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Optimization for partially prestressed high strength concrete girders
Abstract
Partially prestressing acts as an intermediate design alternative between fully prestressed and conventional reinforced concrete through relaxing the allowable concrete tensile stresses. Consequently, this results in lower prestressing forces, which subsequently reduces prestressing steel and the overall cost. The adoption of high-strength concrete (HSC) with partial prestressing improves both the economic and durability aspects. However, limited research has been conducted to investigate the effect of HSC on the serviceability requirements of partially prestressed girders. This paper presents a numerical investigation into the behavior of such girders under quasi-static loading. The presented numerical model was validated against experimental results in terms of deflection and cracking performance at different loading stages. Then it was conducted in a parametric study to assess the effect of concrete compressive strength, prestressing force, and non-prestressed reinforcement ratios on the behavior of the partial prestressed girders using full-scale sections. The proposed study presents different design optimization regimes for HSC partially prestressed girders.
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This study numerically examines the prospects of replacing steel tendons with fibre reinforced polymer (FRP) tendons in precast segmental concrete girders/beams (PSCBs) for mitigating the corrosion damage to precast structures using finite element (FE) software Abaqus. This is the first study in the published literature that successfully builds an experimentally-verified 3D FE model of dry-joined PSCBs internally prestressed with unbonded FRP tendons to thoroughly investigate the beam’s flexural behaviour. The effect of segments’ interface imperfection on the initial stiffness of PSCBs was successfully captured in this study. The distinguished working mechanisms between segmental and monolithic beams, and between FRP and steel tendons in both tension- and compression-governed cases were comprehensively discussed. An intensive parametric study was also conducted to examine the effect of primary parameters (effective prestressing level, prestressing reinforcement ratio, span-to-depth ratio and different types of FRP tendons) on the flexural response of PSCBs. The results have proven that commonly available CFRP tendons (Young’s modulus Ep =145 GPa) can well replace steel tendons in PSCBs while high-modulus CFRP tendons (Ep =200 GPa) should be used with caution to ensure the PSCBs can achieve sufficient deformability. Moreover, among some existing models, ACI 440.4R-04’s model gave the most accurate predictions of the ultimate stress of unbonded FRP tendons (fpu) in PSCBs compared to the numerical results but its estimation was slightly unconservative and scattered. A new bond reduction factor was, hence, proposed for better prediction of fpu of FRP tendons in PSCBs.
The ultimate stress of unbonded FRP tendons in PSCBs should be limited within 75% of the tendon’s tensile strength in design to account for the deformation concentration at the joints and the brittle failure characteristics of FRP tendons.
An experimental investigation into the dynamic compressive response of high-strength concrete with three different strengths – 60MPa, 80MPa and 110MPa, denoted by C60, C80 and C110, respectively – was undertaken. Concrete specimens were subjected to quasi-static and dynamic compression, using a Denison Universal Testing Machine and a Split Hopkinson Pressure Bar (SHPB) device, and the effects of strain rate on their mechanical properties (e.g. stress-strain relationship, compressive strength) examined. Significant rate dependence was observed for all three concretes – i.e. the compressive strength increases with strain rate and the dynamic strength is much higher than the static value; C60 and C80 exhibited similar rate sensitivity, while C110 displayed a relatively noticeably lower rate dependence. The rate sensitivity was quantified via a Dynamic Increase Factor (DIF, the ratio between the dynamic and static strength), and this was compared with predictions by the CEB-FIP 2010 equation, commonly utilised to estimate rate sensitivity for normal strength concrete. The comparison indicates that the model is not suitable for high-strength concrete, as it predicts a sharper rise in rate-sensitivity, and the mismatch increases with concrete strength, becoming notably significant for C110. Interpretation of rate dependence of concrete materials based on SHPB test results, as to whether it is an intrinsic material property, or generated primarily by radial inertia, was examined by finite element modelling of SHPB tests. Concrete material properties were taken to correspond to a concrete damaged plasticity model, and the quasi-static stress-strain response, coupled with the Dynamic Increase Factor determined from dynamic tests, was utilised. The simulation results correlated closely with experiments, in terms of strain gauge signal histories in the SHPB loading bars, indicating that for the strain rate range investigated (30-110s⁻¹), radial inertia is not significant, and the rate dependence observed is attributable to material response.
The past several years have witnessed an increase in research on the nonlinear analysis of the structures made from reinforced concrete. Several mathematical models were created to analyze the behavior of concrete and the reinforcements. Factors including inelasticity, time dependence, cracking and the interactive effects between reinforcement and concrete were considered. The crushing of the concrete in compression and the cracking of the concrete in tension
are the two common failure modes of concrete. Material models were
introduced for analyzing the behavior of unconfined concrete, and a possible constitutive model was the concrete damage plasticity (CDP) model. Due to the complexity of the CDP theory, the procedure was simplified and a simplified concrete damage plasticity (SCDP) model was developed in this paper. The SCDP model was further characterized in tabular forms to simulate the behavior of unconfined concrete. The parameters of the concrete damage plasticity model, including a damage parameter, strain hardening/softening rules,
and certain other elements, were presented through the tables shown in the paper for concrete grades B20, B30, B40 and B50. All the aspects were discussed in relation to the effective application of a finite element method in the analysis. Finally, a simply supported prestressed beam was analyzed with respect to four different concrete grades through the finite element program.
The results showed that the proposed model had good correlation with prior arts and empirical formulations.
Building codes consider the tension stiffening when calculating the crack width of the flexural members. A simple analytical procedure is proposed for the determination of forces, stresses and strains acting on a reinforced concrete section subjected to flexure considering the concrete contribution in tension up to tensile concrete strain corresponding to the cracking strength of concrete. This analytical method gives the minimum value (lower bound) of tension stiffening. Also, a commercial Finite Element Program (ABAQUS 2007) was used to perform non-linear analysis in order to evaluate the total contribution of the tensioned concrete in carrying loads which may be considered as the upper bound of tension stiffening. In addition, a comparison is carried out among the different codes using four reinforced concrete rectangular models to compare and evaluate the tension stiffening with proposed analytical lower bound tension stiffening and upper bound as obtained by ABAQUS. The models include different percentages of flexural steel ratio. The comparison revealed that the codes’ equations always consider tension stiffening lying between lower and upper bound of tension stiffening proposed in this study. Also, the study showed that the tension stiffening decreases with the increase of the percentage of the flexural reinforcement ratio.
This paper describes a three-dimensional approach to modeling the nonlinear behavior of partial-depth precast prestressed concrete bridge decks under increasing static loading. Six full-size panels were analyzed with this approach where the damage plasticity constitutive model was used to model concrete. Numerical results were compared and validated with the experimental data and showed reasonable agreement. The discrepancy between numerical and experimental values of load capacities was within six while the discrepancy of mid-span displacement was within 10 %. Parametric study was also conducted to show that higher accuracy could be achieved with lower values of the viscosity parameter but with an increase in the calculation effort.
In the last few decades, prestressed concrete has been rapidly used in bridge engineering due to the enormous develop-ment in the construction techniques and the increasing need for long span bridges. High strength concrete has been also more widely spread than the past. It currently becomes more desirable as it has better mechanical properties and dura-bility performance. Major defect of fully prestressed concrete is its low ductility; it may produce less alarming signs than ordinary reinforced concrete via smaller deflection and limited cracking. Therefore, partially prestressing is consi-dered an intermediate design between the two extremes. So, combining high strength concrete with partial prestressing will result in a considerable development in the use of prestressed concrete structures regarding the economical and durability view points. This study presents the results of seven partially prestressed high strength concrete beams in flexure. The tested beams are used to investigate the influence of concrete compressive strength, prestressing steel ratio and flange width on the behavior of partially prestressed beams. The experimentally observed behaviors of all beams were presented in terms of the cracking load, ultimate load, deflection, cracking behavior and failure modes.
Bending test of seven reinforced concrete beams are modeled in finite element program to validate the modeling strategies by comparing the structural response of the beams. Three beams in the set are pre-damaged and strengthened with fiber reinforced composites before the bending tests. Cracks are implemented into the model by inserting geometrical discontinuities to represent the pre-damaged beams. Parametric variables such as crack width, length and interval are chosen to simulate different pre-damage levels. Once the proposed modeling strategies are validated by real experimental tests then 196 finite element models are created to study the effects of pre-damage levels on the moment capacity of reinforced concrete beams repaired with CFRP. Results indicate that inclusion of pre-damage levels by means of cracks into the cross sections have significant effect on beams moment capacity.
A test setup and adequate instrumentation were developed to record the tension properties of high-strength concrete, including the postpeak softening response. The direct uniaxial tension tests were performed under a strain-controlled mode through a close-loop testing machine. The splitting tensile strength and modulus of rupture were also recorded conforming to standard ASTM test procedures. Test results revealed that high-strength concrete exhibits a more brittle and stiffer behavior with a large initial modulus of elasticity and a more sharply descending branch of the stress-deformation curve beyond the peak load. The unique softening behavior and the more brittle nature of high-strength concrete were expressed in terms of a stress-displacement (crack width) diagram and fracture energy. The fracture energy of high-strength concrete is estimated to be about five times the area under the ascending portion of the stress-deformation curve, compared to a corresponding value of 10 estimated for normal-strength concrete. Based on the test results, a constitutive relationship is recommended for the behavior of high-strength concrete in tension, including postpeak softening response.
Fiber reinforced polymer (FRP) has been used as an alternative to steel in some appropriate conditions. In this study, a model was developed for prediction of tension stiffening in FRP RC beams with various reinforcement ratios by introducing a coefficient, named correction factor. By using an inverse approach to obtain the optimal correction factor, the results of finite element analysis were consistent with the experimental results in both load-midspan displacement curves and cracking patterns. Uneven distributions in the strain of FRP bars were also observed. A relationship between the correction factor and the reinforcement ratio was proposed by fitting and verified by additional simulations that were in agreement with the corresponding experiments. It indicates that the proposed model is suitable for predicting the behavior of FRP RC beams with various reinforcement ratios.
Prestressed concrete is widely used for various types of structural applications, and unexpected fire during its service life can lead to premature tendon rupture. Prestressed tendons in high tensile stress are vulnerable to fracture at elevated temperatures and result in low fire resistance due to spalling of concrete with temperature rise. A good understanding of the failure mechanism and fire response behaviour of prestressed members would lead to the development of prestressed concrete members with enhanced fire resistance. In this paper, a detailed and elaborate literature survey on the performance of prestressed concrete members under elevated temperature has been undertaken. The fire response behaviour of prestressed concrete members has been extensively studied, and various research studies highlighting the critical temperature and failure mechanism of concrete and prestressing steel are discussed. The factors responsible for bond strength degradation were determined from the literature. The parameters influencing the fire performance of prestressed concrete members are also identified and the parameters such as concrete cover, aggregate type, the volume of polypropylene fibres, and cement blend with a lesser amount of silica fume are found to have a significant effect on improving fire resistance. The fire response of sustainable precast prestressed members with Carbon Fibre Reinforced Polymer (CFRP) tendons was also studied and it has been found that the performance of such members under elevated temperature depends mainly on concrete ingredients and volume of polypropylene fibres used in concrete.
In this paper, a concrete damaged plasticity model is presented for simulating the behaviour of high-strength concrete; C60, C80 and C110 under static and dynamic loading conditions. This model is based on the ground-breaking studies recorded in recently completed studies to improve and develop the original concrete damaged plasticity (CDP) model in ABAQUS software. In this CDP model, the stress-strain curves in compressive behavior and tensile behavior during the softening phase (after stress reaches peak strength) consider the effect of mesh size in Finite Element model. Through recently published results, these curves show the advantages compared to the previous studies. At the same time, the tensile damage variable (dt) and the compressive damage variable (dc) are presented using an exponential function to replace the values reported in previous researches. Especially, in the case of dynamic problems, the Dynamic Increase Factor (DIF) according to the fib MODEL CODE 2010 (MC2010) is used in this study as a significant parameter to determine the effects of strain rate on compressive strength of high-strength concrete. To prove the reliability and effectiveness of the proposed model, numerical simulation of the static compressive tests is implemented to verify its suitability in case of static loading problems. Then, Split-Hopkinson pressure bar (SHPB) test is simulated to determine the level of accuracy of DIF in simulating the dynamic loading problems. The results show that the present CDP model introduced in this study has an acceptable agreement with the experimental results for both cases; static and dynamic loading conditions, with high reliability.
Prestressed Hollow Core Slabs (PHCSs) have become widely used in the construction industry owing to their economic benefits. During their service life, changes that would require openings to be situated along their spans may arise. A strengthening technique to recover or improve the original serviceability and resistances becomes indispensable. Limited research interest has been given to develop appropriate strengthening methods for the PHCSs with openings. The Near Surface Mounted (NSM) strengthening technique is among the practical and feasible solutions to rehabilitate or enhance the performance of these PHCSs. This paper demonstrates a Finite Element (FE) analysis technique to predict the responses of the PHCSs with openings, either unstrengthened or strengthened with NSM strips. The Concrete Damage Plasticity (CDP) model was successfully implemented to model the non-linear behaviour of concrete. The prestressing transmission length and the bond behaviour between the epoxy adhesive and concrete interfaces were put into practice. Acceptable agreements were found, upon validating the FE analysis results against the experimental data available in the literature. Maximum differences , compared to the experimentally attained results in the ultimate loads and the corresponding deformations of nearly 4% and − 8.4%, respectively, were detected. An extensive parametric study was executed to assess the effect of various parameters on the overall behaviour of the examined slabs. The PHCS cross-sectional shape, CFRP reinforcement percentage, average precompression, opening location and size and the concrete compressive strength were taken as parameters. Above all, a gap of knowledge exits regarding the presence of design guidelines that evaluate reductions in the ultimate capacities of the PHCSs associated with the presence of openings at multiple locations along their spans and improvements experienced by employing the NSM strengthening technique. This could be bridged by utilizing the suggested modelling approach and the para-metric study results in this research.
Various tests, focusing on the effects of the type and composition of cementitious materials (ordinary Portland cement, fly ash, slag, low-heat cement, and their combinations) on the durability performance of high-strength concrete. Firstly, mix proportions were designed based on a number of trails into account their applicability to prestressed bridges. Durability related properties, such as carbonation test, water permeability test, resistance to chloride-ion penetration and electrical resistivity, were determined. The effects of supplementary cementitious materials such as fly ash and alccofine on durability properties of high-strength concrete have been demonstrated.
This paper presents an experimental investigation into the behavior of Glass Fiber-Reinforced Polymer (GFRP) bar reinforced high strength concrete and ultra-high strength concrete beams. In total, twelve GFRP bar reinforced concrete beams (GFRP-RC beams) were constructed and tested. Six GFRP-RC beams were tested under static loading. Higher strength concrete was found to influence the overall behavior of GFRP-RC beams under static loading in terms of load carrying capacity, deflection, and post-cracking bending stiffness. Six GFRP-RC beams were tested under impact loading at various levels of impact energy. The GFRP-RC beams displayed a shift in the failure mode (from shear failure to flexure failure) as a result of the use of ultra-high strength concrete under impact loading.
The ACI 318 Building Code permits calculation of immediate
deflections for cracked prestressed concrete slabs and beams based
on either a bilinear moment deflection relationship or an effective
moment of inertia. The effective moment of inertia Ie is taken
as a weighted average of the uncracked moment of inertia Ig and
cracked moment of inertia Icr. Accuracy of deflection calculations
based on Ie depends on the value of cracking moment and requires
an upwards shift in the Icr response. A new approach is proposed
for computing service load deflections of cracked prestressed
members. The proposed approach is compared with the existing
ACI 318 approaches using the measured load-deflection response
of prestressed beams and is shown to provide a more accurate and
consistent prediction of deflections than the existing approaches.
An alternative trilinear model that is much simpler but not as accurate
is shown to provide reasonable results as well. It is recommended
to compute deflection of cracked prestressed members
using the trilinear approach except in those instances where higher
accuracy is needed.
The purpose of this paper is to investigate the phenomenon of tension stiffening in concrete reinforced with glass fibre polymer (GFRP) bars. The nature of the tension stiffening phenomenon is first described according to theory. Then, the results of an experimental campaign aiming to investigate tension stiffening quantitatively are presented and critically discussed, examining potential factors such as shrinkage that could have affected the measurements. Finally, the numerical models that reproduce the experiments are described and the results compared with both the theory and the experiments themselves. Good agreement is found between model and experimental data.
A stress-strain relationship for Grade 270 low-relaxation prestressing strands is presented. It is based on recent extensive testing by the authors requested by the PCI Industry Handbook Committee. The testing has resullted in refined constants of the previously developed power formula which has been shown in several studies to predict prestressing steel stress for a given strain to within 1 perrcent error of any prescribed experimental value. Tables and stress-strain graphs for other common types pf prestressing steel are reproduced here, from an earlier study, for the convenience of readers.
An experimental investigation of high strength concrete bridge girders was conducted. The investigation included fabrication and testing of 70 ft (21.3 m) long, 54 in. (1372 mm) deep, pretensioned, prestressed high strength concrete bulb-tee girders. The design concrete compressive strength for the girders was 10,000 psi (69 MPa). Two girders were used to evaluate long-term static load and fatigue performance. Results from the girder used to determine long-term static load behavior indicated prestress losses that were significantly less than those predicted by the AASHTO Standard. The girder used to determine fatigue performance withstood more than 5 million cycles of fatigue loading and satisfied all serviceability requirements. Upon completion of the long-term static load and fatigue test, measured flexural properties for both girders were adequate with respect to both design and specification requirements. Based on results from this investigation, high strength concrete bridge girders can be expected to perform adequately over the long-term when designed and fabricated in accordance with current AASHTO provisions.
This paper proposes provisions to extend the current American Association of State Highway and Transportation Officials' AASHTO LRFD Bridge Design Specifications to include prediction of the ultimate flexural strength of prestressed concrete girders with concrete compressive strengths up to 18 ksi (124 MPa). The proposed design provisions include composite action of a high-strength concrete (HSC) girder with normal-strength concrete (NSC) deck slab. Nine 40-ft-long (12 m) AASHTO Type II HSC girders were tested with and without cast-in-place NSC decks of differing widths to achieve various possible modes of failure. The concrete used for the girder was designed for three target compressive strengths of 10 ksi, 14 ksi, and 18 ksi (69 MPa, 97 MPa, and 124 MPa). The experimental program investigated failure modes of three different types of compression zones: one with NSC only, one with HSC only, and one with both NSC and HSC. All girders were tested to failure under static loading to study the different limit-state behaviors, including prestress losses, initiation of cracking, yielding, and final failure mode.
In the technical literature the combination of conventional steel reinforcement and prestressing steel as strength reinforcement in a flexural concrete member is usually implied by the term partial prestressed element. Partially prestressed elements are used in the practice and their design is based on rational analysis, on the satisfaction of the requirements of both serviceability and ultimate strength limitations and finally on the engineering judgment. In the present work the estimation of the required partial prestressing based mainly on the crack control of concrete is proposed. First, based on the allowable crack width as it is stated by the codes (ACI 318 or Eurocode 2), the stress of the non-prestressed reinforcement is estimated. Then the depth of compression zone is derived using a cubic equation formed for this purpose. Further the required effective pre-strain of the prestressing steel and henceforth the required prestress force are calculated. Design charts and three numerical paradigms are also presented and commented herein.
The fatigue behavior of 12 different sets of partially prestressed concrete beams was experimentally investigated. All beams were rectangular, 9 × 4.5 in. (229 × 114 mm) in cross section, simply supported on a 9 ft (2.74 m) span and loaded in 4 point bending. Each set consisted of 2 identical specimens designed with the same input parameters. One control beam was tested under static load up to ultimate. The second beam was tested in cyclic fatigue at a constant load range varying between 40% and 60% of the ultimate load capacity of the static specimen. The main input variables were the partial prestressing ratio PPR and the reinforcing index ω. Four different levels of PPR and three different levels of ω covering both fully prestressed and fully reinforced were explored. Typical results and observed trends are described. Throughout the tests, measurements of strains in the reinforcement, deflections, crack widths, curvatures and their variation under static and cyclic fatigue loading were systematically recorded. The six partially prestressed and the three fully reinforced beams survived 5,000,000 cycles without suffering fatigue failure. The three fully prestressed beams which were loaded beyond cracking failed, respectively, at 1.21 × 106, 2.17 × 106 and 1.94 × 106 cycles.
Nonlinear three-dimensional finite element modeling of precast, prestressed concrete spandrel beams is a challenging task and requires exploration of the effects of material parameters and modeling assumptions. To this end, the numerical results obtained using the commercial software ABAQUS/Standard were compared with existing experimental data. The sensitivity of the spandrel beam response to various parameters such as finite element type, dilation angle, fracture energy, tension stiffening, bearing stress distribution and support representation was investigated. The behavior of precast, prestressed concrete spandrels under vertical loading was found to be sensitive to the type of element, the dilation angle for the concrete, bearing stress distribution at the supports, and deck-tie stiffness. Many of the findings reported are believed to be applicable to other types of reinforced concrete structures.
High-performance materials, such as high-strength concrete (HSC) and high-strength steel (HSS), are often adopted in tall buildings to reduce member size and save space. The use of HSC and/or HSS can significantly increase the flexural strength of concrete members but may also adversely affect the flexural ductility and deformability. Herein, the pros and cons of using HSC and HSS in concrete beams are investigated in terms of the limits of flexural strength, ductility and deformability that can be simultaneously achieved using nonlinear moment-curvature analysis with stress-path dependence of the reinforcement taken into account. The results reveal that the use of HSC or both HSC and HSS in concrete beams can at the same strength increase the ductility and deformability, or increase the strength without depleting the ductility and deformability. However, the use of HSS has no such benefit, albeit it can reduce the steel area required. Copyright © 2010 John Wiley & Sons, Ltd.
Partial prestressing, which fills the gap between fully prestressed concrete and reinforced concrete, has now been accepted and become normal practice in many regions. The research and development of partially prestressed concrete members with bonded and unbonded tendons made of steel as well as fibre-reinforced polymer (FRP) are reviewed. The behaviour of bonded partially prestressed concrete members has been extensively studied, and this review mainly focuses on fatigue behaviour, serviceability analysis and time-dependent effects. The research on unbonded partially prestressed concrete members has mainly focused on prediction of flexural resistance, which is closely related to the ultimate tendon stress at flexural failure. Investigations of the service and ductility behaviour of unbonded partially prestressed concrete members are comparatively limited. Although external prestressing is effective in strengthening flexural concrete members, the strength acquired is accompanied by a reduction in ductility of flexural failure. The amount of prestressing tendons should therefore be carefully chosen to maintain the necessary ductility of the strengthened members. When FRP tendons are used in partially prestressed concrete members, deformability is a key indicator of safety.
For modelling fracture behaviour of concrete various types of deformation controlled uniaxial tests were performed on normal weight and on lightweight concrete. These two types of concrete were compared with respect to their envelope curves, material stiffness and degradation during post-peak cycles, and residual compressive deformation on crack closure. Differences in behaviour were explained on the basis of the properties of the aggregates which result in specific fracture surfaces. Based on narrow specimens with uniform stress distribution, unique stress deformation curves were determined and the descending branches were modelled. These models were applied to calculate the stress distribution in wide specimens with a sawcut. The total force was in good agreement with the experiment. Probable reasons for the different behaviour of lightweight and normalweight concrete are discussed.
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