Uniaxial Bending Moment Research Articles

Design of Concrete Columns by prEN1992-1-1/2021

Design of concrete columns subjected to axial force and uniaxial bending moment from the point of view of prepared prEN1992-1-1/2021. A comparison by interaction diagrams for concrete strength classes C30/37 and C90/105 for symmetrically and asymmetrically reinforced cross-section and for symmetrical cross-sections only to one axis, respectively.

M-N interaction curves for rectangular concrete-filled steel tube columns subjected to uniaxial bending moments

abstract: In this paper, a computational code was developed to obtain M-N interaction curves for rectangular concrete-filled steel tube columns considering the strain compatibility in the cross-section. Considering the composite section subjected to uniaxial bending moments, expressions were developed to determine normal force, moment resistance, neutral axis depth and components resistance of cross-section. Such expressions were implemented in a computational tool developed to the authors and that allows to obtain the M-N pairs of strength. The steel and concrete ultimate strains were defined with the aid of the Brazilian standard for reinforced concrete structures ABNT NBR 6118. The obtained results were compared to simplified curves defined according to the theoretical models of ABNT NBR 8800, ABNT NBR 16239, EN 1994-1-1 and literature data. The proposed model showed good agreement with literature results and had good precision to estimate the ultimate moment values. To further understand the resistance of composite columns under uniaxial bending moments, parametric study was performed to evaluate the influence of the compressive strength of concrete, yielding strength of steel and steel area ratio on M-N interaction curves. The results indicate that the yielding strength of steel and the steel area ratio were the variables that most influenced the values of composite columns resistance (normal force and bending moment).

Reliability analysis of slender columns using the general method with linear creep theory

Abstract To analyze the reliability of slender columns subjected to axial force and uniaxial bending moment, with a slenderness index between 100 and 140, 216 columns were modeled. The square cross-section was adopted, with three different configurations for longitudinal reinforcement. In the calculation, the general method with the linear creep theory was applied. Several factors were varied: slenderness index, reinforcement ratio, steel bars arrangement, compressive strength of concrete, and first-order relative eccentricity. For analysis purposes, the Monte Carlo method was adopted, followed by the First Order Reliability Method (FORM). Considering the results obtained, it was observed that the reliability index is usually higher for lower reinforcement ratios and varies according to the configuration of the cross-section.

Stainless Steel SHS and RHS Beam‐column Design Proposal

AbstractPresented research investigates behaviour of stainless steel square hollow section (SHS) and rectangular hollow section (RHS) members loaded by compressive force and uniaxial bending moment combination. Experimental program of 20 eccentrically loaded pin‐ended compressed austenitic stainless steel member tests was carried out. Numerical model using geometrically and materially non‐linear analysis with imperfections (GMNIA) was created in finite element software Abaqus. Validation of the numerical model was made based on the data obtained from the experimental program. The validated model was used for a comprehensive numerical parametric study which covered austenitic, ferritic and duplex stainless steel types. Furthermore, member slenderness, cross‐section slenderness and ratio between compressive force and flexural buckling resistance were set as variables as well. Bending moment was considered uniform along the member length. Data obtained from the numerical parametric study were used for the comparison with the existing stainless steel SHS and RHS beam‐column design procedures. Furthermore, new interaction formulae were proposed and evaluated by a reliability analysis.

Unified code-compliant equations for bending and ductility capacity of full and hollow rectangular RC sections

Simple closed-form code-compliant equations for determining the bending capacity of full and hollow rectangular reinforced concrete (RC) sections at yielding and ultimate are proposed. The equations, based on the material models of ACI 318-14 and EN 1992:2005, are fully parameterized and allow modeling square and rectangular cross-sections with steel arbitrarily distributed on all four sides and subjected to axial force and uniaxial bending moment. Because of their simplicity, the equations provide an efficient tool for performing parametric and stochastic massive analyses, and for rapidly assessing existing territorially-distributed infrastructural systems, such as highways and railways. The equations require the definition of the cross-sections material and geometrical properties and are of general validity, since any geometrical configurations, reinforcement arrangements and concrete constitutive models can be employed. The accuracy of the equations in predicting bending capacity (resisting moment), ductility and axial force-bending moment interaction domain of a representative sample of realistic full and hollow RC sections is demonstrated through comparisons with fiber analysis performed in OpenSees.

Flexural Response Prediction of Reinforced Concrete Members Based on Statistical Observations

Seismic assessment of reinforced concrete (RC) structures requires the determination of inelastic deformation capacity of structural members. Inelastic deformation capacity of members is determined by performing analytical moment–curvature analysis. Due to definition of high amount of data, this type of analysis increases the computational efforts and time when applied to large structures. Considering this situation, this paper proposes simple equations to express inelastic deformation capacity of rectangular RC sections subjected to axial load and uniaxial bending moment. Deformation of members is described in domains of strength and deformations at yield and ultimate. In order to increase applicability and coverage of equations, numerous RC sections were analyzed for various axial load levels by combination of different section aspect ratios, longitudinal and transverse reinforcement configurations and distinct structural materials. During the analysis, nonlinear characteristics of constitutive materials are modeled and some remarkable effects are considered: capacity of concrete in tension, yield elongation and hardening of the longitudinal reinforcement. Equations are then proposed by investigating the effect of sectional and material parameters on the moment–curvature responses and contribution of parameters assigned to prediction equations by extensive statistical evaluations. Reliability of proposed equations is eventually investigated and validated by numerical, experimental and analytical moment–curvature analysis results. It is expected that proposed equations, in close precision, can be helpful for rapid visualization of inelastic capacities of RC members.

CO2 and cost optimization of reinforced concrete footings subjected to uniaxial uplift

A multi-objective optimization of CO2 emissions and cost for the design of reinforced concrete footings under uniaxial bending moments is developed. The analysis and design procedures are based on specifications prescribed by the American Concrete Institute (ACI 318-11) for concrete design as well as geotechnical limit states. In addition, a theoretical analysis procedure for reinforced concrete footings subjected to uniaxial uplift is derived and compared to simplified analysis procedures typically used in practice. The multi-objective optimization uses a hybrid Big Bang–Big Crunch algorithm. Pareto fronts for cost and CO2 emissions are developed for design examples to compare the theoretical analysis to simplified analysis and investigate trade-offs between CO2 emissions and cost. Also, design results show the impact on CO2 emissions and cost by allowing uplift of the footing.

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.

A practical approach for the strength evaluation of RC columns reinforced with RC jackets

Reinforced concrete (RC) jacketing is nowadays one of the most common techniques adopted for seismic retrofitting of existing RC columns. It is used to increase load-carrying capacity and ductility of weak existing members by means of a simple and cheap method. The structural efficiency is related to two main effects: – the enlargement of the transverse cross section; – the confinement action provided by the external jacket to the inner core. Several theoretical and experimental studies were addressed in the past to investigate on how it is possible to calculate the strength enhancement due to these effects and to highlight the main key parameters influencing the structural behavior of jacketed columns. Most of theoretical studies analyzed members subjected to axial compression while the case of axial force and bending moment was adapted only with complex formulations based on numerical approaches, which require the use of a suitable algorithm (e.g. non-linear finite element analyses, sectional fiber models). This paper presents a simplified approach, able to calculate the strength domains for jacketed columns subjected to axial force and uniaxial bending moment. The model takes into account the effects of confinement with proper stress-block parameters, the latter adapted for confined concrete, and of the composite action of jacket and core; buckling of longitudinal bars is considered and discussed with an appropriate stress–strain law for steel in compression. Results are compared with numerical analyses carried-out with the fiber model approach implemented in a commercial software (SAP2000), showing the accuracy of proposed method. Comparisons are also made with experimental results available in the literature in order to validate the model. Finally parametric considerations are made on the basis of adopted model, useful for design/verification purposes.

Strength performance of mortise and loose-tenon furniture joints under uniaxial bending moment

We determined the effects of adhesive type and loose tenon dimensions (length and thickness) on bending strength of T-shaped mortise and loose-tenon joints. Polyvinyl acetate (PVAc) and two-component polyurethane (PU) adhesives were used to construct joint specimens. The bending moment capacity of joints increased significantly with increased length and thickness of the loose tenon. Bending moment capacity of joints constructed with PU adhesive was approximately 13% higher than for joints constructed with PVAc adhesive. We developed a predictive equation as a function of adhesive type and loose tenon dimensions to estimate the strength of the joints constructed of oriental beech (Fagus orientalis L.) under uniaxial bending load.

Optimum cost design of RC columns using artificial bee colony algorithm

Optimum cost design of columns subjected to axial force and uniaxial bending moment is presented in this paper. In the formulation of the optimum design problem, the height and width of the column, diameter and number of reinforcement bars are treated as design variables. The design constraints are implemented according to ACI 318-08 and studies in the literature. The objective function is taken as the cost of unit length of the column consisting the cost of concrete, steel, and shuttering. The solution of the design problem is obtained using the artificial bee colony algorithm which is one of the recent additions to metaheuristic techniques. The Artificial Bee Colony Algorithm is imitated the foraging behaviors of bee swarms. In application of this algorithm to the constraint problem, Deb's constraint handling method is used. Obtained results showed that the optimum value of numerical example is nearly same with the existing values in the literature.

An improved design formula for a biaxially loaded slender RC column

Nonlinear analyses are conducted to evaluate the ultimate resisting capacity of slender reinforced concrete (RC) columns subjected to an axial load with biaxial bending moments. Consideration is given to the geometric nonlinearities caused by the P – Δ effect and the long-term behavior of concrete and to the material nonlinearities caused by the cracking of concrete and the yielding of steel. In addition, the biaxial stress state in an RC section is simulated on the basis of a fiber model. Because of the complexity of Bresler’s load contour method, which was introduced in the ACI 318 code, this paper introduces a new design approach to the construction of the failure surface of a slender RC column subjected to biaxial bending. Through a parametric study of slender RC columns, where consideration is given to the P – Δ effect and the time-dependent deformation of concrete, two regression formulas are proposed on the basis of the slenderness ratio and the creep deformation of concrete. Furthermore, the direct multiplication of the proposed formulas on the P – M interaction diagram for a short RC column subjected to axial force and a uniaxial bending moment enables a P – M interaction diagram to be generated for a slender RC column subjected to long-term axial force and biaxial bending moments. Correlation studies between analytical and experimental results are conducted with the objective of establishing the validity of the introduced numerical model. In addition, the ultimate resisting capacities calculated from the regression formula are compared with those obtained from rigorous nonlinear analyses and from the ACI formula, with the objective of establishing the relative efficiency of the proposed regression formula.

Capacity of RC rectangular sections subjected to biaxial bending: simplification to an increased uniaxial bending moment

This paper proposes a new method for determining the capacity of reinforced concrete (RC) rectangular sections with doubly symmetrical reinforcement subjected to combined axial load and biaxial bending. The method is based on the simplification to an increased uniaxial bending analysis and is valid for both normal- and high-strength concretes and for different bar arrangements, which can be equal at the four corners, uniformly distributed over the contour or symmetrical at opposite faces. The proposed method has been suggested from an analytical calculation that adopts the assumption of Eurocode 2. The method was compared with theoretical results and experimental tests from the literature. The method allows reinforced concrete sections to be checked and designed in a simple but accurate way, which is very interesting for practising engineers.

2축 편심 축력을 받는 고강도 콘크리트 기둥의 수정 등가응력블럭

In the previous experimental study, it is verified that the ultimate strain of concrete ( =0.003) and coefficient of equivalent stress block () can be used for the analysis of RC beams under biaxial and uniaxial bending moment. However, the characteristics of stress distribution of non rectangular compressed area in the RC columns are different to those of rectangular compressed area. The properties of compressive stress distribution of concrete have minor effect on the pure bending moment such as beams, but for the columns subjected to combined axial load and biaxial bending moment, the properties of compressive stress distribution are influencing factors. Nevertheless, in ACI 318-99 code, the design tables for columns subjected to axial loads with bidirectional eccentricities are based on the parameters recommended for rectangular stress block(RSB) of rectangular compressed areas. In this study the characteristics of stress distribution through both angle and depth of neutral axis are observed and formulated rationally. And the modified parameters of rectangular stress block(MRSB) for non rectangular compressed area is proposed. And the computer program using MRSB for the biaxial bending analysis of RC columns is developed and the results of MRSB are compared to RSB and experimental results respectively.

Design of circular and rectangular hollow section columns

An analytical method for computing the ultimate failure loads of inelastic columns subjected to axial thrust and uniaxial bending moments is presented. As part of the computational procedure, a rapid method of calculating the moment thrust curvature relations is described. The procedure uses the well known Gauss quadrature formulae. With the aid of a mapping device, any quadrilateral part of the cross-section can be considered including any arbitrary residual stress pattern. This enables the analysis of a wide variety of cross-sections, including circular and rectangular hollow sections. The ultimate failure loads are obtained by finding the highest load for which an equilibrium deflected shape can be calculated. A generalised Newton-Raphson method has been adopted for the calculation of the deflected shape of the column. The computer program developed has been used to examine the validity of the newly proposed design curves in ECCS Recommendations as well as he draft BS 5400 : Part 3 applicable to circular and rectangular hollow sections. it is concluded that the ECCS recommendations are safe, but the proposals in BS 5400 : Part 3 are found to be unduly conservative.