madrs 0.1.2

Modified Acceleration-Displacement Response Spectrum (MADRS) seismic analysis method

MADRS — Modified Acceleration-Displacement Response Spectrum

A Python package implementing the MADRS method of FEMA 440 for seismic performance-point calculation using pushover curves and response spectra.

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Installation

From PyPI (once published)

pip install madrs

Directly from GitHub

pip install git+https://github.com/YOUR_USERNAME/MADRS.git

Local development install (editable)

git clone https://github.com/YOUR_USERNAME/MADRS.git
cd MADRS
pip install -e .

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Quick Start

import numpy as np
from madrs import MADRS_Method

# --- Pushover curve: columns = [displacement (m), base shear (kN)] ---
PO = np.loadtxt("pushover.csv", delimiter=",")

# --- Demand curve: columns = [period (s), Sa (g)] ---
DC = np.loadtxt("spectrum.csv", delimiter=",")

# --- Modal / structural parameters ---
pf1       = 1.30    # Modal participation factor (1st mode)
alpha1    = 0.85    # Modal mass coefficient (1st mode)
wt        = 5000.0  # Seismic weight (kN)
phi_roof1 = 1.0     # 1st-mode shape at roof

tol  = 1e-4   # Area-balance tolerance for bilinear fitting
CP1  = 0.5    # Lower ay search bound (fraction of api)
CP2  = 0.95   # Upper ay search bound (fraction of api)

results = MADRS_Method(PO, DC, pf1, alpha1, wt, phi_roof1, tol, CP1, CP2)

dpi, api, dy, ay, roof_disp, flag, *_ = results

if flag:
    print(f"Performance point — Sd: {dpi:.4f} m  |  Sa: {api:.4f} g")
    print(f"Roof displacement : {roof_disp:.4f} m")
else:
    print("No performance point found — adjust CP1, CP2, or tol.")

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API Reference

MADRS_Method

MADRS_Method(PO, DC, pf1, alpha1, wt, phi_roof1, tol, CP1, CP2,
             show_intermediate_plots=True)

Parameter	Type	Description
PO	ndarray (N, 2)	Pushover curve — [displacement (m), base shear (kN)]
DC	ndarray (M, 2)	Demand/response spectrum — [period (s), Sa (g)]
pf1	float	Modal participation factor (1st mode)
alpha1	float	Modal mass coefficient (1st mode)
wt	float	Seismic weight (kN)
phi_roof1	float	1st-mode shape value at roof
tol	float	Tolerance for bilinear area balance
CP1	float	Lower multiplier for ay search
CP2	float	Upper multiplier for ay search
show_intermediate_plots	bool	Show 6-panel diagnostic figure (default True)

Returns (dpi, api, dy, ay, roof_disp, flag, Sd_spectra, Sa_Spectranew, Sd, Sa, x_bilinear, y_bilinear)

Helper functions

from madrs import curve_intersections, closest_point_on_curve, area_between_curves

• curve_intersections(x1, y1, x2, y2) — find intersection points between two polylines
• closest_point_on_curve(P, x_curve, y_curve) — nearest point on a polyline to point P
• area_between_curves(x, y1, y2) — signed area between two curves via Simpson's rule

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Requirements

• Python ≥ 3.9
• numpy ≥ 1.24
• scipy ≥ 1.10
• matplotlib ≥ 3.7

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License

MIT