CELE Steel & Timber Design — Timber DesignMemory Anchors
Memory anchors for Timber Design — mnemonic devices, acronyms, and tricks that make the CELE Steel & Timber Design 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 Steel & Timber Design under a "Core" label, with Timber Design in the 5th slot across 5 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 Steel & Timber Design questions. Date to watch: May and November 2026.
Timber Design - Memory Anchors
Memory techniques can boost long-term retention by up to 400% compared to passive re-reading. For Timber Design, the challenge is remembering a web of adjustment factors, three stress-check formulas, and the column stability equation — all under exam pressure. These anchors use mnemonics, analogies, micro-stories, and visual hooks to wire each concept into your long-term memory. When you see the recall trigger in an exam question, the full concept should snap back instantly. Work through each anchor, visualize it, then test yourself with the Revision Game at the end.
Anchors
Tags
- formula
- definition
- process
Topic
ASD Framework
Concept
ASD Framework: F' = F × (product of all C factors)
Anchor Id
A1
Difficulty
easy
Memory Aid
Think of F (reference value) as the BASE SALARY of a timber beam — the amount it earns under perfect, ideal conditions. Each adjustment factor C is a PERFORMANCE MODIFIER: working overtime (C_D = 1.6 for wind), being wet (C_M reduces pay), being too tall (C_F size effect). Your actual take-home pay is F' = F × all modifiers. The beam's job is to make sure its actual stress f never exceeds F' — it must not overspend its allowance.
Anchor Type
analogy
Why It Works
Salary/pay analogies are universally relatable to Filipino reviewees preparing for professional life. The multiplicative nature of the factors mirrors how multipliers stack in payroll.
Example Usage
When asked for F'_b, immediately write F_b × C_D × C_M × C_t × C_F × C_L × C_r. Then check: is f_b ≤ F'_b?
Recall Trigger
Base salary × all performance multipliers = F'
Tags
- classification
- sequence
- definition
Topic
Adjustment Factors
Concept
The 7 main adjustment factors and their meanings
Anchor Id
A2
Difficulty
medium
Memory Aid
Remember the acronym: D-M-T-F-L-P-R → 'Dami Mo Talaga, Fafa Lang Po Rin' (a playful Filipino phrase: 'You have so many, Fafa, just a bit more'). D = C_D (Duration), M = C_M (Moisture/wet service), T = C_t (Temperature), F = C_F (size Factor), L = C_L (Lateral beam stability), P = C_P (column stability — P for Post/Poste), R = C_r (Repetitive member). Visualize a timber post (Poste) soaking wet (M) in Manila summer heat (T) carrying repeated loads (R) for years (D) at different sizes (F) without buckling (L).
Anchor Type
acronym
Why It Works
A Filipino-flavored acronym creates an emotional and cultural hook. Each letter directly maps to one factor, preventing omission on exam day.
Example Usage
When listing adjustment factors for F'_b, recall the phrase: Duration, Moisture, Temperature, size Factor, Lateral stability, Post stability, Repetitive. Check which apply to bending (C_P does NOT apply to bending).
Recall Trigger
'Dami Mo Talaga, Fafa Lang Po Rin' → D-M-T-F-L-P-R
Tags
- classification
- sequence
- formula
Topic
Load Duration Factor C_D
Concept
C_D (Load Duration Factor) values: 0.9, 1.0, 1.15, 1.25, 1.6, 2.0
Anchor Id
A3
Difficulty
medium
Memory Aid
Use the sentence: 'Permanently Old Teachers Live Well, Indeed!' Each word's first letter + a mapped value: P = Permanent (C_D = 0.9), O = Ordinary/10-year (1.0), T = Two-month (1.15), L = Last-7-days (1.25), W = Wind/seismic (1.6), I = Impact (2.0). The order goes from LOWEST to HIGHEST — the longer the load duration, the LOWER the allowable (wood creeps and fatigues), and the SHORTER the duration, the HIGHER C_D (wood can take a punch for a moment).
Anchor Type
mnemonic
Why It Works
A sentence mnemonic with ascending values creates a directional memory hook. The logic (short duration = wood stronger temporarily) adds conceptual reinforcement.
Example Usage
Problem states 'wind load governs.' Recall W = Wind = C_D = 1.6. Multiply F_b × 1.6 (and other C factors) to get F'_b.
Recall Trigger
'Permanently Old Teachers Live Well, Indeed' → 0.9, 1.0, 1.15, 1.25, 1.6, 2.0
Tags
- formula
- process
Topic
Bending Stress Check
Concept
Bending stress formula: f_b = M/S ≤ F'_b
Anchor Id
A4
Difficulty
easy
Memory Aid
Chant this during review: 'M over S is what you see, compare to F-prime-b to set it free. If f_b is less, the beam will stay — if f_b is more, redesign today!' Section modulus S = bh²/6 for rectangle. Think of S as the beam's STRENGTH SHAPE — a deeper beam has a much bigger S (h is squared!), which is why you make beams TALL, not wide.
Anchor Type
rhyme
Why It Works
Rhymes activate the phonological loop in working memory, making the sequence stick even under stress. The design logic (make beams tall) adds engineering intuition.
Example Usage
Given M = 12 kN·m and a 100×300 mm beam: S = 100(300²)/6 = 1.5×10⁶ mm³; f_b = 12×10⁶/1.5×10⁶ = 8 MPa. Compare to F'_b.
Recall Trigger
'M over S' chant → f_b = M/S, then check ≤ F'_b
Tags
- formula
- process
Topic
Shear Stress Check
Concept
Horizontal shear formula: f_v = 3V/2A for rectangular sections
Anchor Id
A5
Difficulty
easy
Memory Aid
Picture a JEEPNEY overloaded with passengers. The floor (horizontal plane) is where the shear tends to slide — this is shear PARALLEL to grain in timber. The factor 3/2 = 1.5 is the same 1.5 parabolic shape factor you see in concrete and steel beams. Visualize the number 1.5 written on the side of the jeepney. The formula: f_v = 3V/(2A) = 1.5 × V/A. The actual shear stress is 50% more than the average V/A because it peaks at the neutral axis.
Anchor Type
visual_association
Why It Works
The jeepney is an iconic Filipino cultural image that creates a vivid spatial memory. Connecting 3V/2A to the universal 1.5 parabolic factor reduces cognitive load.
Example Usage
V = 15 kN, A = 100×300 = 30,000 mm²: f_v = 3(15,000)/(2×30,000) = 0.75 MPa. Compare to F'_v.
Recall Trigger
Overloaded jeepney floor + 1.5 × average shear
Tags
- process
- definition
Topic
Notched Beam Shear
Concept
Notched beam shear: reduced capacity — a classic CELE trap
Anchor Id
A6
Difficulty
hard
Memory Aid
Imagine Mang Jose, a carpenter, notches a beam at the support to make it sit flush on the ledger — a neat, tidy joint. But during inspection, Engineer Reyes flags it immediately: 'Mang Jose, you just cut the beam's shear throat!' The notch reduces the effective depth from d to d_n (net depth), and the shear stress at the notch is amplified by (d/d_n). A 20% notch depth reduction can cause a 25% stress increase. The CELE board loves this trap: always use d_n, never d, at a notched support.
Anchor Type
micro_story
Why It Works
A character-based micro-story with a Filipino setting (carpenter + engineer) creates an emotional narrative. The surprise/warning emotion of the story enhances memory consolidation.
Example Usage
If a beam is notched at support, replace full depth d with net depth d_n in shear calculation. Shear capacity drops — watch for this in problems stating a notch or bird's mouth cut.
Recall Trigger
Mang Jose's notch → use d_n, NOT d at notched support
Tags
- formula
- process
- definition
Topic
Column Compression
Concept
Compression parallel to grain: f_c = P/A ≤ F'_c = F*_c × C_P
Anchor Id
A7
Difficulty
medium
Memory Aid
A timber column is like a BAMBOO POLE holding a load. First, check its 'pure crush strength' — F*_c (all factors except C_P). But if the pole is tall and slender, it will BUCKLE before it crushes. C_P is the buckling penalty: it ranges from near 1.0 (stocky, safe) down toward 0 (slender, about to snap). Think of C_P as the BAMBOO'S CONFIDENCE RATING — a short fat bamboo is confident (C_P ≈ 1.0); a tall thin one is shaky (C_P ≈ 0.3). Multiply F*_c × C_P to get the actual allowable F'_c.
Anchor Type
analogy
Why It Works
Bamboo is the Filipino analog of timber columns — culturally resonant and structurally analogous. The confidence metaphor maps perfectly to the 0-to-1 range of C_P.
Example Usage
Given F*_c = 10 MPa and C_P = 0.781: F'_c = 10 × 0.781 = 7.81 MPa. Then P_allow = F'_c × A.
Recall Trigger
Bamboo confidence rating = C_P; F'_c = F*_c × C_P
Tags
- formula
- process
Topic
Column Stability Factor C_P
Concept
Critical buckling stress for timber column: F_cE = 0.822 E'_min / (ℓ_e/d)²
Anchor Id
A8
Difficulty
hard
Memory Aid
Remember '0.822 as Euler's timber twin.' Euler's column formula uses π²E/(KL/r)² — timber's version replaces π²/... with 0.822 and uses slenderness (ℓ_e/d) with section dimension d instead of radius of gyration r. The magic number 0.822 is derived from reliability calibration in ASD. Memory hook: '0.822 = almost 1 minus one-sixth' (1 - 1/6 ≈ 0.833 ≈ 0.822). Or just memorize '8-2-2' as the area code of Metro Manila — timber columns in Manila buckle at 0.822.
Anchor Type
mnemonic
Why It Works
Linking 0.822 to Metro Manila's area code (02) creates a location-based memory anchor. The Euler parallel reduces the formula to a familiar structure.
Example Usage
ℓ_e/d = 20, E'_min = 6500 MPa: F_cE = 0.822(6500)/400 = 13.36 MPa. This becomes β = F_cE/F*_c for the C_P formula.
Recall Trigger
Metro Manila area code 8-2-2 → 0.822 E'_min / (ℓ_e/d)²
Tags
- formula
- definition
- classification
Topic
Column Stability Factor C_P
Concept
C_P formula structure and the β ratio
Anchor Id
A9
Difficulty
hard
Memory Aid
Visualize C_P as a TRAFFIC LIGHT DIMMER for a column. β = F_cE/F*_c is the RATIO of Euler buckling stress to crush stress. When β > 1 (buckling stress > crush stress), the column is stocky — the light is GREEN (C_P approaches 1.0). When β < 1 (buckling governs before crushing), the light turns AMBER then RED — C_P drops. The formula (1+β)/2c − √[...] is the dimmer dial that smoothly transitions between fully ON and fully OFF. For sawn lumber: c = 0.8 (slightly imperfect wood). For glulam: c = 0.90 (better quality control).
Anchor Type
visual_association
Why It Works
Traffic light metaphors are universally understood and map to the 0-to-1 behavior of C_P. The c = 0.8 vs 0.9 distinction is anchored to quality (sawn vs glulam).
Example Usage
In C_P formula, always identify c first: is it sawn lumber (c = 0.8) or glulam (c = 0.90)? Then compute β = F_cE/F*_c and substitute into the full expression.
Recall Trigger
Traffic light dimmer: β > 1 = green (C_P near 1); c = 0.8 sawn, 0.9 glulam
Tags
- classification
- definition
Topic
Column Stability Factor C_P
Concept
c = 0.8 for sawn lumber, c = 0.90 for glulam
Anchor Id
A10
Difficulty
easy
Memory Aid
Remember: SAWN lumber is ROUGH and imperfect → lower c = 0.8. GLULAM is GLUED and precise → higher c = 0.90. Memory trick: 'Rough Sawn = 0.8 = ate (eight in Filipino English slang for older sister — rough, tough).' 'Glam Glulam = 0.90 = ninety percent glam = more perfect.' Or simply: G for Glulam, G is the 7th letter — closer to 0.90 (90 = 9 × 10, both higher numbers than 8).
Anchor Type
mnemonic
Why It Works
Pairing quality (rough vs. glam) with the numerical values creates a semantic link. The Filipino slang 'ate' for 0.8 adds cultural humor and stickiness.
Example Usage
Problem says 'sawn lumber column' → use c = 0.8 in C_P formula. Problem says 'glulam' → use c = 0.90.
Recall Trigger
Rough sawn = 0.8; Glam glulam = 0.90
Tags
- process
- definition
Topic
Shear Stress Check
Concept
Shear parallel to grain often governs for short, deep timber beams
Anchor Id
A11
Difficulty
medium
Memory Aid
Picture a short, stocky barangay captain (short, deep beam) — he rarely bends (bending is not the issue), but under heavy community pressure (large shear near supports), he SPLITS along the grain — horizontally. In contrast, a tall, slender timber (like a basketball player beam) bends gracefully but rarely splits horizontally. The lesson: SHORT + DEEP = shear governs. LONG + SLENDER = bending governs. Always check BOTH, but know which to suspect first.
Anchor Type
micro_story
Why It Works
The barangay captain vs. basketball player analogy is culturally vivid and maps directly to the geometry-governed behavior of timber beams.
Example Usage
If a problem gives a short, heavily loaded beam near the support, immediately suspect shear. Compute f_v = 3V/2A and compare to F'_v before celebrating with bending.
Recall Trigger
Barangay captain (short-deep) → shear governs; basketball player (tall-slender) → bending governs
Tags
- definition
- classification
Topic
Adjustment Factors
Concept
C_r (Repetitive Member Factor) — bending only, value ≈ 1.15
Anchor Id
A12
Difficulty
medium
Memory Aid
A single katig (outrigger) on a bangka is isolated — it carries its load alone. But three katig spaced closely together share the load through the hull; each individual katig is more reliable because others can redistribute. This is C_r = 1.15: when three or more members are spaced ≤ 600 mm apart (floor joists, rafters), the bending allowable increases by 15% because load sharing kicks in. It applies ONLY to bending — shear and compression don't get this bonus.
Anchor Type
analogy
Why It Works
The bangka (Filipino outrigger canoe) analogy is culturally specific and structurally analogous to repetitive-member floor systems. The 'load-sharing' concept is intuitive.
Example Usage
Problem: floor joists at 400 mm on-center, 3 or more joists → apply C_r = 1.15 to F'_b only. Do NOT apply to F'_v or F'_c.
Recall Trigger
Three katig sharing load = C_r = 1.15, bending only, spacing ≤ 600 mm
Tags
- process
- classification
Topic
Bending Adjustment Factors
Concept
C_L (Beam Stability) vs C_F (Size Factor) — use smaller controlling value
Anchor Id
A13
Difficulty
hard
Memory Aid
Two strict teachers, Ms. Lateral (C_L) and Mr. Size (C_F), both give a student a grade reduction. The school rule is: take the HARSHER grade — whichever is lower controls. If Ms. Lateral gives 0.95 and Mr. Size gives 0.85, the student's final grade is 0.85 — Mr. Size wins. In NSCP, C_L and C_F are not simply multiplied together for sawn lumber bending — the more restrictive (lower) value governs the design.
Anchor Type
micro_story
Why It Works
The 'two strict teachers' story creates a decision-rule narrative. The exam often trips students who blindly multiply all factors without knowing this exception.
Example Usage
If C_L = 0.95 and C_F = 0.85, use C_F = 0.85 (not 0.95 × 0.85 = 0.81) in the F'_b calculation for sawn lumber.
Recall Trigger
Two strict teachers — apply the LOWER of C_L and C_F for bending
Tags
- definition
- classification
Topic
ASD Framework
Concept
ASD vs LRFD — wood uses ASD (Allowable Stress Design)
Anchor Id
A14
Difficulty
easy
Memory Aid
Remember: 'Wood is OLD school — ASD!' Steel and concrete went modern (LRFD/strength design), but timber design in NSCP 2015 Chapter 6 stays with Allowable Stress Design. The mnemonic: 'Ancient Stressed Dendrophytes' = ASD for wood (dendrophyte = tree lover). In ASD: actual stress f ≤ allowable F'. Never apply LRFD load factors (1.2D + 1.6L) to a timber ASD check — that's a classic exam pitfall.
Anchor Type
mnemonic
Why It Works
Contrasting wood's ASD with concrete/steel LRFD sets a clear boundary in the student's mind, preventing formula mixing under exam pressure.
Example Usage
When a mixed problem has timber and steel, use ASD (unfactored D+L) for the timber check and LRFD (1.2D+1.6L) for the steel member check separately.
Recall Trigger
Wood = ASD = Ancient Stressed Dendrophytes; check f ≤ F', NOT factored loads
Tags
- formula
Topic
Bending Stress Check
Concept
Section modulus S = bh²/6 for rectangular sections
Anchor Id
A15
Difficulty
easy
Memory Aid
Rap it: 'B-H-squared over six — that's your S, no other tricks! Width times height-squared, then divide by six, find the section modulus — that's the fix!' The key insight: h is SQUARED, not b — make the beam DEEP (increase h) to dramatically increase S. Doubling h quadruples S; doubling b only doubles S. That's why timber beams are always oriented with the longer dimension vertical.
Anchor Type
rhyme
Why It Works
The rap mnemonic makes the formula phonetically memorable. The design insight (h squared effect) adds conceptual understanding beyond rote memorization.
Example Usage
100×300 mm beam (b=100, h=300): S = 100(300²)/6 = 100(90,000)/6 = 1,500,000 mm³ = 1.5×10⁶ mm³.
Recall Trigger
'B-H-squared over six' rap → S = bh²/6; h squared means depth dominates
Tags
- formula
- process
- definition
Topic
Column Compression
Concept
Effective length ℓ_e and slenderness ratio ℓ_e/d for timber columns
Anchor Id
A16
Difficulty
medium
Memory Aid
Think of ℓ_e/d as the SLIMNESS RATIO of a model — the taller and thinner, the wobblier. For timber, d is the least cross-section dimension (not the radius of gyration as in steel). Maximum practical slenderness ℓ_e/d = 50 for sawn lumber (some references). For a 150×150 column: d = 150 mm regardless of axis (square). For a 100×200 column: use d = 100 mm (the weak axis, least dimension). Always use the SMALLEST d to find the CRITICAL (highest) slenderness.
Anchor Type
analogy
Why It Works
The fashion model analogy is memorable and the 'use least d = worst case' rule is a key exam trap that this analogy prevents.
Example Usage
150×200 mm column with ℓ_e = 3.0 m: use d = 150 mm (least dimension) → ℓ_e/d = 3000/150 = 20.
Recall Trigger
Slimmest dimension = most critical; use least d for ℓ_e/d
Tags
- formula
- definition
- sequence
Topic
Column Compression
Concept
F*_c = F_c × all C factors EXCEPT C_P
Anchor Id
A17
Difficulty
medium
Memory Aid
Picture a timber column with a star (*) stamped on it — like a star student who has passed ALL the adjustment tests EXCEPT the final slenderness/buckling exam (C_P). F*_c is the intermediate result — the column's adjusted capacity before the buckling check is applied. Then C_P reduces it further. The star (*) literally means 'C_P not yet included.' When you see F*_c in a problem or formula, remember: NO C_P yet — it comes next.
Anchor Type
visual_association
Why It Works
The star symbol (*) is already in the notation — linking it to a 'star student awaiting the last exam' creates a memorable visual hook tied directly to the mathematical notation.
Example Usage
F_c = 10 MPa, C_D = 1.0, C_M = 1.0, C_t = 1.0, C_F = 1.0 → F*_c = 10 MPa. Then apply C_P = 0.781 → F'_c = 7.81 MPa.
Recall Trigger
Star (*) = all factors EXCEPT C_P; C_P comes after
Tags
- definition
- classification
Topic
Adjustment Factors
Concept
C_M (Wet Service Factor) — reduces reference values when moisture > 19% for sawn lumber
Anchor Id
A18
Difficulty
medium
Memory Aid
During typhoon season in the province, Lola Caring's narra kitchen shelf is always wet from roof leaks. Engineer nieto notices it has sagged more than the dry shelf in the sala. Wet wood is WEAKER — moisture breaks down the hydrogen bonds in the wood fibers. C_M < 1.0 when in service moisture content exceeds 19% (sawn lumber). In Lola Caring's kitchen (wet exposure), all F values must be multiplied by C_M — some values drop to as low as 0.67.
Anchor Type
micro_story
Why It Works
The relatable Filipino household scenario (typhoon, lola's kitchen, roof leaks) creates an emotional memory that ties moisture content to reduced capacity in a concrete, personal way.
Example Usage
Problem states timber used in a wet environment or submerged → apply C_M values (e.g., C_M = 0.85 for F_b) to all reference design values before other calculations.
Recall Trigger
Lola's wet kitchen shelf → C_M < 1.0 when moisture > 19%
Tags
- sequence
- process
- formula
Topic
ASD Framework
Concept
The three main stress checks in timber design: bending, shear, compression
Anchor Id
A19
Difficulty
easy
Memory Aid
Remember BSC: 'Build Strong Columns!' B = Bending (f_b = M/S ≤ F'_b), S = Shear (f_v = 3V/2A ≤ F'_v), C = Compression (f_c = P/A ≤ F'_c). These are the THREE fundamental checks every timber member must pass. In an exam, always ask: Is it a BEAM? → Check B and S. Is it a COLUMN? → Check C (with C_P). Is it a BEAM-COLUMN? → Check all three and interaction.
Anchor Type
acronym
Why It Works
BSC is a minimal, memorable acronym with an actionable phrase. The routing logic (beam → B+S, column → C) converts it into a decision algorithm for exam use.
Example Usage
Exam gives a simply supported timber beam under uniform load: check B (compute M_max = wL²/8, then f_b) and S (compute V_max = wL/2, then f_v). Both must be ≤ their respective F'.
Recall Trigger
Build Strong Columns → B (bending), S (shear), C (compression)
Tags
- classification
- definition
Topic
Load Duration Factor C_D
Concept
Impact load has the highest C_D = 2.0 — wood doubles its allowable for instantaneous loads
Anchor Id
A20
Difficulty
easy
Memory Aid
Visualize a HAMMER BLOW on a wooden block — it takes the hit but doesn't break, even though a slow sustained load of the same magnitude would crush it over months. Wood is viscoelastic: under impact, the load is gone before the fibers can creep and fail. C_D = 2.0 means: for impact, wood is allowed twice the stress it would handle permanently. Picture a 'x2 COMBO' bonus in a Filipino video game — impact gives wood its highest power-up.
Anchor Type
visual_association
Why It Works
The video game 'x2 COMBO' is culturally familiar to Filipino reviewees and maps perfectly to C_D = 2.0. The physics intuition (viscoelastic behavior) adds depth.
Example Usage
Problem says 'impact load from dropped equipment' → use C_D = 2.0. F'_b = F_b × 2.0 × (other C factors). This is the maximum C_D — no load has a higher value.
Recall Trigger
x2 COMBO = impact = C_D = 2.0 (highest possible)
Revision Game
F_cE = 0.822 E'_min / (ℓ_e/d)² — Critical Euler buckling stress for timber columns
Clue
I am the timber version of Euler's buckling formula. I use 0.822 instead of π². What am I?
Memory Link
A8 — Metro Manila area code 8-2-2 = 0.822
The effective depth drops from d to d_n (net depth at notch), increasing shear stress — use d_n, not d, at a notched support.
Clue
A carpenter notches a beam at its support. Why does Engineer Reyes panic? What changes in the shear formula?
Memory Link
A6 — Mang Jose's notch story
C_r (Repetitive Member Factor) = 1.15, applied to F'_b only when 3 or more members are spaced ≤ 600 mm apart.
Clue
A timber joist is one of 6 joists spaced at 400 mm on center. Which adjustment factor rewards this arrangement, and what is its typical value?
Memory Link
A12 — Three katig on the bangka sharing load
C_D = 2.0 for impact — wood can handle double its long-term stress for a split second because the load is gone before creep and fiber failure can occur.
Clue
An impact load (e.g., a dropped precast panel) hits a timber floor. What C_D do you use, and why is it the highest possible value?
Memory Link
A20 — x2 COMBO in a Filipino video game
C_P — the Column Stability Factor. F'_c = F*_c × C_P.
Clue
I separate star-c from final-allowable-c in column design. I penalize slender columns. I range from near 1 (stocky) to near 0 (slender). Who am I?
Memory Link
A7 — Bamboo confidence rating; A9 — Traffic light dimmer
Shear (f_v = 3V/2A) governs short, deep beams. The high shear force near supports combined with small span length makes horizontal shear critical.
Clue
Your timber beam is very short and very deep — like a stubby, stocky barangay official. Which stress check most likely governs?
Memory Link
A11 — Barangay captain vs. basketball player analogy
Use C_F = 0.85 (the lower, more restrictive value). For sawn lumber bending, C_L and C_F are NOT simply multiplied together — the governing (lower) value applies.
Clue
Two teachers give separate penalties: Ms. Lateral (C_L = 0.95) and Mr. Size (C_F = 0.85). What value do you use in the bending allowable calculation for sawn lumber?
Memory Link
A13 — Two strict teachers: take the harsher grade
Permanently (0.9), Old/Ordinary-10yr (1.0), Teachers/Two-month (1.15), Lived/Last-7-days (1.25), Well/Wind (1.6), In = Impact (2.0).
Clue
Fill in the blanks: 'Permanently Old Teachers Lived Well In _____' — and give the corresponding C_D values.
Memory Link
A3 — 'Permanently Old Teachers Lived Well, Indeed' mnemonic
Formula Mnemonics
Formula
F' = F × C_D × C_M × C_t × C_F × C_L × C_P × C_r (applicable subset)
Mnemonic
'Dami Mo Talaga, Fafa Lang Po Rin' → D, M, T, F, L, P, R. Pick the applicable subset: bending uses D, M, T, F, L, r (not P); compression uses D, M, T, F, P (not L, r).
When To Use
Every timber stress check — apply the applicable subset of C factors to the reference value F before comparing to actual stress f.
What Each Part Means
F = reference design value (species/grade table). C_D = load duration. C_M = wet service. C_t = temperature. C_F = size factor (sawn). C_L = beam stability (bending). C_P = column stability (compression). C_r = repetitive member (bending).
Formula
f_b = M / S ≤ F'_b, where S = bh²/6
Mnemonic
'M over S, b-h-squared over six' — the bending duo. f_b is actual; F'_b is allowable. Beam passes if f_b ≤ F'_b.
When To Use
All timber beam bending checks — simply supported, cantilever, continuous. Use M_max from loading diagram.
What Each Part Means
f_b = actual extreme fiber bending stress (MPa). M = maximum bending moment (N·mm). S = section modulus (mm³) = bh²/6 for rectangle. b = width (mm). h = total depth (mm). F'_b = adjusted allowable bending stress.
Formula
f_v = 3V / (2A) ≤ F'_v
Mnemonic
'Three-Vee over Two-Ay' — horizontal shear in wood. Factor 1.5 (= 3/2) is the parabolic peak-to-average ratio for rectangles.
When To Use
Timber beam shear check — critical near supports, especially for short spans and notched members. Use net depth d_n at notches.
What Each Part Means
f_v = actual horizontal shear stress at neutral axis (MPa). V = maximum shear force (N). A = full cross-sectional area (mm²) = b×h. F'_v = adjusted allowable shear stress parallel to grain.
Formula
f_c = P / A ≤ F'_c = F*_c × C_P
Mnemonic
'P over A — check the C_P penalty.' F*_c is the crush capacity; C_P knocks it down for buckling. Always find F*_c first, then compute C_P, then get F'_c.
When To Use
Timber column design — any axially loaded wood post or strut.
What Each Part Means
f_c = actual compressive stress (MPa). P = axial load (N). A = cross-sectional area (mm²). F'_c = adjusted allowable compression. F*_c = F_c × C_D × C_M × C_t × C_F (all except C_P). C_P = column stability factor (0 to 1).
Formula
F_cE = 0.822 E'_min / (ℓ_e/d)²
Mnemonic
'0.822 — Metro Manila's timber Euler.' Replaces π²/... with 0.822 (ASD calibrated). Slenderness (ℓ_e/d) is squared in denominator — more slender = lower F_cE = lower C_P.
When To Use
Step 1 of C_P calculation — always compute F_cE before β and then C_P.
What Each Part Means
F_cE = critical buckling stress for timber column (MPa). 0.822 = calibration constant (ASD format). E'_min = adjusted modulus of elasticity for stability (MPa). ℓ_e = effective length = K×L (mm). d = least cross-section dimension (mm).
Formula
β = F_cE / F*_c; C_P = (1+β)/(2c) − √[(1+β)/(2c)]² − β/c
Mnemonic
'Beta is the ratio — is buckling or crushing the boss? C_P smoothly blends both using the c = 0.8 imperfection factor.' Think: β > 1 means buckling stress > crush stress → stocky column (C_P → 1). β < 1 means buckling governs → slender (C_P → β/1 ≈ low).
When To Use
Any timber column problem where slenderness (ℓ_e/d) is given. Required for full column design — not needed for very short columns where ℓ_e/d is negligible.
What Each Part Means
β = ratio of Euler buckling stress to adjusted crush stress. c = 0.8 for sawn lumber; 0.90 for glulam (imperfection parameter). C_P = column stability factor used to reduce F*_c to F'_c.
Formula
S_req = M / F'_b (design for bending); A_req = P / F'_c (design for compression)
Mnemonic
'Required = Demand over Allowable.' Flip the check formula: instead of computing stress and comparing, compute the required property directly. Then select a section with S ≥ S_req or A ≥ A_req.
When To Use
Section selection/design problems — when you need to CHOOSE or SIZE the member rather than CHECK an existing one.
What Each Part Means
S_req = minimum required section modulus (mm³). A_req = minimum required cross-sectional area (mm²). M, P = applied moment or load. F'_b, F'_c = adjusted allowable stresses (already computed with all C factors).
Quick Recall Chains
Chain Title
C_D Values in Ascending Order (Permanent to Impact)
Recall Test
Without looking: what is C_D for (a) a permanent dead load, (b) wind load, (c) a 7-day load, and (d) an impact? Answers: 0.9, 1.6, 1.25, 2.0.
Memory Chain
Use the story: 'A PERMANENTLY OLD TEACHER LIVED WELL IN IMPACT ZONE.' Permanent (0.9) → Old/Ordinary 10-yr (1.0) → Teacher = Two-month (1.15) → Lived = Last-7-days (1.25) → Well = Wind (1.6) → Impact (2.0). Each step up means SHORTER duration = HIGHER allowable, because wood is stronger for brief loads.
Items To Remember
- Permanent → C_D = 0.9
- 10-year (occupancy) → C_D = 1.0
- 2-month (construction) → C_D = 1.15
- 7-day (short-term) → C_D = 1.25
- Wind / Seismic → C_D = 1.6
- Impact → C_D = 2.0
Chain Title
Step-by-Step Timber Column Design (C_P Procedure)
Recall Test
Cover this chain and write the 8 steps of timber column design from memory. Then verify each step with Example 4 from the reference notes.
Memory Chain
Story: 'The STAR student (F*_c) studied in the LEAST-lit room (least d), found the EULER score (F_cE = 0.822E/slenderness²), computed the BETA ratio (β), checked if SAWN or GLULAM (c), solved the QUADRATIC (C_P), got the FINAL GRADE (F'_c), and PASSED the load check (f_c ≤ F'_c).' Eight steps, eight story beats.
Items To Remember
- Step 1: Compute F*_c = F_c × C_D × C_M × C_t × C_F (exclude C_P)
- Step 2: Compute slenderness ℓ_e/d using LEAST dimension d
- Step 3: Compute F_cE = 0.822 E'_min / (ℓ_e/d)²
- Step 4: Compute β = F_cE / F*_c
- Step 5: Identify c (0.8 sawn, 0.90 glulam)
- Step 6: Solve C_P from the quadratic formula
- Step 7: F'_c = F*_c × C_P
- Step 8: Check f_c = P/A ≤ F'_c
Chain Title
Three Timber Stress Checks — BSC Framework
Recall Test
For a timber floor joist (beam): which checks apply? For a timber wall stud (column with axial only): which check applies? Answers: B and S for joist; C for stud.
Memory Chain
'BUILD STRONG COLUMNS!' B = Bending with section modulus S = bh²/6. S = Shear at 1.5× average, watch for notches. C = Compression with the C_P buckling penalty. For beams: do B and S. For columns: do C. For beam-columns: do all three plus interaction check.
Items To Remember
- Bending: f_b = M/S ≤ F'_b (F'_b uses C_D, C_M, C_t, C_F, C_L, C_r)
- Shear: f_v = 3V/2A ≤ F'_v (use d_n at notches)
- Compression: f_c = P/A ≤ F'_c = F*_c × C_P
Chain Title
Adjustment Factors — Which Apply to Bending vs. Compression
Recall Test
Write the full formula for F'_b and F'_c from memory, including all C factors. Identify which factors appear in one but NOT the other.
Memory Chain
Remember: 'C_P is for Posts (columns), C_L is for Lateral-beam (bending only), C_r is for Repetitive-bending (bending only).' The universal trio C_D, C_M, C_t applies to everything. C_F (size) applies to bending and compression but check tables for shear — often 1.0 for shear.
Items To Remember
- Bending F'_b: C_D, C_M, C_t, C_F, C_L, C_r (NOT C_P)
- Shear F'_v: C_D, C_M, C_t (limited set)
- Compression F*_c (before C_P): C_D, C_M, C_t, C_F
- C_P applies ONLY to compression parallel (columns)
- C_r applies ONLY to bending (repetitive members)
- C_L applies ONLY to bending (beam stability)
Chain Title
Board-Exam Pitfalls — What NOT to Do
Recall Test
A problem gives a timber beam with a notch at support. List every pitfall you must avoid. Then solve: V = 10 kN, b = 100 mm, d = 250 mm, d_n = 200 mm. Find f_v at the notch. Answer: f_v = 3(10,000)/[2(100×200)] = 0.75 MPa.
Memory Chain
'SEVEN DEADLY TIMBER SINS: Naked F, Wrong Duration, Wrong Shape, Ignoring Notch, Double Penalizing Stability, Loading Factor Mix-Up, Wrong Dimension.' Each sin corresponds to one pitfall. Recite the 7 sins before starting any timber problem.
Items To Remember
- Do NOT forget to apply C factors — bare F_b is never the allowable
- Do NOT use wrong C_D — match it to the load duration given
- Do NOT use 3V/2A for non-rectangular sections (use VQ/Ib instead)
- Do NOT use full depth d at a notched support — use d_n
- Do NOT multiply C_L and C_F both for sawn lumber — use the lower one
- Do NOT mix LRFD load factors with ASD timber check
- Do NOT use b for least dimension in ℓ_e/d if h < b — always use least d
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