Moment redistribution in continuous plated RC flexural members. Part 2: Flexural rigidity approach

doi:10.1016/j.engstruct.2004.08.004

Engineering Structures

Volume 26, Issue 14, December 2004, Pages 2209-2218

https://doi.org/10.1016/j.engstruct.2004.08.004 Get rights and content

Abstract

Adhesive bonding plates to the surfaces of reinforced concrete members is now frequently used to increase both the strength and stiffness. However, because of the brittle nature of the plate debonding mechanisms, plating is often assumed to reduce the ductility to such an extent that guidelines often preclude moment redistribution. Tests on seven full-scale flexural members have shown that significant amounts of moment can be redistributed from steel and carbon fibre reinforced polymer (FRP) plated regions. In this paper, a procedure is developed for quantifying the amount of moment redistribution that can occur in externally bonded steel or FRP plated members which can be used to design plated members for ductility.

Introduction

It was suggested in the companion [1] paper that the neutral axis parameter (k_u) approach used in international standards for controlling the moment redistribution in reinforced concrete structures depends on both the concrete crushing and the existence of a horizontal plateau in the moment/curvature relationship. Both requirements seldom occur in plated structures due to intermediate crack, IC, debonding of the plate; so the k_u approach is felt to be unsuitable for this new form of plated structure. Instead, an alternative approach based on flexural rigidities has been developed to quantify moment redistribution in plated members in which IC debonding controls the ultimate strength.

Section snippets

Moment redistribution concept

In order to illustrate the phenomenon of moment redistribution, that is the ability of statically indeterminate beams to redistribute moment, let us consider the encastre or built in beam of length L in Fig. 1(c), which can also be considered to represent an internal span of a continuous beam. For convenience, let us assume that the same longitudinal reinforcing bars are in the top and bottom of the beam. Hence, the hogging (hog) and sagging (sag) regions have the same moment/curvature (M/χ)

Moment redistribution approach for plated beams

To determine whether a beam is ductile enough to redistribute moment is an extremely complex problem [2] and there is much good ongoing research [2], [3], [4], [5], [6] to develop a comprehensive and simple solution. The problem is to understand how the beam can deform to accommodate the non-elastic distribution of moment (line B in Fig. 1(b) and also shown in Fig. 2(a)) and then to determine whether the deformation capacity of the beam can accommodate this required deformation. Two approaches

Flexural rigidity model

In order to apply the flexural rigidity approach, the test specimens [1] have been idealised as propped cantilevers about the line of symmetry, as in Fig. 5, where the flexural rigidity in the hogging region EI₂ and in the sagging region EI₁ vary but are constant within a region. This distribution of EI is not meant to represent the general behaviour, such as would be required for determining the deflection, but it is only meant to represent moment redistribution where the differences in EI

Elastic and plastic components of moment redistribution

Moment redistribution has been defined [1] as the change in the moment from that when the flexural rigidity of the beam is the same throughout its length, that is when EI₁=EI₂ in Fig. 5. This definition of moment redistribution was given in the companion paper [1] as $MR_{tot} = (M_{hog})_{EI.const} − (M_{hog})_{test} (M_{hog})_{EI.const}$ where for a given applied load and hence applied static moment M_static, the hogging moment (M_hog)_EI.const is derived from an elastic analysis where EI is constant and (M_hog)_test is the

Application

Let us consider the amount of moment redistribution that can occur in an internal span which is represented by the encastre beam in Fig. 9 and which is plated in the hogging region. For this beam with a uniformly distributed load w, the moment redistribution can be determined from the following equations which were derived using the techniques used to derive , : $x= L 2 − L^{2} 4 − 2M_{hog} w_{5}$ $w_{6} =24M_{hog} x EI_{1} + EI_{2} ((L / 2) −x) (EI_{2} − EI_{1})(6x^{2} L−4x^{3}) + EI_{2} L^{3}$

The moment M_hog in Eq. (5) is the hogging moment in the beam when a

Summary

A mathematical model has been developed for quantifying the amount of moment redistribution that can occur in steel or FRP externally bonded plated beams that debond prior to concrete crushing. The mathematical model is based on the maximum strain at debonding and a parametric study suggests that substantial amounts of moment redistribution can occur in steel plated sections if designed with care. However, CFRP plated sections show a limited ability to redistribute moment at their maximum

References (10)

S.A. El-Refaie et al.
Strengthening of reinforced concrete continuous beams with CFRP composites
D.J. Oehlers et al.
A Structural Engineering Approach to Adhesive Bonding Longitudinal Plates to RC Beams and Slabs
Composites Part A
(2003)
J.G. Teng et al.
Intermediate crack-induced debonding in RC beams and slabs
Construction and Building Materials
(2003)
Oehlers DJ, Ju G, Liu I, Seracino, R. Moment redistribution in continuous plated RC flexural members. Part 1: neutral...
CEB-FIP. Ductility of Reinforced Concrete Structures—synthesis report and individual contributions. Bulletin 242,...

There are more references available in the full text version of this article.

Cited by (35)

Moment redistribution capacity of continuous RC beams with High-Strength steel reinforcement
2023, Structures
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.
Seismic performance of stabilised/unstabilised rammed earth walls
2021, Engineering Structures
This experimental study investigates the in-plane seismic performance of unstabilised/stabilised rammed earth (RE) walls. The experimental program consists of five specimens including three unstabilised and two stabilised walls. All walls are $1000 m m$ long, $900 m m$ tall and $200 m m$ thick. To simulate earthquake forces at the presence of gravity loads, the walls are subjected to an in-plane cyclic loading reversal combined with a constant vertical pre-compression stress. The experimental parameters comprise pre-compression stress (0.1, 0.3 and 0.5 MPa) and stabiliser type (lime and cement). The outcomes are compared in terms of failure mode, hysteretic response, ductility, energy dissipation, stiffness degradation, residual deformation and damage index. Further discussion is also provided by evaluating the envelope curves of the hysteretic load–displacement responses implementing a capacity spectrum approach. It is indicated that the level of vertical stress affects the hysteretic response of the walls with higher levels producing more favourable responses. However, increased vertical stress is caused by the greater gravity loads which in turn intensify the seismic induced forces that may dominate the seismic response of the walls. In addition, the effect of stabilisation process is highly dependent on the stabiliser type.
Flexural behaviour of hybrid steel-GFRP reinforced concrete continuous T-beams
2020, Composite Structures
This paper presents test results of six full scale reinforced concrete continuous T beams. One beam was reinforced with glass fibre reinforced polymer (GFRP) bars while the other five beams were reinforced with a different combination of GFRP and steel bars. The ratio of GFRP to steel reinforcement at both mid-span and middle-support sections was the main parameter investigated. The results showed that adding steel reinforcement to GFRP reinforced concrete T-beams improves the flexural stiffness, ductility and serviceability in terms of crack width and deflection control. However, the moment redistribution at failure was limited because of the early yielding of steel reinforcement at a beam section that does not reach its moment capacity and could still carry more loads due to the presence of FRP reinforcement.
The experimental results were compared with the ultimate moment prediction of ACI 440.2R-17, and with the existing theoretical equations for deflection prediction. It was found that the ACI 440.2R-17 reasonably estimated the moment capacity of both mid-span and middle support sections. Conversely, the available theoretical deflection models underestimated the deflection of hybrid reinforced concrete T-beams at all load stages.
Moment redistribution versus neutral axis depth in continuous PSC beams with external CFRP tendons
2020, Engineering Structures
Citation Excerpt :
Although a few studies on continuous PSC beams with external FRP tendons have been carried out [15,16,20,21], the redistribution behaviour of these beams has not been fully understood. For example, while the importance of stiffness difference is recognised [21,26], its influence on the global redistribution and neutral axis behaviour of continuous PSC beams with external FRP tendons has never been addressed. Although code equations using neutral axis depth for redistribution quantification are available [23–25], these equations may not be reasonable because of the neglect of stiffness difference impact.
The neutral axis depth is adopted by many codes of practice as an indicator of flexural ductility to quantify moment redistribution in continuous prestressed concrete (PSC) beams. Moment redistribution, however, does not only depend on ductility but also on differences in stiffness along the length of the beam. Therefore, the effectiveness of using solely the neutral axis depth for redistribution quantification needs to be further evaluated. This study examines moment redistribution against neutral axis depth in two-span PSC beams with external CFRP tendons by applying a validated finite element model. The main variable is the content of non-prestressed reinforcement either at the positive or negative moment zone to generate varying stiffness differences between critical sections. The study shows that the use of neutral axis depth as a key parameter is inadequate when quantifying moment redistribution in these beams. Modifications of CSA, BSI and EC2 equations are proposed by introducing a parameter reflecting the impact of stiffness difference. The proposed equations show much better fit to the actual redistribution than that provided by equations in current design codes.
Effect of steel fibres in combination with different reinforcing ratios on the performance of continuous beams
2019, Construction and Building Materials
Citation Excerpt :
A moment curvature relationship in which a plateaux is reached after the peak moment is ideal for moment redistribution. The ability of steel fibres to contribute towards moment redistribution therefore depends on the post-peak moment curvature behaviour of the fibres, where a flatter slope, tending towards deflection hardening behaviour, is optimal [4]. Literature reviewed on the effect of steel fibres in combination with reinforcing bars provides seemingly contradictory results, a contradiction which stems from the changes in ductility caused by the addition of steel fibres.
The ability of statically indeterminate structures to redistribute moments, thus fully utilising the capacity of non-critical sections, leads to improved structural efficiency. The effect of steel fibres on moment redistribution in reinforced concrete beams was investigated to determine whether the addition of fibres affects the ability of beams to redistribute moments. The results of fifteen two-span continuous beams, each containing a unique combination of steel fibres and reinforcing bars, indicated significant moment redistribution before plastic behaviour. An optimum 1.5% fibre content in terms of moment redistribution corresponded with a flatter post-peak moment-curvature relationship. The addition of fibres led to reduced deflections, with fibre effectiveness increasing with increasing reinforcing ratios.
Finite element modelling and testing of two-span concrete slab strips strengthened by externally-bonded composites and mechanical anchors
2017, Engineering Structures
Citation Excerpt :
If moment redistribution is to be relied on in the design of continuous RC structures, a rigorous analytical investigation should be conducted to ensure that the inelastic rotation capacity (available ductility) at the proposed plastic hinge location is in excess of the required plastic rotation (ductility demand). Published analytical models on the behaviour of continuous RC structures strengthened with EB-FRP were onerous from a computational viewpoint and difficult to use by practitioners [19,21]. In such cases, validated finite element (FE) models can serve as a powerful tool to simulate the nonlinear structural behaviour of strengthened continuous RC structural members including moment redistribution during all stages of loading until failure.
Ten three-dimensional finite element (FE) models were developed in this paper to simulate the nonlinear behaviour of two-span reinforced concrete (RC) slab strips. Two slabs were unstrengthened and eight slabs were strengthened in either the sagging or the hogging region by externally-bonded carbon fiber-reinforced polymer (EB-CFRP) laminates with or without mechanical anchors. The tensile steel in the strengthened region was approximately 30% of that of the unstrengthened region to represent a continuous RC flexural element in need of strengthening. Laboratory tests were carried out to verify the accuracy and validity of the FE models. Each specimen had a total length of 3800 mm, a width of 400 mm and a depth of 125 mm. The provision of mechanical anchors in the hogging strengthening prevented the CFRP debonding mode of failure, slightly improved the strength gain, and significantly improved the slab ductility. Failure of the slab strips strengthened in the sagging regions was not dominated by CFRP debonding, and hence, the effect of including mechanical anchors in the sagging strengthening was concealed. Unstrengthened specimens exhibited significant deviations from the elastic response. Sagging strengthening decreased the deviation from the elastic response. Specimens strengthened in the hogging region exhibited insignificant moment redistribution ratios. The developed FE models captured the nonlinear behaviour of the tested slab strips with good accuracy. The inclusion of an interfacial bond stress-slip model in the analysis between the CFRP and the concrete had insignificant effect on the predicted response of strengthened specimens.

View all citing articles on Scopus

View full text