Applications of the Bienamé and Tchebycheff Inequalities for the ‘Structural Reliability’ and ‘Engineering Planning and Design’ Courses

Abstract

Some examples are given to elucidate an application of the Bienamé and Tchebycheff inequalities in the probabilistic strength of materials. These inequalities are discussed in the elective undergraduate or first-year graduate courses ‘structural reliability’ or ‘engineering planning and design’. These examples, hopefully, will be beneficial to students, in that they illustrate how simple calculations can be performed to derive estimates of structural reliability with limited information. The material discussed in this paper can be covered in a single, standard fifty-minute lecture.