--- title: "FBD and equilibrium: meaning and importance" subject: "Applied Mechanics" chapter: 2 key: "semester_1/applied_mechanics:fbd-physical-meaning-equilibrium-importance" source: https://www.bctengineer.com/q/semester_1/applied_mechanics/fbd-physical-meaning-equilibrium-importance site: BCT Engineering --- # FBD and equilibrium: meaning and importance Applied Mechanics · Chapter 2: Basic Concept in Statics and Static Equilibrium - Asked in: 2069 Chaitra, 2+2+2+2 marks - Video: [Complete Concept of Free Body Diagram II Mechanics II Fundamental of Mechanical Engineering II FBD](https://www.youtube.com/watch?v=MbYsyXtSA7k) — Shailendra's Academy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/fbd-physical-meaning-equilibrium-importance - Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-2 ## Question Describe Free Body Diagram and physical meaning of equilibrium. Also describe the importance of Free Body Diagram and equilibrium in structural analysis. ## Short answer A free body diagram isolates a part and shows all external forces. Equilibrium (ΣF=0, ΣM=0) means no translation or rotation, ensuring stability. FBD is essential to correctly apply equilibrium equations for support reactions and internal forces in structural analysis. ## Answer #### Free body diagram (FBD) A free body diagram is a sketch of a body, or part of a structure, isolated from its surroundings, on which all external forces and moments are shown: applied loads, self-weight, and the reactions of the removed supports and neighbouring members. Typical reactions: roller gives one force normal to the surface, hinge gives two components, fixed support gives two components and a moment, cable gives a tension. ```text Beam with load FBD of the beam P P | | v v A o=========o B =========== /\ (roller) ^ ^ A_y B_y (and A_x at A) ``` #### Physical meaning of equilibrium A body is in equilibrium when the resultant force and the resultant moment acting on it are zero (ΣF = 0, ΣM = 0). Physically, the body has no tendency to start or change translation or rotation. It remains at rest (static equilibrium) or moves with constant velocity. All actions on the body are balanced by reactions. #### Importance in structural analysis **Of the free body diagram** - It shows all forces on a part of a structure clearly, so no force is missed or repeated. - It gives the unknown reactions and internal forces in the correct sense. - Cutting a member and drawing the FBD of one side gives axial force, shear force and bending moment at that section. - It is the first and most important step in any statics problem. **Of equilibrium** - The equations ΣFx = 0, ΣFy = 0, ΣM = 0 give the support reactions of beams, frames and trusses. - They give member forces in trusses (method of joints, method of sections). - A structure that cannot be in equilibrium under its loads is unstable and would collapse. - Counting the unknowns against the equations decides whether a structure is statically determinate. - Overturning and sliding of walls, dams and foundations are checked using equilibrium. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. An FBD includes: A. Stress values B. Only the structure C. Only reactions D. Applied loads, self-weight and reactions of removed supports Answer: D. All external actions are shown. (Key point: FBD contents) 2. Equilibrium means the resultant force and moment are: A. Zero B. Maximum C. Equal to the weight D. Constant but non-zero Answer: A. SF = 0 and SM = 0. (Key point: Equilibrium) 3. The FBD helps in structural analysis because it: A. Replaces equilibrium equations B. Gives the deflection C. Gives material properties D. Ensures no force is missed or repeated Answer: D. It is the first step and prevents errors. (Key point: FBD importance) 4. A structure that cannot be in equilibrium under its loads is: A. Unstable and would collapse B. Statically determinate C. Safe D. Rigid Answer: A. Equilibrium is the condition for stability. 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