Flexural Limit State Research Articles

Probabilistic evaluation of chloride-induced corrosion effects on design parameters of RC beams

The chloride-induced corrosion in reinforced concrete (RC) structures could decrease their service life. In this regard, studying the effects of corrosion on the designing parameters could prevent these costly expenses. The presence of uncertainties in the corrosion process requires probabilistic models to be applied. Therefore, in this study, Monte Carlo simulations have been used to investigate the effects of corrosion in RC elements. To do so, the remained area of reinforcements, changes in yield stress, ductility and flexural capacity of RC beam sections under propagating corrosion were studied. These changes were applied to a singly reinforced beam model and its behavior in the flexural limit state was investigated. Results have indicated that statistical dispersion in remained area of rebars and their yield stress increases over time. As a result of a decrease in yield stress, the balanced steel ratio in cross-section increases. Moreover, the ductility of the beam decreases as corrosion propagates. Reliability analysis of the beam in different conditions emphasized the deteriorating effect of reducing concrete cover, increasing the w/c ratio and using reinforcements with smaller diameters or lower yield stress. Furthermore, reliability analysis of corroded RC beams can effectively be used in planning inspections of existing structures.

Load and resistance factor design for bamboo reinforced concrete beam in ultimate flexural limit state

Building sustainable infrastructure brings back the idea of using environmentally friendly materials, such as bamboo, for reinforcing concrete structures. However, a design framework for bamboo reinforced concrete (BRC) structures is still in its early stages due to the inherent uncertainties in the properties of bamboo. The present work focuses on developing a load and resistance factor design (LRFD) framework for BRC beams subjected to flexure. Before developing the design framework, the major variables affecting the behaviour of BRC beams are identified — the tensile properties of bamboo, the compressive properties of concrete, the bond strength between them, and the load. BRC beams, with various reinforcement percentages, are investigated through real-life experiments and finite element (FE) based numerical experiments. We show that the FE models provide good agreement with the real-life experiments if the major variables are chosen as per their descriptive statistics. The FE model is used to generate a synthetic dataset, using which Monte Carlo simulations are performed. The BRC beam is assumed to be governed by the limit state of collapse in flexure. The partial safety factors for bamboo with different dead and live load combinations are calibrated to different target reliability. Designers can make use of the proposed partial safety factors for designing BRC flexural members.

Experimental Investigation of the Flexural Performance of Hybrid (GFRP and STEEL) Reinforced Concrete Beams

The corrosion of steel reinforcement is a key contributor to the inability of concrete buildings to withstand long-term exposure to the elements. Fiber-reinforced polymer (FRP) has become an alternative to steel reinforcement in concrete structures to solve this problem. One drawback is GFRP's low modulus of elasticity is one drawback. The main objective of this study is to develop a practical hybrid FRP bar for concrete structures, especially for marine and harbor concrete structures, using the concept of material hybridization. The purpose of hybridization is to increase the elastic modulus of GFRP bars with acceptable tensile strength and improve their flexural ductility, as well as enhance the corrosion protection performance of both GFRP. GFRP crust with steel core bar is being considered in the development of hybrid FRP bars. The elastic modulus of the hybrid GFRP bar can be increased by up to 280 percent, according to the findings of this study. The bars are manufactured locally, utilizing a double-part die mold and locally sourced raw materials. Four-line static loading is used to examine the flexural limit states of nine beams with parameters of 200 mm width x 350 mm thickness x 2000 mm length, including pre-cracking behavior, cracking pattern, deflection, load capacity and strain, and failure mechanism.

Bent, not broken, and material properties from a different angle

The lexicon of material properties is constantly evolving. Some behaviors can assume accepted meaning and practical usage, depending on the current needs of the research community. In this issue of Matter, Peng, Grayson, and Snyder propose a figure of merit for bendability, for comparing the flexural limit state of materials.

The cyclic behavior of Butterfly-shaped Link Steel Plate Shear Walls with and without Buckling-restrainers

The Butterfly-shaped Link Steel Plate Shear Wall as a novel lateral resisting system is proposed and experimentally investigated. In this system, by creating the peripheral Butterfly-shaped links in the web plate, the lateral load resisting mechanism is determined by the shear strength of the links. The geometric attributes of the links are effective parameters for predicting the values of stiffness and strength of the proposed system, as investigated in this paper. To fulfill this aim, four experimental specimens with different geometric parameters containing the taper, slenderness, and width ratios are constructed. The samples are loaded by using the cyclic loading protocol to investigate the behavior of the system. The experimental results confirm that the link dominant limit state controls the stiffness, strength, and ductility of the specimens. The Butterfly-shaped link geometry with the dominant shear limit state results in higher stiffness and strength, and the link geometry with a dominant flexural limit state shows the higher ductility. Besides, the hysteresis diagram of specimens shows the optimal ductility and high energy dissipation even at low drifts. Then, by numerical modeling verification, Butterfly-shaped Links Steel Plate Shear Wall with the restrained web plate is intended to improve the cyclic behavior. The principal purpose of the numerical study is to investigate the restrainer's impact on the energy dissipation capacity of the samples. The results show that the out-of-plane instability is reduced, the pinching phenomena eliminated, and the dissipated energy of the specimens is increased considerably by the web plate restraining.

Study of bending resistance of sandwich structures

Article deals with the study of the flexural limit state of sandwich structures based on fiberglass and polymeric foams. Whether geometrical and material parameters influence the resulting load-bearing capacity of these structures are studied experimentally using FEM models. This study shows it is necessary to particular emphasis attention to the issue of flexural strength, the load capacity when of the walls designing sandwich shell products to avoid possible failures in the practical use of these types of structures. Subsequently, Horn’s evaluation method is used to compare the experimental testing and the FEM model.

Model Uncertainty in Predicting Facing Tensile Forces of Soil Nail Walls Using Bayesian Approach

The model uncertainty in prediction of facing tensile forces using the default Federal Highway Administration (FHWA) simplified equation is assessed in this study based on the Bayesian inference method and a large number of measured lower and upper bound facing tensile force data collected from the literature. Model uncertainty was quantified by model bias which is the ratio of measured to nominal facing tensile force. The Bayesian assessment was carried out assuming normal and lognormal distributions of model bias. Based on the collected facing tensile force data, it is shown that both the on-average accuracy and the spread in prediction accuracy of the default FHWA simplified facing tensile force equation depend largely upon the distribution assumptions. Two regression approaches were used to calibrate the default FHWA simplified facing tensile force equation for accuracy improvement. The Bayesian Information Criterion was adopted to quantitatively compare the rationality between the competing normal and lognormal statistical models that were intended for description of model bias. A case study is provided in the end to demonstrate both the importance of model uncertainty and the influence of distribution assumptions on model bias in reliability-based design of soil nail walls against facing flexural limit state.

Effect of local instability on fire response of steel beams

Purpose This purpose of this paper is to quantify the effect of local instability arising from high shear loading on response of steel girders subjected to fire conditions. Design/methodology/approach A three-dimensional nonlinear finite element model able to evaluate behavior of fire-exposed steel girders is developed. This model, is capable of predicting fire response of steel girders taking into consideration flexural, shear and deflection limit states. Findings Results obtained from numerical studies show that shear capacity can degrade at a higher pace than flexural capacity under certain loading scenarios, and hence, failure can result from shear effects prior to attaining failure in flexural mode. Originality/value The developed model is unique and provides valuable insight (and information) to the fire response of typical hot-rolled steel girder subjected to high shear loading.

Reliability assessment of wall-frame structures

Abstract Assessment of the reliability of wall-frame structures using simulation based method is often prohibited by the costly and lengthily computations. The present paper introduces a response surface based technique to quickly extract the reliability and safety information. The proposed method couples the finite element (FE) model of wall-frame structure, an improved response surface scheme and the second order reliability method (SORM). At the beginning, the large number of the random variables is reduced via preliminary sensitivity analysis. Then, the failure region is reached through a repetitive strategy integrated with recommended experimental designs. The efficiency and accuracy of the scheme are verified using Monte Carlo simulation. Moreover, both serviceability and flexural limit states are used in the verification. Tens of simulations are used instead of hundreds or thousands. The method is simple, efficient and can be easily implemented. For the considered example, the lateral load and the wall stiffness are the most important variables.

Condition Assessment of Existing RC Highway Bridges in China Based on SIE2011

AbstractSubjective or inaccurate condition assessment is the most critical technical barrier to effective management of highway bridges. In 2011, the promulgation of the specification for the inspection and evaluation of the load-bearing capacities of highway bridges (SIE2011) in China promoted quantitative evaluation of Chinese highway bridges, but a series of empirical coefficients of load-bearing capacity needs to be calibrated to determine the deterioration of material strength and rigidity of bridge cross sections in such evaluations. In this paper, the coefficients are integrated into the performance function used to determine the flexural limit state of highway bridges, and a Monte Carlo sampling method is used to calculate the reliability indices of existing RC simply supported T-beam highway bridges and to predict the probability of failure of the existing highway bridges in each condition state and at each age. Based on statistical data from 1,228 bridges constructed between 1978 and 2008 in Bei...

Strength and Ductility Trends for Concrete Members Strengthened in Flexure with Carbon Fiber-Reinforced Polymer Reinforcement

For reinforced concrete (RC) beams and slabs under-reinforced with steel and strengthened in flexure with carbon fiber-reinforced polymers (CFRPs), the yield plateau is eliminated and post-yield flexural capacity increases linearly by elastic straining in the CFRP. At the ultimate flexural limit state, failure occurs by either concrete crushing or CFRP rupture. The consequence is an increase in strength and decrease in ductility. In this study, a parametric analysis is presented where strength and energy ratios are investigated as a function of existing steel and strengthening CFRP reinforcements. Both normal-strength and high-strength concretes are considered. A graphical representation showing the controlling strength limit state is developed. Strength and energy ratios for various service, yield, and ultimate limit state combinations show that strength increase and ductility loss are significantly affected by the amounts of steel and CFRP reinforcements. The ultimate-to-yield strength ratio increases rapidly with decreasing steel and CFRP reinforcements; consequently, the service strength approaches the yield strength. Ductility loss is nonlinear and inversely related to the amounts of steel and CFRP reinforcements. For the parameters considered, ductility relative to the unstrengthened condition was reduced between 35 and 93%.

Flexural Tests and Associated Study of a Full-Scale 65-kW Wind Turbine Tower

Full-scale static test to failure was conducted on a 21.9-m-long 65-kW wind turbine tower to evaluate the flexural strength and failure mode. The test was conducted in a displacement-control mode. The flexural limit state in the form of local buckling near the tower base was developed. The buckling occurred in the elastic range because of a high diameter-thickness ratio of the section. Although local buckling caused slight strength degradation, the reduction was not very significant and the recorded response showed a good amount of post-buckling ductility. The local buckling flexural strengths predicted from established standards correlated very well with the measured buckling strength. A parametric finite-element analysis was also conducted. By properly modeling the boundary condition and a local dent on the tower wall, a good correlation of the structural response and failure mode was also achieved. It was found that the ultimate strength and failure mode were sensitive to the boundary condition considered in the model. The presence of a local dent would affect both the location and type of local buckling, although the failure load is less sensitive to local dent.

Structural optimization and proposition of pre-sizing parameters for beams in reinforced concrete buildings

The aim of the present paper is to show the application of optimization strategies for the cost of beams in reinforced concrete buildings and to propose pre-sizing parameters. In order for these goals to be met, an optimization software program was developed. The program combines the analysis of structures by the grid model, reinforced concrete sizing, and the simulated annealing optimization heuristic. Sizing is compliant with the NBR 6118 (2007) Brazilian standard, according to which flexural, shearing, torsion, and web reinforcements and serviceability limit states (deflection and crack width limitation) are checked. Besides the dimensions of the situations mentioned above, the influence the cost of each material (steel, concrete and formwork) has on the overall cost of structures was also determined.

Analytical Model for RC Beams with Externally Bonded Laminates Using Strut-and-Tie Method

An analytical model for RC beam strengthened with externally bonded laminates based on the strut-and-tie method is reported herein for predicting the strength and mode of failure of the strengthened RC beam. From the proposed model, four inequality equations were derived corresponding to four possible modes of failure. These four inequality equations define a safe domain. When the loading path up to the ultimate flexural limit state of a beam is plotted on the same diagram, the mode of failure and strength of the beam can be identified. The possible modes of failure consist of both flexure-type and shear-type failures. Flexure-type failure is due to the yielding of internal longitudinal reinforcement or the yielding of externally bonded laminates, whereas shear-type failure is due to the crushing of the diagonal compressive concrete strut or the yielding of the shear reinforcement. The failure mode initiated by one flexure-type followed by another is possible. Mode of failure initiated by one flexure-type followed by a shear-type is also possible but not otherwise. In short, this model describes the mode of failure and the corresponding strength of an RC beam strengthened with externally bonded laminates, which can be used to verify the adequacy of design for beam strengthening.

Experimental Study on Concrete T-Beams Strengthened with Carbon Fiber Reinforced Polymer (CFRP) Sheets on Three Sides

In this paper, through test of concrete T-beams strengthened with carbon fiber reinforced polymer (CFRP) sheets on three sides, the failure modes, ultimate flexural limit states and designing demands are discussed. The allowed stress of carbon fiber sheets is also analyzed according to the measured stress, which is important in civil engineering.

Mechanical behaviour of pitting corrosion of flexural and shear reinforcement and its effect on structural reliability of corroding RC beams

A spatial time-dependent reliability model is developed for a RC beam subject to corrosion-induced pitting corrosion, for shear and flexural limit states. The analysis considers the spatial and time-dependent variability of pitting corrosion, structural resistance and load effects. The amount of corrosion loss can significantly affect the mechanical behaviour of reinforcement, namely low corrosion loss can result in ductile yielding, whereas a higher corrosion loss can result in brittle fracture. The progression from ductile to brittle behaviour is spatially and time-dependent. To estimate how such phenomena affects structural reliability the structural resistance of reinforcement is modelled as either (i) perfectly ductile parallel system or (ii) perfectly brittle parallel system. It was found that the probability of failure assuming brittle reinforcement behaviour is up to 450% higher than assuming ductile behaviour.

Impact of 1994 Northridge earthquake on masonry: design and build tall reinforced masonry buildings

AbstractThe 1994 Northridge earthquake confirmed the fact that it is now possible to design tall masonry buildings that have excellent and predictable earthquake performance. In general, masonry buildings performed well during the Northridge earthquake, and when construction practice was good the structural performance of masonry buildings was excellent. However, since most masonry buildings are stiff, low‐rise structures, the amount of non‐structural damage was significant. This is because the high floor accelerations that occur in low‐rise buildings during earthquakes usually results in increased damage to non‐structural components. Tall masonry buildings are more flexible and respond to earthquake shaking with longer periods of vibration than low‐rise buildings. This result is lower floor accelerations and consequently less non‐structural damage. In addition, tall masonry walls can be designed to respond in flexural limit states that are inherently more ductile and predictable than the behavior of short, squat walls. This means that the structural performance of tall masonry buildings in future earthquakes will be better than that observed in low‐rise buildings during the 1994 Northridge earthquake. It is thus clear that tall masonry buildings will provide an improvement to the proven earthquake response of masonry structures. Copyright © 2004 John Wiley & Sons, Ltd.

Reliability-based Criterion for Maximum Reinforcement Ratio of Reinforced Concrete Beam Sections

This paper presents a reliability-based approach for the maximum reinforcement ratio of reinforced concrete flexural members. The study was based on sensitivity analysis of beams at their flexural limit state. The statistical characteristics of strength parameters under the prevailing construction practices in Saudi Arabia are employed. The maximum reinforcement ratio specified by ACI 318M-95 is critically examined. At the maximum reinforcement and employing local materials (concrete and reinforcement), the probability of brittle flexural failure was found to be higher than that reported in literature. This is mainly attributed to the high yield strength of the reinforcement and low compressive strength of the concrete. Two approaches were proposed to control the probability of brittle failure. The first approach includes replacing the nominal strength values of reinforcement and concrete by the corresponding mean values in the ACI formula for maximum reinforcement ratio. The second approach includes determination of the acceptable probability of brittle failure at the limit state and calculation of the maximum reinforcement ratio from the relationships developed in this study.

Reliability analysis for highway bridge deck assessment

An assessment procedure based on structural system reliability principles, has been developed for highway bridges with concrete or composite decks. It concentrates on the ultimate flexural limit state of slabs and takes account of the fact that the failure of the structure is dependent on the combination of the applied loads, their variability, both spatial and in amplitude, and on the variability of geometric and material properties. Recognising that each of a number of topologically distinct collapse mechanisms may contribute to the overall probability of system failure, an optimisation technique is used in conjunction with structural reliability analysis in order to establish for each mechanism the critical geometry and the associated probability of occurrence. The procedure can be implemented in the assessment of existing bridge structures, where the use of plastic analysis may reveal strength reserves not utilised in design and, hence, alleviate the need for strengthening. By modelling the bridge as a virtual series system and analysing a finite number of collapse mechanisms, bounds on system failure probability in flexure can be estimated. An example of its intended use is presented for a solid slab concrete bridge deck.

Assessment Of Brittle Failure At TheUltimate Flexural Limit State Of R.C.Beams By Computer Simulation

Reinforced concrete beams at the ultimate flexural limit state may fail by concrete crushing even when they are reinforced below the maximum reinforcement ratio specified by the ACI Code. One of the factors contributing to this uncertainty is the variability of the strength of concrete and reinforcing steel. This paper presents the relationship between probability of brittle failure of reinforced concrete beams at the limit state and the variability in the yield strength of reinforcing steel and compressive strength of concrete. Monte-Carlo simulation is employed to randomly generate strength parameters. Results indicated that probability of brittle failure at the limit state is adversely affected by low quality of concrete and high yield strength of reinforcing steel. A criterion for maximum reinforcement ratio to contain the risk of brittle failure within an acceptable level is proposed.