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)
Function Usage
These days, I still use my function:

  • with straight Python (works very well)
  • with CoCalc (works very well using SageMath)
  • with PyXLL as an Excel function (works very well)

Tributary loadings for the working points of a structure are easily calculated

The function allows calculation of loads on all types of geometries including:

  • rectangular/cylindrical
  • closed/open
Reference PDFs

Derivation

ASCE Wind Integration Derivation 11192016KLH.pdf

Example — by hand calculation

ASCE Wind Integration Examples 06132021KLH.pdf

Example — above hand calculations are verified using Cocalc/Jupyter/SageMath

SageMath slides.pdf

Tributary Loading

ASCE Wind Integration Tributary 06092021KLH.pdf

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