Free Course Image Statistics Engineering Mechanics

Free online courseStatistics Engineering Mechanics

Duration of the online course: 2 hours and 38 minutes

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Build rock-solid statics skills with a free online course: vectors, moments, trusses, friction, and diagrams—learn faster and earn a certificate-ready edge.

In this free course, learn about

  • Resolve 2D/3D force vectors into components; perform vector addition and find resultants
  • Use dot product, unit vectors, and direction angles to compute components and angles of forces
  • Draw correct free-body diagrams for particles, joints, pulleys, cables, and springs
  • Apply particle equilibrium (ΣFx=0, ΣFy=0, ΣFz=0) to solve tensions and spring stiffness k
  • Apply rigid-body equilibrium (ΣF=0, ΣM=0) and know why ΣF=0 alone may not ensure equilibrium
  • Compute moments in 2D/3D using cross products and find moment components about a point
  • Determine support reaction forces using moment equations and support-constraint knowledge
  • Analyze trusses via method of joints and method of sections; identify tension vs compression
  • Construct shear-force and bending-moment diagrams for point, distributed, triangular, symmetric loads
  • Replace distributed loads with equivalent resultants and locate their lines of action
  • Find centroids/centers of mass/center of gravity for composite areas and bodies
  • Compute hydrostatic pressure resultants on submerged vertical/slanted surfaces and related reactions
  • Solve dry friction problems: impending motion, ladders/poles, stacked objects, and contact reactions
  • Identify types of supports and connections and their associated reaction components

Course Description

Turn real-world loads and structures into clear, solvable engineering problems with this free online course in engineering mechanics statics. If you have ever looked at a beam, a truss, a cable system, or a gate under fluid pressure and wondered how engineers confidently predict what happens next, this course gives you the practical workflow to get there. You will build the ability to translate messy situations into clean models, choose the right idealizations, and compute forces and moments with accuracy.

The learning experience emphasizes the habits that matter in industry and in further mechanical and industrial studies: drawing correct free body diagrams, keeping sign conventions consistent, resolving vectors into components, and checking whether results make physical sense. You will practice working in 2D and 3D using unit vectors, dot products, and cross products to move smoothly from geometry to mechanics. That foundation helps you handle everything from tension in cables and spring equilibrium to reaction forces at supports without guesswork.

As you progress, you will develop confidence in rigid body equilibrium and moment balance, including how torque is created and why a body can still rotate even when forces appear to cancel. You will also learn how engineers analyze common structural systems using efficient approaches for trusses, selecting strategies that fit the goal of the problem rather than forcing one method everywhere. The same practical mindset carries into shear and bending moment interpretation, where you connect external loading to internal response in a way that supports design decisions.

The course expands beyond dry-body statics into applications you will meet in the field, such as hydrostatic pressure on submerged surfaces and the reasoning used to prevent overturning and rotation in structures like gates and dams. You will also sharpen your understanding of friction, including when motion begins, how contact conditions change system behavior, and how to reason about slipping versus sticking in setups like ladders, stacked objects, and pulling scenarios.

By the end, you will have a stronger, more employable grasp of mechanical and industrial basics: model creation, equilibrium reasoning, and calculation discipline. Whether you are preparing for more advanced engineering topics or strengthening professional skills for technical work, this course helps you build competence that transfers directly to problems you will see in practice.

Course content

  • Video class: Force Vectors and VECTOR COMPONENTS in 11 Minutes! - STATICS 11m
  • Exercise: When determining the reaction forces and internal forces in a static structure subjected to external loads, which step is essential before performing operations like addition and subtraction of forces?
  • Video class: 2D Vector Addition in 2 Minutes! (Statics) 01m
  • Exercise: If three vectors F1, F2, and F3 are combined and the horizontal component of the resulting vector is zero, which of the following values of theta will satisfy this condition?
  • Video class: 3D Vector Addition in 3 Minutes! (Statics) 03m
  • Exercise: Given vectors F1 and F2, which statement correctly describes the x-component of the resultant vector R if R is the sum of these vectors?
  • Video class: 3D Vectors, DOT PRODUCT in 2 Minutes! (Statics) 02m
  • Exercise: If the tension forces Tb and Tc act on a flagpole with magnitudes of 560 N and 700 N respectively, what would be the x-component of the force Tb assuming the x distance is 2 meters and the overall cable length is 7 meters?
  • Video class: 2D Unit Vector Notation in 1 Minute! (Statics Example) 01m
  • Exercise: When using unit vector notation to find the resultant force from two given vectors, if the resultant makes an angle of 213.7 degrees with the positive x-axis, what is the most direct way to calculate this angle?
  • Video class: FREE BODY DIAGRAMS and Particle Equilibrium in 9 Minutes! (Statics) 09m
  • Video class: Free Body Diagram of Joint Particle in 1 Minute! (Statics) 01m
  • Exercise: In a pin-connected truss system with forces acting at a joint, which method is appropriate for determining the forces F1 and F2 required for equilibrium, considering known angles and given force magnitudes?
  • Video class: Pulley and Cables Free Body Diagram in 2 Minutes! (Example) 01m
  • Exercise: A block weighing 20 pounds is being pulled up at a uniform velocity. Given that the tension in the cable is the same throughout, what is the correct angle theta for equilibrium?
  • Video class: Extension Spring Particle Equilibrium in 2 Minutes! 01m
  • Exercise: A spring with an unstretched length of 2 meters is used to hold a 40-kilogram box in place. If the extension of the spring is known, how do we determine the stiffness (spring constant, k) required to maintain equilibrium?
  • Video class: Tension Cables in Particle Equilibrium in 90 Seconds! 01m
  • Exercise: Consider a system in equilibrium involving a 30 kg pipe supported by multiple chords at a joint. If a free body diagram shows that the force exerted by the chord FHA is equal to 294 Newtons, what assumption is made about the forces in the chords?
  • Video class: Sum of MOMENTS and Rigid Body Equilibrium in 13 Minutes! (Statics) 13m
  • Exercise: What is the key reason that a rigid body might not be in a state of equilibrium, even if the sum of forces on it is zero?
  • Video class: 2D Sum of Moments in 2 Minutes! 02m
  • Video class: CROSS PRODUCT, Sum of Moments in 3D in Under 3 Minutes! 02m
  • Video class: CROSS PRODUCT, 3D Sum of Moments Example in 90 Seconds! 01m
  • Exercise: Determine the cartesian components of the moment of a force about point P if the position vector from point P to point A is given by 5i + 6j - 3k meters and the force vector F is 10i + 0j + 4k Newtons.
  • Video class: REACTION Forces Calculations Using Moments, in 2 Minutes! 02m
  • Exercise: In analyzing a beam with supports at points A and B, which statement is true concerning the reactions at these supports?
  • Video class: TRUSSES - Method of Joints 12m
  • Video class: Trusses METHOD OF JOINTS, NO Reactions Needed, in 3 Minutes! 03m
  • Exercise: How should you start solving a truss problem when external loads are applied at a joint?
  • Video class: TRUSSES Method of Joints, WITH Reactions Required, in 3 Minutes! 03m
  • Exercise: In a truss analysis problem, after calculating the reaction forces at the supports, which method is commonly used to find the forces in the members by isolating each joint and writing equilibrium equations?
  • Video class: Trusses METHOD OF SECTIONS, No Reactions Needed in 2 Minutes! 02m
  • Exercise: Using the method of sections for the truss, if F_dc is solved to be compressive, what are the states of internal forces in members F_hi and F_hc respectively?
  • Video class: TRUSSES Method of Sections, Reactions Required in 2 Minutes! 02m
  • Exercise: When analyzing a truss, what method would be more efficient for finding internal forces if you are only interested in specific members and why?
  • Video class: SHEAR and BENDING Moment Diagrams in 13 Minutes! 13m
  • Exercise: When analyzing a beam subjected to various loads, which type of external load is specifically responsible for causing bending in the member?
  • Video class: Finding Reactions with SHEAR and BENDING Diagrams in 2 Minutes! 02m
  • Exercise: When analyzing a cantilever beam with point loads, which steps are necessary to create shear and moment diagrams?
  • Video class: Distributed load in SHEAR and BENDING Moment Diagrams in 2 Minutes! 02m
  • Video class: TRIANGULAR Distributed load in Shear and Bending Moment Diagrams in 3 Minutes! 03m
  • Exercise: For a simply supported beam subjected to a triangular distributed load with an external couple at point C, how do you determine the location of the equivalent point load from the triangular load?
  • Video class: SYMMETRIC External Loads in Shear and Bending Moment DIAGRAMS in 2 Minutes! 01m
  • Video class: CENTROIDS and Center of Mass in 10 Minutes! 09m
  • Exercise: In statics, the centroid of a composite area constructed from simple geometries can be determined by:
  • Video class: CENTROID of Composite Area in 2 Minutes! 02m
  • Exercise: For a given compound shape consisting of a green triangle, a red square, and a purple triangle, the centroid coordinates are calculated. Which of the following options correctly represents the centroid coordinates of this shape?
  • Video class: Finding the CENTROID of a Composite Body in Under 2 Minutes! 01m
  • Exercise: In the process of determining the centroid of a composite area involving a triangle, a square, and a quarter circle, which mathematical operation is used to account for the semicircle when finding the centroid coordinates?
  • Video class: CENTER OF GRAVITY of Buoy, by Addition, in 90 Seconds! 01m
  • Video class: CENTER OF GRAVITY of a Function-Described Body in 2 Minutes! 01m
  • Video class: HYDROSTATIC PRESSURE (Fluid Pressure) in 8 Minutes! 08m
  • Exercise: Which of the following statements is true regarding hydrostatic pressure on a submerged vertical surface?
  • Video class: Gravity Dam HYDROSTATIC Pressure in 2 Minutes! 01m
  • Exercise: A concrete gravity dam is maintained in position by its own weight. If the density of concrete is 2.5 megagrams per cubic meter and water has a density of 1 megagram per cubic meter, which principle is primarily used to ensure the dam does not overturn due to water pressure?
  • Video class: Hydrostatic Pressure of SUBMERGED Gate in 2 Minutes! 01m
  • Exercise: A 2 meter wide rectangular gate is subject to hydrostatic pressure. The gate is pinned at its center 'a' and prevented from rotating by the block at 'b'. The pressure distribution is trapezoidal. Which of the following statements about calculating the reactions at supports 'a' and 'b' is true?
  • Video class: Hydrostatic Pressure of submerged, SLANTED Gate in 2 Minutes! 01m
  • Exercise: Calculate the magnitude of the resultant force acting on a submerged rectangular gate due to hydrostatic pressure, given that the horizontal force is 73.58 kN and the vertical force is 70.1 kN. Use these components to determine the overall resultant force.
  • Video class: FRICTION in 10 Minutes! (Statics/Physics) 10m
  • Exercise: Which scenario will occur first when a horizontal force is applied to a stack of two boxes with a static friction coefficient of 0.52 between them and 0.28 with the floor, as the force increases from 0 N?
  • Video class: Friction in Pole or Ladder AGAINST A WALL in 2 Minutes! 02m
  • Exercise: A uniform pole of weight 30 pounds and length 26 feet is placed against a smooth wall and a rough floor with a distance of 10 feet between the wall and the point of contact at the floor. The coefficient of static friction is 0.3. What is the maximum distance the pole can be placed from the smooth wall and not slip?
  • Video class: FRICTION! Number of Books Without Dropping Them in 3 Minutes 02m
  • Exercise: A person is trying to hold a stack of books by applying a horizontal compressive force of 120 N. Each book has a mass of 0.95 kg. The coefficient of friction between the person's hands and the books is 0.6, and between any two books is 0.4. What is the greatest number of books that can be supported in the stack if the person uses their hands to hold them?
  • Video class: Tongues Holding Crate FRICTION EXAMPLE in 2 Minutes! 02m
  • Exercise: In a statics problem involving tongs used to lift a crate, the method of joints is applied to determine certain forces involved in the system. If the crate weighs 150 kilograms, what role does the static friction coefficient play at the pivot blocks during the process of lifting the crate?
  • Video class: Static FRICTION at the Wall Example in 2 Minutes! 02m
  • Exercise: A spool of wire weighing 300 pounds rests on the ground and against a wall. Given a static friction coefficient of μ = 0.25 at both points of contact, what is the force P required to start pulling the wire horizontally off the spool?
  • Video class: Types of Supports and Connections in 4 Minutes! - Statics 03m

This free course includes:

2 hours and 38 minutes of online video course

Digital certificate of course completion (Free)

Exercises to train your knowledge

100% free, from content to certificate

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