Post-Tensioning and Prestressing Systems

Introduction: Fundamental Principles of Prestressing

Prestressing is a technique that involves applying a permanent compressive stress to a concrete member before it is subjected to service loads. Concrete is a material that is strong in compression but weak in tension. By pre-compressing it, the tensile stresses induced by loads are neutralized, allowing for longer spans, thinner sections, and lighter structures.

Post-tensioning is a method of prestressing where the cables (strands or bars) are tensioned after the concrete has been placed and has cured. The cables are placed in ducts (conduits) before pouring, then tensioned using hydraulic jacks once the concrete has reached the required strength. This technique is widely used in bridges, viaducts, parking garage slabs, foundations, and long-span structures.

For the Red Seal exam, you must master not only the installation procedures but also elongation calculations, tension losses, tolerances, and specific safety rules.

Difference Between Pre-tensioning and Post-tensioning

Characteristic	Pre-tensioning	Post-tensioning
Timing of tensioning	Before concrete placement	After concrete has cured
Anchorage	Direct steel-concrete bond	Mechanical anchorages at ends
Duct	None	Metal or plastic duct required
Jacks	Fixed prestressing bed	Portable jacks on site
Typical application	Precast beams in factory	Cast-in-place slabs, bridges

Pre-tensioning is done in the factory: the cables are tensioned between fixed abutments, concrete is poured, and once cured, the cables are released. Post-tensioning is done on site or in the factory for larger elements, and it is the method that primarily concerns you in this chapter.

Components of a Post-Tensioning System

Strands and Bars

Strands are cables composed of 7 high-strength steel wires (nominal diameter of 12.7 mm or 15.24 mm). They are classified according to their ultimate tensile strength:

Grade 1860 MPa: the most common (15.24 mm wires)

Grade 1725 MPa: for certain specific applications

Prestressing bars (Dywidag or equivalent) are used for specific applications such as anchor tie-backs or repairs. They have diameters ranging from 25 to 40 mm and strengths from 1030 to 1080 MPa.

Ducts

Ducts are conduits that house the strands and allow them to slide during tensioning. They can be:

Metal (corrugated steel): for bridges and heavy structures

Plastic (polypropylene or polyethylene): for building slabs, with permanent grease (non-grouted system) or for subsequent grouting

The inside diameter of the duct must be at least 6 mm larger than the strand diameter to allow free movement.

Anchorages

Anchorages are the devices that transfer the prestressing force to the concrete. There are two types:

Active anchorages: the side where the jack pulls the strands

Passive anchorages: the fixed side, often embedded in the concrete

Anchorages are classified according to their capacity (number of strands): from 1 strand (thin slab) to 55 strands (major bridges). Each anchorage includes a bearing plate, wedges (cones), and a load distribution block.

Installation Procedure: Step by Step

1. Duct Placement

Before pouring, the ducts are positioned according to the prestressing drawings. They must be:

Securely fastened using supports spaced 60 to 90 cm apart

Watertight at all joints (duct tape or sleeves)

Protected against crushing during concrete placement

Profiles can be straight, parabolic, or polygonal. Curved profiles create friction losses that must be calculated.

2. Concrete Placement

During pouring, the concrete must be vibrated carefully around the ducts. Excessive vibration can displace the ducts; insufficient vibration leaves voids that weaken the bond. Ducts must be maintained in position within ± 15 mm of the theoretical profile.

3. Tensioning

Tensioning begins only when the concrete has reached the specified minimum strength (generally 70 to 80% of the 28-day strength). This value is indicated on the drawings and must be verified by cylinder test results.

The hydraulic jack is positioned on the active anchorage. Tension is applied in successive increments (10%, 50%, 80%, 100% of the final force). At each stage, you verify:

The force (hydraulic pressure)

The elongation of the strand (measured with a caliper or graduated ruler)

4. Theoretical Elongation Calculation

The elongation ΔL of a strand is calculated according to Hooke's Law:

ΔL = (F × L) / (E × A)

Where:

F = prestressing force (N)

L = free length of the strand between anchorages (m)

E = modulus of elasticity of steel (195,000 MPa)

A = cross-sectional area of the strand (mm²)

For a 15.24 mm strand: A = 140 mm², E = 195,000 MPa.

Example: A 15.24 mm strand, 25 m long, with a force of 195 kN.

ΔL = (195,000 N × 25,000 mm) / (195,000 MPa × 140 mm²) = 4,875,000,000 / 27,300,000 = 178.6 mm

This theoretical elongation is compared to the measured elongation. The tolerance is ± 7% between the theoretical and measured values. If the difference exceeds this tolerance, you must stop and investigate (excessive friction, stuck strand, defective anchorage).

5. Duct Grouting

After tensioning, the ducts are grouted with cement grout (for bonded systems). The grout:

Protects the strands against corrosion

Ensures the bond between steel and concrete

Distributes stresses over the entire length

The grout is composed of cement, water, and admixtures (superplasticizer, expanding agent). The water/cement ratio must be less than 0.45. Grouting is done from the lowest point, and air is evacuated through vents at high points.

Prestressing Losses

Prestressing losses are the reductions in force between the force applied at the jack and the effective force in the concrete. They are classified into two categories:

Immediate Losses (at the time of tensioning)

Type of Loss	Cause	Typical Value
Friction	Strand-duct contact on curves	5 to 15% depending on angle
Anchorage seating	Wedge slip when the jack is released	3 to 6 mm of slip
Elastic shortening of concrete	Concrete compresses under the force	1 to 3%

The friction loss is calculated using the formula:

F(x) = F₀ × e^(-μθ - kx)

Where:

F₀ = force at the jack

μ = strand-duct friction coefficient (0.15 to 0.25 for metal duct, 0.05 to 0.10 for greased plastic duct)

θ = cumulative angle of the profile (radians)

k = parasitic friction coefficient (0.001 to 0.003 per meter)

x = distance from the jack (m)

Time-Dependent Losses (over time)

Type of Loss	Cause	Typical Value
Concrete shrinkage	Concrete drying	5 to 10%
Concrete creep	Deformation under sustained load	10 to 20%
Steel relaxation	Decrease in stress at constant length	2 to 8%

These losses are generally estimated at 15 to 25% of the initial force for preliminary calculations.

Safety Rules and Regulations

Canadian Electrical Code, Part I

Post-tensioning work involves the use of electric hydraulic jacks. According to the Canadian Electrical Code, Part I, construction sites must comply with electrical contact protection rules. Rule 8-200 requires that all portable electrical equipment be supplied by a circuit protected by a ground fault circuit interrupter (GFCI) rated at 5 mA. Hydraulic jacks must be grounded in accordance with Rule 10-200.

CSA B149.1 (Natural Gas and Propane Code)

Although rarely directly applicable to post-tensioning, this standard may apply if gas heating systems are used to accelerate concrete curing in cold weather. Section 5.4 requires adequate ventilation in confined spaces.

Specific Safety Rules for Post-Tensioning

78.Danger zone: A safety perimeter of at least 3 meters must be established around the tensioning area. No one should stand behind the jack or in line with the strands.

79.Personal protective equipment: Hard hat, safety glasses, gloves, steel-toed boots. Loose clothing is prohibited.

80.Equipment verification: Jacks must be calibrated annually or after 500 cycles. Pressure gauges must be checked before each use.

81.Emergency procedure: In the event of a strand rupture, the force is released immediately. The jack must never be disassembled under pressure.

82.Work at height: Tensioning platforms must have guardrails compliant with provincial health and safety standards (which vary, but the basic principles are universal).

Practical Calculations for the Exam

Calculating the Prestressing Force

The initial prestressing force F₀ is generally specified as a percentage of the strand's ultimate tensile strength. For a 15.24 mm strand (area 140 mm², strength 1860 MPa):

F_ultimate = 140 mm² × 1860 MPa = 260,400 N = 260.4 kN

The tensioning force is typically 75 to 80% of the ultimate force:

F₀ = 0.78 × 260.4 kN = 203.1 kN

Calculating Hydraulic Pressure

The pressure P of the jack is related to the force by the piston area:

P = F / A_piston

Example: Jack with a 50 cm² piston, required force of 203 kN.

P = 203,000 N / 5,000 mm² = 40.6 MPa

Verifying Elongation

The measured elongation must be compared to the theoretical elongation. The tolerance is ± 7%.

Example: Theoretical elongation of 178.6 mm, measured elongation of 190 mm.

Difference = (190 - 178.6) / 178.6 × 100 = 6.4% → Acceptable (less than 7%)

If the difference is 8% or more, you must:

99.Check the jack's pressure gauge

100.Verify that the strand is not stuck

101.Increase the force (within the 80% of ultimate limit) or release and start over

Anchorages and Tensioning Equipment

Types of Anchorages

Type	Use	Capacity
Mono-strand anchorage	Building slabs, thin beams	1 strand
Multi-strand anchorage	Bridges, main beams	4 to 55 strands
Bar anchorage	Tie-backs, repairs	1 bar
Passive (dead) anchorage	Fixed end	Variable

Anchorages must be positioned perpendicular to the strand axis. An inclination of more than 2° can cause stress concentration and premature failure.

The Tensioning Jack

The jack is a hydraulic cylinder with a hollow center piston that allows strands to pass through. Important characteristics:

Stroke: maximum pulling distance (typically 200 to 300 mm)

Capacity: maximum force (typically 100 to 600 tons)

Calibration: the pressure-force relationship must be verified with a calibrated load cell

Quality Control and Inspection

Before Tensioning

113.Verify that the concrete has reached the specified minimum strength (cylinder test report)

114.Verify that the anchorages are clean and free of debris

115.Verify that the strands are free in the ducts (sliding test)

116.Verify the alignment of the jack with the anchorage

During Tensioning

118.Measure elongation at each load increment

119.Monitor hydraulic pressure (no sudden drops)

120.Listen for abnormal noises (excessive friction, wire breakage)

121.Verify that the anchorage is not deforming

After Tensioning

123.Mark the strands at the anchorage to detect any subsequent slip

124.Cut the excess strands (at 25-50 mm from the anchorage)

125.Grout the ducts within 14 days of tensioning

126.Protect exposed anchorages with concrete or an anti-corrosion product

Pitfalls to Avoid

128.Confusing pre-tensioning and post-tensioning: Pre-tensioning is done before concrete placement, post-tensioning after. This is a classic multiple-choice question.

129.Forgetting friction losses: In elongation calculations, you must use the average force along the strand, not the force at the jack, if the profile is curved.

130.Neglecting the ± 7% tolerance: A measured elongation 10% above the theoretical value indicates a problem, not simply imprecision.

131.Ignoring the minimum concrete strength: Tensioning before the concrete reaches the specified strength can cause localized crushing at the anchorage.

132.Confusing units: Calculations often use MPa (N/mm²) and kN. Always check unit consistency.

133.Forgetting anchorage seating: The wedge slip when the jack is released (3-6 mm) must be added to the measured elongation for comparison with theory.

134.Not knowing the friction coefficients: μ = 0.15-0.25 for metal duct, μ = 0.05-0.10 for greased plastic duct. These values are often given in questions.

135.Underestimating danger zones: The 3-meter zone around the jack is a fundamental safety rule. A strand that breaks releases enormous energy.

Summary

Post-tensioning consists of tensioning cables after concrete placement, creating compression that improves tensile strength.

The key components are: strands (1860 MPa steel), ducts (metal or plastic), and anchorages (active and passive).

The procedure includes: duct placement → concrete placement → waiting for strength → tensioning → grouting.

Theoretical elongation is calculated using ΔL = (F × L) / (E × A). The tolerance is ± 7% compared to the measurement.

Losses are immediate (friction, anchorage seating, elastic shortening) and time-dependent (shrinkage, creep, relaxation). They total 15 to 25%.

Safety requires a 3 m danger zone, calibrated jacks, and compliance with the Canadian Electrical Code (Rule 8-200 for GFCIs).

Quality control verifies concrete strength, strand freedom, elongation, and duct watertightness.

Sample Exam Questions

145.Question: A 15.24 mm strand (A = 140 mm²) is tensioned to 195 kN over a length of 30 m. E = 195,000 MPa. What is the theoretical elongation?

Answer: ΔL = (195,000 × 30,000) / (195,000 × 140) = 5,850,000,000 / 27,300,000 = 214.3 mm

147.Question: The ultimate strength of a strand is 260 kN. The tensioning force is 78% of this value. What is the force?

Answer: F = 0.78 × 260 = 202.8 kN

149.Question: A jack has a 40 cm² piston. What pressure is required for a force of 200 kN?

Answer: P = 200,000 N / 4,000 mm² = 50 MPa

151.Question: The theoretical elongation is 200 mm, the measured elongation is 215 mm. Is this acceptable?

Answer: Difference = (215 - 200) / 200 × 100 = 7.5% → No, exceeds the 7% tolerance. You must investigate.

153.Question: What is the main difference between an active and a passive anchorage?

Answer: The active anchorage receives the jack and allows tensioning; the passive anchorage is fixed and embedded in the concrete.

This chapter covers all the knowledge required for the Red Seal exam on post-tensioning. Master the formulas, tolerances, and safety procedures, and you will be well prepared for the exam questions.

Post-Tensioning and Prestressing Systems