Guidelines for Use of External and Unbonded Prestressing Tendons in Bridge Structures

IRC SP 67: Introduction - Key Points & Specifications

• Scope: Guidelines for design, materials, detailing, and protection of prestressing steel in bridges.

• Frequency of Cable Vibration: [ f = \frac{F}{2L \sqrt{m}} ] Where:

  • (f) = Frequency (cycles/sec)
  • (F) = Tension in cable (force units)
  • (L) = Length between supports (anchorages/deviators)
  • (m) = Vibrating mass per unit length (duct + grout)

• Minimum Radius of Curvature at Deviators (Table 1):

• Protection of Prestressing Steel:

  • Temporary: Water-soluble oils, grease.
  • Permanent: Cement grout, nuclear-grade grease, epoxy paint for external steel.
  • Regular inspection & maintenance recommended.

• Ultimate Moment of Resistance Assumptions:

  • Plane sections remain plane.
  • Concrete compression stress from design curve, reduced by factor (1.5).
  • Concrete tensile strength ignored.
  • Prestressing steel stress from stress-strain curve, reduced by factor (1.15).
  • Strain limits: Concrete max strain = 0.0035; unbonded tendons strain increase limited.

• References: IRC codes (IRC:6, IRC:18, IRC:24), BS 4447-1973, FIB 1993.

This summary covers the introductory essentials of IRC SP 67 relevant to prestressed concrete bridge design and detailing. For detailed design, consult respective chapters and specialist literature.

Scope of IRC SP 67: Prestressing in Bridges

• Covers design, materials, detailing, protection, and application of unbonded prestressing systems in bridges.
• Applies to external tendons housed in HDPE or steel sheaths, requiring leak-tight ducts per Clause 1.1.
• Includes provisions for deviators, anchorages, and accessories per IRC:24-2001 and IRC:21-2000.
• Addresses durability and protection of prestressing steel during construction and service (Clause 7).
• Refers to related IRC codes (IRC:6-2000, IRC:18-2000, IRC:21-2000) and standards like BS 4447-1973 and FIB guidelines.
• Design philosophy: Prestressing treated partly as load and partly as load-resisting mechanism; both Serviceability and Ultimate Limit States must be checked.

Key Table: Minimum Radius of Curvature at Deviators (Clause 6.3)

Key Formula: Frequency of Vibrations (Clause 1.2)

[ f = \frac{1}{2L} \sqrt{\frac{F}{m}} ]

• f = frequency (cycles/sec)
• L = length between supports (m)
• F = tension in cable (force units)
• m = vibrating mass per unit length (including duct and grout)

Summary Diagram: Prestressing System Components

graph LR
A[External Tendon] --> B[HDPE/Steel Sheath]
B --> C[Anchorages]
B --> D[Deviators]
C --> E[Bearings & Supports]
D --> F[Protection Coatings]

Note: Designers should consult specialist literature and latest editions of referenced standards for detailed design and testing requirements.

Unbonded Prestressing - Application (IRC SP 67)

Key Specifications:

• Sheathing for External Tendons:

  • Use HDPE or metallic steel sheaths with smooth internal surfaces.
  • Sheaths and joints must be fully leak-tight against pressure = 1.1 × (max gravity head + grouting pressure).
  • Materials must comply with relevant Indian/IRC standards.

• Deviators, Anchorage Brackets, Suspenders:

  • Made of R.C.C/P.S.C or steel embedded/fixed to structure.
  • Steel and welding materials per IRC:24-2001; reinforcing steel per IRC:21-2000.

• Anchorages & Guide Tubes:

  • Prefer replaceable/reusable anchorages.
  • Factory-made with strict QA/QC.
  • Must pass dynamic fatigue test: 2 million cycles (FIB/BS:4447-1973).
  • Independent lab certification required.

Design Approach:

• Prestressing treated as:
  • Part load: Permanent load varying between initial prestress and after losses (±20% losses).
  • Part strength: Contribution to section strength considered in ultimate design.
• Follow IRC:6-2000, IRC:18-2000, IRC:21-2000 for design.
• Check both ULS and SLS per Limit State Design philosophy.

Load Combinations:

• Use provisions from IRC:5-1998, IRC:18-2000, IRC:21-2000.

Summary Table for Sheath Pressure Resistance

flowchart TD
    A[External Tendon] --> B[Sheath (HDPE/Steel)]
    B --> C[Leak-tight Joints]
    C --> D[Anchorages (Replaceable)]
    D --> E[Deviators & Brackets (RCC/Steel)]
    E --> F[Prestressing Force]
    F --> G[Load + Strength Contribution]

For detailed design, refer to IRC:18-2000 and IRC:

IRC SP 67 - Materials Key Points

1. Sheathing Materials

• External tendons housed in HDPE or metallic steel sheaths.
• Sheaths must be smooth internally and leak-tight against water pressure =
  1.1 × (max gravity head of grout + grouting pressure).
• Materials conform to relevant Indian Standards / IRC Standards.

2. Prestressing Steel Protection

• Temporary: coated with water-soluble oils, grease.
• Permanent: protected by cement grout, nuclear-grade grease (low sulphur), or equivalent.
• External steel parts (deviators, brackets) protected by clear epoxy paint.
• Periodic inspection and maintenance mandatory.

3. Deviators & Anchorage Materials

• Made of RCC/PSC or steel.
• Steel fasteners, welding to conform to IRC:24-2001.
• RCC reinforcement per IRC:21-2000.
• Anchorages preferably replaceable/reusable.
• Must pass dynamic fatigue test: 2 million cycles (FIB/BS 4447-1973).
• Quality assurance and acceptance testing mandatory.

4. Curvature Radius for Tendons at Deviators (Table 1)

5. Ultimate Moment of Resistance Assumptions

• Concrete compression strain max: 0.0035.
• Concrete design strength: (2/3) × f_ck / 1.5.
• Steel strength reduction factor: γ_s = 1.15.
• Tensile strength of concrete ignored.
• Strain compatibility assumed (plane sections remain plane).

flowchart TD
    A[Materials] --> B[Sheathing: HDPE/Steel]
    A --> C[Prestressing Steel Protection]
    A --> D[De

Key Design Formulas, Tables, and Specifications from IRC SP 67

1. Frequency of Vibrating Tendon (Clause 1.2)

[ f = \frac{1}{2L} \sqrt{\frac{F}{m}} ]

• f = Frequency (cycles/sec)
• L = Length between supports (m)
• F = Tension in cable (force units)
• m = Vibrating mass per unit length (including duct & grout)

2. Minimum Radius of Curvature at Deviators (Clause 6.3)

Wire cables with equivalent ultimate strength may adopt these radii.

3. Ultimate Moment of Resistance (Appendix Summary)

• Concrete compressive strain limit: 0.0035
• Concrete design strength: ( \frac{2}{3} f_{cu} / \gamma_c ) where ( \gamma_c = 1.5 )
• Steel strength reduction factor: ( \gamma_s = 1.15 )
• Tensile strength of concrete ignored.
• Plane sections remain plane assumption.
• Unbonded tendon strains generally constant after losses, except as noted.

4. Shear Resistance (Clause 5.3.3)

• For full unbonded prestressing, treat section as reinforced concrete with axial load.
• Partial bonded prestress: check shear as prestressed member; unbonded prestress contributes only axial force.
• Partial load factor for prestressing load in shear: 0.9.
• Additional elongation of prestressing steel due to shear deformation neglected.

5. Design of Anchorages/Deviators (Clause 5.3.4)

• Anchorages and deviators designed for full nominal ultimate tendon capacity.
• Local zones around anchorages must have adequate spalling and bursting reinforcement.

Key Detailing Specifications from IRC SP 67 for Prestressed Concrete:

1. Curvature at Deviators (Clause 6.3)

Minimum radius of curvature for tendons at deviators (to avoid damage):

Applies also to wire cables with equivalent ultimate strength.

2. Protection of Prestressing Steel (Clause 7)

• Temporary protection: water-soluble oils, grease.
• Permanent protection: cement grout, nuclear-grade grease (low sulfur), or epoxy paint for exposed steel.
• Regular inspection and maintenance mandatory.

3. Alignment and Anchorage (Clauses 4.4, 6.1)

• External tendons housed in HDPE or metallic sheaths, fully leak-tight.
• Anchorages should be replaceable/reusable.
• Anchorages, deviators, brackets designed for full ultimate tendon capacity.
• Straight cable segments ≤ 12 × beam depth or 12 m.
• Deviators must project outward to ensure tendon tension keeps cable pressed.

4. Ultimate Strength & Section Analysis (Clause A-1)

• Concrete compressive strain max: 0.0035.
• Concrete design strength = (2/3) × f_ck / γ_c (γ_c=1.5).
• Steel strength reduction γ_s = 1.15.
• Tensile strength of concrete ignored.
• Prestressing steel strain limits: AEP + Epo < Epu (ultimate strain).
• Local zones around anchorages must be reinforced to resist bursting/spalling.

5. Frequency of Cable Vibration (Clause 1.2)

[ f = \frac{1}{2L} \sqrt{\frac{F}{m}} ]

• (f): frequency (cycles/sec)
• (L): length between supports (m)
• (F): tension in cable (force units)
• (m): vibrating mass per unit length (including duct

Protection of Prestressing Steel / Anchorages / Deviators (IRC SP 67)

1. Protection Measures:

• Temporary exposure: Coat prestressing steel with water-soluble oils, grease, or suitable protective agents.
• Permanent protection: Use cement grout, nuclear-grade grease (low sulfur), or equivalent.
• External steel parts (deviators, brackets): Protect with clear epoxy paint.
• Regular inspection and maintenance are mandatory.

2. Curvature at Deviators (Table 1):

• Applies also to wire cables with equivalent ultimate strength.

3. Sheathing Requirements:

• External tendons housed in HDPE or metallic sheaths with smooth internal surfaces.
• Sheaths and joints must be leak-tight against 1.1 × (max gravity head + grouting pressure).
• Materials must conform to relevant Indian/IRC standards.

4. Design & Load Considerations:

• Anchorages and deviators designed for full ultimate tendon capacity.
• Local concrete zones reinforced to resist bursting/spalling (manufacturer's recommendations).
• Deviators and anchorages must comply with IRC:18, IRC:21, IRC:24.
• Anchorages preferably replaceable/reusable.
• Dynamic testing of cable/anchorage assemblies for 2 million cycles per FIB/BS 4447.

Key Formula: Frequency of Vibrations (Clause 1.2)

[ f = \frac{1}{2L} \sqrt{\frac{F}{m}} ]

Where:

• ( f ) = frequency (cycles/sec)
• ( L ) = length between supports (anchorages/deviators)
• ( F ) = tension force in cable
• ( m ) = vibrating mass per unit length (duct + grout)

Summary Diagram of Tendon Protection & Deviator Arrangement

graph LR
A[Prestressing

Key Formulas and Specifications for "Other Structures" (IRC SP 67)

1. Frequency of Vibrations of Cable (Clause 1.2)

[ f = \frac{1}{2L} \sqrt{\frac{F}{m}} ]

• f = Frequency (cycles/sec)
• L = Length between supports (m)
• F = Tension force in cable (N)
• m = Vibrating mass per unit length (kg/m), includes duct and grout

2. Minimum Radius of Curvature at Deviators (Clause 6.3)

• Applies also to wire cables with equivalent ultimate strength.

3. Protection of Prestressing Steel (Clause 7)

• Temporary: water-soluble oils, grease.
• Permanent: cement grout, nuclear-grade grease (low sulfur), or epoxy paint for external steel parts.
• Regular inspection and maintenance recommended.

4. Ultimate Moment of Resistance (Summary from Appendix A-1(1))

• Concrete compressive strain at extreme fiber: 0.0035
• Concrete design strength: ( \frac{2}{3} f_{cu} ) divided by safety factor ( \gamma_c = 1.5 )
• Steel strength reduction factor: ( \gamma_s = 1.15 )
• Tensile strength of concrete ignored.
• Strain compatibility assumed (plane sections remain plane).
• Tendon strain assumptions differ for bonded and unbonded tendons.

References for Further Details (Clause 9.1)

• IRC:6-2000, IRC:18-2000, IRC:24-2001
• BS 4447-1973 (Prestressing Anchorages)
• FIB Recommendations 1993

flowchart LR
    A[Prestressing

Key Formulas and Tables from IRC SP 67

1. Frequency of Vibrations (Clause 1.2)

[ f = \frac{1}{2L} \sqrt{\frac{F}{m}} ]

• f = Frequency in cycles/sec
• L = Length between supports (anchorages or deviators)
• F = Tension in cable (force units)
• m = Vibrating mass per unit length (including duct and grout)

2. Minimum Radius of Curvature at Deviators (Clause 6.3)

• Applies also to wire cables with equivalent ultimate strength.

3. Protection of Prestressing Steel (Clause 7)

• Temporary protection: water-soluble oils, grease, or suitable coatings.
• Permanent protection: cement grout, nuclear-grade grease (low sulfur), or other suitable means.
• External steel parts: clear epoxy paint.
• Regular inspection and maintenance recommended.

4. Ultimate Moment of Resistance (Appendix A-1(1))

• Concrete compression strain: max 0.0035
• Concrete strength reduced to (2/3 × f_ck) / 1.5
• Steel strength reduction factor: γ_s = 1.15
• Tensile strength of concrete ignored.
• Plane sections remain plane assumption.
• Tendons near supports (within h/2) ignored for strength calculations.

5. References (Clause 9.1)

• IRC:6-2000, IRC:18-2000, IRC:21-2000, IRC:24-2001
• BS 4447-1973 (Prestressing Anchorages)
• FIB Recommendation 1993 (Post-Tensioned Systems)

Summary Diagram of Tendon Layout

Ultimate Moment of Resistance Calculation (IRC SP 67 & IRC 18-2000)

Key Assumptions (Clause A-1(1))

• Plane sections remain plane.
• Concrete compression stress from curve with design strength = (2/3)f_ck / γ_c (γ_c = 1.5).
• Max concrete compressive strain = 0.0035.
• Concrete tensile strength ignored.
• Strains in bonded prestressing tendons and reinforcement from plane section assumption + initial prestress strain.
• Steel stresses from stress-strain curve with γ_s = 1.15.
• Unbonded tendon strain assumed constant after losses, except:
  • In slabs/beams near soffit, strain may increase by 0.0005.
  • Or nonlinear analysis may be used.
• Tendons anchored within h/2 ignored for section analysis.

Ultimate Moment Resistance Principles (Clause 5.3)

• Prestressing tendon contribution = additional strength beyond prestress.
• Stress-strain origin shifted by prestress effect (see Fig.1 & Fig.2 in code).
• For unbonded tendons, use rules consistent with above principles (refer Appendix in IRC 18-2000).
• Shear resistance checks as per prestressed or reinforced concrete sections with axial load.

Material Strength Reduction Factors

Stress-Strain Parameters

• Concrete max compressive strain: 0.0035
• Prestressing steel ultimate strain: E_pu
• Prestressing steel pre-elongation: E_po
• Condition: ( E_{pu} > E_{po} + \text{strain due to bending} )

Load Factors for Ultimate Load (Clause 5.1)

• Prestress load factor = 1.0 (IRC 18-2000)
• For indeterminate structures:
  • Unfavorable load factor = 1.2
  • Favorable load factor = 0.9

Simplified Section Analysis Procedure

1. Assume strain profile (linear) across section depth.
2. Calculate concrete compressive force using design stress block.
3. Calculate steel and prestressing tendon stresses from strain and stress-strain curves.
4. Sum internal