Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 295

8.5.2. Peak factor effect

The second error cause lies in the “peak factor effect”: the transposition of
formulae that can be applied to a variance calculation to maxima is generally not
valid. To understand such an effect, we will consider the special case of a structure
that responds according two almost similar contribution modes, the resonance
frequencies of which are quite separate (O 12 !! 1).

In this case, the simple quadratic combination formula well applies to the
variance calculation:

¦

2
nn

ı Į ı

[8.41]

2

x

n

Transposition to maxima would give:

¦

x Į a

[8.42]

2

n

2

max n max

n

The latter formula is only correct if the P n peak factors associated with each A n (t)
process are equal to each other and the X(t)(P X ) as well . If both modes have
neighboring damping ratios, the G n bandwidths will also be close, and providing that
both resonance frequencies are of similar orders, both peak factors will not be very
different either.