Validation of a Shear Model for RC and Hybrid Beams with Two Different Inclinations of Transversal Reinforcement

The validation of an analytical model recently proposed for evaluation of the shear capacity in Reinforced Concrete (RC) beams containing multiple inclination of transverse stirrups is presented. The model is a suitable extension of that currently proposed in Eurocode 2 for the evaluation of the shear resistance, and it is derived by means of the the variable-inclination stress-field theory based on Nielsen’s plastic approach. Experimental and numerical data available in the literature on Hybrid Steel-Trussed Concrete Beams (HSTCBs) are used for model validation and result discussion. Finally, also the comparison with a different analytical approach for the assessment of the shear resistanc…

Interaction between Longitudinal Shear and Transverse Bending in Prestressed Concrete Box Girders

In box girder bridges, the quantity and distribution of reinforcement to be put in concrete elements of sections can be evaluated only by considering the deformation of the cross section in addition to the longitudinal analysis of the static scheme, establishing the entire state of stress of box sections. This leads to a need to evaluate the interaction between internal forces obtained by the global analysis and the ones obtained by the local analysis of the cross sections. The frame effect implies the elastic deformation of slabs and webs, whereas eccentrically applied loads lead to cross-section distortion with the loss of the box shape. Hence, the reinforcement is strongly influenced by …

Stress field model for strengthening of shear-flexure critical RC beams

A model for the design of shear-flexure critical reinforced concrete elements strengthened with fiber-reinforced polymer (FRP) sheets and plates is presented. The model is based on the stress field approach and the equilibrium method and accounts for the different failure modes of FRP, focusing on the debonding of the FRP from the concrete surface. The efficiency of the model in the strength assessment of beams reinforced with FRP by the prediction of the shear-flexure capacity is checked by corroborating the results of several experimental tests found in the literature. Moreover, the presented model's capacity to reproduce experimental behavior is compared with the formulations suggested b…

SHEAR STRENGTH DEGRADATION DUE TO FLEXURAL DUCTILITY DEMAND IN R.C. ELEMENTS

A proposal is formulated that allows to evaluate the residual shear strength of reinforced concrete columns and beams for an assigned flexural ductility demand by limiting the range of the deviation angle between the inclinations of the yield  and the crack lines. In order to take into account the degradation due to cyclic loads, the reduction of the range of the deviation angle is related to the value of cinematic ductility

Bending-Shear interaction domains for externally prestressed concrete girders

In prestressed concrete structures, the evaluation of the safety level is generally carried out by separating the bending moment strength and the shear force capacity. Actually interaction between bending moment (M) and shear force (V) can have significant consequences on evaluations in service life, especially when the ultimate limit state (ULS) is considered. In this paper, the M-V interaction is addressed for prestressed concrete girders, in the cases of both bonded and unbonded prestressing tendons. It can be demonstrated, by drawing the interaction domains (M-V), that a significant reduction of the safety level has to be considered when shear force is evaluated together with bending mo…

RESISTENZA A TAGLIO DI TRAVI CON ARMATURE TRASVERSALI A DIVERSA INCLINAZIONE

Il modello per la valutazione del taglio resistente di elementi in c.a. dotati di staffe adottato dalle recenti Norme Tecniche per le Costruzioni, basato sul modello di Nielsen a campi di tensione ad inclinazione variabile, viene qui esteso per potere modellare il comportamento di travi dotate di due ordini di armature trasversali disposte secondo due diverse giaciture, ed eventualmente anche di armatura longitudinale di parete. Vengono poi presentati i risultati di una indagine numerica condotta con il modello proposto, finalizzata ad evidenziare la disposizione più efficace del secondo ordine di armatura trasversale nel conferire resistenza alle travi.

Concrete arch bridges built by lattice cantilevers

In this paper a study about concrete arch bridges built by lattice cantilevers is presented. Lattice cantilevers are partial structures composed of deck, arch, piers and provisional steel diagonals, organized as reticular cantilever girders, in order to build arch bridges without the use of centrings, supports or temporary towers. Characteristics of this construction methodology with its variants are explained together with their implications in the erection sequence. Partial elastic scheme method is implemented in order to find initial forces of temporary cables and a forward analysis is carried out to follow the actual sequence of construction, by extending a procedure already applied to …

Design procedure for prestressed concrete beams

Abstract. The theoretical basis and the main results of a design procedure, which attempts to provide the optimal layout of ordinary reinforcement in prestressed concrete beams, subjected to bending moment and shear force are presented. The difficulties encountered in simulating the actual behaviour of prestressed concrete beam in presence of coupled forces bending moment - shear force are discussed; particular emphasis is put on plastic models and stress fields approaches. A unified model for reinforced and prestressed concrete beams under axial force - bending moment - shear force interaction is provided. This analytical model is validated against both experimental results collected in li…

Partial Elastic Scheme Method in Cantilever Construction of Concrete Arch Bridges

AbstractIn this paper, a study about stay stressing procedures of concrete arch bridges built by cantilevering with temporary stays is presented. Particularly, the partial elastic scheme method is proposed to find the initial cable forces, and a forward procedure is implemented to follow the actual sequence of construction by extending a procedure already applied to concrete cable–stayed bridges. The theoretical treatment is followed by a numerical application on a case study of a concrete arch bridge, and a comparison between initial cable forces found by the partial elastic scheme method and classical backward analysis is presented here. Results show the effectiveness of the proposed proc…

Influence of axial force and corrosion on failure of prestressed concrete structures considering M-V interaction

Abstract Existing prestressed concrete structures suffer from degradation of prestressing for two main reasons: a defect of the sheath infills (cement grout) of bonded tendons, and corrosion of steel strands. These two causes, often concomitant, lead to a reduction over time of the effectiveness of initial prestressing, in addition to the ordinary tension losses due to concrete shrinkage and creep, and to steel relaxation. In many cases a consequence of bad grouting in bonded tendons is that the structure shows an intermediate behavior between that of external prestressing and that of internal bonded prestressing. This, added to damage to wires due to corrosion, makes it essential for the d…

Evaluation of web reinforcements in prestressed concrete box girders through shear-transverse bending domains

In concrete box girders, the amount and distribution of reinforcements in the webs have to be estimated considering the local effects due to eccentric external loads and cross-sectional distortion and not only the global effect due to the resultant forces of a longitudinal analysis: shear, torsion and bending. This work presents an analytical model that allows designers to take into account the interaction of all these effects, global and local, for the determination of the reinforcements. The model is based on the theory of stress fields and it has been compared to a 3D finite element analysis, in order to validate the interaction domains. The results show how the proposed analytical mode…

Increasing the shear capacity of reinforced concrete beams using pretensioned stainless steel ribbons

In this work, the second part of an experimental campaign investigating the efficiency of an alternative retrofitting method for increasing the flexural and/or shear capacity in reinforced concrete beams, based on the use of prestressed stainless steel ribbons and steel angles, is presented and analytically reproduced. This group of tests focuses on the ability of the adopted retrofitting method to improve the shear strength and ultimate deformation of reinforced concrete structural elements. As described in a companion paper, the adopted retrofitting method is alternative to traditional techniques of reinforced concrete retrofitting, being easy to install and usually reversible, and charac…

Increasing the Capacity of Existing Bridges by Using Unbonded Prestressing Technology: A Case Study

External posttensioning or unbonded prestressing was found to be a powerful tool for retrofitting and for increasing the life extension of existing structures. Since the 1950s, this technique of reinforcement was applied with success to bridge structures in many countries, and was found to provide an efficient and economic solution for a wide range of bridge types and conditions. Unbonded prestressing is defined as a system in which the post-tensioning tendons or bars are located outside the concrete cross-section and the prestressing forces are transmitted to the girder through the end anchorages, deviators, or saddles. In response to the demand for a faster and more efficient transportati…

The influence of time-dependent phenomena in segmental construction of concrete cable-stayed bridges

Construction stages of a cable-stayed bridge are characterized by a sequence in which geometric configuration, restraints and consequently stress and strain patterns vary many times till the final arrangement is achieved. When construction of concrete bridges is made by cantilever method the influence of time-dependent phenomena becomes significant. In this study an evaluation of stay stressing procedures is given by taking into account creep and shrinkage in cantilever construction of concrete cable-stayed bridges. A methodology of stay stressing is proposed with the final target of reaching the desired geometric configuration. Comparison with classical analyses performed by backward metho…

Experimental results of RC columns strengthnened with Fiber Reinforced Cementitious Mortars

The structural behaviour of reinforced concrete columns strengthened with a system made up of fibre nets embedded in an inorganic stabilized cementitious matrix was investigated. Specimens with circular and square cross-section were cast and subjected to monotonic uniaxial compression to investigate the efficiency of a Polypara-phenylene-benzo-bisthiazole (PBO) Fibre Reinforced Cementitious Mortars (FRCM) system in increasing both carrying capacity and ductility. The experimental results show that confinement with PBO fibre produced a noticeable increment in strength and ductility, though the low mechanical ratios of fibre considered were not always able to ensure hardening behaviour up to …

Simple Plastic Model for Shear Critical SFRC Beams

A simple physical model, for prediction of ultimate shear strength of steel fiber reinforced concrete (SFRC) beams is developed on the basis of a plastic approach originally proposed for reinforced concrete (RC) beams without stirrups. It is founded on the hypothesis that cracks can be transformed into yield lines, and thus is know as Crack Sliding Model (CSM). First, the CSM is improved in order to take into account the shear strength increase for deep beams, due to the arch effect. Then, the effectiveness factors for fibrous concrete under biaxial stresses are evaluated, taking into account the post-cracking tensile strength of SFRC and its ability to control slippage along shear cracks. …

A Mixed Approach for Determination of Initial Cable Forces in Cable-Stayed Bridges and the Parameters Variability

The determination of initial cable forces in cable-stayed bridges is an important first step in design and analysis of the structure under external loads. Adjustments of stay forces are often required during construction in order to assure the requested behaviour of the bridge in terms of final geometrical configuration and internal force distribution. An accurate assessment of the stay tensioning system allows designers to obtain a good result at the end of construction, by considering the parameters involved as deterministic quantities, assuring the observance of the execution tolerances during works. Actual loads and their variations need instead a stochastic approach which can give usef…

Experimental test results vs. analytical prediction of welded joint strength in hybrid steel trussed concrete beams (HSTCBs)

The aim of the paper is to provide practical guidelines for the design of welded joints of steel truss for encased composite steel–concrete beams. The results of experimental tests are presented and interpreted. The steel truss is made of a steel plate acting as the bottom chord, made of S355 structural steel, coupled with steel rebars which form the upper chord, and steel inclined web rebars (V-reverse) welded to the two chord elements, both of them made of steel B450C. Butt welded joints of web bar to bottom steel plate and fillet welding joints of inclined web bars to top chord bars were tested, as they are different from the ones which are normally used due to the coupling of different …

Assessment and strengthening of reinforced concrete bridges with half-joint deterioration

Existing Niagara-type concrete cantilever bridges, which in Italy are called Gerber bridges, suffer from degradation due to reinforcement corrosion and a consequent reduced load-bearing capacity. The assessment of these structures is therefore an important part of the procedures for analyzing the state of existing bridges and any interventions required for their retrofitting. In particular, safety against failure of the half-joint must be evaluated with respect to the behavior of the entire bridge and its state of conservation, determining what the conditions are that lead to failure, in terms of loads, state of stress, and possibly cracking state. This evaluation has to be carried out cons…

Increasing the flexural capacity of RC beams using steel angles and pre-tensioned stainless steel ribbons

This article presents an experimental programme on reinforced concrete beams retrofitted with steel angles and pre-stressed stainless steel ribbons to increase their flexural strength and ductility. Two different configurations of the steel ribbon were designed, and two companion specimens for each type considered were subjected to a four-point bending test to facilitate a direct comparison in the analysis of the effectiveness of the retrofitting technique. The influence of longitudinal steel angles and transverse stainless steel ribbons is analysed, and the concrete confinement due to stainless steel ribbons examined. The strengthened beams show remarkable increments in flexural strength a…

Concrete columns confined with fibre reinforced cementitious mortars: Experimentation and modelling

Abstract The structural behaviour of concrete columns strengthened with a system made up of fibre nets embedded in an inorganic stabilized cementitious matrix under an uniaxial load was investigated. Medium size specimens with circular and square cross-section were cast and subjected to monotonic uniaxial compression, to investigate the efficiency of a p-Phenylene BenzobisOxazole (PBO) Fibre Reinforced Cementitious Mortar (FRCM) system in increasing both strength and ductility. The experimental results show that the confinement system adopted produced a noticeable increment in strength and ductility, though the low mechanical ratios of fibre considered were not always able to ensure hardeni…

ELEMENTI IN CALCESTRUZZO CONFINATI CON FRCM ANALISI SPERIMENTALE PER CARICHI MONOTONICI

Vengono presentati i risultati di prove sperimentali su provini di calcestruzzo rinforzati con fibre di materiale composito, soggetti a compressione monotonica fino alla rottura. In particolare si è sperimentato l’impiego degli FRCM (Fiber Reinforced Cementitiuos Matrix), in cui le fibre di rinforzo sono immerse in una matrice cementizia. I risultati ottenuti dimostrano che il confinamento eseguito con questi materiali conferisce agli elementi di calcestruzzo un significativo aumento di capacità portante e di duttilità, sebbene le percentuali di fibra impiegate non abbiano consentito di ottenere comportamenti costantemente incrudenti fino a rottura. In particolare le curve tensione-deformaz…

Recenti sviluppi nei metodi di analisi strutturale per la valutazione della vulnerabilità sismica degli edifici

Construction stages of cable-stayed bridges with composite deck

A cable-stayed bridge is built by following a construction sequence of different subsequent stages that imply changes of the geometric configuration, restraints and consequently stress and strain patterns. A study is presented about stay stressing sequences in cable-stayed bridges with composite deck for the case of construction made by the cantilever method. Initial cable forces are found through partial elastic schemes of construction stages. Different stay stressing procedures are implemented and a comparison between them is proposed in order to evaluate the differences in terms of deformed shape and internal force distribution of the deck and the pylon. Results can be useful to give pra…

Failure by corrosion in PC bridges: A case history of a viaduct in Italy

Purpose The paper illustrates a viaduct collapse due to corrosion phenomena. Moreover, a contribution to the issues related to both the control of existing structures and design methods to be followed for the construction of new buildings is provided. Design/methodology/approach The objectives were achieved by in situ observations and numerical analyses. The effects of corrosion phenomena are investigated, and the progressive collapse analysis is provided to be helpful in this case. Findings The damages induced by corrosion phenomena have caused the collapse of the viaduct taken in to account. The performed numerical analyses were able to reproduce the effects of corrosion in terms of redu…

Generalization of Shear Truss Model to the Case of SFRC Beams with Stirrups

A theoretical model for shear strength evaluation of fibrous concrete beams reinforced with stirrups is proposed. The formulation is founded on the theory of plasticity and the stress field concepts, generalizing a known plastic model for calculating the bearing capacity of reinforced concrete beams, to the case of fibrous concrete. The beneficial effect of steel fibres is estimated taking into account the residual tensile strength of fibrous concrete, by modifying an analytical constitutive law which presents a plastic plateau as a post-peak branch. Around fifty results of experimental tests carried out on steel fibrous concrete beams available in the literature were collected, and a compa…

Experimental in situ behaviour of unreinforced masonry elements retrofitted by pre-tensioned stainless steel ribbons

Abstract The results of in situ tests carried out on unreinforced and reinforced poor rubble masonry full-scale walls in the earthquake prone Messina (Italy) area are presented and discussed. This experimental research was aimed at the assessment of the in plane shear behaviour of ancient masonry strengthened with an innovative system for masonry and retrofitting of reinforced concrete element constituted by three-dimensional pre-tensioned stainless steel ribbons. A comparison between different strengthening configurations was made in order to characterise the behaviour of masonry panels under shear-compression load, focusing attention on the diagonal cracking failure mode. The effectivenes…

Prove sperimentali su travi in c.a. rinforzate con metodo CAM®: valutazione dei meccanismi di flessione (parte 2)

Nel presente contributo sono descritti e valutati criticamente i risultati discendenti da un lavoro finalizzato allo studio del comportamento di travi in calcestruzzo armato (c.a.) rinforzate mediante il sistema CAM. Il lavoro è inserito nell’ambito del progetto di ricerca “In.CAM.M.I.N.O”, acronimo di “INnovazione del CAM Mediante Impiego di Nuove Opzioni di processo”, che ha visto coinvolte l’Università degli Studi di Messina, CHIMETEC S.a.s. e ABI S.r.l. di Ragusa. In particolare sono stati studiati il comportamento, l’evoluzione del danneggiamento ed i possibili meccanismi di rot- tura di quindici travi in c.a. in scala reale rinforzate mediante un sistema di nastri in acciaio di spesso…

Validation of a Shear Model for RC and Hybrid Beams with Two Different Inclinations of Transversal Reinforcement

The validation of an analytical model recently proposed for evaluation of the shear capacity in Reinforced Concrete (RC) beams containing multiple inclination of transverse stirrups is presented. The model is a suitable extension of that currently proposed in Eurocode 2 for the evaluation of the shear resistance, and it is derived by means of the the variable-inclination stressfield theory based on Nielsen’s plastic approach. Experimental and numerical data available in the literature on Hybrid Steel-Trussed Concrete Beams (HSTCBs) are used for model validation and result discussion. Finally, also the comparison with a different analytical approach for the assessment of the shear resistance…

Serviceability and Ultimate Safety Checks of SegmentalConcrete Bridges through N-M and M-V Interaction Domains

In current engineering practice, safety checks on serviceability and determinations of ultimate limit states of segmental bridges built by cantilevering are generally performed, either considering separately the contributions of axial force N, bending moment M, and shear force V, or considering the interaction effects through approximate expressions supplied by building codes. During construction stages and service life, the interaction between internal forces can be of fundamental importance in establishing the actual degree of structural safety and, for this reason, a different philosophy for performing checks in segmental bridges is proposed in this paper, plotting N-M and M-V interactio…

Construction sequence analysis of long-span cable-stayed bridges

Abstract In cantilever construction of long-span cable-stayed bridges the stressing sequence of stays is fundamental for establishing the final configuration of the bridge. The structural behaviour of these bridges is usually evaluated through a forward staged construction analysis, in which the values of the prestressing forces to be applied to stays are the main unknowns. A unified procedure for determining the initial cable forces and for analyzing the entire sequence is presented here, considering the geometric nonlinearity of stays through the Dischinger equivalent elastic modulus. The target is the simultaneous determination of the initial cable forces with the simulation of the const…

Shear resistance analytical evaluation for RC beams with transverse reinforcement with two different inclinations

An analysis-oriented mechanical model for shear strength evaluation of Reinforced Concrete (RC) beams with transverse reinforcement with two different inclinations, which required a numerical analysis, is turned into a design-oriented analytical model that can easily be utilized for practical purposes. The model assessed the shear resistance, according to the “lower-bound solution”, employing a numerical procedure that maximizes the element shear strength varying the stresses in the two sets of transverse reinforcement and the magnitude and inclination of the web concrete compressive stress field. The model is formulated with the aim of representing an extension of Eurocode 2 framework to R…

Steel and composite tied-arch bridges: a conceptual approach to structural design

The behaviour of tied-arch bridges with composite decks (bowstring bridges) is overly sensitive to the different choices made by the designer in the first phases of the conceptual approach, mainly in the design of the arch and the deck. The geometry of the arch shape, the design of the arch–tie joint and the construction sequence can significantly modify the global behaviour in terms of stress state and deformed configuration. After a general discussion on the different parameters affecting the behaviour of bowstring bridges with steel–concrete composite decks, the consequences of choices made in the conceptual design phases are discussed, analysing the effects of each choice on the global…

Shear capacity in concrete beams reinforced by stirrups with two different inclinations

Abstract A model for the estimation of shear capacity in Reinforced Concrete (RC) beams with web reinforcement is provided by introducing a generalization of classical plastic Nielsen’s model, which is based on the variable-inclination stress-field approach. The proposed model is able to predict the shear capacity in RC beams reinforced by means of stirrups having two different inclinations and longitudinal web bars. A numerical comparison with the results of experimental tests and those provided by a Finite Element Model (FEM) based on the well known theory of Modified Compression Field Theory (MCFT) is carried out for validating the robustness of the proposed model. Finally, a set of para…

Ultimate Shear of RC Beams with Corroded Stirrups and Strengthened with FRP

Transverse reinforcement plays a key role in the response behavior of reinforced concrete beams. Therefore, corrosion of steel stirrups may change the failure mode of elements from bending to shear, leading to a brittle and catastrophic crisis. It is important to strengthen reinforced concrete beams with corroded stirrups to enhance the shear resistance. This paper presents a formulation, based on the modified compression field theory, to estimate the ultimate shear of reinforced concrete beams strengthened with FRP, because of stirrup corrosion. The detrimental effect of corrosion on steel stirrup yield strength was taken into account by introducing an empirical decay law. The effective st…

SHEAR RESISTANCE OF R/C BEAMS PROVIDED WITH DIFFERENTLY-INCLINED TRANSVERSE REINFORCEMENT

The model for the evaluation of shear resistance of reinforced concrete member provided with transverse web reinforcement, derived by Nielsen (1999) on the basis of the variable inclination stress field approach, is generalized here to predict the shear strength of r.c. beams equipped with two sets of differently-inclined transversal web reinforcement and longitudinal skin reinforcement. Numerical analyses emphasize the efficiency of double inclined web transverse reinforcement in providing shear strength to beams.

Push-Over Analysis of RC Frame with Corroded Rebar

Abstract As known, the Italian building heritage largely consists of reinforced concrete frames designed before the ‘80s, which are, in many cases, built in the absence of specific anti-seismic criteria. Moreover, many of them, today, are characterized by bad structural conditions. Moreover, the problem of the structural conditions of the existing buildings, and their residual strength capacity, is often linked to the deterioration induced by the corrosive phenomena, which end up having a big impact on steel rebar mechanical properties. In this work, in order to investigate the influence of corrosion-damage on seismic response of existing reinforced concrete structures, a study has been car…

Shear strength degradation due to flexural ductility demand in circular RC columns

An analytical model was developed to estimate the shear-strength degradation and the residual capacity of circular reinforced concrete (RC) columns subjected to seismic action. The proposed model is an upgrade of a previously proposed model for axial force $$N$$ , bending moment $$M$$ and shear force $$V$$ ( $$N$$ – $$M$$ – $$V$$ ) interaction domain evaluation for rectangular and circular cross-section RC elements subjected to static loading. The model was extended to the case of circular cross-sections subjected to seismic actions with limitation of the range of variability of the deviation angle between the directions of the stress fields and the crack inclinations, as a function of the …

Simplified Formulation of Solution for Beams on Winkler Foundation allowing Discontinuities due to Loads and Constraints

The paper discusses material for a course in Structural Mechanics addressed to second-Year Civil Engineering students. The response of beams on a Winkler foundation characterized by discontinuities in both the displacements (deflections and/or slopes) and forces (internal forces and/or loads) is studied. In particular, a simplified formulation for the solution of the discontinuous differential equation governing this problem is given. In some cases, the formulation is able to give the exact solution in a closed form. This is made possible through the use of the generalized functions, such as the well-known Unit Step Function and the Dirac delta function. The cases of discontinuities due to …

BEF Analogy for Concrete Box Girder Analysis of Bridges

<p>Box girder, due to its high torsional stiffness, is very appropriate for railway and highway long- medium span bridges. This type of cross section, subjected to transversely non-uniform loads, present warping and distortion phenomena. Accurate but time-consuming numerical procedures are available for determination of further strains and stresses caused by cross-section deformation. In this paper warping and distortion of box girders is evaluated through BEF analogy, by writing a 4th order differential equation. The problem is solved for practical cases of box girders by considering internal diaphragms stiffness. Graphs are supplied to designers and main design parameters affecting …