Effect of Length on Tensile Strength

Abstract

THE results of a large number of tension tests on nominally identical test pieces can conveniently be represented by a frequency curve in which the ordinate gives the frequency of occurrence of test pieces the strength of which is represented by the abscissa. The frequency of occurrence of test pieces the strength of which falls between the limits x + dx and x is given by f(x)dx. When the frequency curve is integrated with respect to x and between the limits — ∞ and x, an integral curve is obtained the ordinate F(x) of which gives the proportion of test pieces with strength less than x. The proportion of test pieces with strength greater than x is given by 1 — F(x). Where the frequency curve does not depart greatly from normality, its characteristics can conveniently be sumarized by its mean (μ), standard deviation (σ) and skewness √β₁.