performance concrete slender columns

The existing literature concerning the behavior of slender columns made of reinforced ultra-high-performance concrete (UHPC) is severely limited. Furthermore, current design standards lack specific guidelines for reinforced UHPC (R–UHPC) slender columns. Based on this, a comprehensive experimental investigation was conducted on four columns with 2 % steel fiber content subjected to compression to explore the influence of eccentricity ratios (e/h0 = 0, 0.15, 0.3, and 0.6) on the compression behavior of the R–UHPC slender columns. The results revealed that all R–UHPC slender columns experienced failure due to compressive zone UHPC crushing, with no observed concrete spalling. Moreover, a detailed parametric study was conducted on 3000 R–UHPC slender columns using a validated finite element model. By analyzing the parameters and employing the moment magnification method, a statistically derived design equation for effective flexural stiffness (EI) was formulated. The results indicated that EI decreased with increasing eccentricity ratio and increased with rising slenderness ratio. Additionally, calculation formulas for determining cross-section strength were proposed for R–UHPC slender columns, accounting for the contribution of tensile zone UHPC to the overall section strength. Finally, the proposed design approach was validated by comparing predicted results with available experimental data.

Behavior of textile‐reinforced concrete columns

AbstractThis work aims to investigate the behavior of textile‐reinforced concrete (TRC) members subject to compressive loads. An experimental program including concentric compression tests on I‐section columns with different lengths and simply‐supported ends was carried out. From compression tests, load versus lateral deflection curves obtained experimentally are reported along with maximum loads and apparent imperfections determined using the Southwell technique. Failure modes were characterized by excessive lateral deflections for longer columns, whereas concrete crushing failure due to combined bending and axial load occurred for shorter columns. Surrounding concrete was effective in restraining the textile reinforcement against buckling, allowing it to sustain the compressive loads. A single degree‐of‐freedom model accounting for normal‐moment‐curvature relation and tension stiffening behavior is validated against experiments and used to carry out a parametric study. Results show that the nonsway moment magnification method recommended by the ACI Code 440.11‐22 can be applied to TRC columns, although leading to overestimated second‐order effects.

Full-scale cyclic testing of slender RC columns bent in double curvature under high axial load

The development of modern tall and irregular buildings has seen increased slenderness and axial force in columns that seriously jeopardize the seismic safety of the structures. Due to the restrictions of the testing facilities, existing experimental studies on slender RC columns under high-axial force are limited and primarily based on small cross-section specimens bent in single curvature and loaded monotonically. However, due to the size effects, test results from small-scale and monotonic loading experiments may not sufficiently reflect the realistic seismic behavior of double curvature RC columns in full-scale buildings. Furthermore, the applied vertical load in typical single curvature tests could not maintain constant and may reduce significantly upon large deflection. Hence, this study aimed to provide new and critical insights into the seismic performances of full-scale slender and large cross-section RC columns with various transverse reinforcement designs under a constant high axial load of up to 50% of the axial capacity. The full-scale specimens were tested in a double-curvature configuration under lateral displacement reversals and high axial loads. The tested slender columns experienced increasingly significant P-Δ moment magnification effects with further drifts after yielding, imposing greater loading demand on the sections and destabilizing the columns after the peak loads. The robustly anchored transverse reinforcement not only improved the typical seismic performance indicators, including strength retention and drift capacity, but also reduced the P-Δ moment magnification experienced by slender columns, thus enhancing the stability index. Furthermore, the plastic hinge lengths increased in slender columns under high axial load due to P-Δ moment magnification. Lastly, suitable methods for assessing the behavior of slender RC columns based on design codes or existing analytical models are recommended.

Data-driven machine learning methodology for designing slender FRP-RC columns

Current design guidelines for reinforced concrete (RC) with fiber-reinforced polymers (FRP) bars lack provisions for designing slender columns. Limited attempts were made to modify the moment magnification procedure to accommodate FRP-RC columns. This study proposes a novel approach for designing FRP-RC slender columns based on suggesting a simplified slenderness reduction factor to account for the slenderness (ϕslender). The novel reduction factor has been developed using data-driven machine learning, where the available experimental database of short and slender FRP-RC columns has been employed to train a robust generalized artificial neural network (ANN) model. The ANN model is then utilized to generate reduction-factor curves, facilitating a straightforward approach to designing slender FRP-RC columns. For design practice purposes, genetic expression programming (GEP) was used to generate a mathematical equation for calculating ϕslender. The proposed ϕslender is a function of concrete compressive strength, reinforcement ratio, eccentricity, and column slenderness ratio. Statistical correlation analysis indicated that implementing the ϕslender eliminates the axial capacity correlation to the slenderness ratio, indicating a very good representation of the slenderness effect on the FRP-RC columns. The proposed approach revealed higher accuracy and consistent conservatism compared to the moment magnification procedure in predicting the strength of the slender FRP-RC columns.

Test and design of eccentrically-loaded slender circular tubed columns filled with high-strength concrete and reinforcement

The tubed-reinforced concrete (TRC) column is an original reinforced concrete column in which the stirrups are mostly replaced with the steel tube to enhance the confinement to the concrete core. In this study, the eccentrically-loaded behavior of slender circular TRC (CTRC) columns with high-strength materials was experimentally and numerically investigated. Six slender columns with high-strength concrete of 81 MPa and high-strength rebar of 583 MPa were tested to failure under eccentric loading, considering the main parameters of length-to-diameter ratio and load eccentricity. A three-dimensional finite element (FE) model was established and verified for conducting parametric studies and investigating the moment magnification and eccentricity magnification which reflect the second-order effect on the strength of slender columns. The results indicate that all columns fail in a bending mode and show good deformability, even with the use of high-strength materials, and the strength of high-strength rebars can be fully utilized due to the enhanced concrete compressive strain and ductility. Based on the test results and parametric study, a design method is proposed to assist designers to evaluate the load capacity of slender CTRC columns.

Eccentric compression behavior of Steel-FRP composite bars RC columns under coupling action of chloride corrosion and load

In order to investigate the eccentric compression behaviors of steel-FRP composite bar (SFCB) reinforced concrete (RC) columns subjected to chloride corrosion, the mechanical experiments of chloride corroded SFCBs and SFCBs RC eccentric compression columns were conducted. The effect of reinforcement type and ratio, eccentricity, slenderness, stress level and corrosion duration on bearing capacity, deformation, crack and failure pattern were investigated. The results showed that the strength retention ratio of reinforcement decreases with the increase of corrosion duration, the ultimate strengths of steel rebar, SFCB and FRP rebar decreased by 12.2%, 9.9% and 3.6%, respectively, when compared with those of uncorroded counterparts. With the increase of steel content of reinforcement, the load bearing capacity of eccentric compression RC column increases while the deformation decreases gradually. The load bearing capacity of corroded steel, SFCB and FRP RC columns maximally decreased by 16.6%, 12.4% and 7.2%, respectively, when compared with those of uncorroded counterparts. Based on the simplified materials constitutive relations and reasonable basic assumptions, formulae for discriminate failure mode, moment magnification factor and bearing capacity were developed. The predicted failure pattern, moment magnification factor and bearing capacity are in good agreement with the test results, confirming the validity of the proposed formulae, the results can be used as a reference for engineering application.

Evaluation of Stability Resistance Factor for Slender Concrete Columns Internally Reinforced with Fiber-Reinforced Polymer Bars

The validity of the stability resistance factor in the moment magnification procedure for the analysis of slender columns reinforced with fiber-reinforced polymer (FRP) bars (FRP-RC columns) has not yet been considered in the literature. The development of such a factor, compatible with current building codes, is discussed in this paper. In the development process, first, the variability of the ultimate strength of slender FRP-RC columns was investigated, and the effect of variations in geometric and material properties on this variability was determined. The results of the variability study were later used in the first-order reliability analysis to estimate the appropriate stability resistance factor. The results of the analysis show that a stability resistance factor of 0.75 or 0.7, depending on the flexural stiffness expression, is representative of typical slender FRP-RC columns. Thus, we propose the use of this value, in combination with the recommended load factors.

Structural and buckling behavior of full-scale slender UHPC columns

Ultra-high performance concrete (UHPC) is a relatively new class of concrete and cementitious materials with much higher strength and durability than conventional concretes. The use of UHPC is currently expanding worldwide from bridge deck joints and connections to full components and larger applications. With the superior mechanical properties of UHPC, future UHPC columns in buildings and bridges will have compact cross-sections and smaller footprint. The main goal of this study is to provide experimental demonstration and reliable datasets of slender UHPC columns to validate current analytical procedures and inform future designs. This paper presents results and discussions from five full-scale UHPC columns (largest set of axially-tested UHPC columns to-date) at a 4 million-lb [∼18,000 kN] testing facility. The specific objectives are to investigate the structural and buckling behavior of slender UHPC columns under concentric axial loading, and assess the current ACI procedure for slenderness effects using the moment magnification method. When the actual material properties of UHPC and longitudinal bars are used for assessment, the ACI equations were found to overestimate the axial load capacity of slender columns by approximately 9%, on average. The study is concluded by design guidance and several recommendations for applying the moment magnification method for slender UHPC columns, which can be readily incorporated into future design codes.

Eccentric compression behaviour of concrete columns reinforced with steel-FRP composite bars

Eccentric compression behaviour of reinforced concrete (RC) columns reinforced by steel-FRP composite bars (SFCBs) was investigated through experimental work and theoretical analyses. The tension and compression test results show that SFCBs demonstrate a stable post-yield stiffness. The mechanical properties of the composite reinforcement have a significant influence on eccentric compression behaviour of the reinforced concrete columns, in terms of failure mode, crack width, deformation and bearing capacity. Formulae were also developed to discriminate failure mode and to determine moment magnification factor, bearing capacity and crack width of the columns studied, with the theoretical predictions being in a good agreement with the experimental results. In addition, parametric studies were conducted to evaluate the effects of mechanical properties of reinforcement, reinforcement ratio, eccentricity, slenderness ratio, types of reinforcement and concrete on the eccentric compression behaviour of RC columns. The results show that the compressive performance is significantly improved by using the high performance concrete, i.e. reactive powder concrete (RPC) and engineered cementious composites (ECC).

Optimization of Reinforced Concrete Column Using Android- based Mobile Application

Reinforced concrete column has complicated calculations. Designer usually acts trial and error to get the optimum dimension and reinforcement according to the occurred loads. It takes long process and the result is not always be the most economical section. Nowadays smartphone with its various applications is very popular among societies. Besides being more flexible in place and time, smartphone has ease in operation and is commonly used by people. Hence, those advantages can be used to optimize reinforced concrete column quickly and accurately. The application named “C2 App” (Concrete Column Application) had been created by accommodate regulation in Indonesia (SNI 2847:2013). Biaxial calculation used Bresler’s approach, while calculation of slender column applied Moment Magnification Method. The application is able to show interaction diagram, section drawing, and result tables. Moreover, the application was equipped with local database, and detailed calculations in pdf format to support the real project. Validation was done with computer-based software named CSiCol and ASDIP Concrete, whereas the optimization result was compared with other designs which used ACI Diagrams and Particle Swarm Optimization method. The application was pretty accurate and could provide a more economical section.

PRACTICAL METHOD FOR ANALYSIS AND DESIGN OF SLENDER REINFORCED CONCRETE COLUMNS SUBJECTED TO BIAXIAL BENDING AND AXIAL LOAD

Reinforced and concrete-encased composite columns of arbitrarily shaped cross sections subjected to bi axial bending and axial load are commonly used in many structures. For this purpose, an iterative numerical procedure for the strength analysis and design of short and slender reinforced concrete columns with a square cross section under biaxial bending and an axial load by using an EC2 stress-strain model is presented in this paper. The computational procedure takes into account the nonlinear behavior of the materials (i.e., concrete and reinforcing bars) and includes the second order effects due to the additional eccentricity of the applied axial load by the Moment Magnification Method. The ability of the proposed method and its formulation has been tested by comparing its results with the experimental ones reported by some authors. This comparison has shown that a good degree of agreement and accuracy between the experimental and theoretical results have been obtained. An average ratio (proposed to test) of 1.06 with a deviation of 9% is achieved.

Behavior and design of slender square tubed-reinforced-concrete columns subjected to eccentric compression

This paper reports the studies on the behaviors of slender square tubed-reinforced-concrete (TRC) columns under eccentric loading. Eight specimens with the key parameters of length to width ratio (6, 10), load eccentricity (25mm, 50mm), and width to thickness ratio of the steel tube (133, 160) were tested. The test results indicate that the slender square TRC columns exhibit good ductile behavior during the eccentric loading with a global bending failure mode. A finite element (FE) analysis model was developed and the predicted results are in fine agreement with the test results. Parametric analyses were carried out to investigate the influence of the key parameters on the moment magnification factor of square TRC columns. Based on the test and parametric analyses, a regression formula of moment magnification factor is proposed to estimate the second order effect on the slender square TRC columns subjected to eccentric compression.

Tall Hybrid Coupled Structural Walls: Seismic Behavior and Design Suggestions

The seismic behavior of tall hybrid coupled wall systems is studied. For this purpose, nonlinear time history analyses are carried out to investigate the seismic response of eight example systems that are designed in accordance with the current design regulations. The results show that the shear and overturning moment magnification values are 1.6 and 1.4 for 10-story systems, and 1.8 and 1.2 for 30-story systems, due to the dynamic effect. In light of the analysis results, design suggestions are made for the system base shear, lateral force distribution, and coupling beams. In particular, based on the obtained detailed structural response and yielding mechanism, the necessity of adopting different coupling beam designs elaborately tuned to meet the actual vertical beam demand distribution along the structural height is discussed. It is found that a tall coupled wall structure with uniform steel coupling beam sections over the structural height ultimately leads to an average proportion of yielding coupling beams about 80%, which is as satisfactorily as the one with the beam designs carefully tuned according to the vertical demand distribution obtained using effective lateral load analysis.

Behavior and design of slender circular tubed-reinforced-concrete columns subjected to eccentric compression

The tubed-reinforced-concrete (TRC) column is a relatively new kind of confined reinforced-concrete (RC) columns, where the outer encasing thin-walled steel tube is discontinued at the beam–column joint and thus the axial load is transferred to the RC core only. In this paper, the behavior of slender circular TRC columns under eccentric compression loads was studied. A total of sixteen specimens considering the following primary system parameters were tested: two slenderness ratios (24, 40), two load eccentricities (25mm, 50mm), two diameter-to-thickness ratios of the steel tube (133, 160), and two continuity conditions for the steel tube (continuous, discontinuous at mid-height). The test results indicate that the slender circular TRC specimens exhibit fairly ductile behavior and the discontinuity of the steel tube at mid-height has a small effect (≈5% on average) on the bearing capacity. A finite element (FE) model was developed to simulate the behavior of circular TRC columns under eccentric compression loads. The predicted load versus mid-span lateral displacement curves are generally in good agreements with the measured ones. To identify the influence of the key parameters on the second order effects of circular TRC columns, an extensive parametric study was carried out using the FE model. Lastly, a regression formula is suggested to estimate the moment magnification factor and simplified design equations for slender circular TRC columns under eccentric compression loads are proposed based on the section capacity analysis.

Simplified design method for slender hybrid columns

This paper deals with numerical investigations on second-order effects in slender RC columns reinforced by several steel sections, namely hybrid columns, subjected to combined axial load and uniaxial bending moment. A FE model is developed in which geometrical and material nonlinearities as well as the partial interaction effect between the steel profiles and the surrounding concrete are taken into account. This model is then used to perform an extensive numerical parametric study on the ultimate load of hybrid columns considering 1140 different data sets. The comparison between the results obtained with FE analysis and Eurocode simplified methods (moment magnification approach) shows that EC2 and EC4 methods give wide discrepancies where half of case-studies are unsafe. The aim of the paper is to extend the use of the Eurocode moment magnification method to slender hybrid column design. In this method, the second-order bending moment is calculated by multiplying the first-order one by a magnification factor k that depends on the flexural stiffness EI and the equivalent moment distribution. New expressions for the correction factors involved in the determination of the effective flexural stiffness EI are proposed and calibrated by the results of the extended parametric study with 2960 data sets. The comparison of the predictions given by the new expressions against the FE analysis shows that the proposed new expressions of correction factors for moment magnification method provides largely safe designs for slender hybrid columns.

Theoretical and Experimental Study of Slender Concrete Columns Reinforced with GFRP Bars

This paper studies slender concrete columns reinforced with GFRP bars. For this target an experimental work was performed utilizing five such columns. Based on the experimental work the slenderness limit of 22 for unbraced steel-reinforced concrete columns as given by the ACI318-11 code was suggested to be little changed to 23.3 for GFRP reinforced concrete columns. The provisions of the ACI318-11 code for slender concrete columns reinforced with steel bars are reviewed. New expression from the literature for the effective flexural stiffness EI of slender concrete columns reinforced with GFRP bars is used to calculate the moment magnification factor and a procedure for plotting the interaction diagrams of the columns of this research is described.

Analytical behaviour of eccentrically loaded concrete-encased CFST box columns

This paper presents a theoretical study on the performance of concrete-encased concrete-filled steel tube (CFST) box columns subjected to eccentric axial loading. Finite-element analysis (FEA) was used to analyse the composite columns and experimental data reported recently by the authors was used to verify the FEA modelling. Analysis of the behaviour of the composite, including the full-range load versus lateral mid-height deflection, stress distributions, column failure modes and the interactions between steel and concrete, was carried out. The behaviour of the concrete-encased CFST box columns was compared with that of corresponding reinforced concrete columns and CFST built-up columns. Finally, a parametric study was carried out and the moment magnification approach adopted to propose design formulae for eccentrically loaded concrete-encased CFST box columns.

Tests of eccentrically loaded L-shaped section steel fibre high strength reinforced concrete and composite columns

Influence of steel fibres on the behaviour of L-shaped high strength reinforced concrete and concrete-encased composite columns is presented. A total of 16 L-shaped plain and steel fibre columns were constructed and tested in this study. The main parameters were the concrete compressive strength, load eccentricity, slenderness effect and steel fibre content. The experimental results of L-shaped reinforced concrete and composite column specimens were discussed in the paper. In addition, the column specimens were analysed based on a theoretical method considering the nonlinear behaviour of the materials. The slenderness effect of the columns has been taken into account by using The Moment Magnification Method suggested by ACI 318 specification. The results show that the inclusion of steel fibres into high strength concrete has considerable effect on structural behaviour of L-shaped both reinforced concrete and composite columns subjected to biaxial bending and axial load.

Probabilistic Evaluation of Effects of Column Moment Magnification Factor on Seismic Performance of Reinforced Concrete Frames

Enhancing column flexural capacity is the key measure in seismic capacity design to achieve strong column-weak beam failure mode and determinate the probabilistic relation between column moment magnification factor (CMMF). In the paper the effects of column moment magnification factor on seismic performance of reinforced concrete (RC) frames are evaluated to limit the occurrence probability of column-hinging failure modes within an acceptable tolerance. Monte Carlo simulation methodology is used to calculate the probability of drift demand exceeding drift capacity of two typical frame structures with consideration of major uncertainties. And fragility curves are constructed to obtain the relationship between CMMF and probability of structural damages and assess the seismic vulnerability of RC frame structures. Results show that the seismic performance of RC frame structures can be significantly enhanced by improving CMMF. The CMMF is required to be equal to or greater than 2.0 to achieve acceptable probability of exceedance of column-hinging failure mode.

Measurement of a Bluff Body Aerodynamic Yaw Moment Magnification and Damping Using a Dynamic Wind Tunnel Facility

This paper describes a technique for determining the dynamic aerodynamic yaw moment derivative based on the time response data using an oscillating model rig. The aerodynamic yaw moment derivatives are initially estimated using oscillation frequency and amplitude decay. The results from the dynamic measurement are compared with conventional static test and presented in the form of aerodynamic magnification. The yaw moment derivative exceeds that determined statically across reduced frequency range measured. The yaw damping derivative was found to be a function of freestream speed; at low velocities it is negative but progressively increases to a positive value. With further increases in speed, a self-sustained oscillation is observed with almost constant frequency and amplitude. This result is attributed to coupling between the model wake and the model stability; however, the exact behavior of the interaction is not fully understood; this phenomenon is under further investigation.