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Course 1
Course 2
Course 3
Course 4
Course 5
Course 6
Course 7
Course 8
Course 9
Course 10
Course 11
Course 12
Course 13
What is GERTC Lite and Plus
GERTC Online Reference
Mathematics
Algebra
Sample Problems
Plane and Spherical Trigonometry
Sample Problems
Right Triangle
General Triangle
Trigonometric Identities
Plane and Solid Geometry
Sample Problems
Triangle
Circle
Quadrilateral
Polygons
Parabolic Segment and Spandrel
Ellipse
Differential Calculus
Sample Problems
Engineering Economics
Sample Problems
Probability and Statistics
Sample Problems
Surveying and Transportation Engineering
Surveying
Sample Problems
Traffic and Transportation Engineering
Sample Problems
Curves and Earthworks
Sample Problems
Fluid Mechanics and Hydraulics
Fluid Pressure
Sample Problems
Buoyancy and Floatation
Sample Problems
Relative Equilibrium of Liquids
Sample Problems
Fluid Flow and Pipes
Sample Problems
Fluid Flow Measurement
Sample Problems
Open Channel
Sample Problems
Hydrodynamics and Water Hammer
Sample Problems
Geotechnical Engineering
Soil Properties and Classification
Sample Problems
Flow of Water Through Soil
Sample Problems
Stresses in Soil and Stress Distribution
Sample Problems
Settlement and Consolidation
Sample Problems
Shear Strength of Soil (Triaxial)
Sample Problems
Lateral Earth Pressure and Slope Stability
Sample Problems
Bearing Capacity and Piles
Sample Problems
Structural Engineering
Mechanics - Statics
Sample Problems
Strength of Materials
Sample Problems
Theory of Structures
Sample Problems
Cantilever Beam Formulas
Simple Beam Formulas
Propped Beams
Pile Pick-up and Storage Details
Steel Design
Sample Problems
Tension Members
Bolts and Threaded Parts
Bolted Connection
Reinforced Concrete
Sample Problems
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GERTC Review Lectures
Course 1
Lecture 1-1: Engineering Mechanics
Lecture 1-2: Fluid Mechanics
Lecture 1-3: Trigonometry
Lecture 1-4: Algebra and about the Canon f-789sga
Lecture 1-5: Mechanics
Course 2
Lecture 2-1: Mechanics and Strength of Materials
Lecture 2-2: Steel Design
Lecture 2-3: Hydraulics - Plane Surfaces, Curve Surfaces, and Dams
Lecture 2-4: Algebra
Lecture 2-5: Trigonometry
Course 3
Lecture 3-1: Strength of Materials
Lecture 3-2: Algebra
Lecture 3-3: Fluid Mechanics
Lecture 3-4: Steel Design
Lecture 3-5: Surveying
Course 4
Lecture 4-1: Strength of Materials
Lecture 4-2: Steel Design
Lecture 4-3: Algebra
Lecture 4-4: Geometry and Surveying
Lecture 4-5: Fluid Mechanics
Course 5
Lecture 5-1: Strength, Shear and Moment
Lecture 5-2: Analytic Geometry
Lecture 5-3: Geometry
Lecture 5-4: Steel Design
Lecture 5-5: Fluid Mechanics
Course 6
Lecture 6-1: Shear and Moment
Lecture 6-2: Steel Design
Lecture 6-3: Plane Geometry
Lecture 6-4: Analytic Geometry
Lecture 6-5: Fluid Mechanics
Course 7
Lecture 7-1: Shear and Moment and Moving Loads
Lecture 7-2: Analytic Geometry
Lecture 7-3: Solid Geometry
Lecture 7-4: Steel Design
Lecture 7-5: Fluid Mechanics
Course 8
Lecture 8-1: Influence Lines and Moment of Inertia
Lecture 8-2: Beam Deflections
Lecture 8-3: Fluid Mechanics
Lecture 8-4: Solid Geometry
Lecture 8-5: Integral Calculus
Course 9
Lecture 9-1: Torsion and Stresses in Beams
Lecture 9-2: Word Problems and Integral Calculus
Lecture 9-3: Surveying
Lecture 9-4: Beam Deflection
Lecture 9-5: Fluid Mechanics and Geotechnical Engineering
Lecture 9-6: Mechanics
Lecture 9-7: Differential Calculus
Course 10
Lecture 10-1: Stresses in Beams
Lecture 10-2: Surveying
Lecture 10-3: Beam Deflection
Lecture 10-4: Geotechnical Engineering
Lecture 10-5: Counting Principles & Probability
Lecture 10-6: Mechanics
Lecture 10-7: Differential Calculus
Course 11
Lecture 11-1: Stresses in Beams & Reinforced Concrete
Lecture 11-2: Surveying
Lecture 11-3: Indeterminate Beams
Lecture 11-4: Permeability
Lecture 11-5: Probability & Statistics
Lecture 11-6: Forces in Space
Lecture 11-7: Probability and Statistics
Course 12
Lecture 12-1: Reinforced Concrete Design
Lecture 12-2: Transportation Engineering & Earthworks
Lecture 12-3: Indeterminate Beams & Frames
Lecture 12-4: Engineering Economics
Lecture 12-6: Geotechnical Engineering
Lecture 12-7: Dynamics
Course 13
Lecture 13-1: Reinforced Concrete
Lecture 13-2: Seismic and Footing
Lecture 13-3: Geotechnical Engineering
Lecture 13-4: Engineering Economics
Lecture 13-5: Transportation Engineering
Lecture 13-6: Engineering Economics
Course 1
Lecture 1-1:
Engineering Mechanics
Application of Trigonometry and Geometry to Engineering Mechanics
Right triangle
General triangle
Angles
Force components
Using calculator COMPLEX MODE
Application to problems involving cylinder inside a bin
Application to varying load
Application to trusses/transmission tower
Plane Areas
Introduction to Engineering Mechanics
Statics
Scalar and Vector Quantities
Resultant of Forces
Parallel Forces
Concurrent Forces
Lecture 1-2:
Fluid Mechanics
Properties of Fluids
Density and Specific Volume
Specific Gravity
Unit weight
Bulk Modulus of Elasticity
Compressibility
Ideal Gas
Viscosity
Capillarity
Unit Pressures (Absolute, Gage, Atmospheric)
Principles of Hydrostatics
Pascal's Law
Absolute and Gage Pressure
Variations in Pressure
Manometers
Ideal Gas Law
Lecture 1-3:
Trigonometry
Introduction to Trigonometry
Angles
Cartesian/Rectangular Coordinate System
Angles in Standard Position
Applications
Trigonometric Identities
Triangles and Applications
Properties of Triangles and examples
Lecture 1-4:
Algebra and about the Canon f-789sga
Introduction to MSTE
Calculator functions (Mode 1 to Mode 8) with practical application.
Mode 1: General Calculation
Mode 2: Complex
Mode 3: Statistics
Mode 4: Base-N
Mode 5: Equation
Mode 6: Matrix (Mode 7 in Canon)
Mode 7: Table (Mode 6 in Canon)
Mode 8: Vector
Lecture 1-5:
Mechanics
Resultant of Concurrent Forces
Moment of Forces
Distributed Loads
Resultant of Parallel and Non-concurrent Forces
Resultant of Non-Parallel and Non-Concurrent Forces
Equilibrium of Forces
Support Reactions
Equilibrium of Two forces
Equilibrium of Three or More Concurrent and Coplanar Forces
Force Polygon
Course 2
Lecture 2-1:
Mechanics and Strength of Materials
Equilibrium of Concurrent forces - Examples
Equilibrium of Non-Current forces - Examples
Two-Force Members - Explained
Simple Stress
Tensile , Compressive , Shearing , Bearing Stress
Simple Strain
Stress-Strain Diagram
Actual and Allowable Stresses
Axial Deformation
Deformation due to Self-Weight
Thermal Stress
Coefficient of Thermal Expansion
Lecture 2-2:
Steel Design
Steel Design Basics
Review on Simple Stress
Bolts, Nuts, Washers, and Thread
Tensile, compressive, shear
Net and Gross Area
Block shear
Lecture 2-3:
Hydraulics - Plane Surfaces, Curve Surfaces, and Dams
Hydrostatic Forces on Plane Surfaces
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Hydrostatic Forces on Curved Surfaces
Example 1
Example 2
Example 3
Example 4
Example 5
Gravity Dam
Analysis
Example 1 - Triangular dam
Lecture 2-4:
Algebra
Laws of Exponents and Roots
Example 1
Example 2
The nth Root of a number
Law of Radicals
Example 1
Example 2
Logarithms
Example 1
Example 2
Algebraic Expressions
Terms
Degree
Computation with Algebraic Expressions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Product
Example 1
Example 2
Factoring
Examples 1
Examples 2
GCF, HCF, LCM
Example 1 - GCF
Example 2 - LCM
Lecture 2-5:
Trigonometry
Recap of Lecture 1
Triangles
Medians
Altitude
Angle Bisector
Perpendicular Bisectors
Euler Line
Spherical Triangle
Right Triangle
Oblique Triangle
Terrestrial Sphere
Area
Examples
Course 3
Lecture 3-1:
Strength of Materials
Worked Examples:
Allowable Stress / Simple Stress
Column
Bolt and Washer
Cables
Beam Supported by Cable
Double-T Angle Connection
Billboard
Thin-Walled Pressure Vessel
Axial Deformation
Steel Tire
Steel Cable
Due to Self-Weight
Thermal Stress
Lecture 3-2:
Algebra
Functions and Graph
(
Range, Domain)
Examples
Remainder and Factor Theorems
Linear Equations and Inequality
Quadratic Functions
Quadratic Equations and Inequality
Cubic Equations and Inequality
The Rational Zero Theorem
Lecture 3-3:
Fluid Mechanics
Thin-Walled Pressure Vessels
Spherical Shell
Cylindrical
Example 1
Example 2
Example 3 -
Spacing of Hoops
Example 4 - Spherical shell
Example 5 - Hoops
Example 6 - Hoops
Example 7 - Hoops
Buoyancy (Archimedes' Principle)
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Stability of Floating Bodies (Metacenter and Metacentric Height)
Example 1
Lecture 3-4:
Steel Design
Welded Connection
Allowable Stress Design (ASD)
Load and Resistance Factor Design (LRFD)
NSCP Provision for Steel Connections
Load Combinations
Design of Tension Members
Gross and Net areas
Staggered Holes
Shear Lag Factors
Examples
Lecture 3-5:
Surveying
Traverse
Bearings/Azimuths
Latitude and Departures
Missing Data
Area of Closed Traverse
Using Triangles
Using DMD Method
Using DPD Method
Area by Setting a Point Inside a Closed Traverse
Dividing lines
Course 4
Lecture 4-1:
Strength of Materials
Simple Stress Problems (Hankinson's Formula)
Axial Deformation Problems
Heavy Molding
Precast Concrete Slab Supported by Cables
Beam Pinned at One End and Cable Support at the Other End
Timber Member Subject to Three Axial Loads
Deflection of Truss
Statically Indeterminate Problems (axial load)
Steel Tube Filled with Concrete
Slab Supported by Three Cables
Straight Bar Fixed at Both Ends
Load Supported by Three Steel Rods
Load Supported by Three Rods and a Rigid Bar
Stress at an Inclined Plane (Mohr Circle)
Lecture 4-2:
Steel Design
Bolted Connection (LRFD NSCP 2015)
Bolt Bearing
Block Shear
Example - Lap Joint with Nine Bolts
Eccentrically Loaded Connection
Example
Using MODE 3-2
Lecture 4-3:
Algebra
Rational Equations - Examples
Radical Equations - Examples
Simultaneous Linear Equations
Partial Fraction Decomposition - Examples
Case I
Case II
Case III
Lecture 4-4:
Geometry and Surveying
Traverse (Subdivision)
Triangulation Examples
Triangulation Stations
Two Intervisible Points
Sounding Boat
Practice Problems
Plane Geometry
Triangles
Circles (Theorems of Circle)
Sector, Arc, etc
Circle Inscribed in a Triangle
Circle Circumscribed About a Triangle
Circle Escribed About a Triangle
Examples
Area of Inner Triangle
Area of Equilateral Triangle with a Given Point Inside
Area of Corner Lot
Three Circles Tangent Externally
Two Circle Tangent Internally to a Third Circle
Length of Cross Belt
Maximum Area the Goat can Cover
Lecture 4-5:
Fluid Mechanics
Relative Equilibrium of Liquids
Horizontal Motion
Examples
Force Acting on the Side of the Tank
Required Accelerating Force
Total force at the Bottom of the Tank
Water Remaining in the Tank
Inclined Motion
Example 1
Example 2
Vertical Motion
Example 1
Example 2
Rotating Vessel
Example 1
Course 5
Lecture 5-1:
Strength, Shear and Moment
State of Plane Stress
Thin-walled vessels (Mohr Circle)
Triaxial Test (Application)
Examples:
Element subject to stresses presented by Mohr Circle
Bar subjected to uniaxial force
Open tank subject to fluid pressure and axial force
Closed tank subject to internal pressure and axial force
Given an element subject to normal and shearing stresses
Shear and Moment in Beams (Internal forces in beams)
Examples:
Beam subject to axial, shear, torque, and bending
Finding the internal forces a a particular section of a horizontal beam
Finding the internal forces a a particular section of an inclined beam
Internal forces on a section of a frame
Beam with an applied moment
Lecture 5-2:
Analytic Geometr
y
Introduction
Points of Intersection of Linear and quadratic curves
Circle
Points and Segments
Triangle (Centroid, Area, etc)
Straight Lines
Lecture 5-3:
Geometry
Plane Geometry (Examples)
Two perpendicular chords of a circle dividing the circle in 4 parts
Two lines tangent to a circle
(2 examples)
Two intersecting secants of a circle
Area of swimming pool made of overlapping circles
Common chord of intersecting circles
Distance between men walking on a circular track
Height of Mayon Volcano and the smoke
Application to fluid Forces on circular Surfaces
Quadrilaterals
Cyclic Quadrilaterals
Polygons
Example 1
Example 2
Example 3 - A farmer owns two square lots..
Example 4 - Folded rectangle
Example 5 - Building site in the form of a quadrilateral
Example 6 - Quadrilateral inscribed in a circle
Lecture 5-4:
Steel Design
Bolted Connection (Eccentric Load)
Welded Connection (Eccentric Load)
Calculator shortcut
Example - Eccentrically loaded weld
2015 NSCP Provisions on Welds
Example
Weld Strength
Lecture 5-5:
Fluid Mechanics
Rotating Vessel Examples
Open cylindrical tank 1
Open cylindrical tank 2
Open cylindrical tank 3
Rotating tube 1
Rotating tube 2
Rotating bucket
Rotation of closed cylindrical tank more than half full of water
Rotation of closed cylindrical tank filled with water
Fundamentals of Fluid Flow
Laminar/Turbulent Flow
Example 1
Example 2
Example 3
Example 4
Energy and Head
Bernoulli's Equation
Course 6
Lecture 6-1: S
hear and Moment
Cylindrical Tank (Mohr Circle)
Shear and Moment in Beams
Curved Beams
Shear and Moment Equations and Diagrams
Properties of Shear and Moment Diagrams
Cantilever Beams
Simple Beams
Example 1 - Simple beam with uniform and concentrated load
Example 2 - Simple beam with overhang
Example 3 - Simple beam with overhang and applied moment
Example 4 - Beam with fixed end and internal hinge
Example 5 - Concrete Pad with two equal uniform load
Example 6 - Concrete pad subject to unequal uniform load
Example 7 - Pick up point (2 pick-points) of precast concrete pile
Example 8 - Single pick-up point - concrete pile
Lecture 6-2:
Steel Design
Eccentrically loaded welded connection
Axially loaded Members(Columns) (2001 and 2015 NSCP)
Slenderness Limits and Effective Length
Alignment Chart
Example 1 - Column hinged at both ends
Assumptions of alignment chart
Sidesway inhibited vs. uninhibited
The ratio G in the alignment chart
Column reduction factor
Example 2 - Alignment chart
Example 3 - Alignment chart two storey moment frame assuming inelastic behavior
Flexural Members (Beams)
Bending planes
Buckling of Compression Flange
Classification of Sections
Allowable bending stress (2001 NSCP)
Example 4 - Simple beam
Example 5 - Laterally supported beam
Lecture 6-3:
Plane Geometry
Examples:
Cyclic Quadrilaterals (Ptolemy’s Theorem)
Area of quadrilateral
Quadrilateral inscribed in a semi-circle
Irregular four-sided figure inscribed in a circle
Quadrilateral circumscribed about a circle
Parabolic Segment and spandrel of parabola
Spandrel of parabola 1
Spandrel of parabola 2
Regular Pentagon
Scale of a map
Regular hexagon 1
Regular hexagon 2
Regular five-pointed star
Octagonal lot divided into two
Lecture 6-4:
Analytic Geometry
Distance from a Point to a Line
Examples
D
istance of point to a line
Circle tangent to a line
Line bisecting given two lines
Distance Between Parallel Lines
Examples
Distance between two lines
Angle Between Lines
Example
Angle between two lines
Line bisecting the acute angle between given two lines
Circles and lines
Example
Length of line tangent to a circle
Length of tangent line
Radical axis of circles
Line passing through points of intersection of two circles
Equation of curve connecting the centers of circles
Locus of center of circles tangent to y-axis and another circle
Lecture 6-5:
Fluid Mechanics
Bernoulli’s Energy Theorem
Energy and Hydraulic Gradelines
Power and efficiency
Examples:
Pipe with pump 1
Pipe with pump 2
Pipe with turbine
Large tank with compressed air
Water issuing a nozzle
Reynold’s Number
Velocity distribution in pipes
Shear stress in pipe wall
Shear/friction velocity
Head Losses in Pipes
Minor/Major Losses
Example 1
Example 2 - Moody Diagram
Example 3 - Syringe
Course 7
Lecture 7-1:
Shear and Moment and Moving Loads
Shear and moment in beams examples
Simple beam with cable
Linearly varying load (triangular)
Linearly varying load (trapezoidal)
Given shear diagram 1
Given shear diagram 2
Parabolically varying load
Moving loads
Single moving Load
Two and more moving loads
Example
Two moving loads
Three moving loads
Influence lines in beams
Application
H loading crossing a beam with overhang
Lecture 7-2:
Analytic Geometry
Conic sections
Parabola and examples
Equation given vertex and latus rectum
Finding the elements given equation of parabola
Plotting parabolas
Ellipse elements and examples
Given center, eccentricity and focus
Elements of ellipse from given general equation
Hyperbola elements and examples
Equation and elements from given center and lengths of axes
Elements of hyperbola from given general equation
Lecture 7-3:
Solid Geometry
Solid Geometry Formulas
Prisms / Pyramids/frustum / Cones/frustum /Spherical segments/sectors/ Cylinders
Examples
Spider and fly
Pentagonal prism
Block of wood with surface painted blue
Swimming pool with sloping bottom
Truncated prism
Cylinder with inclined axis
Cylindrical boiler made from metal sheet of known area
Water from from big to small tank
Triangular trough
Concrete block placed inside a water tank
Closed tank partially filled with water
Cone formed from a sector of a circle
Right circular cone of known lateral area
Closed conical tank shifted from upright to inverted position
Structural beam with all dimensions reduced
Car scaled to a model car
Lecture 7-4:
Steel Design
Examples:
Beam (2001 NSCP)
Combined axial and bending (2001 NSCP)
Beams (2015 NSCP)
Plastic yielding
Plastic hinge
S
hape classification
Design analysis considerations
Lateral torsional buckling
Flange local buckling
Example 1
Example 2
Base plates
2001 NSCP
2015 NSCP
Example
3
Lecture 7-5:
Fluid Mechanics
Examples
Water pumped from lower to upper tank
Velocity distribution in pipe
Velocity distribution in pipe 2
Velocity distribution in pipe 3
Velocity distribution in pipe 4
Pipe networks
Pipes in series
Pipe in parallel
Three reservoir
Examples:
Pipes in series
Pipes in series 2
Pipes in parallel
Reservoir with pump
Reservoir with turbine
Three reservoir with known pressure at the junction
Fluid flow measurements
Orifice
Example 1
Course 8
Lecture 8-1:
Influence Lines and Moment of Inertia
Influence lines for trusses
Pratt truss
Warren truss
Past board problem
Moment of Inertia
Moment of inertia of common shapes
Addition or subtraction of moment of inertia
Parallel axis theorem
Wide flange section
T-sections
Radius of gyration
Polar moment of inertia
Examples
Wide flange section
T-section
Using STAT Mode
Built-up sections
Irregular concrete beam sections
Composite sections
Trapezoidal beam with hole
Lecture 8-2:
Beam Deflections
Elastic curve
Sign conventions
Displacement equation of elastic curve
Slope equation
Moment and shear equation
Load and shear equation
Beam curvature
Double Integration method
Example
Lecture 8-3:
Fluid Mechanics
Steady flow orifice Examples
Orifice (steady flow)
Orifice with two layers of liquid
Orifice issuing upward
Unsteady flow orifice
and examples
Example - two layers of liquid
Example - three layers of liquid
Example - Non-prismatic tank (frustum)
Example - cylindrical tank with hemisphere at the bottom
Venturi meter
Example 1
Example 2
Weir
Rectangular weirs
Triangular weirs
Cipolletti weir
Examples:
Suppressed rectangular weir
Error in measured head
Unsteady flow examples
V-notch weir
Rectangular weir
Open channel
The Chezy formula
Kutter formula for C
Most efficient sections
Alternate stages of flow
Tractive force
Critical depth
Hydraulic jump
Examples:
Shear stress in rectangular channel
Most efficient section (semi-circular and triangular)
Lecture 8-4:
Solid Geometry
Polyhedrons (examples)
Pyramid and frustum of pyramid
Tetrahedron
Dodecahedron
Octahedron
Icosahedron
Sphere examples
Spherical segment
Hemispherical dome
Frustum of sphere
Ice cream cone
Prismatoid
Primoidal formula
Volume common to two intersecting cylinders
Solids of revolution
Pappus theorems
Examples:
Volume of pit
Solid with circular base and triangular sections
Solid with triangular base and hexagonal sections
Frustum of a cone
Sphere
T
riangular area revolved about a line
Circle revolved about a line
Lecture 8-5:
Integral Calculus
Integral Calculus Application
Area bounded by curves
- examples
Area bounded between parabola and coordinate axes
Area bounded between two parabolas
Area between a parabola and line
Centroid of area - examples
Centroid of area of parabola and coordinate axes
Centroid of area bounded between two parabolas
Centroid of area between a parabola and line
Moment of inertia (second moment of area)
Moment of inertia of area bounded between parabola and coordinate axes
Moment of inertia of area bounded between two parabolas
Moment of inertia of area between a parabola and line
Area, Centroid, and moment of inertia examples:
Between parabola and lines
Example 2
Solids of revolution
Revolution of area bounded by a parabola and coordinate axes
Revolution of area bounded by three graphs
Course 9
Lecture 9-1:
Torsion and Stresses in Beams
Torsion
Example 1
Example 2 - Hallow bar
Example 3 - Required outside diameter of shaft
Stresses in Beams
Radius of Curvature
Bending Stress
Flexural rigidity
Maximum bending stress
Section Modulus
Formulas for rectangular beam
Trapezoidal/Wide Flange/T Section
Shearing Stress
Shear stress diagrams
Rectangular section
Wide flange
Shear stress of any section
Shear and bending stress diagrams of sections
Built-up section
Spacing of bolts
Shear Flow
Shear Center
Examples
Radius of curvature
Cracking moment hallow circular section
Cracking moment - irregular concrete section
Vertical pole subjected to uniform wind pressure
Wooden plank used as retaining wall
Sheet pile with tension rods
Beam with overhang
Cantilever beam with cover plate
Lecture 9-2:
Word Problems and Integral Calculus
Worded problems
Number problems examples
Example 1
Example 2
Age problem examples
Example 1
Example 2 - Mary is ...
Mixture problems examples
Alcohol solutions
Water and alcohol solutions
Work problems examples
Principles discussed
Pipes filling a tank
Chinese restaurant fish pond
Motion-work problems examples
Man days...
Painting job
Motion-rate problem examples
Car and plane
Relative speed - Airplane, wind
Steve Deitmer - Relative speed - Boat, water
Relative speed - Boat, water
Integral calculus
Center of gravity of solids of revolution
Paraboloid
Spandrel of revolution
Spandrel of revolution 2
Cubic curve
Work
Conical water tank emptied to the top
Hemispherical tank emptied to the top
Semi-circular oil tank pumped to the top
Length of curve
Parabolic curve
Length of y = 4x^(3/2)
Surface Area
Graph y = 3x^(1/3)
Graph y = sqrt(x)
Lecture 9-3:
Surveying
Surveying
Traverse Adjustment
Linear error of closure
Balancing latitude and departure (Compass and Transit rules)
Example 1 - (3 sides) Compass Rule
Example 2 - (six sides) Transit Rule
Errors in measurement
Sources of error
Types of error
Precision and accuracy
Statistics (mean, standard deviation, mpv, standard errors, probable error etc)
Error of a sum
Error of a series
Error of a product
Examples
Error of measured distance
-
Using calculator function (Mode Stat)
Error of measured angles
-
Using calculator function (Mode Stat)
Weighted measurement
Angles
Distance
-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 observation
Most probable value of interior angle, multiple observation
Most probable value of angle
Lecture 9-4:
Beam Deflection
Double integration method example
Moment equation
Solving for constant of integration C1 and C2
Solve for the slope at support
Midspan deflection
Deflection at overhang
Maximum deflection
Area moment method
Rules of sign
Solving for slope at support
Slope at any point
Solving for displacement of a point
Solve for maximum deflection
Moment diagram by parts
Example
- Formula-based approach
Lecture 9-5:
Fluid Mechanics and Geotechnical Engineering
Open channel
Example - Most efficient trapezoidal section
Non-uniform flow example
Hydraulic jump
Hydrodynamics
Fixed flat plates
Fixed curved plates
Moving vanes
Work done on moving vane
Examples:
Fixed and moving flat plate
Fixed and moving curved vane
- Solution using COMPLEX Mode
Height a vertical jet of water support a given load
Water Hammer
Velocity (celerity) of pressure wave
Instantaneous, Rapid, and Slow Closure
Example
Soil mechanics
Phase diagrams
Soil properties
Porosity and void ratio
Water content
Degree of saturation
Specific gravity
Unit weight and dry unit of soil
Moist and saturated unit weight
Additional formulas
Relative density
Relative compaction
Suitability number and sorting coefficient
Example 1
Lecture 9-6:
Mechanics
Cables under point loads
Example 1 - Tension in cables and sag
Example 2 - Unequal support elevation
Example 3 - Cable pulled at one end
Parabolic cables
Length of cable
Examples
Symmetrical cable
Unequal support elevation
Unequal support elevation 2
Cable supporting a compound truss
Plane Truss
Type of trusses
Truss components
Zero-force members
Examples
King post truss
Howe truss
Cantilever truss (canopy)
- Using method of section
Transmission tower (K-truss)
Warren truss/K-truss
Truss with cables
Bowstring/Arch truss
Lecture 9-7:
Differential Calculus
Differentiation Rules
Definite Derivatives
Indefinite Derivatives
Implicit Differentiation
Related Rates
Example - Motion of particle
Example - Motion of particle 2
Example - Trigonometric function
Example - Trigonometric function 2
Example - Rate of separation of two automobiles
Example - Rate of separation of LRT Train and car
Example - Rate of separation of two cars
Example - Rate of change of distance between two men on a circular track
Example - Rate of change of commodity supply
Example - Rate of increase of production0
Example - Rate of boat approaching the dock
Example - Ladder resting on a vertical wall
Example - Rate of change of angle of elevation of the rocket to the observer
Course 10
Lecture 10-1:
Stresses in Beams
Examples - Stresses in Beams
Deck of a bridge over a deep ravine (composite beam)
Beam with overhang considering live load pattern
Simple beam with two concentrated loads and cover plate
Spacing of bolts in built-up beam
Bending on both axes - Examples
Crane runway girder subject to vertical and horizontal forces
Spacing of purlins with two sag rods
Combined axial and bending stress
Examples:
Simple beam with uniform load and axial load
Solid circular pole subject to vertical and lateral load
Plain concrete dam
Prestressed concrete
Pre-tensioning
Post-tensioning
Stress calculation
Examples:
Prestressed rectangular beam
Hallow core slab
Double tee concrete joist
Lecture 10-2:
Surveying
Distance measurement
Pacing
Tape corrections
Temperature correction
Pull correction
Sag correction
Slope correction
Reduction to Mean Sea Level
True distance
Stadia surveying
Examples:
Pacing
Area of field measured using a tape too long
Square lot measured using an erroneous tape
Required measurement to layout a building foundation
Distance measurement using a tape too short
Temperature correction problem
Standardized tape
Pull and temperature correction, three segments
Tape supported at four points
Normal pull
Stadia survey - inclined line of sight
Stadia Survey 2
Tacheometer
Leveling
Curvature and refraction
Examples:
Differential leveling
Profile leveling
Two-peg test
Peg adjustment
Trigonometric leveling example
Two hills (inter visible hills)
Line of levels run over soft ground
Lecture 10-3:
Beam Deflection
Virtual work method (Unit load method)
Principles
Example 1
Example 2 - Beam with internal pin
Example 3 - Frame
Cantilever beams
Example 1 - Beam loaded with uniform and concentrated load
Lecture 10-4:
Geotechnical Engineering
Soil properties examples
Example 1
Example 2
Example 3 - Relative compaction
Example 4 - Suitability number and sorting coefficient
Example - Borrow and fill
Atterberg limits
Plasticity index
Liquidity index
Consistency, Flow, Toughness indices
Shrinkage limit
Shrinkage ratio
Specific gravity
Examples:
Example 1
Example 2
Example 3
Soil Classification USCS
Example 1
AASHTO
Lecture 10-5:
Counting Principles & Probability
Counting principles
Examples:
How many different outfits
How many ways can the positions be filled
How many different license plates
Number of four-digit numbers
Number of three-digit numbers
How many numbers between 3000 and 5000 can be ...
Number of ways to be seated in a row
Permutation
Examples:
Number of different words
Number of ways pictures can be hung
Election of club officers
5 persons be seated in a row
5 men and 4 women seat in a row
9 books arranged on a shelf
6 boys and 4 girls seating on a bench
5 men and 3 women seated on a bench
Books arranged on a shelf
Men seated in a row
5 persons seated at a round table
8 persons seated at a round table
Group of engineers seated at a round table
Number of signals
Permutation with some things alike
Examples
Number of signals
Book arrangement
Combination
Examples
Number of handshakes
Number of sets of student to represent in a contest
Number of selection from number of candidates
Select set of books
Selecting a committee
Number of ways 5 red cards can be drawn
Number of ways of drawing 3 aces and 2 face cards
Number of ways of drawing exactly 3 clubs
Number of 5-letter words
Mutually exclusive events and examples
Rides in amusement park
Selecting 1 or more of 4 appliances
Raising any number of 5 different flags
Invite any one or more of your 8 friends
Number of 4-letter words
Number of 3-digit numbers greater than 480
Number of 3-digit numbers less than 530
How many four-letter word beginning with a capital
How 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 examples
Equal support elevation
Unequal support elevation
Gable frame subject to wind forces
Arch with quarter circle and straight member
Friction
Static and dynamic frictions
Impending motion
Angle of friction
Examples:
Box resting on horizontal surface subject to horizontal force
Box resting on horizontal surface subject to inclined force
Box resting on horizontal surface subject to inclined force 2
Bag of rice pulled by a force P
Block on an inclined plane
Block on an inclined plane subject to horizontal force
Block A on top of block B
Force to move the block
Uniform rod resting on a vertical wall
Uniform ladder pushed by a man
Man crossing a beam
Uniform box pushed by a worker
Cylindrical tank subject to inclined force
Belt friction
Example 1 - Block supported by a rope
Example 2 - Rope around a capstan
Example 3 - Flexible belt around a rotating drum
Example 4 - Horse fasten to the rail
Example 5 - Rail suspended from a rope
Example 6 - Rope running over two fixed cylinders
Lecture 10-7:
Differential Calculus
Related Rates
Example 1
- Triangle
Example 2
- Flow into conical tank
Example 3
- Flow into frustum of a cone
Maximum and Minima
Critical Numbers
Second Derivative Test
Example 1 - Critical points of the curve
Example 2 - Relative extrema of a function
Example 3 - Minimum cost
Example 4 - Maximizing the weekly sales
Example 5 - Maximizing the profit
Example 6 - Number of participants to maximize revenue
Example 7 - Point on a curve nearest to an external point
Example 8 - Time when ships are nearest each other
Example 9 - Landing point to reach the destination at shortest time
Example 10 - Field dimension for largest area
Variable Relationship for Maximum or Minimum Values
Example 11 - Position of stake for minimum length of wire
Example 12 - Dimension of cylindrical tank to use the least amount of material
Example 13 - Shortest beam that can reach the building
Example 14 - Observer's position for maximum angle subtended
Curvature of a Curve
Radius of Curvature
Circle of Curvature
Center of Curvature
Example 15 - Curvature of parabola
Example 16 - Radius of curvature
Example 17 - Center of curvature
Example 18 - Curvature of cissoid
Course 11
Lecture 11-1:
Stresses in Beams & Reinforced Concrete
Foundation Pressure
Gross and Net Pressures
With uplift
Examples:
Rectangular footing with axial and moment loads
Rectangular footing supporting a pedestal
Footing subjected to column not at its center
Column subject to axial load and moment
Concrete wall centrally located on a footing
Concrete retaining wall
Footing subject to moments in both axes
Reinforced Concrete
Codes (2015 NSCP)
Spacing of reinforcement
Example
- Rectangular beam
Example - Square column
Bundled bars
Ties and spirals
Development Length
Bars in tension
Modification factors
Bars in compression
Example - cantilever beam
Concrete cover
Shrinkage and temperature reinforcement
Example
Modulus of elasticity, rapture, and modification factor
Immediate deflection
Example
Load factors and combination
Methods of Analysis
Two spans, column ends
Two spans with spandrel beam
Two spans with simple support
Three spans
Example
Lecture 11-2:
Surveying
Curves
Types of horizontal curves
Simple circular curve
Example
Compound curve
Example 1
Example 2
Example 3
Reversed curve
Example 1 - Reversed curved connecting parallel roads
Example 2 - Parallel roads connected by equal turnout
Spiral curves
Example
Lecture 11-3:
Indeterminate Beams
Propped cantilever beams
Example 1
Example 2
Continuous beam
Example - By superposition
Degrees of indeterminacy of frames and trusses
Example - Classify each structure
Trusses
Examples
Frames
Examples
Multi-storey rigid frame
Three-moment equation
Formulas for 6Aa/L and 6Ab/L
Example
Lecture 11-4:
Permeability
Permeability (flow of water through soils)
Darcy's law
Notable formulas
Permeability tests
Constant head test
Falling head test
Equivalent hydraulic conductivities
Parallel (horizontal) flow
Normal (vertical) flow
Pumping wells
Unconfined wells
Confined wells
Example:
Constant head test
Constant head test 2
Falling head test
Falling head test 2
Flow through permeable layer
Equivalent hydraulic conductivity of layered soil
Normal flow through layered soil
Layered soil
Flow through layered soil 2
Confined aquifer
Pumping well
Lecture 11-5:
Probability & Statistics
Simple probability
Examples:
Ball drawn from a box
Card drawn from a deck
Roll a pair of dice. Sum of 1
1
Roll a pair of dice. Sum of 10 or 12
3 balls drawn from a bag
6 books arranged in a shelf
10 books arranged randomly in a shelf
Lottery tickets
3 cards drawn randomly
Poker game
Drawing exactly 3 face cards
Compound probability
Ind
ependent events
Dependent events
Examples:
Probability that a man will be alive
Two bags containing white and black balls
3 cards drawn, all aces
3 students are randomly chosen to get out of the room
Box with defective cell phones
Box with marbles
Mutually exclusive events
Probability of getting at least 1 in two throws of dice
Game of chess
Probability that a problem is solved
Probability that a target is hit
One ball drawn from each of the two bags
Three candidates for an office
Probability that there are at least four face cards
Binomial distribution
Box with defective cell phones
Probability that it will rain
Probability that 5 of the 12 employees have at least one credit card
Throw of 9 dice
Probability of getting a 9 in 3 throws of dice
Probability of getting at least 2 ones...
Probability that fewer than 4 will use a coupon
Odds of getting three heads in tossed coins
Probability to complete 4 years in college
Lecture 11-6:
Forces in Space
Rectangular components of force in space
Unit vector
Using the VECTOR MODE
Examples:
Vector components
Vector components 2
Resultant of forces in space
Moment about an axis
Moment about a point
Example 2
Equilibrium of forces in space
Support reactions
Two-force members
Door hinges
Examples:
To lift a table without tilting ...
Circular steel plate supported by 3 equally spaced posts
Triangular plate supported by 3 vertical cables
Rectangular plate suspended from 4 wires
Load supported by tripod
Using calculator MODE MATRIX
Boom supported by two cables
Homogeneous bar resting on vertical wall
Window supported by a wire
Pole supported by two cables
Two bars supported by a cable
Moment about a line
Boom supported by two cables
Two bars supported by a cable
Lecture 11-7:
Probability and Statistics
Probability and statistics (continuation)
Binomial distribution examples
Probability that the shipment will make it through
Multinomial distribution examples
A fair dice is thrown five times...
Box containing balls
A traffic engineer...
Poisson distribution examples
Road construction projects
Cars approaching an intersection
Defective bulbs
Bad reaction from injection
Defective items
Normal distribution
Examples:
Assembly line
Using calculator MODE STAT
Pollutants dumped into a river
Defective washers
Using calculator MODE STAT
Course 12
Lecture 12-1:
Reinforced Concrete Design
Pattern Loading
Sectional strength
Design strength and required strength
Reduction factors
Shear
Factored shear critical section
What is effective depth?
One-way shear (stirrups)
Nominal shear strength of the section
Limit of Vu
Shear strength provided by concrete
Circular sections
Members with axial compression
Members with significant axial tension
Required nominal shear strength
Shear reinforcement provided by transverse reinforcement
Shear reinforcement perpendicular to the axis
For circular tie or spiral
Maximum spacing of shear reinforcement
What is Av?
Minimum shear reinforcement
Examples:
Example 1 - Design problem
Example 2 - Analysis/investigation problem
Example 3 - Column subject to shear
Flexure and axial
Sectional strength - design assumptions
Value of "a" and Beta1
Assumptions for reinforcement
Minimum area of reinforcement
Tension and compression controlled
Derivation of formula and explanation of code assumptions
Stress in tension and compression steel
Singly-reinforced rectangular beam with fs = fy
Balanced condition
Balance "c"
"Rho" balance
Maximum steel area (Asmax or rho max)
Tension and compression controlled sections
Maximum tension steel (rho_t) of tension controlled section
Minimum steel reinforcement
Design of tension-controlled rectangular section
Singly reinforced
Doubly reinforced
Analysis/investigation of singly-reinforced beams
Additional resources in YouTube
Examples:
Analysis
of one-way slab
Analysis/investigation of singly-reinforced beam
Analysis/investigation of rectangular beam
Design of one-way slab
Lecture 12-2:
Transportation Engineering & Earthworks
Earthworks
Methods of volume measurement
Types of cross-section
Calculating irregular area
Trapezoidal rule
Simpson's 1/3 rule
Volume by cross-section
End area method
Prismoidal formula
Prismoidal correction
Unit area method
Volume of pit or reservoir
End are method
Prismoidal formula
Examples:
Area of cross-section
Area of cross-section 2
Area of cut and fill
Area of land by with straight-line boundary
Volume by prismoidal correction
Volume of cut and fill
Volume of borrow pit by unit area method
Volume of lake/reservoir
Vertical curves
Examples
Symmetrical sag parabolic curves
Symmetrical summit parabolic curve
Unsymmetrical parabolic curves
Transportation Engineering
Spiral curves
Rate of change of centripetal acceleration
Desirable length of spiral
Superelevation rate
Ideal super-elevation
Super-elevation on spiral curve
Sight distances
Aspects of sight distance
Sight distance/passing sight distance/stopping sight distance
Stopping sight distance
Sight distance for horizontal curves
Sight distance for vertical crest curves
Sight distance for vertical sag curves
Criterion for sag curves
Examples:
Spiral curve (desirable length, etc.)
Horizontal curve (max velocity, length of transition curve)
Ramp of NLEX...
Minimum stopping sight distance
Stopping sight distance
Stopping sight distance and length of curve
Vertical summit curve (Practice)
Vertical sag curve sight distance
Lecture 12-3:
Indeterminate Beams & Frames
Fully restrained beams
Fixed-end moment approach
Example - beam with concentrated load
Example - beam with uniform load
Example - beam with varying load
Moment distribution
Fixed-end moment
Beam stiffness
Distribution factor
Example - 2 spans with overhang
-
using the modified "k"
Approximate lateral force analysis
Portal method
Cantilever method
Lecture 12-4:
Engineering Economics
Interest
Example
Interest rate
Example
Simple interest
Example 1
Example 2
Example 3
Example 4
Ordinary and exact interest
Example 5
Example 6
Compound Interest
Compound interest, annual compounding
Example 1
Example 2
Example 3
Example 4
Example 5
Compound interest with periodic compounding
Example 1
Example 2
Example 3
Example 4
Example 5
Continuous compounding
Example 1
Example 2
Example 3
Effective annual interest rate
Example 1
Example 2
Example 3
Example 4
Cash flows
Example 1
Example 2
Example 3
Example 4
Example 5
Annuity
Ordinary annuity
Example 1
Example 2
Example 3
Interest period not the same as payment period
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Annuity Due
Example 1
Example 2
Example 3
Example 4
Deferred Annuity
Example 1
Example 2
Example 3
Perpetuity
Example 1
Example 2
Example 3
Example 4
Lecture 12-6:
Geotechnical Engineering
Stresses in Soil (effective, total, porewater)
Examples:
Example 1
Example 2
Example 3 - With downward seepage
Example 4 - With upward seepage
Example 5 - With seepage
Example 6 - With capillary rise
Flow Nets (flow lines, equipotential lines)
Characteristics of equipotential and flow lines
Isotropic and non-isotropic soils
Example
Stress distribution in soil
Westergaard equation
Boussinesq equation
Distribution due to uniform load (2:1 slope)
Examples:
Example 1
Example 2
Example 3
Shear strength of soil
Direct shear test
Triaxial test
Unconfined test
Examples:
Example 1
Example 2
Example 3
Compressibility of soil (settlement)
Total settlement
Primary settlement
Normally consolidated soil
Overconsolidated soil
Secondary settlement
Elastic settlement
Time rate of consolidation
Compression index
Coefficient of compressibility
Coefficient of volume compressibility
Time of consolidation
Examples:
Example 1
Example 2
Bearing capacity of soil
General shear failure
Rectangular footing
Square footing
Strip footing
Circular footing
Bearing capacity factors
Formulas
Local shear failure
Allowable bearing capacity
Gross allowable
Net allowable
Examples:
Example 1
Example 2
Lecture 12-7:
Dynamics
Dynamics
Kinematics
Motion of Particles
Rectilinear translation
Uniform motion
Variable acceleration
Constant acceleration
Free-falling body
Projectile motion
Examples:
Distance as function of time
Velocity as function of time
Acceleration as function of time
Compound motion - elevator
Motion curve, a-t diagram
Compound motion - Train
Compound motion - car
Variable acceleration - airplane
Free falling body - height of building
Orifice flow
Projectile problem
Airplane dropping a package
Rotation
Examples
Flywheel
Tires of a car
Tires of a truck
Tires of a truck 2
Accelerating car
Kinetics
Newton laws of motion
Pendulum
Examples:
Apparent weight
Block placed on an inclined plane
Block release at the roof
Block pushed by a constant force
-
Impulse-momentum principle
-Work-energy equation
Block is pushed and then released
Colliding train
Law of conservation of momentum
Inelastic collision
Coefficient of restitution
Truck bumps into a car
Perfectly elastic collision
Colliding block moving in opposite direction
Recoil velocity of rifle
Centrifugal and centripetal forces
Angle of banking
Ideal angle of banking
Examples:
Ball revolve in a vertical circle
Bucket with water swung on vertical plane
Block on a horizontally rotating platform
Fastest speed a car can move around a curve
Required angle of banking
Minimum angle of banking
Course 13
Lecture 13-1:
Reinforced Concrete
Worked examples:
Design of rectangular beam with known Mu
Investigation of doubly-reinforced beam
T-beams / Box beam
Analysis of T-beams
Example - Analysis
Example - Design
Example - Box beam analysis
Short columns subject to axial and bending
Plastic centroid and eccentricity
Example
Example:
Column - Balance loading, load that can be applied at "e"
-Interaction diagram
-Solution using MathCad
Example - Interaction diagram, spiral
Transverse reinforcement, special moment frame
Lecture 13-2:
Seismic and Footing
Seismic analysis
Design base shear
Seismic importance factor
Classification of structures
Seismic zone factor
Near source factors
Seismic source types
Seismic coefficient
Numerical coefficient R
Soil profile types
Structure period
Vertical distribution of force
Example 1 - 4 storey structure
Example 2 - Empty structural steel building
Footings
Design of square footing
Load and reactions in footing
Wide beam and punching shear
Moment in footing
Distribution of bars
Wall footing
Pile cap
Lecture 13-3:
Geotechnical Engineering
Piles
End bearing capacity
Skin friction capacity
Alpha method
Lambda method
Beta method
Example 1
Example 2
Example 3 - Single pile in three soil layers
Pile group
Example 1
Example 2
Example 3 - Pile settlement
Slope stability
Infinite slope
Example 1
Example 2
Example 3
Finite slope
Stability number
Critical height
Example 1
Example 2
L
ateral earth pressure (retaining wall)
At rest coefficient of lateral pressure
Rankine active earth pressure
Depth of crack
Active force after tensile crack
Rankine passive earth pressure
Inclined backfill
Coulomb's active and passive earth pressure
Example 1
Example 2
Example 3 - Sheet pile
Lecture 13-4:
Engineering Economics
Bond
Bond cash flow diagram and formula
Example 1
Example 2
Example 3
Example 4
Gradient series
Example 1
Example 2
Example 3
Equivalent uniform annual series
Example 1
Example 2
Example 3
Example 4
Example 5
Capitalized cost
Example 1
Example 2
Example 3
Example 4
Lecture 13-5:
Transportation Engineering
Example - Sight distance (horizontal curve)
Example - Passing sight distance
Traffic flow fundamentals
Volume of flow
Speed
Time mean speed ans space mean speed
Density
Flow, speed, density relationship
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18
Lecture 13-6:
Engineering Economics
Depreciation
Straight line method
Example 1
Example 2
Declining balance and double declining balance method
Example 1
Example 2
Sum-of-year-digits method
Example 1
Example 2
Sinking fund method
Example 1
Example 2
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