Engineering Mechanics: Statics Complete (Course & Examples)

Define scalars as quantities by magnitude only and vectors by magnitude and direction; use examples like length, mass, time, force, and moment to explain vector notation and hand-solving basics.

Learn vector operations in statics: scalar multiplication, direction reversal with negative scalars, parallelogram and triangle rules for addition, special collinear cases, and subtraction to obtain resultant vectors.

This example uses the cosine and sine laws to compute the resultant magnitude and direction for 100 N and 200 N at 45 degrees, about 279.8 N at 30.3 degrees.

Learn to add coplanar forces by resolving each force into x and y components, sum the components using Cartesian vectors, and determine the resultant magnitude and direction.

Resolve forces into x and y components using a 3-4-5 triangle, then sum components to obtain the resultant's magnitude and direction, using arctan to find the angle.

Solve a three-dimensional 100-N force by decomposing into x, y, z components, forming the Cartesian vector, computing magnitude, and finding the direction cosines alpha, beta, gamma via the unit vector.

Resolve two forces into Cartesian components, compute their resultant, and determine its magnitude and the direction angles for statics.

Identify position vector from point a to point b using x, y, z components, compute its magnitude from differences, and derive the unit vector with direction cosines alpha, beta, gamma.

Learn to express a force as a cartesian vector by multiplying the force scalar by the unit vector along the line, using the position vector and its magnitude.

Explore equilibrium of a particle by applying Newton's laws, drawing free body diagrams, and analyzing 2D and 3D force systems with cables, springs, and normal forces.

Draw a free body diagram of a particle in equilibrium to solve a statics example, using a spring (319 N/m) and 30° cable to find delta, X, and AB length.

Explore the moment concept in statics by defining moment as force times distance, perpendicular to the arm, with sign conventions for clockwise and counterclockwise moments and resultant moment calculation.

Use the right hand rule to determine moment direction by aligning your fingers with the force and your thumb with the rotation axis, distinguishing positive and negative z axis.

Calculate moments about a point using force times the perpendicular distance, determine the direction (clockwise or counterclockwise), and apply to various examples with forces in newtons and distances in meters.

Compute the resultant moment about point O by summing forces times their perpendicular distances. Validate the direction with a sign convention and practice solving multiple-force moments in statics.

Compute the cross product a × b to obtain vector c perpendicular to the plane of a and b, with i, j, k components and its magnitude and direction cosines.

Solve a cross product example by computing the vector from given components using a determinant, find its magnitude, and determine the direction angles alpha, beta, and gamma.

explains how to compute the moment of a force in 2d and 3d using the perpendicular distance and vector methods, including Cartesian cross products, moment magnitudes, and direction angles.

Compute the moment of a force about the origin via r cross f, resolve the force into Cartesian components, and determine the moment magnitude and direction angles alpha, beta, gamma.

Learn how to compute the magnitude of the moment of a force about a specific axis, particularly the OEI axis, using the unit vector, the position vector, and cartesian representations.

Explain the moment of a couple formed by two equal and opposite forces; the moment equals force times distance and is independent of the reference point.

Determine the resultant moment of a couple and sum moments about A, B, and C using 200 N and 100 N forces, confirming moment is the same for any point.

Compute a three-dimensional couple moment in statics by using the position vector between two forces and the cross product with the force vector, noting sign and component details.

Learn to simplify force and couple systems by replacing them with a resultant force and moment, transfer forces along lines of action, and apply couple moments when not collinear.

Learn how to replace multiple loadings with a single resultant force and locate it using the sum of forces, moments, distances X, and couple moments.

Learn how to reduce a simple distributed load to a single resultant force and locate it by integrating the load and using area rules for rectangular and triangular distributions.

This lecture introduces two-dimensional equilibrium for a rigid body, outlining three conditions: sum of forces in x, sum of forces in y, and sum of moments equal to zero.

Explore equilibrium in 2-D within engineering mechanics: statics by analyzing support reactions, translation and rotation constraints, and the behavior of cable and link supports using free-body diagrams.

Explore 2-D support types in statics, including smooth surfaces, cables, links, hinges, and fixed supports, and learn to resolve forces into x and y components and moments.

Learn to draw free body diagrams for statics problems, converting distributed loads to concentrated forces, and resolve hinge, fixed, pulley, and cable cases with their moments and forces.

Build a free-body diagram, convert the distributed load to a 20 N concentrated load at 3 m, and determine the fixed-support reactions Ay and X.

Learn the conditions of equilibrium in 3-D, where the sums of forces along X, Y, and Z and the sums of moments about X, Y, and Z are zero.

Solve a three-dimensional statics problem for a fixed support by identifying forces and moments, applying equilibrium equations, and using the cross product to find six reactions.

Explore the types of three-dimensional supports—cable, link, ball and socket, hinge, and fixed support—and learn to draw free-body diagrams and resolve forces and moments into Cartesian components.

Examine three-dimensional supports by detailing single thrust bearing and single journal bearing, showing rotation only about the y-axis and restricted translations, with Cartesian force and moment constraints.

Explore simple trusses in structural analysis, including frictionless joints and loads applied at joints, and learn the method of joints and the method of sections.

Use the joint method to find forces in each member. Draw a free body diagram for a joint, assume tension, and apply sum of forces in x and y.

Apply the joint method to find the force in every member, compute support reactions via moments, and label each member as either tension or compression.

Identify zero-force members in trusses by joints with no external load or support. Apply two cases: two-member joints and three-member joints with two members, where the third is zero.

Explore the method of sections for determining member forces in trusses, including selecting a section crossing three members, drawing the cut, applying equilibrium equations to find tensions and compressions.

Learn the difference between frames and trusses, where forces act on the members in frames, and use McLeans method to separate components and solve six unknowns with six equations.

Explore a beam example to compute support reactions and internal forces by taking sections, drawing shear, normal force, and bending moment, and applying equilibrium equations.

Learn how to build shear and moment diagrams by determining support reactions, interpreting positive and negative areas, and using sectional verification to check moments with constant and linear shear segments.

This example shows how to find centroid of area under y = x^2 from 0 to 1 by calculating area and first moments to get x-bar and y-bar.

Convert a distributed load with gamma and area into a concentrated weight, then apply moment and force balance to determine the support reactions.

Learn to determine a composite area by dividing into simple shapes, establishing a reference axis, finding each shape’s area and centroid, and applying x-bar and y-bar formulas.

Divide the composite figure into triangles and rectangles, compute each part's area and centroid, then find the centroid by summing x times area and y times area over total area.

Explore fluid pressure on a water surface by formulating the distributed load as gamma times height, using width B (assume 1 m if not given) and gamma defined by g.