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Materials and Structures

, Volume 43, Issue 9, pp 1245–1256 | Cite as

Optimal reinforcement of RC columns for biaxial bending

  • Luisa María Gil-Martín
  • Enrique Hernández-Montes
  • Mark Aschheim
Original Article

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.

Keywords

Ultimate strength design Optimal reinforcement Biaxial bending 

List of symbols

Ac

Cross sectional area of concrete section

As

Area of bottom reinforcement

\( A^{\prime}_s\)

Area of top reinforcement

Ap

Area of prestressing tendon

N

Nominal axial strength

Nd

Design value of the applied axial force

M

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

Md

Design value of the applied bending moment

Mx

Flexural moment strength about x-axis

Mxd

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

My

Flexural moment strength about y-axis

Myd

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

fck

Characteristic compressive strength of concrete

fyk

Characteristic yield strength of reinforcement

sh

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

sv

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

σc

Stress in concrete

σp

Stress in prestressing tendon

σs

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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Copyright information

© RILEM 2009

Authors and Affiliations

  • Luisa María Gil-Martín
    • 1
  • Enrique Hernández-Montes
    • 1
  • Mark Aschheim
    • 2
  1. 1.Department of Structural MechanicsUniversity of GranadaGranadaSpain
  2. 2.Department of Civil EngineeringSanta Clara UniversitySanta ClaraUSA

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