madrs 0.1.3

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)
CP3 = 0.5     # Controls initial stiffness of the bi-linear curve (ranges from 0 to 1, preferred 0.5)

results = MADRS_Method(PO, DC, pf1, alpha1, wt, phi_roof1, tol, CP1, CP2, CP3)

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
CP3	float	Controls initial stiffness of the bi-linear curve (ranges from 0 to 1, preferred 0.5)
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