Engineering Mechanics
What to master
Statics: free-body diagrams, equilibrium in two and three dimensions, support reactions (pin, roller, fixed), truss analysis by joints and sections, zero-force member identification, frames and machines, friction (static, kinetic, impending motion, belt friction), centroids, centers of mass, and area moments of inertia including the parallel-axis theorem. Dynamics: particle and rigid-body kinematics (rectilinear, curvilinear, rotational, relative motion), Newton's second law in normal/tangential and cylindrical coordinates, work-energy, impulse-momentum, impact and restitution, and basic vibration.
Traps
- Forgetting a reaction component at a smooth roller (only normal force, no friction) or at a pin (two components).
- Inconsistent sign conventions between the FBD and the equilibrium equations.
- Mass versus weight: dynamics problems need m = W/g.
- Using diameter where a formula requires radius, especially in moment-of-inertia and circular-motion terms.
- Assuming a zero-force member exists without applying the two-member, no-load joint rule.
Worked example
A simply supported beam of span L carries a point load P at midspan. By symmetry each reaction is P/2, the maximum shear is P/2 and the maximum bending moment is PL/4.
Rule of thumb: the parallel-axis theorem is I = I_bar + A*d^2 -- add the area times the square of the offset to the centroidal moment of inertia, never the reverse.