Cable tension computed from parabolic-cable theory: H = wL²/8d (horizontal thrust),
V(x) from shear equilibrium, T(x)=√(H²+V(x)²). A crossing point load P adds
ΔH = Pab/(2dL) and its own shear reactions (a, b = distances to supports). Hanger
forces are the tributary UDL share plus a load-spreading (triangular influence)
share of P, normalised so the hangers' totals still balance the applied load.