Identify forces and couples
Distinguish a force, a moment, and a free couple in planar and spatial systems.
0/1 correctEngineering Statics · deterministic microlearning
Engineering Statics
Forces become solvable when their direction, boundary, and balance are explicit.
0/19correct
Course configuration · engineering-statics
Practice the mechanics, one model at a time.
Choose an exercise micro-lesson from the navigation. Each lesson explains the model, demonstrates the setup, and checks the result with deterministic scoring.
13 lessons19 exercises6 repair routes
All exercise objectives
Calculate force and couple moments
Use perpendicular distance or a cross product with a consistent sign convention.
0/1 correctResolve force vectors
Translate magnitude-and-direction descriptions into signed Cartesian components.
0/3 correctCompute force resultants
Add component vectors and recover a resultant magnitude and direction.
0/3 correctConstruct free-body diagrams
Choose a system boundary and show only the external forces acting on it.
0/2 correctApply particle equilibrium
Use a correct free-body diagram and component equations to solve unknown forces.
0/2 correctCalculate support reactions
Translate support constraints into reaction unknowns and solve rigid-body equilibrium.
0/1 correctCalculate internal forces
Cut a structure and solve axial force, shear force, and bending moment at the section.
0/1 correctDraw shear and moment diagrams
Connect loading, shear slope, and moment slope across a horizontal beam.
0/1 correctCalculate area centroids
Use area-weighted coordinates for simple and composite regions.
0/1 correctCalculate area moments of inertia
Combine standard shapes with the parallel-axis theorem about a specified axis.
0/1 correctDetermine friction forces
Model static or kinetic friction without assuming static friction is always at its limit.
0/1 correctSolve impending-motion systems
Select the likely motion direction and apply limiting friction consistently at each contact.
0/1 correctExercise coverage map
Each outcome a–l has a navigable explanation, worked setup, deterministic exercise, and remediation route.
Identify forces and couples in 2-D and 3-D.
ABET 1 · exercise lesson availableCalculate the moments produced by forces and couples in 2-D and 3-D.
ABET 1 · exercise lesson availableCalculate components of forces and couple moments in 2-D and 3-D.
ABET 1 · exercise lesson availableDetermine the resultants of 2-D and 3-D force/couple systems.
ABET 1 · exercise lesson availableDraw free-body diagrams of rigid structures with various kinds of supports in 2-D and 3-D.
ABET 1, 3 · exercise lesson availableCalculate the external reactions exerted by various supports on rigid structures (trusses, frames, and machines).
ABET 1 · exercise lesson availableCalculate the internal forces (axial, shear, and bending moment) in rigid structures (trusses, frames, and machines).
ABET 1 · exercise lesson availableDraw shear and bending moment diagrams for horizontal beams.
ABET 1, 3 · exercise lesson availableCalculate the centroid of simple and composite areas.
ABET 1 · exercise lesson availableCalculate area moments of inertia for simple and composite areas.
ABET 1 · exercise lesson availableDetermine frictional forces between rough surfaces of contact.
ABET 1 · exercise lesson availableCalculate forces for impending motion in the presence of friction.
ABET 1 · exercise lesson availableABET Criterion 3 outcomes
- An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
- An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
- An ability to communicate effectively with a range of audiences.
- An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
- An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
- An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
- An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Prerequisites and source mapping
- Algebraic rearrangement and simultaneous equations
- Right-triangle trigonometry
- Cartesian coordinates and angle conventions
- Approved syllabus sequence: To be confirmed
Syllabus: Placeholder — map to the approved Engineering Statics source when supplied.
Textbook: Placeholder — map to the approved Engineering Statics source when supplied.
A / Identify the mechanical action
Forces and couples in 2-D and 3-D
Classify forces and couplesIdentify lines of actionDistinguish force vectors from free moments
Core model
A force has magnitude, direction, and a line of action. A couple is formed by equal, opposite, parallel forces separated by a distance; it produces a pure moment with zero resultant force.
2-D and 3-D test
In 2-D, describe a force with x and y components and a couple with a signed scalar moment. In 3-D, both force and couple moment use Cartesian vector components.
Worked setup
Two 80 N horizontal forces act in opposite directions 0.25 m apart. Their force sum is zero, but they create a 20 N·m couple. Use the right-hand rule to assign its direction.
Recognition clueEqual and opposite does not always mean no effect: separated forces can leave a pure couple.
Assessment
Check the model, not just the arithmetic.
Which description identifies a pure couple?
Deterministic remediation