Prestressed Concrete - Concept Map
Prestressed Concrete: Introducing Beneficial Internal Compression to Control Cracking, Deflection, and Enable Long Spans
Related concepts
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
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
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
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
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
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
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
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
Concept connections
- Pre-tensioningBond TransferPre-tensioning transfers prestress via mechanical bond between strand and concrete after release
- Post-tensioningEnd AnchoragePost-tensioning relies on mechanical anchorages at strand ends to transfer tension
- Service Stress AnalysisPrestress LossesEffective prestress Pe (after losses) is used in service stress calculation; initial Pi used at transfer
- Service Stress AnalysisMaterial LimitsCalculated fiber stresses must stay within allowable limits per NSCP 2015 and ACI 318
- Load BalancingParabolic Tendon ProfileParabolic sag creates distributed upward force that exactly cancels balanced gravity load
- Load BalancingService Stress AnalysisUnder balanced load, bending stress reduces to near zero; only axial precompression remains
- Prestress LossesImmediate LossesImmediate losses (elastic, anchorage, friction) occur during/shortly after tensioning; largest single loss component
- Prestress LossesTime-dependent LossesCreep, shrinkage, and relaxation accumulate over years; collectively rival immediate losses
- Prestress LossesEffectiveness RatioR = Pe / Pi summarizes overall loss magnitude; typically 0.75–0.85 for design calculations
- Prestressing MethodsApplicationsPre-tensioning suited for high-volume precast; post-tensioning for on-site flexibility and long spans
- ApplicationsRegulatory FrameworkDesign methods and safety factors vary by application type; NSCP 2015 and ACI 318 provide guidelines
- Material LimitsFailure ModesOver-compression and under-prestressing both lead to failure; allowable limits prevent these extremes
- Failure ModesDurabilityCorrosion, fatigue, and stress concentrations are time-dependent failure mechanisms; durability design mitigates risk
- Transfer StageService StageTransfer stage checks initial stress at Pi; service stage checks final stress at Pe under full load
- Axial PrestressEccentric MomentEccentric placement of prestress below centroid creates beneficial moment counteracting applied loads
- Duct FrictionPost-tensioningFriction loss occurs only in post-tensioned ducts; not applicable to pre-tensioned bond transfer
- Cracking ControlService Stress AnalysisPrestressing keeps top fiber in compression or low tension under service load; limits crack width
- Deflection ControlLoad BalancingBalanced load produces minimal net bending; dramatically reduces deflection compared to ordinary RC
- NSCP 2015Service Stress AnalysisNSCP 2015 Section 5 specifies allowable stress limits and design stress equations for prestressed concrete
- ACI 318Prestress Loss CalculationACI 318 Chapter 27 provides standardized loss models for elastic, friction, creep, shrinkage, and relaxation
- Concrete Compressive StrengthTransfer StageAt transfer, concrete compressive strength is lower (f'ci < f'c); affects allowable stress limits
- Strand RelaxationTime-dependent LossesSteel strand loses load over time due to molecular migration; typically 2–5% additional loss
- Concrete CreepLong-term DeflectionCreep increases member deflection over time; affects serviceability even under balanced load
- Concrete ShrinkagePrestress LossDifferential shrinkage causes additional stress redistribution; contributes 5–10% of total loss
- Anchorage SeatingImmediate LossStrand slip during anchorage lock-in causes stress redistribution and local loss at ends
- Elastic ShorteningPrestressing MethodsElastic shortening is highest immediately after strand release; affects pre-tensioned members most
Diagrams
Prestressed Concrete: Complete Concept Hierarchy
Comprehensive mind map showing the hierarchical structure of prestressed concrete concepts. The root branch covers all major topic areas: prestressing methods (pre vs. post), service stress analysis, prestress losses, load balancing, material limits, applications, regulatory framework, and failure modes. Each branch expands to show sub-concepts relevant to PRC licensure exam preparation.
Service Stress Calculation Procedure
Step-by-step flowchart for calculating service stresses in a prestressed concrete section. Shows the sequence from geometry definition, through axial and eccentric moment components, to applied load effects, and final verification against allowable limits. Includes decision points for design adequacy and iterative adjustment.
Prestress Loss Evaluation & Effective Stress Determination
Detailed flowchart showing the complete procedure for evaluating prestress losses from jacking stage to long-term effective prestress. Distinguishes between pre- and post-tensioning immediate loss sources, then incorporates time-dependent losses (creep, shrinkage, relaxation) per NSCP 2015 / ACI 318. Leads to effective prestress Pe and the critical effectiveness ratio R.
Load Balancing Design Method
Flowchart illustrating the load balancing design philosophy for prestressed concrete members. Shows how to select or calculate tendon sag e to balance a chosen portion of the gravity load, resulting in a member that carries that load primarily as axial precompression with zero or minimal bending. Includes checks for eccentricity limits and verification of concrete stresses per NSCP 2015.
Prestress State Transitions: From Jacking to Long-Term Service
State diagram showing the progression of a prestressed concrete member from jacking through long-term service. Illustrates how stress state, loss mechanisms, and verification requirements change at each stage. Shows critical transition points (transfer, immediate loss, time-dependent loss, final service) and the decision gates at each stage. Helps reviewees understand why different design checks apply at different stages.
Transfer vs. Service Stage Design Check Comparison
Side-by-side flowchart comparison of transfer and service stage design requirements. Shows why different stresses govern each stage: at transfer, the top fiber is vulnerable to cracking and the bottom to over-compression due to high Pi; at service, the controlling factors shift after losses reduce to Pe and the external load moment increases. Highlights the different design checks, allowable limits, and remedial strategies for each stage per NSCP 2015.