⚙️ Stuff Every Engineer Should Know: Training Guide

The SI system and its constants

The International System of Units rests on 7 base units. Every other unit, such as the newton or volt, is built from those seven by multiplication and division. NIST lists 22 derived units with special names and symbols.

After the 2018 vote, the kilogram is defined by the Planck constant, a constant of nature. The old metal cylinder was called Le Grand K. Because the SI fixes the Planck constant exactly, it no longer has measurement uncertainty.

Since the 2019 redefinition, the ampere is defined by fixing the elementary charge. One ampere equals one coulomb per second. This ties current to counting electric charges rather than the force between wires.

Prefixes and derived units

SI prefixes scale units by powers of ten. Capital M means mega, one million. Lowercase m means milli, one thousandth. Capital and lowercase symbols cannot be swapped without a billion times error.

Micro uses the Greek letter mu and means one millionth. Small prefixes step by a factor of a thousand: milli is one thousandth, micro one millionth, nano one billionth.

Derived units combine base units. One newton is one kilogram meter per second squared. A joule is a newton moved through one meter. A watt is one joule per second. A pascal is one newton per square meter.

Measurement quality and mistakes

Significant figures tell how carefully a measurement was made. Leading zeros are never significant. A trailing zero after a decimal point is significant. Writing 4.50 times ten to the minus 3 meters shows three significant figures clearly.

Accuracy is closeness to the true value. Precision is how closely repeated readings agree. A scale that always reads about 5.21 kg for a true 6.00 kg mass is precise but not accurate.

A tolerance is the limit of allowable error from the true value. A dimension of 25.00 mm plus or minus 0.05 mm passes from 24.95 to 25.05 mm. NIST Handbook 44 gives model tolerances for commercial scales and fuel dispensers.

Mass, weight, and unit mixups

Mass is the amount of matter and does not change with location. Weight is the gravitational force on that mass and is measured in newtons. On the Moon, a 5.0 kg wrench keeps its mass but its weight drops.

In US engineering statics, pounds usually mean pounds-force. The unit of mass in that system is the slug. A 100 lb object has a mass of about 3.1 slugs.

The Mars Climate Orbiter was lost in 1999 because ground software used pound-seconds while navigation software expected newton-seconds. One pound-force is about 4.45 newtons, so the thruster effects were off by about that factor.

Equilibrium and free-body diagrams

Statics studies objects that do not accelerate. For an object at rest, F equals ma becomes the sum of forces equals zero, and the sum of moments equals zero. Zero net force can mean constant velocity, not only rest.

A free-body diagram shows one isolated body and the forces acting on it. You cut the body free and replace each support or contact with the force it applies. Forces the body exerts on other things belong on other diagrams.

If a force's line of action passes through the pivot, its moment about that pivot is zero. You can slide a force along its line of action without changing its moment.

Moments and torque

Torque equals force times the perpendicular distance from the pivot to the line of action. Its SI unit is newton meter, written N m, not newton per meter. Pushing a door far from the hinges gives more torque.

In static equilibrium, you may sum moments about any point you choose. Engineers often pick a point where unknown forces act, so those unknowns drop out. Different pivot choices must give the same final answers.

Dry friction

For most material pairs, static friction is larger than kinetic friction. A heavy box is hardest to push just before it moves. Dry steel on steel has static about 0.6 and kinetic about 0.3.

The basic dry friction model says friction equals coefficient times normal force. Wider contact area does not increase friction force. Friction coefficients have no units because they are a ratio of two forces.

Rubber on dry concrete has a static friction coefficient of about 1.0. Ice on ice is near 0.1 and Teflon on steel about 0.04.

Stress, strain, and stiffness

Stress is force per unit area. Strain is the change in length divided by original length, so strain is dimensionless. Small strains are often written as microstrain.

Young's modulus measures stiffness: stress per unit strain. Steel is about 200 GPa, aluminum about 70 GPa, concrete about 20 GPa, and hardwood about 15 GPa.

Hooke's law is F equals negative k times x. The spring constant k has units of newtons per meter. The law only holds up to the proportionality limit.

Past the elastic limit, a metal part stays permanently deformed when unloaded. Below the elastic limit it springs back. A paper clip bent repeatedly shows plastic deformation.

Beam bending and sections

A simply supported beam with a load in the middle sags. The top fibers get shorter in compression and the bottom fibers get longer in tension. Brittle materials crack from the bottom tension side first.

For a homogeneous beam in simple bending, normal bending stress is zero at the neutral axis, which passes through the cross-section's centroid. Stress changes sign across the neutral axis from tension to compression.

An I-beam puts most material far from the bending axis. The flanges carry much of the bending stress and the web separates them and carries shear.

Bending stiffness of a rectangular section follows b times h cubed. Turning a 1 by 1/8 inch ruler on edge makes it 64 times stiffer than bending it flat.

Trusses, columns, and fatigue

A pinned triangle cannot change shape without a member stretching or shortening. Planar trusses are built from triangular subunits. Space trusses use the tetrahedron.

In an ideal pin-jointed truss, each member is a two-force member carrying only axial tension or compression. Real welded or bolted trusses still follow this model closely.

Slender columns in compression fail by buckling. Euler's formula has length squared in the denominator, so halving the length quadruples the critical load. Bracing a column at its midpoint has the same effect.

Fatigue can break a part that never sees a load above yield strength because damage builds over many repeated cycles. Fatigue surfaces often show concentric beach marks.

Many steels (ferrous alloys) have a fatigue endurance limit below which fatigue failure is not expected. Aluminum's S-N curve keeps falling, so designers choose a specified fatigue life instead.

Reinforced concrete and design factors

Ordinary concrete is much stronger in compression than in tension. Steel reinforcing bars are placed where bending creates tension, so the two materials share the work.

NASA's structural standard sets a minimum ultimate design factor of 1.4 for metallic spaceflight structures. A design factor multiplies the limit load, the largest expected service load.

Material property comparisons

Steel is the stiffest common structural metal with an elastic modulus about 30 Msi. Titanium is about 16 Msi and aluminum about 10 Msi. Stiffness means less deflection under the same stress.

Aluminum is the least dense of aluminum, titanium, and iron. Titanium sits between aluminum and iron, so an equal-size titanium part weighs about 60 percent more than an aluminum one.

Titanium is attractive for demanding structures and implants because it combines strength, low density, and corrosion resistance. It is also biocompatible.

Ductile materials show visible stretching before fracture. Brittle materials fracture with little plastic deformation. Percent elongation measures ductility.

Yield strength marks the onset of specified permanent deformation. Ultimate tensile strength is the maximum resistance on an engineering stress-strain curve. Necking can begin near ultimate tensile strength.

Hardness describes resistance to indentation, scratching, and local plastic deformation. Hardness is not the same as stiffness or toughness. Brinell, Rockwell, and Vickers are common tests.

Corrosion, heat treatment, and thermal effects

Corrosion is deterioration through environmental interaction. Control methods include coatings, material selection, environmental control, and electrochemical protection.

Galvanic corrosion occurs when dissimilar metals contact each other in an electrolyte. The more active metal becomes the anode and corrodes faster. Insulating the metals can break the electrical path.

Thermal expansion causes length change equal to expansion coefficient times original length times temperature change. If expansion is restrained, the temperature change can create substantial stress.

Faster quenching of steel usually produces higher hardness but less ductility. Quenched steel is often tempered afterward to reduce brittleness and internal stress. Annealing softens and relieves stress.

Welding can distort a metal assembly even after it cools because local thermal expansion and contraction leave internal stress. Fixtures, balanced weld sequences, and post-weld treatment can reduce distortion.

Polymers and composites

Thermoplastics can usually be softened, reshaped, and reprocessed by heating. Thermosets cannot be melted and remolded once cured because their polymer chains are crosslinked.

In a unidirectional fiber composite, stiffness and strength are greatest along the fibers. Designers align fibers with expected loads. A laminate can stack plies at angles to carry loads in more directions.

Manufacturing processes

Machining is a subtractive process because it cuts material away. Turning, drilling, milling, and grinding shape parts by removing chips or particles.

Casting shapes metal by pouring it molten into a mold. The mold cavity defines the geometry as the liquid cools. Shrinkage and solidification defects must be considered.

Forging shapes heated solid metal through repeated deformation. The deformation can refine and orient the grain structure along the part.

Additive manufacturing adds material layer by layer from a digital model. It can use metals, polymers, or ceramics and create complex internal features.

Computer numerical control directs tool motion from programmed instructions. Common CNC machines include mills, lathes, routers, grinders, and electrical discharge machines.

Geometric dimensioning and tolerancing communicates controlled geometric variation. A datum establishes a reference from which form, orientation, and location can be controlled and measured.

Loads, foundations, and retaining walls

Dead load is a structure's own permanent weight. Live load includes occupants and movable furniture. Wind creates pressure and suction on surfaces. For the same ground acceleration, a heavier structure develops greater earthquake inertia force.

When weak near-surface soil cannot support a heavy structure, a deep foundation may be needed. Piles transfer load by tip bearing, shaft friction, or both. Deep foundations do not guarantee zero settlement.

A retaining wall must resist lateral pressure from retained soil. Lateral earth pressure usually increases with depth because overlying soil weight increases.

Drainage placed behind many retaining walls reduces water pressure behind the wall. A weep hole alone does not guarantee a fully drained wall if filters or drainage paths clog.

Bridge types and expansion joints

A beam bridge uses horizontal beams carried by vertical supports. Loads bend the beams. Intermediate piers shorten each span and reduce beam bending demands.

An arch bridge mainly carries its load along the arch to the end supports. The end supports must resist outward horizontal thrust. Stone and unreinforced masonry suit arches because they work well in compression.

A cable-stayed bridge connects inclined cables directly from the deck to towers. The tower carries large compression and the stays carry tension.

A suspension bridge hangs its roadway from main cables that pass over towers. Vertical suspenders connect the deck to curved main cables. The cables pull on massive anchorages.

Expansion joints accommodate bridge movements from thermal expansion and contraction. Bridge bearings often work with joints by allowing rotation or translation at supports.

Road geometry

A straight road surface is often crowned or cross-sloped to shed rain toward the edges. Too little crown encourages ponding and excessive crown can worsen erosion and vehicle stability.

On a curve, the outside edge of a road is often raised. This banking helps counter lateral acceleration. The chosen slope balances speed, radius, friction, climate, and slow traffic.

Lessons from failures

The first Tacoma Narrows Bridge failure taught designers that aeroelastic flutter can amplify torsional motion. Engineers now use wind-tunnel testing, torsional stiffness, and damping.

In the Hyatt Regency walkway collapse, a changed hanger arrangement made the fourth-floor walkway support the second-floor walkway. A shop-detail change can alter the load path and demands full engineering review.

The Citicorp Center weakness was exposed by wind striking at an angle, which the original checks missed. Construction had substituted bolted brace joints for welded joints. The case teaches checking plausible load cases beyond minimum code assumptions.

Circuit laws, AC, and DC behavior

Kirchhoff's junction rule says currents entering a junction equal currents leaving. It follows from conservation of charge. The loop rule says voltage rises and drops around a closed loop sum to zero, from conservation of energy.

Conventional current flows opposite to electron motion in a metal. Electrons drift very slowly, a fraction of a millimeter per second, but the electrical signal appears instantly because the wire is already full of free charges.

US wall outlets are 120 V AC RMS. The actual peak swings to about 170 V because peak equals RMS times the square root of 2.

A capacitor behaves like an open circuit in steady DC after charging. AC keeps charging and discharging it, so AC gets through. Inductive reactance increases with frequency, while capacitive reactance decreases with frequency.

In an AC circuit with only a capacitor, current leads voltage by 90 degrees. In an inductor, voltage leads current. The memory trick is ELI the ICE man.

An empty capacitor charging through a resistor reaches about 63 percent of full charge after one time constant, tau equals R times C. After about five time constants it is over 99 percent full.

Transformers, motors, and power systems

Faraday's law says induced voltage equals the number of turns times how fast magnetic flux changes. Lenz's law says the induced current opposes the change in flux that made it.

An ideal transformer steps voltage up or down by its turns ratio. Steady DC on a transformer primary produces no sustained secondary voltage, only a brief pulse during switching. Without a changing flux, the primary winding may overheat.

Power companies use very high voltage for long distance transmission because the same power needs less current, and line heating loss grows with current squared. HVDC is used today for sending power long distances.

North America's grid runs at 60 Hz and Europe at 50 Hz. If electricity use suddenly exceeds generation, the grid frequency drops. Three-phase power uses three voltages 120 degrees apart.

A simple DC motor draws the most current when switched on but not yet turning because back emf is zero. Motors and generators have the same basic construction.

In US manufacturing, machine drives use about half of delivered electricity. Most of those drives are electric motors.

Batteries and safety

A 1C rate means the current that drains the whole battery in one hour. For a 100 amp-hour battery, 1C is 100 amps. Discharging at a much higher C-rate reduces the amp-hours you get out.

Specific energy in Wh/kg indicates range for a given weight. Specific power in W/kg indicates maximum power per kilogram. Depth of discharge of at least 80 percent counts as deep discharge.

In a working battery, electrons flow through the outside circuit and ions travel through the electrolyte inside the cell. In a lithium-ion cell the ions are lithium ions.

A GFCI outlet trips when current going out and coming back differs by about 5 milliamps. It does not protect from holding two hot wires at once because the current out still equals current back. Always shut off the breaker and test before touching wiring, even on GFCI circuits.

Copper wire resistance goes up as it gets hotter because more atomic collisions slow electrons. Some materials become superconductors with zero DC resistance when cooled enough.

Silver has the lowest electrical resistivity at room temperature. Copper is used for wiring because it is nearly as good and cheaper. Gold resists corrosion on connector contacts.

Electronics and digital signals

The first working transistor at Bell Labs in 1947 was made from germanium using point contacts. It amplified an input signal up to 100 times.

Jack Kilby demonstrated the first working integrated circuit in 1958 at Texas Instruments. Robert Noyce separately developed a silicon IC soon after.

Gordon Moore revised his prediction in 1975 to chip density doubling every two years. The first microprocessor, Intel's 4-bit 4004 from 1971, had about 2,300 transistors.

MOSFET stands for metal, oxide, semiconductor. CMOS pairs n-channel and p-channel transistors and uses nearly zero power in standby, which made it dominant.

Silicon replaced germanium as the main transistor material because silicon works at much higher temperatures and leaks less current when off.

A NAND gate is universal. From NAND alone you can build NOT, AND, and OR, so NAND can build any Boolean function.

To capture sound up to 20,000 Hz digitally, the sampling rate must be more than 40,000 per second. Frequencies above the Nyquist frequency fold back as fake lower frequencies, so a low-pass filter removes them before sampling.

Fluid statics and buoyancy

Pressure is normal force divided by area. Its SI unit is the pascal, equal to one newton per square meter. The same force produces more pressure on a smaller area.

For a constant-density liquid, pressure rises with depth by rho g h. Deeper points support more fluid above. Container shape does not enter the result.

Pascal's principle says an enclosed fluid transmits a change in pressure undiminished. In a hydraulic system, an output piston with five times the input area produces five times the force, ignoring friction and height differences.

Archimedes' principle says buoyant force equals the weight of displaced fluid. An object floats when its average density is lower than the surrounding fluid. A steel ship floats because its average density includes enclosed air.

Fluid dynamics and pumps

In steady incompressible flow, a pipe that narrows makes the fluid speed up. The same volume must pass each cross-section per second.

Along a level Bernoulli streamline, higher fluid speed means lower static pressure. The simple Bernoulli equation assumes incompressible and frictionless flow.

Reynolds number compares inertial effects with viscous effects. Tube flow below about 2000 is laminar, above about 3000 is turbulent, and 4000 is clearly turbulent. Turbulent flow contains eddies and mixing.

Dynamic viscosity measures a fluid's resistance to shearing flow. In laminar Poiseuille flow, flow rate is proportional to radius to the fourth power, so halving radius reduces flow to one-sixteenth.

A centrifugal pump accelerates fluid with an impeller. A positive-displacement pump moves a nearly fixed volume per cycle, so its flow follows speed. Because a blocked outlet can rapidly raise pressure, positive-displacement systems commonly need relief protection. Cavitation starts when pressure drops below vapor pressure.

Heat transfer

Conduction moves heat through direct physical contact. Convection requires bulk motion of a fluid. Thermal radiation can cross a vacuum and travels as electromagnetic waves.

Insulation R-value measures thermal resistance. It depends on both the material and its thickness. Thermal conductance is the inverse of thermal resistance when units are consistent.

Thermodynamics and efficiency

A large electric motor typically converts input energy into useful work more efficiently than a gasoline engine. An EV turns over 77 percent of grid energy into power at the wheels, while a gasoline car converts about 12 to 30 percent.

The zeroth law says if A is in thermal equilibrium with B and with C, then B and C share a temperature. Thermal equilibrium means no net heat transfer.

The first law with work W done by a system says internal energy change is Q minus W. The second law says heat cannot flow spontaneously from cold to hot. The third law says absolute zero cannot be reached in a finite number of steps.

Heat engine thermal efficiency is work output divided by heat input. The Carnot efficiency between reservoirs at temperatures Th and Tc is 1 minus Tc/Th, using absolute temperatures. No real engine can exceed this limit.

A heating heat pump's coefficient of performance is heat delivered divided by work input. It can exceed one. In a refrigerator, refrigerant absorbs heat in the evaporator while vaporizing.

Simple machines and gear ratios

Mechanical advantage is output force divided by input force. An MA of 5 means an input force of 1 unit produces 5 units of output force. In an ideal machine, the input point moves 5 times farther.

For an ideal pulley system, mechanical advantage is roughly the number of cable segments supporting the load. A single fixed pulley has an MA of 1 and only changes direction.

A 12-tooth motor gear driving a 36-tooth wheel gear has a gear ratio of 3. Output torque triples and rotational speed drops to a third. Real gears lose a little to friction.

Four-stroke engine cycle

A four-stroke engine cycle is intake, compression, power, and exhaust. Four piston strokes require two crankshaft revolutions. Gasoline engines ignite with a spark, while diesel engines inject fuel into hot compressed air.

Control systems

A closed-loop control system uses output feedback. It senses the process variable and adjusts an actuator, letting it respond to disturbances and model errors that an open-loop command cannot see.

The setpoint is the desired process value. The process variable is what the sensor measures. Their difference is the control error used to calculate corrective action.

PID terms use present, accumulated, and changing error. Proportional reacts to current error, integral accumulates past error, and derivative responds to its rate of change.

Engineering practice and safety

Engineering design is iterative rather than a straight line. Engineers compare concepts with requirements, constraints, risks, and stakeholder needs, then revise when analysis or testing exposes a mismatch.

Verification checks compliance with specified requirements. Validation checks whether the product actually serves its intended purpose in a realistic operating environment.

Two redundant components can still fail together if they share one vulnerability, called a common-cause failure. Redundancy helps only when backup paths are sufficiently independent.

The first NSPE fundamental canon puts public safety, health, and welfare above other engineering interests. Engineers should notify appropriate parties if their judgment is overruled in circumstances endangering life or property.

The Challenger investigation identified a solid rocket motor joint pressure-seal design sensitive to temperature. It also found flawed communication and decision processes, showing technical warnings must reach decision-makers clearly.