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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 GB (ACCIDENTAL) LOAD
INTENSITY s1 { FREQUENT | RARE } GROUP i1 SCLASS i2 (DAMP f1) (DELN f2) (SF f3) (AV f4) (PX f5) (PZ f6)

Where:

ParameterDescription
INTENSITY s1 the Fortification Intensity (ref. table 5.1.4-1). Acceptable values are 6, 7, 7A, 8, 8A, or 9.
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)
DELN f2 δn , 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)
AV f4 maximum value of vertical seismic influence coefficient α(v,max) (default=0.0) (ref. section 5.3)

Frequency of seismic action, as specified by either FREQUENT or RARE (ref. table 5.1.2-2)

As a fraction of total vertical load is to be considered such as 0.75Geq, specify the product of the factor on maximum horizontal seismic influence factor and factor of total gravity load as f4. For instance,

  • α(v,max) = 0.65αmax

And

  • Gv,eq = 0.75Geq
  • Specify f4 as (0.65*0.75) i.e., equal to 0.4875
PX f5 optional time period along the X direction
PZ f6 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 } (f7) (ACC f8)

Where:

ParameterDescription
LOAD i load case number
GB LOAD { X | Y | Z } f7 optional factor to multiply horizontal seismic load.
ACC f8 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 GUID-6D9B5C48-9FFF-4548-BFB4-ACAE1E973743.

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).

Note: 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
  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
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:

  1. 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 (αmax);
    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.

    Seismic influence coefficient curve

  2. 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

      γ = 0.9 + 0.05 ζ 0.5 + 5 ζ 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:

      η1 = 0.02+(0.05-ζ)/8 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:

      η 2 = 1 + 0.05 ζ 0.06 + 1.7 ζ
      where
      η2
      =
      the damping adjustment factor, when it is smaller than 0.55 shall equal 0.55.

Calculation 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 (Fig. 2.2):

FEk = α1Geq           E2.4

F i = G i H i j = 1 n G j H j F E k ( 1 δ n ) E2.5

ΔFn = δnFEkE2.6

Calculation of horizontal seismic action

where
FEk
=
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.
Geq
=
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.
Fi
=
characteristic value of horizontal seismic action applied on mass ith level.
Gi, Gj
=
representative values of gravity load concentrated at the masses of ith and jth respectively, which shall be determined by Clause 2.1.
Hi, Hj
=
calculated height of ith and jth from the base of the building respectively.
δn
=
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
ΔFn
=
additional horizontal seismic action applied at top of the building.

Table 2.4 Additional seismic action factors at top of the building

Note: T, is the fundamental period of the structure.

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

V E k i > λ j = 1 n G j
where
VEki
=
the floor ith 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.
Gj
=
the representative value of gravity load in floor jth of the structure.
Table 4. 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:
  1. The values may be selected through interpolation method for structures whose fundamental period is between 3. 5s and 5s.
  2. Values in the brackets are used at the regions with basic seismic acceleration as 0.15g and 0.30g respectively.

Calculation of vertical seismic action

For tall buildings for Intensity 9, the characteristic value of vertical seismic action shall be determined by the following equations (figure 2.3). The effects of vertical seismic action at floor level may be distributed in proportion of representative value of gravity load acting on the members, which should multiply with the amplified factor 1.5:

FEvk = αvmaxGeqE2.8

F i = G i H i j = 1 n G j H j F E v k E2.9
where
FEvk
=
characteristic value of the total vertical seismic actions of the structure.
Fv
=
characteristic value of vertical seismic action at the level of mass ith.
αvmax
=
maximum value of vertical seismic influence coefficient, which may be taken as 65% of the maximum value of the horizontal seismic influence coefficient.
Geq
=
equivalent total gravity load of the structure, which may be taken as 75% of the representative value of the total gravity load of the structure.

Sketch for the computation of vertical seismic action

Complementarities

  1. 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.
  2. Eccentricity: similar to UBC code. The eccentricity value of gravity center on each floor should be ei = ±0.05Li,

    where
    ei
    =
    Eccentricity value of gravity center on ith floor.
    Li
    =
    maximum width of calculated story of the building.
  3. 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 Input

DEFINE GB50011  LOAD
INTENSITY 7 FREQUENT GROUP 2 SCLASS 3

Example Output

*****************************************************************************
* *
* EQUIV. SEISMIC LOADS AS PER SEISMIC DESIGN CODE FOR BUILDINGS *
* (GB50011-2001) OF CHINA ALONG X *
* T CALCULATED = 0.252 SEC. T USER PROVIDED = 1.200 SEC. *
* T USED = 1.200 SEC. *
* MAX. HORIZONTAL SEISMIC INFLUENCE COEFFICIENT = 0.240 *
* CHARACTERISTIC PERIOD = 0.750 SEC. *
* DAMPING RATIO = 0.030 POWER INDEX (GAMMA) = 0.931 *
* DAMPING ADJUSTMENT FACTOR (ETA2) = 1.180 *
* ADJUSTING FACTOR (ETA1) = 0.022 *
* HORIZONTAL SEISMIC INFLUENCE COEFFICIENT (ALPHA1) = 0.183 (18.288%) *
* MINIMUM SHEAR FACTOR AS PER SEC. 5.2.5 (LAMBDA) = 0.050 ( 5.000%) *
* TOTAL HORIZONTAL SEISMIC ACTION = *
* = 0.183 X 285.529 = 52.218 KIP *
* DESIGN BASE SHEAR = 0.750 X 52.218 *
* = 39.164 KIP *
* ADDITIONAL SEISMIC ACTION FACTOR (DELTAN) = 0.020 *
* VERTICAL SEISMIC INFLUENCE COEFFICIENT (ALPHA,VMAX) = -0.108 *
* TOTAL VERTICAL SEISMIC ACTION = *
* = -0.108 X 285.529 = -30.837 KIP *
* TOTAL DESIGN VERTICAL LOAD = 0.750 X -30.837 *
* = -23.128 KIP *
* *
*****************************************************************************
CHECK FOR MINIMUM LATERAL FORCE AT EACH FLOOR [GB50011-2001:5.2.5]
LOAD - 1 FACTOR - 0.750
FLOOR LATERAL GRAVITY LAMBDA LAMBDA ADJUSTMENT
HEIGHT (KIP ) LOAD (KIP ) LOAD (KIP ) (%) MIN (%) FACTOR
------------- ----------- ------------ ------ ------ -----------
30.000 23.406 79.045 29.61 5.00 1.00
20.000 19.208 180.888 10.62 5.00 1.00
10.000 9.604 282.731 3.40 5.00 1.47
JOINT LATERAL TORSIONAL VERTICAL LOAD - 1
LOAD (KIP ) MOMENT (KIP -FEET) LOAD (KIP ) FACTOR - 0.750
----- ------- --------- -----------
17 FX 0.541 MY 0.000 FY -0.221
18 FX 0.663 MY 0.000 FY -0.271
19 FX 0.663 MY 0.000 FY -0.271
20 FX 0.541 MY 0.000 FY -0.221
21 FX 0.663 MY 0.000 FY -0.271
22 FX 0.785 MY 0.000 FY -0.321
23 FX 0.785 MY 0.000 FY -0.321
24 FX 0.663 MY 0.000 FY -0.271
25 FX 0.663 MY 0.000 FY -0.271
26 FX 0.785 MY 0.000 FY -0.321
27 FX 0.785 MY 0.000 FY -0.321
28 FX 0.663 MY 0.000 FY -0.271
29 FX 0.541 MY 0.000 FY -0.221
30 FX 0.663 MY 0.000 FY -0.271
31 FX 0.663 MY 0.000 FY -0.271
32 FX 0.541 MY 0.000 FY -0.221
----------- ----------- ----------------
TOTAL = 10.602 0.000 -0.221 AT LEVEL 10.000 FEET