Engineering Mechanics: Statics (ENGG 130) lessons and practice

Resolve vectors, calculate moments and couples, and reduce planar force systems.

Draw free-body diagrams, model support reactions, and solve particle and rigid-body equilibrium.

Analyze statically determinate trusses, frames, machines, internal forces, and beam diagrams.

Model dry friction, impending motion, inclined surfaces, wedges, belts, and bearings.

Find centroids, centres of gravity, distributed-load resultants, and second moments of area.

Represent forces accurately with units, directions, components, and position vectors.

• 1.1 · Use mechanics models, units, significant figures, and assumptions (written lesson not published)
• 1.2 · Resolve planar forces into Cartesian components (written lesson not published)
• 1.3 · Add planar force vectors and find a resultant (written lesson not published)
• 1.4 · Determine force magnitude and direction from components (written lesson not published)
• 1.5 · Use position and unit vectors to describe force directions (written lesson not published)

Replace forces and couples with equivalent planar force systems.

• 2.1 · Calculate the moment of a force about a point (written lesson not published)
• 2.2 · Use the cross product for force moments (written lesson not published)
• 2.3 · Analyze couples and equivalent couple moments (written lesson not published)
• 2.4 · Reduce a planar force system to a force and couple (written lesson not published)
• 2.5 · Replace a simple distributed load with an equivalent resultant (written lesson not published)

Create free-body diagrams and apply particle and rigid-body equilibrium equations.

• 3.1 · Draw complete free-body diagrams (published written lesson)
• 3.2 · Model pin, roller, cable, link, and fixed-support reactions (published written lesson)
• 3.3 · Solve planar particle-equilibrium problems (published written lesson)
• 3.4 · Solve planar rigid-body equilibrium problems (published written lesson)
• 3.5 · Recognize stability, constraints, and static determinacy (published written lesson)

Model statically determinate planar trusses and find member forces.

• 4.1 · Identify truss assumptions, members, joints, and reactions (written lesson not published)
• 4.2 · Identify zero-force members (written lesson not published)
• 4.3 · Analyze a truss with the method of joints (written lesson not published)
• 4.4 · Analyze selected truss members with the method of sections (written lesson not published)
• 4.5 · Classify member forces as tension or compression and verify equilibrium (written lesson not published)

Separate connected rigid members and solve the equilibrium of frames and machines.

• 5.1 · Recognize two-force and three-force members (written lesson not published)
• 5.2 · Create connected free-body diagrams for a frame (written lesson not published)
• 5.3 · Analyze a statically determinate frame (written lesson not published)
• 5.4 · Analyze forces in a simple machine (written lesson not published)
• 5.5 · Determine internal pin forces between connected members (written lesson not published)

Find internal resultants and construct axial-force, shear-force, and bending-moment diagrams.

• 6.1 · Determine internal normal force, shear force, and bending moment (written lesson not published)
• 6.2 · Choose section cuts and sign conventions (written lesson not published)
• 6.3 · Construct axial-force and shear-force diagrams (written lesson not published)
• 6.4 · Construct bending-moment diagrams (written lesson not published)
• 6.5 · Relate distributed load, shear, and bending moment (written lesson not published)

Model dry friction and determine equilibrium or impending motion.

• 7.1 · Distinguish static, limiting, and kinetic friction (written lesson not published)
• 7.2 · Determine impending motion and friction direction (written lesson not published)
• 7.3 · Solve friction problems on inclined surfaces (written lesson not published)
• 7.4 · Analyze wedges with dry friction (written lesson not published)
• 7.5 · Analyze introductory belt and journal-bearing friction (written lesson not published)

Locate centroids and centres of gravity for lines, areas, and composite bodies.

• 8.1 · Distinguish centroid, centre of mass, and centre of gravity (written lesson not published)
• 8.2 · Find centroids of simple lines and areas by integration (written lesson not published)
• 8.3 · Find centroids of composite areas (written lesson not published)
• 8.4 · Find centres of gravity for composite bodies (written lesson not published)
• 8.5 · Connect a distributed load resultant to an area centroid (written lesson not published)

Calculate geometric area properties used in later beam and structural analysis.

• 9.1 · Interpret the second moment of area and radius of gyration (written lesson not published)
• 9.2 · Calculate second moments of simple areas by integration (written lesson not published)
• 9.3 · Apply the parallel-axis theorem for areas (written lesson not published)
• 9.4 · Calculate second moments of composite areas (written lesson not published)
• 9.5 · Calculate and interpret the product of inertia for an area (written lesson not published)

University of Calgary

Strong overlap in force vectors, equilibrium, structures, beams, friction, and centroids.

Concordia University

Overlaps in equilibrium, trusses, friction, moments of inertia, virtual work, and beam diagrams.

University of Waterloo

Overlaps in rigid-body equilibrium, trusses and frames, distributed forces, centroids, inertia, friction, and virtual work.

University of Waterloo

Covers core Statics with additional applications to musculoskeletal systems.

UBC Okanagan

Overlaps in vectors, free-body diagrams, equilibrium, structures, friction, wedges, pulleys, and belts.

University of Toronto

Includes Statics and beam equilibrium, then extends into stress, strain, and deformation.

University of Ottawa

Includes Statics topics but also introduces particle motion, so the full syllabi are not equivalent.

A bracket is loaded by 300 N to the right and 400 N upward. Find the resultant magnitude and direction.

Worked method: R = √(300² + 400²) = 500 N. The direction is θ = tan⁻¹(400/300) = 53.1° above the positive horizontal axis.

A 6 m beam has a pin at A, a roller at B, and a 12 kN downward point load 2 m from A. Find the vertical reactions.

Worked method: From ΣM_A = 0: 6B_y − 12(2) = 0, so B_y = 4 kN. From ΣF_y = 0: A_y + 4 − 12 = 0, so A_y = 8 kN upward.

Two adjacent rectangles have areas 600 mm² and 400 mm², with centroid coordinates x₁ = 15 mm and x₂ = 50 mm. Find the combined x-coordinate.

Worked method: x̄ = ΣAᵢxᵢ/ΣAᵢ = [600(15) + 400(50)]/1000 = 29 mm. Both areas are positive because neither is a hole.

A 250 N force acts perpendicular to a 0.40 m position vector. Find its moment magnitude.

A block rests on a horizontal surface with μs = 0.30 and normal force 500 N. Find the maximum static friction.