# V. GB 50009-2012 Wind Load generation on Rectangular Building

Verify the calculated wind pressure at the mid-height (4.5 m) on a structure per the Chinese GB 50009-2012 code.

## Problem

This problem determines the pressures applied to a rectangular building at various significant heights, from a wind force that is flowing in the positive X direction (i.e. from X= -infinity to X= + infinity).

A 9 m tall, two story structure is subject to a wind load along the along the global X direction. The building width (along the Z direction, perpendicular to wind) is 6 m. The building length (along the X direction, parallel to wind) is 10 m. The structure is a closed structure. The building is located in Beijing City in the Beijing province.
• The shape factor, μs = 0.8. This is for the left face of the structure and the direction of wind is from left (+X). (+X) means that the wind is originating along the X axis pointing in the +X direction. The plan section type of the structure is rectangle. Refer to table 8.3.1 of the Chinese load code GB 50009-2012.
• The reference wind pressure, w0 = 0.45 kN/m2. Refer to table E.5 in the Chinese load code GB 50009-2012.
• The roughness type is "C"
Wind-induced vibration along-wind is not considered (βz = 1).

## Calculations

Calculate the modified wind shape factor:

μs' = μs × βz = 0.8 × 1.0 = 0.8

Calculate the modified wind height factor:

Per Table 8.2.1 of GB 50009-2012, at a height of z = 4.5 m for a roughness type of "A", μz = 1.09

μz' = μz × βz = 1.09 × 1.0 = 1.09

There is no modification for the reference wind pressure, so w0 = 0.45 kN/m2

The origin value of reference wind pressure is taken from table E.5 in the Chinese load code GB 50009-2012, wo,origin b= 0.45

Calculate the wind pressure characteristic value, wk (wind intensity at height, z = 4.5 m):

wk = βzμzw0 = 1 × 1.09 × 0.45 = 0.491 kN/m2

The height factor for z = 9 is determined by linear interpolation between z = 5 (μz = 1.09) and z = 10 (μz = 1.28): μz = 1.24.

Calculate the wind pressure characteristic value, wk (wind intensity at height, z = 9 m):

wk = βzμzw0 = 1 × 1.24 × 0.45 = 0.558 kN/m2

## Comparison

Result Type Reference STAAD.Pro Difference Comment
Wind pressure characteristic value, wk at z = 4.5 m (kN/m2) 0.491 0.490 negligible
Wind pressure characteristic value, wk at z = 9 m (kN/m2) 0.558 0.559 negligible

These values are compared with the generated intensity values that the STAAD.Pro Analytical workflow adds into the STAAD input file.

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 03-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4.5 0; 3 0 9 0; 5 10 0 0; 6 10 4.5 0; 7 10 9 0; 17 0 0 6;
18 0 4.5 6; 19 0 9 6; 20 10 0 6; 21 10 4.5 6; 22 10 9 6; 23 2.5 4.5 6;
24 5 4.5 6; 25 7.5 4.5 6; 26 2.5 4.5 0; 27 5 4.5 0; 28 7.5 4.5 0; 29 2.5 9 0;
30 5 9 0; 31 7.5 9 0; 32 2.5 9 6; 33 5 9 6; 34 7.5 9 6;
MEMBER INCIDENCES
1 1 2; 2 2 3; 4 2 26; 5 3 29; 7 5 6; 8 6 7; 23 3 19; 24 6 21; 25 7 22;
30 17 18; 31 18 19; 32 18 23; 33 19 32; 34 20 21; 35 21 22; 36 23 24; 37 24 25;
38 25 21; 39 26 27; 40 27 28; 41 28 6; 42 29 30; 43 30 31; 44 31 7; 45 32 33;
46 33 34; 47 34 22; 48 23 26; 49 24 27; 50 25 28; 51 32 29; 52 33 30; 53 34 31;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY CHINESE
1 2 7 8 30 31 34 35 TABLE ST HW400X408
4 5 32 33 36 TO 47 TABLE ST HN500X200
23 TO 25 48 TO 53 TABLE ST HN300X150
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 5 17 20 FIXED
TYPE 1 WIND 1
<! STAAD PRO GENERATED DATA DO NOT MODIFY !!!
GB50009-2012:PARAMS Whole Wind_Group_ID 20210621162429414 Shape_Item "30 : -
CLOSED POLYGON BULDING" Second_Shape_UI "Rectangle" Interference_Factor 1 -
Shape_Factor Shape_Factor_Count 16 "LEFT Wind" "LEFT Face" 0.8 "LEFT Wind" -
"BACK Face" -0.7 "LEFT Wind" "RIGHT Face" -0.5 "LEFT Wind" "FRONT Face" -0.7 -
"RIGHT Wind" "LEFT Face" -0.5 "RIGHT Wind" "BACK Face" -0.7 "RIGHT Wind" -
"RIGHT Face" 0.8 "RIGHT Wind" "FRONT Face" -0.7 "FRONT Wind" "LEFT Face" -
-0.7 "FRONT Wind" "BACK Face" -0.5 "FRONT Wind" "RIGHT Face" -0.7 "FRONT -
Wind" "FRONT Face" 0.8 "BACK Wind" "LEFT Face" -0.7 "BACK Wind" "BACK Face" -
0.8 "BACK Wind" "RIGHT Face" -0.7 "BACK Wind" "FRONT Face" -0.5 -
Building_Height_H 9 Bottom_Elevation 0 z_Provide_Mothod 2 Segment_Count 5 -
Segment_Length 3 z_Special_List "4.5,9" Rough A -
Modify_Factor_of_Height_Factor 1 Province "" City_UI "" Refer_Wind_Press -
0.45 Modify_Factor_of_Press 1 Is_Calc_Vibration_Factor 0 Damp_Ratio 0.01 -
Basic_Period 1 Structure_Type 1 Windward_Width Width_Count 4 "LEFT Wind" -
Bottom_Width 0 Top_Width 0 "RIGHT Wind" Bottom_Width 0 Top_Width 0 "FRONT -
Wind" Bottom_Width 0 Top_Width 0 "BACK Wind" Bottom_Width 0 Top_Width 0 -
Generate_Load_Case 1 Select_Method 0 Face_Info Face_Count 4 "LEFT Face" -
Group "" Member_List "" X_Min 0 X_Max 0 Y_Min 0 Y_Max 0 Z_Min 0 Z_Max 0 -
Is_Open 0 "BACK Face" Group "" Member_List "" X_Min 0 X_Max 0 Y_Min 0 Y_Max -
0 Z_Min 0 Z_Max 0 Is_Open 0 "RIGHT Face" Group "" Member_List "" X_Min 0 -
X_Max 0 Y_Min 0 Y_Max 0 Z_Min 0 Z_Max 0 Is_Open 0 "FRONT Face" Group "" -
Member_List "" X_Min 0 X_Max 0 Y_Min 0 Y_Max 0 Z_Min 0 Z_Max 0 Is_Open 0 -
Build_Rotation_In_Model 0 Each_Type "LEFT Face" "LEFT Wind"
!> END GENERATED DATA BLOCK
INT 0.49 0.559 HEIG  4.5  9
* GB50009-2012:PARAMS Each_Load Wind_Group_ID 20210621162429414 "LEFT Wind"
WIND LOAD X 0.8 TYPE 1
WIND LOAD -Z -0.7 TYPE 1
WIND LOAD -X 0.5 TYPE 1
WIND LOAD -Z 0.7 TYPE 1
* GB50009-2012:PARAMS Each_Load Wind_Group_ID 20210621162429414 "RIGHT Wind"
WIND LOAD -X -0.5 TYPE 1
WIND LOAD -Z -0.7 TYPE 1
WIND LOAD X -0.8 TYPE 1
WIND LOAD -Z 0.7 TYPE 1