Engineering Statics — Open & Free

Learning objectives by module

Unit 1: Concentrated Forces and Their Effects

• Module 1: Representing Interactions Between Bodies
  • Draw force vectors on bodies to reflect their attributes.
  • Identify attributes of forces acting between a body and an attached cable.
  • Identify attributes of forces acting between a body and an attached spring.
  • Identify attributes of forces acting between frictionless contacting bodies.
  • Recognize when two bodies interact.
• Module 2: Introduction to Free Body Diagrams
  • Draw simple FBDs.
  • Explain the purpose of drawing FBDs.
• Module 3: Effects of Force
  • Define the tendency of the force to create rotation as the moment, and quantify the effect of the force magnitude, direction, sense and position on the moment.
  • Determine the moment of a force by identifying the moment arm (perpendicular distance from the moment center).
  • Distinguish between various motions produced by forces on bodies: translation, rotation with clockwise or counter-clockwise direction, and general motion.
  • Recognize the roles of force magnitude, direction, sense, and line of action on the tendencies to cause translation and rotation motions.
• Module 4: Effects of Multiple Forces
  • Add moments due to known forces when their moment arms are given.
  • Determine the components of force vectors.
  • Determine the moment of a force as a sum of the moments of its components parallel and perpendicular to the line between the moment center and the point of application of the force.
  • Determine the moment of a force as a sum of the moments of its vertical and horizontal components.
  • Determine the sum of concurrent forces by summing their components.
  • Find the force magnitude and sense that balances the moment created by other forces.
  • Judiciously choose method of calculating the moment of a force.
  • Recognize that rotational effects of forces combine through the addition of moments.
  • Recognize that translational effects of forces combine as in vector addition.
• Module 5: Equilibrium Under 2D Concentrated Forces
  • Impose the conditions of equilibrium for general coplanar forces for which both force and moment equilibrium need to be explicitly satisfied.
  • Impose the conditions of equilibrium for systems where all the forces act in one direction for which both force and moment equilibrium need to be explicitly satisfied.
  • Impose the conditions of equilibrium for systems with collinear forces for which the net moment about any point on the line is zero.
  • Impose the conditions of equilibrium for systems with concurrent forces for which the net moment about a point of intersection is zero.
  • Recognize the equilibrium conditions under which bodies have no tendency to translate or rotate.

Unit 2: Complex Interactions Between Bodies

• Module 6: Couples
  • Determine the moment of the couple from the forces producing it or balancing it, and recognize that a set of forces that can be represented as couples produces the same net moment about all points regardless of where they are applied.
  • Recognize circumstances in which a multi-force interaction between two bodies can be represented as a couple, and determine the moment of the couple from what the couple interaction is balancing.
  • Recognize that at least two forces are necessary to cause only a rotation of a body, and utilize the concept of a couple and its symbol to represent combinations of forces that produce zero net force (only a tendency to rotate).
• Module 7: Statically Equivalent Loads
  • Distinguish between fully equivalent loadings and statically equivalent loadings.
  • Recognize equivalence between: a) forces acting along the same line of action, b) several forces acting at a point and a single force at that point equal to their vector sum – full equivalence, and c) different combinations of forces that produce zero net force and the same total moment – equivalent couples.
  • Replace a general set of forces and couples with a force and couple at a given point.
  • Replace a general set of forces and couples with a single force at a location that needs to be determined.
  • Replace a single force acting at a point with a statically equivalent force at a different point and an appropriate couple for the following situations: a) moving a force perpendicular to its line of action, and b) moving a force to an arbitrary location.
  • Replace two parallel forces acting in the same direction and opposite senses with a statically equivalent load (force and couple).
  • Replace two parallel forces acting in the same direction and sense with a single force.
• Module 8: Applications of Static Equivalency to Distributed Forces
  • Determine the location of the center of gravity for bodies that can be decomposed into rectangular prisms.
  • Recognize the role of symmetry planes in determining the location of the center of gravity.
  • Replace a simple known distributed load by a single force with an appropriate line of action.
  • Replace symmetrically distributed load per volume/area by a distributed load per length.
  • Represent unknown distributed forces due to contact between symmetrical flat bodies by a statically equivalent force acting at an unknown location somewhere in the contact area.
  • Use symmetry to reduce three-dimensional situations to two-dimensional representations.
  • Use tabulated results to determine the location of the center of gravity for bodies that can be decomposed into simple shapes (and recognize that the location of the center of gravity for prismatic bodies can be determined by integration).
• Module 9: Representing Engineering Connections
  • Recognize pin connections that can be modeled in 2-D even though forces act in different planes in 3-D: (a) symmetrical arrangements under symmetrical or planar loadings, (b) thin connected bodies under planar loadings.
  • Recognize two most common connections: fixed and pinned.
  • Represent interaction between bodies connected by a rigid sliding joint.
  • Represent interaction between bodies connected by a shared pin (roles of Newton’s 3rd law and equilibrium).
  • Represent interactions between a cylindrical rod and contacting surfaces common in connections.
  • Represent interactions between bodies connected by a cable and a mass less pulley.
  • Represent interactions between bodies connected by a link with two pins.
  • Represent interactions between bodies connected by rollers, rockers, and pins in slot.
  • Represent interactions between bodies joined by fixed connections.

Unit 3: Engineering Systems – Single Body Equilibrium

• Module 10: Drawing FBDs of a Single Subsystem
  • For an identified subsystem, which is part of a larger system with engineering connections, represent all interactions with external parts on a FBD labeling all their known and unknown attributes.
• Module 11: Equilibrium of a Single Subsystem
  • Account properly for forces and couples in equilibrium equations, and deduce their actual senses given their signs found from equilibrium and their assumed senses.
  • Account properly for pre-modeled known distributed force described as q(x).
  • Account properly for unknown distributed contact forces, and interpret the results of solution by recognizing physically impossible outcomes.
  • Find the range of a parameter that ensures equilibrium, or the configuration that minimizes or maximizes a force.
  • Use equilibrium conditions in a qualitative way, without actually solving them, to: make informed assumptions about senses of unknowns, or to recognize arrangements incapable of being in equilibrium, or to check the correctness of the senses of forces determined from the solution.
• Module 12: Choosing a Solvable Subsystem
  • Choose solvable subsystems by recognizing two-force members when present.
  • Choose solvable subsystems for simple systems (without engineering connections).
  • Choose solvable subsystems for systems with engineering connections.
  • Choose solvable subsystems for systems with pulleys.

Unit 4: Frames and Machines

• Module 13: Drawing FBDs of Multiple Subsystems
  • Represent all interactions with external parts on FBDs of identified subsystems that are parts of a larger system, indicating all their known and unknown attributes, and obeying Newton’s 3rd law.
• Module 14: Solving Multiple Subsystems
  • For systems with no fully solvable subsystems, identify partially solvable subsystem(s) (or the whole system) and solve subsystems using “back-and-forth” approach (some unknowns in one subsystem, then move to next).
  • Identify a sequence of fully solvable subsystems (step 3) and solve for all unknowns in each subsystem by imposing successive equilibrium equations, each containing one unknown (step 4).
• Module 15: Annotated Practice Problems – Machines
  • Solve complete multi-body statics problems by applying the four Steps of Statics studied in previous modules.

Unit 5: Trusses

• Module 16: Method of Joints
  • Determine forces in bars connected to a single solvable joint.
  • Select a sequentially solvable series of joints that allows all forces in truss members to be determined.
• Module 17: Method of Sections
  • Determine internal forces in bars for a given section.
  • Select subsystems that allow for an efficient solution for the desired forces.

Unit 6: Friction

• Module 18: Friction
  • Determine conditions (load/geometry/friction coefficient) for which motion initiates or is sustained.
  • Given the load, geometry and friction coefficient, determine if the body is stationary or slips.
  • Recognize that the force between contacting bodies may have a normal and a tangential component. Define friction force, its limits and friction coefficients.
  • Recognize that two contacting bodies may remain in contact, slip with respect to one another, or tip. Determine conditions for motion to initiate, and the type of impending motion.

Unit 7: Moments of Inertia

• Module 19: Second Moment of Area
  • Define polar moment of area and recognize circumstances when it matters.
  • Recognize second moment of area as a property relevant when the distribution of area is important rather than merely the area itself, and define second moment of an area.
  • Use parallel axis theorem to find second moments of area about an arbitrary axis.
  • Use tabulated results to determine second moment of area for simple shapes, including composite bodies with common centroidal axis.
• Module 20: Mass Moment of Inertia
  • Recognize that distribution of mass, rather than mass alone, affects resistance to rotational motion, and define mass moment of inertia as measure of resistance to changes in its angular motion.
  • Understand mass radius of gyration as an alternative measure of the resistance to rotation, which replaces an object of complicated shape with an equivalent ring (with same mass moment of inertia).
  • Use parallel axis theorem to find mass moments of inertia about an arbitrary axis.
  • Use tabulated results to determine mass moment of inertia for simple shapes, including composite bodies with common centroidal axis.