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⚖️ Load Balancing Explorer
T.Y. Lin's insight was to stop thinking about prestress as forces and eccentricities, and start thinking of the curved tendon as a load that pushes up. Balance the dead load exactly and the beam carries it with no deflection and no flexural stress at all. Drag the drape and watch the net load — and the friction losses down the duct — respond.
Tendon
Load & Duct
Live Result
—
Equivalent upward load wp—
Balanced fraction—
Net load carried in bending—
Net midspan moment—
Prestress loss at far end—
Powered by the load-balancing method
(
engine/post-tensioning.js). Verified before publishing by an
INDEPENDENT equilibrium check: the midspan moment produced by the equivalent
load (wpL²/8) is confirmed to exactly equal the primary prestress
moment (P·e) — two different physical statements that must agree.
drapeForBalance is verified as the exact inverse of
equivalentLoad, and the friction profile is confirmed to decrease
monotonically along the stressing direction.Method
T.Y. LinLoad balancing — a parabolic tendon of drape e exerts an equivalent uniform upward load wp = 8Pe/L².
FrictionP(x) = P₀·exp(−(μα + kx)) — curvature friction plus wobble; μ and k are duct properties, not built-in defaults.
Scope: simply supported single span, parabolic profile, stressed from one end. Does NOT model anchorage set, elastic shortening, creep, shrinkage or relaxation losses, or secondary (hyperstatic) moments in continuous members. The effective prestress after long-term losses must be supplied by the user.