Yield Line Theory Research Articles

Limit analysis for stiffened eight-bolted base plate connections in EHV transmission towers

Theoretical models based on yield-line theory are presented for predicting the ultimate uplift capacity of stiffened eight-bolted base plate (EBBP) connections in EHV transmission tower. Based on the test observations, the four models for rigid connections consider combined effects of the base plate, stiffeners and anchor bolts and the model for flexible connections merely considers the base plate. The presented models are validated using experimental data from an associated test program and compared with the results calculated by methods in a corresponding code, and reasonable accuracy has been demonstrated. A parametric analysis shows that the presence of the stiffeners makes numerous contribution to the strength of rigid connections in particular cases.

Bending-shear performance of column-to-column bolted-flange connections in prefabricated multi-high-rise steel structures

The bolted-flange connection is a new application for mounting rectangular hollow section (RHS) columns in prefabricated multi-high-rise steel structures, which may bear the combination of bending moment and shear under permanent, live, wind loads or earthquake. The performance of the bolted-flange connection used in the structural column is different from that in its popular usage in the pipe because the subjected force is different. To investigate the bearing performance of a bolted-flange connection under the combination of bending moment and shear, this study conducted static tests and finite element analysis (FEA) of 12 column-to-column bolted-flange connections with different flange thicknesses, bolt edge distances, flange edge widths and bolt hole diameters, as well as one column without a connection. The test agreed well with the FEA, which verifies the FEA. The influences of the flange thickness, bolt edge distance, flange edge width and bolt hole diameter on the stiffness and strength of the connections, bolt tension and contact force were studied, and the failure mode and mechanism of the connection were obtained. A significant prying action occurred on the flange contact surface, increased the bolt tension in the tensile region, and caused the bolt shanks to experience tension and bending moment. The flange thickness had a large impact on the prying force, while other factors had less of an effect. Based on the yield line theory, the bearing mechanism of the connection was obtained. The formulas for the yield bearing capacity were proposed and were verified by the test and FEA.

Compression-bend-shearing performance of column-to-column bolted-flange connections in prefabricated multi-high-rise steel structures

The bolted-flange connection is used to connect rectangular HSS columns in prefabricated multi-story and high-rise steel structures. It may subject to coexisting axial compression, bending moments and shearing under the combination of dead, live, wind loads or earthquake action. The bearing performance is different from that of bolted-flange connections used in pipelines, towers and mast structures. To investigate the bearing performance of a connection subjected to coexisting compression, bending moments and shearing, static tests and a finite element analysis (FEA) were applied to 12 column-to-column bolted-flange connections with different flange thicknesses, bolt edge distances, flange edge widths and bolt hole diameters, as well as one column without connection. The effects of flange thickness, bolt edge distance, flange edge width, and bolt hole diameter on the stiffness and strength of connections, bolt tension levels, and contact forces between flanges were obtained as well as effects on the failure mode and mechanisms of the connections. Flange thickness was found to have a considerable impact on the performance of connections, while the bolt edge distance and flange edge width were found to have a lesser effect. The FEA results agree well with the test results, verifying the finite element model (FEM). Some performance results that could not be obtained through testing were obtained. Based on yield line theory and T-stub analogies, the load transfer mechanism of bolted-flange connections was obtained and formulas for yield-bearing capacity are proposed. The results obtained from the formulas agree well with the test and FEA results.

Flexural behaviour of one-way patched reinforced concrete (RC) slab under concentrated load

Repair of deteriorated reinforced concrete (RC) elements may be necessary to restore their strength and serviceability. In this research, unsaturated polyester resin (UPR)-mortar is used to repair one-way RC slabs. The performance of the patched RC slabs is investigated experimentally by comparing their behaviour under concentrated load with the corresponding normal slab. The obtained load–deflection relationship up to failure and the cracking failure mode are assessed to determine the efficacy of the UPR-mortar in restoring the strength and serviceability of the slabs. In addition, theoretical ultimate loads determined on the basis of the yield line theory are used to assess the effectiveness of UPR-mortar to restore the strength of the damaged RC slab. As long as a proper execution of repair is carried out, the results indicate a satisfactory performance of UPR-mortar to be used for repairing the damaged RC slabs.

Dynamic behaviour of square tubular T-joints under impact loadings

This paper examines the dynamic behaviour of square tubular T-joints under impact loading by means of experimental, numerical and analytical studies. Firstly, a high-performance drop hammer setup is employed to carry out the impact tests on five hot-rolled square tubular T-joints with different chord thickness and width ratio of brace/chord under three levels of impact height. The dynamic responses of tubular T-joints including the deformation patterns and the development of impact force and displacement are described. Based on the experimental results, the impact load-deformation relationships as well as the energy dissipation are further discussed to reveal the mechanical behaviour of T-joints, with emphasis on the effect of width ratio of brace/chord and impact energy. Complementary finite element model for simulating the tubular T-joints under impact is then proposed and validated against the available test results. Finally, the test results and numerical simulations are utilized to investigate the failure mechanism of T-joints under impact load. In particular, the local and global displacements of square chord are estimated by an equivalent area method, and the impact resistance of impacted joints is examined based on the yield line theory. In general, the investigation in this paper can also offer reliable test data and design suggestions to reasonably evaluate the impact behaviour of square tubular T-joints.

Prediction on ultimate strength of tube-gusset KT-joints stiffened by 1/4 ring plates through experimental and numerical study

One typical joint in steel tube tower, i.e. the tube-gusset KT-joints stiffened by 1/4 ring plates, has been paid attention lately due to its merits about reasonable stress distribution and low cost. But the relevant design theory lags obviously other than design recommendations from JSSC and CIDECT. However they are proved less effective with regard to certain failure mode. For this reason, the paper has proposed one design formula to make up the deficit based on yield line theory. Finally the proposed formula is testified to be more accurate and versatile than other design rules.

Punching Shear in Steel Fibre Reinforced Concrete Slabs Without Traditional Reinforcement

The punching shear capacity of steel fibre reinforced concrete (SFRC) slabs without traditional steel bar reinforcement was investigated by conducting central point-load tests on twelve square slabs. The test parameters covered fibres with different multi-hook ends, concrete compressive strength, reinforcing index and slab thickness. The statistical performance of two existing models for the prediction of punching shear capacity of SFRC slabs without traditional reinforcement was examined. The load carrying capacity of these slabs were also assessed using the yield line theory. It is noted that the slabs failed primarily in flexure and the yield line theory predicted the load carrying capacities of the slabs most accurately. The reason for a flexural failure in SFRC slabs without steel bars is attributed to the lesser energy required in the propagation of an existing flexural cracks than in the creation of a new circumferential cracks around the column face.

Structural performance of SFRC slab-on-grade supported on elastic spring system

Slabs-on-grades (SOGs) reinforced with 20, 30 and 40 kg/m3 of steel fibres and supported on an elastic spring system (S25H4) were tested under concentric loading conditions. The S25H4 system, which contained 25 elastic springs and four hinges to simulate Winkler-type soil reactions, was intended to solve problems observed in other subgrade systems used in SOG experiments. Tests showed that the S25H4 system could reproduce the flexural behaviour of a slab supported on soil by an appropriate distribution of moments along the yield lines. A theoretical model was also developed, based on yield line theory, to predict the flexural strength of a SOG supported on the S25H4 system. From comparisons between the model predictions and test results, better predictions were obtained with the equivalent flexural tensile strength incorporating the effect of slab thickness and the rectangular stress blocks in a section determined from sectional equilibrium.

Tensile strength and concrete cone failure in CFT connection with internal diaphragms

Concrete filled tube (CFT) system provides excellent structural performance thanks to the composite effect between the tube and the concrete. However, its closed sections impose complication on the fabrication of the column-to-beam connection and only a small number of connection methods have been developed. In square CFT column-to-beam connections, internal diaphragms reinforce the inside of the column for the loads and moments delivered from the beam. It is required to develop various connection types to secure structural capacity and concrete filling. In the process of making the square Hollow steel section (HSS), diaphragms are placed in channel members in advance and then the two channel members are welded longitudinally to produce a square HSS. It is superior to other connection types in terms of the degree of Complication in placing the internal diaphragms, economical efficiency and workability. In this study, strength formulas were suggested based on the yield line theory to evaluate the load capacity of the column-to-beam connections. For the connection of horizontal diaphragms, the strength of steel tube faces, internal diaphragms, and concrete cone failure were accumulated. For the connection of vertical perforated plates, the strength of steel tube faces, concrete cone failure, and perfobond were accumulated. Although there was a slight difference between the formula and test result, it can be used to estimate the strength of columnto- beam connections.

Punching shear behavior of recycled aggregate reinforced concrete slabs

Preservation of environment and natural resources has recently attracted researchers to study the use of recycled aggregates from demolished concrete in new concrete structures. This paper presents an experimental study on punching shear behavior of simply supported natural and recycled coarse aggregate concrete slabs. The punching shear behavior of interior slab–column connection in flat plates is tested in “The Reinforced Concrete Laboratory of the Faculty of Engineering, Alexandria University”. Eight two-way slab specimens using two different types of aggregate “natural and recycled” and two aggregate nominal sizes (12.5 and 25mm) were cast and tested to failure. The slabs were designed such that they would fail in punching shear only. The experimental work was conducted on (6) recycled coarse aggregate concrete (RCAC) slab specimens and (2) natural coarse aggregate concrete (NCAC) slabs. All the slabs were simply supported on four edges and tested under a central patch load. The ACI mix design procedure was adopted to achieve strength of concrete at 28days of 35MPa. Four concrete mix proportions were used with (0%, 30%, 60% and 100%) replacement of natural coarse aggregate with recycled coarse aggregate for each aggregate size. The test results showed that the first punch crack load, ultimate punch load, stiffness and energy absorption decrease as the replacement of natural coarse aggregate with recycled coarse aggregate increases. Also as the recycled aggregate size increases the cracking and failure load increases. The measured ultimate failure loads have been compared with code predictions (ECP 203, ACI 318, JSCE code, Euro code 2 and yield line theory). The Euro code – 2 equations gave the best correlation with the experimental results.

Yield-line plasticity and tensile membrane action in lightly-reinforced rectangular concrete slabs

The paper provides the systematic derivation of a new analytical approach to tensile membrane action of lightly-reinforced thin concrete slabs at large deflections. The basic motivation for the work comes from the recent use of tensile membrane action as an enhancement, in the fire condition, of the capacity of the thin concrete slabs which are normally made composite with downstand steel beams, at temperatures which have substantially degraded the contribution of these steel beams. The method accepts as a premise that such slabs form a pattern of localized yield lines as an initial small-deflection failure mechanism, and that these yield lines retain their positions as subsequent deflection occurs. As the slab deflects, maintaining the correct kinematics of the articulation and displacement of the system of slab facets, interacting across the yield lines, is extremely important to the horizontal equilibrium of the slab. In this process it becomes necessary to re-think the basic assumption of traditional yield-line theory that any local cross-section of unit width along a yield line equilibrates the force of its concrete compression block with the yielded steel’s tension force, producing constant plastic moment capacities for the mesh in either direction along any yield line. In the approach set out in this paper only overall equilibrium of the system of facets needs to be maintained. As in normal rigid-plastic analysis, concrete acts only when compressed, and then at its compressive strength, and steel acts at its tensile yield strength whilst it remains intact. However, steel in either direction can fracture when the local crack-width causes its local strain to exceed its fracture ductility. When the rebar crossing the diagonal yield lines begins to fracture this generally indicates that the slab’s capacity is about to reduce with further deflection. The paper does not attempt to address how a rebar’s free length across a discrete crack is generated, or the limiting crack widths implied, but this is shown in a range of examples to be a major issue if tensile membrane action is to be used in practice to enhance the capacity of slabs, for example in hazard loading situations. It is important that principles be established in future to quantify this aspect of rebar ductility.

Prediction of the load carrying capacity of elevated steel fibre reinforced concrete slabs

A novel methodology is developed for predicting the load carrying capacity of elevated steel fibre reinforced concrete (E-SFRC) slab systems. In the proposed approach the depth of slab’s cross section is discretized into several layers, and the number of steel fibres per each layer is determined by considering the distribution of fibres along the depth of cross section. This information, together with the one obtained from the three-point notched beam bending tests performed on four series of SFRC made of different concrete strength class and content of fibres, have provided the stress-crack width laws for defining the post-cracking behaviour of each layer. These constitutive laws are implemented in a numerical model developed based on the moment-rotation approach for determining the positive and negative resisting bending moment of the slab’s unit width cross section. By using the yield line theory, the load carrying capacity of E-SFRC slab is predicted for the most current load conditions. Predictive performance of the proposed methodology is assessed comparing to the results recorded in experiment and the ones obtained by the numerical simulation. The developed model is utilised in a parametric study to evaluate the influence of parameters that affect the load-carrying capacity of E-SFRC slabs.

Ground Supported Short Fiber Reinforced Concrete Industry Plate

Abstract The present paper describes the elastic theory and Losberg Yield Line theory with plastic approach of solution. The finite element method for modeling of fiber reinforced concrete plates placed on Winkler foundation was used. There is presented Tsai and Pagano model within micromechanics of composite materials with short fibers. As the application problem it was used example of fiber-reinforced concrete industry plate. The strength obtained from elastic and plastic approach was compared and discussed in the conclusion of the paper.

Effect of casting flow defects on the crack propagation in UHPFRC thin slabs by means of stereovision Digital Image Correlation

Owing to their outstanding compressive strength and considerable cracking resistance, Ultra High Performance Fibre Reinforced Concrete (UHPFRC) have been recently successfully applied to thin bi-dimensional elements, e.g., plate and shells. As a critical aspect of UHPFRC technology,is work aims at experimentally investigating the effect of fibre orientation on the damage behaviour of UHPFRC 2-way thin slabs by means of stereovision digital image analysis. To this aim, the fibre orientation was perturbed by introducing a simple divider line as a temporary barrier to the casting flow of fresh concrete. The casting flow defect affected the fibre distribution by creating a weakened plane with a strong discontinuity. By varying the line direction and the position of the concentrated load position, six different slab configurations were fabricated and tested under punching load with hyperstatic boundary conditions. Then, the 3-D deformation field was measured by means of stereovision-based Digital Image Correlation (DIC). The results showed the critical importance of the fibre distribution on the microcracking growth and the structural ductility. The casting flow defect had a major impact on the observed microcrack pattern and growth especially before the peak load. When the defect crossed the loading point, the microcracks did not fully develop with an important reduction of the load-carrying capacity and the structural ductility. Finally, a simplified application of yield line theory allowed estimating the effect on the fibre distribution of the casting flow defects.

Web crippling of beams under ITF loading: A novel DSM-based design approach

A new approach to estimate the web crippling failure load of cold-formed steel beams under Internal Two Flange (ITF) loading using the Direct Strength Method (DSM) is proposed in this paper. After the description of the existing test data to calibrate the DSM-based formula, the accuracy of the analytical expressions given in Eurocode 3 [1] and the North-American Specification [2] is briefly assessed. In order to obtain additional information on the web crippling behaviour of each test specimen, several types of analyses are performed: (i) quasi-static non-linear analyses (using finite elements), (ii) elastic buckling analyses (using finite elements and the GBTWEB software), and (ii) rigid-plastic analyses (using yield-line theory). The coefficients of a DSM-based formula are determined on the basis of the set of 85 experimental results available in the literature and the corresponding buckling and plastic load values. In spite of the different cross-sections, fastening conditions and test set-ups considered in the calibration procedure, it is possible to establish a clear relationship between the web crippling slenderness and the nominal-to-plastic load ratio. Finally, it is shown that the proposed DSM-based formula for ITF loading yields reasonable predictions of web crippling loads and provides safe estimates of flange crushing loads.

A Comparative Study of Strength of Two-Way Rectangular Slabs with and without Openings

The present work uses yield-line theory to find the strength of uniformly loaded rectangular reinforced concrete slabs with and without rectangular openings. Five positions of openings are considered, i.e. the slab centre, the slab corner, the centre of a short side, the centre of a long side and the opening eccentric to the slab centre. All possible admissible yield line patterns are considered for all given configurations of the slab subjected to uniformly distributed load keeping in view the basic principles of yield line theory. The ratios of the corresponding lengths of the sides of the opening and the slab are different and sizes of opening up to 0.4× the length of the slab sides are considered. Symmetric edge conditions like continuous slab, simply supported, two long sides continuous and two short sides continuous are considered for various sizes of openings in order to plot the design charts for isotropic reinforcement coefficients only. Affine transformation is also performed for slab with openings.

Failure Mode Prediction for One-Way Reinforced Concrete Flat Slabs with Rectangular Columns

Flat slabs are reinforced concrete plates directly supported on columns, without intermediary beams. This structural system has been sufficiently used in the last decade, mainly for successful reach large spans and allowing "layouts" flexible. On the other hand, these slabs can be characterized as two-ways or one-ways, depending on the loading conditions, it is still stand out that NBR 6118 does not distinguish the types of flat slabs and make no reference to how much the punching resistance in the case of the one-ways flat slabs and it is known that normally these flat slabs presents low failure loads compared to the two-ways one. In this work presents a proposal, completely detailed in Damasceno’s master thesis (2007), for forecast the failure mode of one-way flat slabs with rectangular columns and without shear reinforcement, based on the prescriptions of CEB-FIP MC90 and on the Yield Line Theory. Equations that describe the behavior of the slabs in the limit between punching shear and flexure failures, considering the material’s properties, dimensions of the flat slab and the column’s cross sections, rate of flexure reinforcement in two directions, etc. are presented, parameters that influence on the slabs’ behavior. The estimates had been satisfactory and able to forecast one-way flat slabs’ failure modes.

Nonlinear Behavior of Self -Compacting Reinforced Concrete Two-Way Slabs with Central Square Opening under Uniformly Distributed Loads

This research is carried out to investigate the behavior of self-compacting concrete (SCC) two-way slabs with central square opening under uniformly distributed loads. The experimental part of this research is based on casting and testing six SCC simply supported square slabs having the same dimentions and reinforcement. One of these slabs was cast without opening as a control slab. While, the other five slabs having opening ratios (OR) of 2.78%, 6.25%, 11.11%, 17.36% and 25.00%. From the experimental results it is found that the maximum percentage decrease in cracking and ultimate uniform loads were 31.82% and 12.17% compared to control slab for opening ratios (OR) of 11.11% and 6.25% respectively. Also the results showed that as OR is increased from 0.00% to 11.11%, a signifacant increase in deflection was occured. While the increase of OR from 11.11% to 25.00%, a slighlty decrease in deflection was occured compared to control slab within the entire range of loading starting from first cracking load up to ultimate load. The theoretical part of this research is adopted for both simply supported and clamped ends square slabs according to yield line theory. For simply supported slabs, the results showed a decrease in ultimate uniform loads for OR ranging between 0.00% and 25.00%. While beyond this value, an increase in the ultimate uniform load is occured. In addition, it is found that as OR was increased; the total ultimate load is decreased. Also from the theoretical analysis for clamped end slabs it is found that as OR was increased, both the ultimate uniform load and the total ultimate load were increased.
 

Collapse mechanisms and load–deflection curves of unstiffened and stiffened plated structures from bridge design

Cross sections of modern bridges are generally build with stiffened plated elements. The verification methods given in Eurocode EN 1993-1-5, to obtain the ultimate buckling resistance of plated structures, result in a time consuming procedure. In addition, the methods are mainly based on the elasticity theory and reduction factors from e.g. experiments are needed. Therefore, an alternative approach to obtain the ultimate resistance of unstiffened and stiffened plates is used. The method is based on a strain-dependent and geometric nonlinear yield-line theory including imperfections. This theory makes it possible to approximate the decreasing part of the load–deflection curve of such stability sensitive structures. The ultimate resistance, as maximum of the load–deflection curve, is approximated by a defined limit value. Therefore, the use of additional reduction factors is not necessary. Collapse mechanisms, which have been determined with the Finite Element Method (FEM) beforehand, are needed in order to apply the yield-line theory.

강섬유 보강 콘크리트 인장성능 평가방법에 따른 지반 바닥슬래브의 설계

Flexural strength of concrete ground slab reinforced with steel fiber is evaluated using the equivalent flexural strength ratio of steel fiber reinforced concrete based on the yield line theory. Recently, the European standard specifies that the tensile performance of the steel fiber reinforced concrete be evaluated directly from the residual flexural strength after the cracking of concrete. Thus, in the study, an experiment was carried out to evaluate the conventional equivalent flexural strength ratio and the residual flexural strength of the steel fiber reinforced concrete. Then the design flexural strength was investigated according to the location of a point load, based on the ratio of the radius of contact area of the load to the radius of relative stiffness. Design flexural capacity obtained from ACI 360R-10 was smaller than that from TR 34 (2003 & 2013). In addition, TR 34 (2013), which evaluates the design flexural capacity based on the residual flexural strength, showed slightly smaller value than TR 34 (2003).