Yield Line Theory Research Articles

Research on finite element simulation and full-scale-vehicle crash test of B750HL bridge barrier

How to raise the bridge barrier with a concrete base height of only 51 cm to SS level of protection is not yet studied. In order to effectively retrofit an existing concrete barrier design to meet new crash testing criteria, the structural dimensions and concrete strength of the existing bridge barrier were investigated, and finite element simulation analysis was carried out, and simulation suggested the existing barrier was insufficient. Based on the structural dimension design principles of bridge barriers, the existing structure of bridge barrier was designed after adding lightweight and high-strength B750HL material crossbeams and posts on top of the concrete base, and the bearing capacity of the bridge barrier was calculated based on the yield line theory. Then, a finite element simulation analysis model was established to study and analyze the blocking, guiding, and cushioning functions of the improved design of bridge barrier. Finally, full-scale-vehicle crash tests were conducted with the SS-level small car, bus, and tractor-van trailer for this bridge barrier design scheme. This paper is the world’s first to use B750HL steel as the material for the crossbeam and post of a bridge barrier with a concrete base height of only 51 cm. According to the research results, the B750HL bridge barrier, which was designed based on the calculation of structural dimension design and yield line theory, effectively reduces the increased constant load on the bridge deck caused by the extra crossbeams and posts. At the same time, it can reduce material costs and save engineering costs. After being verified by finite element simulation crash tests and full-scale-vehicle crash tests, the protective capacity of the B750HL bridge barrier was proven to meet the SS-level evaluation requirements of the Standard for Safety Performance Evaluation of Highway Barriers (JTG B05-01-2013). The research findings of this paper is that the finite element simulation crash tests can effectively simulate full-scale-vehicle crash test, and the finite element simulation crash tests is reliable. If the safety performance of the barrier in the finite element simulation crash tests meets the requirements, the probability of passing the full-scale-vehicle crash test is higher. Therefore, a design scheme is proposed for the B750HL bridge barrier to improve hybrid bridge barriers at a height of 51 cm or more based on various design methods.

Experimental investigation of flexural and punching behavior for plain PE-ECC slabs with different fiber volume fractions and span-depth ratios

Engineered Cementitious Composite (ECC) exhibits superior tensile ductility, shear capacity, and crack-control ability in comparison to traditional concrete and fiber reinforced concrete. These attributes render ECC a suitable candidate for addressing the brittle punching shear behavior commonly observed in reinforced concrete (RC) flat slabs. To verify the feasibility of using ECC for strengthening the punching shear capacity of concrete slabs, an investigation on the punching behavior of plain ECC slabs was conducted to ascertain their crack patterns, failure mode, strength and energy absorption capacity by means of experiments on twenty-seven 400 mm×400 mm square slabs. The plain ECC slabs were simply supported on a bespoke steel framework with eight supports, centrically loaded with a concentrated load. The fiber volume fraction (FVF) and span-depth ratio (SDR) are the two variables to be examined for their effects on the punching behavior of ECC slabs. Test results revealed that the incorporation of fibers significantly improved the load-bearing capacity, ductility and energy absorption capacity, while it altered the failure mechanism from brittle to ductile. The critical punching shear angles of all tested plain ECC slabs ranged from 40° to 50°. The ECC specimens possessing an FVF of 2 % exhibited markedly superior tensile capabilities compared to those with a 1 % FVF, as evidenced by direct tensile tests. Nevertheless, the ECC slabs with an FVF of 2 % did not demonstrate commensurate improvements in load-bearing capacity relative to their counterparts containing 1 % FVF. The span-depth ratio significantly impacted the failure mode of plain ECC slabs, yielding to punching shear failure at an SDR of 1, and to flexural failure at SDRs of 2 and 3. Moreover, an increase in the SDR value led to a reduction in both the initial cracking load and the ultimate load, concurrently increasing the associated deflection. In addition, a preliminary theoretical analysis was conducted to estimate the bearing capacity of plain ECC slabs. Flexural strength was estimated by yield line theory (YLT) and punching shear resistance was estimated by the model based on theory of plasticity in slab-column systems. The experimental and theoretical investigations could provide insights into the punching and flexural behavior of ECC slabs, laying a groundwork for the design and development of flat systems strengthened with ECC.

Governing Failure Mode of Reinforced Concrete Flat Slabs Under Gravity Load Using the Codes Guidelines and Yield-Line Theory

Governing Failure Mode of Reinforced Concrete Flat Slabs Under Gravity Load Using the Codes Guidelines and Yield-Line Theory

Punching shear tests and design of UHTCC-enhanced RC slab–column joints with shear reinforcements

Reinforced concrete (RC) flat-slab structures may experience progressive collapse, usually caused by the punching shear failure of slab–column joints. Existing research has shown that the use of shear reinforcements or ultra-high toughness cementitious composites (UHTCCs) in slab–column joints is efficient in improving their punching shear performance. In this study, shear reinforcement was introduced into UHTCC-enhanced RC slab–column joints. Specimens of UHTCC-enhanced slab–column joints were tested considering the effect of shear reinforcements. The cracking development process, bearing capacity and ductility were analysed. Yield line theory and critical shear crack theory were adopted to predict flexural and punching shear capacities, respectively. Finally, the failure patterns of the specimens were distinguished by comparing the predicted punching shear and flexural capacities, taking ductility coefficients into account. The theoretical and test results show the effect of shear reinforcement on the behaviour of UHTCC-enhanced joints. Significant improvements in the bearing capacity and ductility of the joints was achieved by applying shear reinforcement. The failure pattern of the joint varied from premature punching shear failure to flexural-triggered punching shear failure with the application of UHTCC, and this transformation was more pronounced with shear reinforcement applied into the UHTCC-enhanced joint.

Tensile behavior of novel column-to-column connection for modular steel construction using high-strength bolts

As an important aspect of the city upgrade plan, installing the elevators for existing multi-story residential buildings means a lot to the residents of the higher floors, especially for old people. To minimize the site disruption and overcome the space limitation of installation, the modular elevator shafts have been widely adopted. The external wall decoration panels are normally pre-installed on the elevator shaft frame elements in the workshop, which makes it difficult for the connection between upper and lower segments using the high-strength bolts due to very limited space for applying the pre-tension. A novel column-to-column connection is presented in this study, consisting of an end plate, web opening of column web and strengthening plate at each of the column end. The tensile behavior of the proposed connection is first investigated through an experiment. Subsequently, a detailed finite element model is built and verified using the test results, with which a parametric study is conducted with the main parameters considered. Finally, a simple analytical solution for predicting the design load of the proposed connection is developed employing the yield line theory. Comparisons with the finite element results indicate the high accuracy of the proposed solution. The presented connection is believed to be a good solution for the on-site connection between H-columns of highly assembled modular structures, not limited to the elevator shafts.

EXPERIMENTAL INVESTIGATION ON STUDYING THE FLEXURAL BEHAVIOUR OF GEOPOLYMER CONCRETE BEAM UNDER FIXED BOUNDARY CONDITION

Geo polymer concrete is one of the emerging construction material as a substitute for conventional cement concrete, eliminating the usage of OPC. This work is aimed to cast and testing of geo-polymer beam elements with restrained edge condition. The size of beam is 1m x 1m x 0.05 m. By using yield line theory, the moment of resistance and maximum deflection under flexural loading are calculated for the of GPC beam. Reinforcement details of these beam are calculated using ultimate load method as per IS code provisions. Geopolymer concrete is the greener concrete, which has the potential technology to reduce the carbon emission and lead to sustainable developments and growth of the concrete industry. During the manufacturing of ordinary Portland cement, large amount of carbon dioxide is released in the atmosphere causing not only air pollution but also highly responsible factor of global warming.

Two-way flexural behavior of biaxial voided slab using cuboidal shape of void formers

A biaxial voided slab is an innovative type of slab system developed recently, that has proven its excellence in terms of its structural, environmental, and economic benefits. In the present research, an experimental study was carried out to investigate the two-way flexural behavior of biaxial voided slab using the cuboidal shape of void formers. Two-way flexure test was performed over two voided slab specimens (VS-100 and VS-140) and one solid slab specimen using a new technique of sixteen-point loading. An innovative type of positioning reinforcement was used to fix the voids at their desired locations in voided slab. The ultimate load carrying capacity, deflection, flexural stiffness, and crack pattern were examined through experimental and theoretical investigations and compared the results with solid slab. Nonlinear finite element analysis was performed to validate the experimental results using ABAQUS software. Parametric study was undertaken to investigate the flexural performance of voided slab thoroughly; varying the factors like type of loading, positioning reinforcement, and grade of concrete. These investigations revealed that the voided slab with a cuboidal shape of void former exhibits classical flexural behavior which was same as that of a solid slab. Also, it was observed that yield line theory and the finite element model predicts the similar load-carrying capacity precisely enough with the experimental investigations. Parametric study reveled that prediction of ultimate load capacity of voided slab depends on type of loading, and with uniformly distributed loading predicting relatively higher load carrying capacity. Incorporating the proposed positioning reinforcement helps to improve the overall two-way flexural behavior of voided slab.

Strengthening of two-way slabs with fiber-reinforced polymer composites: A new system using grooving technique and fans

The flexural capacity of a reinforced concrete (RC) two-way slab can be efficiently enhanced using fiber-reinforced polymer (FRP) composites if FRP debonding is postponed. On the other hand, with the increase in flexural capacity, the vulnerability of the slab to punching shear failure increases. In this context, the current study examines FRP strengthening of lightly reinforced slabs using the externally bonded reinforcement on grooves (EBROG) technique, which has already been proven successful in postponing FRP debonding. Four slab specimens are tested in two groups under concentric loading. The first group consists of two specimens reinforced with headed shear studs: one reference specimen and one specimen strengthened in flexure with FRP. The second group includes two specimens without internal punching shear reinforcement: one reference specimen and one specimen strengthened with a new simultaneous flexural and punching shear strengthening system, taking advantage of FRP fans. According to the results, flexural strengthening of the slab in Group 1 increased its ultimate load capacity by 77%, and the proposed strengthening system in Group 2 led to a 94% enhancement of the ultimate load capacity. A calculation method based on the yield-line theory is presented to predict the load capacity of the test specimens. According to this method, graphs simplifying the estimation of the flexural capacity of FRP-strengthened slabs are proposed.

Development and research of a SS-level universal double-beam assembled bridge barrier

A wide variety of bridge barriers are used on highways. The bearing capacities of different types of deck slabs are measured in this study by applying the yield line theory to determine the worst-case scenario. An improved configuration for the worst-case barrier base and deck slab is developed, namely the universal double-beam assembled bridge barrier, which can enhance the safety performance of exiting concrete-base bridge barriers. According to the simulated impact test results, the new barrier meets SS-level requirements in terms of containment, redirective, and buffering performance as specified in the Standard for Safety Performance Evaluation of Highway Barriers (JTG B05-01-2013). The barrier structure’s compatibility with various bases is also analyzed. SS-level impact tests are conducted on real vehicles, including cars, buss, and trucks. The results show that the safety performance of the new barrier configuration reaches SS-level, and the barrier is universally compatible with concrete bases with a height of 63 cm and above.

Numerical analysis of a prefabricated concrete beam-to-column connection with bolted end plates

Precast concrete structures have been widely used in China in recent years because of the obvious advantages in construction speed, labor saving and quality control. Many experimental and numerical studies have been performed to investigate the seismic behavior of the precast concrete structures. However, the numerical analysis on prefabricated concrete beam-to-column connection with bolted end plates (PCC) under cyclic loading is still limited. Therefore, in this paper, the developed finite element models (FEM) were established to further study the seismic performance of the PCC specimens. The sensitivity analysis were conducted to ensure the reliability and validity of the FEM. Then, the FE models of the typical specimens were validated by test data such as failure modes, hysteresis curves and steel strain. Parametric analysis was carried out to investigate the effect of the end plate thickness, preload of bolt, concrete strength, etc. The key parameters affecting the seismic behavior of the connections were obtained. Eventually, based on the numerical simulation results, the law between the responses of the connections and the key parameters was determined quantitatively by response surface methodology. According to the yield line theory, the theoretical formula on the bending capacity of the connection with thin end plate was derived. Meanwhile, the formulas on the bending capacity of the unbonded prestressed concrete beam were also obtained. The results indicated that the bearing capacity and initial stiffness of the connection were improved with the increase of end plate thickness and bolt preload. The steel box significantly enhanced the shear capacity of joint region of the PCC specimens. Although the bending capacity of the beam can be improved by increasing the concrete strength, high strength concrete significantly reduced the ductility. The calculated value of the connection matched well with the test or simulation data which may provide a reference for predicting the bending capacity of specimens with different failure modes in subsequent studies.

Flexural behavior of modular steel channel–concrete composite floor systems with bolted connections

This paper presents an innovative modular steel channel–concrete composite floor system designed for rapid assembly. This system, compared to traditional steel–concrete composite floors, connects adjacent modules solely through the use of high-strength bolts. This design eliminates the need for on-site wet construction, thereby yielding superior economic benefits. To investigate the proposed system’s mechanical behavior, bending tests were conducted on four composite floors with various support conditions, the numbers of bolts, and the degrees of shear connection. The load–displacement responses, torsional behavior of the channel beams, interfacial slip, and strain development of the composite floor systems were analyzed. The test results show that the simply supported composite floor, without bolted connections, undergoes flexural failure. In contrast, the semi-continuous composite floors, with bolted connections, display punching shear-flexural failure. The pre-tension forces applied to the bolts can effectively mitigate the torsional deformation of the channels and module separation, ensuring that the system maintains excellent structural integrity, sufficient load-bearing capacity, and adequate ductility. The semi-continuous composite floors, when fitted with high-strength bolts, demonstrate an increase in ultimate load-bearing capacity by 13–15%. However, there is a corresponding decrease in ductility by 18–23% when compared to the simply supported composite floor without bolts. The use of perforated steel plates as shear connectors offers efficient shear resistance between the steel channels and concrete slabs, facilitating full composite action of the system throughout the loading process. The paper concludes with the development of a model that calculates the flexural strength and punching shear strength of the composite floors based on the yield-line theory.

Numerical and analytical investigations on punching shear performance of UHTCC-enhanced RC slab-column joints

The excellent tensile strain-hardening behavior of ultra-high toughness cementitious composite (UHTCC) makes it applicable for enhancing the punching shear performance of reinforced concrete (RC) slab-column joints. However, construction of an entire slab-column structure employing UHTCC would inevitably lead to uneconomical designs. To balance the economic benefits with the punching performance, utilizing UHTCC in the core region of a slab-column joint is a promising approach. In this study, the impact of UHTCC application range (UAR) on the punching shear performance of UHTCC-enhanced RC slab-column joints (USCJs) was investigated, and an approach for determining the optimal UAR was also presented. Two USCJ specimens with different UAR were tested, and experimental results were compared with the counterpart numerical results to validate the finite element (FE) models. Twenty FE USCJ models with different UAR were established. Then the impact of UAR on development of critical cracks, ultimate resistance, and ductile behavior was examined. Analytical approaches based on the critical shear crack theory as well as on the combination of critical shear crack theory and yield line theory were adopted to predict the ultimate and flexural resistances, respectively. The failure mode was determined by comparing these two resistances and considering the ductile coefficient, based on which the effect of UAR on the failure mode was determined. The results show that the location of critical shear cracks and the appearance of flexural cracks vary with UAR. By increasing UAR, the ultimate resistance increases, but the ductile coefficient first increases and then slightly decreases. Provided that the UAR is increased to some extent, the growth rate of the ultimate resistance evidently slows down and the ductile coefficient peaks, indicating the optimal UAR considering both the economic efficiency and the punching performance. The presented approach shows promise for determining the optimal UAR in practical engineering designs.

Progressive collapse mode induced by slab-column joint failure in RC flat plate substructures: A new perspective

Majority of progressive collapse incidents of concrete flat plate structures were caused by slab overloading in the form of punching shear failure at a slab-column joint, which exhibit distinctive resistance mechanism from those triggered by column losses. Relevant studies on the slab overloading scenario are scarce. To fill this gap in research and to broaden the perspective on different collapse modes, an experimental test was conducted on a 1/3-scale 2 × 2-bay flat plate substructure specimen by applying an increased downward uniform load on the slab, until the structure was completely damaged following the initial punching shear failure at the interior slab-column joint and was unable to take any further load. In addition, the flexural capacity of the specimen was evaluated using the yield line theory, and an analytical model was also proposed to estimate the post-punching peak load of the specimen. Finally, the experimental results obtained from this study were compared to those of a similar test under an interior column removal scenario. Comparisons indicate that the specimen under the slab overloading scenario displays better collapse resistance than that under the column removal scenario. Nevertheless, the residual resistant capacity of the overloaded specimen may not be adequate enough to prevent the collapse of the entire structure after the initial punching failure.

Punching shear behavior and strength prediction of UHTCC-enhanced RC slab-column joints

RC flat slabs are widely employed in medium-height buildings due to their constructional and architectural advantages. However, due to the tensile brittleness of normal concrete, an RC slab-column structure may suffer progressive collapse induced by punching shear failure of slab-column joints. Considering the excellent tensile strain-hardening behavior of ultra-high toughness cementitious composite (UHTCC), the punching shear behavior of slab-column joints enhanced by UHTCC could be substantially improved. Three slab-column joint specimens with different UHTCC application ranges were tested under vertical monotonic loading. The cracking development process, peak bearing capacity, ductility, and post-punching capacity were recorded and analyzed. Yield line theory and critical shear crack theory were adopted to estimate the flexural capacity and punching shear capacity of the specimens, respectively, and the post-punching capacity was also calculated. Finally, the failure patterns of the specimens were determined by comparing the estimated flexural capacity with the estimated punching shear capacity and taking into account the ductile coefficient. The main conclusions are as follows: (1) applying UHTCC can considerably enhance the peak bearing capacity and ductility of a joint, and a more significant improvement effect is achieved by increasing the UHTCC application range; (2) adopting UHTCC affects the failure pattern of a slab-column joint from premature punching shear failure to flexural-triggered punching shear failure achieving better ductile performance, and flexural behavior becomes more evident with the increase of the UHTCC application range; (3) the post-punching capacity of a joint is improved when the UHTCC application range covers the entire punching shear region. Therefore, the progressive collapse resistance of the RC slab-column structures could be substantially improved by introducing the UHTCC-enhanced joints.

A study on the effect of opening location on ultimate load capacity of an orthogonal solid slab

The aim of the research is to study the effect of the position of the opening on the ultimate load capacity of the orthogonal solid slab. A yield line theory is used for the prediction of the ultimate load capacity of an orthogonal concrete slab with and without rectangular corner opening subjected to uniformly distributed load (UDL). In this study, two locations of the opening are considered: the rectangular opening provided at the corner and the interior corner of the slab. All possible governing, geometrically admissible, collapse mechanisms were identified, virtual work equations were derived, and to solve the equations a computer program has been developed. The same aspect ratios of the slab and the opening, and opening sizes up to 0.4 times the slab length the were considered. Four boundary conditions of the slab with different opening sizes are considered to present the design charts for affine coefficients.

Prediction of progressive collapse resistance of RC frames using deep and cross network model

Compressive membrane/arch action at small deformations and resistance evolution path at large deformations are two key factors in determining whether an RC frame structure can resist progressive collapse. In this study, two deep learning models based on deep and cross network (DCN) are developed to predict the progressive collapse resistance of RC frames. DCN model I is constructed to predict the compressive membrane/arch action resistance, while DCN model II is developed to predict the resistance displacement curve considering the dynamic effect. 464 records regarding structural collapse were collected through extensive literature review and stringent data filtering. They were randomly divided into 80% and 20% for training and testing the two models, to which the column removal scenario, with or without slab, boundary condition, beam net span, beam section, beam reinforcement ratio, and material property were selected as input features. Moreover, Shapley additive explanations (SHAP) method was introduced to interpret the proposed DCN model. The results indicated that the performance of DCN model I in predicting the compressive membrane/arch action resistance was satisfactory with an MAPE value of 10.66% and an R2 value of 0.9799, respectively, while being more accurate than the existing yield line theory and Park’s compressive arch calculation model. The proposed DCN model II can further capture the evolution of the dynamic resistance of RC frames accurately. The two DCN models have been deployed online to public for application.

Evaluation of YLT method to estimate the load carrying capacity of one-way patched reinforced concrete slab under concentrated load

An unsaturated polyester resin (UPR) mortar was applied to repair the damage to the tension zone's one-way reinforced concrete (RC) slabs. The load carrying capacity of the patched RC slab is of interest to justify the effectiveness of the repair. The Yield Line Theory (YLT) may be used to estimate the load carrying capacity of patched RC slabs under concentrated load. The results of the YLT are compared with the experimental results to evaluate the validity of the YLT method. The results confirm that patching alters the yield line formation, mainly when the concentrated load is applied close to the patching zone. Subsequently, the YLT method provides a higher load carrying capacity estimation deviation for slabs with a loading point near the patching zone. On the other hand, the YLT method estimates load carrying capacity accurately when the loading point is away from the patching zone.

Experimental and Numerical Investigation of Compressive Membrane Action in GFRP-Reinforced Concrete Slabs

Experimental and numerical analyses of eight in-plane restrained slabs (1425 mm (length) × 475 mm (width) × 150 mm (thickness)) reinforced with glass fiber-reinforced polymer (GFRP) bars are reported in this paper. The test slabs were installed into a rig, that provided 855 kN/mm in-plane stiffness and rotational stiffness. The effective depths of the reinforcement in the slabs varied from 75 mm to 150 mm, and the amount of reinforcement changed from 0 to 1.2% with 8, 12, and 16 mm bar diameters. A comparison of the service and ultimate limit state behavior of the tested one-way spanning slabs shows that a different design approach is necessary for GFRP-reinforced in-plane restrained slabs that demonstrate compressive membrane action behavior. Design codes based on yield line theory, which considers simply supported and rotationally restrained slabs, are not sufficient to predict the ultimate limit state behavior of restrained GFRP-reinforced slabs. Tests reported a higher failure load for GFRP-reinforced slabs by a factor of 2, which was further validated by numerical models. The experimental investigation was validated by a numerical analysis, and the acceptability of the model was further confirmed by consistent results obtained by analyzing in-plane restrained slab data from the literature.

Ultimate strength of multiplanar KT-type tube–gusset plate joint with half-ring stiffener plates

In this study, full-scale tests, numerical simulations, and theoretical analyses on double KT (DKT)-type tube–gusset plate joints (TGPJs) stiffened with half-ring stiffener plates were performed. The failure modes and mechanisms of DKT-TGPJ under the opposing action of multiplanar loading (e.g., compression vs. tension) were determined to comprise ‘chord failure’, ‘stiffener plate failure’, and ‘combined failure’. The incidence of each failure mode was clearly related to the stiffness of the stiffener plate. When the stiffener plate had low stiffness, the TGPJ exhibited ‘stiffener plate failure’; when the stiffener plate had high stiffness, the TGPJ exhibited ‘chord failure’; and lastly, when the stiffness of stiffener plate is moderate, the TGPJ exhibited ‘combined failure’. A method for calculating the ultimate bearing capacity in the case of stiffener plate failure was proposed based on the yield-line theory. According to the deformation mode of TGPJ in the case of chord failure, a leverage model was established, and a method for calculating the ultimate bearing capacity was obtained. The minimum value obtained from the above two methods was taken as the ultimate load bearing capacity of DKT-TGPJ, which was subsequently verified against the test and finite element model results. The proposed bearing capacity calculation method was shown to reproduce the test and numerical analysis results more accurately than the Japanese and Committee for International Development and Education on Construction of Tubular Structures (CIDECT) codes.

Experimental and theoretical investigation of self-tapping bolt core tube flange column connection of prefabricated steel structure

This study proposes a column-column connection with self-tapping bolts, a core tube, flange plates, and high-strength bolts for a prefabricated steel structure, which can avoid on-site welding of traditional steel structure closed section columns and realize efficient assembly of vertical steel structure components. To determine the mechanical characteristics of the self-tapping bolt core tube flange column connection (SCFC) and the effect of the core tube and self-tapping bolts on SCFC, quasi-static tests were performed. According to the test results, altering the core tube thickness within a specific range had no discernible impact on the SCFC's seismic performance metrics, including hysteresis performance, skeleton curve, and stiffness degradation. The failure modes of test specimens were all steel fractures at the column foot, proving that SCFC can realize the seismic design goal of “strong joint, weak member.” The force mechanism of the SCFC and slip mechanism of the self-tapping bolt were explored. A finite element model (FEM) was established, and the results agreed well with the test results, confirming the accuracy of the FEM. Finite element parametric analyses were performed to further clarify the impact of the thickness of the core tube on the connection performance. Combined with the test and FEM results analyses, the bearing capacity calculation formulas of the SCFC were proposed based on the yield-line theory and verified by the results of the test and FEM. The design criteria for the SCFC were further proposed.