# Exercise 3: sizing a hanger rod
# A steel hanger carries a steady tension of 200 kN. Yield strength 355 MPa.
# Required factor of safety: 1.5. Stock rod diameters (mm): 25, 30, 32, 36, 40.

import math

load_kn = 200
yield_mpa = 355
factor = 1.5
stock = [25, 30, 32, 36, 40]

def area_mm2(d):
    return math.pi * (d / 2) ** 2

def stress_mpa(force_kn, area):
    return force_kn * 1000 / area      # N / mm2 = MPa

needed = load_kn * 1000 * factor / yield_mpa
print(f"required area {needed:.1f} mm2 (diameter {2 * math.sqrt(needed / math.pi):.1f} mm)")

for d in stock:
    a = area_mm2(d)
    s = stress_mpa(load_kn, a)
    print(f"{d} mm: area {a:.1f} mm2, stress {s:.1f} MPa, factor {yield_mpa / s:.2f}")

chosen = next(d for d in stock if area_mm2(d) >= needed)
print("smallest stock rod that works:", chosen, "mm")

# Output (as run):
# required area 845.1 mm2 (diameter 32.8 mm)
# 25 mm: area 490.9 mm2, stress 407.4 MPa, factor 0.87
# 30 mm: area 706.9 mm2, stress 282.9 MPa, factor 1.25
# 32 mm: area 804.2 mm2, stress 248.7 MPa, factor 1.43
# 36 mm: area 1017.9 mm2, stress 196.5 MPa, factor 1.81
# 40 mm: area 1256.6 mm2, stress 159.2 MPa, factor 2.23
# smallest stock rod that works: 36 mm
#
# Notice 32 mm is only just short (1.43 against 1.5). That is why the stock list matters.