6.1. General stress strength model#

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6.1.1. Model description#

The stress strength model is a very general model that can be used to assess the reliability of mechanical components. Typically, the “strength” or resistance \(X_{1}\) and the “stress” or load \(X_{2}\) are the only two variables considered. The limit state function for this model can be written as follows:

\[ g\left( X_1, X_2 \right) = X_1 - X_2 \]

A summary of these variables and their meaning is given in Table 6.1.1.

Table 6.1.1 Input variables for reliability analysis#

Name

Description

Unit

\(X_1\)/X_1

Strength

same as \(X_2\)

\(X_2\)/X_2

Stresses

same as \(X_1\)

\(\rho_{X_1,X_2}\)/rho_X1_X2

Correlation between \(X_1\) and \(X_2\)

\(-\)

6.1.2. Interactive reliability prediction#

This page offers an interactive reliability prediction that lets the user specify the properties of all variables listed in Table 6.1.1. The variables are characterized by:

  • Distribution denoted by “Dist” and can be choosen from a set of parametric probability distributions;

  • Mean value denoted by “E” and can be selected with a slider;

  • Coefficient of variation denoted by “C.o.V.” and can be selected with a slider.

Note

To run the interactive reliability prediction on this page, click the –> Live Code button on the top of the page. Wait a few seconds until the Kernel has loaded and run the cell below with Run.

from nrpmint.booktools import stress_strength

# start the web user-interface
stress_strength.web_ui()