Development Of Plastic Hinges Research Articles

Progressive collapse of a two-story reinforced concrete frame with embedded smartaggregates

This paper reports the experimental and analytical results of a two-story reinforcedconcrete frame instrumented with innovative piezoceramic-based smart aggregates (SAs)and subjected to a monotonic lateral load up to failure. A finite element model of the frameis developed and analyzed using a computer program called Open system for earthquakeengineering simulation (OpenSees). The finite element analysis (FEA) is used to predict theload–deformation curve as well as the development of plastic hinges in the frame. Theload–deformation curve predicted from FEA matched well with the experimental results.The sequence of development of plastic hinges in the frame is also studied from the FEAresults. The locations of the plastic hinges, as obtained from the analysis, weresimilar to those observed during the experiment. An SA-based approach is alsoproposed to evaluate the health status of the concrete frame and identify thedevelopment of plastic hinges during the loading procedure. The results of theFEA are used to validate the SA-based approach for detecting the locations andoccurrence of the plastic hinges leading to the progressive collapse of the frame.The locations and sequential development of the plastic hinges obtained fromthe SA-based approach corresponds well with the FEA results. The proposedSA-based approach, thus validated using FEA and experimental results, has a greatpotential to be applied in the health monitoring of large-scale civil infrastructures.

Strength deterioration of reinforced concrete beam–column joints subjected to cyclic loading

This paper proposes a method to predict the ductile capacity of reinforced concrete beam–column joints failing in shear after the development of plastic hinges at both ends of the adjacent beams. After the plastic hinges occur at both ends of the beams, the longitudinal axial strain at the center of the beam section in the plastic hinge region is expected to increase abruptly because the neutral axis continues to move toward the extreme compressive fiber and the residual strains of the longitudinal bars continue to increase with each cycle of additional inelastic loading cycles. An increase in the axial strain of the beam section after flexural yielding contributes to a widening of the cracks in the beam–column joints, thus leading to a reduction in the shear strength of the beam–column joints. The proposed method includes the effect of longitudinal axial strain of a beam in the plastic hinge region of the beam on the joint longitudinal strain and the strength deterioration of the joint. In order to verify the shear strength and the corresponding deformability of the proposed method, test results of RC beam–column assembly were compared. Comparisons between the observed and calculated shear strengths and their corresponding deformability of the tested assemblies showed reasonable agreement.

Seismic response of single-column bent on pile: evidence of beneficial role of pile and soil inelasticity

While seismic codes do not allow plastic deformation of piles, the Kobe earthquake has shown that limited structural yielding and cracking of piles may not be always detrimental. As a first attempt to investigate the consequences of pile yielding in the response of a pile-column supported bridge structure, this paper explores the soil–pile-bridge pier interaction to seismic loading, with emphasis on structural nonlinearity. The pile–soil interaction is modeled through distributed nonlinear Winkler-type springs and dashpots. Numerical analysis is performed with a constitutive model (Gerolymos and Gazetas 2005a, Soils Found 45(3):147–159, Gerolymos and Gazetas 2005b, Soils Found 45(4):119–132, Gerolymos and Gazetas 2006a, Soil Dyn Earthq Eng 26(5):363–376) materialized in the OpenSees finite element code (Mazzoni et al. 2005, OpenSees command language manual, p 375) which can simulate: the nonlinear behaviour of both pile and soil; the possible separation and gapping between pile and soil; radiation damping; loss of stiffness and strength in pile and soil. The model is applied to the analysis of pile-column supported bridge structures, focusing on the influence of soil compliance, intensity of seismic excitation, pile diameter, above-ground height of the pile, and above or below ground development of plastic hinge, on key performance measures of the pier as is: the displacement (global) and curvature (local) ductility demands and the maximum drift ratio. It is shown that kinematic expressions for performance measure parameters may lead to erroneous results when soil-structure interaction is considered.

Plastic Hinge Development of Frame Members Using a Nonlinear Hardening Rule

A nonlinear hardening rule that defines a yield surface translation for homogeneous frame member materials is proposed. The rule is defined as a nonlinear constitutive relationship that examines material behavior through a postelastic perspective. The gradual development of the postelastic states of a beam along its length and through its section thickness is analyzed. The model uses a hardening index parameter to guide the nonlinear stress–strain relationship, and a smooth function to model the web–flange intersection of frame members. As such, nonlinear curvature distributions with continuous derivatives are determined along the length of the member, which enables lateral displacements to be accurately predicted. Plastic hinge lengths and finite-element displacements are subsequently determined, and a nonlinear stiffness is derived. The model is formulated on a constitutive level and applies a smoothed-over cross section to derive a single internal moment expression for any postelastic state. Results ar...

Experimental Analysis of Flexural Hinging in Hollow Marine Prestressed Pile Shafts

Parametric analysis of hollow precast prestressed piles indicated that under certain conditions of loading and geometry, plastic hinge formation could be expected in the pile shaft below ground level. Four half-scale model precast prestressed piles were tested in flexure to characterize plastic hinge development. The test rig simulated the subgrade moment pattern found in an in situ pile, and simulated external confinement from the soil around the pile shaft. Parameters varied were transverse reinforcement ratio, presence of external confinement, and presence of nonprestressed longitudinal steel in the plastic hinge region. The model piles were found to be insensitive to parameter variation. Failure occurred at similar levels of structural displacement in all cases, and in all cases took the form of compression failure of the pile wall. The piles had limited ductility, less than μΔ = 4 in all cases.

Part 1: General Structures: Experimental Study on Ultimate Behavior at Negative Moment Regions of Composite Bridges

This paper presents experimental results of the ultimate behavior of the negative moment region of a quarter-scale full model and a half-scale subassemblage model of a two-span continuous composite bridge of concrete deck slab on steel girder. The two specimens are based on a prototype bridge that has a large girder spacing [3,800 mm (13 ft)]. At the ultimate state, it is shown that a larger portion of the deck is activated to resist tensile stress compared with the effective width specified in the AASHTO load and resistance factor design bridge specifications. Also, a plastic hinge that forms at the internal support has enough rotational capacity (ductility) to enable development of a second plastic hinge within the span. Experimental results show a reasonably good match with accompanying finite element method analyses.

Reinforced concrete edge beam—column—slab connections subjected to earthquake loading

Four two-thirds-scale reinforced concrete edge beam–column–slab subassemblies (two concentric and two eccentric connections) were tested under quasi-static cyclic lateral loading. Each subassembly represented a cruciform connection in an exterior moment-resisting frame with a monolithic floor slab on one side only, loaded in the longitudinal direction of the edge-beams. The tests explored the effect of eccentricity between beam and column centrelines, and the effect of floor slabs, on the structural performance of edge beam–column–slab connections subjected to earthquake loading. Performance of the specimens was evaluated in terms of overall strength and stiffness, energy dissipation, beam plastic hinge development, joint shear deformation, and joint shear strength. All specimens underwent some beam hinging at the beam/column interfaces. However, both eccentric specimens, and one concentric specimen with a heavily reinforced floor slab, eventually failed as a result of joint shear, whereas the other concentric specimen exhibited more ductile load–displacement response. The eccentric specimens (with different eccentricities and edge-beam widths) underwent similar behaviour before they started to break down, and they also reached similar joint shear strengths. Slab participation was evaluated using slab bar strain gauge data with respect to storey drift. Actual effective slab widths were much larger than the ones typically used in design, especially for the specimens with a column wider than the edge-beams. Finally, floor slabs imposed significant joint shear demand, but they also increased joint shear capacity by expanding effective joint width.

Reinforced concrete edge beam?column?slab connections subjected to earthquake loading

Four two-thirds-scale reinforced concrete edge beam–column–slab subassemblies (two concentric and two eccentric connections) were tested under quasi-static cyclic lateral loading. Each subassembly represented a cruciform connection in an exterior moment-resisting frame with a monolithic floor slab on one side only, loaded in the longitudinal direction of the edge-beams. The tests explored the effect of eccentricity between beam and column centrelines, and the effect of floor slabs, on the structural performance of edge beam–column–slab connections subjected to earthquake loading. Performance of the specimens was evaluated in terms of overall strength and stiffness, energy dissipation, beam plastic hinge development, joint shear deformation, and joint shear strength. All specimens underwent some beam hinging at the beam/column interfaces. However, both eccentric specimens, and one concentric specimen with a heavily reinforced floor slab, eventually failed as a result of joint shear, whereas the other concentric specimen exhibited more ductile load–displacement response. The eccentric specimens (with different eccentricities and edge-beam widths) underwent similar behaviour before they started to break down, and they also reached similar joint shear strengths. Slab participation was evaluated using slab bar strain gauge data with respect to storey drift. Actual effective slab widths were much larger than the ones typically used in design, especially for the specimens with a column wider than the edge-beams. Finally, floor slabs imposed significant joint shear demand, but they also increased joint shear capacity by expanding effective joint width.

Displacement Based Seismic Assessment ForRetrofitting R.C. Structures

The main object of this investigation was to develop a pushover analysis procedure for an existing building in order to define the expected seismic performance and to verify a proposed mathematical equation that calculated the plastic hinge rotations in order to simulate the inelastic behaviour of the building. A series of tests have taken place in the past on the building in question. Based on the results, a critical comparison of the local and global response between the pushover analysis and the experimental data has been made. The analysis results include a clear view of the seismic behaviour, the mechanism of development of plastic hinges, the members and storeys with the maximum vulnerability and the development of the inelastic dissipation mechanism. This paper shows that, during a moderate earthquake, the pushover analysis gives satisfactory results for the global as well as the local response. This paper also shows that, during an intense earthquake, the pushover analysis result only approaches the lower level the experimental local response.

“Seismic Behavior of Dual Systems with Column Hinging”

This paper, presenting interesting and valuable findings, represents a significant contribution to earthquake engineering. The demonstration of the advantages of the expected ductile response of reinforced concrete dual systems will be particularly appreciated by design practitioners. Instead of offering critical comments, this discussion attempts to illustrate similarities with recently suggested displacement-oriented design strategies, particularly applicable to dual systems. The authors advocate relaxations of perceived restrictions of capacity design and propose more extensive admission of the development of plastic hinges in columns of multistory frames, provided that adequate safeguards exist with respect to potential developments of so-called soft stories. A brief review of the aims of ‘‘capacity design,’’ developed some 30 years ago in New Zealand (Park and Paulay 1975, Paulay and Priestley 1992), may assist in clarifying its relationship to the attractive solutions proposed by the authors. The aim of capacity design was to ensure that the functioning of the energydissipating mechanism, chosen for a ductile structural system by the designer, will be preserved. This necessitates a very clearly defined hierarchy of the strengths of components of kinematically admissible mechanisms. It is emphasized that a viable ductile mechanism must be chosen first. Capacity design enables then special detailing to be provided for potential plastic regions, while standard detailing practice may be used for the remainder of the structure, which, by the assignment of excess strength to it, will be protected against inelastic deformation demands. For good reasons clearly enumerated by the authors for multistory frames, resisting forces generated by earthquake-induced displacements, a strong-column/weak-beam system should be chosen. Once the locations of the potential plastic hinges are chosen, capacity design procedures may then be used to ensure that all other components, intended to remain elastic, will have strength in excess of the maximum expected strengths of the ductile components. Capacity design does not influence the choice of the ductile mechanism. If the designer feels that it is justified to choose a frame system in which

Reinforced Concrete Wide-Beam Construction vs. Conventional Construction: Resistance to Lateral Earthquake Loads

Experiments and analyses were conducted to address concerns about performance of reinforced concrete connections with shallow, wide beams subjected to lateral earthquake loading and to compare behavior of wide beam connections to that of conventional connections. Two wide beam-column-slab connections and one conventional beam-column-slab connection were subjected to cycles of reversing lateral displacements up to 5% drift. The conventional beam and wide beam connections exhibited similar overall load-displacement behavior, with similar beam plastic hinge development. The wide beam connections dissipated almost as much energy as the conventional beam connection and had greater slab participation and less joint and beam shear cracking than the conventional beam connection. Experimentally determined wide beam connection stiffness was closer to the conventional beam connection stiffness than had been predicted. Refined models were developed, with features such as rigid end offsets for wide beam connections, to better represent observed behavior. Nonlinear models were also developed that accurately captured differences in energy dissipation as well as stiffness.

Plastic hinges development and crack stability analysis in a circular ring

Abstract The primary purpose of this work is to demonstrate that the location of a crack can strongly affect the sequence of plastic hinge development which in turn affects crack stability of a structure. A specific example of an elastic–plastic ring loaded with diametrically opposite concentrated loads is employed to investigate these effects. The method used is based on elastic superposition to obtain the elastic–plastic behavior and to evaluate the crack stability with plastic hinges present.

General report on local ductility

A series of factors contributes to the poor local ductility of steel structures, which was observed during recent earthquakes in the USA and Japan. These factors are explained. The factors on the resistance side are the discrepancies between real and design yield stress, the value of through thickness resistance of steel, the need for requirements on toughness of the base and weld material and the effect of strain rate. On the action effect side, other factors contributed to a bad ductility: the past underestimates of needed plastic rotations, the existence of 3D stress states created in welded connections of high beams, the consideration of wrong stress distributions in beam ends, a bad design of connections and the influence of the composite character of beams. The recent trends aiming at an improved local ductility are explained. They consist in forcing the development of plastic hinges in beams of moment frames to take place away from the columns, by either a connection strengthening or a beam weakening. Qualified connections are being developed. The other connections should go through a severe qualification process. However, future research work could relax this request by developing explicit requirements on the connections themselves.

Experimental evaluation of the strain field history during plastic progressive folding of aluminium circular tubes

The axisymmetric collapse by plastic progressive folding of a circular tube submitted to axial loading is considered by an experimental approach. The strain field history is measured by means of electric strain gages properly placed on the external surface of the tube so that more than one fold is covered and both axial and circumferential strains are measured. The measured strains are examined both as time-histories and as a deformation field. The formation and development of circumferential plastic hinges are pointed out. The strain histories, reported as a function of the displacement of the testing machine cross-head, are then correlated with the crushing force diagram, leading to a better understanding of the folding mechanics. In particular, the formation of each fold develops through three subsequent phases: the initialization at the closure of the previous fold, the flattening of the upper conical surface, and the flattening of the lower conical surface. While most of the tube wall is pushed outwards of the original cylindrical surface, a portion is pushed inwards of that surface. Moreover, there is a small portion of the wall that is pulled inward during the fold initialization and then pushed outward during the fold closure. The analysis of these histories lead to the validation of the basic assumption of our and other recent kinematical models of the plastic progressive folding.

SIMPLE PUSH-OVER ANALYSIS OF ASYMMETRIC BUILDINGS

A simple method for the non-linear static analysis of complex building structures subjected to monotonically increasing horizontal loading (push-over analysis) is presented. The method is designed to be a part of new methodologies for the seismic design and evaluation of structures. It is based on the extension of a pseudo-three-dimensional mathematical model of a building structure into the non-linear range. The structure consists of planar macroelements. For each planar macroelement, a simple bilinear or multilinear base shear%top displacement relationship is assumed. By a step-by-step analysis an approximate relationship between the global base shear and top displacement is computed. During the analysis the development of plastic hinges throughout the building can be monitored. The method has been implemented into a prototype computer program. In the paper the mathematical model, the base shear%top displacement relationships for different types of macroelements, and the step-by-step computational procedure are described. The method has been applied for the analysis of a symmetric and an asymmetric variant of a seven-storey reinforced concrete frame-wall building, as well as for the analysis of a complex asymmetric 21-storey reinforced concrete wall building. The influence of torsion on structural behaviour is discussed.

The tay bridge disaster—Faulty materials or faulty design?

The first railway bridge over the Firth of Tay in Scotland entered service in May 1878. With a total length of 2 miles it was the longest iron bridge in the world. Over most of the crossing the single-track line ran above lattice-work spans made from wrought iron. However, over the central section of the bridge, the track ran inside the lattice-work spans. This central section (called the “High Girders”) consisted of thirteen spans (eleven of 245 feet and two of 227 feet). In order to allow shipping to pass beneath the bridge there was a clearance of 90 feet between the High Girders and the high-water mark. The High Girders were supported on latticework columns 77 feet high which were bolted to sandstone foundations. Each column consisted of a set of six vertical cast-iron pipes which were braced together by bars of wrought iron. On 28 December 1879 the High Girders were blown into the Tay while a train was passing through them, drowning 75 people. An analysis of the collapse leads to the conclusion that the combined wind loading on the train and the High Girders was sufficient to make the latticework columns fail in shear. The probable wind speed at the instant of collapse was estimated by finding the wind pressure which would have been needed to bring the lightest vehicle in the train (a wooden four-wheeled carriage) to the point of overturning. By following the methods set out in BS 5400 (the British Standard code for bridge design) it was possible to show that the lateral wind force acting at the top of a single column was approximately 60 tons. The shear strength of the column was then found by postulating a plastic collapse mechanism. This involved the gross yielding of the diagonal ties and the development of plastic hinges at the ends of the cast-iron pipes. The model gave a collapse load of ≈163 tons. Experiments performed for the original Court of Inquiry found that the cast-iron housings which held the ends of the bracing bars failed at ≈24 tons. In theory, the housings should have been capable of taking ≈200 tons. Evidence given to the enquiry indicated that the quality of the castings was often poor, and housings were sometimes in a cracked condition when they left the foundry. By comparison, a tie would have yielded at ≈52 tons. Accordingly, the column could not shakedown plastically and behaved as an elastic-brittle structure instead. This gives a collapse load which is nearer to 50 tons, and explains why the columns failed. The suprising conclusion is that, if the ties had been made significantly weaker (with a yield load of less than 24 tons), the structure would have shaken down before the cast-iron lugs could have snapped and the bridge might have survived.

Tests on RC Continuous Beams with Openings

An experimental investigation is carried out on eight reinforced‐concrete continuous beams, each containing a large transverse opening. The beams are rectangular in cross section and all contain the same amount and arrangement of longitudinal reinforcement. The number of spans, the size of opening, and its location along the span are considered as major variables. Detailed results of these tests are presented and discussed in this paper. Test results indicate four distinctly different stages of behavior in the load‐deflection curve of a continuous beam. Final failure of the beam occurs by the formation of a mechanism, and the two opening ends represent the most vulnerable locations for the development of plastic hinges. Besides early cracking, the strength and stiffness of the beam decrease with an increase either in the length or depth of opening. Similarly, openings located in a high moment region produce larger deflections and result in early collapse of the beam.

Size effects in material strength due to crack growth and material non-linearity

Failure by strength and fracture collapse tend to compete with one another when the specimen sizes are varied. Material testing dealing with the determination of tensile strength and hardening is usually carried out with small specimens while the evaluation of fracture mechanics parameters such as critical stress-intensity factor or strain energy density factor requires specimens that are larger in size. The formation of cracks in small specimens does not appreciably affect failure by strength collapse. On the other hand, the fracture process is not disturbed by the development of plastic hinges in the unbroken ligament of the larger specimens.

Seismic Behavior of Moment Connections and Joints

The behavior of moment connections and beam-column joints in moment resisting steel frames subjected to severe earthquakes is studied. The cyclic inelastic deformation capacities of different types of connections are discussed and design recommendations are presented that are intended to assure the development of plastic hinges in beams at the column faces. A conceptual approach to the prediction of the low cycle fatigue life of welded connections under random loading is outlined, utilizing concepts of elastic-plastic fracture mechanics. The shear behavior of beam-column joints subjected to large cyclic beam moment reversals is summarized. Based on experimental evidence and a simplified mathematical model for shear strength, a method for the shear design of joints is proposed that should permit a reduction in the demand for shear stiffeners in joints.

Pressure-Distribution Measurements in Rotary Forging

Experiments on the rotary forging of discs are described in which measurements are taken of pressure distribution under the rocking die using a pressure-sensing platen. The results suggest a deformation mechanism for the spread of the disc, involving the development of plastic hinges away from the immediate die contact area. This would explain central tensile failures and related phenomena observed previously.