Axial Restraint Research Articles

Reliability-based resistance of RC element subjected to membrane action and their sensitivity to uncertainties

Traditional design of reinforced concrete structures is usually based on small deformation theories whereas in order to assess the ultimate load bearing capacity of RC structures against progressive collapse significant deformations should be taken into account. The alternate load paths facilitated by membrane action which develop under large deformation can activate a significant strength reserve, redistribute the loads and hence limit the damage progression in the structure. Up to date, no uniform approach is available on how to incorporate these membrane effects in the structural design or verification procedures against progressive collapse. In this article, sensitivity analyses were performed to investigate the effect of the stochastic nature of membrane action on the load bearing capacity for three distinct RC elements, i.e. a beam, one-way slab and two-way slab. It was found that variables which are usually not explicitly taken into account by traditional design methods, such as the axial restraint stiffness and ultimate reinforcement strain have a significant influence on the resistance of the considered elements. Subsequently, the design resistance of the elements was assessed using a probabilistic method and the ECOV method. It was found that the ECOV method and the probabilistic method considering a lognormal distribution provide similar results in case one observes a single failure mode for which the variability of the resistance is limited. In case of multiple failure modes and a large variability of the resistance, a mixed lognormal distribution proved to enable a more accurate design resistance estimation.

Structural behaviour and design of end-restrained square tubed-reinforced-concrete columns exposed to fire

Tubed-reinforced-concrete columns are gaining increasing usage in engineering practices, whereas research on their fire behaviour is still limited and mainly concentrated on unrestrained columns. Since end-restrained columns might behave differently in fire as compared to the unrestrained columns, the fire behaviour of square tubed-reinforced-concrete columns with end restraints was investigated via numerical modelling in this study. The axial and rotational restraints were modelled using linear springs and then validated against fire test results. The effects of end restraints on the failure mode, axial force and buckling length at failure and fire resistance, and on the evolution of deformations, internal force and bending moment during heating, of end-restrained columns were systematically analysed through parametric studies. The axially-restrained columns mostly undergo axial contraction only in fire; their typical failure mode is uncontrolled overall axial deformation, except for those columns of relatively high axial restraints. An increase in axial restraint leads to a nearly linear decrease of axial force at failure and a linear increase of fire resistance. For rotationally-restrained columns, the typical failure mode is also uncontrolled overall axial deformation. As the rotational restraint increases, the bucking length at failure decreases and the fire resistance increases, which is particularly significant when the rotational restraint is relatively low. A practical design method is proposed for the fire resistance design of square tubed-reinforced-concrete columns with either axial, or rotational, or combined axial and rotational restraints. Both constant and temperature-dependent end restraints have been adopted and the outcome is that they provide very similar results.

Dynamics of a Pipeline Span on an Elastic Seabed

Natural frequencies, mode shapes and modal damping ratios must be estimated to assess subsea pipeline spans for vortex-induced vibrations (VIV) and response to direct wave loading. Several approximate solutions exist for a linearly elastic pipe under constant axial force supported by linearly elastic springs beyond the span's shoulders. An exact analytical solution has only recently been published. That solution is used here in a Rayleigh-Ritz approximation to account for arch action arising from combined effects of sag under gravity loads and axial restraint at the shoulders. The method allows survey data to be used directly to quantify arch action. Its accuracy is confirmed by finite element analysis. Further, the modal damping ratio is estimated based on the fractions of the potential energy in bending, the axial force, and the soil springs, all of which are determined analytically. Thus, it is found that the effective modal damping ratio increases without a bound as the axial load approaches the buckling load in compression.

Effect of rotational restraint conditions on performance of steel columns in fire

This paper presents a parametric analysis about the effect of rotational restraint conditions on the dynamic performance of steel columns in fire. A fine finite element model of restrained steel columns, which adopts an explicit dynamic solver, was developed and validated by test data in literatures. Nine values of rotational restraint stiffness ratio (βR) from 0.0001 to 10.0 were considered. Other considered parameters include the axial restraint stiffness ratio, load ratio and column slenderness ratio. Based on the results, a quantitative criterion of identifying dynamic and quasi-static failures of steel columns in fire was proposed. It is found that βR has a significant effect on the performance of steel columns in fire. With the increase of βR, three failure scenarios about the failure types of steel columns in fire may appear, namely, all the failures are dynamic failures (Scenario I), failures turn from dynamic failure into quasi-static failure (Scenario II), and all the failures are quasi-static failures (Scenario III). In failure scenario I, there exists a βR with which the column shows the minimal dynamic effects. Besides, when βR reaches a critical value (namely βR,cr), the effect of further increasing the value of βR on the response of steel columns becomes slight for all the above scenarios. βR,cr is affected by the axial restraint stiffness ratio, load ratio and column slenderness ratio, and is generally less than 1.5. In fire-resistant design, the steel columns with a βR greater than βR,cr can be considered as rotationally fixed at both ends. Moreover, with the increase of βR, the buckling and critical temperatures of steel columns both increase, and the increase in critical temperature is significantly larger than that in buckling temperature.

Analysis of restrained composite beams exposed to fire

The actions of a restrained steel-concrete composite beam exposed to fire are investigated using the finite element software ABAQUS. A parametric study is performed to examine the influence of axial restraint stiffness, beam slenderness, load level, and axial restraint location. The fire scenario is also examined, and two fires are considered including an ASTM E119 standard fire and a design natural fire. Validation of both the heat transfer and structural analyses are presented to establish confidence in the results. The validation sheds new light on the macro-modeling of composite beams comprised of beam and shell elements. Specifically, the reference of the beam elements should be positioned at the geometric centroid of the end-connection when an axial-restraint is present. The study shows that the length of the beam heavily influences the fire response of a restrained composite beam. Composite beams with short spans tend to fail in the compressive beam-column stage, while composite beams with longer spans tend to fail in the tensile catenary stage. Furthermore, conditions that are favorable for inducing catenary action include longer beam spans, increased axial restraint stiffness, increased load level, and positioning of the axial restraint near the top of the beam. Finally, the results show that, for a beam of length L, catenary action is generally developed after the deflection limit of L/20 is reached, demonstrating that care should be used when using this deflection limit to evaluate the fire resistance of restrained composite beams.

Prediction of Catenary Action Capacity of RC Beam-Column Substructures under a Missing Column Scenario Using Evolutionary Algorithm

Catenary action plays crucial role in resisting the applied vertical load at large deformations stage in reinforced concrete (RC) structures. This paper aims to predict the catenary action capacity of RC beam-column substructures by utilizing the distinctive properties of gene expression programming (GEP). The input parameters selected for the modelling are: double-beam span-to-depth ratio, relative axial restraints stiffness, relative rotational restraints stiffness, bottom and top longitudinal reinforcement ratios, and yield strength of longitudinal rebars. A comprehensive and reliable database was collated from internationally published research articles to develop and verify the model. The GEP-based model was assessed by comparing its performance with regression based model. Various statistical indicators and external validation criteria suggested in literature proved that the model is accurate and possess high prediction and generalization capacity. Sensitivity analysis was carried out to show the contributions of the input parameters, while parametric analysis was performed to show that the proposed model is not merely a combination of the input parameters but can accurately represent the given physical system. The proposed formulation from GEP is found to be simple, robust, and easy to utilize for pre-design purposes.

Modeling fire performance of externally prestressed steel–concrete composite beams

This paper examines the fire performance of uninsulated and uncoated restrained steel-concrete composite beams supplemented with externally prestressed strands through advanced numerical simulation. In this work, a sequentially coupled thermo-mechanical analysis is carried out using ABAQUS. This analysis utilizes a highly nonlinear three-dimensional finite element (FE) model that is specifically developed and validated using full-sized specimens tested in a companion fire testing program. The developed FE model accounts for nonlinearities arising from geometric features and material properties, as well as complexities resulting from prestressing systems, fire conditions, and mechanical loadings. Four factors are of interest to this work including effect of restraints (axial vs. rotational), degree of stiffness of restraints, the configuration of external prestressed tendons, and magnitude of applied loading. The outcome of this analysis demonstrates how the prestressing force in the external tendons is primarily governed by the magnitude of applied loading and experienced temperature level. Interestingly, these results also show that the stiffness of axial restraints has a minor influence on the failure of restrained and prestressed steel-concrete composite beams. When the axial restraint ratio does not exceed 0.5, the critical deflection of the composite beam is lower than that of the composite beam with a restraint ratio of 1.0.

Effect of Axial Restraint and Loading History on the Behavior of Short Reinforced Concrete Coupling Beams

Effect of Axial Restraint and Loading History on the Behavior of Short Reinforced Concrete Coupling Beams

Behaviour of steel columns with realistic boundary restraints under standard fire

The significance of the occurrence of linearly varying rotational restraint with an increase in temperatures during building fires is outlined. A detailed parametric study conducted on seven hundred and twenty specimens using ABAQUS® investigates the effect of linearly varying rotational restraint on the stability of steel columns under standard fire was presented. Surface plots are drawn to understand the interactive effect of slenderness ratio of a column, axial boundary restraint, and temperature (buckling and critical) with linearly varying rotational restraint for different pre-applied axial load and moment ratios. The prevalence of axial force (Pbuckle/PO) at the ends of the columns due to axial restraint against thermal expansion is also assessed and plotted for the above parameters considered. It was found that buckling temperature and buckling load decreases with an increase in pre-applied axial load and moment while critical temperature variation was insignificant. The interaction equation useful for designers is proposed based on the non-linear regression analysis for assessing the critical temperature of steel columns under standard fire. It was found that the Euro code interaction equation (Eq. 4.21) predicted the critical temperature of a column with varying rotational restraint with reasonable accuracy.

A new test setup for simulation of the combined effect of bending and axial restraint in slab-like specimens

This paper presents a long-term experimental campaign for simulation of the combined effects of restrained shrinkage and vertical loads on reinforced concrete (RC) slabs, performed in the scope of the research project “IntegraCrete: a multi-physics and multi-scale approach to the combined effects of applied loads and thermal/shrinkage deformations in reinforced concrete structures”.A new experimental method is applied, in which a restraining device is used to constrain the axial deformation of a slab-like specimen, while allowing it to simultaneously endure bending and shear stresses. The deformation is restrained by two hydraulic actuators connected to one of the slab extremities, allowing a progressive adjustment of the axial force installed whilst controlling the deformation on a pre-defined region (active restraint).The experimental program comprehends the long-term testing of slabs, in a controlled environment room, under four distinct situations by combining the two following conditions: (i) with or without restraint to axial deformations and (ii) with or without application of vertical loads. The structural behaviour of the slabs is continuously monitored over a period of 15 months, while several mechanical properties, as well as the internal relative humidity (RH) of concrete, are assessed in complementary specimens from the same batch.The present work intends to contribute to a deeper understanding of the complex interactions that occur between self-imposed deformations (particularly due to drying shrinkage), concrete viscoelasticity and external loads in the process of crack development. It provides an important and unprecedented database for validation of numerical or analytical approaches for prediction of the structural behaviour of slabs subjected to the abovementioned effects.

Analytical assessment of restraint forces and crack widths in end-restrained building slabs

This paper deals with the analytical assessment of restraint forces and crack widths in end-restrained building slabs. The analysis concentrates on the service limit state (SLS) and the challenge is hereby the appropriate consideration of the combined effect of axial restraint due to imposed deformations and bending cracking due to loading. As for the imposed deformations, the paper regards the drying shrinkage of concrete under indoor conditions, although any other temperature deformation or combination of shrinkage and temperature could be included accordingly.A deformation-based approach is presented, in which imposed deformations are made compatible with the released deformations of the slab due to opening of loading-induced bending cracks. The solution aims an appropriate inclusion of the most relevant effects while still providing a practicable and verifiable solution for the complex problem of assessing the restraint forces as well as the crack widths in end-restrained building slabs.The result of this approach is an analytical quantification of restraint forces to be transferred in the restraining members. In addition, the presented approach enables the determination of crack widths in the restrained conditions. An important asset of the analytical nature of this approach is the explicit correlation between individual system parameters, especially concrete properties and surrounding conditions, member dimensions and provided reinforcement, loading in the SLS and restraining condition.The paper includes the presentation of the general idea of a deformation-based assessment of end-restrained building slabs; the demonstration of this approach with an example from the literature; and the comparison of the analytical design solution with experimental results on the combined effect of bending and axial restraint in slab-like specimens.

Application of hybrid simulation method for seismic performance evaluation of RC coupling beams subjected to realistic boundary condition

SummaryIn a building subjected to seismic loading, large compressive force may develop in reinforced concrete (RC) coupling beams because of axial restraint imposed by the neighboring shear walls against the elongation of the coupling beams during the failure process. The axially compressive force can increase the shear stiffness and strength of the coupling beam and may change its failure mode. In this paper, a novel coupling beam testing procedure adopting hybrid simulation method is proposed in which the axial restraint is determined through hybrid simulation and the calculated axial restraint is imposed on a specimen during the test. RC coupling beams were tested by adopting both the proposed test procedure and the conventional testing approach in which the effect of the axial restraint is not accounted for. Test results depict a clear difference in the response of the coupling beam, such as shear capacity and failure mode, depending on the consideration of the axial restraint during the test. The test outcome demonstrates the usefulness and applicability of the proposed test procedure.

Dynamic progressive collapse of steel moment frames under different fire scenarios

Dynamic mechanisms for progressive collapse of steel moment-resisting frames are studied under different durations of a column removal due to different fire scenarios. Development process of natural fire and gas temperature are modeled and predicted by software fire dynamics simulator (FDS). The steel temperature is then predicted reliably using the method recommended by EN19993–1-2 incorporating the predicted gas temperature by FDS. Steel frames and columns exposed to fire are simulated by BEAM188 in ANSYS with APDL and then validated against experimental data obtained from other researchers. It can be found that the failure duration of a column is different under standard and natural fire conditions, similarly under different boundary conditions, namely, axial load, initial imperfection, axial restraint stiffness ratio and rotational restraint stiffness. Finally, a step-by-step analysis procedure is established using SAP2000 API with Excel VBA to determine structural response versus duration of a column failure. The decay trend of maximum displacement can be described quantitatively by a one-phase exponential decay function, which is drawn after extensive analysis of dynamic response for different structures with various spans, member sections, loads, levels of a building and total number of floors

Investigation on Postfire Residual Capacity of High-Strength Steel Columns with Axial Restraint

AbstractThis paper experimentally and analytically investigates the fire and postfire behavior of axially restrained high-strength steel columns. Tests on the buckling behavior during heating as we...

Experimental and numerical studies on axially restrained cold-formed steel built-up box columns at elevated temperatures

Experimental and numerical studies on the fire resistance of cold-formed steel (CFS) columns with built-up box-shape sections were conducted in this paper. A series of coupon tensile tests were also performed before the fire resistance tests of the columns to obtain the stress–strain relationship of the steel plate from 20 °C to 800 °C. As a benchmark, the load-bearing capacity tests of the columns at ambient temperature were conducted first, and then the fire resistance tests were performed for eight specimens considering different load ratios and axial restraining stiffness. Afterward, numerical models, including heat transfer and structural analyses, were developed to reproduce the fire-resistance behavior of the columns and verified via test results. Finally, parametric analyses were performed to investigate the influence of load ratio, axial restraint, and rotational restraint on the fire-resistance behavior of the columns. Results indicated that the primary failure mode of the specimens was a combination of local and global flexural buckling, which was sensitive to the longitudinally non-uniform temperature field. Moreover, the increase in load ratio and axial restraining stiffness led to a significant decrease in the critical temperature and failure time. Moreover, even a low level of rotational restraint could enhance the fire-resistance behavior of the column.

Behaviour of axially and rotationally restrained reinforced concrete beams in fire

This paper presents a numerical study on the fire response of restrained reinforced concrete (RC) beams using the general finite element software ABAQUS. A comprehensive systematic study of the effects of different levels of axial and rotational restraints on the whole range behaviour of RC beams in fire was conducted, including combined bending and compression due to restrained thermal expansion, bending failure, transition from compression to tension when catenary action develops and complete fracture of reinforcement at ultimate failure. The numerical results show that different bending failure modes (middle span sagging failure, end hogging failure due to fracture of tensile reinforcement, end hogging failure due to concrete crushing) can occur under different levels of boundary restraints. Furthermore, release of a large amount of energy during the rapid transition phase from compression to tension in a beam prevents formation of a three hinge mechanism in the beam under bending. The numerical results have also revealed that reliable catenary action can develop in RC beams at large deflections following bending failure only if bending failure is governed by concrete crushing near the beam ends whereby a continuous tensile catenary action path can develop in the top reinforcement.

3D numerical simulation of the cracking behaviour of a RC one-way slab under the combined effect of thermal, shrinkage and external loads

Cracking control of reinforced concrete (RC) is of paramount importance to ensure a proper service behaviour on RC structures, during their lifespan, without excessive maintenance costs. Current design codes and recommendations for RC structures provide methodologies for reinforcement design on elements subjected to the independent effects of either external loads or restraints due to imposed deformations. However, the determination of restraint forces and crack width control in structures subjected to the combination of such two effects is still a challenge, due to the lack of knowledge about the complex interplay between the effect of bending, viscoelasticity and imposed deformations on crack width development. In this paper, the serviceability behaviour of a restrained one-way slab, subjected to a quasi-permanent load combination, is simulated with a 3D thermo-hygro-mechanical analysis. In this multi-physical approach, which has been cumulatively implemented and validated by this research team over the last years, the thermal and moisture fields of the slab are determined based on a thermo-hygrometric analysis, and the non-uniform distribution of stresses caused by self-imposed deformations due to heat of hydration and drying shrinkage are taken into account in a structural non-linear mechanical model. Results show that the axial restraint force acting on the slab is significantly smaller than the cracking force of the slab if analysed under pure tension. This is caused by bending stresses, as well as self-imposed non-uniform stresses, and is in line with the current state of the art. However, a comparison with simplified approaches, where the effect of heat of hydration is disregarded and/or a uniform moisture field is considered, shows significant differences in behaviour until crack stabilization, in relation to the multi-physical approach presented and adopted in this work.

Axial vibration analysis of a Rayleigh nanorod with deformable boundaries

In this study, the free axial vibration of Rayleigh nanorods with axial restraints is studied via Eringens’ nonlocal elasticity theory. This higher order elasticity theory takes into account the size effect into the formulation due to dealing with micro and nanostructures. The boundary conditions and equation of motion are obtained using Hamilton’s principle. Two symmetrical axial elastic springs are attached to a nanorod at both ends. The novelty of the present study is that it seeks to obtain a general eigen value algorithm for the angular frequencies subjected to the rigid or restrained boundary conditions in a nanorod for the first time. A Fourier sine series is used to work Stokes’ transformation for the Rayleigh nanorods with elastic springs at the ends. Afterward, the effect of the spring coefficient on the the eigen-frequency is investigated. Also, the effects of the nonlocal parameter and the elastic springs on the eigen-frequency is reported.

Prediction model for compressive arch action capacity of RC frame structures under column removal scenario using gene expression programming

Compressive arch action (CAA) is one of the important resistance mechanisms against progressive collapse in reinforced concrete (RC) frame buildings at small deformations. In this study, the distinguishing features of Gene Expression Programming (GEP) are utilized in order to establish a prediction model for the CAA capacity of RC beam-column substructures. The proposed equation correlates CAA capacity with six input parameters, i.e., compressive strength of concrete (fꞌc), double-beam span-to-depth ratio (Ld), width of beam (b), top and bottom longitudinal reinforcement ratio at the joints (ρt &ρb, respectively), and the ratio of axial restraints stiffness to the axial stiffness of beam (α). The data for the above-mentioned variables is collected from different studies to develop the proposed model and subsequently implemented for the verification purpose. Different statistical and external validations criteria recommended in literature are carried out to assess the performance of the developed model. Furthermore, sensitivity and parametric analyses are also performed using criteria available in literature. The performance of the genetically developed GEP model was checked and compared with models developed by using regression techniques. The GEP model demonstrated superior performance to linear and non-linear regression methods. The results show that the developed model is successfully capable of evaluating the CAA capacity of RC beam-column substructures and is incredibly imperative for prediction rationales.

Experimental and analytical studies of reinforced concrete short beams at elevated temperatures

This paper presents an experimental and analytical programme conducted on a total of seven reinforced concrete (RC) short beams, including one test at ambient temperature and six others at elevated temperatures. This study investigates experimentally the behaviour of RC short beams when subjected to elevated temperatures under the effect of shear-span-to-effective-depth (a/d) ratio and thermal-induced axial restraint. From the literature, this type of study on short beams has not been conducted before. It is experimentally shown that, for unrestrained short beams, as a/d increases, mid-span deflections at failure also increase and failure mode changes from diagonal splitting to shear tension. Besides, the influence of axial restraint on short beams is dependent on a/d ratio. For short beams of small a/d ratios (a/d ≤ 2.00), axial restraint increases mid-span deflections and flexural cracking, whereas it restrains deflections and shortens the failure duration of short beams with a/d ratio of 2.50. Furthermore, regardless of a/d, addition of axial restraint generally shifted the failure mode to a more brittle shear mode at elevated temperatures. Secondly, a simplified analytical model based on strut-and-tie-model (STM) is proposed and verified with test data to predict the performance of RC short beams at high temperatures. This model is applicable to both axially-restrained and unrestrained short beams subjected to elevated temperatures. The proposed STM is capable of providing consistently conservative and safe predictions of temperature profile, axial restraint force, load-carrying capacity and failure duration.