Engineers must accommodate uncertainty. Uncertainty always accompanies change. Material properties, load variability, fabrication fidelity, and validity of mathematical models are among concerns to designers.

There are mathematical methods to address uncertainties. The primary techniques are the deterministic and stochastic methods. The deterministic method establishes a design factor based on the absolute uncertainties of a loss-of-function parameter and a maximum allowable parameter. Here the parameter can be load, stress, deflection, etc. Thus, the design factor nd is defined as

nd = loss-of-function parameter / maximum allowable parameter

If the parameter is load (as would be the case for column buckling), then the maximum allowable load can be found from

Maximum allowable load = loss-of-function load / nd

Example : 

Consider that the maximum load on a structure is known with an uncertainty of ±20 percent, and the load causing failure is known within ±15 percent. If the load causing failure is nominally 2000 N, determine the design factor and the maximum allowable load that will offset the absolute uncertainties.

Solution :

To account for its uncertainty, the loss-of-function load must increase to 1/0.85, whereas the maximum allowable load must decrease to 1/1.2. Thus to offset the absolute uncertainties the design factor should be

The maximum allowable load is found to be