Shear Strength of Reinforced Concrete Beams under Uniformly Distributed Loads
TL;DR: In this article, an analytical theory for shear resistance of reinforced concrete beams subjected to uniformly distributed loads is presented, where the impact of size effect in the shear strength of slender beams is taken into account.
Abstract: This paper presents an analytical theory for shear resistance of reinforced concrete beams subjected to uniformly distributed loads. The authors examine slender beams with a span length-to-depth ratio (l/d) greater than 10 and deep beams in which l/d < 10. Simple expressions are derived for the ultimate shear capacity. The impact of size effect in the shear strength of slender beams is taken into account. A criterion for minimum shear reinforcement is also considered. The derived formulas are verified by comparisons to experimental data from the literature. Data were obtained on slender beams and deep beams with various strengths of concrete, longitudinal steel ratios, shear reinforcement ratios, l/d, and geometrical sizes. The shear strength of beams, both slender and deep, under a uniform load is found to be much higher than the shear strength of beams under a loading arrangement of two concentrated loads at the quarter points. The findings also demonstrate that ACI Code predictions for the ultimate shear force of beams under a uniform load are much lower for the cases of small beams and the predictions are higher for larger beams.
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TL;DR: In this article, a two-step numerical approach, which substantially reduces the modelling and computational effort in analysing structural responses to blast loads, was proposed, which solved the responses of the equivalent SDOF system of a structural component during the blast loading phase to obtain the structural displacement and velocity at the end of a blast loading duration.
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TL;DR: In this paper, the authors proposed a new approach to determine the shear capacity of reinforced concrete members without transverse reinforcement by taking into account the very small component of the normal stress of concrete in the tension zone, which is normally neglected when determining the bending capacity.
36 citations
DOI•
01 Jan 2017
TL;DR: In this paper, the experimental results of 23 tests on 20 beams without transverse reinforcement subjected to different loading (concentrated or distributed) and boundary conditions (cantilevers, simply supported or continuous beams) are presented.
Abstract: Since the first applications of structural concrete, the shear behaviour of one-way slabs without transverse reinforcement has been largely investigated. Nevertheless, currently in the scientific community there is no general agreement on the mechanisms of shear failure, on the parameters governing the shear strength and on the predominant shear-transfer actions. Hence, several mechanical models, based on very different hypotheses, and empirical formulations, calibrated on the available experimental results, have been proposed in the last decades. In addition, these experimental results have been traditionally obtained from tests on simply supported beams subjected to point load, whereas in most one-way slabs without transverse reinforcement in practice (foundations, retaining walls, slabs of cut-and-cover tunnels, silos) the boundary and loading conditions are typically different. This thesis has therefore the objective to provide new experimental data on reinforced concrete members without transverse reinforcement tested with different loading and boundary conditions, to increase the understanding on the mechanisms of shear failure and to develop a mechanical model based on the new experimental evidence. In the first part of the thesis, the experimental results of 23 tests on 20 beams without transverse reinforcement subjected to different loading (concentrated or distributed) and boundary conditions (cantilevers, simply supported or continuous beams) are presented. Refined measurement techniques allowed detailed tracking of the development of the crack pattern up to failure. The results show that the location, inclination and kinematics of the critical shear crack play a major role on the shear strength. Moreover, the amount of shear transferred by the various potential shear-transfer actions has been estimated on the basis of the experimental measurements and by using suitable mechanical models for each shear-transfer action. The analyses show that, for slender members, the shear-transfer actions contributing to the shear capacity are the inclination of the compression chord, the residual tensile strength of concrete, the dowelling action and the aggregate interlock, and the latter is the predominant one. For squat members or members in which the critical shear crack develops below the theoretical compression strut, differently, the arching action is predominant. In the second part of the thesis, a mechanical model, consistent with the main ideas of the critical shear crack theory, is presented. The shear force that is transferred through the critical shear crack by the various shear-transfer actions is calculated by integration of simple constitutive laws and a failure criterion is obtained by summing the different contributions. The shear and deformation capacity can thus be calculated by intersection of the failure criterion with a load-deformation relationship. It is shown that the failure criteria obtained by integration of stresses at the crack surface can be approximated by power-law equations. Combining the power-law failure criteria with the load deformation relationship, a closed-form equation has been obtained. The closed-form equation provides almost identical results to the mechanical model and allows for direct design and assessment of existing structures. The accuracy of the mechanical model and the closed-form equation has been checked against a large database, showing a good agreement to the experimental results.
25 citations
TL;DR: In this paper, an effort is made for predicting the shear strength of high-strength concrete (HSC) slender RC beams without stirrups, using regression models and neural networks.
Abstract: High-strength concrete (HSC) is currently popular in the design and construction of heavy structures. Being HSC a brittle material, its cracking is sudden and cracks traverse through the aggregate particles thus producing relatively smooth fracture planes which is contrary to the normal-strength concrete (NSC) wherein cracks go around the aggregate particles. The relatively smooth fracture planes in HSC considerably decrease the concrete shear strength by reducing the contribution of the aggregate interlock. However, the international codes for the design of reinforced concrete (RC) structures make no distinction between NSC and HSC and the assessment of shear capacity of slender RC beams without web steel is still based on the experimental data of beams of NSC. In the present research, an effort is made for predicting the shear strength of HSC slender RC beams without stirrups, using regression models and neural networks. A large database of experimental results for HSC slender beams, covering a wide range of influencing parameters, is used for regression analysis as well as for the development of the artificial neural network models. The results of analysis are compared with major code requirements as well as with the researchers’ design model. The regression based as well as the neural network based models are presented. New empirical design models for the two approaches are also suggested.
21 citations
TL;DR: In this article, a ganz neuer Ansatz zur Beschreibung des Querkraftverhaltens von schubschlanken Stahl-Betonbalken ohne querkraftbewehrung vorgestellt is presented.
Abstract: Es wird ein ganz neuer Ansatz zur Beschreibung des Querkraftverhaltens von schubschlanken Stahlbetonbalken ohne Querkraftbewehrung vorgestellt. Grund fuer diese Untersuchungen war der Widerspruch zwischen der in Versuchen festgestellten und der nach dem EC2 rechnerisch ermittelten Querkrafttragfaehigkeit. Rechnerisch ergeben sich nennenswerte Defizite der Querkrafttragfaehigkeit, die sich durch die Versuchsergebnisse nicht bestaetigen. Die bisher in Regelwerken verwendeten Bemessungsansaetze wurden in der Regel empirisch anhand von Versuchsergebnissen entwickelt. Der Grundgedanke des neuen Ansatzes ist die Analyse der Hauptzugspannungen im Bereich der Rissspitze infolge Biegebeanspruchung. Dabei werden die gleichzeitig wirkenden Einwirkungen aus Biegung und Querkraft beruecksichtigt. Zur Verdeutlichung der Thematik werden zunaechst die wesentlichen Ansaetze zum Querkrafttragverhalten beschrieben. Die massgebenden Komponenten der Querkrafttragfaehigkeit gerissener Stahlbetonbauteile ohne Querkraftbewehrung sind weitgehend bekannt und akzeptiert. Unterschiedlich sind allerdings die Meinungen, wie die einzelnen Komponenten zusammenwirken und zu berechnen sind. Bei den zahlreichen Rechenmodellen lassen sich aus mechanischer Sicht zwei Gruppen unterscheiden. Bei der einen wird die Querkraft der Druck- und Rissprozesszone zugewiesen, bei der anderen bildet die Kornverzahnung den Hauptmechanismus der Querkrafttragfaehigkeit. Beide Ansaetze und ihre Auspraegungen bei unterschiedlichen Berechnungsvarianten werden ausfuehrlich vorgestellt. Anschliessend erfolgt eine eingehende Beschreibung des neuen Ansatzes zum Querkrafttragverhalten von Biegebauteilen. Dazu waren zunaechst die Fragen nach der Ermittlung der Betonspannung in der Zugzone unter Beruecksichtigung des Softening-Effekts und nach der Breite des Schubbandes, in der stabile Mikrorisse vor der Bildung des Makrorisses entstehen koennen, zu klaeren. Auf beide Parameter und die Initiallaenge innerhalb des potenziellen Schubbandes wird ausfuehrlich eingegangen. Mit den diskutierten Parametern ist es moeglich, die Querkrafttragfaehigkeit und die Stelle des zu erwartenden kritischen Schubrisses zu ermitteln. Dabei ist grundlegend zu unterscheiden in Rissentstehung im ungerissenen und im gerissenen Bauteilbereich. Die Ueberpruefung des neuen Ansatzes erfolgte anhand von Versuchsergebnissen. Bei dem neuen Ansatz spielt das Verhaeltnis von Biegung und Querkraft im Bauteil eine entscheidende Rolle. Daher ist es erforderlich, verschiedene Schubfeldarten zu unterscheiden: Schubfeld mit konstanter Querkraft, Schubfeld mit abnehmender Querkraft und zunehmendem Biegemoment sowie Schubfeld mit zunehmender Querkraft und Biegung. Die mit dem neuen Ansatz berechneten Ergebnisse stimmen fuer alle moeglichen Schubfeldtypen zufriedenstellend ueberein. Es zeigt sich, dass sich die Biegebeanspruchung guenstig auf die Querkrafttragfaehigkeit auswirkt. Der neue Ansatz erlaubt sowohl die Erklaerung der Tragfaehigkeit als auch die bei den verschiedenen Schubfeldern auftretenden Rissbilder. ABSTRACT IN ENGLISH: The contribution presents a new model to determine the shear capacity of reinforced concrete members under bending without shear reinforcement. The main idea of the model is the consideration of principal stress in the region of crack tips of the flexural cracks due to bending. A potential band for the formation of a critical shear crack that tends to connect the tips of existing flexural cracks can be assumed. The width of this band decreases with the increasing of the bending moment and gets larger when the shear force becomes higher. This means the bending moment affects positively the shear capacity. With the new model the shear capacity and the crack pattern in previous shear tests with different structural systems and loading conditions can be explained, which is generally not possible with the existing models. (A)
19 citations
Cites background from "Shear Strength of Reinforced Concre..."
...[6] ZARARIS, P. D.; ZARARIS, I. P.: Shear Strength of Reinforced Concrete Beams under Uniformly Distributed Loads....
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...Im Rahmen der bisherigen Untersuchungen konnte dieser Punkt jedoch noch nicht näher betrachtet werden....
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...Die Versuchsdaten für schubschlanke Balken der Typen 1 und 2 (a/d ≥ 3 bzw. l/d ≥ 10) wurden aus den Arbeiten von ZINK [19] und ZARARIS [6] übernommen....
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...l/d ≥ 10) wurden aus den Arbeiten von ZINK [19] und ZARARIS [6] übernommen....
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...Die Schwerpunkte weiterer Untersuchungen liegen in eigenen Versuchen zur Studie des Verhaltens verschiedener Schubfeldtypen mit Variation der wesentlichen Parameter wie M/V-Verhältnis, Bewehrungsgrad sowie Bauteilhöhe, in der gezielten Auswertung der vorhandenen Versuche zur Verifikation der Ansatzfunktionen zur Bestimmung der kritischen Breite des Schubbands sowie in der Bestimmung der Initiallänge zum Auslösen des kritischen Schubrisses....
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