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Capacity models for shear strength of exterior joints in RC frames: state-of-the-art and synoptic examination

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Abstract

Damage observed in existing structures after recent earthquake events pointed out the key importance of beam-to-column joints in influencing the global response of reinforced concrete structures. In the last two decades several theoretical and empirical models have been proposed for evaluating shear strength of beam-to-column joints. The present paper reports an overview of the models currently available in the scientific literature for evaluating shear capacity of exterior beam-to-column joints. The present study is the first step of a wide analysis aimed at assessing such models and improving them. Moreover, the uncertainties deriving by applying the mentioned models will be also quantified therein, by means of well-established procedures for probabilistic seismic analysis of structures. The final results of that study are reported within a companion paper.

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Abbreviations

A c :

Cross-sectional area of column

A g :

Cross-sectional area of joint

A sb,inf :

Bottom flexural reinforcement in the beam

A sb,sup :

Top flexural reinforcement in the beam

A sc :

Area of reinforcement in column

A sc,0 :

Area of the layer of steel farthest from the maximum compression face in a column

A sjh :

Area of horizontal stirrups in the joint panel

A str :

Effective area of the diagonal strut

a s :

Strut depth

a v :

Effective shear span

b b :

Beam width

d b :

Beam depth

d b ′:

Thickness of the cover concrete in beam

b c :

Column width

BI:

Beam reinforcement index

b j :

Effective joint width

c:

Depth of the flexural compression zone of the elastic column

C d :

Diagonal compressive strength in the concrete strut

C d, n :

Nominal diagonal compressive strength in the concrete strut

D:

Force of the diagonal strut

d c :

Column effective depth

d c ′:

Thickness of the cover concrete in column

e b :

Eccentricity between the beam centreline and the column centroid

f c :

Compressive concrete strength

F h and F v :

Horizontal and vertical forces components of the joint mechanism

f yb :

Yielding stress of beam reinforcement

f yc :

Yielding stress of column reinforcement

f yj :

Yielding stress of joint stirrups

h b :

Beam depth

h c :

Column depth

JI:

Joint transverse reinforcement index

λ:

Overstrength factor of the steel

N c :

Axial force in column

ν :

No dimensional compressive stress at the bottom of the top column

θ :

Inclination of the concrete strut

θ crit :

Critical inclination of the concrete strut

R:

Radius of the centreline of the beam bars bent into the joint

ρ b :

beam reinforcement ratio

R c :

Concrete cube strength

ρ c :

Column longitudinal reinforcement ratio

ρ j :

Volumetric joint transverse reinforcement ratio

ρ jh :

Horizontal stirrup ratio

s:

Spacing of the stirrups

σ c :

Column normal stress

σ d,max :

Maximum stress of the diagonal strut

T:

Tensile strength of the top beam reinforcement

V c :

Shear force acting the bottom of the top column

V ch :

Shear strength provided by concrete

v jh :

Shear stress of joint

V jh :

Shear strength of joint

V jh,E :

Shear force acting the joint

V sh :

Shear strength provided by stirrups

z b :

Distance between the bars in tension and the resultant of the compression stresses in the sectional analysis of the beam

z c :

Distance between the two outer bars in the column

χ :

Ratio between the effective shear span and the column effective depth

ζ :

Stiffness coefficient

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Authors and Affiliations

  1. Department of Civil Engineering, University of Salerno, Via Ponte don Melillo, 84084, Fisciano, SA, Italy

    Carmine Lima, Enzo Martinelli & Ciro Faella

Authors
  1. Carmine Lima
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  2. Enzo Martinelli
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  3. Ciro Faella
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Correspondence to Enzo Martinelli.

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Lima, C., Martinelli, E. & Faella, C. Capacity models for shear strength of exterior joints in RC frames: state-of-the-art and synoptic examination. Bull Earthquake Eng 10, 967–983 (2012). https://doi.org/10.1007/s10518-012-9340-4

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  • DOI: https://doi.org/10.1007/s10518-012-9340-4

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