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Stress-strain characteristics of concrete confined in steel spirals under repeated loading

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Abstract

Repeated loadings tests have been conducted on 150 mm dia.×300 mm high concrete cylinders with circular steel spiral confining the concrete. Stress-strain curves obtained in the experiments are presented. Equations are proposed for the envelope, unloading and reloading curves of the stress-strain curves and compared with test results.

Résumé

Des essais de chargement répété ont été réalisés sur des cylindres de béton de 150 mm (diamètre)×300 mm (hauteur) confinés dans une hélice d'acier. On présente ici les courbes expérimentales de contrainte/déformation. On propose des équations pour l'enveloppe des courbes obtenues par chargement répété, et l'on procède à une comparaison avec les résultats d'essai.

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Abbreviations

A 1...A 5 :

constants in the equations

B 1...B 5 :

constants in the equations

C 3 :

constant in an equation

C i :

confinement index=\(\left( {p_b - \bar p_b } \right)f_y /f'_c \);

Dr (1),Dr (2):

expressions given by equations (6a)

Dr (3):

(12a) and (13a) respectively

E c :

initial tangent modulus of the stress-strain curve of plain or confined concrete

E′ c :

secant modulus of the stress-strain curve at the peak stress

E rl :

slope of the initial tangent of the reloading stress-strain curve

E ul :

slope of the initial tangent of the unloading stress-strain curve

F :

stress ratio=\(f_e /\bar f_c \);

F d ,F g :

stress ratios at the pointsD andG on theF−S curves under repeated loading

F e :

stress ratio of a point on the envelope stress-strain\(f_e /\bar f_c \);

f :

stress in concrete

f′ c :

strength of plain concrete cylinder

\(\bar f_c \) :

strength of confined concrete cylinder

f e :

stress at a point on the envelope stress-strain curve

f y :

yield stress or 0.2% proof stress of steel

g(S) :

expression given by equation (1a)

k :

constant (=0.85) in equation (1a)

P b :

ratio of volume of the spiral to the volume of confined concrete

\(\bar p_b \) :

value ofp b when the pitch of the spiral equals the least lateral dimension of the specimen

S :

strain ratio=\(\varepsilon /\bar \varepsilon _c \);

S e :

strain ratio of a point on the envelope stress-strain curve=\(\varepsilon _e /\bar \varepsilon _c \);

S p :

residual strain-ratio=\(\varepsilon _p /\bar \varepsilon _c \);

T rl :

slope of the initial tangent of reloadingF−S curve

T ul :

slope of the initial tangent of unloadingF−S curve

x :

distance inx-direction

y :

distance iny-direction

β:

ratio\(\bar \varepsilon _{0.85} /\bar \varepsilon _c \);

ɛ:

strain in concrete

ɛ′ c :

strain at maximum stress of a plain concrete cylinder

ɛ e :

strain at the stressf e

ɛ p :

residual compressive strain in concrete

\(\bar \varepsilon _{0.85} \) :

strain at 85% maximum stress of confined concrete cylinder in the descending portion of the stress-strain curve.

References

  1. Sundara Raja Iyengar K. T., Prakash Desayi Nagi Reddy K.. —Stress-strain characteristics of concrete confined in steel binders. Magazine of Concrete Research, Vol. 22, No. 72, September 1970, pp. 173–184.

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  2. Sanjeeva Reddy T.—Confined concrete and reinforced concrete members under monotonic, repeated and reversed loading. Ph. D. Thesis, Indian Institute of Science, 1977, p. 573.

  3. Sinha B. P., Gerstle L. H., Tulin, L. G.—Stress-strain relationships for concrete under cyclic loading. Journal of the American Concrete Institute. Proceedings, Vol. 61, No. 2, February 1964, pp. 195–211.

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  4. Karsan I. D., Jirsa, J. O.—Behaviour of concrete under compressive loadings. Journal of the Structural Division. Proceedings of the American Society of Civil Engineers Vol. 95. No. ST12, December 1969, pp. 2543–2563.

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  5. Prakash Desayi, Sundara Raja Iyengar K. T., Sanjeeva Reddy T.—Equation for stress-strain curve of concrete confined in circular steel spiral. Materials and Structures, Research and Testing (R.I.L.E.M. Paris). Vol. 11, No. 65, September–October 1978.

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Science, Bangalore, India

    P. Desayi (Associate Professor) & K. T. Sundara Raja lyengar (Professor)

  2. Civil Engineering, College of Engineering, Anantapur, India

    T. Sanjeeva Reddy (Lecturer)

Authors
  1. P. Desayi
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  2. K. T. Sundara Raja lyengar
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  3. T. Sanjeeva Reddy
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Desayi, P., Sundara Raja lyengar, K.T. & Sanjeeva Reddy, T. Stress-strain characteristics of concrete confined in steel spirals under repeated loading. Mat. Constr. 12, 375–383 (1979). https://doi.org/10.1007/BF02478814

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  • DOI: https://doi.org/10.1007/BF02478814

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