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Utilities module: utils

Overview

The utils module provides cross-cutting helper functions for geometric, mechanical, and mathematical operations commonly needed in structural calculations. It is used internally throughout EurocodePy and is also part of the public API.

Cross sections — utils.crosssection

RectangularCrossSection(width, height) and CircularCrossSection(diameter) give the geometric properties of a section (lengths in the unit of the arguments).

from eurocodepy.utils import RectangularCrossSection, CircularCrossSection

r = RectangularCrossSection(0.30, 0.60)       # m
r.area, r.inertia_y, r.inertia_z               # A, Iy, Iz
r.bend_mod_y, r.bend_mod_z                     # Wy, Wz
r.radius_y, r.radius_z                         # radii of gyration
r.torsional_inertia, r.torsion_modulus, r.polar_inertia
r.shape                                        # CrossSectionShape member

CircularCrossSection(0.40).area

These objects are what the EC5 checks (ec5.uls) take as section.

Reinforced and prestressed sections — utils.section_properties

calc_section_rectangular and calc_section_T return the uncracked and the cracked properties (area, centroid, inertia, section moduli, neutral axis) of a section with passive and prestressed reinforcement, with the steel homogenised by alpha_Es and alpha_Ep. The arguments are consistent units (here m, m², kNm and kN). calc_section_T_uncrack and calc_section_T_crack give each of them separately.

import numpy as np
from eurocodepy.utils import calc_section_rectangular

arr = lambda *v: np.array(v)
uncracked, cracked = calc_section_rectangular(
    h=0.50, b=0.30,
    A_s=arr(8.0e-4), A_sc=arr(0.0), A_p=arr(0.0),      # tension, compression, prestressing steel
    ds=arr(0.46), dsc=arr(0.04), dp=arr(0.50),        # their distances to the top fibre
    alpha_Es=15.0, alpha_Ep=15.0,
    M=arr(150.0), P=arr(0.001),
)
uncracked["Area"], uncracked["Inertia"]
cracked["NeutralAxis"], cracked["Inertia"], cracked["zGs"], cracked["zGi"]

Stress calculations — utils.stress

The six components of the stress tensor are sigxx, sigyy, sigzz, sigxy, sigyz, sigzx.

from eurocodepy.utils import stress

# Principal stresses (ascending) and the normalised principal directions (columns)
values, vectors = stress.principals(10.0, 5.0, 0.0, 2.0, 0.0, 0.0)

# Principal vectors scaled by the principal stresses
stress.principal_vectors(10.0, 5.0, 0.0, 2.0, 0.0, 0.0)

# Invariants: I1, J2, J3, mean stress, equivalent (von Mises) stress, Lode r, z, θ, cos 3θ, triaxiality
i1, j2, j3, mean, eqv, lode_r, lode_z, lode_theta, cos3t, triax = stress.invariants(
    10.0, 5.0, 0.0, 2.0, 0.0, 0.0)

FailureCriteria is an enum of the criteria available (VON_MISES, MOHR_COULOMB, RANKINE, CONCRETE, …).

Usage in other modules

The utils module is re-exported at the top level of eurocodepy:

import eurocodepy as ec

ec.crosssection          # the module utils.crosssection
ec.section_properties    # the module utils.section_properties
ec.stress                # the module utils.stress

Further reading