Prestressed Concrete Structures Lab (CE-704) - Unit 1 Short Notes

UNIT 1: FUNDAMENTALS OF PRESTRESSING & BASIC CONCEPTS

1.1 Introduction & Necessity of Prestressing

Conventional Reinforced Concrete (RCC) is strong in compression but weak in tension. Under service loads, tensile stresses exceed concrete's low tensile strength (~10% of compressive strength), causing cracks and large deflections.

Prestressing introduces controlled compressive stresses into the concrete member before external loads are applied. This pre-compression counteracts tensile stresses from service loads, keeping the concrete predominantly in compression.

Key Advantages of Prestressed Concrete (PSC):

• Higher Strength & Stiffness: Utilizes high-strength materials effectively.

• Longer Spans & Reduced Member Sizes: Lighter, slimmer sections for same span.

• Superior Crack Control: Cracks are minimized or eliminated at service loads.

• Improved Durability: Less cracking means reduced ingress of corrosive agents.

• Better Material Utilization: Concrete in compression, steel in tension—both at their best.

Comparison: RCC vs. PSC

[!TIP] Exam Focus: Be prepared to explain why prestressing is needed by contrasting the fundamental behavioral difference in stress states under load.

1.2 Materials for Prestressed Concrete

A. High-Strength Concrete

Required properties are more stringent than for RCC:

• High Compressive Strength (f'c): Typically ≥ 40 MPa (often 50-70+ MPa). Allows higher prestress and reduces section size.

• High Tensile Strength & Modulus (E_c): High modulus reduces elastic shortening losses.

• Low Creep & Shrinkage: Critical for maintaining prestress over time.

• Durability: Dense, impermeable mix to protect tendons.

Mix Design Considerations:

• Low Water-Cement (w/c) Ratio (< 0.40) for strength & durability.

• High cement content (350-450 kg/m³).

• Use of silica fume and superplasticizers (high-range water reducers) to achieve low w/c without sacrificing workability.

• Well-graded, hard, dense aggregates.

B. Prestressing Tendons/Steel

Must have very high strength and low relaxation.

Material Properties:

• Ultimate Tensile Strength (f_pu): Maximum stress.

• Yield Strength (f_py): 0.1% offset yield stress, typically 0.85-0.9 f_pu.

• Relaxation: Loss of stress under constant strain. Low relaxation (LR) strands are standard.

• Modulus of Elasticity (E_p): ~ 190-200 GPa. High value is crucial.

• Bond: Stress transfer to concrete. Improved by indentations (wires) or helical pattern (strands).

C. Non-Prestressed Steel

Standard reinforcement (mild/thermo-mechanically treated bars) used for shear, temperature, and shrinkage reinforcement.

[!TIP] Common Pitfall: Do not confuse the properties of prestressing steel (high strength, low relaxation) with standard rebar (lower yield strength, higher relaxation).

1.3 Methods of Prestressing

Classification by Timing

Classification by Location

• Internal Prestressing: Tendons are placed within the concrete cross-section (most common).

• External Prestressing: Tendons are placed outside the concrete section, deviated by external deviators. Used for bridge construction/strengthening and segmental construction.

Classification by Force Application

• Linear Prestressing: Tendons are straight or have constant eccentricity. Creates uniform prestress along length.

• Curved/Non-linear Prestressing: Tendons are profiled (harped/draped). The eccentricity varies, creating a prestressing moment along the member to balance external moments (e.g., from UDL).

[!TIP] Exam Key: The primary difference between pre- and post-tensioning is when the prestress is applied relative to concrete casting and how it is transferred (bond at release vs. anchorage).

1.4 Prestressing Systems & Equipment (Lab Relevance)

Pre-tensioning System:

• Bulkhead/Abutment: Strong wall to anchor tendons.

• Anchoring: Individual tendon anchorage (for bars) or collective (for strands).

• Stressing Jacks: Hydraulic jacks to apply force.

• Cutting Equipment: Torch or shears to release tendons.

Post-tensioning System:

• Tendon Types:

  • Monostrand: Single strand stressed individually.

  • Multi-strand: Multiple strands stressed simultaneously via a common anchorage.

• Anchorage Systems:

  • Passive (Wedge-Type): Most common. Wedges grip the strand in a conical anchor (e.g., Gifford-Edstrom, VSL). Bonded after grouting.

  • Active (Button/Swaged): Used for bars; nut tightened on threaded end.

• Grouting (for Bonded Systems):

  • Materials: Cementitious grout (OPC + water + admixtures). Must be fluid, non-segregating, low shrinkage.

  • Equipment: Grout mixer, pump, hoses, vent tubes.

  • Procedure: Pressure grouting from low point to high point until bleed water ceases.

Stressing Equipment & Calibration:

• Hydraulic Jack: Provides force. Capacity must match tendon force.

• Pressure Gauge: Measures hydraulic pressure. Must be calibrated against a load cell.

• Load Cell: Direct force measurement device for calibration and verification.

• Calibration Curve: Relates jack pressure to actual tendon force. F = (A_j * P) / 1000 (kN), where A_j = jack piston area (mm²), P = pressure (MPa). Always use calibrated values.

[!TIP] Lab Safety: Jacks must be securely anchored, and the area behind the jack must be clear. Never stand in line with the jack or tendon during stressing.

1.5 Basic Design Philosophy & Limit States

Design follows Limit State Design (LSD) philosophy, similar to RCC but with unique considerations.

1. Ultimate Limit State (ULS): Concerned with strength and stability at maximum load.

   • Ensure section has sufficient nominal strength (φP_n ≥ P_u).

   • Check for compression/tension failures, shear, and stability (buckling of thin webs).

2. Serviceability Limit State (SLS): Concerned with performance under everyday loads.

   • Cracking: Limit tensile stresses in concrete (f_t ≤ f_t,allow). Primary goal of prestressing.

   • Deflections: Limit deflections to serviceability requirements (e.g., L/250 for beams).

   • Vibrations: For floors/bridges.

Load Balancing Concept:

A fundamental design approach where the prestressing force profile is chosen to counteract (balance) the external service loads. The tendon profile is designed so that the prestressing moment at any section equals the external moment from balanced loads. This keeps concrete stresses within desired limits (often zero or small compression at bottom fiber).

Stress Diagrams:

At any critical section, stresses due to combined effect of prestressing force (P_e) and external loads (M) are computed using elastic theory (stress = force/area ± moment/section modulus). For a simply supported beam with parabolic tendon under UDL:

• At midspan: Prestressing force causes compression at top, tension at bottom. UDL causes compression at top, tension at bottom. Net effect: Both add, so critical stress is at bottom fiber.

• At supports: Prestressing force (low eccentricity) causes small compression. UDL moment is zero. Net effect: Compression at top.

[!TIP] Exam Problem: You will often be asked to sketch stress diagrams (top & bottom) at critical sections (midspan, support) for a given load and tendon profile. Remember: σ = ± P_e/A ± M_e/S.

1.6 Losses of Prestress

The initial prestressing force (f_pi) applied at the jack is greater than the effective prestress (f_pe) available at service stages due to losses. Accounting for losses is critical; underestimation leads to under-designed members.

Classification:

Basic Calculation (Simple Case - Straight Tendon, Pre-tensioning):

For a pre-tensioned member, the major immediate loss is elastic shortening.

$$ \Delta f_{pES} = \frac{E_p}{E_c} \cdot f_{cgp} $$

Where:

• Δf_pES = Loss due to elastic shortening (MPa)

• E_p = Modulus of prestressing steel (~200 GPa)

• E_c = Modulus of concrete (at transfer, ~25-30 GPa)

• f_cgp = Concrete stress at centroid of prestressing steel at transfer (MPa)

Effective Prestress:

$$ f_{pe} = f_{pi} - \text{Sum of All Losses} $$

[!TIP] Critical Point: In post-tensioning, friction loss (Δf_pF) is often the largest immediate loss and must be calculated from the stressing end to any point using: Δf_pF = (f_pi - f_px) = f_pi (1 - e^{-(Kx + μθ)}), where K = wobble coefficient, μ = curvature friction coefficient, x = distance, θ = angular change.

1.7 Analysis of Prestressed Sections (Elastic Theory)

Stresses at a Section:

For a given section with prestressing force P_e (effective) at eccentricity e from the centroid, under external moment M (from service loads):

Stress at Top Fiber:

$$ f_{top} = -\frac{P_e}{A} - \frac{P_e \cdot e}{S_t} + \frac{M}{S_t} $$

Stress at Bottom Fiber:

$$ f_{bottom} = -\frac{P_e}{A} + \frac{P_e \cdot e}{S_b} - \frac{M}{S_b} $$

Where:

• A = Cross-sectional area

• S_t, S_b = Section moduli for top and bottom fibers

• Sign Convention: Compression is negative (-), Tension is positive (+). (Note: Some texts use opposite. Be consistent.)

• The term P_e * e represents the prestressing moment M_p = P_e * e.

Load Balancing Concept:

To achieve a "balanced" condition where concrete is stress-free (or at a desired stress) under a specific load, set the net stress to zero (or a limit) and solve for the required e or tendon profile.

Cable Profile for Balanced UDL:

For a simply supported beam of span L under uniformly distributed load (UDL) w, the required prestressing moment to balance it is M(x) = w·x·(L-x)/2. This is a parabola.

The corresponding eccentricity profile e(x) (for constant P_e) is:

$$ e(x) = \frac{M(x)}{P_e} = \frac{w \cdot x \cdot (L - x)}{2 P_e} $$

This is the classic parabolic drape for post-tensioned beams.

[!TIP] Exam Derivation: You may need to derive the parabolic equation y = (4e/L²) * x * (L - x) from the bending moment equation of a simply supported beam under UDL. e is the maximum eccentricity at midspan (x = L/2).

1.8 Introduction to Laboratory Experiments (Preview)

Objective: To physically observe and quantify the theoretical principles of prestressing.

Typical Introductory Experiments:

1. Material Characterization:

   • Concrete: Testing cubes/cylinders for compressive strength at 7, 14, 28 days. Determine f'c and E_c (from modulus test).

   • Prestressing Steel: Tensile test on wires/strands to determine f_pu, f_py, E_p, and elongation at break. Observe yield plateau (if any) and ultimate failure.

2. Simple Beam Comparison Test:

   • Setup: Test two simply supported beams (same dimensions, mix) side-by-side: one RCC, one PSC (pre-tensioned or post-tensioned).

   • Loading: Apply central point load or UDL incrementally.

   • Measurements:

     • Load vs. Deflection: PSC beam shows stiffer response (less deflection) and higher ultimate load.

     • Crack Pattern: RCC beam cracks early and propagates. PSC beam shows delayed and fewer cracks; cracks are finer and closer to supports.

     • Strains: Use strain gauges on concrete (top/bottom) and steel. In PSC, bottom concrete strain remains compressive at service loads.

3. Loss Measurement (Pre-tensioning):

   • Setup: A single pre-tensioned strand in a concrete prism. Measure initial jack force (F_i) and force in strand after release (F_r) using a load cell or by measuring elongation and using ΔF = E_p * A_p * Δε.

   • Observation: F_r < F_i due to elastic shortening loss. Quantify Δf_pES.

[!TIP] Lab Report: Always correlate observed behavior (deflection, cracks) with the theoretical stress state predicted in Unit 1.7. The lab proves the core advantage: PSC stays compressed under load.