Reliability Analysis for Eccentrically Loaded Columns

ACI Structural Journal, Sep/Oct 2005 by Szerszen, Maria M, Szwed, Aleksander, Nowak, Andrzej S

This paper presents reliability analysis for eccentrically loaded reinforced concrete (RC) columns, based on new improved statistical data for the constituent materials. The strength limit state functions were developed for reinforced rectangular columns, depending on the cross section size, reinforcement ratio, and load eccentricity. For a known eccentricity condition, closed-form solutions for the corresponding force-moment strength in the interaction diagram were developed. The calculations for cast-in-place and plant-cast columns made of normal concrete and high-strength concrete were performed. The statistical parameters of resistance were calculated using Monte Carlo simulations. Sensitivity analyses were performed to determine the design parameters that have the highest influence on the reliability index. Many two- and three-dimensional plots were generated to show the reliability index versus concrete strength, reinforcement ratio, load combination, normalized eccentricity, and tensile strain in steel. The required strength reduction factor is calculated for a predetermined target reliability index to achieve accepted level of structural safety. The strength reduction factor for RC columns is proposed in a convenient form for design procedures, depending on the tensile strain in steel and the reinforcement ratio.

Keywords: columns; eccentricity; reinforced concrete.

(ProQuest Information and Learning: ... denotes formulae omitted.)

INTRODUCTION

Reliability analysis having probabilistic and statistical basis has been recognized as a rational approach in making decisions in the face of uncertainty involved in the design process. The actual capacity of a reinforced concrete (RC) structural member differs from the nominal capacity, which is basically defined by the strengths of constituent materials and the specified geometric properties. The actual concrete compressive strength, section geometry, reinforcing steel yield strength, location of bars, and quality control vary for each structure and therefore are treated as random variables.

In ACI 318-05,1 a safety margin is provided by the use of load and resistance factors, which account for probable overloading and under-strength of RC structural members. The variability in load effect U and ultimate strength R must be evaluated to determine an appropriate resistance factor φ using the strength limit design method. For eccentrically loaded columns with cross sections subjected to combined bending and thrust, the strength is determined by an interaction relationship between axial force P and moment M. For a known eccentricity e, closed-form solutions for the corresponding force-moment strength in the interaction diagram were developed in this study, and thus allowed to avoid iterative procedures typically used in the design practice.

Reliability-based calibration of ACI 318-051 design code for concrete structures has been performed for beams in flexure and axially loaded columns.2,3 This paper presents the derivation of resistance factors for eccentrically loaded columns using reliability analysis. The full range of possible values of load eccentricity, from axial load to pure bending, was investigated in this study. A computer program had been developed to run at least 10,000 simulations for each considered design parameter. The reliability analysis was performed for short RC columns so that the slenderness effects could be neglected. The major resistance-related variables investigated in this study included concrete compressive strength [function of]^sub c^' , reinforcing steel yield strength [function of]^sub y^ , reinforcement ratio ρ, aspect ratio of the cross section, h/b, and load eccentricity.

The statistical parameters related to material, geometry, and modeling influencing the capacity of a column have been provided by the authors in a previous study.2 Material-related parameters include yield strength of steel and compressive strength of concrete. Geometry-related parameters refer to concrete cross-section dimensions, location, and cross-sectional area of reinforcing steel. Modeling-related parameters take into account the influence of design model used in calculation of nominal resistance. The statistical parameters for normal and high-strength concrete, and reinforcing steel presented in Reference 2 were based on actual test results. The resulting cumulative distribution functions of materials properties are used in this paper for computing the strength variability of eccentrically loaded columns.

RESEARCH SIGNIFICANCE

The availability of new statistical data for compressive concrete strength and yield strength of reinforcing steel, as well as incorporation of the new load model into the ACI 318-05 code, require the verification and updating of resistance factors for eccentrically loaded columns. Results from the reliability analyses reported herein were employed in the calculation of the strength reduction factors φ, covering the full range of possible values of load eccentricity from axial load to pure bending. Sensitivity analysis was performed to identify the most important parameters that influence the reliability of a column. Presented research provides a rational basis for the selection and recommendation of new resistance factors for RC columns and for updating the ACI design procedures, including new load model and improved materials.