PRC Mechanical Engineering (MELE) Cheat Sheet

Machine Design, Materials and Shop Practice

30% of exam
Stress Formulas Shafts, Keys, Couplings Gears Belts, Chains, Flywheels Springs + Bearings Bolts, Welds, Rivets Columns + Fatigue Materials + Shop Practice

Industrial and Power Plant Engineering

35% of exam
IPPE Item Counts Power Cycles Boilers + Steam Engines + Performance Pumps, Fans, Compressors Refrigeration + Air Conditioning Plant + Safety Metrics

Mathematics, Engineering Economics and Basic Engineering Sciences

35% of exam
MEEBES Item Counts Economy Factors Depreciation Methods Strength of Materials Thermodynamics + Fluids Chemistry + Physics ME Law + Ethics

Quick Facts

Exam MELE
Board PRC Board of ME
Law RA 8495
Items 300 total, 100 per subject
Schedule 3 days, 8AM-2PM daily
Pass 70% average
Floor No subject below 50%
Calculator Non-programmable only
Retake 1 year after third fail
Feb 2026 passers 51.86% (3,264/6,294)
Blueprint Resolution 57, s. 2013

Column End Fixity MA

Fixing halves it, freeing doubles it
Pinned-pinned: 1.0 Fixed-fixed: 0.5 Fixed-pinned: 0.7 Fixed-free: 2.0

Soderberg vs Goodman MA

Soderberg

Uses yield strength Sy
Most conservative line
No yielding permitted

Goodman

Uses ultimate strength Su
Allows higher mean stress
Standard fatigue line
Yield line vs ultimate

Machine Element Picker MA

Rotating power transmission → Shaft torsion formula ( 16T / (pi d^3) )
Shaft sized by code → PSME cubic formula ( C = 80/53.5/38 )
Torque through hub → Key shear and bearing ( Weaker governs )
Non-parallel shafts → Bevel or worm gears
Long center distance → Belt or chain drive
Exact ratio required → Chain or gear ( Belts slip )
Fluctuating stress → Soderberg or Goodman
Long slender member → Euler buckling ( Check slenderness first )
Short compression member → J.B. Johnson formula
Smoothing speed swings → Flywheel ( Kinetic energy store )

MDMSP Item Counts MA

Kinematics 12 items 2.38%
Machine Design 81 items 25%
Shop Machinery 3 items
Shop Practice 4 items
Subject total 100 items, 30% weight
Design sub-areas 27 topics listed
Each design topic 3 items apiece

PSME Shaft Constants MA

Main 80, line 53.5, short 38
P = D^3 N / C Main power shaft: 80 Line shaft pulleys: 53.5 Small short shaft: 38

Allowance vs Tolerance MA

Allowance

Between mating parts
Sets the fit type

Tolerance

On one dimension
Sets permitted variation
Fit type vs drift

Stress Formulas MA

Axial stress P / A
Direct shear V / A
Bearing stress P / (t x d)
Torsional shear 16T / (pi d^3)
Bending stress M c / I
Section modulus S = I / c
Hoop stress p D / (2t)
Longitudinal stress p D / (4t)
Factor of safety Strength / working stress

Shafts, Keys, Couplings MA

Power from torque P = 2 pi T N
PSME main shaft P = D^3 N / 80
PSME line shaft P = D^3 N / 53.5
PSME short shaft P = D^3 N / 38
Key tangential force F = 2T / D
Key checked twice Shear and bearing
Torsional deflection T L / (J G)
Flange coupling bolts Shear on bolt circle

Gears MA

Module m = D / N
Circular pitch p = pi m
Diametral pitch Pd = N / D
Pitch identity p x Pd = pi
Center distance (D1 + D2) / 2
Velocity ratio N1 / N2 = T2 / T1
Train value Driver teeth / driven teeth
Idler gear Reverses direction only
Mesh condition Same module required

Belts, Chains, Flywheels MA

Tension ratio F1 / F2 = e^(mu theta)
Belt power (F1 - F2) x speed
Contact angle effect More wrap, more capacity
V-belt advantage Wedging raises effective friction
Flywheel energy KE = 0.5 I omega^2
Coefficient of fluctuation Speed swing / mean speed
Chain versus belt No slip, fixed ratio

Springs + Bearings MA

Spring deflection 8 F D^3 n / (G d^4)
Spring rate k = F / delta
Wire diameter effect Stiffness varies d^4
Wahl factor Corrects curvature shear
Bearing rating life L10 = (C / P)^k
Ball bearing k 3
Roller bearing k 10/3
L10 meaning 90% survive rating life

Bolts, Welds, Rivets MA

Bolt torque T = K F d
Nut factor K 0.20 dry, 0.15 lubricated
Fillet weld throat 0.707 x leg
Weld shear area Throat x length
Rivet joint efficiency Joint strength / plate strength
Rivet failure modes Shear, tear, crush
Thread stress area Less than nominal area

Columns + Fatigue MA

Euler load pi^2 E I / (K L)^2
K pinned-pinned 1.0
K fixed-fixed 0.5
K fixed-pinned 0.7
K fixed-free 2.0
Slenderness ratio K L / r
Short column rule Use J.B. Johnson
Soderberg Uses yield strength Sy
Goodman Uses ultimate strength Su

Materials + Shop Practice MA

Cutting speed V = pi D N
Spindle speed N = V / (pi D)
Allowance Intended clearance or interference
Tolerance Permitted variation, one dimension
Annealing Softens, relieves internal stress
Quenching Hardens, forms martensite
Tempering Restores toughness after quench
Eutectoid steel 0.8% carbon at 723 degC
Brinell versus Rockwell Indent size versus depth

Subject Weights PO

Power 35 | Math 35 | Design 30
Power plant: 35% Math sciences: 35% Machine design: 30% 100 items each

Load vs Capacity Factor PO

Load factor

Average over peak load
Measures demand steadiness

Capacity factor

Average over rated capacity
Measures plant utilization
Demand vs installed capacity

Plant + Cycle Picker PO

Spark ignition engine → Otto cycle
Compression ignition engine → Diesel cycle
Gas turbine plant → Brayton cycle
Steam turbine plant → Rankine cycle
Wet turbine exhaust → Add reheat ( Protects last blades )
Need higher efficiency → Add regeneration ( Feedwater heating )
Turbine exhaust heat wasted → Combined cycle
Pump losing suction → Check NPSHa ( Must exceed NPSHr )
Cutting fan power → Reduce speed ( Power varies cubed )
Two-stage compression → Intercool at geometric mean

IPPE Item Counts PO

Power Plant Elements 11 items
Power Plant Design 24 items
Industrial Plant Engineering 13 items
Industrial Plant Design 24 items
Refrigeration 10 items
Air Conditioning 18 items
Subject total 100 items, 35% weight
Refrigeration plus AC 28 of 100 items
Industrial plant share 37 of 100 items

Affinity Laws PO

Flow one, head two, power three
Flow: speed^1 Head: speed^2 Power: speed^3 Same impeller diameter

Range vs Approach PO

Range

Hot minus cold water
Set by heat load

Approach

Cold water minus wet-bulb
Set by tower size
Load-driven vs tower-driven

Power Cycles PO

Carnot 1 - TL / TH
Otto 1 - 1 / rk^(k-1)
Brayton 1 - 1 / rp^((k-1)/k)
Diesel Adds cutoff ratio term
Dual cycle Constant volume plus pressure
Rankine Turbine work / heat added
Reheat Cuts turbine exhaust moisture
Regeneration Extraction heats feedwater
Otto versus Diesel Same rk, Otto higher

Ton of Refrigeration PO

One ton is 3.516 kilowatts
3.516 kW 12,000 Btu/hr 211 kJ/min Rate, not quantity

Indicated vs Brake Power PO

Indicated

From pressure-volume card
Includes friction losses

Brake

From dynamometer
Delivered at shaft
Cylinder vs shaft output

Boilers + Steam PO

Boiler efficiency Steam heat / fuel heat
Factor of evaporation Heat absorbed / 2257 kJ/kg
Equivalent evaporation Steam rate x FE
Boiler horsepower 35,322 kJ/hr each
Dulong HHV 33,820C + 144,212(H-O/8) + 9,304S
Rated boiler HP Water-tube: 10 sq ft
Excess air Above stoichiometric requirement
Draft Pressure difference moving gas

Reheat vs Regeneration PO

Reheat

Second turbine expansion
Cuts exhaust moisture

Regeneration

Extraction heats feedwater
Raises cycle efficiency
Blade safety vs efficiency

Engines + Performance PO

Indicated power From P-V indicator card
Brake power From dynamometer torque
Friction power Indicated minus brake
Mechanical efficiency Brake / indicated power
Brake thermal efficiency Brake power / fuel energy
Bmep Brake work / displacement volume
Heat rate Fuel energy / net output
Overall plant efficiency Product of stage efficiencies

NPSHa vs NPSHr PO

NPSHa

System supplies it
Raise by lowering pump

NPSHr

Pump demands it
Fixed by manufacturer
Available must exceed required

Pumps, Fans, Compressors PO

Water power rho g Q H
Pump efficiency Water power / brake power
Net head Gross head minus friction
NPSHa Atmospheric minus vapor, static, friction
Cavitation starts NPSHa below NPSHr
Affinity: flow Varies with speed
Affinity: head Varies with speed squared
Affinity: power Varies with speed cubed
Fan total pressure Static plus velocity pressure
Ideal intercooler pressure Square root of P1 P2

Refrigeration + Air Conditioning PO

1 ton refrigeration 3.516 kW = 12,000 Btu/hr
COP cooling Refrigerating effect / work
COP heat pump COP cooling plus 1
Latent heat of fusion 335 kJ/kg for water
Specific heat, ice 2.093 kJ/kg-K
Sensible heat factor Sensible / total heat
Bypass factor Air leaving coil untreated
Saturated air Dry-bulb = wet-bulb = dew-point
Equal-friction duct method Same drop per length
Comfort drivers Temperature, humidity, air motion

Plant + Safety Metrics PO

Load factor Average load / peak load
Capacity factor Average load / rated capacity
Use factor Output / capacity x hours
Demand factor Maximum demand / connected load
Diversity factor Sum of demands / peak
Injury frequency rate Injuries x 1,000,000 / man-hours
Injury severity rate Days charged x 1,000,000 / man-hours
Cooling tower range Hot minus cold water
Cooling tower approach Cold water minus wet-bulb

MEEBES Item Split MA

Math 32, Chem 12, Thermo 6
Mathematics: 32 items Analytic geometry: 12 Economics block: 15 Fluid mechanics: 4

Nominal vs Effective Rate MA

Nominal

Stated annual rate
Ignores compounding frequency

Effective

True annual yield
12% monthly = 12.68%
Quoted versus actual

Economy Factor Picker MA

Present to future → F/P factor
Future to present → P/F factor
Series to future → F/A factor
Future to series → A/F sinking fund
Series to present → P/A factor
Present to series → A/P capital recovery
Unequal service lives → Annual worth comparison
Rates compound differently → Convert to effective

MEEBES Item Counts MA

Mathematics 32 items 24%
Analytic Geometry 12 items 8%
Economics, Law, Ethics 15 items 14%
Chemistry 12 items 8%
Physics 10 items 10%
Strength of Materials 9 items 14%
Thermodynamics 6 items 12%
Fluid Mechanics 4 items 10%
Subject total 100 items, 35% weight

PME vs ME MA

PME

Signs and seals plans
4 years practice
Any plant size

ME

Passes written MELE
BSME, no experience
Up to 2000 kW
Seals versus supervises

Who May Take Charge MA

Plant 100 to 300 kW → CPM, ME or PME ( Section 34 )
Plant 300 to 2000 kW → ME or PME
Plant over 2000 kW → PME only
Signing plans, specifications → PME only ( Section 35 )
Pressurized piping, 70 kPa → PME signs proposal
Supervising erection, installation → ME or PME
Teaching professional subjects → PME or postgraduate degree
Every additional plant shift → One more licensee

Economy Factors MA

F/P (1 + i)^n
P/F 1 / (1 + i)^n
F/A Uniform series compound amount
A/F Sinking fund factor
P/A Series present worth
A/P Capital recovery factor
Effective rate (1 + r/m)^m - 1
Continuous compounding e^(rn)
Unequal lives rule Compare annual worth

Depreciation Methods MA

Straight line (FC - SV) / n
Sinking fund (FC - SV) x A/F
Sum-of-years digits Accelerated, digit weights
Declining balance Constant rate on book
Double declining Rate = 2 / n
Book value Cost minus accumulated depreciation
Salvage in declining Not subtracted first
Break-even point Fixed / (price - variable)

Strength of Materials MA

Axial deformation P L / (A E)
Hooke's law limit Valid below proportional limit
Thermal deformation alpha L delta-T
Thermal stress E alpha delta-T
Poisson's ratio Lateral / axial strain
Modulus of rigidity G = E / (2(1 + v))
Maximum shear stress Half principal stress difference
Torsional shear T r / J

Thermodynamics + Fluids MA

Ideal gas law P V = m R T
Isentropic relation P V^k = constant
Isothermal work P1 V1 ln(V2/V1)
First law, closed Q = delta-U + W
Enthalpy h = u + P v
Bernoulli head form Pressure + velocity + elevation
Continuity A1 V1 = A2 V2
Reynolds number rho V D / mu
Laminar threshold Re below 2,000
Darcy head loss f L V^2 / (2 g D)

Chemistry + Physics MA

Avogadro's number 6.022 x 10^23 particles
Molar volume, STP 22.4 L per mole
Half-life decay N0 x 0.5^(t / half-life)
Decay constant 0.693 / half-life
Wave relation v = f lambda
Speed of sound 331 + 0.6t m/s
Decibel level 10 log(I / I0)
Reference intensity 10^-12 W/m^2
Sensible heat m c delta-T
Ohm's law V = I R

ME Law + Ethics MA

Governing law RA 8495, year 1998
Three categories PME, ME, CPM
PME experience 4 years after registration
CPM experience 1 year plant practice
Passing rule 70% average, none below 50%
Third failure Wait one year
Rating release Within 15 days
Sealing threshold Piping at 70 kPa
Penalty range P50,000 to P200,000 fine
License renewal Every 3 years
Law block items Law, Code, Ethics: 1 each

Common Traps

Power plant subject misread

Refrigeration and AC: 28 items ≠ Power plant design: 24

Thermo overweighted in MEEBES

Thermodynamics only 6 items ≠ Chemistry carries 12

Law block is small

ME Law: 1 item ≠ Whole law block: 4

Average cannot rescue

70% general average needed ≠ Any 49% still fails

Idler gear confusion

Changes rotation direction ≠ Never changes speed ratio

Weld sized on leg

Throat is 0.707 leg ≠ Leg overstates strength 41%

Radiation temperature units

Stefan-Boltzmann needs absolute ≠ Celsius gives wrong answer

Hoop versus longitudinal

Hoop is pD / 2t ≠ Longitudinal is pD / 4t

Calculator confiscated

Non-programmable, one unit ≠ FX-991ES models banned

Retake wait misread

No wait after first fail ≠ One year after third

Last Minute

1. Weights: 30 / 35 / 35 percent
2. 100 items in each subject
3. Pass: 70% average, none below 50%
4. Three days, 8AM to 2PM
5. Non-programmable calculator, one unit
6. Machine Design alone: 81 items
7. Refrigeration plus AC: 28 items
8. Soderberg yield; Goodman ultimate
9. Euler K: 1.0, 0.5, 0.7, 2.0
10. Fillet weld throat = 0.707 leg
11. 1 TR = 3.516 kW
12. Load factor peak; capacity rated
13. Affinity: flow, head squared, power cubed
14. Range is load; approach is tower
15. PME seals plans; ME supervises
16. Piping at 70 kPa needs PME
17. Third failure = one year wait
18. Idler changes direction, not ratio

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