Long-term Deflection Research Articles

Development of End-Reduced Pre-Flex Girder

Bridges serve to connect spaces where natural terrain or structures restrict the movement of people or vehicles. Various bridge construction methods have been proposed, and the application of preflex construction methods has recently increased. The end-reduced preflex girder is a method that applies preflex construction and compensates for the decrease in structural performance and long-term deflection of the bridge. However, in the existing preflex construction method, compliance with the minimum clearance height regulations in Korea, necessitates an increase in the end plan height, which requires an additional embankment that narrows the driver's view. This study was conducted to verify and evaluate the performance of an end-reduced preflex girder that can increase the structural strength and secure the minimum clearance height by attaching a shear reinforcement plate to the bottom of the lower flange, enabling an economical design.

Calculation of creep deformation of stiffness-degraded RC beams after strengthening with increased cross-section

The strengthening of existing reinforced concrete beams (RCBs) has mainly focused on short-term mechanical properties such as flexural resistance and shear resistance, while long-term deflection of RCBs has seldom been studied. In this study, six RCBs with different types and degrees of damage were designed and strengthened by the section enlargement method. Mid-span deflection and concrete strain were used to evaluate the influence of stiffness degradation due to fatigue or corrosion damage on the creep behavior of strengthened RCBs (SRCBs). The experiment results revealed that time-varying curves of creep deformation from fatigue or from corrosion-damaged SRCBs were consistent among the six specimens. Creep in a damaged SRCB was found to increase faster than that in an undamaged beam, and to reach over 90 % of final creep in about six months. Based on the mean curvature method and creep models, taking fatigue and corrosion damage as examples of stiffness degradation, a calculation method for creep deformation of SRCBs was established, and sensitivity analysis of stress levels, reinforcement height, consolidation time, and other parameters were carried out. The research results can provide a theoretical basis and guidance for evaluating creep deformation of stiffness-degraded RCBs after reinforcement with increased cross-section.

Comprehensive Review on the Flexure Behaviour of Corroded Reinforcement Concrete Beams Under Sustained Loads

This study presents a comprehensive review of the flexural behaviour of corroded Reinforced Concrete (RC) beams subjected to sustained loads. The investigation synthesizes extant literature to elucidate the complex interaction between concurrent stress and steel corrosion in RC members. Emphasis is placed on the critical necessity of conducting corrosion tests under continuous stress conditions to accurately simulate in-situ structural behaviour. The review encompasses previous numerical studies on deteriorated RC beam performance and provides a critical analysis of historical loading regimes designed to mitigate corrosion in loaded RC beams. Notably, the literature reveals conflicting findings regarding the influence of loading on corrosion rates and crack propagation, highlighting areas necessitating further research. The review also considers the effects of creep, shrinkage, and stress, with particular emphasis on long-term deflection characteristics. This comprehensive analysis aims to consolidate current knowledge and identify critical research gaps in understanding the flexural behaviour of corroded RC beams under sustained loads, thereby providing a foundation for future investigations in this domain.

Age-dependent deflection analysis of high-volume fly ash RC beams: experimental and artificial neural network modelling

This research examines the influence of high-volume fly ash (HVFA) on reinforced concrete (RC) beam deflections over 180 days of continuous loading. The study comprises eight fly ash-based concrete mixes with varying fly ash ratios (0–60%). Experimental assessments were conducted on two load levels, corresponding to 25% and 50% of the initial cracking load. Thirty-two full-scale RC beams, each measuring 100 × 150 × 1800 mm, were fabricated for both load levels. Long-term deflections were monitored for all concrete mixes through sustained four-point bending tests at ages ranging from 1 to 180 days. A comparative analysis of the overall mid-span deflection between conventional and fly ash concrete RC beams was carried out against established design codes. It was determined that high-volume fly ash RC beams exhibited less creep and shrinkage deflection compared with conventional RC beams. Moreover, artificial neural network (ANN) modelling was also carried out to propose a significant model helpful in predicting the total deflection of RC beams containing any fly ash content and at any age of concrete. The present study offers valuable insights for engineers and designers, facilitating the evaluation of age-dependent deflection patterns in RC beams constructed with reinforced high-volume fly ash concrete.

Time-dependant effects on curved precast segmentally constructed balanced cantilever bridges

Excessive long-term deflections and diagonal cracking in the webs are two commonly reported issues in segmentally constructed balanced cantilever bridges. The design of superstructure in such bridges is rather complicated due to the staged construction, secondary restraint forces, and time-dependent effects such as shrinkage, creep, and steel relaxation. The influence of these factors significantly increases by the curvature of the bridge on plan, to the point where it can result in the failure of the bridge if special considerations are not made. In this study, stepwise numerical analyses of a curved pre-cast construction of a balanced cantilever bridge with time-dependent material properties are carried out. The results show the effects of time-dependent losses, especially creep, on deflections during cantilevering and in long-term. It is shown that the curvature of the bridge due to long-term effects can increase the transverse moments in segments that adversely affect the principal tensile stresses, which can lead to diagonal cracking in the web of the segments.

An accurate and low-cost vehicle-induced deflection prediction framework for long-span bridges using deep learning and monitoring data

Accurate vehicle-induced deflection prediction is critical to bridge structural management and maintenance. However, most existing studies use finite element models and weigh-in-motion (WIM) system to predict the deflection of bridges, the cost of building finite element models is expensive. An accurate and low-cost vehicle-induced deflection prediction framework is developed in this study. In this framework, the calculation method of the spatio-temporal distribution matrix of the vehicle loads is proposed. A fusion attention mechanism bidirectional long short-term memory (ATT-BiLSTM) model is used to predict vehicle-induced deflection. Taking a suspension bridge in China as an example, the accuracy of short- and long-term vehicle-induced deflection prediction is tested, and different deep learning models are used for comparison. The results show that the proposed framework can predict short-term vehicle-induced deflection with a mean absolute error (MAE) of less than 2 mm, which can also accurately predict the extrema of vehicle-induced deflection within a certain time window. The proposed framework is independent of finite element models and lowers the cost of bridge deflection prediction.

Serviceability analysis and feasibility study of ballasted rooftop PV system on existing concrete roof slab buildings

Solar Photovoltaic (PV) installation on existing structures became popular for the purpose of reducing carbon emission and improving energy efficiency of buildings. Ballasted PV systems which can impose an additional dead load are preferred by building owners as direct roof penetration method can pose a potential threat to the insulation, water proofing as well as the warranty of roof membranes. Ballasted PV systems have been questioned for structural capability, economic feasibility as well as sustainability stand points. This study focuses on determining an the optimal ballast number to resist uplift wind pressure. It additionally considers concrete roof slab serviceability with respect to long-term deflection, and provides a feasibility study of PV installation. Based on the results of the study, the ballasted PV system does not yield a significant influence on structural serviceability of building. The economic feasibility analysis considers the current level of incentives. Economically a ballasted PV system can be an attractive investment with approximate payback period of 7.6 years. Without incentives, the payback period is 24 years.

Multi-physical analysis of saturation-dependent creep behavior for RC beam under sustained load and wet-dry cycles

A multi-physical and multi-scale analytical method based on thermo-hydro-mechanical models is adopted to evaluate the long-term deflection of RC beams with cracking under sustained loads and cyclic wet-dry conditions. The major physical-mechanical coupling mechanisms considered in this study includes: 1) water transport and phase equilibrium in the microstructure of gel and capillary pores; 2) accelerated moisture transport affected by cracking in concrete; 3) saturation-dependent creep coefficient considering gel and capillary pores; 4) combination of creep deformation and non-uniform shrinkage. The numerical approach is firstly verified by experiments where the thermo-hydro-mechanical interactions are found to be well analyzed. Then, parametric cases of cyclic wet-dry conditions are investigated to achieve deeper and wider conclusions. It has been found that under the cyclic wet-dry ambient conditions, there is an extreme drying state for concrete members depending on the drying humidity and its period. For the long-term mid-span deflection of beams, generally it will grow faster if the drying humidity is lower, which owes to the saturation-dependent creep coefficient, which has been called as Pickett effect. Meanwhile, beam's bottom-side cracking caused by sustained loads may also accelerate the moisture transport, which leads to an uneven drying state between upper and lower part of beams and viaducts, and eventually causes up-warping of them. For some cases, this up-warping can be significant enough to alter the macroscale structural creep deformation. At last, the difference between wet-dry cycle and dry-wet one has also been discussed. It can be proved that for the long-term deformation under wet-dry cycles, the moisture state will greatly affect the time-dependency from many aspects, for which the thermo-hydro-mechanical numerical approach is beneficial and needed in practice.

Three-dimensional creep calculation model for reliability analysis of concrete-filled steel tubular (CFST) structure

For long-span concrete-filled steel tube (CFST) structure, it is essential to implement efficient and realistic prediction models for the long-term processes of core concrete creep. In order to systematically study the main influential factors in CFST structure creep effects, a probabilistic analysis can be performed. The objective of this paper is to analyse the long-term response of CFST structure by using time-dependent reliability method. To address the problem of creep calculation, a novel and comprehensive presentation was developed. By converting the integral-type creep law to a differential-type form with internal variables, based on the Kelvin chain model, an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains was established. We have compiled a three-dimensional (3-D) finite-element analysis programme that considers the creep Poisson effect of core concrete to analyse the long-term performance of the CFST structure. This is achieved by developing a commercial finite element code, such as Usermat in ANSYS. As calculation examples, several time-dependent analyses of a CFST stub column and long-span CFST arch bridge were performed. The calculated results of long-term behaviour agree well with experimental and measured data. Considering the randomness of various input parameters, such as physical dimensions and materials of the CFST structure, we have analysed the uncertainty using the Latin-hypercube-sampling (LHS) stochastic finite-element method. The results of creep sensitivity analysis revealed that coefficient of creep model uncertainty, steel and concrete elastic modulus were the three most influential parameters for CFST stub columns’ creep, and load, coefficient of creep model uncertainty, relative humidity, steel and concrete elastic modulus were the five for CFST arch bridges’ long-term deflection. In addition, the use of Monte Carlo (MC) and response surface (RS) methods for structural stochastic reliability analysis demonstrates the ability of these approaches to assess the reliability index of long-span CFST arch bridges. This provides a valuable reference for the design and performance evaluation of CFST structures.

Improved Deflection Prediction Model for PSC Box Girder with Stay Cable System during Tensioning Phase

To improve the accuracy of deflection prediction for prestressed concrete (PSC) box-girder bridges with a stay cable system (SCS) during tensioning, this study employs the Latin hypercube sampling (LHS) technique to sample random variables affecting long-term deflection of the main girder. A long-term deflection randomness analysis model is established, and the shear stiffness degradation factor is included to quantify the contribution of diagonal web cracking to the main girder deflection. Uncertainty and sensitivity analysis are conducted for the Dongming Huanghe River Highway Bridge. An objective function is applied to select the optimal combination of random variables, and a modified model is established and verified for accuracy. Results show that diagonal web-cracking accounts for 8.8% of total deflection and cannot be ignored, and the prestressed tension control stress, creep uncertainty coefficient, and concrete density significantly impact long-term deflection. The modified model predicts deflection with greater accuracy than the mean value model.

Deflection Monitoring Method for Simply Supported Girder Bridges Using Strain Response under Traffic Loads

Deflection measurements are usually used as a key index in civil engineering for performing structural assessments of bridge safety. However, owing to technical or cost issues, it may be difficult to implement long-term monitoring of bridge deflection, especially for short- or medium-span bridges. Therefore, this study presents a novel method for measuring the deflection of simply supported girder bridges. In the proposed method, the strain measurement was implemented under traffic loading at only one position, such as middle span, and then the strain distribution along the girder was reconstructed to calculate the girder deflection with basic structural mechanical theory. To implement the method, the theory was constructed based on the displacement reciprocal theorem at first to assess the strain distribution along the girder from the strain measurement at some position during traffic loads passing across the bridge. Second, a strain measurement method, namely long-gauge fibre Bragg grating (FBG) sensing technology, was introduced to take strain measurements for a concrete bridge. Third, various finite element (FE) bridge models were developed to validate the proposed method’s accuracy, the results from which indicated that the method accurately implemented deflection measurement with an approximately 5% calculation error. In addition, the influence of some key parameters, such as vehicle type, vehicle speed, and structural damage, was investigated. The simulation results revealed that damage to the hinge joint in the middle location could significantly influence the proposed method’s accuracy such that the error may exceed 10%. Finally, on-site experiments were conducted on a simply supported girder bridge to further validate the proposed method’s accuracy, and an approximately 8% deflection assessment error was found. Considering the additional advantages of FBG sensing technology, the proposed method can also be effective for long-term deflection measurements of short- or medium-span bridges.

Long-term flexural performance of concrete beams with different pozzolanic materials: experimental and analytical study

ABSTRACT In this paper, a set of concrete beams with different cementitious binders are designed and tested to investigate the time-dependent deflection of concrete beams subjected to flexural load over a period of 1 year. Test parameters mainly included the effect of cementitious binders (silica fume (SF), ground-granulated blast-furnace slag (GGBS), and a combination of SF and GGBS), and polypropylene fibers on the time-dependent deflection of concrete. The specimens used in this study are under drying/unsealed conditions. The drying condition was designed to obtain the combination of the creep and the shrinkage that occurred in the common practice of construction. One of the most important problems in the repair of flexural members of concrete structures is the problem of creep and shrinkage, which is a relatively unknown problem in the literature. Furthermore, the experimental results are selected to validate the proposed models. Prediction of time-dependent deflections under flexural loading is proposed by the inverse analysis (IA) method. Based on the results, in comparison to the control specimen, the long-term deflection increases of 5.9% and decreases of 22.1% and 43.2% for specimens containing GGBS, SF and a combination of SF and GGBS, respectively, at the test age of 383 days.

Long-Term Deflection Analysis of Large-Span Continuous Prestressed Concrete Rigid-Frame Bridges Based on a Refined Modeling Approach

Numerical modeling approaches are favored for performing long-term analyses of continuous prestressed concrete rigid-frame (CPCR) bridges due to the complexity and high cost of experimental testing on such structures. In this study, a refined numerical modeling approach is first presented and validated by comparing the field monitor data of an existing long-span CPCR bridge in China. Then, long-term deflection analysis—considering box girder cracks, concrete creep, joint damage behavior and prestress—is conducted based on the proposed refined modeling approach. It is found that the time-dependent loss of longitudinal prestress has the most significant influence on the long-term structural stiffness, while joint damage between different segments has limited impact on overall structural performance, especially for large-span bridge cases. The local stress distribution is significantly influenced by typical damage, albeit with a different scope of impact. Therefore, targeted reinforcement has to be performed to achieve satisfactory repair results under different damage conditions.

STUDY ON DEFLECTION CONTROL OF COMPOSITE SLABS STRENGTHENED WITH BONDED STEEL PLATES

This paper demonstrates how long-term deflection of reinforced concrete slabs can be controlled by creating composite slabs. Three similar reinforced concrete slabs, 1,000 mm wide x 150 mm thick, reinforced with five high-strength (fy – 450 MPa) 12 mm diameter bars, spanning 4,500 mm, were constructed for this research study. The compressive strength of the concrete (fcu) was 25 MPa, with an elastic modulus of 33.6 GPa. One control slab, without bonded plates, formed the baseline for the deflection and was compared with the performance of two composite slabs strengthened with steel plates, one with a 110 mm x 6 mm plate (Comp1) and the other with 2 x two 110 mm x 6 mm plates (Comp 2). The bonding surfaces were prepared by scabbling the concrete to expose the well-bonded large aggregate, and the steel plates were dry grit blasted to a white metal finish to obtain a 100-140 µm blast profile. The steel plates were bonded to the concrete surfaces by means of Pro-Struct 618LV primer and Pro-Struct 617NS epoxy. All the slabs were loaded with a UDL of 1.0 kN/m. The experimental deflection results showed deflections of 20.18mm for the control slab, 16.67 mm for SP1and 16.31mm for SP2. The percentage difference between the theoretically calculated and experimentally measured deflections was 20.54% for the control slab, and-34.85% and-37.58% for SP1 and SP2, respectively.

Prediction and Global Sensitivity Analysis of Long-Term Deflections in Reinforced Concrete Flexural Structures Using Surrogate Models.

Reinforced concrete (RC) is the result of a combination of steel reinforcing rods (which have high tensile) and concrete (which has high compressive strength). Additionally, the prediction of long-term deformations of RC flexural structures and the magnitude of the influence of the relevant material and geometric parameters are important for evaluating their serviceability and safety throughout their life cycles. Empirical methods for predicting the long-term deformation of RC structures are limited due to the difficulty of considering all the influencing factors. In this study, four popular surrogate models, i.e., polynomial chaos expansion (PCE), support vector regression (SVR), Kriging, and radial basis function (RBF), are used to predict the long-term deformation of RC structures. The surrogate models were developed and evaluated using RC simply supported beam examples, and experimental datasets were collected for comparison with common machine learning models (back propagation neural network (BP), multilayer perceptron (MLP), decision tree (DT) and linear regression (LR)). The models were tested using the statistical metrics R2, RAAE, RMAE, RMSE, VAF, PI, A10-index and U95. The results show that all four proposed models can effectively predict the deformation of RC structures, with PCE and SVR having the best accuracy, followed by the Kriging model and RBF. Moreover, the prediction accuracy of the surrogate model is much lower than that of the empirical method and the machine learning model in terms of the RMSE. Furthermore, a global sensitivity analysis of the material and geometric parameters affecting structural deflection using PCE is proposed. It was found that the geometric parameters are more influential than the material parameters. Additionally, there is a coupling effect between material and geometric parameters that works together to influence the long-term deflection of RC structures.

Long-term loss of tension stiffening of concrete containing recycled aggregate and steel fibres

This paper presents experimental results on the long-term loss of tension stiffening of concrete containing recycled aggregate and steel fibres. Washed construction and demolition wastes (CDW) size 20 mm were used as a replacement for the natural coarse aggregate, and hooked-end steel fibres (DRAMIX 3D 65/35BG) were added to the mixes. Square section prisms of concrete (120x120x1200 mm) reinforced with a central steel bar were prepared and cast with different replacement percentages of recycled aggregate and volume fractions of steel fibres. A direct tensile load was applied to the steel bar and the measurements of the strain on the concrete surfaces were then recorded for a period of 35 days to assess the long-term loss of tension stiffening. The results indicated that the substitution of NA by RA increased the loss of tension stiffening over time up to 12.9%. However, the addition of steel fibres proved to be highly beneficial; the inclusion of 0.5% and 1.0% steel fibre content to the NC and RAC reduced the loss up to 9.8% and 20.4%, respectively. According to the obtained results, modifications to the Eurocode2 method for predicting the long-term deflection of reinforced concrete beams were proposed to be implicated in the calculation steps for this type of concrete.

A method to analyze the long-term durability performance of underground reinforced concrete culvert structures under coupled mechanical and environmental loads

The coupling effect of mechanical and environmental loads is the main cause of deterioration in the performance of reinforced concrete structures. However, most studies on the durability of reinforced concrete structures have focused only on mechanical or environmental loads. As a result, it is difficult to fully capture the effects of dry shrinkage and creep caused by temperature and humidity changes within the structure, as well as their impact on the overall deformation of the structure. To address this gap, this paper presents a numerical simulation of underground culvert projects using the DuCOM-COM3D analysis software. The results of the simulation demonstrate that this approach offers a more precise characterization of the porosity, temperature, and humidity inside the concrete, resulting in improved accuracy in predicting the long-term deflection, crack width, and other macro-mechanical indices of the structure. Despite these advantages, some discrepancies were observed between the calculated and measured long-term deflection values. Additionally, a limit analysis was conducted to investigate the potential causes of the large deformation observed in the measurements. Overall, the results contribute to a better understanding of the complex mechanical and environmental loads affecting reinforced concrete structures and provides a methodology for accurately simulating their long-term behavior.

Experimental Study on Long-Term Performance of Concrete T-Beam

In recent years, long-span concrete bridges that have been built frequently expose the problems of excessive deflection and concrete cracking, which even lead to bridge collapse in serious cases. The reason is that, in addition to the insufficient estimation of creep and long-term deflection in current regulations, the rapid growth of traffic volume and the tight use of early-age concrete in construction schedules also have a great impact on long-term deflection. However, at present, the calculation methods of long-term performance are mostly based on the results of material performance tests. However, there are relatively few studies that take bridge components as research objects and consider the influence of load and age factors. The long-term performance of concrete beams is examined and the calculation methods of long-term performance are given by considering various loading levels and ages. Specimens are fabricated using a 1:4 scale model of a standard T-beam with a length of 20 m to conduct the experiment. Based on the long-term observation of the test beam, the variation laws of the mid-span deflection of the concrete T-beam and the concrete strain in the compression zone with time are obtained under the aforementioned conditions. Following a comparative analysis of experimental results with computational results based on existing studies and relevant national and international codes, this study proposes and discusses a set of formulas for the assessment of shrinkage and creep. The obtained creep coefficient test results fall between the values of the Chinese specification and those of AASHTO, where ASSTO is the lower limit and the Chinese specification is the upper limit. The long-term deflection is as follows: 40% of the one-year value at one month, 66% of the one-year value at three months, and 80% of the one-year value at six months. However, the long-term deflection coefficient of beams with an early loading age is larger than the current standard, and the deflection coefficient of T-beams with three-day loading age reaches 6.0. We compare and discuss the test results with the calculation results and related codes obtained in different studies conducted at home and abroad. Based on our present findings, we propose formulas for shrinkage and creep evaluations.

Long-term deflection monitoring of a heritage, timber truss structure, and development of an integrated emergency alarm program

Long-term deflection monitoring of a heritage, timber truss structure, and development of an integrated emergency alarm program

Experimental and Numerical Investigation of Creep Behavior In Isotropic Composites

Creep testing is an important part of the characterization of composite materials. It is crucial to determine long-term deflection levels and time-to-failure for these advanced materials. The work is carried out to investigate creep behavior on isotropic composite columns. Isotropy property was obtained by making a new type of composite made from a paste of particles of carbon fibers mixed with epoxy resin and E-glass particles mixed with epoxy resin. This type of manufacturing process can be called the compression mold composite or the squeeze mold composite. Experimental work was carried out with changing the fiber concentration (30, 40 and 50% mass fraction), cross section shape, and type of composite. The creep results showed that the higher the fiber concentration, the more the creep resistance. Type of fiber plays a very critical role, where carbon/epoxy composite showed much higher creep resistance and also showed much higher modulus of elasticity than the E-glass/epoxy composite. Specimen shape factor noticed to play a very small role. However, square cross sectional area showed slightly higher resistance for creep than the rectangular cross sectional area. This difference is not critical and can be ignored. F.E.M simulation with ANSYS Inc. software was implied and results were compatible with the experimental work with a maximum discrepancy of (17.24%).