# Exercise 2: support reactions for several point loads
# A beam of span 12 m sits on supports A (x = 0) and B (x = 12).
# Loads: 30 kN at 4 m, 50 kN at 9 m.

def reactions(span, loads):
    """loads is a list of (force_kN, distance_from_A_m). Returns (RA, RB)."""
    total = sum(f for f, x in loads)
    moment_about_a = sum(f * x for f, x in loads)
    rb = moment_about_a / span
    ra = total - rb
    return ra, rb

loads = [(30, 4), (50, 9)]
ra, rb = reactions(12, loads)
print(f"RA = {ra:.1f} kN, RB = {rb:.1f} kN")
print("sum of reactions:", ra + rb, "sum of loads:", sum(f for f, x in loads))

# Check by taking moments about B instead:
moment_about_b = sum(f * (12 - x) for f, x in loads)
print("RA by moments about B:", moment_about_b / 12)

# Output (as run):
# RA = 32.5 kN, RB = 47.5 kN
# sum of reactions: 80.0 sum of loads: 80
# RA by moments about B: 32.5
#
# Why: B is closer to the heavier load (at 9 m), so B carries more.