Tension Stiffening Effect Research Articles

A piece-wise linear model for modelling the tension-stiffening effect in steel-reinforced UHPC composites

This study examines the tensile behaviour of Ultra-High Performance Concrete (UHPC) specimens reinforced with varying steel fibre content and rebar diameters. An experimental campaign involving 18 reinforced UHPC specimens was conducted, following individual tensile response characterizations of UHPC and reinforcing steel. These specimens were designed and fabricated with threaded welded steel cages to transfer loads to the central measurement area. Force–displacement curves were measured to derive stress–strain curves for the UHPC component, evaluating the impact of reinforcement rebar and steel fibre content on UHPC’s mechanical response. The analysis revealed that steel fibre volume content significantly influences the tensile response of UHPC reinforcement more than the steel bar diameter and yield strength. Comparing the strain in steel bars to the average strain in reinforced UHPC specimens indicated that post-cracking deformation concentrates at the crack. At the same time, the bond between reinforcement and UHPC remains intact in uncracked sections, allowing effective load transfer. UHPC specimens reinforced with 14 mm diameter steel bars displayed a significant horizontal segment in the descending phase of the stress–strain curve. In contrast, specimens with 18 mm or 22 mm diameter bars exhibit a progressive stress reduction at a nearly constant rate. Stress–strain curves of UHPC were fitted with a five-fold piecewise empirical model applicable to UHPC with a reinforcement ratio higher than 0.09%. The resulting model can be used to model the axial behaviour in UHPC, considering the effects of steel reinforcement.

Maximum Drift Demands of Earthquake Damaged Reinforced Concrete Columns Based on Residual Flexure Cracks

Assessment of existing reinforced concrete (RC) structures after an earthquake is a challenging task that must somehow relate qualitative and quantitative observations in the plastic hinge regions and the associated residual deformation capacity of damaged structures. Having an estimate available for the remaining drift capacity will result in more economical and informed decisions regarding demolition or strengthening options. This study aims to develop a practical methodology to estimate the maximum drift demand of an RC column based on the residual crack width. For this purpose, fiber-based frame elements are used to model the RC column considering appropriately concrete behavior in compression and tension stiffening effects. Afterwards, the accuracy and reliability of the proposed methodology are demonstrated by validating the computational approach with two cyclic experimental results from literature and new test data for a one-bay one-story RC frame conducted within the course of this study. A comprehensive parametric study is performed for RC columns with different axial loads, longitudinal and transverse reinforcement ratios, and ground motions to exhibit the stochastic behavior. The study identifies the axial load ratio as the predominant parameter. Key findings include strong correlations between maximum drift ratios and total residual crack widths, as well as maximum compressive strains, with regression analysis yielding equations for accurate drift ratio estimation. Simple predictive models are proposed to estimate the maximum deformation demands based on observed residual crack widths. Residual cracking exceeding 5 mm poses significant risk for the columns with axial load ratios above 0.4, with 90% probability of exceedance 2% drift ratio.

Effect of local bond behavior degradation on tension stiffness in reinforced concrete with pre-existing longitudinal cracks

Reinforced concrete structures often have cracks when exposed to corrosion of rebars. This induced crack can deteriorate the bond capacity between concrete and rebar, affecting the structural performance of the member. This study conducted pull-out and uniaxial tension tests on cracked specimens to investigate the effect of bond behavior degradation on the tension stiffening effect. It uses an innovative approach to simulate concrete cracking by inserting an aluminum pipe into the concrete and filling it with an expansion agent to replicate the volumetric expansion caused by rebar corrosion. The local bond-slip behavior degradation is modeled using Popovics formulation based on pull-out cracked bond specimens. Furthermore, uniaxial tension tests reveal that induced cracks decrease transverse crack numbers and reduce the tension stiffening effect, primarily due to bond loss. However, this degradation becomes insignificant after a total deformation of 1.5 mm, corresponding to about 0.1% in average strain. Finally, analytical results confirm that tension stiffness does not necessarily decrease with increased induced crack width. Instead, the tension stiffness may increase in case of high bond loss due to induced crack.

Effect of GGBFS and fly ash proportions on fresh, tensile and cracking features of alkali activated concrete with low NaOH concentrations

This study mainly investigated the tensile and cracking features of ash alkali activated concrete with different slag-fly ash proportions and low NaOH concentrations cured at ambient temperature. High-molarity NaOH leads to risk and is costly, whereas, in field conditions, heat curing is difficult. Therefore, in this study three mixes (mix-A, B and C) were developed using 0/100, 20/80, 40/60, 60/40, 80/20, and 100/0 slag-fly ash proportions in this study. Sodium hydroxide (SH) and sodium silicate (SS) were used as activators and concentrations of sodium hydroxide were used as 1M, 2M and 4M in mixes A, B and C respectively, but alkaline ratio (SS/SH) was fixed as 1.5 in all the mixes. Slump, and strength aspects (compressive, split tensile, and flexural) were evaluated. The tensile (tensile strength, tension stiffening) and cracking characteristics (crack spacing, crack width) were evaluated under uniaxial tensile loading on reinforced prismatic members. From test outcomes, workability in terms of slump of the composites decreased with increased percentage of slag or granulated blast furnace slag (GGBFS) in the total binder, but the tensile (tensile stress and tension stiffening effect) and compressive strengths increased with increasing percentage of GGBFS. Better cracking properties (i.e., minimum crack widths and reduced crack spacings) were observed when the mixes contained higher percentages of GGBFS. The obtained crack spacings were correlated with CEB-FIP model code, and existing research studies. The crack spacings obtained in this study are consistent with CEB-FIP model code. Finally, this study demonstrated that when slag-fly ash alkali activated concretes were prepared with solutions containing low NaOH concentrations and cured at room temperature (ambient), there was an increase in the strength and cracking properties with higher percentages GGBFS.

Effect of steel and PVA fibres as monofibres on strength and cracking properties of fly ash and slag-based alkali-activated concrete

The present paper explores the experimental study on the influence of steel fibres (SF) and polyvinyl alcohol fibres (PVAF) as monofibres on the strength, and cracking properties of alkali-activated concrete with varying ground granulated blast furnace slag (GGBFS) and fly ash amounts was examined under ambient curing in this study. The alkali activator was a mixture of sodium hydroxide (NaOH) and sodium silicate (Na2SiO3) solutions. A molarity of 2 M NaOH solution and a fixed alkaline ratio (AR) of 1.5 were used in all mixes. Steel and polyvinyl alcohol (PVA) fibres were employed as monofibres. Steel fibres were added in 0.5%, 0.75%, and 1.00% volume fractions, whereas PVAF were added in 0.15%, 0.30%, and 0.45% volume fractions. In this study, a compressive strength test was performed; furthermore, a uni-axial tension test on reinforced concrete prisms was performed for tensile (first crack load, yield load, tensile stress in concrete, and tension stiffening effect) and cracking (crack spacing and crack width) properties. From the test results, better improvements in compressive strength, first crack load, yield load, tensile stress in concrete, and tension stiffening effect were observed in specimens having 1.00% steel fibres and specimens having 0.30% PVA fibres as monofibres. In the mixes containing 100% GGBFS, there was an improvement in the first crack load of approximately 46% due to 1.00% steel fibres and an approximately 29% improvement due to 0.30% PVA fibres. Furthermore, reduced crack spacings and minimum crack widths were found at 1.00% volume fraction of steel fibres and also in specimens having 0.30% PVA fibres. Overall, this study found that 1.00% steel and 0.3% PVA fibres as monofibres in fly ash-slag-based alkali-activated concrete (FSAAC) were optimal doses in terms of strength and cracking characteristics.

Tension-Stiffening of Reinforced HVFA-SCC Beams

Prediction of cracking behavior and deformation of reinforced concrete is a complex problem, including reinforced concrete that can still bear tensile stress after cracking due to the bond between reinforcement and surrounding concrete, termed the tension-stiffening effect. This research aims to determine the tension-stiffening of reinforced High Volume Fly Ash Self-compacting Concrete (HVFA-SCC) at various tensile reinforcement ratios. In this tension-stiffening analysis, shrinkage and creep effects are taken away. The data used in the analysis was obtained from beams tested with two loading points. The tests were conducted on six reinforced HVFA-SCC beams and six Normal Concrete (NC) beams with dimensions of 150 x 250 x 2000 mm, with tensile reinforcement ratios of 0.61%, 1.10% and 1.55%. The analysis shows that the effect of creep on shrinkage is negligible, so that it can be ignored in the calculation. On the other hand, shrinkage increases the value of the maximum tension-stiffening stress by 1.43% and the ultimate tension-stiffening stress (𝜎𝑡𝑠,u) by 72.51% from the initial tension-stiffening values. The greater the tensile reinforcement ratio in concrete, the smaller the effect of tension-stiffening stress. KEYWORDS: Creep, HVFA-SCC, NC, RC beams, Shrinkage, Tension-stiffening.

Prediction of Strain in Embedded Rebars for RC Member, Application of Hybrid Learning Approach

The aim of this study was to find strains in embedded reinforcement by monitoring surface deformations. Compared with analytical methods, application of the machine learning regression technique imparts a noteworthy reduction in modeling complexity caused by the tension stiffening effect. The present research aimed to achieve a hybrid learning approach for non-contact prediction of embedded strains based on surface deformations monitored by digital image correlation (DIC). However, due to the small training dataset collected by the installed strain gauges, the input dataset was enriched by a semi-empirical equation proposed in a previous study. Therefore, the present study discussed (i) instrumentation by strain gauge and DIC as well as data acquisition and post-processing of the data, accounting for strain gradients on the concrete surface and embedded reinforcement; (ii) input dataset generation for training machine learning regression models approaching hybrid learning; (iii) data regression to predict strains in embedded reinforcement based on monitored surface deformations; and (iv) the results, validation, and post-processing responses to make the method more robust. Finally, the developed model was evaluated through numerous statistical performance measures. The results showed that the proposed method can reasonably predict strain in embedded reinforcement, providing an innovative type of sensing application with highly improved performance.

Cracking behaviour of textile-reinforced concrete with varying concrete cover and textile surface finish

The cracking behaviour of textile-reinforced concrete (TRC) impacts the serviceability and structural integrity of TRC beams. However, textile reinforcement has not yet been standardised and there are numerous available textile reinforcement options. In spite of evidence that the textile properties influence the cracking behaviour of TRC, knowledge of the role of the textile, concrete and geometric parameters on cracking is still limited. This paper investigates a commonly used subset of textile reinforcements, namely epoxy-impregnated textiles with a high yarn count, some of which are prone to induce splitting failure. Through a comprehensive experimental study of 144 uniaxial reinforced concrete tensile tests, the influence of the textile fibre strand geometry and surface finish (plain or sand-coated) on the cracking behaviour was investigated in dependency of the concrete cover thickness. The results show that sand-coating treatment can decrease the transverse crack width to one-third of those observed in analogous plain textile specimens. The geometry of the plain fibre strands, which is affected by the textile fabrication method, also leads to significant differences in the measured crack widths (factor of 2.5). The overall cracking behaviour, however, is decisively influenced by the occurrence of splitting (longitudinal) cracks in the layer of the textile reinforcement, which were observed regardless of the surface treatment for concrete covers thicker than 15 mm. In case of the sand-coated textiles, these splitting cracks initiated immediately after the first main crack and propagated throughout the specimen, which diminished any tension stiffening effect. In the plain textile samples, the cracks led to an excessive spalling of the concrete cover. The results of this study provide a deeper understanding of the cracking behaviour of TRC with epoxy-impregnated textiles and a comprehensive database for further research. This establishes the basis for unified regulations regarding the limit states of TRC structures.

Standardized RC beam tests for modeling the fiber bridging effect in SFRC

Fiber reinforcement is a promising solution to cracking problems and improving the concrete’s structural performance. The residual strength of the cracked concrete can characterize the reinforcement efficiency. However, quantifying the residual performance of steel fiber-reinforced concrete (SFRC) is challenging. The existing methodologies provide empirical formulas for estimating the residual strength using test results of SFRC elements in which a predominant crack governs the mechanical resistance. For instance, the 0.5 mm crack width determines the minimum value considered in the RILEM standard formulas. Thus, the SFRC strength evolution at earlier cracking stages remains unknown. At the same time, such a crack approximation is irrelevant to structural cases when reinforcement bars stimulate the formation of multiple cracks, and the 0.1–0.2 mm crack typically corresponds to the yielding of the steel bars. This study describes an alternative approach for quantifying the average residual stresses in SFRC elements with multiple cracks. It hypothesizes the possibility of separating the mechanical resistance components, corresponding to tension stiffening and fiber bridging effects characteristic of SFRC elements with bar reinforcement, using standardized small-scale specimens to estimate the fiber contribution. The laboratory tests of the plain concrete and SFRC beams with bar reinforcement illustrate the proposed technique. The Rilem standard three-point bending tests and the numerical simulation of full-scale beams verify the analysis’s adequacy. The developed model is suitable for finite element simulations (employing the smeared crack model); the capability of separating the tension stiffening and fiber bridging effects ensures its versatility.

Linear Concrete Tension Stiffening Model for Reinforced Concrete Elements

Linear expressions for tension stiffening of concrete are nowadays widely used in software packages of structural analysis. Nevertheless, more elaborated expressions of tension stiffening available in the literature have been used successfully in the past. The use of linear approximations is justified since the influence of the tension stiffening effect in the deformation of the structure is small but not negligible. In this sense, linear approximations are simpler and can be accurate enough. However, this linear approximation, in its present form, does not provide good results in terms of deformations at the element level. This paper proposes a linear expression of the tension stiffening supported by the experimental formulation used to predict the flexural behavior of concrete beams. A detailed example is presented.

Experimental studies on tensile behavior of reinforced engineered cementitious composite members with double steel rebars

AbstractThis paper investigates the tensile behavior of reinforced engineering cementitious composite (ECC) members. Twelve reinforced ECC members were tested in uniaxial tension. The stress‐average strain curves, failure modes, and the strain of longitudinal reinforcement at selected sections were obtained during testing. The influence of reinforcement ratio on the load resistance and deformation capacity of members was determined. Test results showed that the tensile behavior of reinforced ECC members could be divided into three stages, namely, the elastic stage, the microcracking stage and the major cracking stage. ECC significantly contributed to the load resistance of reinforced ECC members before the formation of major cracks through tension stiffening effect. The load capacity and deformation capacity of reinforced ECC members increased with the increase of reinforcement ratios. For members with ungrooved steel bars, the ultimate load and ultimate strain increased by 130.0% and 115.2% with the reinforcement ratio increased from 1.01% to 2.26%. For members with grooved steel bars, the ultimate load and ultimate strain increased by 123.6% and 98.7% with the reinforcement ratio increased from 0.78% to 2.04%. Based on the test results, the failure mechanism of reinforced ECC members was analyzed and equations for predicting the load capacity of members were proposed. Comparisons between experimental and calculated load capacities suggested that the calculated results were in good agreement with the experimental values. The study on the tensile behavior of reinforced ECC members provides useful results for the design and application of reinforced ECC members.

Unified analysis for tailorable multi-scale fiber reinforced cementitious composites in tension

Fibers applied to reinforce the cementitious matrix exhibit a wide range of scales, from distributed carbon nanomaterials, chopped short fibers to continuous fibrous reinforcements. When a cementitious matrix is jointly toughened by reinforcing fibers at multiple scales, Multi-Scale Fiber Reinforced Cementitious Composite (MSFRC) tailored built on the micromechanics-based approach and bond-slip mechanism is proposed in this study. The composite actions of MSFRC, namely, tension stiffening, ductility enhancing and synergetic effects, are explained within a universal perspective. In addition, a 1-D numerical model using spring elements is developed to simulate the tensile behavior of MSFRC based on the crack band theory, fiber-bridging model and Monte Carlo simulation. The scales, types and contents of reinforcing fibers, interface behavior and stochastic nature can be considered in the model. Finally, it is found that the predicted mechanical response and crack evolution process match well with the experimental results obtained from literatures.

Effect of polyethylene terephthalate fibres on the structural performance of reinforced concrete beams with openings in the shear region

The provision of transverse openings in the shear region of beams to allow passage of services reduces the cracking and ultimate load capacities of the beams and increases deflection under the openings, especially when the size of the opening exceeds 25 % of the overall beam depth. Strengthening of the pre-planned opening regions by use of special steel reinforcements causes reinforcement congestion and difficulties in compaction, calling for alternative ways of strengthening beams with openings. In this study, concrete material was modified by the use of Polyethylene Terephthalate (PET) fibres produced from waste plastic bottles to improve the tensile properties and hence reduce the cracking around the openings and improve the overall performance of the beams. To evaluate the performance of PET fibres in beams with openings, eight (8) reinforced concrete beams with and without fibres of dimensions (150 × 250 × 2000 mm) were cast with varying opening sizes. The horizontal position of the openings was fixed at 300 mm from the support while the vertical position was maintained at the mid-depth of all beams. This performance was evaluated in terms of ultimate and first cracking loads, mid-span deflections, ductility, crack patterns and failure modes, and strain behavior. Test data showed that incorporating PET fibres in beams with openings resulted in a slight increase in ultimate load of 4.1 % and 5.82 % for 0.25 h and 0.35 h beam opening sizes respectively, beyond which the strength was reduced by 9.57 % for beams with 0.45 h opening size, where h was the overall depth of the beam. The first cracking loads increased by 44.12 %, 48.48 %, and 9.38 % for 0.25 h, 0.35 h, and 0.45 h opening sizes, respectively. In addition, a slight improvement in the ductility of PET fibre beams for all opening sizes was observed. The PET fibre beams exhibited a slight change in the mode of failure from dominant shear failure to combined shear and flexure failure characterized by multiple cracks in the flexure region with minimal spacing. An increase in the concrete compressive and tensile strains accompanied by a reduction in concrete and steel shear strains was observed because of the tension stiffening effects of the fibres. The incorporation of PET fibres, therefore, showed a slight improvement in the ultimate performance of beams with 0.25 h and 0.35 h opening size, with no improvement for the control beam and 0.45 h opening sized beam. However, a significant improvement in the serviceability performance for all PET reinforced beams was observed.

Discontinuous yielding in bare and embedded reinforcing bars: Implications on the determination of steel and bond shear stresses from strain measurements

Distinct jumps from the yield strain to the strain at the onset of hardening occur in bare reinforcing bar exhibiting a yield plateau once the yield limit is reached. These strain discountinuities known as Lüders bands nucleate at single locations and travel along the bar axis at a constant load. In contrast, no such strain jumps were observed in recent experiments with such reinforcing bars embedded in concrete and instrumented using distributed fibre optical strain sensing (DFOS). Instead, the strain increased gradually at locations where the yield limit was exceeded. This observation, made possible by the high sensing resolution of DFOS, cannot be explained entirely by the known effect of tension stiffening. While bond stresses cause a variation of steel stresses along the bar axis and, hence, indeed prevent Lüders bands from propagating along embedded bars, distinct strain jumps would still be expected at the locations where the yield stress is reached. The different steel stress–strain behaviour is rather attributed to the three-dimensional stress state induced by the locally concentrated bond forces at the bar ribs. These forces presumably (i) cause the direction of maximum shear stress to vary over the bar cross-section, leading to a loss of the macroscopic yield phenomena, and (ii) reduce the nominal yield stress in axial tension. As a consequence of the altered yield behaviour, a simple conversion from strains to stresses using a steel stress-strain relationship derived from uniaxial tensile tests leads to incorrect results for the strain range slightly below the yield limit up to the onset of hardening. These findings are most relevant for experimental studies investigating bond with DFOS, since researchers rely on the validity of the steel material law to derive and validate bond stress-slip relationships.This paper presents the results of the mentioned experiments, discusses the observed differences between bare and embedded reinforcing bars along with potential explanations, and outlines the implications on the determination of steel and bond shear stresses based on strain measurements in reinforcing bars embedded in concrete.

Time‐dependent elongation and cracking behavior of fiber reinforced concrete tension chords

AbstractThe long‐term (LT) tension stiffening effect in fiber reinforced concrete (FRC) tension chords is investigated in this paper. Six tension tie specimens with varying fiber types (either no fibers, polypropylene, or steel fibers) and reinforcement ratios were subjected to a sustained tensile in‐service load for 560 days. The LT specimens were fitted with gauges to monitor their elongation over the test period. In addition, 12 specimens were subjected to instantaneous loading to capture the entire load‐deformation response of the tension ties, up to and beyond the yielding of the reinforcement. A complete suite of material characterization tests were conducted in conjunction with the tension tie testing. The results from this investigation indicate that the inclusion of the fiber types and dosages adopted in this program improve the short‐term performance with respect to stiffness, tension stiffening, and cracking. Steel fibers improved the LT behavior, while the polypropylene fibers used in this study led to mixed results. Models previously developed by the authors have been shown to describe the behavior with good accuracy.

Synergistic tensile response of reinforced ultra high performance concrete with low fiber contents

From the perspectives of ductility, economic and construction, reinforced ultra high performance concrete (UHPC) structures with low fiber contents have a significant potential in applications. This paper studied the tensile behaviors and damage mechanisms of reinforced UHPC with low fiber contents based on the direct tensile tests accompanied with acoustic emission (AE) detection system. The test results show that the high strength steel bar can prolong the tensile multiple-cracking stage of reinforced UHPC with low fiber contents in some extent at the serviceability stage and further improve its tensile ductility via inducing additional longitudinal cracks at the failure stage. It is found that the low fiber contents and steel bar grades have marginal effect on the tension stiffening at the first cracking of reinforced UHPC. Non-negligible tension stiffening effect still remains at yielding of steel bar and it is more obvious for normal strength steel bar and UHPC with a higher fiber content. The AE weighted peak frequency can identify the tensile damage model of reinforced UHPC with low fiber contents: no internal damage occurs during stage Ⅰ; matrix cracking occurs accompanied by marginal fiber pull-out during stage Ⅱ; matrix cracking and fiber pull-out are dominated during stage III and stage IV, respectively.

Simplified biaxial tension stiffening model for the analysis of shear panels using softened membrane model

Many of the existing tension stress–strain relations for concrete used in smeared shear models consider the contribution of concrete in tension even after steel yielding. Although the contribution of concrete in tension is less significant than its contribution in compression, the use of these existing models often leads to overestimating the shear response of reinforced concrete (RC) panels. An improved concrete tension stiffening model incorporating the effect of biaxial stresses is proposed in this study. The effect of tension stiffening on the behaviour of shear panels under normal and shear stresses is investigated by incorporating tension stiffening in the softened membrane model (SMM). The existing SMM algorithm can be used to estimate the behaviour of RC panels subjected only to pure shear. In the proposed analysis using SMM, a new secant-based algorithm is used to estimate the behaviour of RC panels under combined normal and shear loads. Estimates from the proposed model are compared with estimates from original SMM and experimental results. The comparison shows that the proposed model provides better estimates of shear response for RC panels that undergo high shear strains than the original SMM. Furthermore, the proposed secant-based algorithm estimates panel behaviour under combined loading in reduced computational time.

SHEAR BEHAVIOUR ANALYSIS OF REINFORCED CONCRETE BEAM USING NON-LINEAR FINITE ELEMENT SIMULATION

This paper investigates shear behaviour of reinforced concrete using multi-surface plasticity model. This analysis uses nonlinear finite element simulation using 3D-NLFEA finite element package. The experimental data adopted from the results of experimental test on eighteen beams where nine beams carried out by Bresler and Scordelis in 1963 and similar nine beams carried out by Vecchio and Shim in 2004. The constitutive model for the concrete material which used in this simulation is based on the plasticity-fracture model and considered the tension stiffening effect for the concrete. The result of the numerical simulation latter compared with the experimental test including load-deflection response, cracking pattern, and failure mode. Based on the analysis result, it was found that the load-deflection response shows slightly higher response compared with the experimental result. However, the cracking pattern and failure mode of the beam shows good result which is in compliance with the experimental test.

Microscale Discrete Element Model for Simulating Bridging Behavior of Fractured Glass Laminates

The bridging behavior between fragments is one vital factor in the post-fracture stage of glass laminates. A particle-based discrete element model was developed in this work to simulate the bridging behavior of fractured glass laminates. The model was based on the calibration of hyperelastic PVB material properties using soft-bond model and further validated with the experimental data as well as the observations from through-crack-tensile tests. In order to investigate the bridging performance of fractured glass laminates with multiple fragments under uniaxial tension, three factors encompassing the crack aligning, fragment number and adhesion conditions were considered to perform a parametric study. The results give an exploratory application of the developed discrete element models in the estimation of the post-fracture behaviors. It is found that the smaller fragment size can diminish the tension-stiffening effect in the non-aligned case which might generate an enhancing ratio of initial modulus up to nearly 3.6. The non-aligned cracks can also lead to a very high strength if the adhesion ability can be guaranteed. However, the delamination of fragments is expected to control the post-fracture strength of fractured glass laminates with PVB interlayer.

Analytical model on progressive collapse resistance of prestressed precast concrete frame under middle column removal scenario

This paper investigates an analytical model on progressive collapse resistance of prestressed precast concrete (PC) frame structures. The analytical model is established based on a sub-frame with two stories and two spans under middle column removal scenario, in which the vertical resistance of two-span beam in each story is obtained according to force equilibrium and deformation compatibility of the beam. The tension-stiffening effect and bond slip of top bars near side joint interface are considered in the model to predict the collapse resistance of the beam at compressive arch action (CAA) stage and tensile catenary action (TCA) stage accurately. Besides, to consider the distinct mechanical behavior of beams in failed span in different stories in the process of progressive collapse, the model is related to the restrained stiffness of beam ends, which is determined according to deformation compatibility and force equilibrium of side column in frame. The accuracy of the analytical model is verified according to the results of tests and numerical simulation. Parametric studies are conducted based on the proposed analytical model to investigate the effects of structural parameters and boundary conditions on vertical resistance of the two-span beam in the failed span. The results show that increasing the length of dissipated segment of top bars can improve the structural ductility in progressive collapse, and increase the TCA capacity. Increasing the initial tension of steel strands can enhance the CAA capacity, but the effect of enhancement is alleviated with the increase of initial tension. The larger restrained stiffness can increase the CAA capacity of beam, and the translation stiffness has a more prompt effect on the vertical resistance of beam than the rotation stiffness.