--- title: "Steps for free body diagram; equilibrium 2D/3D" subject: "Applied Mechanics" chapter: 2 key: "semester_1/applied_mechanics:fbd-steps-equilibrium-2d-3d" source: https://www.bctengineer.com/q/semester_1/applied_mechanics/fbd-steps-equilibrium-2d-3d site: BCT Engineering --- # Steps for free body diagram; equilibrium 2D/3D Applied Mechanics · Chapter 2: Basic Concept in Statics and Static Equilibrium - Asked in: 2072 Chaitra, 8 marks; 2071 Chaitra, 2+4 marks (asked 2 times) - Video: [Equilibrium of Rigid Bodies (2D - Coplanar Forces) | Mechanics Statics | (Solved examples)](https://www.youtube.com/watch?v=jQDEOwrR4UU) — Question Solutions - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/fbd-steps-equilibrium-2d-3d - Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-2 ## Question Write down the steps to be considered while drawing a free body diagram. Illustrate equilibrium condition of particle and rigid body in two and three dimensional analysis. ## Short answer Steps: isolate the body, sketch it, show all applied loads and weight, replace supports with reactions, label known and unknown forces, and choose axes. A particle in equilibrium has zero resultant force (2D: ΣFx=0, ΣFy=0; 3D: ΣFx=ΣFy=ΣFz=0). A rigid body also requires zero resultant moment (2D: ΣFx=0, ΣFy=0, ΣM_O=0; 3D: six equations, ΣF=0 and ΣM=0). ## Answer #### Steps in drawing a free body diagram 1. Decide which body (or part of a structure, or a joint) is to be isolated and separate it completely from the surroundings. 2. Sketch the isolated body with its shape and main dimensions and angles. 3. Show the weight of the body at its centre of gravity, and all applied loads (point loads, distributed loads, couples) in their true position and direction. 4. Replace each support or connection by the reaction it develops: - roller or smooth surface: one force normal to the surface, - hinge or pin: two components (or one force of unknown direction), - fixed support: two force components and a moment, - cable: tension along the cable, away from the body, - smooth contact between bodies: normal force, equal and opposite on the two bodies (Newton's third law). 5. Label all forces, known ones with values and unknown ones with letters. Assume a sense for each unknown. A negative answer means the sense is opposite. 6. Choose a reference axis system and show the dimensions needed for moments. #### Equilibrium of a particle A particle is in equilibrium when the resultant force on it is zero. All forces on a particle are concurrent, so no moment equation is needed. - 2D: ΣFx = 0, ΣFy = 0 (two equations, up to two unknowns). - 3D: ΣFx = 0, ΣFy = 0, ΣFz = 0 (three equations, up to three unknowns). #### Equilibrium of a rigid body A rigid body is in equilibrium when the resultant force and the resultant moment about any point are both zero: ΣF = 0 and ΣM = 0. - 2D: ΣFx = 0, ΣFy = 0, ΣM_O = 0 (three equations, up to three unknowns). - 3D: ΣFx = ΣFy = ΣFz = 0 and ΣMx = ΣMy = ΣMz = 0 (six equations, up to six unknowns). In 2D, force equations may be replaced by moment equations: either ΣFx = 0, ΣM_A = 0, ΣM_B = 0 (with line AB not perpendicular to the x axis), or ΣM_A = 0, ΣM_B = 0, ΣM_C = 0 (with A, B and C not on one straight line). Either way, there are never more than three independent equations. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A roller or smooth surface support is replaced in an FBD by: A. Two components of force B. Two force components and a moment C. A force along the surface D. One force normal to the surface Answer: D. A smooth contact can only push normal to the surface. (Key point: Roller reaction) 2. A fixed support is replaced by: A. Two force components and a moment B. Tension along the cable C. A single moment only D. One normal force Answer: A. A fixed support resists horizontal and vertical force and rotation. (Key point: Fixed support) 3. After assuming a sense for an unknown force, a negative answer means: A. The body is not in equilibrium B. The calculation is wrong C. The force acts opposite to the assumed sense D. The force is zero Answer: C. The negative sign only shows the true sense is opposite to that assumed. (Key point: Unknown sense) 4. How many independent equilibrium equations exist for a rigid body in 3D? A. 3 B. 6 C. 4 D. 5 Answer: B. SFx, SFy, SFz and SMx, SMy, SMz give six equations. 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