Statics #05 | Rigid Body Equilibrium: Support Reactions, Three Equations and the Moment-Point Trick

Instructor: Dr. Süleyman Burak ÇELİK

A 4 meter beam rests on two supports; a 600 N load sits not in the middle but 1 meter from the left support. How much does each support carry? Your instinct says the left one carries more; in this lesson we find the number. Force balance alone is not enough: on a rigid body the position of the load changes the answer, so the moment equation enters. Three equations, the types of supports and two fully worked problems, without skipping a single step. In this lesson: - A rigid body at rest neither slides nor turns: ΣFx = 0, ΣFy = 0, ΣM = 0; three equations, at most three unknowns - The moment point can be any point; the trick: choose the point the unknowns pass through so one equation has one unknown - Support catalogue: a cable pulls (1), a roller pushes perpendicular to the surface (1), a pin gives two components (2), a fixed support gives two components plus a moment (3) - Free body diagram of a rigid body: isolate, turn supports into reactions, write the lengths - Problem A: 4 m simply supported beam, 600 N at 1 m → ΣM_A: B = 600 / 4 = 150 N; A = 600 − 150 = 450 N; check ΣM_B = 0; three times closer to A, A carries three times as much - Problem B: 3 m beam, pin at A, cable at B at 30 degrees to the beam, 300 N at midspan → T = 300 N, Ax = 259.8 N, Ay = 150 N; an inclined cable works twice as hard as a vertical one - Four classic traps: a random moment point, forgetting Ax at a pin, the sign of the moment, trying to solve with force balance alone Chapters: 0:00 Intro 0:03 Two supports, one load: who carries what? 1:19 Three equations and the moment-point trick 2:37 Support types and the rigid-body FBD 4:01 Problem A: simply supported beam 6:23 Problem B: pin and cable 9:36 Four traps and one habit 11:05 Summary and next lesson Next lesson: distributed loads and couples. Lesson 5 of the Statics (Engineering Mechanics) series for civil, mechanical and mechatronics engineering students.