Prestressed Concrete Structures Lab (CE-704) - Unit 2 Short Notes

I. Introduction & Laboratory Safety & Instrumentation

A. Safety Protocols in Prestressed Concrete Lab

• Primary Hazards: High tensile forces in strands (risk of snap-back), hydraulic pressure (jack failure), heavy specimens, high-strength concrete splinters.

• Key Precautions:

  • Stressing Area: Establish a safety zone behind and to the sides of the beam during stressing. Never stand in line with the strand.

  • Jack & Pump: Regularly inspect hydraulic hoses, fittings, and gauges. Never exceed rated capacity.

  • Specimen Handling: Use appropriate lifting gear and ensure stable support.

  • PPE: Mandatory use of safety glasses, steel-toed boots, gloves, and hard hat.

B. Calibration and Use of Key Laboratory Instruments

• Hydraulic Jack & Pressure Gauge: Calibrate as a system. Force calculation:

$$P = \frac{A_j \cdot P_g}{1000}$$

\boxed{P = \frac{A_j \cdot P_g}{1000}} where $$\displaystyle A_j $$ = jack piston area (mm²), $$\displaystyle P_g $$ = gauge pressure (N/mm²), $P$ = force (kN).

• Load Cell & DAQ: Provides direct digital force readout. Must be calibrated with known weights.

• Demec/ERSG: Demac (mechanical) for surface strain over gauge length. ERSG (electrical) for point strain, requires careful bonding and temperature compensation.

• LVDT: Measures displacement/deflection. Must be fixed to a stable reference.

• Concrete Testing Machines: Verify calibration certificates. Follow standard loading rates (e.g., IS 516 for cubes: 140 kg/cm²/min).

[!TIP] Common Pitfall: Using an uncalibrated pressure gauge leads to systematic error in all prestress force measurements. Always record gauge calibration factor.

II. Material Characterization for Prestressed Concrete

A. Testing of Prestressing Tendons & Strands

• Objective: Determine $$\displaystyle f_{pu} $$ (ultimate), $$\displaystyle f_{py} $$ (0.1% offset yield), $$\displaystyle E_p $$ (modulus), and elongation at failure.

• Procedure: Specimen (usually 1m length) gripped in tensile testing machine. Extensometer/LVDT for strain. Load and elongation recorded continuously.

• Key Output: Stress-Strain Curve. $$\displaystyle E_p $$ is slope of initial linear portion. $$\displaystyle f_{py} $$ found by offset method.

• Code: IS 1786 specifies requirements for Hysd steel.

B. Testing of Concrete

C. Bond Characteristics

• Pull-Out Test (Pretensioned): A strand embedded in a concrete cylinder is pulled out. Measures bond stress $$\displaystyle \tau = \frac{P}{\pi d l_e} $$ where $$\displaystyle l_e $$ = embedment length.

• Observation: Failure mode (strand slip, concrete splitting) indicates bond quality.

III. Measurement of Prestress Losses (Short-Term & Long-Term)

A. Immediate Losses

1. Elastic Shortening Loss

• Theory: When prestress is transferred to concrete, concrete shortens elastically, reducing strand stress.

• Calculation:

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

\boxed{\Delta f_{pES} = \frac{E_p}{E_c} \cdot f_{pt}} where $$\displaystyle f_{pt} $$ = initial prestress in strand before transfer.

• Experiment: Measure concrete strain at transfer level using embedded ERSG or surface Demec gauges on a dummy member. $$\displaystyle \Delta f_{pES} = E_p \cdot \epsilon_c $$.

2. Friction Losses (Post-Tensioning)

• Theory: Loss due to wobble (random misalignment) and curvature (bending in duct). Governed by coefficients $k$ (wobble, per m) and $\mu$ (curvature coefficient).

• Experiment - Friction Loss Test:

  • Setup: Curved duct (known radius $R$, length $L$). Pressure cell/load cell at jack end and at anchor end. Strand stressed.

  • Procedure: Record jack pressure $$\displaystyle P_j $$ and anchor force $$\displaystyle P_a $$.

  • Calculation: Friction loss fraction: $$\displaystyle 1 - \frac{P_a}{P_j} $$. Effective $\mu$ and $k$ can be back-calculated from:

$$\frac{P_a}{P_j} = e^{-(\mu \theta + k L)}$$

where $$\displaystyle \theta = L/R $$ (radians).

• DiagramCANVAS: Show a curved tendon duct with a jack at one end, a load cell at the anchor end, and a pressure gauge on the jack. Label L, R, θ, Pj, Pa.

3. Anchorage Set (Draw-in) Loss

• Theory: When the jack is released, the wedge/anchors slip into the concrete, causing strand retraction and force loss.

• Experiment: Measure the slip ($s$) of the strand relative to the anchor after initial stressing and anchoring. Loss is a function of slip and strand stiffness.

B. Time-Dependent Losses

• Creep: Long-term strain increase under constant stress. Measured by sustained loading on concrete cylinders, monitoring strain over weeks/months.

• Shrinkage: Measured on sealed, unloaded concrete prisms (length change vs. time).

• Relaxation: Loss of stress in steel at constant strain. Measured by holding a strand at fixed length and monitoring force decay. Typically provided by manufacturer for strand type.

[!TIP] Exam Focus: Be able to distinguish between immediate (ES, Friction, Anchorage) and long-term (Creep, Shrinkage, Relaxation) losses. Friction loss is only for post-tensioning.

IV. Flexural Testing of Prestressed Concrete Beams

A. Pretensioned Beam Testing

1. Fabrication Simulation:

• Mould: Steel bed with abutments. Strands stressed against anchors using hydraulic jacks. Concrete cast and cured. Transfer: Strands cut/released suddenly, transferring prestress to concrete.

2. Test Setup:

• Support: Simply supported.

• Loading: Two-point or third-point loading (to create constant moment region). Loading frame with hydraulic jack or calibrated weights.

• DiagramSEARCH: "simply supported prestressed beam two point loading setup with LVDTs"

3. Instrumentation:

• LVDTs: Mid-span (deflection), quarter-span, support settlements.

• Strain Gauges: Top/bottom concrete at mid-span, strand at mid-span (if accessible).

• Dial Gauge: At ends to measure strand slip after transfer/cracking.

4. Loading & Observations:

• Loading Stages: (a) Pre-transfer, (b) Post-transfer, (c) Service load, (d) Until failure.

• Key Observations:

  • First Crack Load ($$\displaystyle P_{cr} $$): Sudden appearance of flexural crack.

  • Crack Pattern: Vertical flexural cracks propagating from bottom. For shear tests, inclined cracks.

  • Ultimate Load ($$\displaystyle P_u $$): Failure mode: Tension-controlled (strand yields, large deflection) vs. Compression-controlled (concrete crushes, sudden). Ductility is key.

  • Strand Slip: Measured at ends, indicates anchorage efficiency.

• Data Recording: Load, mid-span deflection, strain readings at each increment.

5. Analysis of Results:

• Load-Deflection Curve: Plot $P$ vs. $$\displaystyle \delta_{mid} $$. Identify uncracked, cracked, and ultimate stages.

• Moment-Curvature: $$\displaystyle M = P \cdot a/2 $$ (for two-point), $$\displaystyle \phi = \frac{\epsilon_{top} - \epsilon_{bottom}}{d} $$. Plot $M$ vs. $\phi$.

• Effective Prestress ($$\displaystyle f_{pe} $$): Calculated from measured strain in strand at transfer: $$\displaystyle f_{pe} = f_{pi} - \Delta f_{pES} - \Delta f_{pF}... $$ or directly from strain gauge: $$\displaystyle f_{pe} = E_p \cdot \epsilon_s $$.

• Comparison with Theory: Compare $$\displaystyle P_u $$ with $$\displaystyle M_u / (lever arm) $$. Theoretical $$\displaystyle M_u $$ from strain compatibility or code equations (IS 1343).

B. Post-Tensioned Beam Testing

• Fabrication Differences: Ducts in formwork, strands stressed after concrete hardens, grouting of ducts.

• Testing Focus: Similar loading, but end-zone behavior is critical. Observe for end cracks due to high local bursting stresses.

[!TIP] Common Pitfall: Not allowing sufficient time for elastic shortening losses to stabilize before applying service loads in the lab. Record readings immediately after transfer and after a set time (e.g., 24 hrs).

V. Shear and Torsion Testing of Prestressed Concrete Members

A. Shear Behavior

• Experiment: Test beam with shear span-to-depth ratio (a/d) as parameter.

  • a/d < 2.5 (Deep Beam): Failure by diagonal compression or shear-compression. Stiff response, less ductile.

  • a/d > 2.5 (Flexural-Shear): Failure by diagonal tension (inclined crack). Web reinforcement (stirrups) increases capacity.

• Instrumentation: LVDTs for deflection, strain gauges on web (diagonal direction), crack width measurement (microscope).

• Observation: Inclined crack initiation and propagation. Load at first inclined crack.

B. Torsion

• Experiment: Apply pure torque (e.g., using lever arms) to a hollow/solid section.

• Observation: Spiral crack pattern at ~45°. Angle of twist measured at ends.

• Data: Torque vs. angle of twist curve. Stiffness degradation after cracking.

VI. Anchorage Zone & End-Plate Testing

A. End-Block Stress Distribution

• Objective: Verify stress distribution (bursting, spalling, bearing) under post-tensioning force.

• Experiment:

  • Specimen: Concrete end-block (cube or cylinder) with one or multiple ducts.

  • Loading: Apply force $P$ via a jack against a bearing plate, simulating anchor.

  • Instrumentation: Grid of Demec gauges or ERSGs on the end-block face and sides to measure surface strains in two directions.

  • DiagramCANVAS: Square end-block with a central duct. Show a grid of points (e.g., 5x5) on the face where Demec gauge readings are taken. Arrows indicate principal stress directions.

• Analysis:

  1. Convert surface strains to surface stresses using $$\displaystyle E_c $$ and Poisson's ratio.

  2. Plot stress contours (bursting stress radial from duct, transverse splitting stress).

  3. Compare maximum measured bursting stress with code prediction (e.g., Guyon's method for a single duct: $$\displaystyle \sigma_b = \frac{P}{A_n} \left(1 - \frac{e^2}{r^2}\right) + \frac{P e y}{I_n r} $$ simplified).

  4. Check if reinforcement (if provided) is adequate.

B. Anchor Plate/Head Test

• Objective: Check bearing stress under anchor head/plate.

• Procedure: Place anchor plate on concrete cube. Apply load through plate. Measure concrete deformation or use pressure film to map bearing pressure.

• Failure Mode: Local crushing of concrete under plate. Ensure bearing stress $$\displaystyle < $$ code limit (e.g., $$\displaystyle 0.6 f_{ck} $$ for IS 1343).

VII. Data Analysis, Reporting, and Code Correlation

A. Processing Experimental Data

• Force from Pressure: $$\displaystyle P = (A_j \times P_g \times C_f) / 1000 $$ ($$\displaystyle C_f $$ = calibration factor).

• Strain to Stress: $$\displaystyle \sigma = E \times \epsilon $$ (for steel and concrete in elastic range).

• Deflection Correction: Subtract support settlements, machine compliance.

• Graphs: Load-Deflection, Load-Strain (concrete & steel), Moment-Curvature.

B. Standard Lab Report Structure

1. Objective: Clear statement of test purpose.

2. Theory: Relevant equations, code clauses.

3. Apparatus: Sketch with key dimensions.

4. Procedure: Step-by-step, chronological.

5. Observations: Raw data tables (load, pressure, strain, deflection readings).

6. Calculations: Sample calculations for key results (e.g., $$\displaystyle f_{ck} $$, $$\displaystyle f_{pu} $$, $$\displaystyle \Delta f_{pES} $$).

7. Results: Tables of computed values, plotted graphs.

8. Discussion: Compare exp. vs. theory. Explain discrepancies (e.g., friction higher due to duct roughness, lower strength due to poor compaction). Comment on failure mode and ductility.

9. Conclusion: Summary of findings, verification of design principles.

C. Correlation with Design Codes (IS 1343 / ACI 318)

• Ultimate Strength: Compare $$\displaystyle P_u^{exp} $$ with $$\displaystyle P_u^{code} $$. Calculate ratio.

• Serviceability: Compare max crack width (measured with microscope) and deflection with code limits (e.g., L/250 for simply supported).

• Ductility: Check if tension-controlled failure (large $$\displaystyle \delta_u $$, strand yield visible). Code requires $$\displaystyle \epsilon_{cu} \geq 0.005 $$ for ductile members.

VIII. Advanced/Optional Experiments

• Dynamic Testing: Impact hammer or shaker to find natural frequency $$\displaystyle f_n $$. Compare with theoretical $$\displaystyle f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}} $$.

• NDT on Tested Member: Ultrasonic Pulse Velocity (UPV) to assess crack damage (lower velocity). Rebound hammer for surface hardness.

• Fatigue Testing: Cyclic loading (constant amplitude). Plot S-N curve for the beam. Monitor crack growth.

• Grout Quality: Cube tests from grout samples. Pull-out test of strand from grouted duct to measure bond strength.

[!TIP] Final Exam Strategy: For any test, be ready to sketch the setup, list the instruments and their purpose, write the key formula(s) used for calculation, and describe the expected failure mode. Always link the experiment to a design concept (e.g., "This friction loss test justifies the need for $k$ and $\mu$ values in post-tensioning design").