Shear and Torsion Design of Prestressed and Non-Prestressed Concrete Beams

Collins, Michael P.; Mitchell, Denis

doi:10.15554/pcij.09011980.32.100

Cited by 152 publications

(114 citation statements)

References 6 publications

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“…Thürlimann and Lüchinger [151] used a space truss model similar to Kupfer's approach to compute the deformations of beams subjected to torsion and flexure. While Kupfer's and Baumann's work constitutes a linear compression field approach, Collins and Mitchell independently developed a similar, non-linear approach for torsion [103] and shear [27] problems and presented a comprehensive paper on the analysis and the design of prestressed and non-prestressed concrete beams subjected to combined actions [29]. Starting from the observation that the behaviour of webs of concrete girders without tensile strength is similar to the post-buckling behaviour of thin-webbed metal girders in shear [160], they obtained the condition for the inclination of the compression diagonals with respect to the x-axis.…”

Section: Original Compression Field Approachesmentioning

confidence: 99%

Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces

Kaufmann¹

1998

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PrefaceThe present doctoral thesis was developed within the framework of the research project "Deformation Capacity of Structural Concrete". This project aims at developing a consistent and experimentally verified theory of the deformation capacity of structural concrete. Previous work included the development of a theoretical model, the so-called Tension Chord Model, which allows a comprehensive description of the load-deformation behaviour of tension members in non-prestressed and prestressed concrete structures.The present work focuses on a new theoretical model, the so-called Cracked Membrane Model. For members subjected to in-plane forces this new model combines the basic concepts of the modified compression field theory and the tension chord model. Crack spacings and tension stiffening effects in cracked membranes are determined from first principles and the link to plasticity theory methods is maintained since equilibrium conditions are formulated in terms of stresses at the cracks rather than average stresses between the cracks.The research project "Deformation Capacity of Structural Concrete" has been funded by the Swiss National Science Foundation and the Association of the Swiss Cement Producers. This support is gratefully acknowledged. Zurich, July 1998Prof. Dr. Peter Marti AbstractThis thesis aims at contributing to a better understanding of the load-carrying and deformational behaviour of structural concrete subjected to in-plane shear and normal forces. Simple, consistent physical models reflecting the influences of the governing parameters are developed on whose basis (i) a realistic assessment of the deformation capacity of structural concrete subjected to in-plane loading is possible, (ii) the limits of applicability of the theory of plasticity to structural concrete can be explored, and (iii) current design provisions can be critically reviewed, supplemented and harmonised.In the first part of this thesis relevant properties of concrete and reinforcement are examined, basic aspects of the theory of plasticity and its application to structural concrete are summarised, previous work on plane stress in structural concrete is reviewed, and fundamental aspects of the behaviour of cracked concrete membranes are investigated.In the second part a new model for cracked, orthogonally reinforced concrete panels subjected to a homogeneous state of plane stress is presented. The cracked membrane model combines the basic concepts of original compression field approaches and a recently developed tension chord model. Crack spacings and tensile stresses between the cracks are determined from first principles and the link to limit analysis methods is maintained since equilibrium conditions are expressed in terms of stresses at the cracks rather than average stresses between the cracks. Both a general numerical method and an approximate analytical solution are derived and the results are compared with previous theoretical and experimental work. Simple expressions for the ultimate load of reinforced concrete pane...

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Section: Original Compression Field Approachesmentioning

confidence: 99%

Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces

Kaufmann¹

1998

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“…Rather we adopt the method introduced into the truss model by Collins (1978) in his compression field theory, in which he used the compatibility condition for the average strains in the truss in a similar way as Wagner (1929) used the compatibility condition for approximate analysis of the shear buckling of the webs of steel beams (Collins and Mitchell 1981). The average strains of the truss are defined as the strains of a homogeneously deforming continuum that is attached to the joints of the truss at the nodes (tops and bottoms of the stirrups).…”

Section: Beam With Stirrupsmentioning

confidence: 99%

“…[For the precise method in which the strains entering (18) are calculated, see Collins (1978) and Collins and Mitchell (1981)]. The foregoing calculation, of course, requires that the diagonal cracks and the struts be aligned with the direction of the compressive principal strain, which coincides with the direction of the compressive principal stress.…”

Section: Beam With Stirrupsmentioning

confidence: 99%

Fracturing Truss Model: Size Effect in Shear Failure of Reinforced Concrete

Bažant

1997

J. Eng. Mech.

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The classical truss model (or strut-and-tie model) for shear failure of reinforced concrete beams is modified to describe fracture phenomena during failure. The failure is assumed to be caused by propagation of a compression fracture across the concrete strut during the portion of the loading history in which the maximum load is reached. The compression fracture may consist of a band of splitting cracks that later interconnect to form a shear crack or a shear fracture band inclined to the strut. The width of the fracture band is assumed to occupy only a portion of the strut length and to represent a fixed material property independent of the beam depth. The energy release from the truss is calculated using two alternative approximate methods: (1) using the potential energy change deduced from the concept of stress relief zones; and (2) using the complementary energy change due to stress redistribution caused by propagation of the fracture band across the compressed concrete strut. Both approaches show that a size effect on the nominal strength of shear failure must exist and that it should approximately follow the size effect law proposed by BaZant in 1984. The physical mechanism of the size effect is also explained in a clear and simple intuitive manner. Finally, it is shown that the applied nominal shear stress that causes large initial diagonal cracks to form also exhibits a size effect.

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“…Çelik için gerilme-birim şekil değiştirme ilişkisi, pekleşme de göz önüne alınarak, üç parçalı doğrusal eğri olarak varsayılmıştır. Kirişlerin kesit analizleri, kesitin katmanlara bölünerek betonda varsayılan bir maksimum basma birim şekil değiştirmesine (ε cc ) denk gelen moment ve eğriliğin kuvvetlerin dengesinden hesaplanması ve bu varsayılan ε cc değerinin -0,010'a kadar geniş bir aralıkta değiştirilerek moment-eğrilik ilişkisinin tamamının elde edilmesi suretiyle yapılmıştır [16]. Elde edilen moment-eğrilik davranışı Şekil 7'de verilmektedir.…”

Section: Sonuçlar Ve Tartişmalar (Results and Discussion)unclassified

Çelik fiber katkılı etriyesiz betonarme kirişlerin davranışı

Saatcı¹,

Batarlar²

2017

Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi

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In this study, effects of steel fibers on the bending behavior of reinforced concrete beams of varying longitudinal reinforcement ratios and without stirrups are investigated experimentally and analytically. In the experimental work, two groups of simply supported beams of low and high longitudinal reinforcement ratio were manufactured. Each group had 0%, 0.5%, 1.0% and 1.5% steel fiber ratio in volume. Eight beams were tested under a load applied at midspan. In the group with lower longitudinal reinforcement ratio, steel fibers increased the bending capacity by almost 50%. However, since deformations were concentrated on a single crack, longitudinal reinforcement has ruptured and the beams could not displace as much compared to the one without steel fibers. In the group with higher longitudinal reinforcement ratio, steel fibers acted like stirrups and changed the brittle shear failure mode to a ductile bending failure. Although increasing the steel fiber ratio affected crack distributions, it did not cause a significant difference in the behavior. When analytically modeled using a common model that assume constant tensile stress at crack, computed bending capacities were lower than actual, although on the safe side. More precise models that relate tensile stresses to the crack width could give better estimations.

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Shear and Torsion Design of Prestressed and Non-Prestressed Concrete Beams

Abstract: PCI JOURNAUSeptember-October 1 9e0 'For SI units f, shall he taken as 0.85 for strengths fi LIP to 30 MPa and shall be reduced continuously at a rate of 0.08 for each 10 MPa of strength in excess of 30 MPa but ,B, shall not be taken less than 0.65.

Cited by 152 publications

References 6 publications

Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces

Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces

Fracturing Truss Model: Size Effect in Shear Failure of Reinforced Concrete

Çelik fiber katkılı etriyesiz betonarme kirişlerin davranışı

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