Residual Moment Capacity Research Articles

Effect of different material constitutive models in estimating the residual moment capacity of RC beams subjected to natural corrosion

PurposeExisting deterministic models that predict the capacity of corroded reinforced concrete (RC) beams have limited applicability because they were based on accelerated tests that induce general corrosion. This research gap was addressed by performing a combined numerical and statistical analysis on RC beams, subjected to natural corrosion, to achieve a much better forecast.Design/methodology/approachData of 42 naturally corroded beams were collected from the literature and analyzed numerically. Four constitutive models and their combinations were considered: the elastic-semi-plastic and elastic-perfectly-plastic models for steel, and two tensile models for concrete with and without the post-cracking stresses. Meanwhile, Popovics’ model was used to describe the behavior of concrete under compression. Corrosion coefficients were developed as functions of corrosion degree and beam parameters through linear regression analysis to fit the theoretical moment capacities with test data. The performance of the coefficients derived from different combinations of constitutive laws was then compared and validated.FindingsThe results showed that the highest accuracy (R2 = 0.90) was achieved when the tensile response of concrete was modeled without the residual stresses after cracking and the steel was analyzed as an elastic-perfectly-plastic material. The proposed procedure and regression model also showed reasonable agreement with experimental data, even performing better than the current models derived from accelerated tests and traditional procedures.Originality/valueThis study presents a simple but reliable approach for quantifying the capacity of RC beams under more realistic conditions than previously reported. This method is simple and requires only a few variables to be employed. Civil engineers can use it to obtain a quick and rough estimate of the structural condition of corroding RC beams.

Flexural Strengthening of Fire Damaged Reinforced Concrete Structural Member

Fire causes extreme damage leading to huge loss of life and property. An extensive damage also occurs to structural members when exposed to fire. Therefore, after fire structural members need to be strengthened to restore their load carrying capacity to withstand the future service loads. The selection of strengthening technique depends on the residual capacity of fire exposed structures and required ultimate load carrying capacity. Further if strengthen structure is exposed to fire in future then strengthening techniques should also have good fire performance and remain intact with the base concrete. In this paper, efforts have been made to study and understand the effectiveness of fire damaged reinforced concrete jacked flexural member. Limited information is available on the flexural performance of fire damaged strengthen members with reinforced concrete jacket and concrete jacket. This work presents a simple and efficient technique to strengthen reinforced concrete beam in flexure using traditional materials. This paper discusses in detail the strengthening strategy program of two-hour fire exposed beam to restore its original load carrying capacity. The reinforced concrete beam is simulated in finite element-based software to compute the thermal profile, which used to calculate residual load capacity. The obtained result of thermal distribution and residual moment capacity are compared with proposed literature models and design code equations. The performance of fire damaged and strengthen beams are studied through moment-curvature relationship load-deflection behaviour. This paper provides a simplified analytical approach to determine the residual capacity of fire damaged beams along with that expected improvements in their capacity after strengthen by reinforced concrete and concrete jacket.

Analytical and numerical analyses of RC beams exposed to fire adopting a LITS trilinear constitutive law for concrete

A trilinear compressive constitutive law for concretes exposed to fire is proposed. Concrete stress-strain relation as a function of temperature is characterized by means of only two parameters (residual values of concrete compressive strength and modulus of elasticity). The modulus of elasticity is determined through a Load Induced Thermal Strain (LITS) semi empirical model. The compressive strength is established through the design specifications. The constitutive law is implemented in finite element numerical models and in a simplified cross-sectional procedure. In the latter case, a simple methodology is proposed to estimate the residual moment capacity and the midspan deflection at any given time. The uncoupled two-step solution includes a thermal homogenization procedure followed by a sectional analysis. The deflection is estimated considering a constant equivalent stiffness for the RC beam. The case studies included the structural response under transient (hot state) condition of both a reinforced-high strength concrete (R-HSC) beam and a reinforced-ultra-high performance fiber reinforced concrete (R-UHPFRC) beam. The results are compared with experimental tests carried out in literature, showing a good approximation. Moreover, a steady state (after cooling) cross-sectional analysis of a R-HSC beam is performed. The load bearing capacity, the failure type and the midspan deflections are estimated. The analytical results approximate the experimental values, demonstrating the reliability of the proposed simplified procedures for the cases investigated.

Moment capacity of H-section steel beam with randomly located pitting corrosion

The H-section steel beam is one of the most commonly used steel components in buildings, industrial structures (e.g., bridges and ocean platforms), and industrial equipment. These steel beams are inevitably subjected to corrosion, most commonly the pitting type. The moment capacity of steel beams is the most important parameter influencing the performance of steel structures. This work examines the effects of pitting corrosion on the moment capacity of H-section steel beams with random pitting corrosion. Stochastic finite element method was utilized to analyze the influence of pitting corrosion. Focus is given on the relationship between moment capacity and mass-loss ratio. Corrosion occurrences at the tensioning flange and the compression flange are investigated. A method of predicting the residual moment capacity of corroded steel beam is proposed. The proposed analytical formula can be a convenient and applicable way for estimating the moment capacity of H-section beams.

Reliability analysis of the residual moment capacity of high‐strength concrete beams after elevated temperatures

AbstractA series of tests were conducted to study the variability of the residual compressive strength for high‐strength concrete (HSC) after elevated temperatures, and then a calculation process was developed to study the reliability of the residual moment capacity of HSC beams after a fire. The experimental results indicated that the mean values and the characteristic values of the residual compressive strength of HSC were reduced with the increasing elevated temperatures. The standard deviation of the residual compressive strength of HSC was increased when the temperature ranged from 20 to 400°C and decreased from 400 to 800°C. Regardless of the elevated temperatures, the residual compressive strength of HSC followed the normal distribution. The reliability index of the residual moment capacity of HSC beam was decreased with the increasing fire duration. The decrease rate of the reliability index became lower and kept constant when the section height–width ratio was beyond 2.75 and the longitudinal reinforcement ratio was higher than 1.43%. As the load effect ratio was increased, the decrease rate of the reliability index was reduced regardless of the section size, the height–width ratio, and the reinforcement ratio.

Influence of random pitting corrosion on moment capacity of thin-walled circular tubes subjected to compression force

Thin-walled circular tubes have been widely used in space lattice structures and other industrial areas. Steel tubes are prone to corrosion during their service life, significantly reducing their loading capacity and threatening the structural safety. This work aimed to investigate the residual moment capacity of corroded circular steel tubes (CSTs) subjected to compression force. The second-order effect of steel tubes was studied based on CSTs with outer diameter D = 100 mm. The effects of corrosion thickness, diameter of corrosion pit, and material strength on the residual moment capacity of CSTs were also investigated. The analytical formula with a second-order polynomial form was proposed for predicting the residual moment capacity of CSTs. The values of tc/t were assumed to be 0.1, 0.3, 0.5, and 0.7, and the values of F/Fu were set to 0, 0.5, and 0.7 to reveal the influence of corroded thickness with different axial compression ratios. The applicability of the proposed formula for CST with yield strength equal to 235, 345, and 460 MPa was also confirmed. According to the findings, the proposed analytical formula can accurately predict the residual moment capacity of CSTs with random pitting corrosion.

Influence of random pit corrosion on axial stiffness of thin-walled circular tubes

Thin-walled circular tubes have been widely used in space lattice structures and other industrial areas. Corrosion is inevitable for steel tubes in terms of service life, and it will considerably reduce the axial stiffness and change the mechanical behavior of the entire structure. The present work aims to investigate the axial stiffness of corroded circular steel tubes (CSTs) subjected to compression force. Initial and elastoplastic stiffness values were investigated, and an analytical formula was proposed. The influence of corrosion thickness tc and material strength fy on the residual moment capacity of CSTs was also investigated. The proposed analytical formula can accurately predict the axial stiffness of CSTs with random pitting corrosion.

Fire resistance of corroded high-strength structural concrete

Purpose The exposure of reinforced concrete structures such as high-rise residential buildings, bridges and piers to saline environments, including exposure to de-icing salts, increases their susceptibility to corrosion of the reinforcing steel. The exposure to fire can further deteriorate the structural integrity of corroded concrete structures. This combined effect of corrosion damage and fire exposure is not generally addressed in the structural concrete design codes. The synergistic combination of the effects of corrosion and fire forms the basis of this paper. Design/methodology/approach Concrete beam specimens with different strengths were prepared, moist-cured and corroded with impressed current. Later, they were “crack-scored” for corrosion evaluation, after which half were exposed to fire in a gas kiln. The fire damage was evaluated by nondestructive testing using ultrasonic pulse velocity. Next, all specimens were tested for residual flexural strength. They were then autopsied, and the level of corrosion was determined based on mass loss of the reinforcement. Findings For corroded specimens, the flexural capacity loss because of fire exposure increases as the compressive strength increases. In general, the higher the crack score, the higher the corresponding mass loss, unless some partial/segmental debonding of the reinforcement occurred. The degree of corrosion increases with decreasing compressive strength. The residual moment capacity, based on analytically determined capacities of uncorroded and nonfire-exposed beams, was significantly lower than those of uncorroded beams exposed to fire. Originality/value The combined effects of corrosion and fire on the mechanical properties of structural concrete are relatively unknown, and no guidance is available in the existing design codes to address this issue. Accordingly, the findings of the paper are expected to be valuable to both researchers and design engineers and can be regarded as the initial investigation on this topic.

Evaluation of Flexural Capacity of RC Elements Exposed to Fire

When Reinforced concrete flexural members of a structure are exposed to fire they tend to lose their original flexural capacity. It is important to assess the reduction in flexural capacity. This paper presents a simple numerical model for prediction of residual moment capacity of fire damaged RC flexural element after cooling to ambient temperature. The prediction of residual moment capacity of fire damaged RC element has been carried out by assessing the residual properties of fire affected concrete and steel.

Experimental investigations on inelastic behaviour and modified Gerber joint for double-span steel trapezoidal sheeting

Cold-formed steel trapezoidal profiles provide efficient solutions for roofing and often use the Gerber joint to effectively utilize capacities. The previous design of Gerber joint was sensitive to uneven distribution of loads and accidental loads, which imposed bending moments in the joint and lead to its failure. In this experimental program, the design of Gerber joint has been modified to work as a hinge under service loads and carry moments in accidental conditions. Also, the design of CFS is based on elastic methods that underestimate their capacity, especially for multi-span systems. Full-scale tests were conducted on highly stiffened double-span trapezoidal sheeting profiles with modified Gerber joint to investigate elastic capacity, inelastic behaviour, moment redistribution in the post-elastic phase, ultimate load capacity and feasibility of modified Gerber joint. Comparison of elastic load capacity with EWM and DSM predictions revealed that EWM design predictions were conservative by 30% while DSM predictions were accurate. For multi-span application, residual moment capacity ratios of 0.76 and 0.81 in the post-elastic phase allowed for moment redistribution and increased ultimate load capacity by 7.14% and 8.80% for 0.85 mm and 1 mm thick profiles respectively. Performance of modified Gerber joint to behave as a hinge under service loads and as continuous in the post-elastic phase was also found to be satisfactory. The study concluded that the economy in design and capacity utilization of multi-span CFS profiles can be improved by allowing for moment redistribution and using the modified Gerber joint.

Assessment of reinforced concrete slabs post-fire performance

An analytical study is presented of the post-fire structural performance of one-way RC solid slabs that have been cooled off from various scenarios of fire events. Three possible fire scenarios were considered for a mid-span section: Fire below or above the slab and a simultaneous fire above and below it. According to the fire scenario and duration, the profile along the slab cross-section's height of the temperatures, from which the slab has cooled off, is calculated. Then, existing models of the residual constitutive relations of the steel and of the concrete are applied in cross-sectional moment-curvature analyses. The results are presented and analyzed in terms of the residual moment-curvature curves and two non-dimensional ratios, which are indicative of the residual moment capacity and ductility. It is noted that the residual deformation capacity, indicated by the latter ductility ratio, has been rarely examined in studies that deal with the residual, post-fire performance of RC members. Findings of this study show that evaluation of the post-fire load bearing capacity may not be enough in order to assess its performance. They clearly indicate that the possibility of decrease of its ductility due to the exposure to fire needs to be assessed as well.

Condition assessment of RC beams using artificial neural networks

In this study, an imaged-based methodology for condition assessment of Reinforced Concrete (RC) road bridge components is presented. The study is divided into experiments on RC rectangular beams and scaled (1:12) T-beams, validation of numerical models for T-beams and training of corresponding artificial neural networks (ANNs). In the experimental work, Digital Image Correlation (DIC) was used as a virtual sensor for data extraction. Rectangular RC beams of size 1800 mm × 150 mm × 200 mm and scaled (1:12) RC T-beams were tested under four-point flexural loading on a 100-ton dynamic testing machine. The experimental stress-strain curves obtained from the compression test on prism specimens at 28 days were used as input data for material model parameters in finite element model (FEM) software SAP2000. To assess the condition of structural components, a local damage index (LDI) was developed. Validation of FEM results with experimental results enables derivation of moment-curvature backbone curve for full-scale bridge girders, which enables further quantification of damage and residual moment capacity of full-scale bridges designed by Ministry of Road Transport and Highways (MoRTH). The correlation between the experiments, simulation and ANN predictions was found to be very satisfactory.

Predicting residual moment capacity of thermally insulated RC beams exposed to fire using artificial neural networks

This paper presents a method using artificial neural networks (ANNs) to predict the residual moment capacity of thermally insulated reinforced concrete (RC) beams exposed to fire. The use of heat resistant insulation material protects concrete beams against the harmful effects of fire. If it is desired to calculate the residual moment capacity of the beams in this state, the determination of the moment capacity of thermally insulated beams exposed to fire involves several consecutive calculations, which is significantly easier when ANNs are used. Beam width, beam effective depth, fire duration, concrete compressive and steel tensile strength, steel area, thermal conductivity of insulation material can influence behavior of RC beams exposed to high temperatures. In this study, a finite difference method was used to calculate the temperature distribution in a cross section of the beam, and temperature distribution, reduction mechanical properties of concrete and reinforcing steel and moment capacity were calculated using existing relations in literature. Data was generated for 336 beams with different beam width (bw), beam account height (h), fire duration (t), mechanical properties of concrete (fcd) and reinforcing steel (fyd), steel area (As), insulation material thermal conductivity (kinsulation). Five input parameters (bw, h, fcd, fyd, As and kinsulation) were used in the ANN to estimate the moment capacity (Mr). The trained model allowed the investigation of the effects on the moment capacity of the insulation material and the results indicated that the use of insulation materials with the smallest value of the thermal conductivities used in calculations is effective in protecting the RC beam against fire.

A mathematical model of predicting residual moment capacity of RC elements after fire exposure

PurposeThis paper aims to present a mathematical model of predicting the residual moment capacity of fire-damaged reinforced concrete (RC) elements after cooling to ambient temperature which also reflects the role of bond between steel rebar and surrounding concrete.Design/methodology/approachThe prediction of residual moment capacity of fire-damaged RC element has been carried out for two scenarios: by assuming perfect bond between surrounding concrete and steel rebar after fire exposure and by incorporating a relative slip between surrounding concrete and steel rebar and hence assuming partial bond between them after fire scenario. The predicted results are then compared with the experimental results available in different literatures.FindingsIt is found that on comparison between the predicted results and the experimental results, the proposed mathematical prediction model, when bond-characteristics are considered, shows better agreement with the experimental results as compared with those by conventional method with perfect bond assumption.Originality/valueThe constitutive relationship for thermal residual properties of steel rebar and concrete has been used in the proposed prediction model along with relative slip approach between surrounding concrete and steel rebar after fire scenario and consequently to predict the residual moment capacity of the fire-damaged RC element after cooling.

Post-crack performance of fibre reinforced concrete and its effect on the first peak cracking load of slabs

Concrete slabs-on-grade and other plate elements have for a long time been designed on the basis of elastic analyses of stress distribution. This typically results in a very conservative estimate of the minimum thickness required to resist design point loads because an elastic analysis does not account for the capacity of even quasi-brittle materials to redistribute stress following initial cracking. Fibre-reinforced concrete (FRC) is a material that can exhibit significant post-crack performance. The existence of a residual moment capacity in a FRC slab allows the slab to redistribute stress such that the peak in load resistance may occur beyond the point of first cracking in the concrete matrix. The present experimental investigation has demonstrated that residual moment capacity in the immediate post-crack range can influence the magnitude of the first peak in load resistance associated with cracking. The results suggest that the method of structural analysis used to design concrete slabs should consider the residual moment resistance in the immediate post-crack range when estimating the first peak load resistance associated with cracking.

Distributed inelasticity planar frame element with localized semi-rigid connections for nonlinear analysis of steel structures

A macro-element model with spread of inelasticity and localized nonlinear semi-rigid hinges is presented in this paper. The element is formulated through force-based approach. Spread of inelasticity along element length and section depth is captured by fiber discretization of monitoring sections, and introduction of localized connections enable representation of any type of linear or nonlinear semi-rigid (partially restrained) connection behavior along element length without any increase in number of degrees of freedom. The element is used in conjunction with corotational formulation for the capture of nonlinear geometric effects. The proposed element is used for the analysis of steel structures considering the presence of beam to column semi-rigid connections in this paper. For a true representation of the hysteretic energy dissipation characteristic of a beam to column connection a quadra-linear moment–rotation based model is implemented incorporating pinching, damage, the possibility of residual moment capacity and degradation of stiffness under various scenarios. The behavior is calibrated via experimental data available in the literature. Robustness and accuracy of the proposed element and hysteretic connection model are assessed through numerical and experimental data, and the importance of accurate modeling of cyclic behavior of semi-rigid connections is demonstrated through analysis of a steel moment resisting frame.

Mechanical properties of a large scale synthetic fibre reinforced concrete ground slab

The existing design code for Concrete Industrial Ground Floors, TR34, by the Concrete Society states that “Macro synthetic fibres provide some post-cracking or residual moment capacity but with significantly lower performance than steel fibres. They are not known to be used in industrial floor construction”. This paper presents results of an ongoing investigation undertaken by the authors concerning the mechanical and physical properties of fibre reinforced concrete ground slabs at an industrial scale. This paper focuses and presents results concerning the punching shear failure of a 6.00m×6.00m×0.15m synthetic fibre reinforced ground supported slab. The paper demonstrates clearly the methodology adopted and the infrastructure used throughout this investigation. The presented results show clearly that the punching shear failure values obtained in this investigation are comparable to values reported for the steel fibre slabs under similar conditions. This work could potentially question the validity of the above statement in TR34. The significance of this research also is in the size of the slab investigated, as there is very limited work, if any, reported within the literature.

An analytical study of residual displacements in RC bridge columns subjected to near-fault earthquakes

One of the important measures of post-earthquake functionality in bridges is residual displacement. This study focused on the analyses of six reinforced concrete bridge columns subjected to near fault ground motion using fiber elements to estimate the residual displacement. Another part of the study was aimed at determining the residual drift ratio limit beyond which bridge columns would be unsafe. The ability of models to estimate residual displacement was assessed by comparison of the results of the analyses to experimental data. It was determined that fiber element models were generally successful in estimating residual displacements. To determine residual displacement limits, a large number of reinforced concrete bridge columns with different geometries and steel ratios were analyzed subjected to truck loading. The residual moment capacity of the column and the moment due to the trucks and the P-Delta effects were used in the study. The residual drift ratio limit was found to be 1.2% or more for typical bridge columns.

Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty

AbstractIncremental dynamic analysis (IDA) is presented as a powerful tool to evaluate the variability in the seismic demand and capacity of non‐deterministic structural models, building upon existing methodologies of Monte Carlo simulation and approximate moment‐estimation. A nine‐story steel moment‐resisting frame is used as a testbed, employing parameterized moment‐rotation relationships with non‐deterministic quadrilinear backbones for the beam plastic‐hinges. The uncertain properties of the backbones include the yield moment, the post‐yield hardening ratio, the end‐of‐hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear timehistory analyses for a suite of ground motion records. Sensitivity analyses on both the IDA and the static pushover level reveal the yield moment and the two rotational‐ductility parameters to be the most influential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ (a) Monte Carlo simulation with latin hypercube sampling, (b) point‐estimate and (c) first‐order second‐moment techniques, thus offering competing methods that represent different compromises between speed and accuracy. The final results provide firm ground for challenging current assumptions in seismic guidelines on using a median‐parameter model to estimate the median seismic performance and employing the well‐known square‐root‐sum‐of‐squares rule to combine aleatory randomness and epistemic uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.