Offers on updating the normative formula
for the definition of seismic loads (SNiP P781)
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 onedimensional (cantilever)
models. While using threedimensional models it is necessary to take into account the
nonuniformity 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
threedimensional model.
Definition of the projections Sikj of the direction j of a seismic load Sik at imode 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 ith 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;
Xkhorizontal (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 (frameskeleton and tied
 frame structure, largepanel, largeblock, 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 imodes of own oscillations
vibrations of vertical elements of the cross direction (coordinate xk for onedimensional
model of the Codes are replaced with coordinates zk of the threedimensional model), and
tj by the formula
(10)
where Vj(Xkr)
 ordinates of the jmode 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 nonuniformity of the field of oscillations of soil
and resonant oscillations of a structure under influence of the number of longperiod
earthquakes with the prevailing periods Ts=0.61.5 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. 