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An ultimate shear strength theory for reinforced concrete T-beams without web reinforcement

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Abstract

A theory is presented to predict the ultimate shear strength of T-beams of long shear span without web reinforcement. Failure is assumed to occur in the compression zone above the diagonal crack due to the combined shearing and compressive stresses, and is based on Mohr's failure theory. Both equilibrium and compatibility conditions are considered, as well as the shear force due to dowel action of the longitudinal reinforcement. The theory is compared with the test results of the authors and other investigators, and is shown to predict the test results well. The theory is also compared with the ACI-ASCE and the Unified Code methods, and is shown to predict the results better.

Résumé

La rupture en cisaillement des poutres en T en béton armé s'accomplit en deux étapes. La première de ces étapes est caractérisée par une fissure oblique qui survient dans l'âme, et la seconde étape par la ruine définitive; lorsque la ruine se produit, à la force de cisaillement qui s'exerce sur la poutre s'oppose la zone de compression, la structure formée par l'agrégat et l'effet de goujon de l'armature longitudinale.

On présente ici une théorie susceptible de prédire la résistance ultime au cisaillement des poutres en T à grand intervalle de cisaillement sans renforcement de l'âme. Il est supposé que la ruine se produit dans la zone de compression au-dessus de la fissure diagonale engendrée par l'action combinée des contraintes de cisaillement et de compression, et elle s'appuie sur la théorie de la rupture de Mohr dans les conditions de sollicitations biaxiales. On examine à la fois les conditions d'équilibre et de compatibilité et l'on suppose que la distribution des contraintes de cisaillement et de compression dans la zone de compression critique au moment de la ruine par cisaillement est uniforme et rectangulaire. On suppose aussi que l'effet de goujon prend 10% de l'effort de cisaillement exercé. Comparée aux résultats d'essai obtenus par les auteurs et par d'autres chercheurs pour un certain nombre de paramètres, la théorie se révèle satisfaisante. La comparaison avec les codes britanniques et américains est à son avantage pour la précision des résultats d'essai.

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Abbreviations

a :

shear span

A s :

area of tension steel

A sb :

area of tension steel for balanced design

b :

width of compression flange

b c :

rib width

C :

compressive force in the compression zone

d :

effective depth

f :

normal stress

f 1,f 2,f 3 :

principal stresses

f c :

compressive stress in extreme fibre, or average compressive stress in the compression zone at the critical section at shear failure

f t ′ :

limiting normal tensile strength-split cylinder strength

f c ′ :

cylinder crushing strength

f c ″ :

limiting normal compressive stress, equal to 0.85f c ′)

k 2 :

a constant

k f d :

depth of compression zone at flexural failure

k s d :

depth of compression zone at shear failure

K :

a constant

k i :

interaction coefficient

t :

flange thickness

v :

shear stress

v c ′ :

limiting stress in pure shear

V c :

shear resistance of concrete in the compression zone at the critical section

V d :

shear resistance of main tensile steel due to dowel action

V u :

ultime shear strength of beams without web reinforcement

ϕ:

ratio of tensile to compressive strength concrete,f t ′/f c ″

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Authors and Affiliations

  1. Department of Civil and Structural Engineering, University of Sheffield, UK

    R. N. Swamy M. Eng., Ph.D., C. Eng., M.I.C.E., M.I. Struct E., M.A.S.C.E.

  2. Department of Civil Engineering, University of Sind, West Pakistan

    S. A. Qureshi B. Eng., M. Eng., Ph.D.

Authors
  1. R. N. Swamy M. Eng., Ph.D., C. Eng., M.I.C.E., M.I. Struct E., M.A.S.C.E.
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  2. S. A. Qureshi B. Eng., M. Eng., Ph.D.
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Swamy, R.N., Qureshi, S.A. An ultimate shear strength theory for reinforced concrete T-beams without web reinforcement. Mat. Constr. 7, 181–189 (1974). https://doi.org/10.1007/BF02473833

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