Engineering Statics

Resolve concurrent forces into components, apply equilibrium equations to particles, and analyze cable, pulley, and spring systems using free-body diagrams in two dimensions.

Extend force analysis to three dimensions using direction cosines, position vectors, and cross products, and solve 3D particle equilibrium problems with cable and support systems.

Compute moments about points and axes, simplify force systems into equivalent resultants, and solve rigid-body equilibrium problems for beams and 3D structures.

Locate centroids of areas, volumes, and composite shapes using integration and tabulated formulas, then replace distributed loads with equivalent concentrated forces for beam analysis.

Analyze trusses using the method of joints and method of sections, identify zero-force members, and determine internal forces in frames, machines, and pulley systems.

Determine internal normal forces, shear forces, and bending moments at any beam cross-section, and construct shear and moment diagrams using load-shear-moment relationships.

Apply Coulomb friction laws to solve equilibrium problems involving inclined planes, wedges, and belt-and-rope systems, and distinguish between slipping and tipping failure modes.

Calculate second moments of area for simple and composite cross-sections using integration, the parallel-axis theorem, and product-of-inertia formulas.