CELE Strength of Materials — Simple Stresses and StrainsMemory Anchors
Under the clock, Simple Stresses and Strains facts fade unless they have a hook. Mnemonics are the hook. This page collects the memory anchors that reliably work for Filipino CELE candidates on Professional Regulation Commission (PRC) — Board of Civil Engineering's Strength of Materials items — acronyms, visual pairings, and short rhymes you can rehearse on your commute.
Exam context
For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Strength of Materials under a "Core" label, with Simple Stresses and Strains in the 1st slot across 8 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 Strength of Materials questions. Date to watch: May and November 2026.
Simple Stresses and Strains - Memory Anchors
Memory techniques can increase retention by up to 300% compared to passive reading. For the PRC Civil Engineer Licensure Examination, where you must recall formulas under pressure in minutes, memory anchors are your secret weapon. This collection uses mnemonics (acronyms and rhymes), vivid analogies, micro-stories, and visual associations to make every formula and concept in Simple Stresses and Strains stick permanently. The technique works because your brain remembers stories, images, and emotions far better than naked equations. Link each anchor to the formula, and you can reconstruct any derivation on exam day — even if you are nervous. Work through all 20 anchors, test yourself with the recall chains and revision games, and you will own this chapter.
Anchors
Tags
- formula
- definition
- axial stress
Topic
Normal (Axial) Stress
Concept
Normal Stress Formula: σ = P/A
Anchor Id
A1
Difficulty
easy
Memory Aid
Imagine pressing your THUMB (force P) onto a piece of PANDESAL (area A). The smaller the pandesal, the more it gets squished — the higher the STRESS. Big pandesal, same thumb = less squishing. Stress is always 'how hard you push divided by how much surface takes the hit.' σ = P/A. Think: Pressure on Pandesal Area.
Anchor Type
analogy
Why It Works
Everyday Filipino food reference creates a sensory, tactile memory. The analogy directly maps force over area to a physical experience everyone has had.
Example Usage
Exam question: A 25 mm diameter rod carries 60 kN. Think 'thumb on pandesal' → σ = P/A = 60,000 / (π/4 × 25²) = 122.2 MPa.
Recall Trigger
Pressing your thumb on pandesal
Tags
- formula
- shear
- single shear
- double shear
Topic
Shear Stress
Concept
Shear Stress: single shear τ = V/A; double shear τ = V/2A
Anchor Id
A2
Difficulty
easy
Memory Aid
Think of a SCISSOR vs TWO SCISSORS cutting a rope (bolt). ONE scissor blade = SINGLE SHEAR — all the cutting on one area (τ = V/A). TWO scissor blades clamping the rope at two spots = DOUBLE SHEAR — stress is HALVED (τ = V/2A). Remember: 'Double the blades, HALVE the stress.' For double shear, divide by 2A.
Anchor Type
mnemonic
Why It Works
The scissor image is physical and intuitive. Students can mentally count the cutting planes (1 or 2) to decide which formula to use.
Example Usage
A 20 mm bolt in DOUBLE shear carries 50 kN. Two blades → τ = 50,000 / (2 × π/4 × 20²) = 79.6 MPa. If it were SINGLE shear, that number would double — a dangerous error!
Recall Trigger
Counting scissor blades on the bolt
Tags
- formula
- bearing stress
- projected area
Topic
Bearing Stress
Concept
Bearing Stress: σ_b = P / (d × t) — projected area
Anchor Id
A3
Difficulty
easy
Memory Aid
Picture a BOLT pressing sideways against a WALL of cheese. The cheese does not feel the full round bolt — it only feels the bolt's SHADOW (the projected rectangle = diameter d × thickness t). BEARING STRESS = Force / SHADOW AREA. Draw the shadow: it's d wide and t tall. σ_b = P / (d·t). The 'shadow trick' tells you: never use πd²/4 for bearing — use the flat rectangle.
Anchor Type
visual_association
Why It Works
Visualizing a shadow (projection) is a powerful spatial memory cue. It also prevents the classic exam error of using the bolt's circular area for bearing.
Example Usage
Bolt d=20 mm, plate t=12 mm, P=50 kN. Shadow area = 20×12 = 240 mm². σ_b = 50,000/240 = 208.3 MPa.
Recall Trigger
The shadow a bolt casts on a plate
Tags
- formula
- definition
- strain
Topic
Strain
Concept
Strain: ε = δ/L (deformation per unit length, dimensionless)
Anchor Id
A4
Difficulty
easy
Memory Aid
Think of a rubber SANDO (undershirt). You pull the sando and it stretches 20 cm. But the meaning of that stretch depends on how LONG the sando was originally. A 20 cm stretch on a 1 m sando is huge (ε = 0.20). A 20 cm stretch on a 10 m shirt is tiny (ε = 0.02). STRAIN tells you the stretch relative to the original — it's the STRETCH RATIO of the sando. ε = δ/L.
Anchor Type
analogy
Why It Works
The Filipino sando is a familiar, tactile object. The analogy highlights that absolute deformation is meaningless without the original length — strain is a ratio.
Example Usage
A 3 m bar elongates 1.83 mm. ε = δ/L = 1.83/3000 = 0.00061 (dimensionless). No units — it is a ratio.
Recall Trigger
Pulling your sando and comparing stretch to original length
Tags
- formula
- Hooke's Law
- elastic modulus
Topic
Hooke's Law
Concept
Hooke's Law: σ = Eε (stress is proportional to strain within elastic limit)
Anchor Id
A5
Difficulty
easy
Memory Aid
Imagine Robert Hooke as a strict MANG PANDOY (an old strict teacher) who always says: 'STRESS has CONSEQUENCES proportional to your ACTIONS.' If you push steel a little (small ε), it pushes back proportionally (small σ). Push harder, it resists harder — always E times your strain. The moment you exceed the proportional limit, Mang Pandoy loses his temper and the relationship breaks down. Hooke's Law: σ = E·ε — valid only inside the straight-line region.
Anchor Type
micro_story
Why It Works
Personifying Hooke as a strict teacher creates an emotional narrative. The 'breaking down' of the relationship maps to exceeding the elastic limit — a concept often confused with yielding.
Example Usage
At σ = 122.2 MPa, E = 200,000 MPa → ε = σ/E = 122.2/200,000 = 0.000611. Works only below the proportional limit.
Recall Trigger
Mang Pandoy saying 'consequences proportional to actions'
Tags
- formula
- deformation
- key formula
Topic
Axial Deformation
Concept
Axial Deformation: δ = PL/(AE) — the single most important SoM formula
Anchor Id
A6
Difficulty
easy
Memory Aid
Remember the word PLEA: P·L / (E·A). 'File a PLEA to the bar: how much will it deform?' → δ = PLEA = P × L / (E × A). Say it out loud: 'P-L over E-A.' Alternatively, think: 'Please Let Everything go Axially.' P=force, L=length, E=modulus, A=area. This is the ONLY formula you cannot forget in Strength of Materials.
Anchor Type
mnemonic
Why It Works
PLEA is a 4-letter word linking all four variables in the correct numerator-denominator arrangement. It is short, phonetically distinct, and emotionally loaded (you 'plead' with the bar not to break).
Example Usage
P=60,000 N, L=3,000 mm, A=490.87 mm², E=200,000 MPa. δ = (60,000×3,000)/(490.87×200,000) = 1.83 mm. PLEA in your head: P·L / E·A.
Recall Trigger
PLEA — filing a plea for deformation
Tags
- sequence
- stress-strain
- definition
Topic
Stress-Strain Diagram
Concept
Stress–Strain Diagram landmarks: Proportional Limit → Elastic Limit → Yield Point → Ultimate Strength → Rupture
Anchor Id
A7
Difficulty
medium
Memory Aid
Use the acronym PEYUR (say it 'PAY-YUR') for the five landmarks in order: P = Proportional limit, E = Elastic limit, Y = Yield point, U = Ultimate strength, R = Rupture. 'You PEYUR for the material's strength, from proportional to rupture.' Trace the stress-strain curve from left to right and say P-E-Y-U-R at each landmark.
Anchor Type
acronym
Why It Works
Acronyms compress a 5-item ordered list into a single pronounceable word. The phonetic hook 'PEYUR' is unusual enough to be memorable and the order is preserved.
Example Usage
Exam question: 'Which stress is higher — elastic limit or yield point?' PEYUR: E comes before Y → elastic limit < yield point. Correct.
Recall Trigger
PEYUR — reading the stress-strain curve from left to right
Tags
- formula
- definition
- Poisson
- lateral strain
Topic
Poisson's Ratio
Concept
Poisson's Ratio: ν = -ε_lateral / ε_axial (lateral contraction accompanies axial stretch)
Anchor Id
A8
Difficulty
medium
Memory Aid
Squeeze a HOTDOG lengthwise (push it axially). It gets LONGER in the axial direction but THINNER laterally. Poisson's ratio measures how fat → thin it gets relative to how short → long it becomes. ν = -(fat-to-thin ratio)/(short-to-long ratio). Steel ≈ 0.27–0.30; rubber ≈ 0.50 (very squeezable laterally). The NEGATIVE sign makes ν positive because lateral and axial strains have opposite signs.
Anchor Type
analogy
Why It Works
The hotdog is a familiar food. The squeezing action gives a physical, tactile sense of why lateral strain is always opposite to axial strain. It also explains the negative sign naturally.
Example Usage
Axial strain = +0.001 (tension). ν = 0.30. Lateral strain = −0.30 × 0.001 = −0.0003 (contraction). The negative sign is built in.
Recall Trigger
Squeezing a hotdog and watching it thin
Tags
- formula
- shear modulus
- Poisson
- relationship
Topic
Elastic Constants
Concept
Relationship: G = E / [2(1+ν)] — linking Young's modulus, shear modulus, and Poisson's ratio
Anchor Id
A9
Difficulty
medium
Memory Aid
Rhyme: 'G is E over two-times-one-plus-nu, link the three constants — it's always true!' G = E / [2(1+ν)]. For steel: G = 200,000 / [2(1+0.30)] = 76,923 MPa ≈ 77 GPa. Remember: G is ALWAYS SMALLER than E because 2(1+ν) > 2. The shear modulus is the 'younger sibling' — always less than E.
Anchor Type
rhyme
Why It Works
Rhymes exploit phonological memory. The image of G as a 'younger sibling' of E reinforces the magnitude relationship, preventing the common error of computing G > E.
Example Usage
Given E=200 GPa, ν=0.30. G = 200,000/[2(1.30)] = 76,923 MPa = 76.9 GPa. Check: G < E ✓
Recall Trigger
The rhyme 'G is E over two-times-one-plus-nu'
Tags
- formula
- thermal
- deformation
Topic
Thermal Stress and Deformation
Concept
Thermal Deformation: δ_T = α·L·ΔT (free expansion — no stress if unrestrained)
Anchor Id
A10
Difficulty
medium
Memory Aid
In summer, the railroad track near Tondo EXPANDS. The barangay engineer says: 'Libre ang papalaki — walang stress hangga't hindi nahadlangan!' (Free to grow — no stress as long as it's not blocked!) The formula for how much it grows is: δ_T = α·L·ΔT. Alpha (α) is the material's 'desire to expand per degree.' L is how long the track is. ΔT is how hot it got. FREE expansion → deformation only, NO STRESS. BLOCKED → stress builds.
Anchor Type
micro_story
Why It Works
The Filipino railroad-in-summer narrative is culturally relatable. The Tagalog phrase reinforces the critical concept: free expansion = no thermal stress, only deformation.
Example Usage
12 m steel rail, ΔT=20°C, α=11.7×10⁻⁶/°C. FREE: δ_T = 11.7×10⁻⁶ × 12,000 × 20 = 2.81 mm. Stress = 0. BLOCKED: stress = EαΔT.
Recall Trigger
Barangay engineer: 'Libre ang papalaki — walang stress!'
Tags
- formula
- thermal stress
- restrained
Topic
Thermal Stress and Deformation
Concept
Thermal Stress (fully restrained): σ_T = E·α·ΔT (compressive when heated)
Anchor Id
A11
Difficulty
medium
Memory Aid
Visualize a steel bar TRAPPED between two GIANT CONCRETE WALLS (like being stuck in an MRT tunnel that won't let you move). The bar WANTS to expand (EαΔT of desire) but cannot. So all that expansive energy turns into COMPRESSIVE STRESS — the walls push back. σ_T = E·α·ΔT. When heated: COMPRESSION. When cooled: TENSION. The walls always fight the bar's thermal impulse.
Anchor Type
visual_association
Why It Works
MRT is a Filipino reference that students immediately picture. The wall-fighting-expansion image directly maps restrained thermal expansion to compressive stress — the most common exam scenario.
Example Usage
ΔT=40°C, α=11.7×10⁻⁶/°C, E=200,000 MPa. σ_T = 200,000 × 11.7×10⁻⁶ × 40 = 93.6 MPa (compression).
Recall Trigger
Bar trapped in MRT tunnel trying to expand
Tags
- procedure
- indeterminate
- sequence
- compatibility
Topic
Statically Indeterminate Axial Members
Concept
Statically Indeterminate Axial Members: Need Equilibrium + Compatibility + Force-Deformation
Anchor Id
A12
Difficulty
hard
Memory Aid
The three steps are ECF — 'Every Civil engineer's Formula': E = Equilibrium (ΣF=0), C = Compatibility (deformations must fit together — δ₁=δ₂ or total δ=0), F = Force-deformation (substitute δ=PL/AE for each member). Always solve in order E→C→F for statically indeterminate problems. Remember: 'ECF — Every Civil engineer's Formula for indeterminate members.'
Anchor Type
acronym
Why It Works
ECF is a 3-step ordered procedure acronym tailored to the target audience (Civil engineers). The alliterative full form reinforces professional identity.
Example Usage
Composite column (steel pipe + concrete): E: P_s+P_c=600 kN. C: δ_s=δ_c → P_s L/(A_s E_s) = P_c L/(A_c E_c). F: solve → P_s=200 kN, P_c=400 kN.
Recall Trigger
ECF — Every Civil engineer's Formula
Tags
- concept
- composite
- load sharing
- stiffness
Topic
Statically Indeterminate Axial Members
Concept
Load sharing in composite members: stiffer material (higher AE) carries more load
Anchor Id
A13
Difficulty
hard
Memory Aid
Picture two JEEPNEY PASSENGERS sharing a bench — one is a heavy weightlifter (steel, high AE) and one is a small child (concrete, lower AE). When the jeep hits a pothole, the weightlifter's rigid body takes most of the jolt. The stiffer passenger (higher AE) ATTRACTS more load. In a composite column, load distributes in proportion to axial rigidity (AE) — not equal, not by area alone.
Anchor Type
analogy
Why It Works
The jeepney is a deeply familiar Filipino image. The 'stiffer passenger takes more jolt' analogy gives an intuitive physical sense of why stiffness governs load sharing.
Example Usage
Steel AE = 3000×200,000 = 6×10⁸; Concrete AE = 60,000×20,000 = 12×10⁸. Ratio 1:2. Steel carries P_s, concrete carries 2P_s. Steel is STIFFER? Wait — concrete has higher AE here, so it carries MORE. Always compare AE values.
Recall Trigger
Weightlifter vs child on a jeepney bench during a pothole
Tags
- concept
- definition
- St. Venant
- stress distribution
Topic
Normal (Axial) Stress
Concept
St. Venant's Principle: stress concentrations near load points die out within ~1 member-width
Anchor Id
A14
Difficulty
medium
Memory Aid
Think of dropping a stone (load) in a FISHPOND (the cross-section) near the edge. Right where the stone hits, the water is chaotic (stress concentration). But ONE 'pond-width' away, the ripples smooth out and the water is calm and uniform. St. Venant says: move your analysis section at least one 'width' away from the load point and the simple formula σ=P/A is valid. Near the load: complex. Far from the load: simple and uniform.
Anchor Type
micro_story
Why It Works
The fishpond ripple story is visual, calming, and maps distance-from-disturbance directly to the principle. Filipino students often have personal memories of fishpond (palaisdaan) settings.
Example Usage
A concentrated load is applied at the top of a column. Stress at 1 diameter below the load is already nearly uniform — σ=P/A is applicable there.
Recall Trigger
Ripples in a fishpond calming one width away
Tags
- formula
- definition
- factor of safety
- design
Topic
Allowable Stress and Factor of Safety
Concept
Factor of Safety: F.S. = σ_failure / σ_allowable
Anchor Id
A15
Difficulty
easy
Memory Aid
Imagine a BANGKETA (sidewalk) rated for 500 kg/m². You only let people walk if the calculated load is 250 kg/m² — that's a Factor of Safety of 2.0. The bangketa's 'real strength' divided by 'what you allow' = F.S. If the bangketa were to carry 500 kg/m² every day, one minor defect and it collapses. The safety factor is your engineering cushion against the unexpected. F.S. = σ_failure / σ_allow.
Anchor Type
analogy
Why It Works
Bangketa is a very Filipino concept — sidewalk overloading stories are common in Philippine engineering news. It grounds the abstract ratio in everyday civil infrastructure.
Example Usage
Steel bar, yield stress = 250 MPa, F.S. = 1.5. Allowable = 250/1.5 = 167 MPa. Do not design the bar to work above 167 MPa.
Recall Trigger
Bangketa rated for 500 but you only allow 250
Tags
- formula
- segments
- series
- deformation
Topic
Axial Deformation
Concept
Segments in series (varying P, A, E): δ_total = Σ(P_i L_i / A_i E_i)
Anchor Id
A16
Difficulty
medium
Memory Aid
Visualize a BAHAY-KUBO made of bamboo poles of different lengths and thicknesses, tied end-to-end vertically. Each pole is a SEGMENT. To find how much the whole assembly stretches, you calculate the stretch of EACH POLE (using its own P, L, A, E) and ADD them all up. Total deformation = SUM of each bamboo pole's PLEA (P·L/A·E). The bamboo image reminds you: each segment has its own properties.
Anchor Type
visual_association
Why It Works
Bahay kubo (nipa hut) bamboo poles are a strong Filipino visual. The image of different-thickness poles stacked vertically maps perfectly to bar segments in series.
Example Usage
Three-segment bar: δ = P₁L₁/(A₁E₁) + P₂L₂/(A₂E₂) + P₃L₃/(A₃E₃). Each segment gets its own PLEA.
Recall Trigger
Bamboo poles of different sizes tied end-to-end in a bahay kubo
Tags
- formula
- biaxial
- triaxial
- Hooke's Law
Topic
Generalized Hooke's Law
Concept
Generalized Hooke's Law: εx = [σx − ν(σy + σz)] / E
Anchor Id
A17
Difficulty
hard
Memory Aid
Use the phrase 'DIRECT MINUS POISSON'S PULL' for each strain equation. The strain in x-direction = (DIRECT stress in x) MINUS (Poisson pulling from the OTHER two directions, σy and σz), all divided by E. It's like you get 'credit' for pulling in your direction but lose some because the sides are also being pulled. For each axis: εx = [σx − ν(σy + σz)]/E — same pattern rotated for y and z.
Anchor Type
mnemonic
Why It Works
The phrase 'direct minus Poisson's pull' is a semantic anchor that reconstructs the formula structure. Students recall the subtraction and the factor ν naturally from the phrase.
Example Usage
σx=100 MPa, σy=50 MPa, σz=0, ν=0.30, E=200,000 MPa. εx = [100 − 0.30(50+0)]/200,000 = [100−15]/200,000 = 0.000425.
Recall Trigger
Direct minus Poisson's Pull, divided by E
Tags
- units
- common error
- numerics
Topic
Units and Numerical Discipline
Concept
Units discipline: use N and mm → stress in MPa (N/mm²); avoid mixing kN and m
Anchor Id
A18
Difficulty
easy
Memory Aid
Rhyme: 'N and mm gives MPa — use kN and m and you'll go astray!' The safest habit: convert everything to Newtons (N) and millimeters (mm) at the START of every problem. Then σ = P(N)/A(mm²) comes out directly in N/mm² = MPa. Mixing kN with mm or N with m is the NUMBER ONE arithmetic error in PRC board exams.
Anchor Type
rhyme
Why It Works
Rhymes are remembered under exam stress. The warning about the most common error gives it emotional salience — students fear making unit mistakes on exam day.
Example Usage
P = 60 kN = 60,000 N; A = 490.87 mm². σ = 60,000/490.87 = 122.2 N/mm² = 122.2 MPa. ✓ If you had used 60 and 490.87 in wrong units, you'd get 0.1222 — off by 1,000×.
Recall Trigger
N and mm gives MPa — the exam-day mantra
Tags
- concept
- Poisson
- volumetric strain
- incompressible
Topic
Generalized Hooke's Law / Volumetric Strain
Concept
Volumetric Strain: ε_v = (1−2ν)/E × (σx+σy+σz); ν=0.5 means incompressible
Anchor Id
A19
Difficulty
hard
Memory Aid
Think of rubber ERASERS (ν≈0.5). Squeeze one — it doesn't get smaller overall! The volume stays the same. That's because ε_v = (1−2×0.5)/E × (sum of stresses) = 0 — zero volumetric strain. Now squeeze steel (ν≈0.30): (1−0.6) = 0.4 > 0, so it DOES compress slightly in volume. Rubber is the benchmark for incompressible. Ν=0.5 = eraser = volume preserved.
Anchor Type
analogy
Why It Works
The rubber eraser is a universal tactile experience in Filipino classrooms. Connecting ν=0.5 to the incompressible eraser makes the abstract volumetric strain condition immediately physical.
Example Usage
For a rubber seal with ν=0.50: ε_v = (1−2×0.50)/E × Σσ = 0. Volume unchanged. For steel with ν=0.30: ε_v = (1−0.60)/E × Σσ = 0.40/E × Σσ ≠ 0.
Recall Trigger
Squeezing a rubber eraser that doesn't shrink
Tags
- common error
- bearing stress
- projected area
Topic
Bearing Stress
Concept
Common board-exam pitfall: bearing area = d×t (projected), NOT π/4 × d²
Anchor Id
A20
Difficulty
easy
Memory Aid
There was a board examinee named Boyong who failed bearing stress because he used the bolt's CIRCULAR area πd²/4. His professor told him: 'Boyong! The plate does not hug the whole bolt circle — it only SEES the flat shadow! Use d×t!' Boyong passed the board the second time after tattooing 'SHADOW = d×t' on his review notebook. Every time you see bearing stress, think of Boyong's mistake and use d×t.
Anchor Type
micro_story
Why It Works
A named character (Boyong — a classic Filipino name) who made the exact error creates a warning story. Students who hear Boyong's story become emotionally invested in not repeating his mistake.
Example Usage
Bolt d=20 mm, plate t=12 mm. WRONG: A=π/4×20²=314 mm². RIGHT: A_b=20×12=240 mm². σ_b=P/240. Boyong used 314 — do NOT be Boyong.
Recall Trigger
Boyong's mistake — he used πd²/4 for bearing and failed
Revision Game
PLEA (δ = PL/AE) — the axial deformation formula
Clue
I am used everywhere in Strength of Materials. I am four letters. I describe the deformation of a bar under axial load. My formula has the load and length on top, area and modulus below. What am I?
Memory Link
A6 — PLEA mnemonic: P×L over A×E
Bearing Stress — σ_b = P/(d×t), using projected area d×t
Clue
I am Boyong's biggest mistake. He used the wrong area for me — he used the round bolt area instead of the flat shadow. What type of stress am I?
Memory Link
A20 — Boyong's story and A3 — shadow area visual
Compressive thermal stress develops: σ_T = E·α·ΔT = 200,000 × 11.7×10⁻⁶ × 40 = 93.6 MPa (compression)
Clue
A steel bar is trapped between two walls. The temperature rises 40°C. The bar wants to grow but cannot. What happens and what is the formula for the resulting stress?
Memory Link
A11 — bar trapped in MRT tunnel
PEYUR: Proportional limit → Elastic limit → Yield point → Ultimate strength → Rupture
Clue
I am five landmarks on the stress-strain curve of mild steel. Spell my acronym and name each landmark in order from lowest stress to highest.
Memory Link
A7 — PEYUR acronym and quick recall chain
ECF — Every Civil engineer's Formula: Equilibrium → Compatibility → Force-deformation (δ=PL/AE)
Clue
I am the three-step method for solving statically indeterminate axial problems. I am also an acronym that sounds like a civil engineer's motto. What am I?
Memory Link
A12 — ECF acronym and quick recall chain
τ = V/(2A) for double shear. Single scissor vs two scissors — count the planes!
Clue
A bolt connects plates in DOUBLE shear carrying load V. I am the shear stress formula. If you forget the factor of 2 in the denominator, your answer is exactly double what it should be — a dangerous overestimate of stress!
Memory Link
A2 — scissor analogy for single vs double shear
G = E/[2(1+ν)]. Since ν > 0 always, 2(1+ν) > 2, so G < E/2 < E. The younger sibling is always smaller.
Clue
I relate shear modulus G to Young's modulus E and Poisson's ratio ν. I guarantee that G is ALWAYS smaller than E. What is my formula and why is G < E always true?
Memory Link
A9 — rhyme 'G is E over two-times-one-plus-nu' and younger sibling image
Normal Strain ε = δ/L (dimensionless). Shear strain γ = change in angle (radians).
Clue
I am dimensionless. I am the ratio of deformation to original length. I am NOT stress — I am what happens GEOMETRICALLY when a bar stretches. My shear counterpart is measured in radians.
Memory Link
A4 — sando (undershirt) stretch ratio analogy
Formula Mnemonics
Formula
σ = P/A
Mnemonic
PAPA (P over A, Pressure on Any Area). 'PAPA carries the load P over the area A.'
When To Use
Any axial tensile or compressive member where the load passes through the centroid and you are far from load application points (St. Venant)
What Each Part Means
σ = normal stress (MPa = N/mm²); P = axial force perpendicular to section (N); A = cross-sectional area (mm²)
Formula
τ = V/A (single) or V/(2A) (double shear)
Mnemonic
'ONE blade, ONE area. TWO blades, HALF the stress.' Count the shear planes first.
When To Use
Bolts, rivets, pins, keys — whenever a connector is being cut by shear. Count the number of shear planes to determine single or double.
What Each Part Means
τ = shear stress (MPa); V = shear force (N); A = area of one cross-section of connector (mm²); factor 2 in denominator for double shear
Formula
σ_b = P/(d×t)
Mnemonic
SHADOW AREA: bearing stress = Force / (diameter × thickness). 'Shadow = d × t, never πd²/4.'
When To Use
Contact pressure between a fastener and the plate/member it presses against — bolt-plate connections, pin-clevis connections, rivet-sheet connections
What Each Part Means
σ_b = bearing stress (MPa); P = force (N); d = bolt/rivet diameter (mm); t = plate thickness (mm); d×t = projected (shadow) area
Formula
ε = δ/L
Mnemonic
'Deformation over Length = strain. DL = strain. δivide the deformation by the Length.'
When To Use
Any problem asking for strain given deformation and length, or converting stress to deformation
What Each Part Means
ε = normal strain (dimensionless); δ = axial deformation/elongation (mm); L = original length (mm). Sign convention: positive = elongation
Formula
δ = PL/(AE)
Mnemonic
PLEA: P × L / (A × E). 'File a PLEA for deformation: how much does the bar lengthen?'
When To Use
Single uniform member under axial load. For multiple segments, sum each segment's PLEA: δ = Σ(P_i L_i / A_i E_i)
What Each Part Means
δ = axial deformation (mm); P = axial force (N); L = length (mm); A = cross-sectional area (mm²); E = modulus of elasticity (MPa)
Formula
δ_T = α·L·ΔT
Mnemonic
'ALL Temperatures expand: Alpha × Length × ΔTemp = ALT deformation.' Mnemonic: A·L·T (not altitude, but alpha-L-T).
When To Use
Any member experiencing temperature change — FREE member (no stress, only deformation). If RESTRAINED, also compute thermal stress.
What Each Part Means
δ_T = thermal deformation (mm); α = coefficient of thermal expansion (/°C); L = length (mm); ΔT = temperature change (°C). Result is elongation when heated, shortening when cooled.
Formula
σ_T = E·α·ΔT (fully restrained)
Mnemonic
'Every Alpha-Temp is a stress — EαΔT.' Think: the bar WANTS to do ALT expansion but is BLOCKED, so the energy turns into E × (what it wanted to do per unit length).
When To Use
Member with ZERO thermal deformation (both ends fixed). For partial restraint or gap problems, use compatibility: α·L·ΔT − PL/(AE) = gap, then solve for P.
What Each Part Means
σ_T = thermal stress (MPa, compressive when heated); E = modulus (MPa); α = thermal expansion coefficient (/°C); ΔT = temperature rise (°C)
Formula
G = E / [2(1+ν)]
Mnemonic
Rhyme: 'G is E over two times one plus nu — the shear modulus formula, always true!' G < E always.
When To Use
Converting between E and G, or finding G when only E and ν are given. For steel: G ≈ 77–80 GPa.
What Each Part Means
G = shear modulus/modulus of rigidity (MPa); E = Young's modulus (MPa); ν = Poisson's ratio (dimensionless, 0.25–0.35 for metals)
Formula
ν = −ε_lateral / ε_axial
Mnemonic
'NEGATIVE lateral over axial = nu.' The negative sign makes ν positive because lateral and axial strains always oppose each other.
When To Use
When a problem gives axial strain and asks for lateral strain (or vice versa), or when computing multi-dimensional strain states
What Each Part Means
ν = Poisson's ratio; ε_lateral = strain perpendicular to loading axis (negative in tension); ε_axial = strain along loading axis (positive in tension)
Formula
F.S. = σ_failure / σ_allowable
Mnemonic
'Factor of Safety = Failure over Allowed. FF/AA. How many times stronger than allowed is the real limit?'
When To Use
Checking adequacy of a member in working stress design; computing allowable stress from given factor of safety and material strength
What Each Part Means
F.S. = factor of safety (dimensionless, always > 1); σ_failure = yield stress or ultimate stress (MPa); σ_allowable = design working stress (MPa)
Quick Recall Chains
Chain Title
Stress-Strain Curve Landmarks (PEYUR Chain)
Recall Test
Without looking: name the 5 landmarks of the ductile steel stress-strain curve in order. Spell out PEYUR and expand each letter.
Memory Chain
PEYUR (pay-yur): Imagine an overworked engineer who PAYS (P) for his Elastic (E) Yield (Y) Until Rupture (UR). As you trace the stress-strain curve left to right, say P-E-Y-U-R. Each letter is a landmark in order. 'You PEYUR (pay dear) when you push a material to its limits.' P=Proportional, E=Elastic, Y=Yield, U=Ultimate, R=Rupture.
Items To Remember
- Proportional Limit
- Elastic Limit
- Yield Point
- Ultimate Strength
- Rupture (Fracture)
Chain Title
Three Steps for Indeterminate Axial Members (ECF Chain)
Recall Test
Given a bar fixed at both ends with a mid-point load, list the three equations you need. Use ECF to reconstruct the sequence without looking.
Memory Chain
ECF = Every Civil engineer's Formula. Say: 'Equilibrium first, Compatibility second, Force-deformation third. ECF — always in that order.' To recall: E = You need to BALANCE the forces first (equilibrium). C = The pieces must FIT together (compatibility — geometry). F = Now do the MATH with δ=PL/AE (force-deformation). Never skip the order.
Items To Remember
- Step 1: Equilibrium — write ΣF=0
- Step 2: Compatibility — set deformations equal or sum to zero
- Step 3: Force-Deformation — substitute δ=PL/AE for each member
Chain Title
Types of Simple Stress (SBS Chain)
Recall Test
A 20 mm bolt connects two plates (double shear), carrying 50 kN through a 12 mm plate. Write the formula and numerical answer for all THREE types of stress acting in this connection.
Memory Chain
SBS — 'Squeezing, But Sideways': Normal stress SQUEEZES or stretches (perpendicular). Shear stress acts SIDEWAYS (parallel, like scissors). Bearing is the SQUEEZING between two surfaces (contact). SBS. Alternatively: 'NBA — Normal, Bearing, shear (shAr with an A)' — but SBS preserves the physical image better. Recall: Normal=perpendicular; Shear=parallel; Bearing=contact shadow area.
Items To Remember
- Normal (Axial) Stress — σ = P/A, force perpendicular to area
- Shear Stress — τ = V/A, force parallel to area
- Bearing Stress — σ_b = P/(d×t), contact pressure on projected area
Chain Title
Four Variables in Axial Deformation (PLEA Chain)
Recall Test
Without looking, write the formula for axial deformation. Now explain: which variables INCREASE δ when they increase, and which DECREASE δ?
Memory Chain
PLEA: P·L / (A·E) = δ. Read top-to-bottom: P and L multiply (numerator) → A and E multiply (denominator). To remember arrangement: 'Please (PL) Allow (AE) deformation.' P and L are friends in the numerator (both increase deformation when larger). A and E are friends in the denominator (both resist deformation when larger).
Items To Remember
- P = Axial Force (N)
- L = Length (mm)
- A = Cross-sectional area (mm²)
- E = Modulus of elasticity (MPa)
Chain Title
Elastic Constants Relationship Chain
Recall Test
Given E=200 GPa and ν=0.30, compute G and K. Use the family relationships to write both formulas from memory.
Memory Chain
Think of a FAMILY: E is the FATHER (largest, most important). G is the SON (shear, always smaller than E). ν is the MOTHER (Poisson, connects father and son via G=E/[2(1+ν)]). K is the UNCLE (bulk, appears in volumetric problems, K=E/[3(1−2ν)]). The family is held together by ν. If you know E and ν, you can find EVERY other elastic constant.
Items To Remember
- E = Young's modulus (tension/compression stiffness)
- G = Shear modulus (shear stiffness), always < E
- ν = Poisson's ratio (lateral-to-axial strain ratio)
- K = Bulk modulus (volumetric stiffness)
- Link: G = E/[2(1+ν)]; K = E/[3(1−2ν)]
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