--- title: "Rigid vs deformable bodies; free body diagram" subject: "Applied Mechanics" chapter: 2 key: "semester_1/applied_mechanics:rigid-deformable-bodies-fbd" source: https://www.bctengineer.com/q/semester_1/applied_mechanics/rigid-deformable-bodies-fbd site: BCT Engineering --- # Rigid vs deformable bodies; free body diagram Applied Mechanics · Chapter 2: Basic Concept in Statics and Static Equilibrium - Asked in: 2073 Shrawan, 8 marks; 2072 Kartik, 2+2 marks (asked 2 times) - Video: [Concept of Rigid Body and Deformable Body](https://www.youtube.com/watch?v=4UVygVqwWRk) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/rigid-deformable-bodies-fbd - Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-2 ## Question Write down the concept of rigid bodies and deformable bodies. What is Free Body Diagram and why is it used during analysis of structure? ## Short answer A rigid body is an idealization where distances between points remain constant under load, used in statics. A deformable body changes shape under load, studied in strength of materials. A free body diagram (FBD) isolates a body showing all external forces and moments, enabling correct application of equilibrium equations and determination of internal forces. ## Answer #### Rigid body A rigid body is an ideal body in which the distance between any two points never changes under load. It does not deform. Statics treats bodies as rigid, which allows the equilibrium equations to be written for the original geometry, and the principle of transmissibility to be used. #### Deformable body A deformable body changes its size and shape when loaded. The change depends on the load and the material. The study of stresses, strains and deflections of such bodies belongs to strength of materials. | Rigid body | Deformable body | |---|---| | Ideal, no deformation | Real, deforms under load | | Distance between points constant | Distance changes | | Used in statics and dynamics | Used in strength of materials | | Transmissibility valid | Not valid | #### Free body diagram (FBD) A free body diagram is a sketch of a body or part of a structure, separated from its surroundings, in which all external forces and moments acting on it (applied loads, weight, support reactions and contact forces) are shown. #### Why it is used in structural analysis - It turns a physical structure into a clear force system to which ΣFx = 0, ΣFy = 0 and ΣM = 0 can be applied. - It shows which forces are known and which reactions are unknown, so no force is missed or counted twice. - Cutting a structure at a section and drawing the FBD of one part gives internal forces: axial force, shear force and bending moment, or member forces in a truss. - It helps in checking whether the problem is statically determinate. - A correct FBD is the first step of every statics problem. Most errors come from a wrong or incomplete FBD. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which principle is valid for a rigid body but not for a deformable body? A. Law of gravitation B. Principle of transmissibility C. Parallelogram law D. Newton's third law Answer: B. Sliding a force along its line of action changes the deformation of a deformable body. (Key point: Transmissibility) 2. A free body diagram is: A. A diagram of the structure with all supports left attached B. A sketch of the body isolated, showing all external forces and moments C. A drawing of internal stresses only D. A graph of load against deflection Answer: B. It shows the separated body with loads, weight, reactions and contact forces. (Key point: FBD meaning) 3. The main reason an FBD is used in structural analysis is that it: A. Shows the final deflection B. Turns the structure into a clear force system for applying the equilibrium equations C. Removes the need for equilibrium equations D. Gives the material strength Answer: B. It identifies known and unknown forces so SFx, SFy, SM = 0 can be applied. (Key point: Why use FBD) 4. How are the axial force, shear and bending moment at a section found? A. Use the modulus of elasticity B. Assume them equal to the loads C. Add all the support reactions D. Cut at the section and draw the FBD of one part Answer: D. The FBD of one part exposes the internal forces, which equilibrium then gives. 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