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

ntc-spec

weight-data

Refer to Common Weight Data for information on how to specify structure weight for seismic loads.

Where:

ntc-spec = { ZONE f1 QX f2 QZ f3 GROUP f4 (SHADOWED) (REGULAR) (REDUCE) (PX f5) (PZ f6) }

where:

Parameter	Description
ZONE f1	Zone number specified in number such as 1, 2, 3 or 4
QX f2	seismic behavior factor of the structure along X direction as a parameter according 3.2.4.
QZ f3	seismic behavior factor of the structure along Z direction as a parameter according 3.2.4.
GROUP f4	Group of structure entered as A or B
PX f5	Optional Period of structure (in sec) in X-direction to be used as fundamental period of the structure instead of the value calculated by the program using Rayleigh-Quotient method
PZ f6	Optional Period of structure (in sec) in Z-direction to be used as fundamental period of the structure instead of the value calculated by the program using Rayleigh-Quotient method

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, $V = \frac{c}{Q'} \overset{N}{\sum_{n = 1}} W_{n}$

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

Note: For additional details on the application of a seismic load definition used to generate loads, refer to TR.32.12.2 Generation of Seismic Loads.

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

Vo / Wo = c / Q

where

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

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{matrix} (1 + 3 \frac{T}{T_{a}}) \frac{c}{4} when T < T_{a} \\ c when T_{a} \leq T \leq T_{b} \\ q \cdot c when T_{b} < T \end{matrix}

Where:

q = (T_b/T)^r

Q^{'} = \begin{matrix} Q when T \geq T_{a} \\ 1 + (\frac{T}{T_{a}}) (Q - 1) when T < T_{a} \end{matrix}

If not regular, then Q’ = Q’ x 0.8

T_a, T_b and r are taken from table 5-13 (Table 3.1 in the NTC).

Table 2. Values of T_a, T_band 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{matrix} W_{o} a / Q^{'} when T \leq T_{b} \\ \frac{Σ W_{i} a}{Q^{'} (K_{1} h_{i} + K_{2} h_{i}^{2})} when T > T_{b} \end{matrix}

Where:

K_{1} = \frac{q [1 - r (1 - q)] Σ W_{i}}{Σ (W_{i} / h_{i})}

K_{2} = \frac{1.5 r q (1 - q) Σ W_{i}}{Σ (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.

Example

UNIT KGS METER
DEFINE NTC LOAD
ZONE 2 QX .5 QZ 0.9 GROUP B
SELFWEIGHT
ELEMENT  WEIGHT
1577 TO 1619 PRESSURE 275
LOAD 1 ( SEISMIC LOAD IN X DIRECTION )
NTC  LOAD  X 1.0
LOAD 2 ( SEISMIC LOAD IN Z DIRECTION )
NTC  LOAD  Z 1.0