Engineering Statics online course Complete Course & examples

Explore the general concept of force, two-dimensional and three-dimensional force vectors, and the basics of moments, couples, and resultants for engineering statics.

Analyze force in statics by distinguishing single versus system forces, external versus internal, and apply transmissibility to treat forces as sliding vectors along their line of action.

Classify forces as contact or body forces, with examples, and discuss concentrated versus distributed forces, center of gravity, measurement methods, and force components.

Explore how to decompose a force into rectangular components fx and fy, sum vector components, and determine the resultant of concurrent forces using unit vectors.

Explore moment, torque, and the right-hand rule, showing how force and moment arm produce rotation about an axis via the perpendicular distance.

Use cross product r cross F to compute the moment about a point; apply the right-hand rule for direction, and note that the moment equals the sum of its components.

Learn how a pure couple from equal and opposite forces yields a moment, independent of point, using the cross product r × F and the right-hand rule.

Learn how the resultant replaces a system of forces with a single vector that preserves external effects on a rigid body, yielding equilibrium for zero resultant and dynamics when nonzero.

Use the algebraic method to find the resultant force and its line of action by transferring all forces to a convenient reference point and computing moments about that point.

Learn to resolve a force into rectangular components (f_x, f_y, f_z) using the line of action or two angles, and apply unit vectors i, j, k with a right-hand rule.

Compute the dot product as the projection of p onto q, equal to the product of magnitudes |p| and |q| times cos theta, capturing vector components along axes.

Relate the moment and couple using the moment arm and cross product; compute torque as r cross F, and resolve about axes with the right-hand rule.

Explore chapter two's first example, deriving vector components and directions for three forces using x and y components, angles with the horizontal, and triangle methods.

Calculate the moment of a 600 unit force about a point using multiple methods—perpendicular distance, components, transmissibility, and vector cross product—at 4 m height and 40°.

Resolve the force into x and y components using i and j from the angle; apply sign conventions, compute moments about a point using the lever arm via cross product.

Introduce equilibrium in statics, examining rigid bodies, forces, moments, and two-dimensional systems, and establish necessary and sufficient conditions for static equilibrium.

Isolate the mechanical system in two dimensions and draw a free body diagram capturing all contact and body forces, including gravity and magnetic forces.

Examine common contact types in statics, including smooth and rough surfaces, rolling supports, and flexible cables, and apply Newton's third law to analyze two-dimensional force systems.

Master the three two-dimensional equilibrium conditions: the sum of all forces is zero, the sum of all moments is zero about any point, ensuring complete equilibrium.

Discover four categories of equilibrium: colinear forces with a common line of action, and coplanar concurrent forces solvable with force equations, often without needing moments.

Explore two-force members by analyzing concurrent lines of action of two forces, producing zero moment, and learn to reduce multiple forces to a three-force member for equilibrium.

Explains three-force and two-force members and how equilibrium arises when forces are equal, opposite, and colinear, regardless of member shape, with member weights neglected, for trusses and similar structures.

Identify four three-dimensional equilibrium categories and apply the equations: concurrent forces through a point; forces along a line; parallel forces; and the general case needing all force and moment equations.

Assess how constraints and supports determine whether a rigid body is statically determinate or indeterminate, using redundancy, unknown external forces, and equilibrium equations to solve the problem.

Extending equilibrium to three dimensions, the lecture shows that a body is in equilibrium when the resultant force and the resultant moment are zero, yielding six independent equations.

Explore types of contact and the origins of contact forces, including normal and tangential forces on smooth and rough surfaces, plus constraints, joints, and fixed connections in statics.

Assess the magnitude of five forces at a joint in a bridge truss using a free-body diagram and solve for T and C via x and y equilibrium.

Explore structural types and methods in engineering statics, focusing on internal forces, free-body diagrams, and the analysis of trusses, frames, and machines.

Learn how plane trusses form rigid frames from two‑force members joined at joints to create triangles, distinguish rigid versus nonrigid frames, and use diagonals to prevent collapse under loads.

Apply the method of joints to determine forces in truss members under equilibrium, using free-body diagrams and the two independent equilibrium equations to identify tension or compression in each member.

Explains redundancy in trusses, distinguishing external versus internal determinacy, the role of joints and members, and the necessary (not sufficient) condition for stability.

Use the method of sections to analyze a truss by cutting through up to three unknown members and applying equilibrium to solve for member forces.

Explore distributed forces, their centers of mass and centroids, and when to model such forces as a single resultant in statics, including real-world contact areas like tire pavement.

Compute center of mass for composite bodies by summing each part's mass times its centroid under the principle of moments; extend to areas and volumes with holes as negative contributions.

Apply the theorem of Pappus to compute surface areas and volumes of revolution by relating the generating curve or area to the centroid’s path around a non-intersecting axis.

Explore the main types of friction, including dry friction, fluid friction, and internal friction in solids. Learn how each regime depends on contact conditions, velocity, and material properties.

Static friction resists impending motion up to the maximum, which equals mu_s times the normal force; kinetic friction equals mu_k times the normal force and may decrease with velocity.

Identify friction problem types: static equilibrium, impending motion, or motion, and use equilibrium equations to find static friction or the limiting value.

Introduce the concept of work as the dot product of force and displacement, and compare equilibrium methods with the virtual work approach for interconnected moving bodies.

The improvers chapter explains that a couple—two equal and opposite forces—creates a rotating moment. The work equals the moment times the angular displacement, with sign from rotation sense.

Use the virtual work principle in static equilibrium by analyzing the work of a force during a virtual displacement, assuming constant constraints and neglecting higher-order terms.

Explain the principle of virtual work: for a system in equilibrium, the total work by external active forces is zero for any virtual displacement, with friction and reactive forces considered.

Explore moment of inertia and the second moment of area, deriving rotation about axes for distributed loads and stress distributions in engineering mechanics.

Learn how to transfer moments of inertia for an area from a centroid axis to parallel axes, using the parallel axis theorem and the radius of gyration about the centroid.