Qwestrum Engineering360 · Civil Engineering · Prestressed Concrete
Losses of Prestress
Add up the individual losses — elastic shortening, shrinkage, creep, steel relaxation, and (for post-tensioning) friction and anchorage slip — and subtract from the jacking force to get the effective prestress P_e.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.
Key formulas & points
Skim these first — then read the full notes below.
- Total loss typically 15–25% of initial jacking force
- Anchorage slip and wobble add to post-tension losses
Topic details
Introduction
Prestress is not constant; it decreases over time and during transfer, so design must use the effective prestress after all losses. The total loss is typically 15–20% for pre-tensioned and 20–25% for post-tensioned members.
Scope in B.Tech and GATE syllabus
Losses split into immediate (elastic shortening, anchorage slip, friction) and time-dependent (concrete shrinkage, concrete creep, steel relaxation). Pre-tensioning has no friction loss but suffers full elastic shortening; post-tensioning tensioned sequentially reduces elastic loss but adds friction and slip.
Why this topic matters in practice
A typical exam question tabulates each loss as a stress reduction, sums them, and expresses the effective prestress as a percentage of the initial jacking stress — so systematic bookkeeping is the key skill.
Key relations & formulas
(pre-tension)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Notation and sign conventions
Relation 1 —
(pre-tension)
Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Fundamentals and definitions
Elastic shortening occurs because prestressing compresses the concrete, which shortens and relieves some tendon strain; in pre-tensioning the full loss develops at once, whereas in sequential post-tensioning earlier cables lose more than later ones.
Governing relations in practice
Shrinkage is the drying contraction of concrete over time, and creep is its continued deformation under sustained compressive stress; both shorten the member and reduce tendon strain, and both are larger for younger concrete and higher stress levels. Steel relaxation is the gradual loss of stress in the tendon held at constant strain.
Design and analysis considerations
In post-tensioning, friction between the tendon and duct causes the force to decay along the length according to P_x = P_0 e^(−μα − kx), combining the curvature effect (μα) and the wobble effect (kx). Anchorage slip is the small pull-in of the wedge when the jack is released.
Advanced theory and extensions
The effective prestress P_e = P_0 − Σ losses is what resists service loads, so underestimating losses leads to cracking while overestimating them wastes steel — accurate loss estimation is central to economical PSC design.
Assumptions and validity limits
State assumptions explicitly before using any relation for losses of prestress — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Prestressed Concrete viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Prestressed Concrete papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to losses of prestress.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to losses of prestress.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
Losses of Prestress appears in long-span bridges and parking floors. In Indian civil curricula this topic is tested because it connects theory to PSC beams and loss calculations.
GATE and semester exams often combine losses of prestress with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use losses of prestress?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
• Applying friction loss to a pre-tensioned member (it has none).
• Using the full elastic-shortening loss for every post-tensioned cable regardless of sequence.
• Forgetting anchorage slip loss, significant in short members.
• Reporting initial rather than effective prestress in service-stress checks.
• Using the full elastic-shortening loss for every post-tensioned cable regardless of sequence.
• Forgetting anchorage slip loss, significant in short members.
• Reporting initial rather than effective prestress in service-stress checks.
Quick revision checklist
Before attempting losses of prestress problems, confirm you can:
1. Total loss typically 15–25% of initial jacking force
2. Anchorage slip and wobble add to post-tension losses
3.
2. Anchorage slip and wobble add to post-tension losses
3.
Revise the solved examples in Prestressed Concrete — N. Krishna Raju and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Effective prestress after losses
Problem
A tendon is jacked to an initial stress of 1200 MPa. The estimated losses are: elastic shortening 40 MPa, shrinkage 45 MPa, creep 70 MPa, and relaxation 35 MPa. Find the effective prestress and the percentage loss.
Solution
Total loss Σ = 40 + 45 + 70 + 35 = 190 MPa. Effective prestress σ_e = 1200 − 190 = 1010 MPa. Percentage loss = 190/1200 × 100 = 15.8%, which lies in the typical 15–25% range and confirms the estimate is reasonable.
Conceptual check — Losses of Prestress
Problem
In a Prestressed Concrete semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of losses of prestress." What should a complete answer include?
Exams & GATE
Krishna Raju Ch. 5 — tabulate losses for typical exam problem.
📖 Standard books (India)
Prestressed Concrete — N. Krishna Raju
Read: Syllabus unit
PSC systems, losses, and design
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