# V. GB 50011-2001 Static Seismic - Case2

Calculate the base shear and its distribution along the height using the equivalent lateral force method in GB 50011-2001 using a equivalent gravity load factor for horizontal seismic action of 1.0.

## Details

Structure to be modelled:
• height = 3× 4m = 12m
• plan dimension X = 4m
• plan dimension Z = 5m
Input parameters:
• Frequency of seismic event: Frequent
• Classification of seismic design: Group 2
• Site class: II
• Period in the X direction: T = 0.467s
• Equivalent gravity load factor for horizontal seismic action: 1.0
• Damping ratio, ζ = 0.05 (default in STAAD.Pro)

The section of all members is HW300X300, and the seismic weight for each floor is assumed as 280 kN applied as joint weight of 70 kN to nodes 2, 3, 5, 6, 8, 9, and 11 to 16. S

## Validation

The effective weight of the structure:

The max value of the horizontal seismic influence for a "frequent" earthquake with intensity of 8, ɑmax = 0.16 (Table 5.1.4-1)

The characteristic period, Tg = 0.4s (Table 5.1.4-2)

The power index of the curvilinear decrease section:

$γ = 0.9 + 0.05 - ζ 0.5 + 5 ζ = 0.9$

$η 2 = 1 + 0.05 - ζ 0.06 + 1.7 ζ = 1.0$

Tg < T < 5Tg

The horizontal seismic influence coefficient corresponding to the fundamental period of the structure:

$ɑ 1 = ( T g T ) γ η 2 × ɑ max = ( 0.4 0.467 ) 0.9 1.0 × 0.16 = 0.139$

The characteristic value of the total horizontal seismic action of the structure:

 (Eq. 2.5)

T = 0.467 < 1.4Tg = 0.56

Additional seismic action factors at the top of the building δn = 0

Additional horizontal seismic action applied at top of the building ΔFn = δn × FEk = 0

Characteristic value of horizontal seismic action applied at the ith mass:

$F i = G i H i ∑ j = 1 n G j H j F E k ( 1 - δ n )$
Story Level Gi

(kN)

Hi

(m)

GiHi

(kN·m)

GiHi/ΣGiHi Fi

(kN)

ΔFn

(kN)

Vi

(kN)

3rd 280 12 3,360 0.5 58.457 0 58.457
2nd 280 8 2,240 0.333 38.971 97.428
1st 280 4 1,120 0.167 19.486 116.914
Σ 840 6,720 1

(kN)

(kN)

λ

(%)

λmin

(%)

Factor

3rd 58.457 280 20.88 3.2 1
2nd 97.428 560 17.4 3.2 1
1st 116.914 840 13.92 3.2 1

## Results

Table 1. Comparison of results
Story Shear, Fi (kN) 1st 19.486 19.486 negligible
2nd 38.971 38.971 negligible
3rd 58.457 58.457 negligible
Base Shear, V (kN) 116.914 116.914 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\GB 50011\GB 50011-2001 Static Seismic - Case2.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-May-15
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4 0; 3 4 4 0; 4 4 0 0; 5 0 8 0; 6 4 8 0; 7 0 0 5; 8 0 4 5;
9 4 4 5; 10 4 0 5; 11 0 8 5; 12 4 8 5; 13 0 12 0; 14 4 12 0; 15 0 12 5;
16 4 12 5;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 5 6; 6 6 3; 7 2 8; 8 3 9; 9 5 11; 10 6 12;
11 7 8; 12 8 9; 13 9 10; 14 8 11; 15 11 12; 16 12 9; 17 5 13; 18 6 14;
19 11 15; 20 12 16; 21 13 14; 22 13 15; 23 14 16; 24 15 16;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY CHINESE
1 TO 24 TABLE ST HW300X300
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 7 10 FIXED
2 3 5 6 8 9 11 TO 16 FY -70
INTENSITY 8 FREQUENT GROUP 2 SCLASS 2 GFA 1.0 PX 0.467
R1 1.0
PRINT ANALYSIS RESULTS
FINISH


   LOADING     1  LOADTYPE SEISMIC  TITLE EL-X DIR
-----------
*****************************************************************************
*                                                                           *
* EQUIV. SEISMIC LOADS AS PER SEISMIC DESIGN CODE FOR BUILDINGS             *
*                              (GB50011:2001) OF CHINA ALONG X              *
*  T CALCULATED =  0.685 SEC.      T USER PROVIDED =  0.467 SEC.            *
*  T USED =  0.467 SEC.                                                     *
*  MAX. HORIZONTAL SEISMIC INFLUENCE COEFFICIENT =  0.160                   *
*  CHARACTERISTIC PERIOD =  0.400 SEC.                                      *
*  DAMPING RATIO =  0.050    POWER INDEX (GAMMA) = 0.900                    *
*  DAMPING ADJUSTMENT FACTOR (ETA2) =  1.000                                *
*  ADJUSTING FACTOR (ETA1) =  0.020                                         *
*  HORIZONTAL SEISMIC INFLUENCE COEFFICIENT (ALPHA1) =  0.139  (13.918%)    *
*  MINIMUM SHEAR FACTOR AS PER SEC. 5.2.5 (LAMBDA) =   0.032  (  3.200%)    *
*  EQUIVALENT GRAVITY LOAD FACTOR FOR HORIZONTAL SEISMIC ACTION =  1.000    *
*  TOTAL HORIZONTAL SEISMIC ACTION =                                        *
*          =  0.139 X      1.000 X    840.000 =      116.914  KN            *
*  DESIGN BASE SHEAR =  1.000 X      116.914                                *
*                    =      116.914  KN                                     *
*  ADDITIONAL SEISMIC ACTION FACTOR (DELTAN) =  0.000                       *
*****************************************************************************
CHECK FOR MINIMUM LATERAL FORCE AT EACH FLOOR [GB50011:5.2.5]
LOAD -    1    FACTOR -   1.000
FLOOR            LATERAL          GRAVITY         LAMBDA   LAMBDA   ADJUSTMENT
HEIGHT (METE)    LOAD (KN  )      LOAD (KN  )      (%)     MIN (%)   FACTOR
-------------    -----------      ------------    ------   ------   -----------
12.000           58.457          280.000       20.88     3.20     1.00
8.000           97.429          560.000       17.40     3.20     1.00
4.000          116.914          840.000       13.92     3.20     1.00
JOINT            LATERAL          TORSIONAL            VERTICAL      LOAD -    1
LOAD (KN  )      MOMENT (KN  -METE)   LOAD (KN  )    FACTOR -   1.000
-----            -------          ---------           -----------
2     FX        4.871    MY        0.000           FY        0.000
3     FX        4.871    MY        0.000           FY        0.000
8     FX        4.871    MY        0.000           FY        0.000
9     FX        4.871    MY        0.000           FY        0.000
-----------        -----------           ----------------
TOTAL =     19.486              0.000                     0.000    AT LEVEL     4.000 METE
STAAD SPACE                                              -- PAGE NO.    4
5     FX        9.743    MY        0.000           FY        0.000
6     FX        9.743    MY        0.000           FY        0.000
11     FX        9.743    MY        0.000           FY        0.000
12     FX        9.743    MY        0.000           FY        0.000
-----------        -----------           ----------------
TOTAL =     38.971              0.000                     0.000    AT LEVEL     8.000 METE
13     FX       14.614    MY        0.000           FY        0.000
14     FX       14.614    MY        0.000           FY        0.000
15     FX       14.614    MY        0.000           FY        0.000
16     FX       14.614    MY        0.000           FY        0.000
-----------        -----------           ----------------
TOTAL =     58.457              0.000                     0.000    AT LEVEL    12.000 METE
************ END OF DATA FROM INTERNAL STORAGE ************
51. PRINT ANALYSIS RESULTS
ANALYSIS RESULTS
STAAD SPACE                                              -- PAGE NO.    5
JOINT DISPLACEMENT (CM   RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
1    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
2    1     0.7616    0.0162    0.0000    0.0000    0.0000   -0.0017
3    1     0.7616   -0.0162    0.0000    0.0000    0.0000   -0.0017
4    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
5    1     1.7446    0.0252    0.0000    0.0000    0.0000   -0.0015
6    1     1.7446   -0.0252    0.0000    0.0000    0.0000   -0.0015
7    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
8    1     0.7616    0.0162    0.0000    0.0000    0.0000   -0.0017
9    1     0.7616   -0.0162    0.0000    0.0000    0.0000   -0.0017
10    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
11    1     1.7446    0.0252    0.0000    0.0000    0.0000   -0.0015
12    1     1.7446   -0.0252    0.0000    0.0000    0.0000   -0.0015
13    1     2.4099    0.0282    0.0000    0.0000    0.0000   -0.0008
14    1     2.4099   -0.0282    0.0000    0.0000    0.0000   -0.0008
15    1     2.4099    0.0282    0.0000    0.0000    0.0000   -0.0008
16    1     2.4099   -0.0282    0.0000    0.0000    0.0000   -0.0008
STAAD SPACE                                              -- PAGE NO.    6
SUPPORT REACTIONS -UNIT KN   METE    STRUCTURE TYPE = SPACE
-----------------
JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
1    1    -29.23    -98.49      0.00      0.00      0.00     75.81
4    1    -29.23     98.49      0.00      0.00      0.00     75.81
7    1    -29.23    -98.49      0.00      0.00      0.00     75.81
10    1    -29.23     98.49      0.00      0.00      0.00     75.81
STAAD SPACE                                              -- PAGE NO.    7
MEMBER END FORCES    STRUCTURE TYPE = SPACE
-----------------
ALL UNITS ARE -- KN   METE     (LOCAL )
MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
1    1     1    -98.49     29.23    -0.00     -0.00      0.00      75.81
2     98.49    -29.23     0.00      0.00      0.00      41.10
2    1     2      0.00    -43.80    -0.00      0.00      0.00     -87.59
3     -0.00     43.80     0.00     -0.00      0.00     -87.59
3    1     3     98.49     29.23    -0.00     -0.00      0.00      41.10
4    -98.49    -29.23     0.00      0.00      0.00      75.81
4    1     2    -54.70     24.36    -0.00     -0.00      0.00      46.49
5     54.70    -24.36     0.00      0.00      0.00      50.94
5    1     5     -0.00    -36.65    -0.00      0.00      0.00     -73.31
6      0.00     36.65     0.00     -0.00      0.00     -73.31
6    1     6     54.70     24.36    -0.00     -0.00      0.00      50.94
3    -54.70    -24.36     0.00      0.00      0.00      46.49
7    1     2     -0.00     -0.00     0.00      0.00     -0.00      -0.00
8      0.00      0.00    -0.00     -0.00     -0.00      -0.00
8    1     3     -0.00      0.00     0.00      0.00     -0.00       0.00
9      0.00     -0.00    -0.00     -0.00     -0.00       0.00
9    1     5      0.00     -0.00     0.00      0.00     -0.00      -0.00
11     -0.00      0.00    -0.00     -0.00     -0.00      -0.00
10    1     6     -0.00      0.00     0.00      0.00     -0.00       0.00
12      0.00     -0.00    -0.00     -0.00     -0.00       0.00
11    1     7    -98.49     29.23    -0.00     -0.00      0.00      75.81
8     98.49    -29.23     0.00      0.00      0.00      41.10
12    1     8      0.00    -43.80    -0.00      0.00      0.00     -87.59
9      0.00     43.80     0.00     -0.00      0.00     -87.59
13    1     9     98.49     29.23    -0.00     -0.00      0.00      41.10
10    -98.49    -29.23     0.00      0.00      0.00      75.81
14    1     8    -54.70     24.36    -0.00     -0.00      0.00      46.49
11     54.70    -24.36     0.00      0.00      0.00      50.94
15    1    11     -0.00    -36.65    -0.00      0.00      0.00     -73.31
12      0.00     36.65     0.00     -0.00      0.00     -73.31
STAAD SPACE                                              -- PAGE NO.    8
MEMBER END FORCES    STRUCTURE TYPE = SPACE
-----------------
ALL UNITS ARE -- KN   METE     (LOCAL )
MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
16    1    12     54.70     24.36    -0.00     -0.00      0.00      50.94
9    -54.70    -24.36     0.00      0.00      0.00      46.49
17    1     5    -18.05     14.61    -0.00     -0.00      0.00      22.37
13     18.05    -14.61     0.00      0.00      0.00      36.09
18    1     6     18.05     14.61     0.00     -0.00     -0.00      22.37
14    -18.05    -14.61    -0.00      0.00     -0.00      36.09
19    1    11    -18.05     14.61    -0.00     -0.00      0.00      22.37
15     18.05    -14.61     0.00      0.00      0.00      36.09
20    1    12     18.05     14.61     0.00     -0.00     -0.00      22.37
16    -18.05    -14.61    -0.00      0.00     -0.00      36.09
21    1    13      0.00    -18.05    -0.00      0.00      0.00     -36.09
14      0.00     18.05     0.00     -0.00      0.00     -36.09
22    1    13      0.00     -0.00     0.00     -0.00     -0.00      -0.00
15     -0.00      0.00    -0.00      0.00     -0.00      -0.00
23    1    14     -0.00      0.00     0.00     -0.00     -0.00       0.00
16      0.00     -0.00    -0.00      0.00     -0.00       0.00
24    1    15      0.00    -18.05    -0.00      0.00      0.00     -36.09
16      0.00     18.05     0.00     -0.00      0.00     -36.09
************** END OF LATEST ANALYSIS RESULT **************