Moment Redistribution Research Articles

Research in Redistribution of Bending Moments in the Beams of Reinforced Concrete Early Loaded

This paper presents results of a study of a reinforced concrete beam, simulating a double-span beam, early loaded. The beam was designed with limited redistribution of bending moments from the support to the span. The tested element was loaded at the operational load level, after the concrete had reached 80% of its predicted compressive strength. In a two-month test it was observed that the distribution of bending moments changed in the direction opposite to what was expected, i.e. from the span to the support. Moment redistribution in the tested beam leads to a reduction of security level in the middle support section of the beam.

Decoupling algorithm for evaluating multiple beam damages in steel moment‐resisting frames

SummaryPost‐earthquake safety evaluation of steel moment‐resisting frames mainly relies on the inspection of seismic damage to beam–column connections. Recently, in order to evaluate seismic damage of steel connections in a prompt and precise manner, a local damage evaluation method based on dynamic strain responses has been proposed and receives attention. In the evaluation method where strain responses are measured by piezoelectric strain sensors, a strain‐based damage index has been developed for evaluating individual seismic beam damage in a steel frame. However, for a steel frame suffering multiple beam damages, the damage index deteriorates its performance in identifying small damages with the presence of neighboring severe damages because of the moment redistributions induced by larger damages. This paper presents a decoupling algorithm that removes the issue of damage interaction and improves the performance of the damage index. The decoupling algorithm was derived on the basis of damage‐induced moment release and redistribution mechanism. The effectiveness of the decoupling algorithm was numerically and experimentally investigated using a nine‐story steel frame model and a large scale five‐story steel frame testbed that can simulate multiple fractures at beam ends. Copyright © 2016 John Wiley & Sons, Ltd.

Quantifying moment redistribution in FRP-strengthened RC beams

Consideration of moment redistribution (MR) in the design of continuous reinforced concrete (RC) beams results in an efficient and economical design. Adding fibre-reinforced polymer (FRP) materials to reinforced structures to enhance flexural capacity leads to a reduction in ductility, such that design standards severely limit use of the MR in their design. This has forced engineers to use elastic analyses for strengthening design, which can lead to FRP wastage. To overcome this, complicated or empirical solutions have been applied to solve the problem of MR in strengthened concrete members, with limited success. This paper presents a novel theoretical strategy for quantifying and tracking MR in such members by employing basic structural mechanics without any need for estimating rotation capacity or ductility. Fully non-linear flexural behaviour of continuous strengthened members can be predicted and any geometry, loading arrangement and strengthening technique or configuration can be considered. The numerical model is validated against existing experimental data from the literature. Good agreement is shown between the experimental and numerical data, with the significance of this work being that, potentially, for the first time MR could credibly and confidently be incorporated into design guides for FRP strengthening of RC structures.

Tests on ferritic stainless steel simply supported and continuous SHS and RHS beams

AbstractDevelopment of efficient design guidance for stainless steel structures (considering non‐linear behaviour, strain hardening and allowing for moment redistribution in indeterminate structures) is crucial for the widespread use of this corrosion‐resistant material. This paper presents an experimental programme involving ferritic stainless steel simply supported and continuous beams (RHS and SHS) and the assessment of existing cross‐sectional classifications and different plastic design methods available in the literature for indeterminate stainless steel structures, not currently allowed in stainless steel standards. The analysis indicated that some cross‐sectional classification limits seem to be too optimistic for ferritic stainless steels and further research is needed in order to extend plastic design to these grades.

Advanced numerical investigation into structural behaviour of high-strength cold-formed steel lapped Z-sections with different overlapping lengths

In order to improve buildability of cold-formed steel structures, a series of research and development projects have been undertaken by the authors to examine structural behaviour of bolted moment connections between cold-formed steel sections. In this article, a systematic numerical investigation with advanced finite element modelling technique into the structural behaviour of high-strength cold-formed steel lapped Z-sections under gravity loads is presented, and details of the modelling techniques are presented thoroughly. It aims to examine deformation characteristics of these lapped Z-sections with different overlapping lengths. After careful calibration of advanced finite element models of lapped Z-sections against test data, it is demonstrated that the predicted moment rotation curves of these models follow closely the measured data not only up to the maximum applied moments but also at large deformations. In general, all of these lapped Z-sections are unable to resist sustained loadings after section failure under combined bending and shear, and they exhibit sudden unloadings once the maximum applied loads are attained. Hence, the proposed finite element models are able to simulate highly non-ductile deformation characteristics of these Z-sections. While long overlapping lengths over internal supports in multi-span cold-formed steel purlin systems are often advantageous in terms of both ‘stiffness and strength’, more steel materials are used at the same time. Hence, it is very desirable to establish an efficient use of the lapped Z-sections with optimal overlapping lengths. A total of six models with different overlapping lengths are then extended to simulate the structural behaviour of lapped double-span beams, and extensive material and geometrical non-linear analyses have been carried out. It is found that lapped double-span beams with practical overlapping lengths tend to behave superior to continuous double-span beams in terms of both load resistances and deformations. Depending on the overlapping lengths of the lapped Z-sections, different system failure mechanisms have been clearly identified after significant moment redistribution within the beams, and their structural behaviour has been compared in a rational manner. Consequently, these models will be readily employed to investigate the structural behaviour of high-strength cold-formed steel lapped Z-sections under a wide range of practical loading and boundary loading conditions for possible development of effective design rules.

Compressive Membrane Action Effects on Punching Strength of Flat RC Slabs

The design of reinforced concrete flat slabs in practice can be governed at failure by punching shear close to concentrated loads or columns. Punching shear resistance formulations provided by codes are calibrated on the basis of experimental tests on isolated slabs supported on columns in axisymmetric conditions. Nevertheless, the behavior of flat slabs can be different than isolated specimens due to the potentially beneficial contributions of moment redistributions and compressive membrane actions. Accounting for the significance of these effects, nonlinear finite element analyses are performed with the crack model PARC_CL implemented in Abaqus. This paper aims to investigate a series of punching shear tests on slabs with and without shear reinforcement, different reinforcement ratios and loading conditions accounting for the potential contribution to the enhancement of the punching strength due to compressive membrane action (CMA). The numerical results with a multi – layered shell modeling are then post – processed adopting the failure criterion of the Critical Shear Crack Theory (CSCT). The results pointed out the significant outcomes and differences between standard specimens and actual members showing how the current codes of practice may underestimate the punching capacity.

Mechanics‐based closed‐form solutions for moment redistribution in RC beams

AbstractWhen it comes to the efficient design of reinforced concrete beams and frames, moment redistribution is used to: reduce the absolute maximum magnitude of the moment in the critical region, equalize the critical moments on either side of interior columns and fully utilize the capacity of the non‐critical regions of a member. Although important, historically, moment redistribution has proved to be difficult to quantify due to the complexity of quantifying hinge rotations. Although numerous empirical expressions exist for plastic hinge lengths, i.e. the length over which the ultimate curvature can be integrated in order to give hinge rotations, a comparison with a global dataset yields poor results. Using a recently developed mechanics‐based moment‐rotation approach, it is possible to quantify the moment‐rotation characteristics of reinforced concrete hinges. In the tension region, the approach applies partial interaction theory directly to simulate the mechanisms associated with slip of the reinforcement relative to the surrounding concrete as cracks widen, whereas in the compression region, partial interaction shear‐friction theory is used to describe the formation and failure of concrete softening wedges. It is shown how the moment‐rotation approach explicitly allows for the size dependency. Furthermore, mechanics‐based solutions for moment redistribution are then derived and it is shown how these can be simplified at the ultimate limit state for use in the design office.

Behavior of Glass Fiber–Reinforced Polymer Reinforced Concrete Continuous T-Beams

AbstractIn this paper, test results of six large-scale glass fiber–reinforced polymer (GFRP) RC continuous T-beams are presented. The test specimens include one steel RC beam to serve as reference, one GFRP RC beam designed to meet the serviceability criteria at the service load level calculated for the reference beam, and four GFRP RC beams designed to achieve the same theoretical ultimate load of the reference beam. The test variables included the assumed percentage of moment redistribution, the spacing of lateral reinforcement in flange, and the arrangement of shear reinforcement. The test results showed that moment redistribution from the hogging to the sagging moment region occurred in GFRP RC beams with T-sections and that a small spacing of stirrups enhanced the moment redistribution percentage. In addition, decreasing the spacing of lateral reinforcement in the flange improved the moment redistribution through enhancing the stiffness of the sagging moment region.

Response of continuous concrete beams internally prestressed with unbonded FRP and steel tendons

This paper analyzes the global behavior of two-span continuous prestressed concrete beams with internal unbonded fiber reinforced polymer (FRP) and steel tendons. A nonlinear model is introduced and calibrated by the experimental results of unbonded prestressed specimens. Aramid and carbon fibers are used as composite tendons. The tendon area varies from 200 to 1700mm2 so as to generate a wide range of prestressing reinforcement index. The analysis shows that rupture of unbonded FRP tendons is unlikely to take place even at a very low prestressing reinforcement index. The type of unbonded tendons has practically no influence on the cracking mode and moment redistribution while it has limited effects on the development of deformation, nonprestressed steel stress and neutral axis depth. The effect of prestressing reinforcement index on the structural response is important. The ACI code may overestimate the ultimate stress in unbonded tendons in continuous beams at a low prestressing reinforcement index while it is conservative in predicting the permissible moment redistribution. The results also demonstrate that the type and amount of auxiliary bonded bars affect significantly the member behavior.

Strain-dependent electronic and magnetic of Co-doped monolayer of WSe2

We perform first-principles calculation to investigate electronic and magnetic properties of Co-doped WSe2 monolayer with strains from −10% to 10%. We find that Co can induce magnetic moment about 0.894μB, the Co-doped WSe2 monolayer is a magnetic semiconductor material without strain. The doped system shows half-metallic properties under tensile strain, and the largest half-metal gap is 0.147eV at 8% strain. The magnetic moment (0.894μB) increases slightly from 0% to 6%, and jumps into about 3μB at 8% and 10%, which presents high-spin state configurations. When we applied compressive strain, the doped system shows a half-metallic feature at −2% strain, and the magnetic moment jumps into 1.623μB at −4% strain, almost two times as the original moment 0.894μB at 0% strain. The magnetic moment vanishes at −7% strain. The Co-doped WSe2 can endure strain from −6% to 10%. Strain changes the redistribution of charges and magnetic moment. Our calculation results show that the Co-doped WSe2 monolayer can transform from magnetic semiconductor to half-metallic material under strain.

Nonlinear Flexural Response of Continuous Concrete Slab Strips Strengthened with Near Surface–Mounted Composites

AbstractThis paper aims to study the nonlinear flexural response of continuous RC slab strips strengthened with near surface–mounted (NSM) composite reinforcement in either the sagging or the hogging region. The study comprised experimental testing and three-dimensional finite-element (FE) modeling of eight two-span RC slab strips, 400×125×3,800 mm each. The amount of internal steel in the strengthened regions was approximately 30% of that of the unstrengthened regions. Flexural strengthening with NSM composites improved the stiffness and load capacity of continuous RC slab strips with no or insignificant reduction in the deflection at ultimate load. The gain in the load capacity due to strengthening was more pronounced for the slab strips strengthened in the sagging regions. Flexural strengthening reduced the moment redistribution ratio of the slab strips. The ratio further decreased by increasing the axial stiffness of the NSM composite reinforcement in the strengthened regions. The developed FE models...

Prediction of Capacity for Moment Redistribution in FRP-Strengthened Continuous RC T-Beams

AbstractBecause of the premature debonding of fiber-reinforced polymer (FRP) materials that results in a reduction in ductility, the problem of how to exploit moment redistribution (MR) in FRP-strengthened continuous reinforced concrete (RC) structures is unresolved. To date, limited research has been conducted into MR in such structures; a reliable and rigorous solution for quantifying MR throughout the loading cycle remains elusive. This paper aims to quantify MR and predict the capacity at reasonable accuracy, to encourage the use of FRP for the strengthening of existing continuous RC structures. Experiments conducted on 12 continuous T-beams are reported, and the findings are discussed. Strengthening configuration and anchorage scheme are the main variables. A new analytical strategy is described for quantifying MR, and the analytical results are then validated against the experimental results. Both experimental and analytical results confirm that there is no reason to restrict MR into strengthened zo...

Premature destruction of two-span RC beams exposed to high temperature caused by a redistribution of shear forces

When multi-span RC elements are exposed to fire one usually observes a yielding of span cross-sections while a safety reserve of support cross-sections is still significant. Due to this phenomenon a redistribution of bending moments occurs and the values of sagging moment in span cross-sections decrease while the values of hogging moment in support cross-sections increase. This paper shows the results of tests conducted on two-span RC beams in a situation when only one span has been exposed to high temperature from the bottom. The beams were 12×16 cm in their cross-section. The length of the span was 165 cm. The load has been applied by two forces put on each span. The beams were made of C25/30 concrete with siliceous aggregate. As a result of significant stiffness decrease of the heated span, redistribution of shear forces and bending moment occurs. Due to this redistribution the tested beams were prematurely damaged due to exhaust of the shear load bearing capacity in the middle part of the beam span where there was no transverse reinforcement.

Shakedown Behavior of a Continuous Steel Bridge Girder Strengthened With Post-Installed Shear Connectors

An economical method for strengthening non-composite steel girder bridges is to create composite action by “post-installing” shear connectors to engage the steel girder and concrete deck to act as a unit. Concepts of inelastic moment redistribution can be used to further increase the load-carrying capacity of continuous bridges. This paper presents results from experimental testing of a large-scale girder specimen with post-installed shear connectors under large repeated loads leading to moment redistribution at the shakedown limit state.

Flexural response of aluminium alloy SHS and RHS with internal stiffeners

Tubular profiles, such as square and rectangular hollow sections (SHS and RHS) are widely used in a range of structural engineering applications. Their thin-walled nature means that local buckling is a key design concern, which is usually addressed by adhering to specified slenderness limits. An alternative approach is to employ local plate stiffeners, which can be practically achieved in extruded aluminium alloy sections through the introduction of internal cross stiffeners. The flexural behaviour and design of aluminium alloy SHS and RHS with internal stiffeners is the subject of investigation of the present paper. The primary aims of the study are to generate experimental and numerical data for these new types of cross-section in bending, as well as to assess the applicability of different approaches to their design at cross-sectional and system levels. First, an experimental investigation was performed on aluminium alloy SHS and RHS beams with internal stiffeners subjected to three-point bending, four-point bending and five-point bending (i.e. continuous beams over three supports) of three different configurations. Finite element (FE) models were also developed and validated against the presented test data. Once validated, the models were employed to generate additional structural performance data through numerical parametric studies. Comparisons are then made between the experimental/numerical capacities and the design capacities predicted using a series of international design specifications for aluminium alloy structures, as well as the continuous strength method (CSM). The design strengths predicted by the American and Australian/New Zealand specifications were found to be conservative, while improved predictions are achieved by Eurocode 9. The most accurate and consistent predictions are obtained using the CSM, which was able to capture the significant observed strain hardening at the cross-sectional level and moment redistribution at the global system level.

Time-Dependent Deflection of Slab Affected by Construction Load

Long-term deflection is a critical issue in the design and construction of long-span flat-plate slabs that have become popular for tall buildings. In the present study, a numerical analysis method was developed to predict the long-term deflection of flat plates. In the proposed method, variations of construction load, moment redistribution due to slab cracking, and long-term effect of creep and shrinkage were addressed. The proposed method was applied to slabs in two actual multi-story buildings under construction. The predicted long-term deflections were compared with the on-site measurements. The results showed that the immediate deflection due to the construction load significantly increased the long-term deflection, and the predictions agree with the measurements.

Effect of corrosion degree on different steel ductility parameters, based on “Equivalent Steel” criterion

Purpose One of the meaningful effects of concrete reinforcement steel corrosion on concrete structures is the decrease of mechanical properties, specifically the ductility of steel. The term ductility of steel refers to a group of properties which determine the reinforced concrete structures and it is necessary to take this property into account for the recalculation of structures that have been already corroded until the point to condition in many occasions the analysis methodology. Design/methodology/approach This research studies the variation on ductility of concrete embedded steels bars after going through an accelerated corrosion process. Tensile strength of high ductility reinforcements with different corrosion levels has been tested. Ductility was studied in terms of ultimate tensile strength, yield strength, ultimate strain, energy density of deformation and “equivalent steel” criterion. It also makes some considerations about what is the best methodology of structural analysis according to the obtained results. Findings Based on the obtained results, conclusions are established that determine whether the corroded steel satisfy the requirements of different codes in order to identify them as “steels with special characteristics of ductility” assessing in each case the possibility of reallocating solicitations in structures which might need to be repaired. Originality/value The analysis of existing RC structures should address moment redistribution to be able to compare ultimate strength values, rather than to a single value obtained with elastic linear models to a range of values centred on the elastic and linear values obtained and defining an interval equal to double the value of the maximum redistribution capacity. This greatly enhances the possibility of “saving” a standing structure. In ductile structures the effect of actions can be distributed. The ascertainment of corroded reinforcement ductility variation is of key importance in structural re‐engineering and recalculation of structures. The research developed in this article is motivated by the need to contribute to knowledge of the behavior of reinforced concrete structures with reinforcement damaged.

Deflection of unbonded partially prestressed concrete continuous beams

Continuous beams are preferred to simply supported beams because of economy, fewer expansion/contraction joints and possible benefits from moment redistribution. In the design of unbonded partially prestressed concrete (UPPC) continuous beams, it is necessary to estimate their deflections under service loads in order to satisfy the requirements of serviceability limit state. A method is developed to convert the cross sectional area of unbonded prestressed tendons to the equivalent cross sectional area of non-prestressed steel. Then the moment of inertia of cracked section as well as Branson’s effective moment of inertia in a UPPC continuous beam can be easily determined. The computed deflections are compared with some available experimental results, including beams with external unbonded steel tendons and those with external unbonded aramid fibre reinforced polymer tendons. The proposed method gives satisfactory predictions of deflection till the yielding of non-prestressed steel. Another equation for moment of inertia of cracked section, which was originally suggested by the precast/prestressed concrete institute (PCI) Design Handbook for bonded partially prestressed concrete beams, is also evaluated in the study. In most cases the PCI equation can also give satisfactory results but in some cases its discrepancy of deflections is larger than that of the proposed method. Compared with the method recommended in the current Chinese Code, the proposed method is applicable not only to members with the conventional high-strength steel prestressing tendons, but also to those with tendons made of other materials such as fibre-reinforced polymer.

Punching behaviour of RC flat slabs under reversed horizontal cyclic loading

The aim of this work is to study the behaviour of reinforced concrete flat slab structures under combined vertical and horizontal cyclic loading. A total of five specimens were cast and tested: a control specimen was punched without eccentricity, one specimen was tested under constant vertical loading and monotonically increased eccentricity until failure and the remaining three were tested under constant vertical load, at different shear ratios, and cyclic horizontal loading with increasing horizontal drift ratios. All slabs were similar, measuring 4.25×1.85×0.15m3. The reinforced concrete slab specimens were connected to two steel half columns by 0.25×0.25m2 rigid steel plates, prestressed against the slab using steel bolts, to ensure monolithic behaviour. The cyclic tests were performed using an innovative test setup that allows bending moment redistribution, line of inflection mobility, assures equal vertical displacements at the North-South borders and symmetrical shear forces. Results show that cyclic horizontal actions are very harmful to the slab–column connection, resulting in low horizontal drifts and energy dissipation.

Evaluation of seismic performance of pile‐supported models in liquefiable soils

SummaryThe seismic performance of four pile‐supported models is studied for two conditions: (i) transient to full liquefaction condition, i.e. the phase when excess pore pressure gradually increases during the shaking; (ii) full liquefaction condition, i.e. defined as the state where the seismically induced excess pore pressure equalises to the overburden stress. The paper describes two complementary analyses consisting of an experimental investigation, carried out at normal gravity on a shaking table, and a simplified numerical analysis, whereby the soil–structure interaction (SSI) is modelled through non‐linear Winkler springs (commonly known as p–y curves). The effects of liquefaction on the SSI are taken into account by reducing strength and stiffness of the non‐liquefied p–y curves by a factor widely known as p‐multiplier and by using a new set of p–y curves. The seismic performance of each of the four models is evaluated by considering two different criteria: (i) strength criterion expressed in terms of bending moment envelopes along the piles; (ii) damage criterion expressed in terms of maximum global displacement. Comparison between experimental results and numerical predictions shows that the proposed p–y curves have the advantage of better predicting the redistribution of bending moments at deeper elevations as the soil liquefies. Furthermore, the proposed method predicts with reasonable accuracy the displacement demand exhibited by the models at the full liquefaction condition. However, disparities between computed and experimental maximum bending moments (in both transient and full liquefaction conditions) and displacement demands (during transient to liquefaction condition) highlight the need for further studies. Copyright © 2016 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.