Spline Interpolation of the Stress-Strain Curves for Concrete in Compression

Abstract

Generating a rational analytical expression of the stress-strain curve for concrete in compression is one of the basic prerequisites for the establishment of a new concrete mechanics. Since Whitney, in 1942, gave the first complete stress-strain curves with its descending branch obtained from the tests carried out on concrete cylinders, this topic has been paid close attention to. In the last four decades, some investigators begin with experiments, and various expressions of the stress-strain relationships were reported. However, an optimal expression for the complete stress-strain curves, the descending portion in particular, has not yet been found so far. Therefore, this problem has been one of the subjects discussed by publications. How can we solve it A best way is to combine concrete mechanics with mathematics. In other words, we have to extensively inspect some typical experimental curves and introduce the correspinding mathematics results in to our work. Then the rational form for the stress-strain can be found. It is fortunate that mathematicians made a good contribution for us, namely spline function.