ASCE Exact Wind Integration (closed form equations) Jun 2021

Closed Form Exact ASCE Wind Calculations

Five years back, I developed a Python function to calculate closed form exact values for wind forces and wind CGs.

I use only calculus — no more bar charts with 0′ to 15′, 20′ to 25′, 25′ to 30′, et cetera —- a curve rather than a step function.

The ASCE function for kz is discontinuous at z = 15′:

when $z < 15'$ , $K_{z} = 2.01(15/z_{g})^{2/\alpha}$ , a constant
when $z \geq 15'$ , $K_{z} = 2.01(z/z_{g})^{2/\alpha}$

Function Specification

We must simply integrate over the two domains $[ \text{ 0' to 15'} , \text{15' to } & z_{g} & \text{ } ]$ . Of course, my function is called only once, internally the function incorporates the two domains.

$f(n, xbasis, ybasis, x1, y1, x2, y2, w, cf, v, i, exposure, g, kd, datum=0)$

n: allows calculation for say n=3 identical tributary areas (or lines)
xbasis: allows determining moment about a vertical offset, say an xbasis = 5′ to the left
ybasis: allows determining moment about a horizontal offset, say a ybasis = 20′ elevation (maybe calculating a vessel supported on lugs)
x1, y1: starting coordinate of tributary line (diagonal lines are allowed)
x2, y2: ending coordinate of tributary line (diagonal lines are allowed)
w: width of tributary area (or line)
- To model a W10 truss diagonal say 13′ long on a 5:12 slope
- Set (x1, y1, x2, y2, w) = (0, 0, 12, 5, 0.833)
cf: ASCE force coefficient
v: wind velocity
i: importance factor (now 1.0 in ASCE 7/16)
g: gust factor
kd: directionality factor
datum=0: grade elevation (default=0, user specified otherwise)
- (datum specification allows use of real world elevations)