On the Correct Application of the 100-40-40 Rule for Combining Responses Due to three Directions of Earthquake Loading

The 100-40-40 rule is often used with the response spectrum analysis method to determine the maximum seismic responses from structural responses resulting from the three spatial earthquake components. This rule has been referenced in several recent Design Certification applications of nuclear power plants, and appears to be gaining in popularity. However, this rule is described differently in ASCE 4-98 and Regulatory Guide 1.92, consequently causing confusion on correct implementation of this rule in practice. The square root of the sum of the squares method is another acceptable spatial combination method and was used to justify the adequacy of the 100-40-40 rule during the development of the Regulatory Guide 1.92. The 100-40-40 rule, when applied correctly, is almost always conservative compared to the SRSS method, and is only slightly unconservative in rare cases. The purpose of this paper is to describe in detail the proper application of the 100-40-40 rule, as prescribed in ASCE 4-98 and in Regulatory Guide 1.92, and to clarify the confusion caused by the two different formats of this rule.