Moment Redistribution Capacity Research Articles

Moment redistribution capacity in prestressed concrete continuous beams

In prestressed concrete continuous beams, building code provisions often allow for a reduction in the moment at a critical section (calculated through elastic analysis). This reduction is permitted as long as the moments in all other sections are adjusted to maintain equilibrium and support the designated loads. However, the allowable moment redistribution percentage (MRP) for prestressed concrete beams (PCBs) remains a topic of debate. Many codes currently assign a similar MRP limitation to both PCBs and reinforced concrete beams (RCBs). This approach might be over-simplistic for PCBs due to their unique behaviour. A method for identifying the maximum available MRP is proposed in this article. An in-depth study was conducted on the maximum available MRP of PCBs based on calibrated finite-element models. The results showed that parameters such as the passive reinforcement ratio, steel yield strength, slenderness ratio, eccentricity of prestressing tendons, concrete grade and load pattern, which are not considered in the codes, influence the maximum available MRP to an extent. Using the same permissible MRP as RCBs may thus be inappropriate. An equation is proposed to estimate the maximum available MRP for PCBs.

Punching tests on edge slab-column connections with refined measurements

Due to the significant shear forces developing around columns and the potential brittle failure associated, the punching capacity of flat slabs is the main concern at ultimate limit state. An effective way to understand the behaviour of slab-column connections has typically been by testing isolated specimens in the laboratory. While there exist many slab-column connection types in actual slabs, most research efforts have focused on the punching resistance at internal columns. Specifically, edge connections appear largely underrepresented in the literature when the number of existing tests is compared to their importance in typical building floor configurations. Furthermore, the favourable effect of slab continuity is generally neglected in this type of tests. This paper presents the results of an experimental campaign on two edge slab-column connections: one had no shear reinforcement, while the other had a large amount of shear reinforcement to evaluate maximum punching. A novel test setup was conceived to apply representative boundary conditions of actual continuous slabs, introducing moment continuity perpendicularly to the slab free edge. Refined measurement techniques were extensively used, monitoring the visible slab faces using Digital Image Correlation, and instrumenting the flexural and shear reinforcement with distributed fibre-optic sensors. The failure of the slab-column connection without shear reinforcement was triggered in the region of shear stress concentrations and propagated around the column thereafter. Well-anchored vertical legs of flexural reinforcement at the free face induced a smeared-like shear crack pattern. In the shear-reinforced slab-column connection, an initial crushing of the concrete at the column front corners was followed by the formation of a local yield line along the slab axis. In addition to the enhancement of the resistance and rotation capacity, the shear studs also served for increasing the moment redistribution capacity of the system. The experimental results are compared to different codes of practice, showing that improvements are needed to better assess the resistance of edge columns.

Symmetric and Asymmetric Strengthening of Two-Span RC Beams Using FRCM Systems

This paper reports on the feasibility of using fabric-reinforced cementitious matrix (FRCM) systems to strengthen two-span reinforced concrete (RC) beams that are structurally deficient in their sagging regions. In addition to one unstrengthened control beam, nine beams strengthened either symmetrically or asymmetrically with polyparaphenylene benzobisoxazole (PBOFRCM), carbon (CFRCM), and carbon fiber–reinforced polymer (CFRP) sheets were tested under a five-point load configuration. Test results showed that increasing the strengthening ratio resulted in significant increases in the yielding and load-carrying capacity of the beams. Beams symmetrically strengthened with PBOFRCM showed high ductility indices ranging between 100% and 121% of that of the control beam, whereas those strengthened with CFRCM and CFRP showed ductility indices of 45% and 34% of that of the control beam, respectively. Moreover, beams symmetrically strengthened with PBOFRCM systems encountered moment redistribution ratios between 42% and 82% of that of the control beam compared with 10% and 9% only for those strengthened with CFRCM and CFRP systems, respectively. The asymmetric strengthening configuration in which FRCM systems were used along with CFRP sheets proved to be an efficient method to enhance the ductility and moment redistribution capacity of the strengthened beams. Analytically, the rigid-body-rotation approach was modified to predict the moments and curvatures at the plastic hinges of the strengthened sections. The predicted moments and curvatures showed a notable agreement with the experimental values.

Moment redistribution capacity of continuous RC beams with High-Strength steel reinforcement

Moment redistribution (MR), a nonlinear behavior occurring in continuous reinforced concrete (RC) beams, is related to the redistributed section's ductility and the stiffness distribution along the whole beam. The use of high-strength steel (HSS) reinforcement could affect the redistributed section’s ductility and can delay or even prevent the formation of plastic hinge after another. The lack of research regarding the influence of those phenomena on MR is one of the reasons that hinder design engineers from using HSS. This paper conducts a broad-range parametric study through finite element (FE) method to check if the design provisions on MR are still applicable to beams with HSS reinforcement of yield strength of more than 600 MPa. The critical sections' yield state (whether the plastic hinge is formed) at the ultimate limit state (ULS) and its influences on MR are investigated. The study demonstrations that the MR capacity decreases with the increase in yield strength of reinforcement, especially when the midspan section cannot yield at ULS due to the use of HSS reinforcement. Besides, the yield state is influenced by the coupling effect of multi-parameters and significantly affects the influence degree of each parameter on MR. A new method considering the yield state is proposed to estimate the MR capacity of the continuous beams. This method's reasonable accuracy is proved. It is recommended to reduce the specified MR by about 6% for every 100 MPa increase in yield strength of reinforcement.

ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ КОЭФФИЦИЕНТА ПЕРЕРАСПРЕДЕЛЕНИЯ МОМЕНТОВ В СТАТИЧЕСКИ НЕОПРЕДЕЛИМЫХ ЖЕЛЕЗОБЕТОННЫХ БАЛКАХ

This article investigates the coefficient of moments redistribution in statically indeterminate RC beams through an experimental and analytical approach. Two-span statically indeterminate RC beams were tested under bending moment. A discussion of the results of the mode of failure, load-deformation, load-strain, and the coefficient of the moments redistribution were conducted. Moreover, the experimental results were compared to the analytical predictions of the related existing models, including the ACI 318-19 and CSA A23.3-19 codes, and others. The results show that the coefficient of moment redistribution is affected by the reinforcement ratio (µs1) and can be accurately predicted by a recent mathematical analysis. The experimental results also reveal that the moment redistribution capacity of the beams exceeds the values predicted by the other existing models.

Prediction of moment redistribution capacity in reinforced concrete beams using gene expression programming

Moment redistribution can play an important role in making the design of reinforced concrete (RC) structures more realistic and economical. In this paper, a new comprehensive formula has been proposed that considers four input parameters that are thought to influence moment redistribution the most in statically indeterminate RC beams using gene expression programming (GEP). For this reason, an experimental database of 108 data points was collected from experimental studies in the literature to predict the moment redistribution of the RC beams using genetic programming. All of these collected data points belong to two-span RC continuous beams. The results of the GEP formulation were statistically compared with the experimental results obtained from the literature and the results from the equations provided by the current design code provisions. The results of the comparison revealed that the proposed GEP-based formulation has the best performance and accuracy among the proposed models. Moreover, the sensitivity analysis and parametric study were also carried out to evaluate the most critical parameters affecting on moment redistribution of RC continuous beams.

Rotation and moment redistribution capacity of fiber‐reinforced concrete beams: Parametric analysis and code compliance

AbstractFiber‐reinforced concrete (FRC) has been proved to be a competitive solution for structural purposes. Extensive research has highlighted the benefits of adding fibers on the post‐cracking strength, reduced crack spacing and crack width, and improved durability, among others. However, these aspects are related to serviceability limit states, and significant work remains to be done in terms of ultimate limit state behavior of FRC members. As recent publications have emphasized, reinforced concrete beams with low reinforcement ratios may result in a reduction of deformation capacity and, hence, to a loss of ductility. To further investigate this topic, this paper presents the results of a numerical parametric study of simply and continuous supported hybrid‐reinforced concrete (HRC) beams made with different amounts of fibers and reinforcement ratios. The deformation, rotational, and moment redistribution capacity of those were assessed by means of a finite‐element model previously calibrated using experimental results available in the literature. The results showed that there is a significant reduction of rotation capacity and moment redistribution for lightly reinforced (hybrid) members. Finally, the paper contains practical recommendations in terms of minimum reinforcement ratios that guarantee adequate rotation and redistribution capacity of HRC members. As such, the results of this study can provide a contribution toward more reliable structural designs of HRC members.

A new anchorage system for CFRP strips in externally strengthened RC continuous beams

Attaching fiber-reinforced polymer (FRP) strips externally on the surface is a beneficial strategy for retrofitting and repairing reinforced concrete (RC) beams subjected to flexural loading. Despite widespread usage of continuous RC beams, research addressing their performance when reinforced externally with FRP strips is scarce. The loading capacity, moment redistribution capacity, and ductility of FRP strip-reinforced RC members are lower than those of RC beams without FRP strips, due to debonding failures. To avoid early failure in an RC beam reinforced with FRP strips, various anchorage techniques have been proposed. An experimental study was carried out in this research to investigate the flexural performance and moment redistribution capacity of continuous (two-span) RC beams reinforced with carbon fiber-reinforced polymer (CFRP) strips. To avoid untimely failure and improve load-carrying and moment redistribution capacity, as well as ductility, an end anchorage mechanism was proposed. Here, four 6000-mm continuous beams with 250 × 150-mm sections were constructed. The obtained results indicated that utilizing the proposed anchor for the CFRP strips in the continuous beams led to a considerable increase in the loading capacity, moment redistribution ratio, and ductility in comparison with the CFRP-reinforced beams without the anchor. Furthermore, for predicting the load-bearing capacity of a continuous RC beam reinforced using CFRP strips, an analytical model was put forward, whose results showed proper agreement with the test results.

Experimental investigation of moment redistribution in ultra-high performance fibre reinforced concrete beams

In the design of statically indeterminate structures the concept of moment redistribution is used to reduce the absolute magnitudes of moments in critical regions, to fully utilise the capacity of non-critical cross sections, and to simplify detailing by enabling a reduction in reinforcement ratios. Due to the complex mechanisms which control the formation and rotation of plastic hinges, moment redistribution capacities are commonly empirically based, and hence not necessarily applicable outside of the bounds of the testing regime from which they were derived. This paper presents the results of an experimental study of the moment redistribution capacity of four two-span continuous beams constructed from ultra-high performance fibre reinforced concrete (UHPFRC) and with various reinforcement ratios, such that the suitability of extending of exiting empirical design approaches to UHPFRC can be investigated. The results of the experimental investigation show that for beams where the hinge formed at the support, the observed moment redistribution was greater than the code predictions. However for the beam where the hinge formed under the load points, observed moment redistribution was significantly less than codes predictions. Hence, the results of this study show current design guidelines do not always provide a conservative prediction of moment redistribution in UHPFRC beams.

Experimental study on ferritic stainless steel simply supported and continuous beams

Development of efficient design guidance for stainless steel structures is key for the increased use of this corrosion-resistant material by considering both nonlinear behaviour and strain hardening into resistance prediction expressions, together with the moment redistribution in indeterminate structures. With the aim of analysing the bending moment redistribution capacity of ferritic stainless steel beams, a comprehensive experimental programme on continuous beams is presented. These tests contribute to the assessment of EN1993-1-4 specifications, where no plastic design is allowed, and the classical and new plastic design methods available in the literature for indeterminate stainless steel structures. Four three-point and eight four-point bending tests are also reported for the assessment of current codified and revised cross-sectional classification limits, analysing the different methods for the prediction of the ultimate bending capacities of ferritic hollow sections. Additional test results reported by other authors in different stainless steel grades and carbon steel are also studied and presented. The analysis indicates that Class 1 cross-sectional classification limits are too optimistic for ferritic stainless steels and further research is needed for the extension of plastic design to these grades, although promising predictions of ultimate loads are obtained for austenitic and lean duplex stainless steels.

NSM technique to increase the load carrying capacity of continuous RC slabs

This work presents and analysis the results of an ongoing research project on the use of the Near Surface Mounted (NSM) carbon fiber-reinforced polymer (CFRP) laminates for the increase of the load carrying capacity of statically indeterminate (two spans) reinforced concrete (RC) slabs. The test program consisted of seventeen slab strips, grouped in two series that are different on the adopted strengthening scheme: H series, where H is the notation to identify the slabs strengthened with NSM CFRP laminates exclusively applied in the hogging region; HS series, where HS is the notation to identify the slabs strengthened with NSM CFRP laminates applied in both hogging and sagging regions. The program includes six unstrengthened reference RC slab strips, and eleven strengthened with CFRP NSM configurations designed to increase in 25% or 50% the load carrying capacity of the corresponding reference RC slabs. An extensive monitoring system was applied in the constituent materials, in the critical regions of the tested slabs, in order to collect information for the discussion about the effectiveness of NSM technique in terms of load carrying and moment redistribution capacity. The strengthening procedures adopted in the laboratory tests followed, as much as possible, the real strengthening practice for this type of interventions. The obtained results show that the proposed technique is able to increase significantly the load carrying capacity of statically indeterminate RC slabs, even for those with relatively high steel reinforcement ratios. The load carrying capacity of the strengthened slabs was limited by its shear capacity or by the detachment of the strengthened concrete cover layer. At failure of the strengthened slabs, the longitudinal steel bars at intermediate support (hogging region) and at loaded sections (sagging regions) have already yielded, and the deflection was quite large. However, for some strengthening configurations, the CFRP laminates led to a decrease of the moment redistribution capacity of the slabs.

Ductility and moment redistribution capacity of multi-span T-section concrete beams reinforced with GFRP bars

Glass fibre reinforced polymer (GFRP) bars are being increasingly used to reinforce concrete members as an alternative to steel, particularly in harsh environments, owing to their main advantages that include high strength, low self-weight, electromagnetic transparency and non-corrodibility. However, besides being relatively expensive, GFRP bars have low elasticity modulus and exhibit linear elastic behaviour until failure, thereby providing no contribution to structural members’ ductility. This paper presents experimental and numerical investigations about the flexural behaviour of continuous concrete beams reinforced with GFRP bars, in particular on their capacity to redistribute internal forces. Small-scale flexural tests were carried out on 7 two-span beams with T cross-section: the main parameters analysed were the GFRP reinforcement ratio and the confinement level in critical zones of the beams, namely at the central support. The behaviour of the beams was analysed and compared in terms of serviceability and failure responses. The numerical investigations included the development of non-linear finite element (FE) models of all beams tested. After validation and calibration with the test data, a comprehensive parametric study was performed, in which the effects of (i) the span, (ii) the cross-section geometry, and (iii) the longitudinal GFRP reinforcement ratio on the moment redistribution capacity of full-scale continuous beams were evaluated. Results obtained show that moment redistribution occurs and that elastic analyses are considerably conservative. The confinement of the concrete at critical cross sections may be a good solution to enhance the plastic hinge ductility and consequently, the moment redistribution in GFRP reinforced concrete beams.

Design for Moment Redistribution in RC Beams Retrofitted with Steel Plates

It is now common practice to retrofit reinforced concrete members by adhesively bonding steel or fibre reinforced polymer plates to their surfaces. However, tests have shown that these plated RC structures tend to have less member ductility, or rotational capacity, than the unplated structure because of premature plate debonding. In this paper, structural mechanics approaches are described for both: quantifying the moment rotation capacity, or member ductility, of steel plated RC flexural members; and quantifying the moment redistribution capacity from the moment rotation capacity. It is shown how the moment redistribution structural mechanics model can be used to design for member ductility directly and, furthermore, it is applied to both externally bonded and near surface mounted steel plates. As would be expected, it is shown that steel plating produces more ductile members than fibre reinforced polymer plating.

Experimental study of moment redistribution and load carrying capacity of externally prestressed continuous composite beams

A comparative experimental study of prestressed continuous steel-concrete composite beams was carried out. Two continuous composite beams were tested, one of which was plain continuous steel-concrete composite beam, while the other was a composite beam prestressed with external tendons. Cracking behavior and the load carrying capacity of the beams were investigated experimentally. Full plasticity was developed in the mid-span section each beam, the maximum moments attained at the internal support sections however were governed by local buckling which was related to the slenderness of composite section. It was found that in hogging moment regions, the ultimate resistance of an externally prestressed composite beam would be governed by either distortional lateral buckling or local buckling, or interactive mode of these two buckling patterns. The results show that exerting prestressing on a continuous composite beam with external tendons will increase the extent of internal force and moment redistribution in the beam. The influences of local and distortional buckling on the behaviors of the composite continuous beams are discussed. The Moment redistribution and the load carrying capacity of the prestressed continuous composite beams are evaluated, and it is found that at the ultimate state, the moment redistribution in the prestrssed continuous composite beams is greater than that in non-prestressed composite beams.

Two-dimensional FE model for evaluation of composite beams, II: Parametric study

In the present paper, the 2D finite element (FE) model presented and validated in the companion paper “Two-dimensional FE model for evaluation of composite beams, I: Formulation and Validation” is used to undertake a parametric study focused on both the required and available rotations and the moment redistribution capacity of semi-continuous composite beams. The investigation has shown that some tendencies already established in the literature regarding beams with full shear connection are not applicable to cases with partial shear connection.

Investigation of Monotonic and Cyclic Response of Fiber-Reinforced Polymer Strengthened Beams

This study investigates the hysteretic characteristics, ductility and moment redistribution capacity of beams strengthened with fiber reinforced polymer (FRP) materials. Three different FRP strengthening schemes were tested for their effectiveness in improving strength and ductility of existing, nonconforming reinforced concrete beams. Eight full-size, two-span rectangular beams were considered in pairs, tested under monotonic or cyclic loading. Six were strengthened in flexure using top, bottom, or side face FRP sheets or surface mounted FRP rods, while transversely-wrapped glass FRP sheets were applied in all three pairs to prevent shear failure. One control pair was detailed with conventional steel reinforcement only for ductile flexural response. Results showed that monotonically loaded beams failed in flexure. Unlike top and bottom face strengthened beams, side strengthened beams exhibited superior performance comparable with the control, in terms of overstrength, ductility, and deformation capacity. All beams under increasing amplitude cyclic response were unable to develop the montonic capacity of a flexural mechanism. No matter which method of FRP strengthening had been used, cyclic behavior exhibited severe pinching and gradual strength and stiffness degradation.

Redistribution of longitudinal moments in straight, continuous concrete slab – steel girder composite bridges

The effect of loading and geometric parameters on the transverse and longitudinal redistribution of moments in continuous composite bridges, comprising a concrete slab on parallel steel girders, is investigated with the nonlinear finite element method. Fifty bridges are analyzed over their entire range of loading up to failure, and their moment redistribution factors are determined and compared with the relevant predictions of the Canadian Highway Bridge Design Code (CHBDC) and the AASHTO LRFD Bridge Design Specifications. The parameters studied included truck position along the bridge, number of loaded lanes, bridge width, number of girders, slab thickness, degree of composite action, and presence of diaphragms. The study reveals that among the preceding parameters only the number of loaded lanes and the bridge width significantly affect transverse redistribution of moments at ultimate limit state (ULS). However, most of the preceding parameters affect longitudinal redistribution at ULS. Finally, it is demonstrated that plastic analysis of composite multi-girder continuous bridges, treated as an equivalent beam, provides a reasonable estimate of their longitudinal moment redistribution capacity at ULS. It is demonstrated that the actual load-carrying capacity of a composite bridge may be more than 50% higher than that predicted by the CHBDC or AASHTO code. Such higher predicted capacity may obviate the need for retrofit in some cases.Key words: analysis, bridge, composite, concrete, distribution, finite element, inelastic, load, steel.

Moment redistribution in continuous profiled steel–concrete composite slabs

The moment redistribution behaviour of continuous cold-formed profiled steel deck and concrete composite slab was studied both experimentally and numerically. An experimental programme consisting of three two-span continuous composite slabs was performed. The experimental results indicated that the composite slabs have adequate ductility for redistributing moments, and the ultimate capacity of continuous composite slabs can be increased significantly. The short-term deflection at the increased service load satisfies the serviceability criteria. A numerical procedure to determine the negative to positive moment redistribution capacity and the corresponding deflection at serviceability for profiled steel–concrete composite slab was validated using the experimental results.