# How Bridges Work 5, Exercise 1: which material for a cable, which for a column?
# For each material below (rounded, illustrative figures: density kg/m3, tension
# strength MPa, compression strength MPa) work out the length of a uniform bar
# that just carries its own weight, length = strength / (density x g), in km,
# for tension and for compression. Print the table, then rank the materials
# for a hanging cable (tension) and for a column (compression).
G = 9.81
MATS = {
    "timber (along grain)": (500, 20, 25),
    "brick":                (1900, 1, 20),
    "granite":              (2700, 8, 150),
    "plain concrete":       (2400, 3, 40),
    "cast iron":            (7200, 150, 600),
    "wrought iron":         (7700, 250, 250),
    "structural steel":     (7850, 355, 355),
}

def length_km(mpa, rho):
    return mpa * 1e6 / (rho * G) / 1000

rows = {n: (length_km(t, r), length_km(c, r)) for n, (r, t, c) in MATS.items()}
for n, (lt, lc) in rows.items():
    print(f"{n:22} {lt:6.2f} {lc:6.2f}")

print("cable:", [n for n, _ in sorted(rows.items(), key=lambda kv: -kv[1][0])])
print("column:", [n for n, _ in sorted(rows.items(), key=lambda kv: -kv[1][1])])

# Output when run:
# timber (along grain)     4.08   5.10
# brick                    0.05   1.07
# granite                  0.30   5.66
# plain concrete           0.13   1.70
# cast iron                2.12   8.49
# wrought iron             3.31   3.31
# structural steel         4.61   4.61
# cable: ['structural steel', 'timber (along grain)', 'wrought iron', 'cast iron', 'granite', 'plain concrete', 'brick']
# column: ['cast iron', 'granite', 'timber (along grain)', 'structural steel', 'wrought iron', 'plain concrete', 'brick']
#
# Reading the table: for a hanging cable, steel (4.61 km) beats timber (4.08),
# wrought iron (3.31) and cast iron (2.12); brick, plain concrete and granite
# manage only tens or hundreds of metres, so they cannot hang from a tower.
# For a column, cast iron (8.49 km) and granite (5.66) lead, with timber (5.10)
# and steel (4.61) next, and brick and concrete far behind. The figures are
# rounded and illustrative, and the length ignores buckling, joints and
# brittleness (cast iron's compression strength is useful but it fails
# without warning in tension). The pattern is what matters: stone and
# concrete belong in compression, steel in tension, and timber is
# surprisingly efficient for its weight.