How we validate MathCanvas. Run every check yourself.

"""Independent recomputation of the AltoDocs validation references.

A second implementation in another language, sharing no code with the
calculation engine: plain Python floats, inputs typed in by hand from the
cases on altodocs.io/validation. Run it with any Python 3:

    python3 references.py

It prints every reference in the order the validation page lists them, in
the units shown there. The engine's test suite runs this script and checks
that it agrees with the published case data.
"""
import json
from math import pi, sqrt

kN, m, mm, cm, MPa, GPa = 1e3, 1.0, 1e-3, 1e-2, 1e6, 1e9  # SI: N, m, Pa
SQRT3 = sqrt(3)

# Engineering benchmarks, in each check's unit.
q, L, E, I = 12 * kN / m, 6 * m, 210 * GPa, 8356 * cm**4
W_pl, f_y = 628.4 * cm**3, 235 * MPa
M_c_Rd = W_pl * f_y / 1.0
benchmarks = [
    q * L**2 / 8 / (kN * m),                       # M = qL²/8 [kN m]
    q * L / 2 / kN,                                # V = qL/2 [kN]
    5 * q * L**4 / (384 * E * I) / mm,             # δ = 5qL⁴/(384EI) [mm]
    M_c_Rd / (kN * m),                             # M_c,Rd = W_pl f_y / γ_M0 [kN m]
    54 * kN * m / M_c_Rd,                          # η = M_Ed / M_c,Rd [-]
    pi**2 * E * I / (6 * m) ** 2 / kN,             # N_cr = π²EI/L_cr² [kN]
    1.0 * 30 * MPa / 1.5 / MPa,                    # f_cd = α_cc f_ck / γ_c [MPa]
    120 * kN * m / (300 * mm * (450 * mm) ** 2 * (20 * MPa)),  # μ [-]
    0.6 * 800 * MPa * 245 * mm**2 / 1.25 / kN,     # F_v,Rd [kN]
    (1.35 * 10 + 1.5 * 5),                         # E_d [kN/m]
    25 * 0.2,                                      # g = ρh [kN/m²]
    0.8 * 1.0 * 1.0 * 1.0,                         # s = μ₁ C_e C_t s_k [kN/m²]
    12e-6 * 30 * 10 * m / mm,                      # ΔL = α ΔT L [mm]
    1.2 * 20**2 / 8,                               # M = wL²/8 [kip ft]
]

# Published worked examples (JRC EUR 27346 EN), from the printed inputs.
published = [
    170.9 * cm**2 * 355 * MPa / 1.00 / kN,                       # N_c,Rd [kN]
    pi * sqrt(210 * GPa / (355 * MPa)),                          # λ₁
    4.335 * m / (7.53 * cm),                                     # λ_z
    57.57 / 76.41,                                               # λ̄_z
    0.5 * (1 + 0.49 * (0.75 - 0.2) + 0.75**2),                   # Φ_z
    1 / (0.92 + sqrt(0.92**2 - 0.75**2)),                        # χ_z
    0.69 * 170.9 * cm**2 * 355 * MPa / 1.00 / kN,                # N_b,Rd [kN]
    1307 * cm**3 * 355 * MPa / 1.00 / (kN * m),                  # M_c,Rd [kN m]
    42.69 * cm**2 * 355 * MPa / (SQRT3 * 1.00) / kN,             # V_pl,Rd [kN]
    sqrt(1307 * cm**3 * 355 * MPa / (164.7 * kN * m)),           # λ̄_LT
    0.5 * (1 + 0.34 * (1.68 - 0.2) + 1.68**2),                   # Φ_LT
    1 / (2.16 + sqrt(2.16**2 - 1.68**2)),                        # χ_LT
    0.28 * 1307 * cm**3 * 355 * MPa / 1.00 / (kN * m),           # M_b,Rd [kN m]
    6.2 * mm * 130 * mm * 235 * MPa / (SQRT3 * 1.00) / kN,       # V_pl,Rd beam web [kN]
    0.6 * 157 * mm**2 * 400 * MPa / 1.25 / kN,                   # F_v,Rd M16 [kN]
    2 * 3 * mm * 130 * mm * 360 * MPa / (SQRT3 * 0.8 * 1.25) / kN,  # F_w,Rd [kN]
    0.6 * 245 * mm**2 * 500 * MPa / 1.25 / kN,                   # F_v,Rd M20 [kN]
    2.5 * 0.659 * 20 * mm * 5.6 * mm * 360 * MPa / 1.25 / kN,    # F_b,Rd beam web [kN]
    (0.5 * 290 * mm**2 * 360 * MPa / 1.25 + 670 * mm**2 * 235 * MPa / (SQRT3 * 1.00)) / kN,      # V_eff,2,Rd fin plate [kN]
    10 * mm * 140 * mm * 235 * MPa / (SQRT3 * 1.00) / kN,        # V_pl,Rd fin plate [kN]
    (0.5 * 162.4 * mm**2 * 360 * MPa / 1.25 + 515.2 * mm**2 * 235 * MPa / (SQRT3 * 1.00)) / kN,  # V_eff,2,Rd beam web [kN]
    (10 * mm * (140 * mm) ** 2 / 6) * 235 * MPa / 1.00 / (kN * m),  # M_el,Rd [kN m]
]

if __name__ == '__main__':
    print(json.dumps({'benchmarks': benchmarks, 'published': published}, indent=2))