Optimal number of load combinations in structural analysis

P.C.J. Hoogenboom

Delft University of Technology, Faculty of Civil Engineering and Geosciences, the Netherlands

In this paper, the optimal number of load combinations is calculated for analysing engineering structures. This number depends on the quantity of load cases, the cost of the structure and the cost of analysing one load combination. The problem can be reduced to a geometrical challenge: find polytopes that fit a sphere in hyperspace. Three examples show that the optimal number can be much larger than the number applied in current practice.

Key words: Partial factors, LRFD, safety factors, load cases, load combinations, structural reliability, structural design, structural analysis, convex polytopes, circum-sphere, in-sphere