Analytical Model to Predict the Influence of Shear on Longitudinal Steel Tension in Reinforced Concrete Beams

Abstract

This paper presents an analytical model to predict the increase in longitudinal reinforcement tension due to shear in reinforced concrete beams. Based on a smeared truss idealization with an inclined compression chord, the model assumes that the profiles of compression chord can be represented by the simple power law of which curvature effect equilibrates a constant fraction of the shear along the span. Thereby, the sectional equilibrium and compatibility conditions are established between the forces and deformations associated with the chords and those associated with the web. The modified compression field theory is employed to evaluate the shear deformation of the web. From these equilibrium and compatibility conditions, the influence of shear on the longitudinal steel tension is determined at each cross section of a beam. The accuracy of the model is examined by comparisons with the measured values which are available in literatures. A good agreement is observed between the predicted and the measured at every loading stage in each test beam. Also the model is compared with the shift-rule in the current design codes, and the differences are discussed.

Keywords

arch action reinforced concrete beam shear compatibility steel tension truss model

Get full access to this article

View all access options for this article.

References

AASHTO (2004). AASHTO LRFD Bridge Design Specifications, SI Units, Third Edition. American Association of State Highway and Transportation Officials, Washington, DC.

Bazant

Z.P.

and Kim

J.K.

(1984). “Size effect in shear failure of longitudinally reinforced beams”, ACI Journal, Vol. 81, No. 5, pp. 456–468.

Belarbi

and Hsu

T.T.C.

(1995). “Constitutive laws of softened concrete in bi-axial tension-compression”, ACI Structural Journal, Vol. 92, No. 5, pp. 562–573.

Comite Euro International Du Beton (CEB/FIP) (1978). CEB-FIP Model Code for Concrete Structures. Bulletin d'Information, 124/125, 437 pp.

Commission of the European Communities (2002). Eurocode 2(EC2), Design of Concrete Structures, Part 1: General Rules and Rules for Buildings, ENV 1992-1-1. Brussels, Belgium.

Hsu

T.T.C.

(1993). Unified Theory of Reinforced Concrete. CRC Press, Boca Raton, Fla.

Kani

G.N.J.

(1964). “The riddle of shear failure and its solution”, ACI Journal, Vol. 61, No. 4, pp. 441–467.

Kim

D.-J.

Kim

and White

R.N.

(1998). “Prediction of reinforcement tension produced by arch action in RC beams”, Journal of Structural Engineering, ASCE, Vol. 124, No. 6, pp. 611–622.

Leonhardt

(1965). “Reducing the shear reinforcement in reinforced concrete beams and slabs”, Magazine of Concrete Research, Vol. 17, No. 53, pp. 187–198.

10.

Lorentsen

(1965). “Theory for the combined action of bending moment and shear in reinforced concrete and prestressed concrete beams”, ACI Journal, Vol. 62, No. 4, pp. 403–419.

11.

Mains

R.M.

(1951). “Measurement of the distribution of tensile and bond stresses along reinforcing bars”, ACI Journal, Vol. 48, No. 3, pp. 225–252.

12.

Ngo

, and Scordelis

A.C.

(1967). “Finite element analysis of reinforced concrete beams”, ACI Journal, Vol. 64, No. 3, pp. 152–163.

13.

Park

and Paulay

(1975). Reinforced Concrete Structures. Wiley, New York.

14.

Vecchio

F.J.

and Collins

M.P.

(1986). “The modified compression field theory for reinforced concrete elements subjected to shear”, ACI Journal, Vol. 83, No. 2, pp. 219–231.