Yield Line Method Research Articles

Experimental Evaluation of Brick Unreinforced Masonry Wall Out-of-Plane Capacity and Modeling Using the Yield Line Method

Experimental Evaluation of Brick Unreinforced Masonry Wall Out-of-Plane Capacity and Modeling Using the Yield Line Method

Progressive collapse resistance of RC beam-slab substructure under two-adjacent-edge-columns removal scenario

The progressive collapse resistance of reinforced concrete (RC) frame structures has attracted much attention following a series of catastrophic accidents of collapse in the history. Of the numerous studies conducted in the past, the majority devoted to single-column removal cases. However, more than one column may initially fail when the structures are subjected to accidental actions. Meanwhile, the peripheral edge-columns of the structures are most vulnerable to threats due to their accessibility to the public. To this end, this study aims to investigate the progressive collapse resistance of the RC frame structures after removing two-adjacent-edge-columns. First, a quasi-static push-down experiment was performed on an RC beam−slab substructure under the scenario of two-adjacent-edge-columns removal. The experimental results found that the resistance of the beam−slab substructure at the beam mechanism stage was mainly provided by the flexural action (FA) of the beams and slabs, as well as the compressive arching action (CAA) of the beams and the compressive membrane action (CMA) of the slabs along the edge direction. The resistance increased again after entering the catenary mechanism stage, which mainly benefited from the development of the catenary action (CTA) of the edge-beams and the tensile membrane action (TMA) of the slabs along the edge direction. Second, a validated numerical model was employed to further investigate the collapse-resistant mechanism of the substructure. The numerical results indicated that the contribution of the CTA in the edge-beams to the progressive collapse resistance was approximately 51 % at the ultimate state, which was greater than that of the TMA of the slabs. Thereafter, parametric studies were conducted to quantify the contribution of the slabs and the influence of the number of removed columns on the progressive collapse resistance of the substructure. It was found that the ultimate resistance of the beam−slab substructure was 61 % higher than that of the substructure without slab, and the equivalent uniform load that the substructure could resist in the case of two-adjacent-edge-columns removal was about two-thirds of that in the case of one edge-column removal. Finally, the first peak resistance of the RC beam−slab substructure was predicted using yield-line method, resulting in a conservative result because the CAA of the beams and the CMA of the slabs were not considered.

Experimental study on the collapse response of flat slab structures with drop panels under gravity loading condition

This paper presents the results of an experimental study on the collapse behavior of two reinforced concrete flat slab assemblies with drop panel connections subjected to uniformly distributed loads applied through 24 loading points. The two tests, named MC and PC, simulated local failures at mid-span columns and penultimate columns, respectively. Both assemblies exhibited elastic behavior until cracking values were reached, followed by degradation of stiffness due to crack development beyond the elastic zone and a long plateau near collapse. The main differences between the assemblies were the higher collapse load of the MC assembly, attributed to slab additional slab extension surrounding two test panels, and the load redistribution pattern. Both assemblies showed ductile behavior in the inelastic region, with large deformation capacity allowing tensile membrane action to mobilize. The collapse modes observed were the failure of the outer compressive ring and the tearing out of tension slab reinforcement from the concrete. The traditional yield-line method may not be suitable for quantifying the collapse resistance of this type of structure, and numerical simulations are suggested for this purpose. The experimental data from these tests, as well as previous tests, could be valuable for validating simulation models.

Post punching shear pattern and progressive collapse of flat slab building

Abstract The possibility of the occurrence of a second punching shear failure and of a Progressive Collapse after a punching shear failure had occurred in one flat slab column connection is investigated in two building structures, using Eberick and SAP2000 softwares and the Yield Line Method, and codes ACI318:2019, EUROCODE2:2004 and NBR6118:2014. It is shown that slab column connections should be designed and detailed to prevent Progressive Collapse and that Integrity Reinforcement should always be present, and that the remaining capacity of floors after punching failures depends on the i) post-punching resistance of the connection being punched; ii) post-punching resistance of the neighbors’ connections; iii) flexural resistance of the slabs, and that the flexural resistance of the slab’s floors can be evaluated by the Yield Line Method.

Design of steel transmission pole base plates using yield line method

Steel transmission poles are widely used for their strength, ease of construction, small footprint, and aesthetic appearance. These poles can be either directly embedded into their foundations or supported on based plates which are connected to the reinforced concrete footings via group of anchor bolts.There are few available published methods for the analysis and design of this type of base plate connection. These methods are not widely used in the industry as they are either complex, lack solid theoretical background, or yield results that are not consistent with manufacturer's time-tested proprietary design methods. Therefore, there is a need for an accurate method suitable for technical or design office for designing these connections when subjected to axial loads, bending moments or the combined effect of both.This paper presents a numerical study performed on the base plates of polygonal steel poles that are supported directly on anchor bolts with levelling nuts and subjected to bending moment and axial load. The Finite Element (FE) analysis part of the work is carried out using ADINA software and the results obtained from the analyses are compared with published experimental results from which it is concluded that the finite element model can accurately predict the behaviour of these connections.Parametric investigation is then conducted to gain more insight into the behaviour of these base plate connections and to use the obtained data the validation of the proposed design method. The parametric investigation covered the behaviour of these connections under pure axial load and pure bending moment while the varying parameters considered included number of shaft sides, base plate thickness, number of anchor bolts and anchor bolt diameter.Design formulae based on the yield line theory are then proposed and a comparison between the yield loads calculated using the proposed expressions and finite element results is presented. The yield loads resulting from using the proposed design method agreed with the finite element results with a maximum calculated difference of 13%.

An Analytical Method for Determining the Residual Strength of Reinforced Concrete Beam-Slab Specimens

This paper proposed one new method to determine the residual ultimate loads of the fire-damaged beam-slab specimens. Based on the conventional yield line method, the stiffness and deflection of the edge beam was considered to establish the theoretical method, and the residual ultimate loads of several beam-slab specimens in the literature were analyzed, and the predicted results were compared to the experimental results. Results show that the conventional simply-supported and fixed-end yield line method tended to underestimate or overestimate the residual ultimate loads of the specimens, and the present method can reasonably predict the ultimate loads of the beam-slab specimens.

Influence of openings on two-way bending capacity of unreinforced masonry walls

Perforated unreinforced masonry (URM) walls in out-of-plane (OOP) two-way bending are commonly encountered in natural hazard investigations. However, related research is rather limited. This study focuses on the influence of openings on the two-way bending capacity of URM walls. An experimental database about the perforated URM walls in OOP two-way bending was created. A brief review of the experimental results show that the arrangement of the opening area can significantly affect the two-way bending capacity of walls (defined as the peak pressure on the wall net area): when the opening area is non-covered and non-loaded, the two-way bending capacity of the perforated wall is higher than that of its solid counterpart; when the opening area is covered with timber or glass plates loaded as the rest of the wall, the two-way bending capacity of the perforated wall is lower than that of the corresponding solid wall. These observations from the experiments were confirmed by an analytical estimation using the Yield Line Method (YLM). Next, to study the influence of openings on the two-way bending capacity, a numerical study has been carried out by employing the 3D simplified brick-to-brick modelling approach. The results of calibration and validation show that this modelling approach can precisely predict the two-way bending capacity and crack patterns. By applying the validated numerical models, the influence of the arrangement for the opening area from the experimental results and YLM evaluation was confirmed. Further, a parametric study focusing mainly on cases with the opening area non-covered and non-loaded was conducted. The influence of the geometric parameters of openings, namely, the opening size, shape and position was investigated on walls with different aspect ratios. Results show that the two-way bending capacity increases as the opening size or aspect ratio (height to width) increase, but it is insensitive to the opening position. Eventually, based on the numerical results, analytical equations were proposed to account for the influence of the considered parameters on the two-way bending capacity. A comparison with the Australian Standard (AS3700) indicates that the proposed equations incorporate more opening parameters such as opening shape.

Performance and Capacity Assessment of Concrete Barriers Subject to Lateral Loading

Abstract Current specifications for concrete barrier design (AASHTO-LRFD Section 13) indicate that the yield line method (YLM) should be used to ensure that a barrier has the adequate flexural capa...

Seismic tests and nonlinear model of beam-CFDST column joints with blind fasteners

In recent years, substantial research efforts have turned towards concrete filled double skin steel tubular (CFDST) column due to its superior mechanical performance. However, an effective and convenient connection method between a CFDST column and a beam still needs to be investigated in depth. This paper tried to adopt the blind bolting technology in a CFDST column to beam connection. A series of joint specimens were prefabricated and designed with different end plate types, column hollow ratios and beam types to carry out pseudo-dynamic tests. Excellent seismic performance was detected for all test specimens. It was observed that increasing the column hollow ratio could moderately increase the ultimate strength and the specimen with extended end plate had higher ultimate strength stiffness compared with that with flush end plate. To accurately capture the dynamic response for this type of joint, an analytical model was developed considering the shear performance of panel zone and moment-rotation behavior of connection. Shear strength of CFDST column panel zone was modified from that of CFST column panel zone based on the yield line method for including the contribution of confined compression strut. It indicated that two potential yield mechanism might appear depending on the column hollow ration (χ). The analytical model could well predict the test results. The research and analytical results provided an effective connection method to assemble a CFDST column to a beam and supply a feasible analytical model to predict the joint performance.

Assessment of reinforced concrete slab of historical structures by the yield-line method

AbstractThe study demonstrates and evaluates an approach in the structural analysis phase when assessing reinforced concrete slabs.Due to different values of a parameter in the tests’ results, 10 models was crated for the first case study and 4 models for the second one.In order to compare the results in terms of the flexural bearing capacity, the slabs were analyzed by using elastic finite element analysis and yield-line analysis.Comparing the results shows that minor modification in the parameters associated with bearing capacity and the boundary conditions can affect the adequacy factor considerably, while the parameters those relate to boundary conditions affect the distribution of the yield lines.

Comparison of Modified Yield-Line and Punching Shear Capacities for Concrete Traffic Barriers and Bridge Rails

The traditional, triangular yield-line method used by most departments of transportation for analyzing concrete traffic barriers and bridge rails has been largely unchanged since 1978. Testing of concrete barriers since this time has indicated that the triangular yield-line method is not qualitatively representative of observed damage patterns and is overconservative. Further, the conversion from NCHRP Report 350 to the crash test criteria from the Manual for Assessing Safety Hardware (MASH) will result in increases to lateral impact loads; therefore, overconservative analysis practices may result in many concrete barriers being unnecessarily deemed inadequate. In this research, alternative analysis methods for concrete barriers were extracted from an extensive literature review of concrete barrier investigations. These methods were applied to a sample of eight concrete barriers to demonstrate and compare their effects on capacity estimates. Alternative methods included trapezoidal yield-line mechanisms, effects of impact heights lower than the top of the barrier, punching shear evaluation, and consideration of expected material strengths. Capacity estimates of the selected barriers were increased by an average of 47 percent when alternative methods were cumulatively applied. Although the traditional method does not consider punching shear, the capacity of one of the eight barriers was controlled by punching shear rather than by yield-line flexure. With the alternative methods applied, seven of the eight barriers were deemed adequate relative to the increased lateral loads corresponding to MASH criteria for Test Levels 2 through 5. By contrast, if analyzed according to the traditional method, three of the eight barriers would have been deemed insufficient considering MASH loads.

Bidirectional loading performance of gusset plates in buckling restrained braced frames

A study is conducted to evaluate the performance of gusset plates (GPs) in buckling restrained braced frames (BRBFs) subjected to bidirectional loading. It involves an experimental test, a parametric numerical study and a comparison with Thornton, AISC, Takeuchi’s and Notional Load Yield Line (NLYL) methods. The experimental test was conducted on a one-storey BRBF with pinned beam connections under both unidirectional and bidirectional cyclic loading.It was found that bidirectional loading decreases the GP axial strength by up to 18%, but there is no clear correlation with GP thickness. The parametric study indicated that greater out-of-plane (OOP) drifts reduce the GP axial strength. The methods evaluated with respect to the parametric study generally provided conservative strength predictions. The AISC method with an effective length factor of 2.0, which does not explicitly account for out-of-plane loading, was the most conservative among all methods. The strength predicted ranged from 69% to 92% of the actual strength. Similarly, both Takeuchi’s and NLYL method under bidirectional loading are conservative when the GPs have a rotational stiffness within the likely range of practical applications. However, they are non-conservative for BRBF GPs with a very low rotational stiffness. The NLYL method is less conservative than Takeuchi’s method. The NLYL method is always conservative for the limited range of CBF GP configurations investigated.

On the application of the yield-line method to masonry infills subjected to combined in-plane and out-of-plane loads

The influence of infills on the seismic response of frame structures has been long recognised. On the one hand, the presence of infills may be beneficial, due to their contribution to dissipate energy. On the other hand, irregular infill distributions in plan or elevation can lead to concentration of the displacement demand in localised parts of the building. It is noted that the lack of one or more panels may depend on the original building layout or may be generated by the infill collapse during a seismic event. It is therefore of interest the assessment of their capacity to resist out-of-plane loads.In this paper, the use of the yield-line theory for the estimation of the out-of-plane infill strength is investigated. The method is described in detail and an example of derivation of the related equations is presented. Afterward, a modification of such equations is suggested to account for different contact conditions at the infill-frame interface. Moreover, specific attention is paid to the assessment of the masonry flexural strength, which is a basic parameter for the application of the method. Finally, a reduction factor is calibrated to extend the method to those cases in which previous in-plane damage is present. Experimental tests available in the literature are used to verify and calibrate the proposed equations and coefficients.

Capacity of unreinforced masonry walls in out-of-plane two-way bending: A review of analytical formulations

Investigations of post-seismic events show that the collapse of walls in out-of-plane (OOP) two-way bending can be one of the most predominant failure mechanisms for unreinforced masonry (URM) structures. To assess the force capacity of URM walls in OOP two-way bending, various analytical formulations have been developed during past decades. However, the accuracy and the application range of these analytical formulations have been evaluated against only a limited number of experiments. For this purpose, a dataset of 46 testing specimens from 8 international testing campaigns was created and used to evaluate current analytical formulations, namely Eurocode 6 based on the yield line method, Australian Standard AS3700 based on the virtual work method, and two other virtual work formulations related to AS3700. A general comparison shows that within the listed dataset, AS3700 overall provides the most accurate predictions. More specifically, AS3700 is the most accurate assessing walls assumed to be partially clamped and walls with openings. Testing specimens were divided into groups to study the influence of crucial factors, such as material properties, boundary conditions, pre-compression, aspect ratio and openings. However, only in a few cases clear trends were identified from the testing data. Sensitivity studies were carried out to reveal how the analytical formulations assess the influence of the crucial factors on the force capacity of the walls. Results expose drawbacks and limitations of the considered analytical formulations. Eventually, potential directions for improving the accuracy and the application range of the analytical formulations are pointed out.

Experimental Investigation and Yield Line Prediction for Ultimate Capacity of Recycled Aggregate Concrete Slabs

The present investigation was conducted to evaluate the influence of recycled aggregates on structural behaviour of reinforced concrete (RC) slabs. Concrete mixtures of 0.6 and 0.4 water/cement ratios were used to produce normal strength concretes and high strength concretes, respectively. Various concrete mixtures were prepared by replacing 19 mm natural coarse aggregates with 0, 25, 50, 100% recycled coarse aggregate (RCA) then used to cast RC slabs of size 500 x 300 x 100 mm thick, and 100 mm cubes. The two-way concrete slabs were reinforced orthotropically with Y12 steel bars. Workability, compressive strength, and split tensile strength properties of concrete were measured, while the RC slabs were subjected to monotonic loading until failure. The experimental results obtained were compared with theoretical failure loads predicted using the yield line theory. It was found that the use of RCA in concrete generally leads to reduction of workability and concrete strength in proportion with the RCA content incorporated into the mixture. The yield line method gave a conservative and accurate theoretical prediction of the actual ultimate loads for control concretes, predicting 10% lower values, but it exhibited loss of prediction accuracy for RCA concretes of normal strengths basically overestimating their failure loads. Accordingly, it would be unsafe to employ the yield line method for design of RCA concrete slabs of normal strengths. Generally, the adverse effects of RCA on concrete properties and structural behaviour can be mitigated significantly by adjusting mixture designs to higher strengths or by employing high strength concretes

Conjugate Cellular Automata and Neural Network Approach: Failure Load Prediction of Masonry Panels

The intricate interplay between the microscopic constituents and their macroscopic properties for masonry structures complicates their failure analysis modelling. A composite strategy incorporating neural network (NN) and cellular automata (CA) is developed to predict the failure load for masonry panels with and without openings subjected to lateral loadings. The discretized panels are modelled by the CA methodology using nine neighbour cells, which derive their state values from geometric parameters and opening location placement for the panels. An identification coefficient dictated by these geometric parameters and experimental data is fed together as the input training data for the NN. The NN uses a backpropagation algorithm and two hidden layers with sigmoid activation functions to predict failure loads. This method achieves greater accuracy in prediction when compared with the yield line and finite elemental analysis (FEA) methods. The results attained elucidate the feasibility of the current methodology to complement conventional approaches such as FEA to provide additional insight into the failure mechanism of masonry panels under varied loading conditions.

Plastic limit analysis for eight-bolted base plate based on slip-line field theory

Eight-bolted base plates have gradually been employed in the UHV transmission lines. On the basis of slip-line field theory, this paper derived new calculation methods for predicting the uplift bearing capacities of rigid and flexible base plate, their reasonable accuracy has been validated by comparing with test observations and yield-line method results. The relevant parametric analysis demonstrated these two methods have consistent variation tendency and the thickness of base plates is of paramount impact on ultimate strength. Design suggestions considered four possible failure modes and their corresponding calculation formulae were presented for evaluating the controlling capacities of base plates, one of which associated with slip-line method adopted the least-square fitting to obtain correction coefficients so as to get explicit solutions for calculations. Their applicability and accuracy have been verified by comparing with the test and corresponding code.

Full-scale test of a steel moment-resisting frame with composite floor under a penultimate edge column removal scenario

This study investigates the structural behavior and load-resisting mechanism of a typical composite floor system subjected to the penultimate edge column removal scenario. A 2 × 1 bay full-scale composite floor system is quasi-statically pushed down to failure under the displacement loading scheme. Full scale, moment-resisting connection, and continuous steel deck are three main features of this test. Based on this test, load-deflection responses, load-carrying mechanisms, deformation manners, and failure modes are discussed. The maximum load-carrying capacity was achieved at the flexural stage before the fracture of the girder-to-column connection, after that, the resistance decreased slightly and plateaued. The maximum static and dynamic load carrying capacities of the tested specimen is 4.2 times and 3.6 times of the ASCE load combination for accidental events, respectively. The damaged area of the composite floor is concentrated neighboring to the removed column, which is caused by the girder-to-column connection failure. Yield line method is used to predict the load-carrying capacity of this composite floor system, and the prediction agrees well with the maximum resistance measured in the test. After the failure of the girder-to-column connection in the removed column area, the measured loads are 15.9% ∼ 24.5% higher than the predicted values. This is because the yield line method does not count the contribution of the tensile membrane action in the slab. By comparing with the results from previous experimental studies, the effectiveness of the moment-resisting connection and the continuous steel deck on improving the load-carrying capacity of the composite floor system has been validated.

Moment resistance of blind-bolted SHS column splice joint subjected to eccentric compression

A new type of splice joint for Square Hollow Section (SHS) columns has been introduced in this paper. The spliced SHS columns are bolted to an inner sleeve which fits snugly to the internal surfaces of both columns. The moment resistances of such joints are studied analytically and experimentally. Under bending moment, the bearing interaction between the columns and the inner sleeve forms the Lever-Hold Effect which contributes to the moment resistance of the spliced joint. The mechanism of the Lever-Hold Effect can be simplified as the failure problem of a “semi-infinite” plate. It is found that the yield line method tends to overestimate the bearing capacity of the “semi-infinite” plate due to false yield line pattern and will result in overestimation of the contribution from the Lever-Hold Effect. To solve this issue, a revised yield line pattern is proposed in accordance with the forming process of yield lines on the “semi-infinite” plate. Numerical analyses and experimental study on the moment resistance of the joints have been carried out to validate the proposed analytical pattern. Based on the FEM analyses and test results, the formulae to estimate the moment resistance of RHS column splice connection with inner sleeves are proposed.

Two-Way Flexural Behavior of Donut-Type Voided Slabs

Voided slab systems were developed using segmented void formers such as spherical or oval plastic balls for two-way slab applications. This type of slab is expected to behave like a general two-way reinforced concrete slab because it has segmented voids, rather than the continuous voids of hollow core slabs. However, the structural behaviors of two-way voided slabs with segmented voids have not been clearly verified. Therefore, this paper analyzes the possibility of applying a donut-type two-way voided slab, which was investigated with a 12-point two-way bending test focused on global behaviors, including its load bearing capacity, flexural stiffness, ductility, deflection, and load distribution. In addition, the design method of a donut-type two-way voided slab was reviewed through the yield line method. The test results showed that one donut-type two-way voided slab acted like a conventional two-way reinforced concrete slab with the load distributed evenly between the different directions; however, another donut-type two-way voided slab with different characteristics showed uneven load distribution with different crack patterns. In addition, the yield line method could predict the load bearing capacities of the donut-type voided slabs with approximately 95% accuracy.