Stress and strength

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Stress can refer to any effect impinging on the component or system that could cause it to fail, for example: pressure, temperature, applied voltage, torque.

Strength is the limit at which the component can withstand the applied stress. It has the same units as the stress variable, of course. The figure below shows how both of these can be random variables. The stress applied to a component or system can be a random variable dependent on weather and other operating conditions, the mode of use, etc. The strength of the component will vary somewhat from one component to another due to age, amount of use, manufacturing variability, etc. Thus, for any randomly selected component, its strength is also a random variable.

Here we pose the question: What is the probability that the applied stress is greater than the strength of the component? Scenarios of interest occur in the shaded overlap area in the figure above. In formal mathematics this requires doing an algebraic integration, which may not be possible depending on the distributions of stress and strain. However, with simulation we can determine this very easily. The example model Stress and strength shows an example.