TR.31.2.5 Chinese Static Seismic per GB50011-2001

This set of commands may be used to define and generate static equivalent seismic loads as per Chinese specifications GB50011-2001. This load uses a static equivalent approach, similar to that found in the UBC. Depending on this definition, equivalent lateral loads will be generated in the horizontal direction(s).

General Format

The following general format should be used to generate loads in a particular direction.

DEFINE GB50011 2001 (ACCIDENTAL) LOAD

Note: The GB50011-2001 static seismic has superseded the 2010 edition. In order to use the 2001 edition you must directly specify the code year. Otherwise, the program will default to the latest code edition as is typical for STAAD.Pro.

INTENSITY s1 { FREQUENT | RARE } GROUP i1 SCLASS i2 (DAMP f1) GFACTOR { 0.85 | 1.0 } (DELN f2) (SF f3) (PX f4) (PZ f5)

Where:

Parameter	Definition
INTENSITY `s1`	the Fortification Intensity (ref. table 5.1.4-1). Acceptable values are 6, 7, 7A, 8, 8A, or 9. 7A represents 7 (0.15g), 8A represents 8 (0.30g).
FREQUENT \| RARE	Frequency of seismic action, as specified by `FREQUENT` or `RARE` (ref. table 5.1.4-1).
GROUP `i1`	Design Seismic Group (ref. table 5.1.4-2). Acceptable values are 1,2, or 3.
SCLASS `i2`	Site-Class (ref. table 5.1.4-2). Acceptable values are 1, 2, 3, or 4.
DAMP `f1`	Damping ratio (default = 0.05 for 5% damping)
GFACTOR	Equivalent factor of gravity load of horizontal seismic action, as specified by 0.85 or 1.0 (ref. clause 5.2.1). The default value is 0.85.
DELN `f2`	δ_n , Additional seismic action factor at the top of the building (default as calculated from Table 5.2.1)
SF `f3`	Shear Factor, λ, Minimum seismic shear factor of the floor (default as calculated from Table 5.2.5)
PX `f4`	optional time period along the X direction
PZ `f5`	optional time period along the Z direction

Generation of GB50011 Seismic Load

To apply the load in any load case, following command would be used

LOAD CASE i

GB LOAD { X | Y | Z } (f6) (ACC f7)

Where:

Parameter	Definition
LOAD `i`	load case number
GB LOAD { X \| Y \| Z } `f6`	An optional factor to multiply horizontal seismic load.
ACC `f7`	The multiplying factor for Accidental Torsion, to be used to multiply the accidental torsion load (default = 1.0). May be negative (otherwise, the default sign for MY is used based on the direction of the generated lateral forces).

Note: If the ACCIDENTAL option is specified, the accidental torsion will be calculated per the GB specifications. The value of the accidental torsion is based on the "center of mass" for each level. The "center of mass" is calculated from the SELFWEIGHT, JOINT WEIGHTs and MEMBER WEIGHTs you have specified.

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.

Notes:

When the seismic load is defined as per topic TR.32.12.2 Generation of Seismic Loads, then currently only the accidental torsion ACC is supported, DEC is not supported.
If the ACCIDENTAL option is specified, the accidental torsion will be calculated per the GB 50011-2001 specifications. The value of the accidental torsion is based on the center of mass for each level. The center of mass is calculated from the selfweight, joint weights and member weights you have specified. 
The seismic load generator can be used to generate lateral loads in the X and Z directions for Y up and the X and Y directions for Z up; where Y up or Z up is the vertical axis parallel to 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.
This method of seismic load generation is limited in use to buildings not taller than 40 meters, with deformations predominantly due to shear, and a rather uniform distribution of mass and stiffness in elevation. Alternately, for buildings modeled as a single-mass system, a simplified method such as this base shear method, may be used.

Gravity Loads for Design

In the computation of seismic action, the representative value of gravity load of the building shall be taken as the sum of characteristic values of the weight of the structure and members plus the combination values of variable loads on the structure. The combination coefficients for different variable loads shall be taken from the following table.

Table 1. Combinations of different load effects per GB50011-2001
Type of Variable	land Combination coefficient
Snow load	0.5
Dust load on roof	0.5
Live load on roof	Not considering
Live load on the floor, calculated according to actual state	1.0
Live load on the floor, calculated according to equivalent uniform state	Library, archives	0.8
	Other civil buildings	0.5
Gravity for hanging object of crane	Hard hooks	0.3
Gravity for hanging object of crane	Soft hooks	Not considering

Seismic Influence Coefficient

This shall be determined for building structures according to the Intensity, Site-class, Design seismic group, and natural period and damping ratio of the structure. The maximum value of horizontal seismic influence coefficient shall be taken from Table 2.2; the characteristic period shall be taken as Table 2.3 according to Site-class and Design seismic group, that shall be increased 0.05s for rarely earthquake of Intensity 8 and 9.

Table 2. Earthquake influence per GB50011-2001
Earthquake influence	Intensity 6	Intensity 7	Intensity 8	Intensity 9
Frequent earthquake	0.04	0.08 (0.12)	0.16(0.24)	0.32
Rarely earthquake	-	0.50(0.72)	0.90(1.20)	1.40

Note: The values in parenthesis are separately used for where the design basic seismic acceleration is 0.15g and 0.30g.

Table 3. Earthquake group per GB50011-2001
Earthquake Group	Site class
Earthquake Group	I	II	III	IV
1	0.25	0.35	0.45	0.65
2	0.30	0.40	0.55	0.75
3	0.35	0.45	0.65	0.90

Calculation of Seismic Influence Coefficient

The design base shear is computed in accordance with the equations shown below.

The damping adjusting and forming parameters on the building seismic influence coefficient curve (Fig.2.1) shall comply with the following requirements:

The damping ratio of building structures shall select 0.05 except otherwise provided, the damping adjusting coefficient of the seismic influence coefficient curve shall select 1.0, and the coefficient of shape shall conform to the following provisions:
1. Linear increase section, whose period (T) is less than 0.1 s;
2. Horizontal section, whose period form 0. is thought to characteristic period, shall select the maximum value (α_max);
3. Curvilinear decrease section, whose period from characteristic period thought to 5 times of the characteristic period, the power index (γ) shall choose 0.9.
4. Linear decrease section, whose period from 5 times characteristic period thought to 6s, the adjusting factor of slope (η₁) shall choose 0.02.
Figure 1. Seismic influence coefficient curve
When the damping adjusting and forming parameters on the seismic influence coefficient curve shall comply with the following requirements:
1. The power index of the curvilinear decreased section shall be determined according to the following equation E2.1
  
  (E2.1)
  
  where
  
  γ
  =
  
  the power index of the curvilinear decrease section
  
  ξ
  =
  
  the damping ratio
2. The adjusting factor of slope for the linear decrease section shall be determined from following equation:
  
  (E2.2)
  
  where
  
  η₁
  =
  
  the adjusting factor of slope for the linear decrease section, when it is less than 0, shall equal 0.
3. The damping adjustment factor shall be determined according to the following equation:
  
  (E2.3)
  
  where
  
  η₂
  =
  
  the damping adjustment factor, when it is smaller than 0.55 shall equal 0.55.

Calculation of Horizontal Seismic Action

Characteristic Value of Horizontal Seismic Action

When the base shear force method is used, only one degree of freedom may be considered for each story; the characteristic value of horizontal seismic action of the structure shall be determined by the following equations:

(E2.4)(E2.5)(E2.6)

Figure 2. Calculation of horizontal seismic action

F_Ek: characteristic value of the total horizontal seismic action of the structure
α₁: horizontal seismic influence coefficient corresponding to the fundamental period of the structure, which shall be determined by using Clause 2.3. For multistory masonry buildings and multi-story brick buildings with bottom-frames or inner-frames, the maximum value of horizontal seismic influence coefficient should be taken.
G_eq: equivalent total gravity load of a structure. When the structure is modeled as a single-mass system, the representative value of the total gravity load shall be used; and when the structure is modeled as a multi-mass system, the 85% of the representative value of the total gravity load may be used.
F_i: characteristic value of horizontal seismic action applied on mass i^th level.
G_i , G_j: representative values of gravity load concentrated at the masses of i^th and j^th respectively, which shall be determined by Clause 2.1.
H_i , H_j: calculated height of i^th and j^th from the base of the building respectively.
δ_n: additional seismic action factors at the top of the building; for multi-story reinforced concrete buildings, it may be taken using Table 2.4; for multi-story brick buildings with inner-frames, a value of 0.2 may be used; no need to consider for other buildings
ΔF_n: additional horizontal seismic action applied at top of the building.

Table 4. Additional seismic action factors at top of the building (Table 5.2.1 from GB50011)
T_g (s)	T₁ > 1.4T_g	T₁ ≤ 1.4T_g
T_g ≤ 0.35	0.08T₁ + 0.07	0
0.35 < T_g ≤ 0.55	0.08T₁ + 0.01
T_g > 0.55	0.08T₁ − 0.02

Note: T₁ is the fundamental period of the structure.

Horizontal Seismic Shear Force Verification

The horizontal seismic shear force at each floor level of the structure shall comply with the requirement of the following equation:

(E2.7)

where

V_Eki: the floor i^th shear corresponding to horizontal seismic action characteristic value.
λ: Shear factor, it shall not be less than values in Table 2.5; for the weak location of vertical irregular structure, these values shall be multiplied by the amplifying factor of 1.15.
G_j: the representative value of gravity load in floor j^th of the structure.

Table 5. Minimum seismic shear factor value of the floor level per GB50011-2001
Structures	Intensity 7	Intensity 8	Intensity 9
structures with obvious torsion effect or fundamental period is less than 3.5s	0.16 (0.024)	0.032 (0.048)	0.064
Structures with fundamental period greater than 5.0s	0.012 (0.018)	0.024 (0.032)	0.040

Note:

The values may be selected through interpolation method for structures whose fundamental period is between 3. 5s and 5s.
Values in the brackets are used at the regions with basic seismic acceleration as 0.15g and 0.30g respectively.

Notes

Structures having the oblique direction lateral-force-resisting members and the oblique angel to major orthogonal axes is greater than 150, the horizontal seismic action along the direction of each lateral-force-resisting member shall he considered respectively. So we could consider this though the item, the action of the oblique member could be multiplied by this factor as design force.
Eccentricity: similar to UBC code. The eccentricity value of gravity center on each floor should be e_i= ±0.05L_i ,

e_i
=

Eccentricity value of gravity center on i^th floor.

L_i
=

maximum width of calculated story of the building.
Structures having obviously asymmetric mass and stiffness distribution, the torsion effects caused by both two orthogonal horizontal direction seismic action shall be considered; and other structures, it is permitted that a simplified method, such as adjusting the seismic effects method, to consider their seismic torsion effects.

Example

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 12-Oct-09
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 9 0; 3 0 3 0; 4 0 6 0;
MEMBER INCIDENCES
1 1 3; 2 3 4; 3 4 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY CHINESE
1 TO 3 TABLE ST HW400X400
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
DEFINE GB50011 2001 LOAD
INTENSITY 7 FREQUENT GROUP 2 SCLASS 3 DAMP 0.06 AV 0.03 PX 1.5 PZ 0.6
SELFWEIGHT 1
JOINT WEIGHT
2 TO 4 WEIGHT 10
LOAD 1
GB50011 LOAD X 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
PRINT SUPPORT REACTION LIST 1
PRINT JOINT DISPLACEMENTS LIST 1 TO 4
PERFORM ANALYSIS PRINT STATICS CHECK
FINISH