TR.31.2.19 CFE (Comisión Federal De Electricidad) Seismic Load

The purpose of this command is to define and generate static equivalent seismic loads as per Manuel de Diseño por Sismo - Seismic Design Handbook Comisión Federal De Electricidad - Electric Power Federal Comission - October 1993 (Chapters 3.1, 3.2, 3.3 and 3.4) specifications. Depending on this definition, equivalent lateral loads will be generated in horizontal direction(s). This is a code used in the country of Mexico.

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 CFE  (ACCIDENTAL) LOAD

cfe-spec

weight-data

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

Where:

cfe-spec = { ZONE  f1  QX f2 QZ f3 GROUP f4 STYP f5 (REGULAR) (TS f6) (PX f7) (PZ f8) }

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
STYPE f5	Soil type entered as 1 or 2 or 3
TS f6	site characteristic period
PX f7	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 f8	Optional Period of structure (in sec) in Z direction (or Y if SET Z UP is used) to be used as fundamental period of the structure instead of the value calculated by the program using Rayleigh-Quotient method

The optional parameter REGULAR is entered to consider the structure as a regular structure. By default, all structures are considered as irregular.

Generation of CFE Seismic Load

To provide a CFE Seismic load in any load case:

LOAD i

CFE LOAD  {X | Y | Z}  (f)

Where:

Parameter	Description
LOAD i	load case number
CFE LOAD { X \| Y \| Z \| f	factor to multiply horizontal seismic load. Choose horizontal directions only

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

Seismic zone coefficient and parameter values are supplied by the user through the DEFINE CFE LOAD command.

Program calculates the natural period of building T utilizing Rayleigh-Quotient method. If time period is provided in the input file, that is used in stead of calculated period.

The acceleration a is calculated according to the following:

a = \begin{matrix} a_{0} + (c - a_{0}) \frac{T}{T_{a}} when T < T_{a} \\ c when T_{a} \leq T \leq T_{b} \\ c {(T_{b} / T)}^{r} when T_{b} < T \end{matrix}

Where:

c = Seismic coefficient is extracted from table 3.1
a₀, T_a, T_b, and r are obtained form table 3.1

The ductility reduction factor Q’ is calculated according to section 3.2.5.

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

If the period T_s of the soil is known and the soil type II or III T_a and T_b will be modified according to section 3.3.2.

Lateral loads for each direction are calculated for:

When T ≤ T_b, Eq. 4.5. Section 3.4.4.2 is used:

P_{n} = W_{n} h_{n} \frac{Σ_{n = 1}^{N} (W_{n}) a}{Σ_{n = 1}^{N} (W_{n} h_{n}) Q'}

When T > T_b, Eq. 4.6/7/8. Section 3.4.4.2 is used:

P_{n} = W_{n} (a / Q) (K_{1} h_{i} + K_{2} h_{i}^{2})

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})}

q = (T_b/T)^r

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 CFE LOAD
ZONE 2 QX .5 QZ 0.9 STYP 2 GROUP B TS 0.2
SELFWEIGHT
MEMBER WEIGHT
1 TO 36 41 TO 50 UNI 300
JOINT  WEIGHT
51 56 93 100 WEIGHT 1440
101 106 143 150 WEIGHT 1000
FLOOR WEIGHT
YRA 11.8 12.2 FLOAD 400 -
XRA -1 11 ZRA -1 21
LOAD 1 ( SEISMIC LOAD IN X DIRECTION )
CFE  LOAD  X 1.0
LOAD 2 ( SEISMIC LOAD IN -Z DIRECTION )
CFE  LOAD  Z -1.0