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GERTC Review Lectures
GERTC Review Lectures
Course 1
Course 1
Application of Trigonometry and Geometry to Engineering MechanicsRight triangleGeneral triangleAnglesForce componentsUsing calculator COMPLEX MODEApplication to problems involving cylinder inside a binApplication to varying loadApplication to trusses/transmission towerPlane AreasIntroduction to Engineering MechanicsStaticsScalar and Vector QuantitiesResultant of ForcesParallel ForcesConcurrent Forces
Properties of FluidsDensity and Specific VolumeSpecific GravityUnit weightBulk Modulus of ElasticityCompressibilityIdeal GasViscosityCapillarityUnit Pressures (Absolute, Gage, Atmospheric)Principles of HydrostaticsPascal's LawAbsolute and Gage PressureVariations in PressureManometersIdeal Gas Law
Introduction to TrigonometryAnglesCartesian/Rectangular Coordinate SystemAngles in Standard PositionApplicationsTrigonometric IdentitiesTriangles and ApplicationsProperties of Triangles and examples
Introduction to MSTECalculator functions (Mode 1 to Mode 8) with practical application.Mode 1: General CalculationMode 2: ComplexMode 3: StatisticsMode 4: Base-NMode 5: EquationMode 6: Matrix (Mode 7 in Canon)Mode 7: Table (Mode 6 in Canon)Mode 8: Vector
Resultant of Concurrent ForcesMoment of ForcesDistributed LoadsResultant of Parallel and Non-concurrent ForcesResultant of Non-Parallel and Non-Concurrent ForcesEquilibrium of ForcesSupport ReactionsEquilibrium of Two forcesEquilibrium of Three or More Concurrent and Coplanar ForcesForce Polygon
Course 2
Course 2
Equilibrium of Concurrent forces - ExamplesEquilibrium of Non-Current forces - ExamplesTwo-Force Members - ExplainedSimple StressTensile , Compressive , Shearing , Bearing StressSimple StrainStress-Strain DiagramActual and Allowable StressesAxial DeformationDeformation due to Self-WeightThermal StressCoefficient of Thermal Expansion
Steel Design BasicsReview on Simple StressBolts, Nuts, Washers, and ThreadTensile, compressive, shearNet and Gross AreaBlock shear
Hydrostatic Forces on Plane SurfacesExample 1Example 2Example 3Example 4Example 5Example 6Example 7Hydrostatic Forces on Curved SurfacesExample 1Example 2Example 3Example 4Example 5Gravity DamAnalysisExample 1 - Triangular dam
Laws of Exponents and RootsExample 1Example 2The nth Root of a numberLaw of RadicalsExample 1Example 2LogarithmsExample 1Example 2Algebraic ExpressionsTermsDegreeComputation with Algebraic ExpressionsExample 1Example 2Example 3Example 4Example 5Example 6Example 7ProductExample 1Example 2FactoringExamples 1Examples 2GCF, HCF, LCMExample 1 - GCFExample 2 - LCM
Recap of Lecture 1TrianglesMediansAltitudeAngle BisectorPerpendicular BisectorsEuler LineSpherical TriangleRight TriangleOblique TriangleTerrestrial SphereAreaExamples
Course 3
Course 3
Worked Examples:Allowable Stress / Simple StressColumnBolt and WasherCablesBeam Supported by CableDouble-T Angle ConnectionBillboardThin-Walled Pressure VesselAxial DeformationSteel TireSteel CableDue to Self-WeightThermal Stress
Functions and Graph (Range, Domain)ExamplesRemainder and Factor TheoremsLinear Equations and InequalityQuadratic FunctionsQuadratic Equations and InequalityCubic Equations and InequalityThe Rational Zero Theorem
Thin-Walled Pressure VesselsSpherical ShellCylindricalExample 1Example 2Example 3 - Spacing of HoopsExample 4 - Spherical shellExample 5 - HoopsExample 6 - Hoops Example 7 - HoopsBuoyancy (Archimedes' Principle)Example 1Example 2Example 3Example 4Example 5Example 6Example 7Example 8Example 9Example 10Stability of Floating Bodies (Metacenter and Metacentric Height)Example 1
Welded ConnectionAllowable Stress Design (ASD)Load and Resistance Factor Design (LRFD)NSCP Provision for Steel ConnectionsLoad CombinationsDesign of Tension MembersGross and Net areasStaggered HolesShear Lag FactorsExamples
TraverseBearings/AzimuthsLatitude and DeparturesMissing DataArea of Closed TraverseUsing TrianglesUsing DMD MethodUsing DPD MethodArea by Setting a Point Inside a Closed TraverseDividing lines
Course 4
Course 4
Simple Stress Problems (Hankinson's Formula)Axial Deformation ProblemsHeavy MoldingPrecast Concrete Slab Supported by CablesBeam Pinned at One End and Cable Support at the Other EndTimber Member Subject to Three Axial LoadsDeflection of TrussStatically Indeterminate Problems (axial load)Steel Tube Filled with ConcreteSlab Supported by Three CablesStraight Bar Fixed at Both EndsLoad Supported by Three Steel RodsLoad Supported by Three Rods and a Rigid BarStress at an Inclined Plane (Mohr Circle)
Bolted Connection (LRFD NSCP 2015)Bolt BearingBlock ShearExample - Lap Joint with Nine BoltsEccentrically Loaded ConnectionExampleUsing MODE 3-2
Rational Equations - ExamplesRadical Equations - ExamplesSimultaneous Linear EquationsPartial Fraction Decomposition - ExamplesCase ICase IICase III
Traverse (Subdivision)Triangulation ExamplesTriangulation StationsTwo Intervisible PointsSounding BoatPractice ProblemsPlane GeometryTrianglesCircles (Theorems of Circle)Sector, Arc, etcCircle Inscribed in a TriangleCircle Circumscribed About a TriangleCircle Escribed About a TriangleExamplesArea of Inner TriangleArea of Equilateral Triangle with a Given Point InsideArea of Corner LotThree Circles Tangent ExternallyTwo Circle Tangent Internally to a Third CircleLength of Cross BeltMaximum Area the Goat can Cover
Relative Equilibrium of LiquidsHorizontal MotionExamplesForce Acting on the Side of the TankRequired Accelerating ForceTotal force at the Bottom of the TankWater Remaining in the TankInclined MotionExample 1Example 2Vertical MotionExample 1Example 2Rotating VesselExample 1
Course 5
Course 5
State of Plane StressThin-walled vessels (Mohr Circle)Triaxial Test (Application)Examples:Element subject to stresses presented by Mohr CircleBar subjected to uniaxial forceOpen tank subject to fluid pressure and axial forceClosed tank subject to internal pressure and axial forceGiven an element subject to normal and shearing stressesShear and Moment in Beams (Internal forces in beams)Examples:Beam subject to axial, shear, torque, and bendingFinding the internal forces a a particular section of a horizontal beamFinding the internal forces a a particular section of an inclined beamInternal forces on a section of a frameBeam with an applied moment
IntroductionPoints of Intersection of Linear and quadratic curvesCirclePoints and SegmentsTriangle (Centroid, Area, etc)Straight Lines
Plane Geometry (Examples)Two perpendicular chords of a circle dividing the circle in 4 partsTwo lines tangent to a circle (2 examples)Two intersecting secants of a circleArea of swimming pool made of overlapping circlesCommon chord of intersecting circlesDistance between men walking on a circular trackHeight of Mayon Volcano and the smokeApplication to fluid Forces on circular SurfacesQuadrilateralsCyclic QuadrilateralsPolygonsExample 1Example 2Example 3 - A farmer owns two square lots..Example 4 - Folded rectangleExample 5 - Building site in the form of a quadrilateralExample 6 - Quadrilateral inscribed in a circle
Bolted Connection (Eccentric Load)Welded Connection (Eccentric Load)Calculator shortcutExample - Eccentrically loaded weld2015 NSCP Provisions on WeldsExampleWeld Strength
Rotating Vessel ExamplesOpen cylindrical tank 1Open cylindrical tank 2Open cylindrical tank 3Rotating tube 1Rotating tube 2Rotating bucketRotation of closed cylindrical tank more than half full of waterRotation of closed cylindrical tank filled with waterFundamentals of Fluid FlowLaminar/Turbulent FlowExample 1Example 2Example 3Example 4Energy and HeadBernoulli's Equation
Course 6
Course 6
Cylindrical Tank (Mohr Circle)Shear and Moment in BeamsCurved BeamsShear and Moment Equations and DiagramsProperties of Shear and Moment DiagramsCantilever BeamsSimple BeamsExample 1 - Simple beam with uniform and concentrated loadExample 2 - Simple beam with overhangExample 3 - Simple beam with overhang and applied momentExample 4 - Beam with fixed end and internal hingeExample 5 - Concrete Pad with two equal uniform loadExample 6 - Concrete pad subject to unequal uniform load Example 7 - Pick up point (2 pick-points) of precast concrete pileExample 8 - Single pick-up point - concrete pile
Eccentrically loaded welded connectionAxially loaded Members(Columns) (2001 and 2015 NSCP)Slenderness Limits and Effective LengthAlignment ChartExample 1 - Column hinged at both ends Assumptions of alignment chartSidesway inhibited vs. uninhibitedThe ratio G in the alignment chartColumn reduction factorExample 2 - Alignment chartExample 3 - Alignment chart two storey moment frame assuming inelastic behavior Flexural Members (Beams)Bending planesBuckling of Compression FlangeClassification of SectionsAllowable bending stress (2001 NSCP)Example 4 - Simple beamExample 5 - Laterally supported beam
Examples:Cyclic Quadrilaterals (Ptolemy’s Theorem)Area of quadrilateralQuadrilateral inscribed in a semi-circleIrregular four-sided figure inscribed in a circleQuadrilateral circumscribed about a circleParabolic Segment and spandrel of parabolaSpandrel of parabola 1Spandrel of parabola 2Regular PentagonScale of a mapRegular hexagon 1Regular hexagon 2Regular five-pointed starOctagonal lot divided into two
Distance from a Point to a LineExamplesDistance of point to a lineCircle tangent to a lineLine bisecting given two linesDistance Between Parallel LinesExamplesDistance between two linesAngle Between LinesExampleAngle between two linesLine bisecting the acute angle between given two linesCircles and linesExampleLength of line tangent to a circleLength of tangent lineRadical axis of circlesLine passing through points of intersection of two circlesEquation of curve connecting the centers of circlesLocus of center of circles tangent to y-axis and another circle
Bernoulli’s Energy TheoremEnergy and Hydraulic GradelinesPower and efficiencyExamples:Pipe with pump 1Pipe with pump 2Pipe with turbineLarge tank with compressed airWater issuing a nozzleReynold’s NumberVelocity distribution in pipesShear stress in pipe wallShear/friction velocityHead Losses in PipesMinor/Major LossesExample 1Example 2 - Moody DiagramExample 3 - Syringe
Course 7
Course 7
Shear and moment in beams examplesSimple beam with cableLinearly varying load (triangular)Linearly varying load (trapezoidal)Given shear diagram 1Given shear diagram 2Parabolically varying loadMoving loadsSingle moving LoadTwo and more moving loadsExampleTwo moving loadsThree moving loadsInfluence lines in beamsApplicationH loading crossing a beam with overhang
Conic sectionsParabola and examplesEquation given vertex and latus rectumFinding the elements given equation of parabolaPlotting parabolasEllipse elements and examplesGiven center, eccentricity and focusElements of ellipse from given general equationHyperbola elements and examplesEquation and elements from given center and lengths of axesElements of hyperbola from given general equation
Solid Geometry FormulasPrisms / Pyramids/frustum / Cones/frustum /Spherical segments/sectors/ CylindersExamplesSpider and flyPentagonal prismBlock of wood with surface painted blueSwimming pool with sloping bottomTruncated prismCylinder with inclined axisCylindrical boiler made from metal sheet of known areaWater from from big to small tankTriangular troughConcrete block placed inside a water tankClosed tank partially filled with waterCone formed from a sector of a circleRight circular cone of known lateral areaClosed conical tank shifted from upright to inverted positionStructural beam with all dimensions reducedCar scaled to a model car
Examples:Beam (2001 NSCP)Combined axial and bending (2001 NSCP)Beams (2015 NSCP)Plastic yieldingPlastic hingeShape classificationDesign analysis considerationsLateral torsional bucklingFlange local bucklingExample 1Example 2Base plates2001 NSCP2015 NSCPExample 3
ExamplesWater pumped from lower to upper tankVelocity distribution in pipeVelocity distribution in pipe 2Velocity distribution in pipe 3Velocity distribution in pipe 4Pipe networksPipes in seriesPipe in parallelThree reservoirExamples: Pipes in seriesPipes in series 2Pipes in parallelReservoir with pumpReservoir with turbineThree reservoir with known pressure at the junctionFluid flow measurementsOrificeExample 1
Course 8
Course 8
Influence lines for trussesPratt trussWarren trussPast board problemMoment of InertiaMoment of inertia of common shapesAddition or subtraction of moment of inertiaParallel axis theoremWide flange sectionT-sectionsRadius of gyrationPolar moment of inertiaExamplesWide flange sectionT-sectionUsing STAT ModeBuilt-up sectionsIrregular concrete beam sectionsComposite sectionsTrapezoidal beam with hole
Elastic curveSign conventionsDisplacement equation of elastic curveSlope equationMoment and shear equationLoad and shear equationBeam curvatureDouble Integration methodExample
Steady flow orifice ExamplesOrifice (steady flow)Orifice with two layers of liquidOrifice issuing upwardUnsteady flow orifice and examplesExample - two layers of liquidExample - three layers of liquidExample - Non-prismatic tank (frustum)Example - cylindrical tank with hemisphere at the bottomVenturi meterExample 1Example 2WeirRectangular weirsTriangular weirsCipolletti weirExamples:Suppressed rectangular weirError in measured headUnsteady flow examplesV-notch weirRectangular weirOpen channelThe Chezy formulaKutter formula for CMost efficient sectionsAlternate stages of flowTractive forceCritical depthHydraulic jumpExamples:Shear stress in rectangular channelMost efficient section (semi-circular and triangular)
Polyhedrons (examples)Pyramid and frustum of pyramidTetrahedronDodecahedronOctahedronIcosahedronSphere examplesSpherical segmentHemispherical domeFrustum of sphereIce cream conePrismatoidPrimoidal formulaVolume common to two intersecting cylindersSolids of revolutionPappus theoremsExamples:Volume of pitSolid with circular base and triangular sectionsSolid with triangular base and hexagonal sectionsFrustum of a coneSphereTriangular area revolved about a lineCircle revolved about a line
Integral Calculus ApplicationArea bounded by curves - examplesArea bounded between parabola and coordinate axesArea bounded between two parabolasArea between a parabola and lineCentroid of area - examplesCentroid of area of parabola and coordinate axesCentroid of area bounded between two parabolasCentroid of area between a parabola and lineMoment of inertia (second moment of area)Moment of inertia of area bounded between parabola and coordinate axesMoment of inertia of area bounded between two parabolasMoment of inertia of area between a parabola and lineArea, Centroid, and moment of inertia examples:Between parabola and linesExample 2Solids of revolutionRevolution of area bounded by a parabola and coordinate axesRevolution of area bounded by three graphs
Course 9
Course 9
TorsionExample 1Example 2 - Hallow barExample 3 - Required outside diameter of shaftStresses in BeamsRadius of CurvatureBending StressFlexural rigidityMaximum bending stressSection ModulusFormulas for rectangular beamTrapezoidal/Wide Flange/T SectionShearing StressShear stress diagramsRectangular sectionWide flangeShear stress of any sectionShear and bending stress diagrams of sectionsBuilt-up sectionSpacing of boltsShear FlowShear CenterExamplesRadius of curvatureCracking moment hallow circular sectionCracking moment - irregular concrete sectionVertical pole subjected to uniform wind pressureWooden plank used as retaining wallSheet pile with tension rodsBeam with overhangCantilever beam with cover plate
Worded problemsNumber problems examplesExample 1Example 2Age problem examplesExample 1Example 2 - Mary is ...Mixture problems examplesAlcohol solutionsWater and alcohol solutionsWork problems examplesPrinciples discussedPipes filling a tankChinese restaurant fish pondMotion-work problems examplesMan days...Painting jobMotion-rate problem examplesCar and planeRelative speed - Airplane, windSteve Deitmer - Relative speed - Boat, waterRelative speed - Boat, waterIntegral calculusCenter of gravity of solids of revolutionParaboloidSpandrel of revolutionSpandrel of revolution 2Cubic curveWorkConical water tank emptied to the topHemispherical tank emptied to the topSemi-circular oil tank pumped to the topLength of curveParabolic curveLength of y = 4x^(3/2)Surface AreaGraph y = 3x^(1/3)Graph y = sqrt(x)
SurveyingTraverse AdjustmentLinear error of closureBalancing latitude and departure (Compass and Transit rules)Example 1 - (3 sides) Compass RuleExample 2 - (six sides) Transit RuleErrors in measurementSources of errorTypes of errorPrecision and accuracyStatistics (mean, standard deviation, mpv, standard errors, probable error etc)Error of a sumError of a seriesError of a productExamplesError of measured distance-Using calculator function (Mode Stat)Error of measured angles-Using calculator function (Mode Stat)Weighted measurementAnglesDistance-Using calculator function (Mode-Stat)Probable error of elevation-Using calculator function (Mode-Stat)Error of elevation run at different routes-Using calculator function (Mode-Stat)Most probable value of interior angles, single observationMost probable value of interior angle, multiple observationMost probable value of angle
Double integration method exampleMoment equationSolving for constant of integration C1 and C2Solve for the slope at supportMidspan deflectionDeflection at overhangMaximum deflectionArea moment methodRules of signSolving for slope at supportSlope at any pointSolving for displacement of a pointSolve for maximum deflectionMoment diagram by partsExample- Formula-based approach
Open channelExample - Most efficient trapezoidal section Non-uniform flow exampleHydraulic jumpHydrodynamicsFixed flat platesFixed curved platesMoving vanesWork done on moving vaneExamples:Fixed and moving flat plateFixed and moving curved vane- Solution using COMPLEX ModeHeight a vertical jet of water support a given loadWater HammerVelocity (celerity) of pressure waveInstantaneous, Rapid, and Slow ClosureExampleSoil mechanicsPhase diagramsSoil propertiesPorosity and void ratioWater contentDegree of saturationSpecific gravityUnit weight and dry unit of soilMoist and saturated unit weightAdditional formulasRelative densityRelative compactionSuitability number and sorting coefficientExample 1
Cables under point loadsExample 1 - Tension in cables and sagExample 2 - Unequal support elevationExample 3 - Cable pulled at one endParabolic cablesLength of cableExamplesSymmetrical cableUnequal support elevationUnequal support elevation 2Cable supporting a compound trussPlane TrussType of trussesTruss componentsZero-force membersExamplesKing post trussHowe trussCantilever truss (canopy)- Using method of sectionTransmission tower (K-truss)Warren truss/K-trussTruss with cablesBowstring/Arch truss
Differentiation RulesDefinite DerivativesIndefinite DerivativesImplicit DifferentiationRelated RatesExample - Motion of particleExample - Motion of particle 2Example - Trigonometric functionExample - Trigonometric function 2Example - Rate of separation of two automobilesExample - Rate of separation of LRT Train and carExample - Rate of separation of two carsExample - Rate of change of distance between two men on a circular trackExample - Rate of change of commodity supplyExample - Rate of increase of production0Example - Rate of boat approaching the dockExample - Ladder resting on a vertical wallExample - Rate of change of angle of elevation of the rocket to the observer
Course 10
Course 10
Examples - Stresses in BeamsDeck of a bridge over a deep ravine (composite beam)Beam with overhang considering live load patternSimple beam with two concentrated loads and cover plateSpacing of bolts in built-up beamBending on both axes - ExamplesCrane runway girder subject to vertical and horizontal forcesSpacing of purlins with two sag rodsCombined axial and bending stressExamples:Simple beam with uniform load and axial loadSolid circular pole subject to vertical and lateral loadPlain concrete damPrestressed concretePre-tensioningPost-tensioningStress calculationExamples:Prestressed rectangular beamHallow core slabDouble tee concrete joist
Distance measurementPacingTape correctionsTemperature correctionPull correctionSag correctionSlope correctionReduction to Mean Sea LevelTrue distanceStadia surveyingExamples:PacingArea of field measured using a tape too longSquare lot measured using an erroneous tapeRequired measurement to layout a building foundationDistance measurement using a tape too shortTemperature correction problemStandardized tapePull and temperature correction, three segmentsTape supported at four pointsNormal pullStadia survey - inclined line of sightStadia Survey 2TacheometerLevelingCurvature and refractionExamples:Differential levelingProfile levelingTwo-peg testPeg adjustmentTrigonometric leveling exampleTwo hills (inter visible hills)Line of levels run over soft ground
Virtual work method (Unit load method)PrinciplesExample 1Example 2 - Beam with internal pinExample 3 - FrameCantilever beamsExample 1 - Beam loaded with uniform and concentrated load
Soil properties examplesExample 1Example 2Example 3 - Relative compactionExample 4 - Suitability number and sorting coefficientExample - Borrow and fillAtterberg limitsPlasticity indexLiquidity indexConsistency, Flow, Toughness indicesShrinkage limitShrinkage ratioSpecific gravityExamples:Example 1Example 2Example 3Soil Classification USCSExample 1AASHTO
Counting principlesExamples:How many different outfitsHow many ways can the positions be filledHow many different license platesNumber of four-digit numbersNumber of three-digit numbersHow many numbers between 3000 and 5000 can be ...Number of ways to be seated in a rowPermutationExamples:Number of different wordsNumber of ways pictures can be hungElection of club officers5 persons be seated in a row5 men and 4 women seat in a row9 books arranged on a shelf6 boys and 4 girls seating on a bench5 men and 3 women seated on a benchBooks arranged on a shelfMen seated in a row5 persons seated at a round table8 persons seated at a round tableGroup of engineers seated at a round tableNumber of signalsPermutation with some things alikeExamplesNumber of signalsBook arrangementCombinationExamplesNumber of handshakesNumber of sets of student to represent in a contestNumber of selection from number of candidatesSelect set of booksSelecting a committeeNumber of ways 5 red cards can be drawnNumber of ways of drawing 3 aces and 2 face cardsNumber of ways of drawing exactly 3 clubsNumber of 5-letter wordsMutually exclusive events and examplesRides in amusement parkSelecting 1 or more of 4 appliancesRaising any number of 5 different flagsInvite any one or more of your 8 friendsNumber of 4-letter wordsNumber of 3-digit numbers greater than 480Number of 3-digit numbers less than 530How many four-letter word beginning with a capitalHow many ways can a committee of 3 members with 1 doctor...6 persons line up if two persons ...7 people seated at a round table with certain 3 people...6 luncheon guests
Three-hinged arch and examplesEqual support elevationUnequal support elevationGable frame subject to wind forcesArch with quarter circle and straight memberFrictionStatic and dynamic frictionsImpending motionAngle of frictionExamples:Box resting on horizontal surface subject to horizontal forceBox resting on horizontal surface subject to inclined forceBox resting on horizontal surface subject to inclined force 2Bag of rice pulled by a force PBlock on an inclined planeBlock on an inclined plane subject to horizontal forceBlock A on top of block BForce to move the blockUniform rod resting on a vertical wallUniform ladder pushed by a manMan crossing a beamUniform box pushed by a workerCylindrical tank subject to inclined forceBelt frictionExample 1 - Block supported by a ropeExample 2 - Rope around a capstanExample 3 - Flexible belt around a rotating drumExample 4 - Horse fasten to the railExample 5 - Rail suspended from a ropeExample 6 - Rope running over two fixed cylinders
Related RatesExample 1 - TriangleExample 2 - Flow into conical tankExample 3 - Flow into frustum of a coneMaximum and MinimaCritical NumbersSecond Derivative TestExample 1 - Critical points of the curveExample 2 - Relative extrema of a functionExample 3 - Minimum costExample 4 - Maximizing the weekly salesExample 5 - Maximizing the profitExample 6 - Number of participants to maximize revenueExample 7 - Point on a curve nearest to an external pointExample 8 - Time when ships are nearest each otherExample 9 - Landing point to reach the destination at shortest timeExample 10 - Field dimension for largest areaVariable Relationship for Maximum or Minimum ValuesExample 11 - Position of stake for minimum length of wireExample 12 - Dimension of cylindrical tank to use the least amount of materialExample 13 - Shortest beam that can reach the buildingExample 14 - Observer's position for maximum angle subtendedCurvature of a CurveRadius of CurvatureCircle of CurvatureCenter of CurvatureExample 15 - Curvature of parabolaExample 16 - Radius of curvatureExample 17 - Center of curvatureExample 18 - Curvature of cissoid
Course 11
Course 11
Foundation PressureGross and Net PressuresWith upliftExamples:Rectangular footing with axial and moment loadsRectangular footing supporting a pedestalFooting subjected to column not at its centerColumn subject to axial load and momentConcrete wall centrally located on a footingConcrete retaining wallFooting subject to moments in both axesReinforced ConcreteCodes (2015 NSCP)Spacing of reinforcementExample - Rectangular beamExample - Square columnBundled barsTies and spiralsDevelopment LengthBars in tensionModification factorsBars in compressionExample - cantilever beamConcrete coverShrinkage and temperature reinforcementExampleModulus of elasticity, rapture, and modification factorImmediate deflectionExampleLoad factors and combinationMethods of AnalysisTwo spans, column endsTwo spans with spandrel beamTwo spans with simple supportThree spansExample
CurvesTypes of horizontal curvesSimple circular curveExampleCompound curveExample 1Example 2Example 3Reversed curveExample 1 - Reversed curved connecting parallel roadsExample 2 - Parallel roads connected by equal turnoutSpiral curvesExample
Propped cantilever beamsExample 1Example 2Continuous beamExample - By superpositionDegrees of indeterminacy of frames and trussesExample - Classify each structureTrussesExamplesFramesExamplesMulti-storey rigid frameThree-moment equationFormulas for 6Aa/L and 6Ab/LExample
Permeability (flow of water through soils)Darcy's lawNotable formulasPermeability testsConstant head testFalling head testEquivalent hydraulic conductivitiesParallel (horizontal) flowNormal (vertical) flowPumping wellsUnconfined wellsConfined wellsExample:Constant head testConstant head test 2Falling head testFalling head test 2Flow through permeable layerEquivalent hydraulic conductivity of layered soilNormal flow through layered soilLayered soilFlow through layered soil 2Confined aquiferPumping well
Simple probabilityExamples:Ball drawn from a boxCard drawn from a deckRoll a pair of dice. Sum of 11Roll a pair of dice. Sum of 10 or 123 balls drawn from a bag6 books arranged in a shelf10 books arranged randomly in a shelfLottery tickets3 cards drawn randomlyPoker gameDrawing exactly 3 face cardsCompound probabilityIndependent eventsDependent eventsExamples:Probability that a man will be aliveTwo bags containing white and black balls3 cards drawn, all aces3 students are randomly chosen to get out of the roomBox with defective cell phonesBox with marblesMutually exclusive eventsProbability of getting at least 1 in two throws of diceGame of chessProbability that a problem is solvedProbability that a target is hitOne ball drawn from each of the two bagsThree candidates for an officeProbability that there are at least four face cardsBinomial distributionBox with defective cell phonesProbability that it will rainProbability that 5 of the 12 employees have at least one credit cardThrow of 9 diceProbability of getting a 9 in 3 throws of diceProbability of getting at least 2 ones...Probability that fewer than 4 will use a couponOdds of getting three heads in tossed coinsProbability to complete 4 years in college
Rectangular components of force in spaceUnit vectorUsing the VECTOR MODEExamples:Vector componentsVector components 2Resultant of forces in spaceMoment about an axisMoment about a pointExample 2Equilibrium of forces in spaceSupport reactionsTwo-force membersDoor hingesExamples:To lift a table without tilting ...Circular steel plate supported by 3 equally spaced postsTriangular plate supported by 3 vertical cablesRectangular plate suspended from 4 wiresLoad supported by tripodUsing calculator MODE MATRIXBoom supported by two cablesHomogeneous bar resting on vertical wallWindow supported by a wirePole supported by two cablesTwo bars supported by a cableMoment about a lineBoom supported by two cablesTwo bars supported by a cable
Probability and statistics (continuation)Binomial distribution examplesProbability that the shipment will make it throughMultinomial distribution examplesA fair dice is thrown five times...Box containing ballsA traffic engineer...Poisson distribution examplesRoad construction projectsCars approaching an intersectionDefective bulbsBad reaction from injectionDefective itemsNormal distributionExamples:Assembly lineUsing calculator MODE STATPollutants dumped into a riverDefective washersUsing calculator MODE STAT
Course 12
Course 12
Pattern LoadingSectional strengthDesign strength and required strengthReduction factorsShearFactored shear critical sectionWhat is effective depth?One-way shear (stirrups)Nominal shear strength of the sectionLimit of VuShear strength provided by concreteCircular sectionsMembers with axial compressionMembers with significant axial tensionRequired nominal shear strengthShear reinforcement provided by transverse reinforcementShear reinforcement perpendicular to the axisFor circular tie or spiralMaximum spacing of shear reinforcementWhat is Av?Minimum shear reinforcementExamples:Example 1 - Design problem Example 2 - Analysis/investigation problemExample 3 - Column subject to shearFlexure and axialSectional strength - design assumptionsValue of "a" and Beta1Assumptions for reinforcementMinimum area of reinforcementTension and compression controlledDerivation of formula and explanation of code assumptionsStress in tension and compression steelSingly-reinforced rectangular beam with fs = fyBalanced conditionBalance "c""Rho" balanceMaximum steel area (Asmax or rho max)Tension and compression controlled sectionsMaximum tension steel (rho_t) of tension controlled sectionMinimum steel reinforcementDesign of tension-controlled rectangular sectionSingly reinforcedDoubly reinforcedAnalysis/investigation of singly-reinforced beamsAdditional resources in YouTubeExamples:Analysis of one-way slabAnalysis/investigation of singly-reinforced beamAnalysis/investigation of rectangular beamDesign of one-way slab
EarthworksMethods of volume measurementTypes of cross-sectionCalculating irregular areaTrapezoidal ruleSimpson's 1/3 ruleVolume by cross-sectionEnd area methodPrismoidal formulaPrismoidal correctionUnit area methodVolume of pit or reservoirEnd are methodPrismoidal formulaExamples:Area of cross-sectionArea of cross-section 2Area of cut and fillArea of land by with straight-line boundaryVolume by prismoidal correctionVolume of cut and fillVolume of borrow pit by unit area methodVolume of lake/reservoirVertical curvesExamplesSymmetrical sag parabolic curvesSymmetrical summit parabolic curveUnsymmetrical parabolic curvesTransportation EngineeringSpiral curvesRate of change of centripetal accelerationDesirable length of spiralSuperelevation rateIdeal super-elevationSuper-elevation on spiral curveSight distancesAspects of sight distanceSight distance/passing sight distance/stopping sight distanceStopping sight distanceSight distance for horizontal curvesSight distance for vertical crest curvesSight distance for vertical sag curvesCriterion for sag curvesExamples:Spiral curve (desirable length, etc.)Horizontal curve (max velocity, length of transition curve)Ramp of NLEX...Minimum stopping sight distanceStopping sight distanceStopping sight distance and length of curveVertical summit curve (Practice)Vertical sag curve sight distance
Fully restrained beamsFixed-end moment approachExample - beam with concentrated loadExample - beam with uniform loadExample - beam with varying loadMoment distributionFixed-end momentBeam stiffnessDistribution factorExample - 2 spans with overhang- using the modified "k"Approximate lateral force analysisPortal methodCantilever method
InterestExampleInterest rateExampleSimple interestExample 1Example 2Example 3Example 4Ordinary and exact interestExample 5Example 6Compound InterestCompound interest, annual compoundingExample 1Example 2Example 3Example 4Example 5Compound interest with periodic compoundingExample 1Example 2Example 3Example 4Example 5Continuous compoundingExample 1Example 2Example 3Effective annual interest rateExample 1Example 2Example 3Example 4Cash flowsExample 1Example 2Example 3Example 4Example 5AnnuityOrdinary annuityExample 1Example 2Example 3Interest period not the same as payment periodExample 1Example 2Example 3Example 4Example 5Example 6Example 7Example 8Example 9Example 10Example 11Example 12Example 13Annuity DueExample 1Example 2Example 3Example 4Deferred AnnuityExample 1Example 2Example 3PerpetuityExample 1Example 2Example 3Example 4
Stresses in Soil (effective, total, porewater)Examples:Example 1Example 2Example 3 - With downward seepageExample 4 - With upward seepageExample 5 - With seepageExample 6 - With capillary riseFlow Nets (flow lines, equipotential lines)Characteristics of equipotential and flow linesIsotropic and non-isotropic soilsExampleStress distribution in soilWestergaard equationBoussinesq equationDistribution due to uniform load (2:1 slope)Examples:Example 1Example 2Example 3Shear strength of soilDirect shear testTriaxial testUnconfined testExamples:Example 1Example 2Example 3Compressibility of soil (settlement)Total settlementPrimary settlementNormally consolidated soilOverconsolidated soilSecondary settlementElastic settlementTime rate of consolidationCompression indexCoefficient of compressibilityCoefficient of volume compressibilityTime of consolidationExamples:Example 1Example 2Bearing capacity of soilGeneral shear failureRectangular footingSquare footingStrip footingCircular footingBearing capacity factorsFormulasLocal shear failureAllowable bearing capacityGross allowableNet allowableExamples:Example 1Example 2
DynamicsKinematicsMotion of ParticlesRectilinear translationUniform motionVariable accelerationConstant accelerationFree-falling bodyProjectile motionExamples:Distance as function of timeVelocity as function of timeAcceleration as function of timeCompound motion - elevatorMotion curve, a-t diagramCompound motion - TrainCompound motion - carVariable acceleration - airplaneFree falling body - height of buildingOrifice flowProjectile problemAirplane dropping a packageRotationExamplesFlywheelTires of a carTires of a truckTires of a truck 2Accelerating carKineticsNewton laws of motionPendulumExamples:Apparent weight Block placed on an inclined planeBlock release at the roofBlock pushed by a constant force-Impulse-momentum principle-Work-energy equationBlock is pushed and then releasedColliding trainLaw of conservation of momentumInelastic collisionCoefficient of restitutionTruck bumps into a carPerfectly elastic collisionColliding block moving in opposite directionRecoil velocity of rifleCentrifugal and centripetal forcesAngle of bankingIdeal angle of bankingExamples:Ball revolve in a vertical circleBucket with water swung on vertical planeBlock on a horizontally rotating platformFastest speed a car can move around a curveRequired angle of bankingMinimum angle of banking
Course 13
Course 13