Course 12

GERTC Review Lectures

Course 12

Lecture 12-1: Reinforced Concrete Design

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

Lecture 12-2: Transportation Engineering & Earthworks

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

Lecture 12-3: Indeterminate Beams & Frames

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

Lecture 12-4: Engineering Economics

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

Lecture 12-6: Geotechnical Engineering

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

Lecture 12-7: Dynamics

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