Structural Mechanics and Analysis
Equilibrium and internal forces
Mechanics and analysis questions test free-body diagrams, reactions, determinacy and stability, shear and moment diagrams, axial-force diagrams, truss analysis by joints and sections, influence lines, deflections by virtual work or moment-area, and stiffness versus flexibility. Know superposition, compatibility, and approximate analysis. Be able to identify zero-force members and recognize when second-order effects matter.
Traps
Sign conventions cause many errors. Forgetting self-weight, mixing kips and pounds or feet and inches, and treating a roller as a pin are common. Do not use superposition where geometry changes significantly, such as second-order sway. For moving loads, maximum moment under a concentrated load occurs at the load, not necessarily at midspan. Also verify support conditions before calculating reactions.
Worked example: A simply supported beam spans 20 ft with a uniform load of 2 kip/ft. Reactions are 20 kip each. Maximum moment at midspan is wL²/8 = 2(20)²/8 = 100 kip-ft, and maximum shear at the supports is 20 kip. If a 10-kip point load is added at midspan, M = 100 + PL/4 = 100 + 50 = 150 kip-ft.
Rule of thumb: For a simply supported beam, Mmax = wL²/8 for uniform load and PL/4 for a midspan point load.