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Steel and Composite Structures
  Volume 12, Number 4, April 2012 , pages 353-379

Accuracy of combination rules and individual effect correlation: MDOF vs SDOF systems
Alfredo Reyes-Salazar*, Federico Valenzuela-Beltran, David de Leon-Escobedo,Eden Bojorquez and Arturo Lopez-Barraza

    The accuracy of the 30% and SRSS rules, commonly used to estimate the combined response of structures, and some related issues, are studied. For complex systems and earthquake loading, the principal components give the maximum seismic response. Both rules underestimate the axial load by about 10% and the COV of the underestimation is about 20%. Both rules overestimate the base shear by about 10%. The uncertainty in the estimation is much larger for axial load than for base shear, and, for axial load, it is much larger for inelastic than for elastic behavior. The effect of individual components may be highly correlated, not only for normal components, but also for totally uncorrelated components. The rules are not always inaccurate for large values of correlation coefficients of the individual effects, and small values of such coefficients are not always related to an accurate estimation of the response. Only for perfectly uncorrelated harmonic excitations and elastic analysis of SDOF systems, the individual effects of the components are uncorrelated and the rules accurately estimate the combined response. In the general case, the level of underestimation or overestimation depends on the degree of correlation of the components, the type of structural system, the response parameter, the location of the structural member and the level of structural deformation. The codes should be more specific regarding the application of these rules. If the percentage rule is used for MDOF systems and earthquake loading, at least a value of 45% should be used for the combination factor.
Key Words
    seismic design codes; combination rules; effect of individual components; steel buildings; correlation of effects; MDOF and SDOF systems.
Alfredo Reyes-Salazar*, Federico Valenzuela-Beltran,Eden Bojorquez and Arturo Lopez-Barraza : Facultad de Ingenieria, Universidad Autonoma de Sinaloa, Ciudad Universitaria, Culiacan Sinaloa, Mexico
David de Leon-Escobedo : Facultad de Ingenieria,Universidad Autonoma del Estado de Mexico, Ciudad Universitaria, Toluca, Estado de Mexico, Mexico

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