Strain gradient effects on flexural strength and ductility design of normal-strength RC beams and columns

Abstract

The stress-strain characteristics of concrete developed in flexure is very important for flexural strength design of reinforced concrete (RC) members. In current RC design codes, the stress-strain curve of concrete developed in flexure is obtained by scaling down the uni-axial stress-strain curve to account for the strain gradient effect. Therefore, the maximum concrete stress that can be developed under flexure is smaller than its uni-axial strength, and the use of which always underestimates the flexural strength of RC beams and columns even though the safety factors for materials are taken as unity. Furthermore, the value of strength underestimation was different for RC beams and columns, which indicates that the extent of strain gradient will affect the maximum concrete stress and stress-strain curve developed under flexure.

To investigate the maximum concrete stress, 29 column specimens were fabricated and tested in this study. They were divided into 9 groups, each of which was poured from the same batch of concrete and contained specimens with identical cross-section properties. In each group, one specimen was tested under concentric load while the rest was/were subjected to eccentric or horizontal load. To study the strain gradient effects, the ratio of the maximum concrete compressive stress developed in the eccentrically/horizontally loaded specimens to the maximum uni-axial compressive stress developed in the counterpart concentrically loaded specimens, denoted by k3, is determined based on axial force and moment equilibriums. Subsequently, the concrete stress block parameters and the equivalent rectangular concrete stress block parameters are determined. It is found that the ratios of the maximum and equivalent concrete stress to uni-axial cylinder strength, denoted respectively by k3 and , depend significantly on strain gradient, while that of the depth of stress block to neutral axis depth, denoted by , remains relatively constant with strain gradient. Design equations are proposed to relate and  with strain gradient for strength calculation, whose applicability is verified by comparing the strengths of RC beams and columns tested by various researchers with their theoretical strengths predicted by the proposed parameters and those evaluated based on provisions of RC codes.

Based on the test results, the stress-strain curve of normal-strength concrete (NSC) developed under strain gradient is derived using least-square method by minimising the errors between the theoretical axial load and moment and the respective measured values. Two formulas are developed to derive the flexural stress-strain curve, whose applicability is verified by comparing the predicted strength with those measured by other researchers.

Lastly, the application of the proposed stress-block parameters and stress-strain curve of NSC will be illustrated by developing some charts for flexural strength design of NSC beams and columns. The application will further be extended to develop strength-ductility charts for NSC beams and columns, which enable simultaneous design of strength and ductility. By adopting the proposed design charts, the flexural strength design, as well as that of the plastic hinge forming mechanism during extreme events, will be more accurate. The resulting design will be safer, more environmentally friendly and cost effective.