Yield Line Theory Research Articles

Design Guidelines for Longitudinal Plate to HSS Connections

Although longitudinal plates have been used widely to connect braces and other attachments to hollow structural sections (HSS), there is no established design method available for this type of connection. Research work has been undertaken both experimentally and analytically to produce a rational design procedure. Specimens with different angles between branch plates and HSS have been tested to rupture under different levels of compression loads on the HSS members. A parametric study, covering 120 different cases, has been carried out using finite element models, and the influences of plate-to-HSS angle, HSS axial force, HSS wall slenderness, plate thickness, plate width, and plate loading case have been investigated. Yield line theory was also used for the analysis of the strength of such connections. From this research work, design guidelines have been created based on an ultimate deformation limit and a serviceability deformation limit for the HSS connecting face, and non-uniformly distributed stress in the plate.

Resistance-Deflection Functions for Concrete Wall Panels with Openings

The design or assessment of wall panels subject to blast loading requires the formulation of a dynamic flexural resistance-deflection function for the element. With the exception of situations in which the explosion occurs at very close proximity to the panel, the resistance to blast loading may be based upon a quasi-static resistance function that subsequently must be modified for dynamic effects. This paper describes a proposed method for the derivation of quasi-static elastic/plastic resistance functions for reinforced concrete wall panels with door and window openings based upon finite element analysis and yield-line theory. This approach is compared with the results of tests on model wall panels. It is shown to produce a conservative value of ultimate load but may underestimate the deflection at the limit of elastic behavior.

A STRESS RESULTANT PLASTICITY MODEL FOR THE ANALYSIS OF REINFORCED CONCRETE SHELL AND BOX STRUCTURES.

This paper concerns the development and implementation of an orthotropic, stress resultant elastoplastic finite-element model for the collapse load analysis of reinforced concrete shells and box beams. The model is based on the accepted rationale of yield line theory for reinforced concrete, with the essential approximations required to obtain closed-form solutions for the yield function for shells. The behaviour of these functions is studied, and modifications are introduced to ensure a robust finite-element model of complex cases involving six stress resultants (M X , M y , M xy , N x , N y , N xy ). Onset of plasticity is always governed by the general yield-line model (YLM), but in some cases the stress-resultant form of a von Mises function is used post-yield to ensure the proper evolution of plastic strains. Case studies are presented, involving isotropic and orthotropic shells and boxes, to assess the behaviour of the yield-line approach. The YLM function is shown to perform extremely well, compared with experiment and analytical solutions, in predicting both the collapse loads and failure mechanisms.

Design of horizontally curved waffle slab structures

Horizontally curved concrete slab structures are often used in bridge superstructures as well as in large auditoriums with a minimum number of supports. A method is developed to analyse and design such structures based on their ultimate load-carrying capacity. The basis of this method is the yield-line theory. The behaviour of prestressed versus reinforced concrete construction is examined. The analytical results are verified and substantiated by tests on horizontally curved waffle slab models subjected to uniformly distributed and concentrated loads.

On M. Kmiecik, usefulness of the yield line theory in design of ship plating vol.8 no.1 (1995) 67–79

On M. Kmiecik, usefulness of the yield line theory in design of ship plating vol.8 no.1 (1995) 67–79

Modeling for Moment-Rotation Characteristics for End-Plate Connections

An analytical procedure is proposed to establish the nonlinear moment-rotation ( M -Φ) characteristics for the bolted end-plate connections in flexibly jointed steel frames. The connection characteristics are assumed to depend on the component behavior of the tension zone, the compression zone, and the shear zone. The column flange and end plate with each bolt row in the tension zone are considered as a series of T-stub assembly with the effective length recommended by the Eurocode 3. Based on the beam and yield-line theory, the elastoplastic force-deformation relationship for each T-stub assembly is derived. With the consideration of the deformation of column web in compression and shear zone, the connection rotation Φ under bending moment M is evaluated accordingly. The proposed analytical model is compared with some experimental results of extended and flush end-plate connections, and the feasibility and validation of the proposed model are demonstrated.

Structural Analysis Model for Mat Foundations

A simplified structural analysis model for mat foundations with grid floor beams as stiffeners is presented here. In the model, the Winkler type of subgrade reaction spring is assumed for the whole area under the mat foundation, and the yield-line theory of slab is used to lump the Winkler springs under slabs to the corresponding locations under the adjacent floor beams of the slabs. Therefore, each floor beam is now supported by springs with a segmentally linearly varied spring constant. The total analysis model for the mat foundation is then simplified to be a grid beam system on an elastic foundation with a segmentally linearly varied spring constant, and is subjected to loadings from the columns of the building structure. Some numerical comparisons with the results by a sophisticated finite-element model are made in order to demonstrate the effectiveness and efficiency of the presented analysis model.

一方向に厚肉帯版を有する周辺を拘束したR/C変厚床スラブの終局財力について

This retort describes the process by which the authors derived an ultimate load bearing capacity formula based on yield line theory for various kinds of floor slabs with unidirectional slab bands. The authors conducted tests on slabs with two unidirectional slab bands as samples to verify their formula. Furthermore, a few model floor slabs were compared with the samples on the basis of elasto-plastic analysis. Slab thickness, width, number of rows, and the span ratio of the slab bands were varied as the load bearing characteristics of the floor slabs with slab bands were compared and studied in various ways.

Yield-line elements: for elastic bending of plates and slabs

A new four-node rectangular element is proposed for the elastic analysis of plates in bending. This element has been formulated in view of the complex nature of existing nonlinear theory. The elastic theory developed in this paper has been derived in a form that allows a natural progression to plastic theory. The proposed method is mixed in the sense that moments and out of plane deflections are chosen as the unknowns. The solution matrix is developed from flexibility and equilibrium equations. Flexibility equations (expressing the relationship between the rotations and nodal moments) assume a partial quadratic moment field and are equated to obtain interelement compatibility. Equilibrium equations are formulated from virtual work expressions used in yield-line theory that are modified to include the twisting moment. For one-way plate action (single curvature), the solution is exact irrespective of the aspect ratio or the number of elements. For two-way action (double curvature), acceptable accuracy is achieved. Comparisons with exact solutions and the displacement method are included to indicate the accuracy of the proposed element.

Nominal Strength of Composite Prestressed Concrete Bridge Deck Panels

Precast prestressed concrete panels have been used as subdecks in bridge construction. To experimentally investigate the nominal flexural and shear strengths of this composite slab system, five full-scale model composite slab specimens were constructed and tested. One specimen modeled bridge deck condition well within a girder span, and the other four specimens represented geometric conditions that occur with skewed concrete diaphragms at 0°, 15°, 30°, and 40°. The slabs were statically loaded through a wheel footprint at preselected locations until failure occurred. To analytically evaluate the nominal strength for these composite slab specimens, yield-line and punching-shear theories were applied to the crack patterns generated during the ultimate load tests. These computations and the observed mode of failure for the specimens indicated that punching shear governed the nominal strength of the slabs. The nominal strength of the slabs significantly exceeded the design load requirements.

Usefulness of the yield line theory in design of ship plating

Abstract The paper contains results of an analysis of the load-carrying capacity of square and rectangular plates subjected to uniform lateral pressure. The analysis was carried out in the elastic plastic range with a finite element method (FEM) computer code called PANFEM. The load-carrying capacity of plates obtained from large deflection theory (LD) is compared with that obtained from small deflection theory (SD). Results of the load-carrying capacity of plates determined using yield line theory (YLT) are also presented. The comparison indicates that only the FEM based on LD is capable of correctly predicting the load-carrying caracity of plates in the elastic-plastic range. To verify the accuracy of the FEM calculations, their results are compared with experimental measurements.

Low-Cycle Fatigue Behavior of Semi-Rigid Top-and-Seat Angle Connections

Constant amplitude reversed cyclic load tests were performed to investigate the low-cycle fatigue behavior of a commonly used class of semi-rigid connection: the top-andseat angle. All specimens had the same geometrical properties. The test results show that the plastic moment capacity and connection stiffness are sensitive to how the nut and bolts are oriented when tightened. However, upper and lower bounds of strength and stiffness can be predicted using standard yield line (plastic) theory. The variability in strength and stiffness does not appear to affect the fatigue life. Fatigue life predictions can be made for this class of connection using relationships analogous to the well-known Manson-Coffin1,2 strain-life equation for metals. Mean rotation (analogous to mean stress) effects are also examined and are shown not to be significant over the range of plastic rotations (0.003 to 0.10 radians) considered. Hysteretic energy-life and energy-rotation relations were also developed. Such relations are useful in seismic damage modeling. For the top-and-seat angle connections considered in this study, the large fatigue based plastic rotation capacity (approx. 3 percent) would generally significantly exceed expected demands for most structural steel systems in a typical US earthquake, where total drift rarely exceeds 2 percent.

周辺を拘束した格子状の厚肉部を有するR/C変厚床スラブの終局耐力について

This report describes the method and results of our study. Yield-line theory was used to derive an equation that calculates the ultimate load bearing capacity of floor slabs with plural slab bands in both orthogonal direction. Two pairs of bands were set at right angles to one another, and tests were run to verify the strength of the floor slabs with slab bands. In addition, using model floor slabs, we compared and studied the bearing load capacity characteristics of the floor slabs with two or more pairs of bands set at right angles to one another.

Fracture of steel beam to box column connections

Abstract This study is aimed at examining the behavior of the beam to interior box column connection. Cruciform type test setups are selected with the column under constant gravity load while both beams under gradually increased cyclic loading in opposite directions to simulate earthquake load. The tearing strength of the column plate by the transmitted out‐of‐plane load from the beam web is analyzed by yield line theory. A simplified method is proposed to establish the relationship between the thickness of beam web and column plate. A series of experimental studies are also conducted to examine the effect of a diaphragm plate on the transmission of applied force from beam flanges. Based on the results of this study, suggestions are made for the design and construction of beam to box column connections to achieve better strength and ductility.

高張力鋼を用いたコンクリート充てん角形鋼管柱-鉄骨はり接合部の力学的挙動に関する研究

Structural behaviors of the connections between concrete filled square tubular high strength (780N/mm^2) steel column and wide flange high strength (590N/mm^2) steel beam have been studied by cruciform tensile tests and beam-and-column subassemblage tests. Stable hysteretic loops of rich energy absorption capacity have been obtained showing good structural behaviors for seismic loading by beam-and column subassemblage tests. Yield and ultimate strengths of the connections have been analysed based on the yield line theory taking the strain behaviors of the connections into consideration. The analytical results agree well with test results.

角形鋼管柱の左右にせいの異なる梁が接合される場合の梁の剛性と耐力に関する研究

At the connection of H-shaped beams and RHS-column as shown in Fig. 2, stiffness and moment capacity of smaller depth beam are govered by rigidity of column flange. In this paper, analytical study for predicting elastic stiffness and moment capacity of beam mentioned above and experimental results are reported. The elastic stiffness of beam was derived by assumig the column flange would behave as grid beams. For the moment capacity, the theoretical expression was developed based on the yield line theory. And to confirm the precision, the analytical results were compared with the experimental results obtained from 14 simple beam type specimens under monotonic loading and 5 cruciform type specimens of beam-to-column sub-assemblage under cyclic loading. In those tests, the parameters of specimens were thickness of RHS-column, disparity between lower beam flange and diaphragm, and width of beam-flange. The analytical results were closely coinside with the corresponding test results.

鉄筋コンクリートスラブの面内圧縮力による曲げ耐力の増加に及ぼす影響因子について : 周辺を固定した正方形鉄筋コンクリートスラブの曲げ耐力の実験結果の考察(その1)

Generally, the ultimate strength of restrained concrete square slabs express larger value than the bending strength obtained from the yield line theory of Johansen. This cause is explained by an arching action due to the development of compression membrane force in the slab. Therefore, in this report we described the relation between the evaluation value and its effecting factors: The evaluation value (E) express a strength grow due to the development of compressive membrane force in the slab. The effecting factors were considered by the items of three: Slab's thickness/span ratio (H/L) or flange thickness/span ((H-h)/L), elastic fixing degree (F_<ix>) and reinforce factor (q). We investigated the relation between the evaluation value and effecting factors as follow: 1) Relation between evaluation value (E) and slab's thickness/span or flange thickness/span ((H-h/L). 2) Relation between evaluation value (E) and elastic fixing degree (F_<ix>). 3) Relation between elastic fixing degree (F_<ix>) and slab's thickness/span ratio (H/L) or flange thickness/span ratio ((H-h)/L). 4) Relation between evaluation value (E) and reinforce factor (q). The results was shown as follow: 1) As the value of slab's thickness/span ratio (H/L) or flange thickness/span ratio ((H-h)/L) increases, the evaluation value (E) showed an increasing tendency. Therefore, the evaluation value (E) was very closely related with slab's thickness/span ratio (H/L) or flange thickness/span ratio ((H-h)/L). 2) As the value of reinforce factor (q) increases, the evaluation value (E) showed a decreasing tendency. 3) Elastic fixing degree (F_<ix>) was very closely related with slab's thickness/span ratio (H/L) or flange thickness/span ratio ((H-h)/L). 4) Elastic fixing degree (F_<ix>) gave an effect in the strength of slab by restrained degree of rotation with surround restrained beam. But it was found that the elastic fixing degree (F_<ix>) gave a small effect to the evaluation value (E).

Reliability assessment of plastic slabs

An integrated form of yield line theory incorporating finite elements and concave quadratic programming is developed. The branch and bound strategy used to solve this mathematical program is simple to operate because it involves only linear programming algorithms. It provides either an upper bound to the reliability index of the stochastic most relevant mechanism for continuous slabs or an exact solution when the yield lines of the collapse mode of the continuous model lie along element boundaries of the finite element model. Algorithms that enumerate other stochastic dominant modes are described and applied to assess the reliability of slabs. Illustrative examples are given.

Triangular Truss Joints Using Rectangular Tubes

This paper deals with the behavior and design of welded joints to the tension chord of triangular trusses, with two Warren-type web planes and a single tension chord, made of rectangular tubes (hollow structural sections or HSS). Experimental programs are outlined in which simplified double-T joints and triangular truss segments with double-K gap joints were tested. Parameters investigated include the gap size, the web-member-width–to-chord-width ratio, the chord-wall-width–to-thickness ratio, and the angle between web planes. The mechanics of deformations of the double-T and double-K joints are discussed in relation to yield line theory, and this theory is shown to give a good prediction of the experimental joint stiffnesses and strengths. Strength equations are proposed to cover tension chord gap joint behavior with respect to chord wall bending and a design example is outlined.

箱形断面柱-H形断面はり接合部のダイアフラム補強に関する研究 : 接合部降伏耐力の評価

Analytical study has been carried out to estimate yield strengths of steel beam to box column connections. The obtained solution, which is based on the yield line theory, predicts accurately experimental behaviors and yield strengths for connections both with and without reinforcing diaphragm as follows : 1) For connection without diaphragm, Eq. (9) gives very close approximation to the experimental general yield strength which varies with type of corner weld of column as well as size of column and beam. 2) For connection reinforced with inner diaphragm, Eq. (21) is proposed. Estimated yield strength agrees well with the experimental strength dependent on several sets of parameters, especially, width to length ratio of diaphragm. It is also shown that the test results presented by K. Ban and K. Imai fairly conform to the formula. 3) For connection reinforced with outer diaphragm (or outside stiffening ring), calculated yield strengths by the formula of Eq. (23) are compared with experimental values offered by M. Tabuchi and K. Kanatani et al. As a result, good agreement is observed between the theory and the test results.