CELE Strength of Materials — Thin-Walled Pressure VesselsCheat Sheet
Thin-Walled Pressure Vessels cheat sheet — the reference card you wish you had on exam day. Condensed from the full study notes, this is the high-yield core of Thin-Walled Pressure Vessels for CELE Strength of Materials. Download, print, revise.
Exam context
On the CELE 2026, the Strength of Materials subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Thin-Walled Pressure Vessels lands at position 8th out of 8 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Strength of Materials on a typical CELE paper.
Thin-Walled Pressure Vessels - Cheat Sheet
Your last-minute reference for cylindrical and spherical pressure vessel stress formulas, design equations, and exam-critical relationships. Covers thin-wall criterion, hoop vs. longitudinal stress, joint efficiency, and design for allowable stress.
Sections
Formulas
Formula
t/r ≤ 1/10 OR r/t ≥ 10
Meaning
t = wall thickness (mm); r = inner radius (mm). Condition for thin-wall formulas to apply.
Watch Out
If t/r > 1/10, use thick-cylinder (Lamé) theory, NOT these formulas. Always use INNER radius/diameter, not outer.
When To Use
ALWAYS verify this first before using any thin-wall stress formula.
Section Title
Thin-Wall Criterion & Validity
Important Facts
- Thin-wall assumption: stress is constant through the wall thickness → simple equilibrium formulas work.
- Derived from cutting the vessel and applying force balance on half or ring element.
- t/r > 1/10 → thick-wall (Lamé) formulas required; thin-wall formulas are INVALID.
- Always use gauge pressure (not absolute) and INNER diameter/radius in formulas.
- Radial stress through thin wall is negligible (approximately zero) compared to membrane stresses.
Key Definitions
Term
Thin-Walled Pressure Vessel
Example
Water pipe D = 600 mm, t = 8 mm: t/r = 8/300 = 0.027 ✓ thin-wall.
Definition
Closed container with wall thickness ≤ 1/10 of inner radius; stress is essentially uniform across thickness; allows equilibrium-based (membrane stress) formulas.
Term
Gauge Pressure
Example
Boiler at 1.5 MPa gauge = 1.6 MPa absolute (if 0.1 MPa atm).
Definition
Internal pressure p measured relative to atmospheric; absolute pressure = p_gauge + p_atm. Always use gauge pressure in these formulas.
Term
Hoop (Circumferential) Stress
Example
Why pressure pipes fail along a longitudinal seam: hoop stress tears the seam.
Definition
Stress acting perpendicular to a longitudinal section (trying to split the vessel along its length); largest stress in cylinders.
Term
Longitudinal (Axial) Stress
Example
σ_l = pD/4t governs circumferential seams and end attachment.
Definition
Stress along the cylinder axis; caused by internal pressure pushing on end caps; equals half the hoop stress in cylinders.
Diagrams To Know
- Free-body diagram of half-cylinder showing internal pressure and hoop stress on the seam.
- Transverse section showing longitudinal stress on end caps and axial force.
- Mohr's circle for cylinder stresses (σ_h and σ_l as principal stresses; radial stress ≈ 0).
Formulas
Formula
σ_h = pD/(2t) = pr/t
Meaning
Hoop (circumferential) stress; p = gauge pressure (Pa or MPa); D = inner diameter (mm); r = inner radius (mm); t = wall thickness (mm).
Watch Out
Denominator is 2t for D or t for r — don't mix. This is TWICE the longitudinal stress. Forget the factor of 2 and fail the design.
When To Use
Always for cylinders under internal pressure; HOOP GOVERNS DESIGN (larger stress).
Formula
σ_l = pD/(4t) = pr/(2t)
Meaning
Longitudinal (axial) stress along cylinder axis.
Watch Out
Denominator is 4t for D or 2t for r. Exactly HALF of hoop stress. Do not use hoop formula for longitudinal.
When To Use
When checking circumferential seams or end attachment; lesser of the two cylinder stresses.
Formula
σ_h = 2σ_l
Meaning
Relationship: hoop stress is always twice the longitudinal in a cylinder.
Watch Out
This is the KEY characteristic of cylinders — memorize it. Sphere is DIFFERENT.
When To Use
Check your calculated stresses; if ratio is not 2:1, you made an error.
Section Title
CYLINDRICAL VESSELS — STRESS FORMULAS
Important Facts
- Hoop stress σ_h = pD/(2t) is THE CRITICAL stress in cylinder design — governs wall thickness.
- Longitudinal stress σ_l = pD/(4t) acts on the end caps and circumferential seams.
- Both stresses are TENSILE (positive) for internal gauge pressure; no compression.
- Hoop stress is twice longitudinal — cylinder fails first along a LONGITUDINAL seam.
- Shear stress: τ_max (in-plane) = (σ_h − σ_l)/2 = pr/(4t); absolute max = σ_h/2 = pr/(2t).
Key Definitions
Term
Membrane Stress
Example
In a cylinder, σ_h and σ_l are membrane stresses; radial stress through wall is ~0.
Definition
Average stress in thin-walled vessel, assumed constant through thickness; acts in the plane of the wall (hoop or longitudinal in cylinders).
Term
Principal Stresses
Example
1.5 MPa pressure → σ_h ≈ 60 MPa, σ_l ≈ 30 MPa, σ_r ≈ 0.
Definition
In a thin cylinder: σ₁ = σ_h, σ₂ = σ_l, σ₃ ≈ 0 (radial). All tensile for internal pressure.
Diagrams To Know
- Half-cylinder FBD with pressure load and hoop stress on the seam.
- Transverse section FBD showing end-cap pressure and longitudinal stress on the wall.
- Mohr's circle: σ_h and σ_l as principal stresses; diameter = σ_h (max shear = σ_h/2).
Reactions Or Equations
Note
This equilibrium approach (not complex theory) is why thin-wall formulas are so simple and powerful.
Equation
Hoop stress derivation: p·D·L/2 = σ_h·t·L → σ_h = pD/(2t)
Conditions
Free-body: half-cylinder length L; pressure p acts on projected area D·L; stress acts on seam area t·L.
Note
End caps push the cylinder apart; stress is half hoop (factor of 2 difference in areas).
Equation
Longitudinal stress derivation: p·π·r² = σ_l·2π·r·t → σ_l = pr/(2t) = pD/(4t)
Conditions
Free-body: transverse slice; pressure acts on end cap (πr²); stress acts on wall annulus (2πrt).
Formulas
Formula
σ = pD/(4t) = pr/(2t)
Meaning
Membrane stress in ALL directions (sphere); p = gauge pressure; D, r, t as before.
Watch Out
Denominator is 4t (for D) or 2t (for r) — SAME as cylinder's LONGITUDINAL. Do not confuse with cylinder's hoop. A sphere is more efficient.
When To Use
All spherical pressure vessels (LPG tanks, gas spheres, high-pressure storage). Same pressure → sphere is stressed HALF of cylinder.
Section Title
SPHERICAL VESSELS — STRESS FORMULA
Important Facts
- Sphere stress = pD/(4t) = pr/(2t) — equals cylinder LONGITUDINAL stress, NOT hoop.
- For equal p, D, t: sphere stress is HALF cylinder hoop stress → sphere is STRONGER.
- No directional weakness in a sphere (unlike cylinder's longitudinal seam); best for high pressure.
- Sphere always fails at a lower internal pressure than an equal-size cylinder.
- Used in practice: LPG tanks, compressed air storage, nuclear reactor vessels.
Key Definitions
Term
Spherical Symmetry
Example
A sphere has no hoop-vs-longitudinal distinction; all directions see the same tensile stress.
Definition
Every great-circle cut of a sphere is identical by geometry; only ONE membrane stress exists, the same in all directions.
Diagrams To Know
- Sphere sectioned by a diametral plane; pressure force on hemisphere equals stress on the edge.
- Comparison sketch: cylinder hoop vs. sphere stress for same p, D, t.
Reactions Or Equations
Note
Same form as cylinder longitudinal; geometry gives the 2:1 advantage over cylinder hoop.
Equation
Sphere equilibrium: p·π·r² = σ·2π·r·t → σ = pr/(2t)
Conditions
Any diametral cut; pressure on hemisphere (πr²) balanced by stress on semicircular edge (2πrt).
Formulas
Formula
t = pD/(2·η·σ_allow) [CYLINDER, hoop governs]
Meaning
Minimum wall thickness; η = joint efficiency (≤ 1); σ_allow = allowable stress (MPa); p, D in consistent units.
Watch Out
Hoop governs (not longitudinal) because σ_h = 2σ_l. If problem is ambiguous, size for hoop (larger). Always verify t/r ≤ 1/10 afterward.
When To Use
Design any cylindrical pressure vessel when p, D, material, and safety factor (implicit in σ_allow) are given.
Formula
t = pD/(4·η·σ_allow) [SPHERE]
Meaning
Minimum wall thickness for spherical vessel; same parameters as cylinder formula but denominator is 4, not 2.
Watch Out
Denominator is 4t (half the cylinder's 2t denominator). Sphere is more efficient. Do not confuse with cylinder hoop formula.
When To Use
Design spherical tanks (LPG, gas). For SAME p, D, σ_allow: sphere t is HALF cylinder t.
Formula
p_max = 2t·η·σ_allow / D [CYLINDER]
Meaning
Maximum allowable internal pressure given wall t, efficiency η, and material allowable stress.
Watch Out
This is just the design formula rearranged. Check thin-wall validity: if given t/r approaches or exceeds 1/10, the result is unreliable.
When To Use
When a vessel already exists and you need to find safe pressure limit.
Formula
p_max = 4t·η·σ_allow / D [SPHERE]
Meaning
Maximum pressure for spherical vessel; denominator is D (not 2D as in cylinder).
Watch Out
Coefficient is 4, not 2. Sphere can hold twice the pressure of equal-size cylinder under same wall and material.
When To Use
Assess existing spherical tank safety or rated pressure.
Section Title
DESIGN FOR ALLOWABLE STRESS
Important Facts
- Hoop stress GOVERNS cylinder design (factor of 2 in numerator vs. 4 for longitudinal).
- Always account for joint efficiency η when seams are present; reduces allowable stress.
- After calculating t, VERIFY thin-wall criterion t/r ≤ 1/10; if violated, formulas are invalid.
- Design formula is rearranged equilibrium + allowable stress limit; no complex theory.
- Sphere requires half the wall thickness of a cylinder for identical p, D, material.
Key Definitions
Term
Joint Efficiency η
Example
η = 0.85 for a specific weld → apply 0.85 × σ_allow across the seam.
Definition
Fraction (≤ 1) representing strength of welded/riveted seam relative to parent plate; reduces effective allowable stress at seams.
Term
Allowable Stress σ_allow
Example
Steel at room temp, η = 1: σ_allow ≈ 80–150 MPa depending on grade and safety factor.
Definition
Maximum working stress; typically material yield/ultimate divided by a safety factor (2–4 for vessels); includes material type, temp, code (ASME, etc.).
Diagrams To Know
- Design flowchart: given p, D, material → find σ_allow → apply η → calculate t → verify t/r ≤ 1/10.
- Graph of wall thickness t vs. pressure p for fixed D and material (linear relationship).
Reactions Or Equations
Note
Rearrange to solve for maximum p or required t depending on the problem.
Equation
Design equilibrium: σ_working = pD/(2t) ≤ η·σ_allow → t ≥ pD/(2·η·σ_allow)
Conditions
Apply factor of safety through σ_allow; joint efficiency reduces seam strength.
Formulas
Formula
τ_max (in-plane) = (σ_h − σ_l) / 2 = pr / (4t) [CYLINDER]
Meaning
Maximum in-plane shear stress in the hoop-longitudinal plane; derived from Mohr's circle of two principal stresses.
Watch Out
This is NOT the absolute maximum shear. Absolute max includes radial stress ≈ 0, giving τ_abs = σ_h/2.
When To Use
When checking failure by shear (von Mises, Tresca) or needing complete stress state.
Formula
τ_abs = σ_h / 2 = pr / (2t) [CYLINDER]
Meaning
Absolute maximum shear stress, accounting for radial stress σ_r ≈ 0; equal to half the hoop stress.
Watch Out
Often the exam uses Tresca (max shear) criterion; this τ_abs is the relevant quantity.
When To Use
Failure theories (max shear / Tresca criterion); more conservative than in-plane shear.
Formula
Radial stress σ_r ≈ 0 (thin-wall assumption)
Meaning
Stress through the wall thickness is negligible in thin-walled vessels; only hoop and longitudinal are significant.
Watch Out
Thick walls (t/r > 1/10) have significant radial stress; thin-wall formulas break down.
When To Use
Justifies treating the vessel as a 2D stress state (hoop and longitudinal principal stresses).
Section Title
SHEAR STRESS & STRESS COMPONENTS
Important Facts
- Thin-wall cylinder is a 2D stress state: only hoop and longitudinal are significant; radial is negligible.
- Mohr's circle has diameter = σ_h (the larger principal stress); max shear = σ_h/2.
- In-plane shear (hoop-long plane) is (σ_h − σ_l)/2; absolute max is σ_h/2 (includes radial dimension).
- Sphere has only ONE non-zero principal stress → max shear = σ/2.
Key Definitions
Term
Principal Stresses
Example
1.5 MPa pressure, D = 600 mm, t = 8 mm: σ₁ ≈ 56 MPa, σ₂ ≈ 28 MPa, σ₃ ≈ 0.
Definition
Normal stresses on planes where shear = 0; in thin cylinder: σ₁ = σ_h (hoop), σ₂ = σ_l (long.), σ₃ ≈ 0 (radial).
Diagrams To Know
- Mohr's circle for cylinder stress state: σ_h and σ_l on horizontal axis, circle diameter = σ_h.
- 3D stress element showing hoop, longitudinal, and radial components (last one ≈ 0).
Reactions Or Equations
Note
Absolute max shear is radius to the σ_r axis, which equals σ_h/2.
Equation
Mohr's circle for cylinder: center = (σ_h + σ_l)/2, radius = (σ_h − σ_l)/2 = pr/(4t)
Conditions
σ_r ≈ 0; both hoop and longitudinal tensile (positive).
Section Title
COMPARISON: CYLINDER vs. SPHERE
Important Facts
- For identical p, D, t: sphere stress = pr/(2t); cylinder hoop = pr/t → SPHERE IS HALF-STRESSED.
- Design: for equal p, D, σ_allow: t_sphere = t_cylinder / 2 → SPHERE NEEDS HALF THE WALL.
- Cylinder has two stresses (hoop 2×, long. 1×); sphere has one (isotropic).
- Cylinder weak along longitudinal seam (hoop pulls it apart); sphere has no weak seam direction.
- Practical outcome: high-pressure storage (LPG, gas) uses SPHERES; low-to-medium pressure uses cylinders (cheaper fabrication).
Diagrams To Know
- Side-by-side stress distribution diagrams: cylinder (hoop vs. long.) vs. sphere (uniform).
- Wall thickness comparison chart: t vs. pressure p for cylinder and sphere.
Formulas
Formula
Effective allowable stress = η · σ_allow
Meaning
Joint efficiency η reduces the strength of a welded or riveted seam; apply this reduced value in design formulas.
Watch Out
If no η is given, assume η = 1 (parent plate strength). If η is given but not used in design, the vessel is over-stressed at the seam.
When To Use
Always when the problem specifies a joint efficiency (e.g., η = 0.85 for longitudinal seam).
Common Values
Value
η = 1.0
Symbol
η
Quantity
Joint Efficiency (fully radiographed weld)
Value
η = 0.85
Symbol
η
Quantity
Joint Efficiency (spot radiographed)
Value
η = 0.60–0.70
Symbol
η
Quantity
Joint Efficiency (no radiography, visual only)
Section Title
SEAMS & JOINT EFFICIENCY
Important Facts
- Hoop stress σ_h = pD/(2t) acts PERPENDICULAR to longitudinal seam → tries to split the seam.
- Longitudinal stress σ_l = pD/(4t) acts ACROSS circumferential seam; smaller stress, less likely to fail.
- Joint efficiency η typically 0.50–1.00 depending on inspection and weld type (radiography increases η).
- If η is given for one seam, problem often requires separate check for the other seam.
- Pressure vessels in code practice (ASME, NSCP 2015) specify η by seam type and inspection method.
Key Definitions
Term
Longitudinal Seam
Example
Cylinder wall thickness is set by hoop stress and the efficiency of the longitudinal seam.
Definition
Weld or rivet line running along the cylinder length; stressed by HOOP stress (the larger one); governs cylinder thickness design.
Term
Circumferential (Girth) Seam
Example
Typically requires less inspection/testing than longitudinal seam because stress is lower.
Definition
Weld running around the cylinder circumference; stressed by LONGITUDINAL stress; less critical (σ_l is smaller).
Diagrams To Know
- Cylinder with visible longitudinal and circumferential seams; annotate which stress acts on which seam.
- Cross-section showing seam orientation and direction of hoop and longitudinal stresses.
Reactions Or Equations
Note
Why cylinders fail along the length in a spectacular burst — hoop stress is the largest.
Equation
Hoop-seam relationship: σ_h = pD/(2t) acts perpendicular (across) longitudinal seam.
Conditions
Longitudinal seam runs along vessel axis; hoop stress pulls it open.
Section Title
WORKED PROBLEM EXAMPLES — CRITICAL PATTERNS
Important Facts
- PATTERN 1: Given p, D, t → FIND stresses: σ_h = pD/(2t), σ_l = pD/(4t); verify t/r ≤ 1/10.
- PATTERN 2: Given p, D, σ_allow, η → FIND t: t = pD/(2·η·σ_allow); round up; verify thin-wall.
- PATTERN 3: Given D, t, σ_allow, η → FIND p_max: p = 2·η·σ_allow·t / D.
- PATTERN 4: Compare cylinder vs. sphere: sphere t ≈ (1/2) × cylinder t for equal p, D, material.
- PATTERN 5: Seam efficiency: if η is given, include in all stress/thickness calculations. If not given, η = 1.
Must Remember
- THIN-WALL CRITERION: t/r ≤ 1/10 MUST BE VERIFIED FIRST. If false, these formulas do not apply.
- CYLINDER HOOP STRESS σ_h = pD/(2t) is ALWAYS the governing stress for cylinder design (larger than σ_l).
- CYLINDER LONGITUDINAL σ_l = pD/(4t) = σ_h/2. This relationship (2:1) is unique to cylinders and is exam-critical.
- SPHERE SINGLE STRESS σ = pD/(4t) = pr/(2t) equals cylinder LONGITUDINAL, NOT hoop. Sphere requires half the wall of a cylinder for the same p, D, material.
- DESIGN FORMULA for cylinder: t = pD/(2·η·σ_allow), where η is joint efficiency. For sphere: t = pD/(4·η·σ_allow).
- HOOP STRESS acts perpendicular to LONGITUDINAL SEAM; longitudinal stress acts across CIRCUMFERENTIAL seam. Hoop is larger → longitudinal seam governs and often has lower η.
- JOINT EFFICIENCY η reduces allowable stress at seams (e.g., η = 0.85 for spot-radiographed welds). Always include in thickness calculation if given; if not given, assume η = 1.
- GAUGE PRESSURE is used in all formulas (internal pressure relative to atmosphere, not absolute). Do not add atmospheric pressure.
- USE INNER DIAMETER/RADIUS in all formulas. If outer dimensions are given, subtract 2t to convert to inner.
- MAXIMUM SHEAR in a cylinder: τ_abs = σ_h/2 = pr/(2t) (accounts for zero radial stress). In-plane shear is (σ_h − σ_l)/2 = pr/(4t) (smaller).
Last Minute Tips
- On any exam problem, DRAW A SMALL CIRCLE OR CYLINDER and LABEL p, D, t, r. Then identify which formula to use. Visual orientation prevents swapping hoop/longitudinal.
- If the problem says 'compare a cylinder and a sphere of the same size and pressure,' answer IMMEDIATELY: sphere wall = (1/2) cylinder wall. Sphere stress = (1/2) cylinder hoop stress. This relationship is tested often.
- ALWAYS calculate t/r at the end of a design problem to verify thin-wall. If it creeps above 0.1, state 'thin-wall assumption invalid; thick-wall theory or iteration required.' Showing this check gains partial credit even if the initial design is slightly off.
- If joint efficiency η is mentioned ANYWHERE in the problem, it MUST appear in your thickness formula. Forgetting it is an instant point loss. Write: t = pD / (2·η·σ_allow) and circle the η.
- When comparing stresses or pressures, always verify the RATIO FIRST before computing. For cylinders: σ_h/σ_l must equal 2.0. For sphere vs. cylinder: stresses must differ by factor of 2. If ratios are wrong, stop and recheck the formula.
Comparison Tables
Rows
Values
- σ_h = pD/(2t) = pr/t
- N/A — single stress only
Property
Hoop/Radial Stress
Values
- σ_l = pD/(4t) = pr/(2t)
- σ = pD/(4t) = pr/(2t) [SAME as cylinder longitudinal]
Property
Longitudinal/Single Stress
Values
- σ_h = 2σ_l (hoop is twice longitudinal)
- Single stress, isotropic (no ratio)
Property
Stress Ratio
Values
- HOOP σ_h (use in thickness formula)
- Single stress σ (no choice)
Property
Governing Design (largest stress)
Values
- t = pD / (2·η·σ_allow)
- t = pD / (4·η·σ_allow) → HALF of cylinder
Property
Design Thickness Formula
Values
- Reference thickness
- Requires t/2 ← SPHERE IS MORE EFFICIENT
Property
For equal p, D, σ_allow
Values
- Longitudinal seam (hoop pulls it open)
- No directional weakness (isotropic)
Property
Weak Seam Direction
Values
- τ_abs = σ_h/2 = pr/(2t)
- τ = σ/2 = pr/(4t) → HALF of cylinder
Property
Maximum Shear (absolute)
Values
- Water mains, penstocks, low–medium pressure; cheaper to fabricate (rolled plates)
- LPG, compressed gas, high-pressure storage; more robust but costlier to fabricate (hemispherical shells)
Property
Common Applications
Columns
- Property
- CYLINDER
- SPHERE
Table Title
Cylinder vs. Sphere — Formulas & Behavior
Rows
Values
- THIN-WALLED
- σ_h = pD/(2t), σ_l = pD/(4t), σ = pD/(4t) for sphere
- D = 600 mm, t = 8 mm, t/r = 0.027 ✓
Property
t/r ≤ 0.1
Values
- THICK-WALLED
- Use Lamé equations (radial stress varies through wall, complex)
- D = 100 mm, t = 15 mm, t/r = 0.3 ✗ (do NOT use simple formulas)
Property
t/r > 0.1
Columns
- Check t/r
- Classification
- Formulas to Use
- Example
Table Title
Thin-Wall vs. Thick-Wall Decision Tree
Rows
Values
- Stress calculated is too low (unsafe design); thickness is undersized
- ALWAYS read 'inner diameter'; if only 'outer' is given, subtract 2t to get inner D.
Property
Use outer radius/diameter instead of INNER
Values
- Apply thin-wall formula to a thick vessel; results are meaningless
- Every problem: calculate t/r first. If > 0.1, stop and state 'thick-wall theory required.'
Property
Forget to check t/r ≤ 1/10
Values
- Wrong stress for design; vessel over- or under-sized
- MEMORIZE: hoop has '2' in denom., longitudinal has '4'. Hoop is twice longitudinal. Hoop GOVERNS cylinder.
Property
Swap hoop and longitudinal stress formulas
Values
- Over-design (too thick wall, wasted material) or under-design (unsafe)
- Problem gives 'internal pressure 1.5 MPa' → use 1.5 MPa as p in formulas (it IS gauge pressure).
Property
Use absolute (gauge + atm) pressure instead of gauge
Values
- Design thickness is too small; vessel fails at seam at lower-than-expected pressure
- If η is mentioned, include in formula: t = pD / (2·η·σ_allow).
Property
Forget joint efficiency η when it's given
Values
- Sphere stress is calculated 2× too high; over-design by factor of 2
- Sphere: σ = pD/(4t). Cylinder hoop: σ_h = pD/(2t). Sphere is the DENOMINATOR with 4, not 2.
Property
Apply cylinder hoop formula to a sphere
Values
- Factor of 2 error (doubled or halved result)
- Read the formula carefully: σ_h = pD/(2t) uses DIAMETER D. σ_h = pr/t uses RADIUS r. Convert if needed: r = D/2.
Property
Mix up D and r in the formula (e.g., use D in formula written for r)
Values
- Calculated t = 14.1 mm used as-is; actual wall is 14 mm and is slightly under-designed
- Always round UP to the next practical size (10 mm, 12 mm, 15 mm, etc.) and RE-CHECK thin-wall criterion.
Property
Not rounding wall thickness UP after calculation
Columns
- Mistake
- Consequence
- How to Avoid
Table Title
Common Exam Mistakes — What Goes Wrong
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