V. ASCE 7-02 Wind Load Generation on Building

Verify the windward loads due to wind on a portion of a building structure calculated per the ASCE 7-02 specification.

Details

The wind load is calculated for a rigid building structure using the procedure for MWFRS of enclosed buildings (ASCE 7-02, Section 6.5.12.2.1). The following assumptions and parameters apply:

Flat roof type
Category II building (Table 1-1)
Basic wind speed = 108 mph
Structure type of "building"
Exposure Category B
Do not consider wind speed-up over hills or escarpments
Building height = 40 ft
Building length along the wind direction, L = 10 ft
Building width normal to wind direction, B = 20 ft
Natural frequency of structure = 2 Hz (i.e., a "rigid" building per Section 6.2)
Damping ratio = 0.05
Enclosed building (per Section 6.2)

Calculate the resulting joint loads on the windward side due to wind along the X axis at the upper wall of one segment of the building.

Building structure with wind load in X direction

Validation

Importance factor, I = 1.0 (Table 6-1)

The velocity pressure exposure coefficients (K^z) are calculated per the formulae given in Table 6-3:

K_{z} = | \begin{matrix} 2.01 {(15 / z_{g})}^{2 / ɑ} & for z < 15 ft \\ 2.01 {(z / z_{g})}^{2 / ɑ} & for 15 ft \leq z \leq z g \end{matrix}

(Table 6-3)

where

ɑ	=	7 (Table 6-2)
z_g	=	1,200 ft (Table 6-2)

See the table below for the values of K^z at discrete values of z.

Directionality factor, K_d = 0.85 (Table 6-4)

Topographic factor, K_zt = 1.0 (i.e., not considered)

Velocity pressure, q_z

q_{z} = 0.00256 K_{z} K_{zt} K_{d} V^{2} I

(Eq. 6-15)

Mean roof height = height of the building = 30 ft. Refer to table below for calculation of q_z at the mean roof height.

Gust effect factor, G

G is calculated per Cl. 26.11.4 for rigid structures:

G = 0.925 (\frac{1 + 1.7 g_{q} I_{\overline{z}} Q}{1 + 1.7 g_{v} I_{\overline{z}}})

(Eq. 6-4)

where

g_q = g_v	=	3.4
$\overline{z}$	=	$max \| \begin{matrix} 30 ft \\ 0.6 \times h \end{matrix} = 30 ft$
ε	=	1/3
ℓ	=	320 ft
c	=	0.3
$L_{\overline{z}}$	=	$ℓ {(\overline{z} / 33)}^{ε} = 309.99 ft$
Q	=	$\sqrt{\frac{1}{1 + 0.63 {(\frac{B + h}{L \overline{z}})}^{0.63}}} = \sqrt{\frac{1}{1 + 0.63 {(\frac{20 + 40}{309.99})}^{0.63}}} = 0.904$
$I_{\overline{z}}$	=	$c {(33 / \overline{z})}^{1 / 6} = 0.305$

Therefore, $G = 0.925 (\frac{1 + 1.7 \times 3.4 \times 0.305 \times 0.904}{1 + 1.7 \times 3.4 \times 0.305}) = 0.8683$

External pressure coefficient, C_p = 0.8 for windward per Fig. 6-6.

The external design pressure, p = q_hGC_p.

The internal pressure coefficient, GC_pi = -0.18 for partially enclosed buildings per Figure 6-5.

The internal design pressure, p_i = q_i(GC_pi) = 19.30 × -0.18 = -3.47 lb/ft²

where

q_i

the velocity pressure evaluated at the building height, h,

q_{h} = 0.00256 K_{z=h} K_{zt} K_{d} V^{2} I = 0.00256 (0.761) (1.0) (0.85) {(108)}^{2} (1.0) = 19.30 {lb/ft}^{2}

The design wind pressure, p, is then calculated as:

p = q_zGC_p - q_i(GC_pi)

(Eq. 6-17)

Table 1. Wind intensity versus height for building structure
h (ft)	K_z	q_z (lb/ft²)	p (lb/ft²)
0	0.575	14.59	13.61
15	0.575	14.59	13.61
20	0.624	15.84	14.48
25	0.665	16.88	15.20
30	0.701	17.78	15.83
35	0.732	18.58	16.38
40	0.761	19.30	16.89

Load on Nodes 1 and 9

Assume that the ground (Y = 0') acts as a bounded edge for the wind load acting on the exterior of the building. This edge transfers load to the columns.

Tributary area for nodes 1 and 9

Wind pressure at half-way between this node and level above (5') = 13.61 lb/ft².

F = (10 ft / 2) × (10 ft / 2) × 13.61 lb/ft² (10)^-3 = 0.34 kips

Load on Node 5

Tributary area for node 5

Wind pressure at half-way between this node and level above (5') = 13.61 lb/ft².

F = (10 ft / 2) × (10 ft) × 13.60 lb/ft² (10)^-3 = 0.68 kips

Load on Nodes 2 and 10

Tributary area for nodes 2 and 10

Wind pressure at half-way between this node and level above (5') = 13.61 lb/ft². This pressure is constant below this height.

F = (10 ft / 2) × (10 ft) × 13.61 lb/ft² (10)^-3 = 0.68 kips

Load on Node 6

Tributary area for node 6

Wind pressure at half-way between this node and level above (5') = 13.61 lb/ft². This pressure is constant below this height.

F = (10 ft) × (10 ft ) × 13.61 lb/ft² (10)^-3 = 1.36 kips

Load on Nodes 13 and 17

Tributary area for nodes 13 and 17

Wind pressure at half-way between this node and level below (15') = 13.61 lb/ft².

Wind pressure at half-way between this node and level above (25') = 15.20 lb/ft².

F = (10 ft /2 ) × (10 ft / 2) × (13.61 lb/ft² + 15.20 lb/ft²) (10)^-3 = 0.72 kips

Load on Node 15

Tributary area for node 15

Wind pressure at half-way between this node and level below (15') = 13.61 lb/ft².

Wind pressure at half-way between this node and level above (25') = 15.20 lb/ft².

F = (10 ft /2 ) × (10 ft) × (13.61 lb/ft² + 15.20 lb/ft²) (10)^-3 = 1.44 kips

Load on Node 19

Tributary area for nodes 19 and 23

Wind pressure at half-way between this node and level below (25') = 15.20 lb/ft².

Wind pressure at half-way between this node and level above (35') = 16.38 lb/ft².

F = (10 ft /2 ) × (10 ft / 2) × (15.20 lb/ft² + 16.38 lb/ft²) (10)^-3 = 0.79 kips

Load on Node 21

Tributary area for node 21

Wind pressure at half-way between this node and level below (25') = 15.20 lb/ft².

Wind pressure at half-way between this node and level above (35') = 16.38 lb/ft².

F = (10 ft) × (10 ft / 2) × (15.20 lb/ft² + 16.38 lb/ft²) (10)^-3 = 1.58 kips

Load on Nodes 25 and 29

Tributary area for nodes 25 and 29

Wind pressure at roof level (40') = 16.89 lb/ft².

F = (10 ft / 2) × (10 ft / 2) × 16.89 lb/ft² (10)^-3 = 0.42 kips

Load on Node 27

Tributary area for node 27

Wind pressure at roof level (40') = 16.89 lb/ft².

F = (10 ft) × (10 ft / 2) × 15.04 lb/ft² (10)^-3 = 0.84 kips

Results

Table 2. Joint loads due to wind (kips)
Result Type	Reference	STAAD.Pro	Difference
Node 1	0.34	0.34	none
Node 5	0.68	0.68	none
Node 2	0.68	0.68	none
Node 6	1.36	1.36	none
Node 13	0.72	0.73	negligible
Node 15	1.44	1.46	negligible
Node 19	0.79	0.80	negligible
Node 21	1.58	1.59	negligible
Node 25	0.42	0.42	none
Node 27	0.84	0.84	none

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\Wind Load\ASCE7-02 Wind Load Generation on Building.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Sep-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 10 0; 3 10 10 0; 4 10 0 0; 5 0 0 10; 6 0 10 10; 7 10 10 10;
8 10 0 10; 9 0 0 20; 10 0 10 20; 11 10 10 20; 12 10 0 20; 13 0 20 0;
14 10 20 0; 15 0 20 10; 16 10 20 10; 17 0 20 20; 18 10 20 20; 19 0 30 0;
20 10 30 0; 21 0 30 10; 22 10 30 10; 23 0 30 20; 24 10 30 20; 25 0 40 0;
26 10 40 0; 27 0 40 10; 28 10 40 10; 29 0 40 20; 30 10 40 20;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 6; 5 3 7; 6 5 6; 7 6 7; 8 7 8; 9 6 10; 10 7 11;
11 9 10; 12 10 11; 13 11 12; 14 2 13; 15 3 14; 16 6 15; 17 7 16; 18 10 17;
19 11 18; 20 13 14; 21 13 15; 22 14 16; 23 15 16; 24 15 17; 25 16 18; 26 17 18;
27 13 19; 28 14 20; 29 15 21; 30 16 22; 31 17 23; 32 18 24; 33 19 20; 34 19 21;
35 20 22; 36 21 22; 37 21 23; 38 22 24; 39 23 24; 40 19 25; 41 20 26; 42 21 27;
43 22 28; 44 23 29; 45 24 30; 46 25 26; 47 25 27; 48 26 28; 49 27 28; 50 27 29;
51 28 30; 52 29 30;
DEFINE MATERIAL START
ISOTROPIC STEEL_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TO 52 TABLE ST W14X873
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
1 4 5 8 9 12 FIXED
DEFINE WIND LOAD
TYPE 1 WIND 1
<! STAAD PRO GENERATED DATA DO NOT MODIFY !!!
ASCE-7-2002:PARAMS 108.000 mph 0 1 1 0 0.000 ft 30.000 ft 10.000 ft 1 2 -
40.000 ft 10.000 ft 20.000 ft 2.000 0.050 0 0 0 0 0 0.761 1.000 1.000 0.850 -
0 0 0 0 0.868 0.800 -0.180
!> END GENERATED DATA BLOCK
INT 0.0136076 0.0136076 0.0139629 0.0142904 0.0145949 0.0148798 0.015148 -
0.0154016 0.0156424 0.0158718 0.0160911 0.0163013 0.0165031 0.0166975 -
0.0168849 HEIG 0 15 16.9231 18.8461 20.7692 22.6923 24.6154 26.5385 28.4615 -
30.3846 32.3077 34.2308 36.1538 38.0769 40
EXP 1 JOINT 1 TO 12
LOAD 1 LOADTYPE Wind  TITLE LOAD CASE 1
WIND LOAD X 1 TYPE 1 YR 0 40
PERFORM ANALYSIS PRINT LOAD DATA
FINISH

STAAD.Pro Output

   LOADING     1  LOADTYPE WIND  TITLE LOAD CASE 1                            
   -----------
   JOINT LOAD - UNIT KIP  FEET
   JOINT   FORCE-X   FORCE-Y     FORCE-Z     MOM-X     MOM-Y     MOM-Z
       1      0.34      0.00        0.00      0.00      0.00      0.00
       2      0.68      0.00        0.00      0.00      0.00      0.00
       5      0.68      0.00        0.00      0.00      0.00      0.00
       6      1.36      0.00        0.00      0.00      0.00      0.00
       9      0.34      0.00        0.00      0.00      0.00      0.00
      10      0.68      0.00        0.00      0.00      0.00      0.00
      13      0.73      0.00        0.00      0.00      0.00      0.00
      15      1.46      0.00        0.00      0.00      0.00      0.00
      17      0.73      0.00        0.00      0.00      0.00      0.00
      19      0.80      0.00        0.00      0.00      0.00      0.00
      21      1.59      0.00        0.00      0.00      0.00      0.00
      23      0.80      0.00        0.00      0.00      0.00      0.00
      25      0.42      0.00        0.00      0.00      0.00      0.00
      27      0.84      0.00        0.00      0.00      0.00      0.00
      29      0.42      0.00        0.00      0.00      0.00      0.00