Qwestrum Engineering360 · Civil Engineering · Prestressed Concrete
Flexural Design of PSC Beam
Superpose the axial (P/A) and eccentricity (Pe/Z) stresses at top and bottom fibres, add the service-load bending stress M/Z, and check the resulting fibre stresses stay within the permissible compression and tension limits at both transfer and service stages.
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.
- Eccentricity e chosen to keep compression at soffit under service load
- Load balancing: upward equivalent load w = 2P sin θ / spacing
- Partial prestressing allows controlled cracking under live load
Topic details
Introduction
Flexural design of a PSC beam is a stress-check problem: at every stage the combined stress at the top and bottom fibres must lie between the permissible tensile and compressive limits. The prestress produces P/A uniform compression plus Pe/Z bending due to eccentricity.
Scope in B.Tech and GATE syllabus
Two critical stages are examined — transfer (large prestress, small dead load, concrete young and weak) and service (reduced prestress after losses, full live load). The eccentricity is chosen so that neither stage causes unacceptable tension.
Why this topic matters in practice
Load balancing is an elegant design view: a parabolic tendon exerts an upward distributed force that can be tuned to cancel the dead load, leaving the section under nearly uniform compression. This concept simplifies many exam problems.
Key relations & formulas
(compression positive convention)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
(internal couple at ultimate)
Notation and sign conventions
Relation 1 —
(compression positive convention)
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 —
(internal couple at ultimate)
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
The stress at any fibre combines three effects: uniform axial compression P/A, the moment due to tendon eccentricity Pe/Z (which relieves the bottom fibre and adds to the top at transfer), and the bending stress M/Z from applied loads. Sign conventions must be handled consistently.
Governing relations in practice
At transfer the prestress is highest and the counteracting dead-load moment lowest, so the bottom fibre risks excessive compression and the top fibre risks tension — the reverse of the service condition. The permissible tensile stress at transfer is small because the concrete is immature.
Design and analysis considerations
At service, after losses reduce P and full live load applies its moment, the bottom fibre must not go into unacceptable tension. Choosing the eccentricity and prestress so both stages satisfy their limits is the core of the design.
Advanced theory and extensions
Load balancing recognises that a draped tendon curving downward at midspan pushes the beam upward with an equivalent uniformly distributed load 8Pe/L²; balancing this against gravity loads gives a member that carries service load with minimal flexural stress, ideal for deflection control.
Assumptions and validity limits
State assumptions explicitly before using any relation for flexural design of psc beam — 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 flexural design of psc beam.
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 flexural design of psc beam.
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
Flexural Design of PSC Beam 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 flexural design of psc beam with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use flexural design of psc beam?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
• Checking only the service stage and missing the often-critical transfer stage.
• Sign errors when superposing Pe/Z with the applied-moment stress.
• Using the effective prestress at transfer (should use the higher initial value there).
• Forgetting that permissible tensile stress at transfer is very low for young concrete.
• Sign errors when superposing Pe/Z with the applied-moment stress.
• Using the effective prestress at transfer (should use the higher initial value there).
• Forgetting that permissible tensile stress at transfer is very low for young concrete.
Quick revision checklist
Before attempting flexural design of psc beam problems, confirm you can:
1. Eccentricity e chosen to keep compression at soffit under service load
2. Load balancing: upward equivalent load w = 2P sin θ / spacing
3. Partial prestressing allows controlled cracking under live load
2. Load balancing: upward equivalent load w = 2P sin θ / spacing
3. Partial prestressing allows controlled cracking under live load
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.
Extreme fibre stresses under prestress
Problem
A rectangular PSC beam 300 × 600 mm carries an effective prestress P = 800 kN at an eccentricity e = 150 mm. Find the top and bottom fibre stresses due to prestress alone (ignore applied moment).
Solution
Area A = 300 × 600 = 180 000 mm². Section modulus Z = bh²/6 = 300 × 600²/6 = 1.8 × 10⁷ mm³ (same top and bottom for a rectangle). Axial stress P/A = 800 000/180 000 = 4.44 MPa (compression). Bending stress Pe/Z = 800 000 × 150 / 1.8 × 10⁷ = 6.67 MPa. Top fibre: σ_top = 4.44 − 6.67 = −2.23 MPa (tension); bottom fibre: σ_bottom = 4.44 + 6.67 = 11.11 MPa (compression). The top tension at transfer must be checked against the permissible limit.
Conceptual check — Flexural Design of PSC Beam
Problem
In a Prestressed Concrete semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of flexural design of psc beam." What should a complete answer include?
Exams & GATE
Krishna Raju — stress diagram at transfer and at service load stages.
📖 Standard books (India)
Prestressed Concrete — N. Krishna Raju
Read: Syllabus unit
PSC systems, losses, and design
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