Course 8

GERTC Review Lectures

Course 8

Lecture 8-1: Influence Lines and Moment of Inertia

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

Lecture 8-2: Beam Deflections

Elastic curveSign conventionsDisplacement equation of elastic curveSlope equationMoment and shear equationLoad and shear equationBeam curvatureDouble Integration methodExample

Lecture 8-3: Fluid Mechanics

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)

Lecture 8-4: Solid Geometry

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

Lecture 8-5: Calculus

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