Course 6

GERTC Review Lectures

Course 6

Lecture 6-1: Shear and Moment

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

Lecture 6-2: Steel Design

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

Lecture 6-3: Plane Geometry

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

Lecture 6-4: Analytic Geometry

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

Lecture 6-5: Fluid Mechanics

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