Building Wind-Load Post-Processing

The building use case turns a pressure time series on a building surface into the engineering deliverables of a wind study: per-floor force and moment coefficients, the modal dynamic response, occupant-comfort accelerations, design load cases, and a multi-direction fan-out over a parametric study.

It composes the v3 recipes and ops (see Data sources, ops, and pipelines (v3 paradigm)); nothing here is high-rise-specific – the same helpers serve low-rise studies. The Python surface lives under cfdmod.building; the modal model it consumes is produced by the importers in Structural Model Import (Dynamics).

The pipeline

A case runs through a fixed sequence of stages, each a thin composition of library recipes:

pressure time series (surface)
  -> Cp                              (cp_from_pressure)
  -> per-floor Cf / Cm               (cf_per_floor, cm_per_floor)
  -> floor-load points               (floor_load_source)
  -> modal dynamic response          (solve_building_response)
  -> floor accelerations + comfort   (floor_accelerations, comfort_limit)
  -> load-case tables                (generate_load_cases)

A single case is aggregated into a BuildingCase, which carries the pressure time series, the dynamic pressure and the geometry so the downstream stages read a single value object rather than a pile of loose arrays.

Per-floor coefficients

The building surface is partitioned into floors (a height binning of the triangles), and the pressure coefficient time series is integrated over each floor’s triangles into a per-floor force and moment coefficient. The floor force coefficient is

\[ C_{f,i} = \frac{1}{A_{ref}} \sum_{t \in \text{floor } i} C_{p,t}\, \hat{n}_t\, A_t \]

with the outward normal \(\hat{n}_t\) and triangle area \(A_t\), and the moment coefficient likewise about the floor reference point. Normalisation uses an explicit reference area / volume (nominal_area / nominal_volume), not a per-region bounding-box area, so the coefficients convert back to real-scale forces unambiguously.

Peak estimation

Each deliverable reduces a fluctuating response (acceleration, floor force, displacement) to a single design peak. Three methods are selectable per deliverable (peak_value()):

• "max" – the observed extreme (optionally of the absolute value).

• "peak-factor" – Davenport Davenport[1]: \(\hat{x} = \bar{x} + g\,\sigma_x\), with the gust peak factor

  \[ g = \sqrt{2 \ln(\nu T)} + \frac{0.5772}{\sqrt{2 \ln(\nu T)}} \]

  where \(\nu\) is the mean up-crossing rate (taken as the response frequency \(f_0\), in Hz) and \(T\) the averaging duration (default 600 s). The constant 0.5772 is the Euler-Mascheroni constant.

• "gumbel" – fit a Gumbel distribution to block maxima and read the design fractile off it (more stable than the raw max for short records). See the extreme-value discussion in Statistics.

Dynamic response

Tall, flexible buildings resonate with the fluctuating wind load, so the response is not simply the static application of the peak load. The building is solved as a modal single-degree-of-freedom (SDOF) system per mode (solve_building_response()):

1. The per-floor load coefficients are dimensionalised into a floor-load PointsDataSource (per-floor \(f_x\), \(f_y\), \(m_z\)) by the case dynamic pressure and reference area (floor_load_source()).

2. Each mode shape is mass-normalized to unit generalized mass, \(\sum_i M_i\,(\phi_{x,i}^2 + \phi_{y,i}^2 + (R_i\,\phi_{rz,i})^2) = 1\), the precondition the modal solver assumes.

3. The floor loads are projected onto each mode to a generalized modal load, the modal SDOF equation

   \[ \ddot{q}_j + 2\,\xi_j\,\omega_j\,\dot{q}_j + \omega_j^2\,q_j = p_j(t) \]

   is integrated in time (RK45) with damping ratio \(\xi_j\) and natural frequency \(\omega_j\), and the modal coordinates are recomposed into per-floor displacements (\(d_x\), \(d_y\)) and torsional rotation (\(r_z\)).

4. The response is reported as per-floor displacements plus static-equivalent floor forces / moments (\(f_{eq,x}\), \(f_{eq,y}\), \(m_{eq,z}\)) that the structural engineer applies statically, and as per-floor horizontal accelerations at an off-centre occupant point (floor_accelerations()).

The natural periods, per-floor mass, radius of gyration, centre of mass and mode shapes come from the structural model (BuildingStructuralData); see Structural Model Import (Dynamics) for how that model is imported from TQS or Eberick.

Occupant comfort

Occupant comfort is judged by comparing the peak horizontal acceleration at the top floor against a standard’s acceptance limit. Three criteria are supported (comfort_limit()); all return the limit in SI \(m/s^2\) (convert to milli-g with mps2_to_milli_g()).

NBR 6123 (serviceability limit, sec. 9.6.2), a decreasing power law in the fundamental sway frequency \(f_0\) Nbr[2]:

\[ a_{lim} = 0.01\, k_c\, f_0^{-0.445} \quad [m/s^2] \]

with \(k_c = 4.08\) (residential) or \(6.12\) (commercial / office), valid over \(0.06 \le f_0 \le 1.00\) Hz at a 1-year return period.

Melbourne and Palmer (1992) serviceable-acceleration curve, a function of \(f_0\) and the return period \(R\) in years Melbourne and Palmer[3]:

\[ a = \sqrt{2 \ln(f_0 T)}\,\left(0.68 + \frac{\ln R}{5}\right)\, e^{-3.65 - 0.41 \ln f_0} \quad [m/s^2] \]

with \(T = 600\) s, valid over \(0.06 < f_0 < 1.0\) Hz and \(0.5 < R < 10\) years.

NBCC occupant-comfort criterion, a flat (frequency-independent) limit at a 10-year return period: 15 milli-g residential, 25 milli-g office / commercial.

Design load cases

For the structural hand-off, the multi-direction response is reduced to per-floor load-case tables (generate_load_cases(), written with save_load_case_tables()):

• Effective-load envelopes – per-floor \(F_x\) / \(F_y\) / \(M_z\), one column per wind direction, for min / max (the signed per-floor envelopes) and peak (the governing envelope, whichever of min / max has the larger mean magnitude per direction and axis).

• Companion load cases – for each principal axis the critical direction is selected and the accompanying loads on the other axes are carried along, in the form the structural software (e.g. Eberick) ingests.

Multi-direction fan-out

Real consulting cases process many wind directions (and bodies, and Cp configurations). The v3 building path solves one case at a time; the fan-out driver (run_fanout() with a FanoutPlan) maps every (direction, body, config) key through the whole Cp -> per-floor Cf/Cm -> dynamic-response chain and collects the results in a Container – the exact shape the multi-direction reducers (cfdmod.dynamics.cases) and the load-case tables above consume.

Note

The examples/high_rise/ suite in the repository is the reference layout: thin notebooks, one per stage, orchestrating the cfdmod.building helpers end-to-end and writing versioned debug / deliverable output roots.

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[1]

Alan Garnett Davenport. Note on the distribution of the largest value of a random function with application to gust loading. Proceedings of the Institution of Civil Engineers, 28(2):187–196, 1964.

[2]

ABNT Nbr. 6123: forças devidas ao vento em edificações. ABNT Editora, Rio de Janeiro, Brasil, 1988.

[3]

William H Melbourne and Trevor R Palmer. Accelerations and comfort criteria for buildings undergoing complex motions. Journal of Wind Engineering and Industrial Aerodynamics, 41(1-3):105–116, 1992.