CELE Reinforced & Prestressed Concrete — Prestressed ConcreteMemory Anchors
Memory anchors for Prestressed Concrete — mnemonic devices, acronyms, and tricks that make the CELE Reinforced & Prestressed Concrete syllabus stick. Use these when a concept just will not stay in your head.
Exam context
For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Reinforced & Prestressed Concrete under a "Core" label, with Prestressed Concrete in the 7th slot across 7 chapters. CELE candidates must clear the 70% weighted average, no sub-test below 50% cut on the 2026 paper, which draws about a meaningful share of Reinforced & Prestressed Concrete questions. Date to watch: May and November 2026.
Prestressed Concrete - Memory Anchors
Memory techniques transform abstract engineering formulas into vivid mental images that survive exam pressure. Research shows that mnemonic anchors improve recall by up to 300% compared to passive re-reading. For the PRC Civil Engineer board exam, where you must recall formulas, sign conventions, and design checks under time pressure, having a 'mental hook' for every concept is the difference between a confident answer and a blank mind. This set of 18+ anchors uses mnemonics, analogies, micro-stories, visual maps, and rhymes — each tied to a specific exam-critical concept in Prestressed Concrete.
Anchors
Tags
- definition
- concept
- analogy
Topic
Overview of Prestressing
Concept
What prestressing does — keeps concrete in compression
Anchor Id
A1
Difficulty
easy
Memory Aid
Imagine squeezing a stack of books tightly together horizontally with your hands. Even if you tip the stack slightly, the books stay together because the squeeze holds them. Prestressing is exactly that squeeze — applied to concrete BEFORE the load arrives, so the concrete stays 'hugged' together and never cracks apart.
Anchor Type
analogy
Why It Works
The book-squeezing image is physical and tactile. You can literally feel what compression does. The analogy maps directly: hands = tendons, books = concrete, tipping = applied moment.
Example Usage
Q: Why is prestressed concrete better at controlling cracks? A: Just like squeezed books stay together even when tilted, the precompression keeps concrete in compression so tension cracks never form.
Recall Trigger
Squeeze a stack of books
Tags
- classification
- definition
- mnemonic
Topic
Pre-tensioning vs Post-tensioning
Concept
Pre-tensioning vs Post-tensioning — the key difference
Anchor Id
A2
Difficulty
easy
Memory Aid
Use the word order as your guide: PRE = before, POST = after. Think of it as a PARTY: PRE-tensioning is like preparing the decorations BEFORE the guests (concrete) arrive — you stretch the strands BEFORE casting. POST-tensioning is like rearranging furniture AFTER the party — you tension the strands AFTER the concrete has hardened. Also remember: PRE = Plant (factory-made); POST = Place (cast-in-place on site).
Anchor Type
mnemonic
Why It Works
The party analogy ties a familiar social event to a technical sequence. The alliteration (PRE=Plant, POST=Place) creates a paired memory cue that fires both associations simultaneously.
Example Usage
Q: Which method is used for precast hollow-core slabs? A: PRE-tensioning — because Pre = Plant-produced, strands tensioned before casting.
Recall Trigger
PARTY: decorations before vs rearranging after
Tags
- process
- classification
Topic
Pre-tensioning vs Post-tensioning
Concept
Pre-tensioning transfers force by BOND; post-tensioning by END ANCHORAGE
Anchor Id
A3
Difficulty
medium
Memory Aid
Picture a tug-of-war rope buried in clay (pre-tensioning): the rope grips along its entire length by BOND — no end anchor needed. Now picture a guitar string (post-tensioning): tighten it at the tuning peg at the END — that's ANCHORAGE. The guitar peg = the anchor plate at the end of a post-tensioned beam.
Anchor Type
visual_association
Why It Works
The tug-of-war rope and guitar string are completely different visual objects, making the two transfer mechanisms easy to distinguish and hard to confuse.
Example Usage
Q: How does a pre-tensioned pile transfer prestress? A: By BOND between strand and concrete — like a rope gripping clay along its length.
Recall Trigger
Rope in clay (bond) vs guitar string tuning peg (anchorage)
Tags
- formula
- sign convention
- process
Topic
Service Stresses
Concept
Service stress formula — correct sign convention
Anchor Id
A4
Difficulty
hard
Memory Aid
Use the acronym PAPA-PM: P over A, Plus Pec/I at bottom, Minus Mc/I at bottom (sagging moment). At the TOP it reverses: P/A MINUS Pec/I (eccentric prestress relieves top) PLUS Mc/I (sagging loads stress top). Chant: 'At the BOTTOM, prestress is your BEST FRIEND — it ADDS compression. At the TOP, prestress TAKES AWAY compression (relieves it).'
Anchor Type
mnemonic
Why It Works
The phrase 'prestress is your best friend at the bottom' creates an emotional hook. Sign errors are the #1 board exam trap in prestressed concrete, so a memorable mantra prevents mistakes.
Example Usage
Q: Compute f_bottom. A: f_bot = P/A + Pec/I - Mc/I — prestress terms ADD at bottom, moment term SUBTRACTS (sagging relieves bottom compression).
Recall Trigger
BOTTOM = prestress BEST FRIEND (adds compression)
Tags
- concept
- sign convention
Topic
Service Stresses
Concept
Eccentric prestress effect — below-centroid tendon adds compression at bottom
Anchor Id
A5
Difficulty
medium
Memory Aid
Imagine a weightlifter (the tendon) standing BELOW the center of a see-saw (the beam cross-section). He pushes UP at the bottom. The bottom goes INTO the ground (compression). The top lifts UP (decompression/tension). Now the applied load (a heavy crate placed on top) pushes the top DOWN — that's the +Mc/I term fighting back. The weightlifter below and the crate above are always in a tug-of-war over the fiber stresses.
Anchor Type
micro_story
Why It Works
The see-saw and weightlifter create a spatial, physical story that makes the direction of each stress component intuitive rather than formula-dependent.
Example Usage
Q: A tendon is 150 mm below centroid. Does it add or remove compression at the bottom fiber? A: ADDS — the weightlifter (tendon below) pushes the bottom INTO compression.
Recall Trigger
Weightlifter below the see-saw center
Tags
- sequence
- definition
- acronym
Topic
Prestress Losses
Concept
Prestress losses — categories
Anchor Id
A6
Difficulty
medium
Memory Aid
Remember FEARS-C for ALL six prestress losses: F = Friction (duct friction, post-tensioning only), E = Elastic shortening of concrete, A = Anchorage seating (slip), R = Relaxation of steel, S = Shrinkage of concrete, C = Creep of concrete. Group them: IMMEDIATE = F, E, A (happen right away). TIME-DEPENDENT = R, S, C (happen slowly over months/years). The 'F-E-A-R' of losing prestress is IMMEDIATE; then 'S-C-R-eep and Shrinkage' come later.
Anchor Type
acronym
Why It Works
FEARS-C is a near-word that evokes the concept of 'fearing' prestress loss. The immediate vs time-dependent grouping adds a second layer of structure to the memory.
Example Usage
Q: List all sources of prestress loss. A: FEARS-C — Friction, Elastic shortening, Anchorage seating, Relaxation, Shrinkage, Creep. Immediate: F, E, A. Long-term: R, S, C.
Recall Trigger
FEARS-C — the six losses
Tags
- fact
- classification
- rhyme
Topic
Prestress Losses
Concept
Typical total prestress loss percentages
Anchor Id
A7
Difficulty
easy
Memory Aid
Sing to the tune of counting: 'POST loses FIFTEEN to TWENTY percent — anchors gripped tight, so less force is spent. PRE loses EIGHTEEN to TWENTY-FIVE — elastic shortening hits when strands come alive!' Remember: Post-tensioned = LESS loss (15–20%) because elastic shortening can be compensated; Pre-tensioned = MORE loss (18–25%) because elastic shortening hits all strands simultaneously.
Anchor Type
rhyme
Why It Works
Rhyme and melody exploit auditory memory pathways. The reasoning (why post has less loss) is embedded in the rhyme, so the number sticks with its justification.
Example Usage
Q: Estimate effective prestress if Pi = 1000 kN for a post-tensioned beam. A: Losses ≈ 15–20%, so Pe ≈ 800–850 kN.
Recall Trigger
Sing the counting rhyme — 'POST loses fifteen to twenty'
Tags
- concept
- analogy
- formula
Topic
Load Balancing
Concept
Load-balancing concept — parabolic tendon exerts upward load
Anchor Id
A8
Difficulty
medium
Memory Aid
Think of a bow and arrow held upside down under the beam. The tendon is the bowstring pulled tight (prestress force P). The bow's arch (parabolic sag e) pushes the arrow (the beam) UPWARD against gravity. When the upward push exactly equals the beam's self-weight, the beam 'floats' — no bending, just uniform compression. You chose P and e like choosing how hard to pull a bowstring.
Anchor Type
analogy
Why It Works
The bow-and-arrow image is universally familiar and physically correct: a curved tensioned string does push outward perpendicularly — exactly what a parabolic tendon does to the concrete.
Example Usage
Q: Explain load balancing. A: The parabolic tendon acts like an upside-down bow — it pushes the beam up with w_bal = 8Pe/L², canceling gravity loads.
Recall Trigger
Upside-down bow and arrow under the beam
Tags
- formula
- chunking
Topic
Load Balancing
Concept
Load-balancing formula: w_bal = 8Pe/L²
Anchor Id
A9
Difficulty
medium
Memory Aid
Chunk it as EIGHT-PEL-squared: '8 times P times e, divided by L squared.' Say it fast: EIGHT-PEL-squared. The '8' comes from the geometry of a parabola (the catenary factor). Think: 8 = 2³ = the 'doubling' from both sides of the parabola contributing. P = pull, e = eccentricity (sag), L = span. Units check: kN × m / m² = kN/m ✓
Anchor Type
chunking
Why It Works
Chunking compresses a formula into a 3-syllable verbal pattern (EIGHT-PEL-squared) that can be retrieved as a single memory unit rather than four separate variables.
Example Usage
Q: Find w_bal for P = 900 kN, e = 0.15 m, L = 10 m. A: w_bal = 8(900)(0.15)/10² = 1080/100 = 10.8 kN/m.
Recall Trigger
EIGHT-PEL-squared
Tags
- concept
- formula
- visual
Topic
Load Balancing
Concept
Under balanced load — beam has ONLY uniform axial precompression (P/A)
Anchor Id
A10
Difficulty
medium
Memory Aid
Picture a perfectly balanced Libra scale (load balancing!). When the scale is perfectly level, there is NO tilting moment — just the weight of the scale itself pressing down evenly on the table (P/A). The balanced state = no bending = pure P/A. The scale tips only when extra weight is added beyond balance — that's the 'unbalanced' moment that bending theory must carry.
Anchor Type
visual_association
Why It Works
The Libra scale is a perfect visual metaphor for 'balance' and directly maps equilibrium to the zero-bending condition. The board exam often asks what stress exists at the balanced load — the answer is simply P/A.
Example Usage
Q: At the balanced load, what is the stress at midspan top fiber? A: f = P/A (uniform axial compression only — no bending moment term since load is balanced).
Recall Trigger
Libra scale perfectly balanced — only P/A remains
Tags
- process
- design check
- sequence
Topic
Service Stresses — Design Checks
Concept
Check BOTH transfer and service conditions
Anchor Id
A11
Difficulty
hard
Memory Aid
Two detectives must BOTH clear a suspect: Detective TRANSFER (using Pi, the initial prestress, with minimal live load) and Detective SERVICE (using Pe, the effective prestress, with full load). The suspect is your beam design. If either detective finds a violation (overstress in tension or compression), your design is arrested. Pre-tensioning's transfer stage is especially dangerous for the TOP fiber — it gets tension because the big Pi acts before the load arrives.
Anchor Type
micro_story
Why It Works
The detective narrative creates a procedural memory: you MUST question both detectives (both stages) before declaring the design safe. This prevents the common exam error of checking only one condition.
Example Usage
Q: Which prestress force is used for transfer stage? A: Pi (initial, before losses) — Detective Transfer checks with Pi and minimal load.
Recall Trigger
Two detectives — Transfer and Service — both must approve
Tags
- design check
- sign convention
- process
Topic
Transfer vs Service Design
Concept
Critical fiber flips between transfer and service
Anchor Id
A12
Difficulty
hard
Memory Aid
Visualize a seesaw with a big fat 'Pi' sitting on one end (transfer stage — big prestress, no live load). The seesaw tilts so the TOP goes down (into tension). At service, the live load 'M' sits on top of the beam, pressing the TOP down into compression. The seesaw tilts the other way. The CRITICAL FIBER switches! Transfer: watch the TOP for tension. Service: watch the BOTTOM for tension (if prestress is too small).
Anchor Type
visual_association
Why It Works
The seesaw tilting in opposite directions creates a reversible spatial image that captures why the critical fiber location changes between stages — a concept that confuses many students.
Example Usage
Q: Which fiber is critical at transfer? A: TOP fiber — large Pi with no counterbalancing live load creates tension at the top (eccentric prestress pulls top upward).
Recall Trigger
Seesaw tilting left then right — critical fiber switches sides
Tags
- formula
- definition
- analogy
Topic
Prestress Losses
Concept
Effectiveness ratio R = Pe/Pi ≈ 0.80–0.85
Anchor Id
A13
Difficulty
easy
Memory Aid
R = 'Retained' force fraction. Think of R as your salary after tax deductions (losses). If you earn Pi = ₱1,200,000 (jacking force) but the government (losses) takes 15–20%, you take home Pe = ₱1,000,000 (effective prestress). The RETENTION RATE is R = 0.80–0.85. Always use your take-home pay (Pe) when the beam is in service — not your gross salary (Pi)!
Anchor Type
mnemonic
Why It Works
The salary/tax analogy resonates deeply with Filipino reviewees who are highly aware of income tax deductions. The emotional relevance makes the retention ratio memorable.
Example Usage
Q: Pi = 1200 kN, losses = 16.7%. Find Pe. A: Pe = 0.833 × 1200 = 1000 kN. Use Pe = ₱1,000,000 take-home for service design.
Recall Trigger
Take-home salary after tax = Pe; gross salary = Pi
Tags
- classification
- definition
- process
Topic
Prestress Losses
Concept
Friction loss occurs only in POST-tensioning
Anchor Id
A14
Difficulty
medium
Memory Aid
Imagine dragging a rope through a curved pipe (the duct). The more bends in the pipe, the more friction eats your pulling force. In PRE-tensioning, the strands are straight and in the open air — no pipe, no friction. In POST-tensioning, you're yanking the tendon through a curved duct buried in concrete — LOTS of friction. So friction loss = post-tensioning only. Remember: 'POST = PIPE = Friction Problem.'
Anchor Type
micro_story
Why It Works
The physical experience of dragging a rope through a bent pipe is intuitive. The alliterative phrase 'POST = PIPE = Friction Problem' creates a triple-link memory chain.
Example Usage
Q: List losses applicable to pre-tensioned piles. A: Elastic shortening, relaxation, shrinkage, creep — NO friction or anchorage seating (those are POST only).
Recall Trigger
POST = PIPE = Friction Problem
Tags
- concept
- process
- analogy
Topic
Prestress Losses
Concept
Elastic shortening — concrete shortens when prestress is applied, reducing strand force
Anchor Id
A15
Difficulty
hard
Memory Aid
Think of pressing a spring (the concrete) against a wall while wearing a rubber band around it (the strand). As the spring compresses, the rubber band relaxes slightly — it no longer stretches as far. Elastic shortening = the concrete squeezes shorter, so the strand follows it and loses some stretch. For pre-tensioning, ALL strands are equally affected simultaneously. For post-tensioning, strands are tensioned one by one — the first tendon suffers shortening from all later tensioned tendons.
Anchor Type
analogy
Why It Works
The spring-rubber-band model is physically accurate and kinesthetic. The distinction between all-at-once (pre) vs sequential (post) elastic shortening is captured by the timing of the analogy.
Example Usage
Q: Why is elastic shortening worse in pre-tensioning? A: All strands are released simultaneously — every strand loses force equally from the same shortening. In post-tensioning, later tendons don't cause shortening in already-tensioned ones.
Recall Trigger
Rubber band around a compressed spring
Tags
- classification
- definition
- rhyme
Topic
Prestress Losses
Concept
Creep and shrinkage are TIME-DEPENDENT losses (long-term)
Anchor Id
A16
Difficulty
medium
Memory Aid
Rhyme: 'Creep and Shrink take time to think — they slowly drain the force you sink.' Creep = concrete deforms MORE over time under sustained stress (like a mattress compressing slowly under weight). Shrinkage = concrete dries out and gets smaller over months. Both act over years, not days. Both eat your prestress slowly — like interest compounding in reverse on your prestress investment.
Anchor Type
rhyme
Why It Works
The rhyme creates an auditory anchor. The mattress analogy for creep and the drying analogy for shrinkage are familiar physical phenomena. The reverse-interest metaphor reinforces the time-dependent nature.
Example Usage
Q: Which losses increase significantly over the lifetime of a prestressed bridge? A: Creep and shrinkage (time-dependent) — they accumulate over years, unlike immediate losses.
Recall Trigger
Rhyme: 'Creep and Shrink take time to think'
Tags
- definition
- analogy
- concept
Topic
Prestress Losses
Concept
Steel relaxation — strand loses stress at CONSTANT strain (temperature, time effects)
Anchor Id
A17
Difficulty
medium
Memory Aid
Imagine stretching a rubber band to a fixed length around a box and leaving it there for a year. When you come back, the rubber band is still the same length (constant strain) but it feels LOOSER — it no longer pulls as hard. That's relaxation: the steel strand slowly loses stress even though the concrete length hasn't changed. Low-relaxation (LR) strands are engineered to fight this better — they're 'younger and more energetic' rubber bands.
Anchor Type
analogy
Why It Works
The rubber-band-around-a-box experiment is easy to visualize and clearly distinguishes relaxation (loss of stress at constant strain) from creep (additional strain under constant stress).
Example Usage
Q: What is relaxation loss? A: The strand loses stress over time at constant strain — like a stretched rubber band going slack. Low-relaxation strands reduce this loss.
Recall Trigger
Old stretched rubber band around a box — still stretched, less pull
Tags
- formula
- units
- common error
Topic
Load Balancing
Concept
Units discipline in w_bal = 8Pe/L²
Anchor Id
A18
Difficulty
easy
Memory Aid
Use the phrase 'Keep P in kilonewtons, e and L in meters — the answer pops out in kN/m.' Remember the units as 'kN·m/m² = kN/m' — the m² in L² eats one 'm' from e, leaving kN/m. COMMON TRAP: mixing mm for e and m for L, or kN for P and N for something else. Chant: 'All SI, all metric, all meters for geometry — P in kN only!'
Anchor Type
mnemonic
Why It Works
Unit errors are a major source of lost marks in board exams. A dedicated chant for unit discipline targets this specific weakness. The 'units cancel' visualization is a quick check.
Example Usage
Q: P = 900 kN, e = 150 mm, L = 10 m. Find w_bal. A: Convert e to 0.15 m first! w_bal = 8(900)(0.15)/10² = 10.8 kN/m.
Recall Trigger
Chant: 'kN, meters, meters — answer in kN/m'
Tags
- definition
- classification
- acronym
Topic
Overview of Prestressing
Concept
Prestressed concrete advantages — crack control, span, deflection
Anchor Id
A19
Difficulty
easy
Memory Aid
Remember CSD: Crack control, Span (longer), Deflection (less). Prestressed concrete gives you CSD = Clearly Superior Design over ordinary RC for long spans. Filipino engineers often use prestressed beams for long-span commercial buildings and bridges — think of the NLEX and SLEX flyovers as examples of post-tensioned structures serving millions daily.
Anchor Type
acronym
Why It Works
The acronym CSD is memorable and the local engineering context (NLEX/SLEX) makes it culturally relevant for Filipino reviewees, creating a geographic memory anchor.
Example Usage
Q: State three advantages of prestressed over ordinary RC. A: CSD — better Crack control, longer Span capability, smaller Deflection under service loads.
Recall Trigger
CSD — Cracks, Span, Deflection — Clearly Superior Design
Tags
- formula
- definition
- method_of_loci
Topic
Service Stresses
Concept
Section properties for stress calculations — A, I, c
Anchor Id
A20
Difficulty
medium
Memory Aid
Place yourself in a rectangular room (the beam cross-section). The FLOOR is the bottom fiber (c_bot = h/2 for a symmetric section), the CEILING is the top fiber (c_top = h/2), the AIR VOLUME is the area A = bh, and the CHANDELIER at the center represents the centroid. The I (moment of inertia) is like how hard it is to spin the whole room — bh³/12. Every time you walk into this mental room, you immediately see A, I, c_top, c_bot in their correct positions.
Anchor Type
method_of_loci
Why It Works
The method of loci (memory palace) places abstract values into a physical space you can mentally walk through. The room metaphor is spatially consistent with the beam cross-section orientation.
Example Usage
Q: For a 300×600 mm beam, find A, I, and c. A: Walk into the beam room: A = 300×600 = 180,000 mm², I = 300(600³)/12 = 5.4×10⁹ mm⁴, c = 300 mm (half depth).
Recall Trigger
Step into the 'beam room' — floor=bottom, ceiling=top, chandelier=centroid
Revision Game
w_bal = 8Pe/L² (Load-balancing formula)
Clue
I am the formula that tells you how much upward push a curved tendon gives. I have an '8' in me, and I need to know the sag and the span. What am I?
Memory Link
A9 — EIGHT-PEL-squared chunking mnemonic
Transfer stage (using Pi, initial prestress, with dead load only or no live load)
Clue
I am the stage where the prestress force is at its BIGGEST and the external load is at its SMALLEST. I make the TOP fiber nervous about tension. Which stage am I?
Memory Link
A11, A12 — Two detectives and seesaw visual association
Friction loss (duct friction in post-tensioned members)
Clue
I only happen when a tendon is dragged through a curved pipe buried in concrete. I am an IMMEDIATE loss. I do NOT happen in pre-tensioned members. Who am I?
Memory Link
A14 — POST = PIPE = Friction Problem micro-story
Steel relaxation (stress loss in the tendon at constant strain)
Clue
I am like a stretched rubber band around a rigid box. The box does not change size. But over time, I lose my grip. I am a steel loss, not a concrete loss. Name me.
Memory Link
A17 — Old rubber band around a box analogy
Friction, Elastic shortening, Anchorage seating (immediate); Relaxation, Shrinkage, Creep (long-term/slow)
Clue
Six of us rob the prestress force. Our names spell FEARS-C. Three of us strike immediately, three of us are slow criminals. Name all six and identify the slow ones.
Memory Link
A6 — FEARS-C acronym and quick recall chain
Uniform axial compression = P/A only (no bending stress — the tendon's upward load cancels the gravity load perfectly)
Clue
When a beam is under its balanced load, what is the stress distribution across the entire cross-section? (Hint: it is embarrassingly simple.)
Memory Link
A10 — Libra scale perfectly balanced visual association
Effectiveness ratio R = Pe/Pi ≈ 0.80–0.85
Clue
I am the ratio of the take-home pay to the gross salary in the world of prestressing. My typical value is 0.80 to 0.85. What is my name and formula?
Memory Link
A13 — Salary/tax analogy for retention ratio
Bottom fiber — f_bot = P/A + Pec_bot/I − Mc_bot/I. The Mc/I term reduces the bottom compression under sagging moment.
Clue
I am the fiber that gets EXTRA compression from the eccentric tendon (below the centroid) in a sagging beam. At service, the applied load actually RELIEVES me. Which fiber am I at service, and what is my stress formula?
Memory Link
A4, A5 — PAPA-PM mnemonic and weightlifter below see-saw story
Formula Mnemonics
Formula
f_top = P/A − Pec_top/I + Mc_top/I
Mnemonic
TOP fiber: Axial IN, Eccentric OUT, Moment IN (sagging adds compression at top). Remember: 'TOP = Plus-Minus-Plus in order of P/A, Pec/I, Mc/I' → '+−+' pattern at top.
When To Use
Computing top fiber stress in a simply supported prestressed beam with tendon below centroid under positive (sagging) moment.
What Each Part Means
P/A = uniform axial precompression (always positive = compression); −Pec_top/I = eccentric prestress RELIEVES the top fiber (negative = less compression); +Mc_top/I = sagging moment ADDS compression at top (positive).
Formula
f_bot = P/A + Pec_bot/I − Mc_bot/I
Mnemonic
BOTTOM fiber: Axial IN, Eccentric IN, Moment OUT (sagging relieves bottom). Pattern at bottom: '+−+' for top becomes '+−+' reversed to '++−' at bottom. Or chant: 'Bottom gets DOUBLE compression from prestress, then moment takes some away.'
When To Use
Computing bottom fiber stress in a simply supported prestressed beam with tendon below centroid under positive (sagging) moment.
What Each Part Means
P/A = axial precompression; +Pec_bot/I = eccentric prestress ADDS compression at bottom (positive — best friend!); −Mc_bot/I = sagging moment reduces bottom compression (negative).
Formula
w_bal = 8Pe/L²
Mnemonic
EIGHT-PEL-squared: '8 times P times e over L-squared.' The 8 = the catenary geometry constant for a parabola. Think 'eight pieces of gravity I can balance with one tendon pull.'
When To Use
Finding the load a parabolic prestressing tendon balances, OR finding the required P or e to balance a given gravity load.
What Each Part Means
8 = geometric constant for parabolic tendon; P = effective prestress force (kN); e = tendon sag/eccentricity at midspan (m); L = span length (m); w_bal = balanced upward distributed load (kN/m).
Formula
Pe = R × Pi, where R ≈ 0.80–0.85
Mnemonic
TAKE-HOME formula: Pe = take-home pay, Pi = gross salary, R = retention after tax (losses). Filipino engineers: 'Bawas ang buwis (losses), ito ang natitira (Pe).' R = 0.80–0.85 means losses = 15–20%.
When To Use
Converting between initial and effective prestress. Use Pi at TRANSFER stage; use Pe at SERVICE stage.
What Each Part Means
Pe = effective prestress after all losses; Pi = initial prestress (at jacking/transfer); R = effectiveness ratio (decimal); 1−R = total fractional loss.
Formula
I = bh³/12 (rectangular section)
Mnemonic
B-H-cubed-TWELVE: 'Breadth times Height-cubed, divide by twelve.' Remember: the 12 is like 12 months — it's always there at the bottom of the year (denominator). For section modulus S = I/c = bh²/6.
When To Use
Computing section properties for a rectangular prestressed beam before substituting into the stress formula.
What Each Part Means
b = width of rectangular section; h = total depth; I = moment of inertia about centroidal axis; c = h/2 for symmetric section; S = bh²/6 = section modulus.
Quick Recall Chains
Chain Title
Six Prestress Losses (FEARS-C)
Recall Test
Without looking, list all 6 prestress losses in order. Which three are immediate? Which three are time-dependent?
Memory Chain
A superhero named FEARS-C: He is Frightened of Earthquakes (Friction), and Every morning he does Aerobics (Elastic shortening), Arrives home late (Anchorage seating). Over time, he Rests too much (Relaxation), Shrinks from fatigue (Shrinkage), and Creeps to the couch (Creep). IMMEDIATE losses = F, E, A (the morning routine); LONG-TERM = R, S, C (evening decline).
Items To Remember
- Friction
- Elastic shortening
- Anchorage seating
- Relaxation
- Shrinkage
- Creep
Chain Title
Service Stress Calculation Steps
Recall Test
Walk through the 7 steps for computing stress at the bottom fiber of a prestressed beam. What is the sign of the Pec/I term at the bottom?
Memory Chain
A-I-C, P-e, Three Terms, Two Signs, One Check: Think 'AIC first (section), then PE (force), then TRIPLE TERM COMBO (P/A ± Pec/I ∓ Mc/I), signs by location (top=+−+, bot=++−), final LIMIT CHECK.' Seven steps, seven beats: 'AIC, PE, THREE TERMS, SIGNS, CHECK — done!'
Items To Remember
- Compute section properties (A, I, c)
- Identify P and e
- Compute P/A (axial term)
- Compute Pec/I (eccentric term)
- Compute Mc/I (moment term)
- Apply signs: top = +−+, bottom = ++−
- Check allowable limits
Chain Title
Pre-tensioning vs Post-tensioning Key Differences
Recall Test
Name two characteristics unique to pre-tensioning and two unique to post-tensioning. Which one has friction losses?
Memory Chain
PRE is like a PREPARED meal (done in the factory before serving): Before casting, Plant-produced, Bond transfer, No end anchor. POST is like ordering à la carte (done on site after): After curing, on-site Placement, end Anchorage, friction Problem. 4Bs for Pre (Before, Bond, Based-in-plant, No-Bolt-anchor); 4As for Post (After, Anchorage, on-site Assembly, friction Acts).
Items To Remember
- Pre: before casting
- Pre: plant-produced
- Pre: bond transfer
- Pre: no end anchor needed
- Post: after casting
- Post: cast-in-place
- Post: end anchorage
- Post: friction loss exists
Chain Title
Load Balancing Problem-Solving Steps
Recall Test
Using PELWUC, solve: P = 1200 kN, e = 0.20 m, L = 12 m. What is w_bal?
Memory Chain
PELWUC: P first, E second, L third, Write formula, Units check, Compare. Say 'PELWUC' like 'pel-wuk' — it sounds like a robot announcing the steps. 'PELWUC activated: P=900kN, e=0.15m, L=10m — Wuc! Answer = 10.8 kN/m!'
Items To Remember
- Identify P (effective prestress)
- Identify e (midspan sag)
- Identify L (span)
- Apply w_bal = 8Pe/L²
- Convert units to kN and m
- Compare w_bal with actual load
- If w_bal > actual load: balanced region OK
Chain Title
Transfer vs Service Design Check Sequence
Recall Test
At the transfer stage, which fiber is most likely to be in tension for a below-centroid tendon? At service, which fiber is most likely to be in tension if Pe is too small?
Memory Chain
Two detectives, two crime scenes. Detective TRANSFER investigates the TOP for tension clues using Pi (the big force). Detective SERVICE investigates the BOTTOM for tension clues using Pe (the smaller force). Both must file clear reports (satisfy allowable stresses) before the beam goes to work. If either detective finds a violation — redesign!
Items To Remember
- Stage 1: Transfer — use Pi, dead load only (or none)
- Check top fiber for tension (may govern)
- Check bottom fiber for compression (may be excessive)
- Stage 2: Service — use Pe, full dead + live load
- Check bottom fiber for tension (may govern)
- Check top fiber for compression (may be excessive)
- Both stages must pass — design is bilateral
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