An analytical model with tension softening for the prediction of the capacity of prestressed concrete beams under pure torsion and under torsion combined with shear and flexure is introduced The proposed approach employs bilinear stress-strain relationship with post cracking tension softening branch for the concrete in tension and special failure criteria for biaxial stress states Further, for the solution of the governing equations a special numerical scheme is adopted which can be applied to elements with practically any cross-section since it utilizes a numerical mapping The proposed method is mainly applied to plain prestressed concrete elements, but is also applicable to prestressed concrete beams with light transverse reinforcement The aim of the present work is twofold; first, the validation of the approach by comparison between experimental results and analytical predictions and second, a parametrical study of the influence of concentric and eccentric prestressing on the torsional capacity of concrete elements and the interaction between torsion and shear for various levels of prestressing The results of this investigation presented in the form of interaction curves, are compared to experimental results and code provisions

Strength of prestressed concrete beams in torsion

A set of generalized strength equations based on the skewbending model has been developed to predict the torsional strength and failure mode of reinforced concrete beams with or without a small transverse opening A torsion‐bending‐shear interaction surface is generated using the proposed strength equations Twenty‐four rectangular reinforced‐concrete beams containing a transverse opening of constant dimensions were grouped into four different series and were tested under various combinations of torsion, bending, and shear The parameters were the ratio between top and bottom longitudinal reinforcement, the torsion‐moment ratio, and the moment‐shear ratio Close agreement is observed between the theoretical predictions and the test results of the writers and of other investigators

Beams with Small Rectangular Opening Under Torsion, Bending, and Shear

Many structural elements are subjected to the effects of combined torsional and flexural movements. This paper presents an extension of an existing simplified method for combined stress-resultants model. The extension is used for the design and analysis of reinforced and partially- and fully-prestressed concrete beams subjected to combined torsional and bending moments. The interaction between torsion and flexure is achieved by superposing the steel required for the two moments. The observed ultimate loads of 111 beams are compared with the calculations of the proposed model. This includes comparing interaction diagrams and the effects of concrete strength, stirrups spacing, and T-beam flange width on the ultimate capacity. Very good agreement was obtained. The calculations by the American Concrete Institute code equations are also evaluated and shown to give satisfactory and, in some cases, overly conservative, results. Design and analysis examples are used to demonstrate the simplicity of the proposed model.

Combined Torsion and Bending in Reinforced and Prestressed Concrete Beams Using Simplified Method for Combined Stress-Resultants

Current specifications set up by American Association of State Highway and Transportation Officials Load and Resistance Factor Design (AASHTO-LRFD) guidelines allow two different procedures for the design of concrete beams subjected to torsion and shear. These are based on a simplification of the equations of the modified compression field theory. This article reports on a study that evaluated this procedure. The author compares his results with available test data on beams subjected to various load combinations such as pure torsion, combined torsion and bending, combined torsion, bending and shear, and combined torsion and axial compression. Typical interaction diagrams between torsion, shear and bending, and axial load are also presented. The results show that the method generally provides conservative results and accurate representations of the interaction between torsion and the other stress resultants; it also calculated the shape of the interaction diagrams and surfaces with reasonable accuracy. The author cautions that the standard equation used to calculate the torsional shearing stress is not accurate.

Evaluation of AASHTO-LRFD general procedure for torsion and combined loading

In this study, a torsional behavior analysis model is developed for reinforced concrete (RC) members subjected to combined loads. In the analytical model, a member section is considered to be idealized as panel elements, on which a flexural analysis is first done considering axial forces to derive normal stresses acting on the cross-section. The panel elements are then analyzed with the normal stresses using the smeared truss model that satisfies the equilibrium and compatibility conditions. The various member forces are combined in terms of stress, in which the initial crack angle, the effective thickness affected by the combined stresses, and the distribution of the longitudinal reinforcement are reflected. From the combined stresses in the idealized panel elements, the member strengths are determined by applying multi-potential capacity criteria in which aggregate interlock failure, concrete crushing, and spalling of concrete cover are considered. The analytical model is verified by comparing it with existing test results, and it is found that the proposed model well evaluates the torsional behavior of RC members with and without shear force, bending moment, and axial force.

Analytical model for torsional behavior of RC members combined with bending, shear, and axial loads

The results of tests on 18 rectangular reinforced concrete beams subjected to combined bending torsion and shear are reported. The principal variables were the ratio of twisting to bending moment, the transverse shear force, and the reinforcement configuration. The beams failed by one of three different modes which were characterized by the formation of a hinge adjacent to one face of the beam and yielding of the reinforcement adjacent to the face opposite to the hinge. In beams subjected to a constant twisting moment and a varying bending moment, failures with the hinge located adjacent to the bottom face occurred in the region subjected to the lowest bending moment and failures with the hinge located adjacent to the top face occurred in the region of highest bending moment. Idealized failure surfaces are defined and expressions for the strength of these beams are derived using an equilibrium approach. The results are presented both in tabular form and in interaction diagrams. Good correlation is obtained between the predicted and observed mode of failure and strength.

Concrete Beams in Bending, Torsion and Shear

An ultimate strength interaction criterion for web reinforced, prestressed concrete beams under torsion, bending moment and flexural shear is presented. Principal variables considered are the level of prestress and its eccentricity, torque: bending moment ratio, and flexural shear. Test results for 54 rectangular beams include beam properties, ultimate strength, angle of twist at failure, torque-twist curves and typical crack patterns. Bending moment in moderate amounts increases the torsional strength, but the effect of flexural shear is always detrimental. Within limits, the web reinforcement provides a ductile type behavior with ample rotation capacity at failure. The initial torsional stiffness is not affected by the variables considered. Higher levels of prestress and web reinforcement increase the pure torsional strength. Torsion-bending moment interaction is represented by a second degree parabola, and a three-dimensional curved interaction surface is envisaged when flexural shear is also present. Proposed interaction equations indicate good correlation with test data.

Torsion, bending, and shear in prestressed concrete

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Concrete Beams in Bending, Torsion and Shear

Torsion, bending, and shear in prestressed concrete