Àssociation for Ukrainian
Earthquake Engineering

Offers on updating the normative formula
for the definition of seismic loads (SNiP P-7-81)

To realize in practice theoretical research and to really raise the reliability of structures it is necessary to make changes in codes.

The formula for definition of seismic forces in a more general view, applicable to the different models is offered. In a specific case formula (7) transforms into the known normative formula for the definition of seismic forces for one-dimensional (cantilever) models. While using three-dimensional models it is necessary to take into account the non-uniformity of the field of soil according to the length and the width of the building (structure).

Item 2.5. of the the Codes needs changes (changes are underlined) which have to be stated in the following edition:
2.5. For buildings and structures of columnar type such as (L/B *2; H/L*3; L, B, H- length, width, height) calculation seismic load... and further in the text.
.
It is necessary to state item 2.8 of the Codes in the following edition:
2.8. For buildings and structures having complex configuration or asymmetrical in plan distribution of rigidities and masses, seismic loads should be determined according to the three-dimensional model.
Definition of the projections Sikj of the direction j of a seismic load Sik at i-mode of oscillations, influencing an element with weight Qk, relating to a point "k" of the model of a building, is made after the formula

(7)

similar to the formulas (1) and (2) of the Codes.
Thus the coefficients of the forms *ikj are determined after the formula

(8)

Where Uikj - projections of displacements of points "k" in three mutually orthogonal directions (j=1,2,3) for i-th frequency of free oscillations;
cos(Uikj, U0) - cosines of angles between directions of the vector of seismic impact and displacements Uikj;
fkj - ordinates of the field of oscillations of ground determined after the formulas:
fkjl = 1 - for the horizontal direction 1 of seismic impact (along the building);

for the horizontal direction 2 of seismic impact (across the building);

for the vertical direction 3 of seismic impact;

 Fig. 7 Spectral coefficients according to the lengths of seismic waves: í1 - for progressive, í2 - for torsional, í3 - for flexural in plan oscillations of a building or a structure ;M1 ((t), M2 ((t), M3 ((t) - wave spectral coefficients determined depending on Dt=L/c=LTs / l in the diagrams on the fig. 7; c - speed of the distribution of seismic waves in ground; l - length of a seismic wave; Ts - prevailing period of seismic waves; Xk-horizontal (direction 1) coordinate of the point "k"; m is the ratio between the maximal accelerations of soil at vertical and horizontal oscillations (m=0.5 - 0.75).

It is necessary to state the item 2.9 of the Codes in the following edition:
2.9. For buildings and structures of relatively regular structure (frame-skeleton and tied - frame structure, large-panel, large-block, brick inhabited and public buildings), center of rigidity and the mass center of which are in the longitudinal plane of the symmetry, seismic loads should be accepted as horizontal in the direction of longitudinal and cross axes. In the first case seismic loads are determined after the formulas (1) and (2) of the Codes; in the second case- after the formula (7) of these "Offers", coefficients of the modes *ikj of which are calculated after the formula

(9)

where hikj are determined by the formula (6) of the Codes for averaged i-modes of own oscillations vibrations of vertical elements of the cross direction (coordinate xk for one-dimensional model of the Codes are replaced with coordinates zk of the three-dimensional model), and tj -by the formula

(10)

where Vj(Xkr) - ordinates of the j-mode of own oscillations of floors at the points of concentration of masses íkr (k- number of the floor, r- number of the vertical element of the cross direction);
fkr2 - ordinates of the field of oscillations of the ground determined after the formula (8) of the "Offers", m - number of vertical elements of the cross direction.

It is necessary to state the item to state the item 2.15 of the Codes in the following edition:

2.15. Especially important structures (atomic power or chemical plants, dams, high extended buildings etc.) can be designed according to the item 2.2. "b" of the Codes with use of tool records of accelerations or according to the linear - spectral theory with taking into account the non-uniformity of the field of oscillations of soil and resonant oscillations of a structure under influence of the number of long-period earthquakes with the prevailing periods Ts=0.6-1.5 c.
Seismic forces are determined after the formula (7) of the "Offers".
Dynamic coefficient
bi is equal

(11)

where Ti - period of own oscillations of a structure.