# V. GB 50011-2010 Static Seismic - Case2

Calculate the base shear and its distribution along the height using the equivalent lateral force method in GB 50011-2010.

## Details

Structure to be modelled:
• height = 3× 4m = 12m
• plan dimension X = 4m
• plan dimension Z = 5m
Input parameters:
• Frequency of seismic event: Rare
• Classification of seismic design: Group 3
• Site class: I0
• Period in the X direction: T = 0.40s
• Equivalent gravity load factor for horizontal seismic action: 0.85 (default in STAAD.Pro)
• 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 "rare" earthquake with intensity of 6, ɑmax = 0.28 (Table 5.1.4-1)

The characteristic period, Tg = 0.30 + 0.05 = 0.35s (Table 5.1.4-2)

The power index of the curvilinear decrease section:

$γ = 0.9 + 0.05 - ζ 0.5 + 5 ζ = 0.9$

The damping adjustment factor:

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

Tg < T < 5Tg

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

$ɑ 1 = ( T g T ) γ η 2 × ɑ max = ( 0.35 0.4 ) 0.9 1.0 × 0.28 = 0.248$

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

 (Eq. 2.5)

T = 0.4 < 1.4Tg = 0.49

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 88.640 0 88.640
2nd 280 8 2,240 0.333 59.093 147.73
1st 280 4 1,120 0.167 29.547 177.28
Σ 840 6,720 1
Story Level Lateral Load

(kN)

(kN)

λ

(%)

λmin

(%)

Factor

3rd 88.640 280 31.66 0.8 1
2nd 147.73 560 26.38 0.8 1
1st 177.28 840 21.10 0.8 1

## Results

Table 1. Comparison of results
Story Shear, Fi (kN) 1st 29.547 29.547 none
2nd 59.093 59.094 negligible
3rd 88.640 88.641 negligible
Base Shear, V (kN) 117.28 117.282 negligible

## STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\GB 50011\GB 50011-2010 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
END DEFINE REFERENCE LOADS
DEFINE GB50011 2010 LOAD
INTENSITY 6 RARE GROUP 3 SCLASS 0 GFA 0.85 PX 0.4
R1 1.0
LOAD 1 LOADTYPE Seismic  TITLE EL-X DIR
GB50011 LOAD X 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
FINISH


   LOADING     1  LOADTYPE SEISMIC  TITLE EL-X DIR
-----------
*****************************************************************************
*                                                                           *
* EQUIV. SEISMIC LOADS AS PER SEISMIC DESIGN CODE FOR BUILDINGS             *
*                              (GB50011:2010) OF CHINA ALONG X              *
*  T CALCULATED =  0.685 SEC.      T USER PROVIDED =  0.400 SEC.            *
*  T USED =  0.400 SEC.                                                     *
*  MAX. HORIZONTAL SEISMIC INFLUENCE COEFFICIENT =  0.280                   *
*  CHARACTERISTIC PERIOD =  0.350 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) =  0.248  (24.829%)    *
*  MINIMUM SHEAR FACTOR AS PER SEC. 5.2.5 (LAMBDA) =   0.008  (  0.800%)    *
*  EQUIVALENT GRAVITY LOAD FACTOR FOR HORIZONTAL SEISMIC ACTION =  0.850    *
*  TOTAL HORIZONTAL SEISMIC ACTION =                                        *
*          =  0.248 X      0.850 X    840.000 =      177.282  KN            *
*  DESIGN BASE SHEAR =  1.000 X      177.282                                *
*                    =      177.282  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           88.641          280.000       31.66     0.80     1.00
8.000          147.735          560.000       26.38     0.80     1.00
4.000          177.282          840.000       21.10     0.80     1.00
JOINT            LATERAL          TORSIONAL            VERTICAL      LOAD -    1
LOAD (KN  )      MOMENT (KN  -METE)   LOAD (KN  )    FACTOR -   1.000
-----            -------          ---------           -----------
2     FX        7.387    MY        0.000           FY        0.000
3     FX        7.387    MY        0.000           FY        0.000
8     FX        7.387    MY        0.000           FY        0.000
9     FX        7.387    MY        0.000           FY        0.000
-----------        -----------           ----------------
TOTAL =     29.547              0.000                     0.000    AT LEVEL     4.000 METE
STAAD SPACE                                              -- PAGE NO.    4
5     FX       14.773    MY        0.000           FY        0.000
6     FX       14.773    MY        0.000           FY        0.000
11     FX       14.773    MY        0.000           FY        0.000
12     FX       14.773    MY        0.000           FY        0.000
-----------        -----------           ----------------
TOTAL =     59.094              0.000                     0.000    AT LEVEL     8.000 METE
13     FX       22.160    MY        0.000           FY        0.000
14     FX       22.160    MY        0.000           FY        0.000
15     FX       22.160    MY        0.000           FY        0.000
16     FX       22.160    MY        0.000           FY        0.000
-----------        -----------           ----------------
TOTAL =     88.641              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     1.1549    0.0246    0.0000    0.0000    0.0000   -0.0025
3    1     1.1549   -0.0246    0.0000    0.0000    0.0000   -0.0025
4    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
5    1     2.6455    0.0383    0.0000    0.0000    0.0000   -0.0022
6    1     2.6455   -0.0383    0.0000    0.0000    0.0000   -0.0022
7    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
8    1     1.1549    0.0246    0.0000    0.0000    0.0000   -0.0025
9    1     1.1549   -0.0246    0.0000    0.0000    0.0000   -0.0025
10    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
11    1     2.6455    0.0383    0.0000    0.0000    0.0000   -0.0022
12    1     2.6455   -0.0383    0.0000    0.0000    0.0000   -0.0022
13    1     3.6542    0.0428    0.0000    0.0000    0.0000   -0.0012
14    1     3.6542   -0.0428    0.0000    0.0000    0.0000   -0.0012
15    1     3.6542    0.0428    0.0000    0.0000    0.0000   -0.0012
16    1     3.6542   -0.0428    0.0000    0.0000    0.0000   -0.0012
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    -44.32   -149.35      0.00      0.00      0.00    114.95
4    1    -44.32    149.35      0.00      0.00      0.00    114.95
7    1    -44.32   -149.35      0.00      0.00      0.00    114.95
10    1    -44.32    149.35      0.00      0.00      0.00    114.95
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   -149.35     44.32    -0.00     -0.00      0.00     114.95
2    149.35    -44.32     0.00      0.00      0.00      62.33
2    1     2      0.00    -66.41    -0.00      0.00      0.00    -132.82
3     -0.00     66.41     0.00     -0.00      0.00    -132.82
3    1     3    149.35     44.32    -0.00     -0.00      0.00      62.33
4   -149.35    -44.32     0.00      0.00      0.00     114.95
4    1     2    -82.94     36.93    -0.00     -0.00      0.00      70.49
5     82.94    -36.93     0.00      0.00      0.00      77.24
5    1     5     -0.00    -55.58    -0.00      0.00      0.00    -111.16
6      0.00     55.58     0.00     -0.00      0.00    -111.16
6    1     6     82.94     36.93    -0.00     -0.00      0.00      77.24
3    -82.94    -36.93     0.00      0.00      0.00      70.49
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   -149.35     44.32    -0.00     -0.00      0.00     114.95
8    149.35    -44.32     0.00      0.00      0.00      62.33
12    1     8     -0.00    -66.41    -0.00      0.00      0.00    -132.82
9      0.00     66.41     0.00     -0.00      0.00    -132.82
13    1     9    149.35     44.32    -0.00     -0.00      0.00      62.33
10   -149.35    -44.32     0.00      0.00      0.00     114.95
14    1     8    -82.94     36.93    -0.00     -0.00      0.00      70.49
11     82.94    -36.93     0.00      0.00      0.00      77.24
15    1    11      0.00    -55.58    -0.00      0.00      0.00    -111.16
12      0.00     55.58     0.00     -0.00      0.00    -111.16
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     82.94     36.93    -0.00     -0.00      0.00      77.24
9    -82.94    -36.93     0.00      0.00      0.00      70.49
17    1     5    -27.36     22.16    -0.00     -0.00      0.00      33.91
13     27.36    -22.16     0.00      0.00      0.00      54.73
18    1     6     27.36     22.16     0.00     -0.00     -0.00      33.91
14    -27.36    -22.16    -0.00      0.00     -0.00      54.73
19    1    11    -27.36     22.16    -0.00     -0.00      0.00      33.91
15     27.36    -22.16     0.00      0.00      0.00      54.73
20    1    12     27.36     22.16     0.00     -0.00     -0.00      33.91
16    -27.36    -22.16    -0.00      0.00     -0.00      54.73
21    1    13      0.00    -27.36    -0.00      0.00      0.00     -54.73
14      0.00     27.36     0.00     -0.00      0.00     -54.73
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    -27.36    -0.00      0.00      0.00     -54.73
16     -0.00     27.36     0.00     -0.00      0.00     -54.73
************** END OF LATEST ANALYSIS RESULT **************
52. FINISH
STAAD SPACE                                              -- PAGE NO.    9
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= JUL  6,2021   TIME= 23:34:56 ****
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