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Optimal reinforcement of RC columns for biaxial bending

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Abstract

The Reinforcement Sizing Diagram (RSD) approach to determining optimal reinforcement for reinforced concrete beam and column sections subjected to uniaxial bending is extended to the case of biaxial bending. Conventional constraints on the distribution of longitudinal reinforcement are relaxed, leading to an infinite number of reinforcement solutions, from which the optimal solution and a corresponding quasi-optimal pragmatic is determined. First, all possibilities of reinforcement arrangements are considered for a biaxial loading, including symmetric and non-symmetric configurations, subject to the constraint that the reinforcement is located in a single layer near the circumference of the section. This theoretical approach establishes the context for obtaining pragmatic distributions of reinforcement that are more suitable for construction, in which distributions having double symmetry are considered. This contrasts with conventional approaches for the design of column reinforcement, in which a predetermined distribution of longitudinal reinforcement is assumed, even though such a distribution generally is non-optimal in any given design. Column and wall sections that are subjected to uniaxial or biaxial loading may be designed using this method. The solutions are displayed using a biaxial RSD and can be obtained with relatively simple algorithms implemented in widely accessible software programs such as Mathematica® and Excel®. Several examples illustrate the method and the savings in reinforcement that can be obtained relative to conventional solutions.

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Abbreviations

A c :

Cross sectional area of concrete section

A s :

Area of bottom reinforcement

\( A^{\prime}_s\) :

Area of top reinforcement

A p :

Area of prestressing tendon

N :

Nominal axial strength

N d :

Design value of the applied axial force

M :

Bending moment applied at the center of gravity of the gross section

M d :

Design value of the applied bending moment

M x :

Flexural moment strength about x-axis

M xd :

Design value of the bending moment applied about the x-axis

M y :

Flexural moment strength about y-axis

M yd :

Design value of the bending moment applied about the x-axis

f ck :

Characteristic compressive strength of concrete

f yk :

Characteristic yield strength of reinforcement

s h :

Distance between centroids of consecutive bars of the top and bottom reinforcement

s v :

Distance between centroids of consecutive bars of side reinforcement

x :

Depth to neutral axis from top fiber of cross section

y :

Vertical coordinate measures from the center of gravity of the gross section

σ c :

Stress in concrete

σ p :

Stress in prestressing tendon

σ s :

Stress in bottom reinforcement

\( \sigma^{\prime}_s\) :

Stress in top reinforcement

ξ:

Intersection of the neutral axis with the y-axis

φ:

Angle of the neutral fiber

Φ:

Bar diameter

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Authors and Affiliations

  1. Department of Structural Mechanics, University of Granada, E.T.S. Ingenieros de Caminos, Campus Universitario de Fuentenueva, 18072, Granada, Spain

    Luisa María Gil-Martín & Enrique Hernández-Montes

  2. Department of Civil Engineering, Santa Clara University, 500 El Camino Real, Santa Clara, CA, 95053, USA

    Mark Aschheim

Authors
  1. Luisa María Gil-Martín
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  2. Enrique Hernández-Montes
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  3. Mark Aschheim
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Correspondence to Luisa María Gil-Martín.

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Gil-Martín, L.M., Hernández-Montes, E. & Aschheim, M. Optimal reinforcement of RC columns for biaxial bending. Mater Struct 43, 1245–1256 (2010). https://doi.org/10.1617/s11527-009-9576-x

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