Some limitations of modal analysis in seismic design

  • R. Shepherd University of Canterbury, Christchurch, New Zealand


In the normal-mode, response-spectrum approach to earthquake resistant design of multistorey buildings the extended elastic seismic design loads are frequently calculated as the square root of the sum of the squares of the modal responses. The individual member forces are then determined using these seismic design loads. Previous research workers have examined the limitations of this technique and it is accepted as being generally applicable in practical design procedures.

Recent computer analyses of projected New Zealand high-rise buildings have illustrated two conditions in which the “square root of the sum of the modal responses squared” rule is inapplicable.

In this note these situations are described and suggestions are made of an alternative approach which may be adopted when deriving design loads in such cases.


Skinner, R.I. Earthquake-Generated Forces and Movements in Tall Buildings, New Zealand D.S.1.R. Bulletin 166, 1964.

Shepherd, R. The Determination of Seismic Design Loads in a Framed Structure. N.Z. Engineering, 1967, 22(2), 56-61.

Shepherd, R. The Dynamic Analysis of an Apartment Building, Bulletin of the Seismological Society of America, 1966, 56 (1), 13-36.

Shepherd, R, Lateral Load Analyses of the Auckland Customs House. N.Z. Engineering 1967, 22 (7), 213-211.

Shepherd, R. Seismic Lateral Load Analysis of a Steel Framed Building. N.Z. Engineering 1967, 22 (10), 407-413.

Merchant, H.C( & Hudson, D.E, Mode Superposition in Multi-degree of Freedom Systems Using Earthquake Response Spectrum Data. Bulletin of the Seismological Society of America 1962, 52 (2), 405-416.

Basic Design Loads. N.Z.S.S. 1900, Chapter 8, 1964. New Zealand Standards Institute.

Shepherd, R. & Donald, R.A.H. Seismic Response of Torsionally Unbalanced Buildings. Journal of Sound and Vibration 1967, 6 (1), 20-37.

Shepherd, R. Prediction of the Response of a Torsionally Unbalanced High-Rise Building to Earthquake Loading. Proceedings, First Australasian Conference on the Mechanics of Structures and Materials. Sydney 1967, 16-31.

How to Cite
Shepherd, R. (1969). Some limitations of modal analysis in seismic design. Bulletin of the New Zealand Society for Earthquake Engineering, 2(3), 284-288.