Course 10

GERTC Review Lectures

Course 10

Lecture 10-1: Stresses in Beams

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

Lecture 10-2: Surveying

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

Lecture 10-3: Beam Deflection

Virtual work method (Unit load method)PrinciplesExample 1Example 2 - Beam with internal pinExample 3 - FrameCantilever beamsExample 1 - Beam loaded with uniform and concentrated load

Lecture 10-4: Geotechnical Engineering

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

Lecture 10-5: Counting Principles & Probability

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

Lecture 10-6: Mechanics

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

Lecture 10-7: Differential Calculus

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