A post-tensioned beam with a curved tendon profile, designed to China's GB 50010, makes friction loss along the tendon's length a truly significant part of the calculation — the longer and more curved the tendon path, the more the prestress force actually delivered to the far end of the beam differs from what was applied at the jacking end.

Every check above runs automatically inside the Structyze Prestressed Concrete Beam module — this particular module is part of the full desktop catalogue rather than the free browser trial, since the trial only carries a curated flagship set. You can still try the free trial modules right now to see the same calculation style in action on RCC Beam, Column, Slab and a handful of others.

The Example We'll Use

• Beam: 350 mm × 650 mm, span 18.0 m, post-tensioned with a parabolic tendon profile, stressed from one end only
• Jacking force: 1,450 kN at the stressed end
• Friction coefficient μ (duct-tendon friction): 0.25, wobble coefficient k: 0.0015 per metre (per GB 50010's friction loss provisions)
• Cumulative angular change of the tendon profile from the jacking end to mid-span: 0.18 radians

Working Through It

Friction loss along the tendon follows the standard exponential friction-loss relationship: force at a point = jacking force × e^(−(μα + kx)), where α is cumulative angular change and x is distance along the tendon.

At mid-span (x = 9.0 m, α = 0.18 rad): force = 1450 × e^(−(0.25 × 0.18 + 0.0015 × 9.0)) = 1450 × e^(−0.0585) = 1,368 kN — a loss of about 5.7% by mid-span alone.

At the far (non-stressed) end (x = 18.0 m, α = 0.36 rad, assuming a symmetric parabolic profile): force = 1450 × e^(−(0.25 × 0.36 + 0.0015 × 18.0)) = 1450 × e^(−0.117) = 1,289 kN — a loss of about 11.1% by the far end, roughly double the mid-span loss.

Because the beam is stressed from only one end, the effective prestress force used in the mid-span flexural and stress checks is the mid-span value (1,368 kN before further long-term losses are applied), not the jacking-end value — using the jacking force at mid-span would overstate the beam's actual effective prestress there.

With the correctly reduced mid-span force carried forward through further long-term loss calculations, the beam's service and ultimate checks both clear comfortably, with ultimate flexural utilization at 0.76.

What Governs, and Why

Friction loss isn't itself a pass/fail check, but getting it right is what makes every downstream check (transfer stress, service stress, ultimate capacity) actually correct — using the jacking-end force uniformly along the tendon instead of the position-specific, friction-reduced force would have overstated the beam's effective prestress everywhere except right at the jacking end itself, understating stress and overstating capacity at every other section.

Where Structyze Takes Over

Every check above runs automatically inside the Structyze Prestressed Concrete Beam module — this particular module is part of the full desktop catalogue rather than the free browser trial, since the trial only carries a curated flagship set. You can still try the free trial modules right now to see the same calculation style in action on RCC Beam, Column, Slab and a handful of others.

For Prestressed Concrete Beam and the rest of the full catalogue — 80+ components across RCC, Steel, Composite, Timber, Masonry and more, across 20+ design codes — buy the full Structyze desktop app or see everything it does on the Software page.

Quick FAQ

Would stressing the tendon from both ends reduce friction losses?

Yes — stressing from both ends (where practical) roughly halves the maximum friction loss at any point along the tendon compared to stressing from one end only, since each end only has to overcome friction over half the tendon's total length and angular change rather than the full length.

Does a straighter tendon profile reduce friction loss?

Yes significantly — friction loss depends on the tendon's cumulative angular change, so a straighter profile with less curvature accumulates less angular change and correspondingly less friction loss than a more sharply curved profile over the same span.

Final Thoughts

A post-tensioned tendon's effective prestress force isn't one number for the whole beam — it's a curve that drops off along the tendon's length as friction eats into it. That's why every section's design checks need the locally correct, position-specific prestress force rather than a single value borrowed from the jacking end.