Presentation on theme: "ENGR-1100 Introduction to Engineering Analysis"— Presentation transcript:
1ENGR-1100 Introduction to Engineering Analysis Lecture 12
2Lecture OutlineRigid body equilibrium.FBD- Free Body Diagram.
3Rigid BodiesA rigid body is an ideal object that has dimensions and mass but does not deform under loading.The size and shape does significantly affect the response (reaction at supports) to applied force/s- A force applied to a rigid body may be translated along its line of action without altering its effects (principle of transmissibility)
4Necessary and Sufficient Conditions of Equilibrium of a Rigid Body The necessary AND sufficient condition for a rigid body to be in equilibrium is that the resultant force and couple acting on the rigid body must be zero.Particle equilibriumThose are vector equations.How many scalar equations in the 2D?in the 3D?Rigid body equilibrium
6Isolation of bodies: Free Body Diagram -In a system of interacting bodies, to be able to apply Newton’s laws properly, a systematic technique is to:isolate each of the bodies or a collection of bodiesidentify the forces acting on each of the bodies, and thenapply the equilibrium equations to each.-The sketch of the isolated body or system of bodies considered as a single body, with all the external forces acting on itby mechanical contact with other bodiesby gravitational attraction (weight)when the rest of the bodies are imagined to be replaced by their actions, it is known as a free body diagram.
7Isolation of bodies: Free Body Diagram The free body diagram is the most important single step in the solution of problems in mechanics.Remember:The forces on the isolated body (or system of bodies) are to be considered.2. Apply Newton’s Third Law (every action has an equal, opposite and collinear reaction) carefully
8Steps of Drawing a FBDClearly identify the body (or system of bodies) to be isolated (the FREE body).Draw a diagram of this “free body” completely isolated from the rest of the bodies.Traverse the boundary of this “free body” and indicate ALL forces acting ON the free body (contact forces with other bodies forces)Known forces: Show vector arrows with proper magnitude (UNITS!!), direction and sense.Unknown magnitude but known direction of force: Show vector arrows with magnitude assumed as positive (if calculations show that the magnitude is negative, the minus sign indicates that the sense is opposite to the one assumed)Unknown magnitude and direction of force: Show x- and y- components of the vector with unknown magnitudes.4. Show coordinate directions on the diagram
9Two-dimensional reaction at supports and connections 1. Gravitational attraction2. Flexible cord, rope, chain, or cable