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Memory AnchorsCELE · Strength of MaterialsReal content

CELE Strength of MaterialsSimple 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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