TR.31.2.20 NTC (Normas Técnicas Complementarias) Seismic Load
The purpose of this command is to define and generate static equivalent seismic loads as per Code of the México Federal District (Reglamento de Construcciones del Distrito Federal de México) and Complementary Technical Standards for Seismic Design (y Normas Técnicas Complementarias (NTC) para Diseño por Sismo Nov. 1987) (Chapters 8.1 8.2 8.6 and 8.8) specifications. Depending on this definition, equivalent lateral loads will be generated in horizontal direction(s).
The seismic load generator can be used to generate lateral loads in the X & Z directions for Y up or X & Y for Z up. Y up or Z up is the vertical axis and the direction of gravity loads (See the SET Z UP command in TR.5 Set Command Specification). All vertical coordinates of the floors above the base must be positive and the vertical axis must be perpendicular to the floors.
General Format
DEFINE NTC LOAD
ntcspec
weightdata
Refer to Common Weight Data for information on how to specify structure weight for seismic loads.
Where:
ntcspec = { ZONE f1 QX f2 QZ f3 GROUP f4 (SHADOWED) (REGULAR) (REDUCE) (PX f5) (PZ f6) }
where:
 REGULAR is an optional parameter which is entered to consider the structure as a regular structure. By default, all structures are considered as irregular.
 SHADOWED is an optional parameter which is used to define the shaded zone II as the site of the structure. By default regular zone II is used.
 REDUCE is an optional parameter which allows to reduce the seismic factors as described above. Otherwise the following formula is used to calculate base shear, $V=\frac{c}{Q\prime}\stackrel{N}{\sum _{n=1}}{W}_{n}$
Generation of NTC Seismic Load
To provide NTC Seismic load in any load case:
LOAD i
NTC LOAD {X/Y/Z} (f)
where:
Parameter  Description 

LOAD i  load case number 
NTC LOAD { X  Y  Z } f  factor to multiply horizontal seismic load 
Methodology
The design base shear is computed in accordance with Sections 8.1 or 8.2 of the NTC as decided by the user.

Base Shear is given as
whereVo / Wo = c / Q  c
= Seismic Coefficient, which is obtained by the program from the following table
Table 1. Seismic coefficient per NTC Seismic Coefficient, c Group A Group B I 0.24 0.16 II not shaded 0.48 0.32 III (and II where shaded) 0.60 0.40  Q
=  is entered by the user as a parameter

Base shear is given as
Vo / Wo = a / Q’
Where Reduction of Shear Forces are requested
Time Period T of the structure is:calculated by the program based on using Rayleigh quotient technique.
you may override the period that the program calculates by specifying these in the input
a and Q’ are calculated according to the sections 3 and 4 of the NTC, that is to say:
$a=\begin{array}{c}(1+3\frac{T}{{T}_{a}})\frac{c}{4}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}T<{T}_{a}\\ c\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}{T}_{a}\le T\le {T}_{b}\\ q\cdot c\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}{T}_{b}<T\end{array}$Where:
q = (T_{b}/T)^{r}
${Q}^{\prime}=\begin{array}{c}Q\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}T\ge {T}_{a}\\ 1+\left(\frac{T}{{T}_{a}}\right)(Q1)\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}T<{T}_{a}\end{array}$If not regular, then Q’ = Q’ x 0.8
T_{a}, T_{b} and r are taken from table 513 (Table 3.1 in the NTC).
Table 2. Values of T_{a}, T_{b}and r per NTC Zone T_{a} T_{b} r I 0.2 0.6 1/2 II not shaded 0.3 1.5 2/3 III (and II where shaded) 0.6 3.9 1.0 a shall not be less than c/4
V_{o} for each direction is calculated:
${V}_{o}=\begin{array}{c}{W}_{o}a/{Q}^{\prime}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}T\le {T}_{b}\\ \frac{\Sigma {W}_{i}a}{{Q}^{\prime}({K}_{1}{h}_{i}+{K}_{2}{h}_{i}^{2})}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}T>{T}_{b}\end{array}$Where:
${K}_{1}=\frac{q[1\text{}r(1q\left)\right]\Sigma {W}_{i}}{\Sigma ({W}_{i}/{h}_{i})}$ ${K}_{2}=\frac{1.5rq(1q)\Sigma {W}_{i}}{\Sigma ({W}_{i}/{h}_{i}^{2})}$ W_{i} and h_{i} the weight and the height of the i^{th} mass over the soil or embedment level.
The base shear are distributed proportionally to the height if T ≤ T_{b} or with the quadratic equation mentioned if T > T_{b}. The distributed base shears are subsequently applied as lateral loads on the structure.