# Site map

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*MATHalino*.- Advance Engineering Mathematics
- Infinite Series
- Laplace Transform
- Laplace Transform by Direct Integration
- Table of Laplace Transforms of Elementary Functions
- Linearity Property | Laplace Transform
- First Shifting Property | Laplace Transform
- Second Shifting Property | Laplace Transform
- Change of Scale Property | Laplace Transform
- Multiplication by Power of t | Laplace Transform
- Division by t | Laplace Transform
- Laplace Transform of Derivatives
- Laplace Transform of Intergrals

- The Inverse Laplace Transform

- Algebra
- Laws of Exponents and Radicals
- Logarithm and Other Important Properties in Algebra
- Quadratic Equations in One Variable
- Special Products and Factoring
- Arithmetic, geometric, and harmonic progressions
- Binomial Theorem
- System of Equations
- Example 01 - Simultaneous Non-Linear Equations of Three Unknowns
- Example 02 - Simultaneous Non-Linear Equations of Three Unknowns
- Example 03 - Simultaneous Non-Linear Equations of Three Unknowns
- Example 04 - Simultaneous Non-Linear Equations of Three Unknowns
- Example 05 - Simultaneous Non-Linear Equations of Two Unknowns
- Example 06 - Simultaneous Non-Linear Equations of Two Unknowns
- Example 07 - Simultaneous Non-Linear Equations of Two Unknowns
- Number of Civil, Electrical, and Mechanical Engineers and Their Average Ages
- Smallest number for given remainders

- Variation / Proportional
- Verbal Problems in Algebra
- Age-related Problems
- Clock-related Problems
- Digit-related Problems
- Geometry-related Problems
- Mixture-related Problems
- Money-related Problems
- Motion-related Problems
- 01 - Sound of impact of the bullet hitting the target
- 02 - Cars moving in opposite directions
- 03 - In rowing a boat: find the rate of stream
- 04 - Two runners moving in the same direction in an oval track
- 05 - Two runners moving in opposite directions in a circular track
- 06 - The Battleship Was Brought to Full Stop After 1 Hour of Voyage
- 07 - A Man Covers an Unknown Distance at Different Rates
- 08 - Sound of Impact be Heard Before the Report of the Gun
- 09 - Number of Leaps to Take to Catch the Lead

- Number-related Problems
- Work-related Problems

- Probability and Statistics
- Counting Techniques
- Probability
- Number of Marbles in a Bag Containing Black and White Marbles
- Probability that a Large Shipment is Accepted or Not Accepted due to Defective Items
- Probability: A Family of Five Children
- Three Men Shoot and Only One of Them Hits the Target. Find the Probability that it was the First Man
- Probability Problems Involving Cards
- Poisson Probability Distribution

- Derivation of Formulas

- Differential Calculus
- Chapter 1 - Fundamentals
- Chapter 2 - Algebraic Functions
- Chapter 3 - Applications
- Maxima and Minima | Applications
- Application of Maxima and Minima
- 01 - 04 Number Problems in Maxima and Minima
- 05 - 08 Number Problems in Maxima and Minima
- 09 - 11 Rectangular Lot Problems in Maxima and Minima
- 12 - 14 Rectangular Lot Problems in Maxima and Minima
- 15 - 17 Box open at the top in maxima and minima
- 18 - 20 Rectangular beam in maxima and minima problems
- 21 - 24 Solved problems in maxima and minima
- 25 - 27 Solved problems in maxima and minima
- 28 - Solved problem in maxima and minima
- 29 - 31 Solved problems in maxima and minima
- 32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle
- 35 - 37 Solved problems in maxima and minima
- 38 - 40 Solved problems in maxima and minima
- 41 - 42 Maxima and Minima Problems Involving Trapezoidal Gutter
- 43 - 45 Solved problems in maxima and minima
- 46 - 47 Solved Problems in Maxima and Minima
- 48 - 49 Shortest distance from a point to a curve by maxima and minima
- 50 - 52 Nearest distance from a given point to a given curve
- 53 - 55 Solved Problems in Maxima and Minima
- 56 - 57 Maxima and minima problems of square box and silo
- 58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone
- 60 - 61 Maxima and minima problems of a folded page
- 62 - 63 Maxima and minima: cylinder inscribed in a cone and cone inscribed in a sphere
- 64 - 65 Maxima and minima: cone inscribed in a sphere and cone circumscribed about a sphere
- 66 - 68 Maxima and minima: Pyramid inscribed in a sphere and Indian tepee
- 69 - 71 Shortest and most economical path of motorboat
- 72 - 74 Light intensity of illumination and theory of attraction
- Cylinder of maximum volume and maximum lateral area inscribed in a cone
- Distance between projection points on the legs of right triangle (solution by Calculus)
- Largest parabolic section from right circular cone

- 01 Minimum length of cables linking to one point
- 02 Location of the third point on the parabola for largest triangle
- 03 Maximum Revenue for Tour Bus of 80 Seats
- 04 Largest Right Triangle of Given Hypotenuse

- Application of Maxima and Minima
- Time Rates | Applications
- 01-02 Water flowing into cylindrical tank
- 03 Water flowing into rectangular trough
- 04-05 Water flowing into triangular trough
- 06-07 Ladder slides down the wall
- 08-09 Rate of movement of shadow on the ground
- 10 - A boy on a bike
- 11-12 Two trains; one going to east, and the other is heading north
- 13-14 Water flowing into trapezoidal trough
- 15-16 Movement of shadow from light at eye level
- 17-18 Rate of shadow in the wall of a building
- 19-21 Two cars driving in parallel roads
- 22-24 One car from a city starts north, another car from nearby city starts east
- 25 Two cars that may collide at 12:30 PM
- 26-27 Time Rates: Kite moving horizontally
- 28-29 Time Rates: Two cars driving on roads that intersects at 60 degree
- 30 - Two trains in perpendicular railroad tracks
- 31-32 Train in an elevated track and car in perpendicular road
- 33-34 Time Rates: A car traveling east and airplane traveling north
- 35-36 Time Rates: Lengthening of shadow and movement of its tip in 3D space
- 37-38 How fast a ship leaving from its starting point
- Rate of change of surface area of sphere

- Maxima and Minima | Applications
- Chapter 4 - Trigonometric and Inverse Trigonometric Functions
- Maxima and Minima Using Trigonometric Functions
- 01 Rectangle of maximum perimeter inscribed in a circle
- 02 - Cylinder of maximum convex area inscribed in a sphere
- 03 - Heaviest cylinder that can be made from a shot
- 04-05 Stiffness and strength of timber beam
- 06-09 Trapezoidal gutter of greatest capacity
- 10 - Largest conical tent of given slant height
- 11 - Triangular gutter of maximum carrying capacity
- 12 - Cone of maximum convex area inscribed in a sphere
- 13 - Sphere cut into a circular cone
- 14-15 Ladder reaching the house from the ground outside the wall
- 16 - Light placed above the center of circular area
- 17-18 A man in a motorboat needs to catch a bus
- 19 Direction of the man to reach his destination as soon as possible
- 20-21 Width of the second corridor for a pole to pass horizontally
- 22 - Smallest cone that may circumscribe a sphere
- 23 - Sphere cut into a pyramid
- 24-25 Largest rectangle inscribed in a circular quadrant
- 26-27 Horizontal rod entering into a room from a perpendicular corridor
- Length of one side for maximum area of trapezoid (solution by Calculus)

- Problems in Caculus Involving Inverse Trigonometric Functions
- 37 - A ladder sliding downward
- 38 - Rate of rotation of search light pointing to a ship
- 39 - Rate of increase of angle of elevation of the line of sight
- 40 - Base angle of a growing right triangle
- 44 - Angle of elevation of the rope tied to a rowboat on shore
- 45 - Angle of elevation of the the kite's cord
- 46-48 Rate of rotation of the searchlight
- 49-51 Ship sailing east and turned N 30d E
- 52-53 Two cars traveling from the same point but going to different directions
- 55 - Greatest angle subtended by a picture

- Maxima and Minima Using Trigonometric Functions
- Partial Derivatives

- Elementary Differential Equations
- Elimination of Arbitrary Constants
- Differential Equations of Order One
- Separation of Variables | Equations of Order One
- Problem 01 | Separation of Variables
- Problem 02 | Separation of Variables
- Problem 03 | Separation of Variables
- Problem 04 | Separation of Variables
- Problem 05 | Separation of Variables
- Problem 06 | Separation of Variables
- Problem 07 | Separation of Variables
- Problem 08 | Separation of Variables
- Problem 09 | Separation of Variables
- Problem 10 | Separation of Variables
- Problem 11 | Separation of Variables
- Problem 12 | Separation of Variables
- Problem 13 | Separation of Variables
- Problem 14 - 15 | Separation of Variables
- Problem 16 | Separation of Variables
- Problem 17 | Separation of Variables
- Problem 18 | Separation of Variables
- Problem 19 | Separation of Variables
- Problem 20 | Separation of Variables
- Problem 21 | Separation of Variables
- Problem 22 | Separation of Variables
- Problem 23 | Separation of Variables

- Homogeneous Functions | Equations of Order One
- Exact Equations | Equations of Order One
- Linear Equations | Equations of Order One

- Separation of Variables | Equations of Order One
- Additional Topics on the Equations of Order One
- Integrating Factors Found by Inspection
- Problem 01 | Integrating Factors Found by Inspection
- Problem 02 | Integrating Factors Found by Inspection
- Problem 03 | Integrating Factors Found by Inspection
- Problem 04 | Integrating Factors Found by Inspection
- Problem 05 | Integrating Factors Found by Inspection
- Problem 06 - 07 | Integrating Factors Found by Inspection
- Problem 11 | Integrating Factors Found by Inspection
- Equation of a curve with given equation of slope and passing through a point

- The Determination of Integrating Factor
- Substitution Suggested by the Equation | Bernoulli's Equation

- Integrating Factors Found by Inspection
- Elementary Applications

- Fluid Mechanics and Hydraulics
- Principles of Hydrostatic Pressures
- Variation of Pressure with Depth in a Fluid
- Problem 01 - Variation of Pressure
- Problem 02 - Variation of Pressure
- Problem 03 - Variation of Pressure
- Problem 04 - Variation of Pressure
- Problem 05 - Variation of Pressure
- Problem 06 - Variation of Pressure
- Problem 07 - Variation of Pressure
- Problem 08 - Variation of Pressure
- Problem 09 - Variation of Pressure
- Problem 10 - Variation of Pressure
- Problem 11 - Variation of Pressure
- Problem 12 - Variation of Pressure

- Manometers

- Variation of Pressure with Depth in a Fluid
- Hydrostatic Pressure on Surfaces
- Relative Equilibrium of Liquids
- Fundamentals of Fluid Flow
- Discharge or Flow Rate
- Energy and Head of Flow
- Problem 01 - Bernoulli's Energy Theorem
- Problem 02 - Bernoulli's Energy Theorem
- Problem 03 - Bernoulli's Energy Theorem
- Problem 04 - Bernoulli's Energy Theorem
- Problem 05 - Bernoulli's Energy Theorem
- Problem 06 - Bernoulli's Energy Theorem
- Problem 07 - Bernoulli's Energy Theorem
- Problem 08 - Bernoulli's Energy Theorem
- Problem 09 - Bernoulli's Energy Theorem
- Problem 10 - Bernoulli's Energy Theorem
- Problem 11 - Bernoulli's Energy Theorem
- Problem 12 - Bernoulli's Energy Theorem
- Problem 13 - Bernoulli's Energy Theorem
- Problem 14 - Bernoulli's Energy Theorem
- Problem 15 - Bernoulli's Energy Theorem
- Problem 16 - Bernoulli's Energy Theorem
- Problem 17 - Bernoulli's Energy Theorem
- Problem 18 - Bernoulli's Energy Theorem
- Problem 19 - Bernoulli's Energy Theorem
- Problem 20 - Bernoulli's Energy Theorem

- Three Reservoirs Connected by Pipes at a Common Junction

- Principles of Hydrostatic Pressures

- Integral Calculus
- Chapter 1 - Fundamental Theorems of Calculus
- Chapter 2 - Fundamental Integration Formulas
- The General Power Formula | Fundamental Integration Formulas
- Logarithmic Functions | Fundamental Integration Formulas
- Exponential Functions | Fundamental Integration Formulas
- Trigonometric Functions | Fundamental Integration Formulas
- Inverse Trigonometric Functions | Fundamental Integration Formulas

- Chapter 3 - Techniques of Integration
- Chapter 4 - Applications of Integration
- Plane Areas in Rectangular Coordinates | Applications of Integration
- Example 1 | Plane Areas in Rectangular Coordinates
- Example 2 | Plane Areas in Rectangular Coordinates
- Example 3 | Plane Areas in Rectangular Coordinates
- Example 4 | Plane Areas in Rectangular Coordinates
- Example 5 | Plane Areas in Rectangular Coordinates
- Example 6 | Plane Areas in Rectangular Coordinates
- Example 7 | Area inside the square not common to the quarter circles
- Example 8 | Area bounded by arcs of quarter circles

- Plane Areas in Polar Coordinates | Applications of Integration
- 01 Area Enclosed by r = 2a cos^2 θ
- 01 Area Enclosed by r = 2a sin^2 θ
- 02 Area Bounded by the Lemniscate of Bernoulli r^2 = a^2 cos 2θ
- 03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)
- 03 Area Inside the Cardioid r = a(1 + cos θ) but Outside the Circle r = a
- 04 Area of the Inner Loop of the Limacon r = a(1 + 2 cos θ)
- 05 Area Enclosed by Four-Leaved Rose r = a cos 2θ
- 05 Area Enclosed by r = a sin 2θ and r = a cos 2θ
- 06 Area Within the Curve r^2 = 16 cos θ
- 07 Area Enclosed by r = 2a cos θ and r = 2a sin θ
- 08 Area Enclosed by r = a sin 3θ and r = a cos 3θ
- Area for grazing by the goat tied to a silo

- Length of Arc in Polar Plane | Applications of Integration
- Length of Arc in XY-Plane | Applications of Integration
- Volumes of Solids of Revolution | Applications of Integration

- Plane Areas in Rectangular Coordinates | Applications of Integration

- Plane Geometry
- The Triangle
- The Quadrilateral
- The Polygon
- The Circle
- Relationship Between Central Angle and Inscribed Angle
- 01 Arcs of quarter circles
- 02 Area bounded by arcs of quarter circles
- 03 Area enclosed by pairs of overlapping quarter circles
- 04 Four overlapping semi-circles inside a square
- 05 Three identical cirular arcs inside a circle
- 06 Circular arcs inside and tangent to an equilateral triangle
- 07 Area inside the larger circle but outside the smaller circle
- 08 Circles with diameters equal to corresponding sides of the triangle
- 09 Areas outside the overlapping circles indicated as shaded regions
- 10 Swimming pool in the shape of two intersecting circles
- 11 - Area inside a circle but outside three other externally tangent circles
- 12 - Circular sector inscribed in a square
- 13 - Length of Belt Connecting Two Pulleys
- 14 - Area the goat can graze inside a right triangular lot

- Reinforced Concrete Design

- Solid Geometry
- Solids for which Volume = Area of base times Altitude
- The Prism
- Common Prisms: Cube and Rectangular Parallelepiped
- Solved Problem 01 | Cube
- Solved Problem 02 | Cube
- Solved Problem 03 | Cube
- Solved Problem 04 | Cube
- Solved Problem 05 | Cube
- Solved Problem 06 | Cube
- Solved Problem 07 | Cube
- Solved Problem 08 | Cube
- Solved Problem 09 | Cube
- Solved Problem 10 | Cube
- Solved Problem 01 | Rectangular Parallelepiped
- Solved Problem 02 | Rectangular Parallelepiped
- Solved Problem 03 | Rectangular Parallelepiped
- Solved Problem 04 | Rectangular Parallelepiped
- Solved Problem 05 | Rectangular Parallelepiped
- Solved Problem 06 | Rectangular Parallelepiped
- Solved Problem 07 | Rectangular Parallelepiped
- Solved Problem 08 | Rectangular Parallelepiped
- Solved Problem 09 | Rectangular Parallelepiped
- Solved Problem 12 | Rectangular Parallelepiped
- Solved Problem 13 | Rectangular Parallelepiped
- Solved Problem 14 | Rectangular Parallelepiped

- Common Prisms: Cube and Rectangular Parallelepiped
- The Cylinder
- 001 A wire of given density and total mass

- The Prism
- Solids for which Volume = 1/3 Area of Base times Altitude
- Frustum
- Similar Figures
- The Sphere
- Spherical Sector
- Spherical Segment
- Spherical Wedge and Spherical Lune
- Spherical Zone
- 001 Solid steel ball remolded into hollow steel ball
- 002 Weight of snow ball
- 003 Weight of an iron shell
- 004 Hemispherical dome covered with gold
- 005 Weight of ivory billiard balls
- 006 Weight of steel ball bearings
- 007 - 008 Volume and surface area of earth and balloon
- 009 Price of Oranges
- 010 Volume of snow blocks in an igloo
- 011 Equal spheres piled to form a pyramid
- 012 Sphere circumscribed about a right circular cylinder
- 013 Insciribed and circumscribed sphere about a cube - volume comparison
- 014 Water poured into a jar of marbles
- 015 Two unequal balls inside the cylinder
- 016 Radius of the sphere circumscribing a regular triangular pyramid

- Summary and Review
- 001 Review Problem - Weight of a brass water pipe
- 002 Review Problem - Great wall of China moved to the equator
- 003 Review Problem - Sphere melted into cylinder
- 004 Review Problem - Size of a column in Fingal's Cave
- 005 Review Problem - Weight of gravity dam
- 006 Review Problem - Area illuminated by light placed in front of the globe
- 007 Review Problem - Length of wire
- 008 Review Problem - Pint tin can
- 009 Review Problem - Volume of anchor ring
- 010 Review Problem - Volume of a stick
- 011 Review Problem - Cutting the strongest square timber
- 012 Review Problem - Lake for household water supply
- 013 Review Problem - Volume of water inside the Venturi meter
- 014 Review Problem - Weight of concrete surge chamber when full of water
- 015 Review Problem - Volume of spherical shell
- 016 Review Problem - Mammoth Dredges Used in Panama Canal
- 017 Review Problem - Amount of water to fill the large network of city pipes
- 018 Review Problem - Volume of Stone Bridge
- 019 Review Problem - Which buy is more economical?
- 020 Review Problem - Volume of a factory chimney
- 021 Review Problem - Finding the volume of a stone
- 022 Review Problem - Tin required to create a funnel
- 023 Review Problem - Lead pipe melt into a cube
- 024 Review Problem - Will the pail hold all the water in the pipe?
- 025 Review Problem - Time required to fill a reservoir of water
- 026 Review Problem - Find the diameter of a wooden ball
- 027 Review Problem - Amount of concrete in making fencing posts
- 028 Review Problem - Amount of metal sheet used to construct a water tank
- 029 Review Problem - Chinese coin pierced by a square hole
- 030 Review Problem - Amount of molten glass in a lump
- 031 Review Problem - Cost of mainline sewer pipe
- 032 Review Problem - How many cups of coffee a coffee pot can hold?
- 033 Review Problem - Finding which one is the better bargain
- 034 Review Problem - Sphere dropped into a cone
- 035 Review Problem - Amount of concrete in a caisson
- 036 Review Problem - Circular hole bored through a sphere
- 037 Review Problem - Amount of material the factory chimney contain
- 038 Review Problem - Circular log with non-uniform cross-section
- 039 Review Problem - Bushels of wheat the grain elevator can hold
- 040 Review Problem - Volume comparisons of two water crystals
- 041 Review Problem - Weight capacity of industrial soap kettle
- 042 Review Problem - Water is poured by tilting the glass

- Solids for which Volume = Area of base times Altitude

- Surveying and Transportation Engineering

- Timber Design
- Bending Stress and Shearing Stress in Timber Beam
- Example 01: Maximum bending stress, shear stress, and deflection
- Example 02: Required Diameter of Circular Log Used for Footbridge Based on Shear Alone
- Example 03: Moment Capacity of a Timber Beam Reinforced with Steel and Aluminum Strips
- Example 04: Required Depth of Rectangular Timber Beam Based on Allowable Bending, Shear, and Deflection

- Bolted Connection
- Notching on Beams
- Working Stresses of Philippine Woods at 50% Stress Grade
- Working Stresses of Philippine Woods at 80% Stress Grade
- Allowable Loads on One Bolt in Timber Connection

- Bending Stress and Shearing Stress in Timber Beam

- Engineering Mechanics
- Principles of Statics
- Components of a Force
- 001 Horizontal and vertical componets of planar forces
- 002 Components of forces with given slope
- 003 Components of a 3D force with given distances
- 004 Components of a 3D force with given angles
- 005 Components of a force in rotated axes
- 006 Components of a force in axes that are not perpendicular to each other
- 007 Components of a force parallel and perpendicular to the incline
- 008 Components of a force at different pairs of axes
- 009 Force with given component parallel to the incline
- 010 Components of force normal and tangent to hypotenuse of a triangle
- 016 Components of a force parallel to supporting bars
- 017 Computation of force with given component parallel to a frame member

- Moment of a Force
- 226 - Moment of force about different points
- 227 - Moment of resultant force about a point
- 228 Intercepts of the resultant force
- 229 Y-coordinate of the point of application of the force
- 230 Distance from truss member to truss joint
- 231 Force P producing a clockwise moment about the origin
- 232 Moment of a force about points O and B
- 233 A force creating counterclockwise and clockwise moments

- Couples
- 245 - Couple in the box
- 246 - System with couples and forces on it
- 247 - Resultant of couples in a 3-step pulley
- 248 - Broken handwheel replaced by lever to close a gate valve
- 249 - Reactions at the bolts of speed reducer gear box
- 250 Reaction at the supports of cantilever truss
- 251 Two forces producing a couple and a force
- 252 Equivalent single force for a force and a couple
- 253-254 Equivalent single force to replace a force and a couple
- 255 Equivalent loads to a compression member with eccentric load
- 256 Twisting and bending effects
- 257 Horizontal couple equivalent to vertical forces
- 258 Equivalent horizontal and vertical couples

- Resultant of Concurrent Force System
- Resultant of Parallel Force System
- 236 Computation of the resultant of parallel forces acting on the lever
- 237 Finding the resultant of parallel forces acting on both sides of the rocker arm
- 238 Finding the resultant of trapezoidal loading
- 239 Resultant of lift on the wing of an airplane
- 240 How to locate the centroid of metal plate with circular hole
- 241 Finding the resultant of vertical forces acting on the Fink truss
- 242 Finding the unknown two forces with given resultant
- 243 Finding the magnitude and position of the missing force

- Resultant of Non-Concurrent Force System
- Problem 260 - 261 | Resultant of Non-Concurrent Force System
- Problem 262 | Resultant of Non-Concurrent Force System
- Problem 263 | Resultant of Non-Concurrent Force System
- Problem 264 | Resultant of Non-Concurrent Force System
- Problem 265 | Resultant of Non-Concurrent Force System
- Problem 266 | Resultant of Non-Concurrent Force System
- Problem 267 | Resultant of Non-Concurrent Force System
- Problem 268 | Resultant of Non-Concurrent Force System
- Problem 269 | Resultant of Non-Concurrent Force System
- Problem 270 | Resultant of Non-Concurrent Force System
- Problem 271 | Resultant of Non-Concurrent Force System

- Components of a Force
- Equilibrium of Force System
- Equilibrium of Concurrent Force System
- Problem 308 | Equilibrium of Concurrent Force System
- Problem 309 | Equilibrium of Concurrent Force System
- Problem 310 - 311 | Equilibrium of Concurrent Force System
- Problem 312 | Equilibrium of Concurrent Force System
- Problem 313 | Equilibrium of Concurrent Force System
- Problem 314 | Equilibrium of Concurrent Force System
- Problem 315 | Equilibrium of Concurrent Force System
- Problem 316 | Equilibrium of Concurrent Force System
- Problem 317 | Equilibrium of Concurrent Force System
- Problem 318 | Equilibrium of Concurrent Force System
- Problem 319 | Equilibrium of Concurrent Force System
- Problem 322 | Equilibrium of Force System
- Problem 323 | Equilibrium of Force System
- Problem 324 | Equilibrium of Three-force System
- Problem 325 | Equilibrium of Three-force System
- Problem 326 | Equilibrium of Force System
- Problem 327 | Equilibrium of Force System
- Problem 328 | Equilibrium of Force System

- Equilibrium of Parallel Force System
- Problem 329 | Equilibrium of Force System
- Problem 332 | Equilibrium of Parallel Force System
- Problem 333 | Equilibrium of Parallel Force System
- Problem 334 | Equilibrium of Parallel Force System
- Problem 335 | Equilibrium of Parallel Force System
- Problem 336 | Equilibrium of Parallel Force System
- Problem 337 | Equilibrium of Parallel Force System
- Problem 338 | Equilibrium of Parallel Force System
- Problem 339 | Equilibrium of Parallel Force System
- Problem 340 - 341 | Equilibrium of Parallel Force System
- Problem 342 | Equilibrium of Parallel Force System
- Problem 343 | Equilibrium of Parallel Force System
- Reactions of Tripod Made from Wood Planks
- Support Reactions of a Trapezoidal Slab with Three Points of Support

- Equilibrium of Non-Concurrent Force System
- Problem 346 | Equilibrium of Non-Concurrent Force System
- Problem 347 | Equilibrium of Non-Concurrent Force System
- Problem 348 | Equilibrium of Non-Concurrent Force System
- Problem 349 | Equilibrium of Non-Concurrent Force System
- Problem 350 | Equilibrium of Non-Concurrent Force System
- Problem 351 | Equilibrium of Non-Concurrent Force System
- Problem 352 | Equilibrium of Non-Concurrent Force System
- Problem 353 | Equilibrium of Non-Concurrent Force System
- Problem 354 | Equilibrium of Non-Concurrent Force System
- Problem 355 | Equilibrium of Non-Concurrent Force System
- Problem 356 | Equilibrium of Non-Concurrent Force System
- Problem 357 | Equilibrium of Non-Concurrent Force System
- Problem 358 | Equilibrium of Non-Concurrent Force System
- Problem 359 | Equilibrium of Non-Concurrent Force System
- Problem 360 | Equilibrium of Non-Concurrent Force System
- Problem 361 | Equilibrium of Non-Concurrent Force System

- Equilibrium of Concurrent Force System
- Analysis of Structures
- Method of Joints | Analysis of Simple Trusses
- Problem 001-mj | Method of Joints
- Problem 002-mj | Method of Joints
- Problem 003-mj | Method of Joints
- Problem 004-mj | Method of Joints
- Problem 005-mj | Method of Joints
- Problem 403 | Method of Joints
- Problem 404 Roof Truss - Method of Joints
- Problem 405 | Method of Joints
- Problem 406 Cantilever Truss - Method of Joints
- Problem 407 Cantilever Truss - Method of Joints
- Problem 408 Warren Truss - Method of Joints
- Problem 409 Howe Roof Truss - Method of Joints
- Problem 410 Pratt Roof Truss - Method of Joints
- Problem 411 Cantilever Truss by Method of Joints
- Problem 412 Right Triangular Truss by Method of Joints
- Problem 413 Crane by Method of Joints
- Problem 414 Truss by Method of Joints

- Method of Sections | Analysis of Simple Trusses
- Problem 001-ms | Method of Sections
- Problem 002-ms | Method of Sections
- Problem 003-ms | Method of Sections
- Problem 004-ms | Method of Sections
- Problem 005-ms | Method of Sections
- Problem 417 - Roof Truss by Method of Sections
- Problem 418 - Warren Truss by Method of Sections
- Problem 419 - Warren Truss by Method of Sections
- Problem 420 - Howe Truss by Method of Sections
- Problem 421 - Cantilever Truss by Method of Sections
- Problem 422 - Right-triangular Truss by Method of Sections
- Problem 423 - Howe Roof Truss by Method of Sections
- Problem 424 - Method of Joints Checked by Method of Sections
- Problem 425 - Fink Truss by Method of Sections
- Problem 426 - Fink Truss by Method of Sections
- Problem 427 - Interior Members of Nacelle Truss by Method of Sections
- Problem 428 - Howe Truss by Method of Sections
- Problem 429 - Cantilever Truss by Method of Sections
- Problem 430 - Parker Truss by Method of Sections
- Problem 431 - Members in the Third Panel of a Parker Truss
- Problem 432 - Force in Members of a Truss by Method of Sections
- Problem 433 - Scissors Truss by Method of Sections
- Problem 434 - Scissors Truss by Method of Sections
- Problem 435 - Transmission Tower by Method of Sections
- Problem 436 - Howe Truss With Counter Braces
- Problem 437 - Truss With Counter Diagonals
- Problem 438 - Truss With Redundant Members

- Method of Members | Frames Containing Three-Force Members
- Problem 001-mm | Method of Members
- Problem 002-mm | Method of Members
- Problem 003-mm | Method of Members
- Problem 004-mm | Method of Members
- Problem 005-mm | Method of Members
- Problem 006-fr | Analysis of Simple Frame
- Problem 007-cb | Analysis of Cabled Frame
- Problem 440 - Frame Analysis by Method of Members
- Problem 441 - Analysis of Frame by Method of Members
- Problem 442 - Analysis of Frame by Method of Members
- Problem 443 - Analysis of Frame by Method of Members
- Problem 444 - Analysis of an A-Frame by Method of Members
- Problem 445 - Analysis of an X-Frame by Method of Members
- Problem 446 - Compound Truss Formed Into Three-Hinged Arch
- Problem 447 - Compound Truss Formed Into Three-Hinged Arch
- Problem 448 - Beam of Three Segments Joined by Internal Hinges
- Problem 449 - Reactions at the Supports of a Bridge
- Problem 450 - Reactions at Hinge Support of the Frame Holding
- Problem 451 - Components of Hinge Forces of a Frame
- Problem 452 - Weight Supported by a Cable Which Runs Over a Frictionless Pulley
- Problem 453 - Analysis of A-frame with Weightless Cylinder
- Problem 454 - System of Booms and Pulleys

- Method of Joints | Analysis of Simple Trusses
- Friction
- Problem 506 | Friction
- Problem 507 | Friction
- Problem 508 | Friction
- Problem 509 | Friction
- Problem 510 | Friction
- Problem 511 | Friction
- Problem 512 | Friction
- Problem 513 | Friction
- Problem 514 | Friction
- Problem 515 | Friction
- Problem 516 | Friction
- Problem 519 | Friction
- Problem 520 | Friction
- Problem 521 | Friction
- Problem 522 | Friction
- Problem 523 | Friction
- Problem 524 | Friction
- Problem 525 | Friction
- Problem 526 | Friction
- Problem 527 and Problem 528 | Friction
- Problem 529 | Friction
- Problem 530 | Friction
- Problem 531 | Friction
- Problem 532 | Friction
- Problem 533 | Friction
- Problem 535 | Friction on Wedges
- Problem 536 | Friction on Wedges
- Problem 537 | Friction on Wedges
- Problem 538 | Friction on Wedges
- Problem 539 | Friction on Wedges
- Problem 540 | Friction on Wedges
- Problem 541 | Friction on Wedges
- Problem 542 | Friction on Wedges
- Problem 543 | Friction on Wedges
- Problem 544 | Friction on Wedges

- Centroids and Centers of Gravity
- 705 Centroid of parabolic segment by integration
- 706 Centroid of quarter circle by integration
- 707 Centroid of quarter ellipse by integration
- 708 Centroid and area of spandrel by integration
- 709 Centroid of the area bounded by one arc of sine curve and the x-axis
- 714 Inverted T-section | Centroid of Composite Figure
- 715 Semicircle and Triangle | Centroid of Composite Figure
- 716 Semicircular Arc and Lines | Centroid of Composite Figure
- 717 Symmetrical Arcs and a Line | Centroid of Composite Line
- 718 Square and Triangles | Centroid of Composite Area
- 719 Closed Straight Lines | Centroid of Composite Lines
- 720 Two triangles | Centroid of Composite Area
- 721 Increasing the width of flange to lower the centroid of inverted T-beam
- 722 Semicircle and quarter circle | Centroid of composite area
- 723 Rectangle, quarter circle and triangle | Centroid of Composite Area
- 724 Rectangle, semicircle, quarter-circle, and triangle | Centroid of Composite Area
- 725 Centroid of windlift of airplane wing | Centroid of area
- 726 Area enclosed by parabola and straigh line | Centroid of Composite Area

- Moment of Inertia and Radius of Gyration
- 816 Polar moment of inertia and radius of gyration at one corner of rectangle
- 817 Hollow Tube | Moment of Inertia and Radius of Gyration
- 818 Hollow square section | Moment of Inertia and Radius of Gyration
- 819 Inverted T-section | Moment of Inertia
- 820 Unsymmetrical I-section | Moment of Inertia
- 821 Rectangle minus semi-circle | Moment of Inertia
- Area, moment of inertia, and radius of gyration of parabolic section

- Dynamics
- Kinematics
- 1002 Location of warning torpedo | Rectilinear Translation
- 1003 Return in 10 seconds | Rectilinear Translation
- 1004 Relative velocity | Rectilinear Translation
- 1005 Finding the depth of well by dropping a stone | Rectilinear Translation
- 1007 Finding when and where the stones pass each other | Rectilinear Translation
- 1008 Stones thrown vertically upward | Rectilinear Translation
- 1009 Initial velocity of the second ball | Rectilinear Translation
- 1010 Time to wait in dropping a stone | Rectilinear Translation
- 1011 Time of launching a ship | Rectilinear Translation
- 1012 Train at constant deceleration | Rectilinear Translation
- 1019 Velocity and acceleration from the equation of distance | Motion with Variable Acceleration
- Two particles released from the same height and reached the base at the same time

- Curvilinear Translation (Projectile Motion)

- Kinematics
- Force Systems in Space

- Principles of Statics

- Strength of Materials
- Chapter 01 - Simple Stresses
- Normal Stresses
- Solution to Problem 104 Normal Stress
- Solution to Problem 105 | Normal Stress
- Solution to Problem 106 Normal Stress
- Solution to Problem 107 Normal Stress
- Solution to Problem 108 Normal Stress
- Solution to Problem 109 Normal Stress
- Solution to Problem 110 Normal Stress
- Solution to Problem 111 Normal Stress
- Solution to Problem 112 Normal Stress
- Solution to Problem 113 Normal Stress
- Solution to Problem 114 Normal Stress

- Shear Stress
- Solution to Problem 115 Shear Stress
- Solution to Problem 116 Shear Stress
- Solution to Problem 117 Shear Stress
- Solution to Problem 118 Shear Stress
- Solution to Problem 119 Shear Stress
- Solution to Problem 120 Shear Stress
- Solution to Problem 121 Shear Stress
- Solution to Problem 122 Shear Stress
- Solution to Problem 123 Shear Stress

- Bearing Stress
- Thin-walled Pressure Vessels
- Solution to Problem 133 Pressure Vessel
- Solution to Problem 134 Pressure Vessel
- Solution to Problem 135 Pressure Vessel
- Solution to Problem 136 Pressure Vessel
- Solution to Problem 137 Pressure Vessel
- Solution to Problem 138 Pressure Vessel
- Solution to Problem 139 Pressure Vessel
- Solution to Problem 140 Pressure Vessel
- Solution to Problem 141 Pressure Vessel
- Solution to Problem 142 Pressure Vessel

- Normal Stresses
- Chapter 02 - Strain
- Simple Strain
- Stress-strain Diagram
- Axial Deformation
- Solution to Problem 203 Stress-strain Diagram
- Solution to Problem 204 Stress-strain Diagram
- Solution to Problem 205 Axial Deformation
- Solution to Problem 206 Axial Deformation
- Solution to Problem 207 Axial Deformation
- Solution to Problem 208 Axial Deformation
- Solution to Problem 209 Axial Deformation
- Solution to Problem 210 Axial Deformation
- Solution to Problem 211 Axial Deformation
- Solution to Problem 212 Axial Deformation
- Solution to Problem 213 Axial Deformation
- Solution to Problem 214 Axial Deformation
- Solution to Problem 215 Axial Deformation
- Solution to Problem 216 Axial Deformation
- Solution to Problem 217 Axial Deformation
- Solution to Problem 218 Axial Deformation
- Solution to Problem 219 Axial Deformation

- Shearing Deformation
- Solution to Problem 222 Poisson's Ratio
- Solution to Problem 223 Triaxial Deformation
- Solution to Problem 224 Triaxial Deformation
- Solution to Problem 225 Biaxial Deformation
- Solution to Problem 226 Biaxial Deformation
- Solution to Problem 227 Biaxial Deformation
- Solution to Problem 228 Biaxial Deformation

- Statically Indeterminate Members
- Solution to Problem 233 Statically Indeterminate
- Solution to Problem 234 Statically Indeterminate
- Solution to Problem 235 Statically Indeterminate
- Solution to Problem 236 Statically Indeterminate
- Solution to Problem 237 Statically Indeterminate
- Solution to Problem 238 Statically Indeterminate
- Solution to Problem 239 Statically Indeterminate
- Solution to Problem 240 Statically Indeterminate
- Solution to Problem 241 Statically Indeterminate
- Solution to Problem 242 Statically Indeterminate
- Solution to Problem 243 Statically Indeterminate
- Solution to Problem 244 Statically Indeterminate
- Solution to Problem 245 Statically Indeterminate
- Solution to Problem 246 Statically Indeterminate
- Solution to Problem 247 Statically Indeterminate
- Solution to Problem 248 Statically Indeterminate
- Solution to Problem 249 Statically Indeterminate
- Solution to Problem 250 Statically Indeterminate
- Solution to Problem 251 Statically Indeterminate
- Solution to Problem 252 Statically Indeterminate
- Solution to Problem 253 Statically Indeterminate
- Solution to Problem 254 Statically Indeterminate
- Solution to Problem 255 Statically Indeterminate
- Solution to Problem 256 Statically Indeterminate
- Solution to Problem 257 Statically Indeterminate

- Thermal Stress
- Solution to Problem 261 Thermal Stress
- Solution to Problem 262 Thermal Stress
- Solution to Problem 263 Thermal Stress
- Solution to Problem 264 Thermal Stress
- Solution to Problem 265 Thermal Stress
- Solution to Problem 266 Thermal Stress
- Solution to Problem 267 Thermal Stress
- Solution to Problem 268 Thermal Stress
- Solution to Problem 269 Thermal Stress
- Solution to Problem 270 Thermal Stress
- Solution to Problem 271 Thermal Stress
- Solution to Problem 272 Thermal Stress
- Solution to Problem 273 Thermal Stress
- Solution to Problem 274 Thermal Stress
- Solution to Problem 275 Thermal Stress
- Solution to Problem 276 Thermal Stress

- Chapter 03 - Torsion
- Torsion
- Solution to Problem 304 Torsion
- Solution to Problem 305 Torsion
- Solution to Problem 306 Torsion
- Solution to Problem 307 Torsion
- Solution to Problem 308 Torsion
- Solution to Problem 309 Torsion
- Solution to Problem 310 Torsion
- Solution to Problem 311 Torsion
- Solution to Problem 312 Torsion
- Solution to Problem 313 Torsion
- Solution to Problem 314 Torsion
- Solution to Problem 315 Torsion
- Solution to Problem 316 Torsion
- Solution to Problem 317 Torsion
- Solution to Problem 318 Torsion
- Solution to Problem 319 Torsion
- Solution to Problem 320 Torsion
- Solution to Problem 321 Torsion
- Solution to Problem 322 Torsion
- Solution to Problem 323 Torsion
- Solution to Problem 324 Torsion
- Solution to Problem 325 Torsion

- Flanged bolt couplings
- Solution to Problem 326 | Flanged bolt couplings
- Solution to Problem 327 | Flanged bolt couplings
- Solution to Problem 328 | Flanged bolt couplings
- Solution to Problem 329 | Flanged bolt couplings
- Solution to Problem 330 | Flanged bolt couplings
- Solution to Problem 331 | Flanged bolt couplings
- Solution to Problem 332 | Flanged bolt couplings
- Solution to Problem 333 | Flanged bolt couplings
- Solution to Problem 334 | Flanged bolt couplings
- Solution to Problem 335 | Flanged bolt couplings

- Torsion of thin-walled tube
- Helical Springs
- Solution to Problem 343 | Helical Springs
- Solution to Problem 344 | Helical Springs
- Solution to Problem 345 | Helical Springs
- Solution to Problem 346 | Helical Springs
- Solution to Problem 347 | Helical Springs
- Solution to Problem 348 | Helical Springs
- Solution to Problem 349 | Helical Springs
- Solution to Problem 350 | Helical Springs

- Torsion
- Chapter 04 - Shear and Moment in Beams
- Shear and Moment Diagrams
- Solution to Problem 403 | Shear and Moment Diagrams
- Solution to Problem 404 | Shear and Moment Diagrams
- Solution to Problem 405 | Shear and Moment Diagrams
- Solution to Problem 406 | Shear and Moment Diagrams
- Solution to Problem 407 | Shear and Moment Diagrams
- Solution to Problem 408 | Shear and Moment Diagrams
- Solution to Problem 409 | Shear and Moment Diagrams
- Solution to Problem 410 | Shear and Moment Diagrams
- Solution to Problem 411 | Shear and Moment Diagrams
- Solution to Problem 412 | Shear and Moment Diagrams
- Solution to Problem 413 | Shear and Moment Diagrams
- Solution to Problem 414 | Shear and Moment Diagrams
- Solution to Problem 415 | Shear and Moment Diagrams
- Solution to Problem 416 | Shear and Moment Diagrams
- Solution to Problem 417 | Shear and Moment Diagrams
- Solution to Problem 418 | Shear and Moment Diagrams
- Solution to Problem 419 | Shear and Moment Diagrams
- Solution to Problem 420 | Shear and Moment Diagrams
- Solution to Problem 421 | Shear and Moment Equations
- Solution to Problem 422 | Shear and Moment Equations

- Relationship Between Load, Shear, and Moment
- Solution to Problem 425 | Relationship Between Load, Shear, and Moment
- Solution to Problem 426 | Relationship Between Load, Shear, and Moment
- Solution to Problem 427 | Relationship Between Load, Shear, and Moment
- Solution to Problem 428 | Relationship Between Load, Shear, and Moment
- Solution to Problem 429 | Relationship Between Load, Shear, and Moment
- Solution to Problem 430 | Relationship Between Load, Shear, and Moment
- Solution to Problem 431 | Relationship Between Load, Shear, and Moment
- Solution to Problem 432 | Relationship Between Load, Shear, and Moment
- Solution to Problem 433 | Relationship Between Load, Shear, and Moment
- Solution to Problem 434 | Relationship Between Load, Shear, and Moment
- Solution to Problem 435 | Relationship Between Load, Shear, and Moment
- Solution to Problem 436 | Relationship Between Load, Shear, and Moment
- Solution to Problem 437 | Relationship Between Load, Shear, and Moment
- Solution to Problem 438 | Relationship Between Load, Shear, and Moment
- Solution to Problem 439 | Relationship Between Load, Shear, and Moment
- Solution to Problem 440 | Relationship Between Load, Shear, and Moment
- Solution to Problem 441 | Relationship Between Load, Shear, and Moment
- Solution to Problem 442 | Relationship Between Load, Shear, and Moment
- Solution to Problem 443 | Relationship Between Load, Shear, and Moment
- Solution to Problem 444 | Relationship Between Load, Shear, and Moment
- Solution to Problem 445 | Relationship Between Load, Shear, and Moment
- Solution to Problem 446 | Relationship Between Load, Shear, and Moment

- Load and moment diagrams for a given shear diagram
- Solution to Problem 447 | Relationship Between Load, Shear, and Moment
- Solution to Problem 448 | Relationship Between Load, Shear, and Moment
- Solution to Problem 449 | Relationship Between Load, Shear, and Moment
- Solution to Problem 450 | Relationship Between Load, Shear, and Moment
- Solution to Problem 451 | Relationship Between Load, Shear, and Moment

- Moving Loads

- Shear and Moment Diagrams
- Chapter 05 - Stresses in Beams
- Flexure Formula
- Section Modulus
- Solution to Problem 503 | Flexure Formula
- Solution to Problem 504 | Flexure Formula
- Solution to Problem 505 | Flexure Formula
- Solution to Problem 506 | Flexure Formula
- Solution to Problem 507 | Flexure Formula
- Solution to Problem 508 | Flexure Formula
- Solution to Problem 509 | Flexure Formula
- Solution to Problem 510 | Flexure Formula
- Solution to Problem 511 | Flexure Formula
- Solution to Problem 512 | Flexure Formula
- Solution to Problem 513 | Flexure Formula
- Solution to Problem 514 | Flexure Formula
- Solution to Problem 515 | Flexure Formula
- Solution to Problem 516 | Flexure Formula
- Solution to Problem 517 | Flexure Formula
- Solution to Problem 518 | Flexure Formula
- Solution to Problem 519 | Flexure Formula
- Solution to Problem 520 | Flexure Formula
- Solution to Problem 521 | Flexure Formula
- Solution to Problem 522 | Flexure Formula
- Solution to Problem 523 | Flexure Formula
- Solution to Problem 524 | Flexure Formula
- Solution to Problem 525 | Flexure Formula
- Solution to Problem 526 | Flexure Formula
- Solution to Problem 527 | Flexure Formula

- Economic Sections
- Solution to Problem 529 | Economic Sections
- Solution to Problem 530 | Economic Sections
- Solution to Problem 531 | Economic Sections
- Solution to Problem 532 | Economic Sections
- Solution to Problem 533 | Economic Sections
- Solution to Problem 534 | Economic Sections
- Solution to Problem 535 | Economic Sections
- Solution to Problem 536 | Economic Sections

- Floor Framing
- Unsymmetrical Beams
- Solution to Problem 548 | Unsymmetrical Beams
- Solution to Problem 549 | Unsymmetrical Beams
- Solution to Problem 550 | Unsymmetrical Beams
- Solution to Problem 551 | Unsymmetrical Beams
- Solution to Problem 552 | Unsymmetrical Beams
- Solution to Problem 553 | Unsymmetrical Beams
- Solution to Problem 554 | Unsymmetrical Beams
- Solution to Problem 555 | Unsymmetrical Beams
- Solution to Problem 556 | Unsymmetrical Beams
- Solution to Problem 557 | Unsymmetrical Beams
- Solution to Problem 558 | Unsymmetrical Beams

- Superimposed or Built-up Beams
- Horizontal Shearing Stress
- Shear Flow
- Solution to Problem 567 | Horizontal Shearing Stress
- Solution to Problem 568 | Horizontal Shearing Stress
- Solution to Problem 569 | Horizontal Shearing Stress
- Solution to Problem 570 | Horizontal Shearing Stress
- Solution to Problem 571 | Horizontal Shearing Stress
- Solution to Problem 572 | Horizontal Shearing Stress
- Solution to Problem 573 | Horizontal Shearing Stress
- Solution to Problem 574 | Horizontal Shearing Stress
- Solution to Problem 575 | Horizontal Shearing Stress
- Solution to Problem 576 | Horizontal Shearing Stress
- Solution to Problem 577 | Horizontal Shearing Stress

- Design for Flexure and Shear
- Solution to Problem 580 | Design for Flexure and Shear
- Solution to Problem 581 | Design for Flexure and Shear
- Solution to Problem 582 | Design for Flexure and Shear
- Solution to Problem 583 | Design for Flexure and Shear
- Solution to Problem 584 | Design for Flexure and Shear
- Solution to Problem 585 | Design for Flexure and Shear
- Solution to Problem 586 | Design for Flexure and Shear
- Solution to Problem 587 | Design for Flexure and Shear
- Solution to Problem 588 | Design for Flexure and Shear
- Solution to Problem 589 | Design for Flexure and Shear
- Solution to Problem 590 | Design for Flexure and Shear

- Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 592 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 593 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 594 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 595 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 596 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 597 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 598 | Spacing of Rivets or Bolts in Built-Up Beams
- Solution to Problem 599 | Spacing of Rivets or Bolts in Built-Up Beams

- Flexure Formula
- Chapter 06 - Beam Deflections
- Double Integration Method | Beam Deflections
- Solution to Problem 605 | Double Integration Method
- Solution to Problem 606 | Double Integration Method
- Solution to Problem 607 | Double Integration Method
- Solution to Problem 608 | Double Integration Method
- Solution to Problem 609 | Double Integration Method
- Solution to Problem 610 | Double Integration Method
- Solution to Problem 611 | Double Integration Method
- Solution to Problem 612 | Double Integration Method
- Solution to Problem 613 | Double Integration Method
- Solution to Problem 614 | Double Integration Method
- Solution to Problem 615 | Double Integration Method
- Solution to Problem 616 | Double Integration Method
- Solution to Problem 617 | Double Integration Method
- Solution to Problem 618 | Double Integration Method
- Solution to Problem 619 | Double Integration Method
- Solution to Problem 620 | Double Integration Method
- Solution to Problem 621 | Double Integration Method

- Moment Diagram by Parts
- Solution to Problem 624 | Moment Diagram by Parts
- Solution to Problem 625 | Moment Diagram by Parts
- Solution to Problem 626 | Moment Diagram by Parts
- Solution to Problem 627 | Moment Diagram by Parts
- Solution to Problem 628 | Moment Diagrams by Parts
- Solution to Problem 629 | Moment Diagrams by Parts
- Solution to Problem 630 | Moment Diagrams by Parts
- Solution to Problem 631 | Moment Diagrams by Parts
- Solution to Problem 632 | Moment Diagrams by Parts

- Area-Moment Method | Beam Deflections
- Deflection of Cantilever Beams | Area-Moment Method
- Solution to Problem 636 | Deflection of Cantilever Beams
- Solution to Problem 637 | Deflection of Cantilever Beams
- Solution to Problem 638 | Deflection of Cantilever Beams
- Solution to Problem 639 | Deflection of Cantilever Beams
- Solution to Problem 640 | Deflection of Cantilever Beams
- Solution to Problem 641 | Deflection of Cantilever Beams
- Solution to Problem 642 | Deflection of Cantilever Beams
- Solution to Problem 643 | Deflection of Cantilever Beams
- Solution to Problem 644 | Deflection of Cantilever Beams
- Solution to Problem 645 | Deflection of Cantilever Beams
- Solution to Problem 646 | Deflection of Cantilever Beams
- Solution to Problem 647 | Deflection of Cantilever Beams
- Solution to Problem 648 | Deflection of Cantilever Beams

- Deflections in Simply Supported Beams | Area-Moment Method
- Solution to Problem 653 | Deflections in Simply Supported Beams
- Solution to Problem 654 | Deflections in Simply Supported Beams
- Solution to Problem 655 | Deflections in Simply Supported Beams
- Solution to Problem 656 | Deflections in Simply Supported Beams
- Solution to Problem 657 | Deflections in Simply Supported Beams
- Solution to Problem 658 | Deflections in Simply Supported Beams
- Solution to Problem 659 | Deflections in Simply Supported Beams
- Solution to Problem 660 | Deflections in Simply Supported Beams
- Solution to Problem 661 | Deflections in Simply Supported Beams
- Solution to Problem 662 | Deflections in Simply Supported Beams
- Solution to Problem 663 | Deflections in Simply Supported Beams
- Solution to Problem 664 | Deflections in Simply Supported Beams
- Solution to Problem 665 | Deflections in Simply Supported Beams
- Solution to Problem 666 | Deflections in Simply Supported Beams
- Solution to Problem 667 | Deflections in Simply Supported Beams
- Solution to Problem 668 | Deflections in Simply Supported Beams
- Solution to Problem 669 | Deflections in Simply Supported Beams
- Solution to Problem 670 | Deflections in Simply Supported Beams

- Deflection of Cantilever Beams | Area-Moment Method
- Midspan Deflection | Deflections in Simply Supported Beams
- Solution to Problem 673 | Midspan Deflection
- Solution to Problem 674 | Midspan Deflection
- Solution to Problem 675 | Midspan Deflection
- Solution to Problem 676 | Midspan Deflection
- Solution to Problem 677 | Midspan Deflection
- Solution to Problem 678 | Midspan Deflection
- Solution to Problem 679 | Midspan Deflection
- Solution to Problem 680 | Midspan Deflection
- Solution to Problem 681 | Midspan Deflection

- Method of Superposition | Beam Deflection
- Solution to Problem 685 | Beam Deflection by Method of Superposition
- Solution to Problem 686 | Beam Deflection by Method of Superposition
- Solution to Problem 687 | Beam Deflection by Method of Superposition
- Solution to Problem 688 | Beam Deflection by Method of Superposition
- Solution to Problem 689 | Beam Deflection by Method of Superposition
- Solution to Problem 690 | Beam Deflection by Method of Superposition
- Solution to Problem 691 | Beam Deflection by Method of Superposition
- Solution to Problem 692 | Beam Deflection by Method of Superposition
- Solution to Problem 693 | Beam Deflection by Method of Superposition
- Solution to Problem 694-695 | Beam Deflection by Method of Superposition
- Solution to Problem 696-697 | Beam Deflection by Method of Superposition

- Conjugate Beam Method | Beam Deflection
- Problem 653 | Beam Deflection by Conjugate Beam Method
- Problem 654 | Beam Deflection by Conjugate Beam Method
- Problem 655 | Beam Deflection by Conjugate Beam Method
- Problem 656 | Beam Deflection by Conjugate Beam Method
- Problem 657 | Beam Deflection by Conjugate Beam Method
- Problem 658 | Beam Deflection by Conjugate Beam Method

- Strain Energy Method (Castigliano’s Theorem) | Beam Deflection

- Double Integration Method | Beam Deflections
- Chapter 07 - Restrained Beams
- Application of Double Integration and Superposition Methods to Restrained Beams
- Problem 704 | Solution of Propped Beam
- Problem 705 | Solution of Propped Beam with Increasing Load
- Problem 706 | Solution of Propped Beam with Decreasing Load
- Problem 707 | Propped Beam with Moment Load
- Problem 708 | Two Indentical Cantilever Beams
- Problem 709 | Propped Beam with Spring Support
- Problem 710 | Two simple beams at 90 degree to each other
- Problem 711 | Cantilever beam with free end on top of a simple beam
- Problem 712 | Propped beam with initial clearance at the roller support
- Problem 713 | Fully restrained beam with symmetrically placed concentrated loads
- Problem 714 | Triangular load over the entire span of fully restrained beam
- Problem 715 | Distributed loads placed symmetrically over fully restrained beam

- Application of Area-Moment Method to Restrained Beams
- Problem 704 | Propped beam with some uniform load by moment-area method
- Problem 707 | Propped beam with moment load at simple support by moment-area method
- Problem 719 | Propped beam with concentrated load at midspan by moment-area method
- Problem 720 | Propped beam with increasing load by moment-area method
- Problem 721 | Propped beam with decreasing load by moment-area method
- Problem 722 | Propped beam with moment load on the span by area-moment method
- Problem 723 | Propped beam with uniform load over half the span
- Problem 724 | Propped beam with partially restrained wall support
- Problem 725 | Propped beam with partially restrained wall and settling simple support
- Problem 726 | Fully restrained beam with concentrated load at midspan
- Problem 727 | Fully restrained beam with uniform load over the entire span
- Problem 728 | Isosceles triangular load over the entire span of fully restrained beam
- Problem 729 | Uniform load over the center part of fixed-ended beam
- Problem 730 | Uniform loads at each end of fully restrained beam
- Problem 731 | Cantilever beam supported by cable at the free-end
- Problem 732 | Cantilever beam supported by a cable at midspan
- Problem 733 | Cantilever beam with moment load at the free end and supported by a rod at midspan
- Problem 734 | Restrained beam with uniform load over half the span
- Problem 735 | Fixed-ended beam with one end not fully restrained
- Problem 736 | Shear and moment diagrams of fully restrained beam under triangular load
- Problem 737 | Fully restrained beam with one support settling
- Problem 738 | Fully restrained beam with moment load

- Fixed-end moments of fully restrained beam

- Application of Double Integration and Superposition Methods to Restrained Beams
- Chapter 08 - Continuous Beams
- The Three-Moment Equation
- Problem 813 | Continuous Beam by Three-Moment Equation
- Problem 814 | Continuous Beam by Three-Moment Equation
- Problem 815 | Continuous Beam by Three-Moment Equation
- Problem 816 | Continuous Beam by Three-Moment Equation
- Problem 817 | Continuous Beam by Three-Moment Equation
- Problem 818 | Continuous Beam by Three-Moment Equation
- Problem 819 | Continuous Beam by Three-Moment Equation
- Problem 820 | Continuous Beam by Three-Moment Equation
- Problem 821 | Continuous Beam by Three-Moment Equation
- Problem 822 | Continuous Beam by Three-Moment Equation
- Problem 823 | Continuous Beam by Three-Moment Equation
- Problem 824 | Continuous Beam by Three-Moment Equation
- Problem 825 | Continuous Beam by Three-Moment Equation
- Problem 826 | Continuous Beam by Three-Moment Equation
- Problem 827 | Continuous Beam by Three-Moment Equation

- Reactions of Continuous Beams | Shear Diagrams
- Problem 829 | Reactions of Continuous Beams
- Problem 830 | Reactions of Continuous Beams
- Problem 831 | Reactions of Continuous Beams
- Problem 832 | Reactions of Continuous Beams
- Problem 833 | Reactions of Continuous Beams
- Problem 834 | Reactions of Continuous Beams
- Problem 835 | Reactions of Continuous Beams
- Problem 836 | Reactions of Continuous Beams

- Continuous Beams with Fixed Ends
- Problem 840 | Continuous Beams with Fixed Ends
- Problem 841 | Continuous Beams with Fixed Ends
- Problem 842 | Continuous Beams with Fixed Ends
- Problem 843 | Continuous Beams with Fixed Ends
- Problem 844 | Continuous Beams with Fixed Ends
- Problem 845 | Continuous Beams with Fixed Ends
- Problem 846 | Continuous Beams with Fixed Ends
- Problem 847 | Continuous Beams with Fixed Ends
- Problem 848 | Continuous Beams with Fixed Ends
- Problem 849 | Continuous Beams with Fixed Ends
- Problem 850 | Continuous Beams with Fixed Ends
- Problem 851 | Continuous Beams with Fixed Ends
- Problem 852 | Continuous Beams with Fixed Ends
- Problem 853 | Continuous Beams with Fixed Ends
- Problem 854 | Continuous Beams with Fixed Ends
- Problem 855 | Continuous Beams with Fixed Ends
- Problem 856 | Continuous Beams with Fixed Ends

- Deflections Determined by Three-Moment Equation
- Problem 860 | Deflection by Three-Moment Equation
- Problem 861 | Deflection by Three-Moment Equation
- Problem 862 | Deflection by Three-Moment Equation
- Problem 863 | Deflection by Three-Moment Equation
- Problem 864 | Deflection by Three-Moment Equation
- Problem 865 | Deflection by Three-Moment Equation
- Problem 866 | Deflection by Three-Moment Equation
- Problem 867 | Deflection by Three-Moment Equation
- Problem 868 | Deflection by Three-Moment Equation
- Problem 869 | Deflection by Three-Moment Equation
- Problem 870 | Beam Deflection by Three-Moment Equation
- Problem 871 | Continuous Beam with Spring End-Support
- Problem 872 | Continuous Beam with Spring End-Support

- The Moment Distribution Method
- Problem 877 | Continuous Beam by Moment Distribution Method
- Problem 878 | Continuous Beam by Moment Distribution Method
- Problem 879 | Continuous Beam by Moment Distribution Method
- Problem 880 | Continuous Beam by Moment Distribution Method
- Problem 881 | Continuous Beam by Moment Distribution Method
- Problem 882 | Continuous Beam by Moment Distribution Method
- Problem 883 | Continuous Beam by Moment Distribution Method
- Problem 884 | Continuous Beam by Moment Distribution Method
- Problem 885 | Continuous Beam by Moment Distribution Method

- The Three-Moment Equation
- Chapter 09 - Combined Stresses
- Combined Axial and Bending
- Problem 903 | Combined Axial and Bending
- Problem 904 | Combined Axial and Bending
- Problem 905 | Combined Axial and Bending
- Problem 906 | Combined Axial and Bending
- Problem 907 | Combined Axial and Bending
- Problem 908 | Combined Axial and Bending
- Problem 909 | Combined Axial and Bending
- Problem 910 | Combined Axial and Bending
- Problem 911 | Combined Axial and Bending
- Problem 912 | Combined Axial and Bending
- Problem 913 | Combined Axial and Bending
- Problem 914 | Combined Axial and Bending
- Problem 915 | Combined Axial and Bending
- Problem 916 | Combined Axial and Bending
- Problem 917 | Combined Axial and Bending

- Problem 01 | Stress in Helical Spring

- Combined Axial and Bending
- Chapter 10 - Reinforced Beams
- Beams with Different Materials
- Problem 1002 | Increase in moment capacity due to steel plate reinforcement
- Problem 1003 | Maximum stresses in wood and steel of composite beam
- Problem 1004 | Increase in moment capacity due to aluminum plate reinforcement
- Problem 1005 | Maximum concentrated load at the midspan that the reinforced timber beam can carry
- Problem 1006 | Width of fastened steel plate for balanced reinforcement
- Problem 1007 | Flexural stresses developed in the wood and steel fibers
- Problem 1008 | Finding the width of steel plate reinforcement
- Problem 1009 | Width of aluminum plate reinforcement for the wood section to resist 14 kN-m moment
- Problem 1010 and Problem 1011 | Investigation of timber reinforced by two steel channels

- Beams with Different Materials

- Chapter 01 - Simple Stresses