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
