CELE Reinforced & Prestressed Concrete — Prestressed ConcreteConcept Map

Concept

Prestressing Methods

Sub Concepts

• Pre-tensioning: Strands tensioned against external abutments before casting; transfer by bond after curing
• Post-tensioning: Strands tensioned after curing via end anchorage; housed in ducts; allows staged loading
• Partial Prestressing: Combination of prestressed and conventional reinforcement for economy

Relationship To Central

Core technique categories that define how prestress is introduced and transferred to concrete

Concept

Service Stress Analysis

Sub Concepts

• Axial prestress component: P/A (uniform compression across section)
• Bending stress from eccentric prestress: ±Pec/I (moment arm effect)
• Applied-load bending stress: ∓Mc/I (external moment effects)
• Superposition of stresses: Combined effect determines fiber stress state
• Transfer stage (P_i): Highest initial stress; often controls top fiber tension
• Service stage (P_e): Effective prestress after losses; controls member behavior under full load

Relationship To Central

Mathematical framework for verifying that stresses remain within safe limits throughout the member's life

Concept

Prestress Losses

Sub Concepts

• Immediate losses (occur during/shortly after tensioning): Elastic shortening, anchorage seating, duct friction
• Time-dependent losses (hours to years): Concrete creep, concrete shrinkage, steel relaxation
• Total loss quantification: Typically 15–25% for post-tensioned; 18–25% for pre-tensioned
• Loss prediction models: ACI 318, NSCP 2015 equations for elastic modulus method
• Effectiveness ratio R = P_e / P_i: Used in design to distinguish between initial and long-term behavior

Relationship To Central

Mechanisms that reduce prestress force from jacking to effective value; critical for design and durability

Concept

Load Balancing Concept

Sub Concepts

• Parabolic tendon profile: Sag e over span L creates distributed upward force
• Balanced load equation: w_bal = 8Pe/L²
• Zero-bending zone: Under balanced load, member carries only axial precompression
• Practical application: Design beam to balance dead load + partial live load; remainder resisted by bending
• Deflection control: Balanced member has minimal initial deflection; highly efficient

Relationship To Central

Innovative design method that cancels gravity loads with draped tendon uplift, minimizing bending

Concept

Material Behavior & Design Limits

Sub Concepts

• Concrete compressive stress limits: At transfer and in service (prevent crushing, excessive creep)
• Concrete tensile stress limits: Cracking control; often zero under service in full prestress design
• Steel yield and rupture limits: Jacking stress, allowable service stress (prevent relaxation, over-stress)
• Initial strand stress at jacking: Typically 0.75–0.80 of ultimate tensile strength (fpu)
• Allowable service stress in strand: Typically 0.55–0.60 of fpu after losses

Relationship To Central

Allowable stresses and material properties that govern safe design per NSCP 2015 and ACI 318

Concept

Applications & Member Types

Sub Concepts

• Pre-tensioned members: Precast piles, hollow-core slabs, I-girders (factory control, high volume)
• Post-tensioned members: Bridge decks, transfer beams, long-span slabs (on-site flexibility, large spans)
• Segmental construction: Precast box girders with post-tensioning (long bridges, architectural freedom)
• Industrial tanks and vessels: Circumferential prestressing for internal pressure resistance
• Flat slabs and waffle decks: Post-tensioning for two-way spanning and architectural aesthetics

Relationship To Central

Real-world use cases where prestressing provides technical and economic advantage over ordinary RC

Concept

Regulatory & Normative Framework

Sub Concepts

• NSCP 2015 (National Structural Code of the Philippines): Prestressed concrete design section, load factors, limit states
• ACI 318-14/19: American concrete code; widely referenced for prestress design methodology
• PCI Design Handbook: Practical design tables and formulas for common prestressed sections
• RA 544 (Building Code of the Philippines): Overall structural safety and occupancy requirements
• PTI (Post-Tensioning Institute) guidelines: Industry best practice for post-tensioning systems

Relationship To Central

Philippine and international codes that establish minimum requirements, design methods, and safety factors

Concept

Failure Modes & Durability

Sub Concepts

• Over-prestressing: Excessive compression causing member brittleness, spalling, loss of ductility
• Insufficient prestressing: Uncontrolled cracking, excessive deflection, water infiltration
• Strand corrosion (post-tensioning): Broken ducts, inadequate grouting; leads to sudden loss of prestress
• Stress concentrations: At anchorages, deviators, and bearing points; local crushing/spalling
• Fatigue under cyclic loading: Repeated stress variation may initiate strand fracture over time
• Detensioning shock: Sudden strand fracture (rare); dramatic load redistribution

Relationship To Central

Mechanisms by which prestressed members can fail or deteriorate; inform design decisions and maintenance

To

Bond Transfer

From

Pre-tensioning

Strength

strong

Relationship

Pre-tensioning transfers prestress via mechanical bond between strand and concrete after release

To

End Anchorage

From

Post-tensioning

Strength

strong

Relationship

Post-tensioning relies on mechanical anchorages at strand ends to transfer tension

To

Prestress Losses

From

Service Stress Analysis

Strength

strong

Relationship

Effective prestress Pe (after losses) is used in service stress calculation; initial Pi used at transfer

To

Material Limits

From

Service Stress Analysis

Strength

strong

Relationship

Calculated fiber stresses must stay within allowable limits per NSCP 2015 and ACI 318

To

Parabolic Tendon Profile

From

Load Balancing

Strength

strong

Relationship

Parabolic sag creates distributed upward force that exactly cancels balanced gravity load

To

Service Stress Analysis

From

Load Balancing

Strength

strong

Relationship

Under balanced load, bending stress reduces to near zero; only axial precompression remains

To

Immediate Losses

From

Prestress Losses

Strength

strong

Relationship

Immediate losses (elastic, anchorage, friction) occur during/shortly after tensioning; largest single loss component

To

Time-dependent Losses

From

Prestress Losses

Strength

strong

Relationship

Creep, shrinkage, and relaxation accumulate over years; collectively rival immediate losses

To

Effectiveness Ratio

From

Prestress Losses

Strength

moderate

Relationship

R = Pe / Pi summarizes overall loss magnitude; typically 0.75–0.85 for design calculations

To

Applications

From

Prestressing Methods

Strength

strong

Relationship

Pre-tensioning suited for high-volume precast; post-tensioning for on-site flexibility and long spans

To

Regulatory Framework

From

Applications

Strength

moderate

Relationship

Design methods and safety factors vary by application type; NSCP 2015 and ACI 318 provide guidelines

To

Failure Modes

From

Material Limits

Strength

strong

Relationship

Over-compression and under-prestressing both lead to failure; allowable limits prevent these extremes

To

Durability

From

Failure Modes

Strength

moderate

Relationship

Corrosion, fatigue, and stress concentrations are time-dependent failure mechanisms; durability design mitigates risk

To

Service Stage

From

Transfer Stage

Strength

strong

Relationship

Transfer stage checks initial stress at Pi; service stage checks final stress at Pe under full load

To

Eccentric Moment

From

Axial Prestress

Strength

strong

Relationship

Eccentric placement of prestress below centroid creates beneficial moment counteracting applied loads

To

Post-tensioning

From

Duct Friction

Strength

strong

Relationship

Friction loss occurs only in post-tensioned ducts; not applicable to pre-tensioned bond transfer

To

Service Stress Analysis

From

Cracking Control

Strength

strong

Relationship

Prestressing keeps top fiber in compression or low tension under service load; limits crack width

To

Load Balancing

From

Deflection Control

Strength

strong

Relationship

Balanced load produces minimal net bending; dramatically reduces deflection compared to ordinary RC

To

Service Stress Analysis

From

NSCP 2015

Strength

strong

Relationship

NSCP 2015 Section 5 specifies allowable stress limits and design stress equations for prestressed concrete

To

Prestress Loss Calculation

From

ACI 318

Strength

strong

Relationship

ACI 318 Chapter 27 provides standardized loss models for elastic, friction, creep, shrinkage, and relaxation

To

Transfer Stage

From

Concrete Compressive Strength

Strength

moderate

Relationship

At transfer, concrete compressive strength is lower (f'ci < f'c); affects allowable stress limits

To

Time-dependent Losses

From

Strand Relaxation

Strength

moderate

Relationship

Steel strand loses load over time due to molecular migration; typically 2–5% additional loss

To

Long-term Deflection

From

Concrete Creep

Strength

moderate

Relationship

Creep increases member deflection over time; affects serviceability even under balanced load

To

Prestress Loss

From

Concrete Shrinkage

Strength

moderate

Relationship

Differential shrinkage causes additional stress redistribution; contributes 5–10% of total loss

To

Immediate Loss

From

Anchorage Seating

Strength

moderate

Relationship

Strand slip during anchorage lock-in causes stress redistribution and local loss at ends

To

Prestressing Methods

From

Elastic Shortening

Strength

moderate

Relationship

Elastic shortening is highest immediately after strand release; affects pre-tensioned members most