Engineering Mechanics
Statics, dynamics, strength of materials, vibrations and machine elements: how forces move and deform things.
106 topics: 37 beginner, 35 intermediate, 34 advanced.
About this discipline
Engineering mechanics explains how forces, moments and motion act on bodies. Every bridge, machine and vehicle must be checked for equilibrium, strength and stiffness, so mechanics is where most structural and mechanical design starts.
The course moves from forces on particles and rigid bodies, through stress, strain and beam bending, to vibration, machine elements and advanced analysis such as finite elements and contact mechanics.
Who it is for
Mechanical, civil, aerospace and automotive students, plus designers and technicians who size parts, supports and mechanisms.
How the levels build
Beginner topics cover forces, moments, equilibrium, trusses and kinematics. Intermediate topics cover stress, strain, bending, torsion, deflection and failure. Advanced topics cover vibration, mechanisms, machine design and computational mechanics.
Use cases
- Sizing a bracket, shaft or beam for a required load.
- Checking whether a truss or frame is stable and finding its member forces.
- Predicting the natural frequency of a machine to avoid resonance.
- Estimating the fatigue life of a part that sees repeated loads.
Beginner Engineering Mechanics
Topic 1ForceA push or pull that can change motion or shape; measured in newtons and treated as a vector.Topic 2Newton's lawsInertia, F=ma and action-reaction are the foundation of classical mechanics.Topic 3Mass vs weightMass is the amount of matter; weight is the gravitational force on it, W=mg.Topic 4Free-body diagramsIsolate a body and draw every external force and moment acting on it before writing equations.Topic 5Resolving forces into componentsSplit forces along axes so equilibrium can be solved with simple algebra.Topic 6Equilibrium of a particleA particle is in equilibrium when the vector sum of forces is zero.Topic 7Moment of a forceTendency to rotate about a point, M=F×d.Topic 8CouplesTwo equal and opposite parallel forces produce pure rotation independent of the reference point.Topic 9Equilibrium of rigid bodiesRequires ΣF=0 and ΣM=0 in all directions.Topic 10Supports and reactionsPins, rollers and fixed supports restrict motion and generate specific reaction forces.Topic 11FrictionResists sliding; static friction is up to μsN and kinetic friction is μkN.Topic 12TrussesFrameworks of two-force members that carry only tension or compression.Topic 13Method of jointsSolve truss member forces by applying equilibrium at each pin.Topic 14Method of sectionsCut through a truss and use equilibrium of one part to find specific member forces.Topic 15Centre of gravity and centroidThe point where weight or area can be considered concentrated.Topic 16Distributed loadsLoads spread over length or area are replaced by an equivalent resultant for analysis.Topic 17Frames and machinesStructures with multi-force members solved by dismantling into free bodies.Topic 18Cables and archesFlexible cables carry load by tension in parabolic or catenary shapes.Topic 19Moment of inertia of areaMeasures how area is distributed from an axis; governs bending stiffness.Topic 20Parallel axis theoremI = I_c + A d² shifts a moment of inertia to a parallel axis.Topic 21Kinematics of a particleDescribes position, velocity and acceleration without considering forces.Topic 22Uniform acceleration equationsv=u+at and s=ut+½at² apply for constant acceleration.Topic 23Projectile motionHorizontal motion at constant speed combined with vertical motion under gravity.Topic 24Relative motionVelocity of one object as seen from another, found by vector subtraction.Topic 25Curvilinear motionMotion along curved paths described in normal-tangential or polar components.Topic 26Newton's second law applicationsSum forces along each axis to compute acceleration of connected bodies.Topic 27Work and energyWork is force times displacement; net work equals change in kinetic energy.Topic 28Potential energyStored energy due to position or deformation, such as mgh or ½kx².Topic 29Conservation of energyTotal mechanical energy stays constant when only conservative forces do work.Topic 30PowerThe rate of doing work, P=Fv or P=Tω.Topic 31Impulse and momentumImpulse equals change of momentum; useful for impacts.Topic 32CollisionsMomentum is conserved; elastic collisions also conserve kinetic energy.Topic 33Coefficient of restitutionRatio of separation to approach speed; describes how elastic an impact is.Topic 34Kinematics of rigid bodiesRelates velocities and accelerations of points on a rotating body.Topic 35Instantaneous centre of rotationA point with zero velocity at an instant, simplifying planar motion analysis.Topic 36Rotational dynamicsΣM=Iα is the rotational analogue of F=ma.Topic 37Mass moment of inertiaResistance of a body to angular acceleration, depending on mass distribution.
Intermediate Engineering Mechanics
Topic 38Angular momentumL=Iω is conserved when no external torque acts.Topic 39Gyroscopic effectsA spinning body resists changes of axis, causing precession.Topic 40Rolling motionRolling without slipping couples translation and rotation, v=ωr.Topic 41Circular motion and centripetal forceMoving on a circle requires inward acceleration v²/r.Topic 42Banked curvesTilting the road lets a component of normal force supply centripetal force.Topic 43StressInternal force per unit area; normal stress σ=F/A, shear stress τ=V/A.Topic 44StrainRelative deformation, ΔL/L; dimensionless.Topic 45Stress-strain curveShows elastic region, yield, ultimate strength and fracture of a material.Topic 46Hooke's lawIn the elastic range stress is proportional to strain, σ=Eε.Topic 47Young's modulusThe stiffness of a material measured by the slope of the elastic stress-strain line.Topic 48Poisson's ratioRatio of lateral contraction to axial extension under load.Topic 49Axial deformationδ=PL/AE gives elongation of a bar under axial load.Topic 50Thermal stressConstrained thermal expansion creates stress σ=EαΔT.Topic 51Factor of safetyRatio of failure load to allowable load; accounts for uncertainty.Topic 52Shear and torsionTwisting a shaft causes shear stress τ=Tr/J and angle θ=TL/GJ.Topic 53Power transmission shaftsShaft diameter is chosen to carry torque with limited shear stress and twist.Topic 54Shear force and bending moment diagramsPlots of internal V and M along a beam used to find critical sections.Topic 55Bending stressThe flexure formula σ=My/I gives stress distribution in a beam.Topic 56Section modulusS=I/c; larger values mean a beam resists more moment for a given stress.Topic 57Beam deflectionFound by integrating EI y''=M or by tables and superposition.Topic 58Statically indeterminate beamsNeed compatibility of deformations in addition to equilibrium.Topic 59Shear stress in beamsτ=VQ/Ib varies across the section, peaking near the neutral axis.Topic 60Combined loadingSuperpose axial, bending, shear and torsion stresses at critical points.Topic 61Mohr's circleA graphical method to transform stresses and find principal stresses.Topic 62Principal stressesMaximum and minimum normal stresses on planes where shear stress is zero.Topic 63Thin-walled pressure vesselsHoop stress pr/t is twice the longitudinal stress pr/2t in a cylinder.Topic 64Failure theoriesTresca and von Mises criteria predict yielding under multiaxial stress.Topic 65Buckling of columnsSlender members fail by instability at Euler load π²EI/(KL)².Topic 66Strain energyEnergy stored in deformed material; used in impact and deflection methods.Topic 67Stress concentrationHoles and notches raise local stress by a factor Kt.Topic 68FatigueRepeated cyclic loading causes cracks at stresses below yield; described by S-N curves.Topic 69Fracture mechanicsPredicts crack growth using stress intensity factor K and fracture toughness.Topic 70CreepSlow permanent deformation under steady load at high temperature.Topic 71Plasticity and yieldingBeyond yield, deformation is permanent and requires plastic analysis.Topic 72Residual stressStresses that remain in a part without external load, from welding or machining.
Advanced Engineering Mechanics
Topic 73Simple harmonic motionRestoring force proportional to displacement gives sinusoidal motion x=A cos(ωt).Topic 74Mass-spring systemNatural frequency ω=√(k/m) sets how fast it oscillates.Topic 75Damped vibrationEnergy loss reduces amplitude; damping ratio ζ determines the response type.Topic 76Forced vibrationA driven system responds with amplitude depending on frequency ratio and damping.Topic 77ResonanceLarge amplitude when excitation frequency matches the natural frequency.Topic 78Vibration isolationSoft mounts reduce transmitted force when driving frequency is well above natural frequency.Topic 79Multi-degree-of-freedom systemsHave several natural frequencies and mode shapes found by eigenvalue analysis.Topic 80Modal analysisDecomposes complex vibration into independent modes.Topic 81Balancing rotating machineryAdding or removing mass cancels unbalanced forces that cause vibration.Topic 82Critical speed of shaftsRotational speed that matches a lateral natural frequency and causes whirl.Topic 83Mechanisms and linkagesAssemblies of rigid links that transform motion, such as four-bar linkages.Topic 84Degrees of freedomGruebler's equation counts independent coordinates needed to define a mechanism position.Topic 85Cams and followersCam profile produces a prescribed follower motion.Topic 86GearsTransmit rotation with fixed ratio; involute teeth maintain constant velocity ratio.Topic 87Gear trainsCombinations of gears give large ratios; planetary trains offer compact high reduction.Topic 88Belt and chain drivesTransmit power between distant shafts with flexible elements.Topic 89BearingsSupport rotating shafts; rolling-element and journal types trade friction, load and life.Topic 90SpringsStore energy elastically; helical spring rate k=Gd⁴/8D³N.Topic 91Fasteners and bolted jointsPreload clamps parts together; fatigue and tightening torque are critical.Topic 92Welded jointsPermanent joints analysed for shear in the throat of the weld.Topic 93Clutches and brakesUse friction to connect shafts or dissipate kinetic energy.Topic 94FlywheelsStore rotational energy to smooth speed fluctuation.Topic 95Machine design processDefine requirements, select concepts, analyse, iterate and validate against standards.Topic 96Tolerances and fitsAllowed dimensional variation determines clearance, transition or interference between parts.Topic 97Engineering drawingsStandardised projections, dimensions and symbols communicate design intent.Topic 98CAD and parametric modellingComputer models driven by dimensions and constraints that update automatically.Topic 99Finite element analysis in mechanicsNumerically solves stress and deformation in complex geometry.Topic 100Topology optimisationAlgorithms remove material from low-stress regions to find lightweight structures.Topic 101Lagrangian mechanicsDerives equations of motion from energy using generalised coordinates.Topic 102Hamiltonian mechanicsReformulates dynamics in terms of position and momentum, useful in advanced analysis.Topic 103Multibody dynamicsSimulates systems of rigid or flexible bodies connected by joints.Topic 104Contact mechanicsStudies stresses where bodies touch, as in Hertzian contact of gears and bearings.Topic 105Fatigue life predictionMiner's rule sums damage ratios of load cycles to estimate remaining life.Topic 106Nonlinear finite element analysisHandles large deformation, plasticity and contact by iterative load stepping.
Frequently asked questions
What is Engineering Mechanics?
Statics, dynamics, strength of materials, vibrations and machine elements: how forces move and deform things.
How many topics are in Engineering Mechanics?
106 topics, ordered from beginner to advanced: 37 beginner, 35 intermediate and 34 advanced.
Where should a beginner start in Engineering Mechanics?
Start with "Force" and work through the list in order. Each topic builds on the one before it.
What is the most important habit in mechanics?
Draw a clear free-body diagram before writing any equation. Most wrong answers come from missing or wrong forces, not from the algebra.
Why do stress and strain both matter?
Stress is the internal force per area that the material carries, and strain is how much it deforms. Strength limits relate to stress, while stiffness and deflection relate to strain.
What is the difference between yield and failure?
Yield is the start of permanent deformation. Failure can mean fracture, buckling or excessive deflection, depending on the design criterion used.
When do I need a computer model?
Use hand methods for simple members and checks. Use finite element analysis for complex geometry, contact or nonlinear behaviour, and always verify it with a simple check.
Why does vibration matter in everyday machines?
Any part with mass and stiffness can vibrate. If an excitation frequency matches a natural frequency, amplitudes grow and fatigue or noise can follow.
Practise in the interactive course with quizzes, tests and labs.