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Shear resistance analytical evaluation for RC beams with transverse reinforcement with two different inclinations

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Abstract

An analysis-oriented mechanical model for shear strength evaluation of Reinforced Concrete (RC) beams with transverse reinforcement with two different inclinations, which required a numerical analysis, is turned into a design-oriented analytical model that can easily be utilized for practical purposes. The model assessed the shear resistance, according to the “lower-bound solution”, employing a numerical procedure that maximizes the element shear strength varying the stresses in the two sets of transverse reinforcement and the magnitude and inclination of the web concrete compressive stress field. The model is formulated with the aim of representing an extension of Eurocode 2 framework to RC beams with two orders of stirrups. In this paper, an analytical procedure is derived, substituting the former numerical maximization procedure, in order to obtain the optimal values of the aforementioned parameters, for any layout and amount of shear reinforcement. Comparison between shear strength predictions provided by the model and test results available in the literature confirms the model’s efficiency.

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Abbreviations

a :

Shear span

b w :

Cross-section minimum web width

d :

Cross-section depth

f c :

Compressive strength of concrete

f cd :

Design compressive strength of concrete

\(f^{\prime }_{\text{cd}}\) :

Design reduced compressive strength of concrete

f yd :

Design tensile strength of steel

stw1 :

Spacing of the first order of transverse reinforcement

s tw2 :

Spacing of the second order of transverse reinforcement

ν :

Non-dimensional shear strength

x c :

Neutral axis

z :

Internal lever arm, equal to 0.9 d

\(A^{\prime }_{\text{s}}\) :

Cross-sectional area of the top longitudinal reinforcement

A s :

Cross-sectional area of the bottom longitudinal reinforcement

A tw1 :

Cross-sectional area of the first order of transverse reinforcement

A tw2 :

Cross-sectional area of the second order of transverse reinforcement

α 1 :

Angle of inclination, with respect to the beam axis, of the first order of transverse reinforcement

α 2 :

Angle of inclination, with respect to the beam axis, of the second order of transverse reinforcement

θ :

Slope of the web concrete stress field

\(\nu^{\prime }\) :

Coefficient to be applied to the compressive strength of concrete fc to take into account the biaxial stress state

ξ :

Non-dimensional neutral axis depth, equal to xc/z

\(\tilde{\sigma }_{\text{cw}}\) :

Non-dimensional stress of the web concrete

\(\tilde{\sigma }_{\text{lw}}\) :

Non-dimensional stress of the web longitudinal reinforcement

\(\tilde{\sigma }_{\text{tw1}}\) :

Non-dimensional stress of the first order of transverse reinforcement

\(\tilde{\sigma }_{\text{tw2}}\) :

Non-dimensional stress of the second order of transverse reinforcement

\(\omega_{\text{lw}}\) :

Mechanical ratio of the web longitudinal reinforcement

\(\omega^{\prime }_{\text{s}}\) :

Mechanical ratio of the top longitudinal reinforcement

ω s :

Mechanical ratio of the bottom longitudinal reinforcement

\(\omega_{\text{tw1}}\) :

Mechanical ratio of the first order of transverse reinforcement

\(\omega_{\text{tw2}}\) :

Mechanical ratio of the second order of transverse reinforcement

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Authors and Affiliations

  1. Department of Engineering, University of Palermo, Viale delle Scienze, Ed. 8, 90128, Palermo, Italy

    Piero Colajanni & Salvatore Pagnotta

  2. Department of Engineering, University of Messina, C. da di Dio 1, Vill. Sant’Agata, 98166, Messina, ME, Italy

    Antonino Recupero & Nino Spinella

Authors
  1. Piero Colajanni
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  2. Salvatore Pagnotta
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  3. Antonino Recupero
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  4. Nino Spinella
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Correspondence to Salvatore Pagnotta.

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Colajanni, P., Pagnotta, S., Recupero, A. et al. Shear resistance analytical evaluation for RC beams with transverse reinforcement with two different inclinations. Mater Struct 53, 18 (2020). https://doi.org/10.1617/s11527-020-1452-8

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