Systems - Engineering Mechanics - Statics - Lecture Slides, Slides of Mechanical Engineering

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Chp 5: FBDs

2D/3D Systems

Free Body Diagrams (FBDs)

• A free-body diagram is a sketch of an object

of interest with all the surrounding objects stripped

away to reveal all of the forces

acting on the body

• The purpose of a free-body force diagram is to

assist with determination of the Net Force and/or

Moment acting on a body

SpaceDiagram

Diagram^ Free Body

Structural Supports

• NonMoving Structures are typically Connected

to Some Sort of Supporting Base

• The connection between the Structure and

Base are usually Called “Structural Supports”

• The Force and/or moments exerted on the

Structure Base are usually called “Structural Reactions” (RCNs for Short)

Structural Supports

• A Support that Prevents Linear Motion

(sliding, translating) of the structure then exerts a Force on the structure

• A Support that Prevents Rotating Motion

(twisting, turning) of the structure then exerts a Couple Moment on the structure

2D Support ReActions

• Cable can only Generate TENSION
• WeightLess Link is 2-Force Element

2D Support ReActions

• Note that in BOTH these Cases the Support ReAction is NORMAL (Perpendicular) to the Supporting Surface
• RCN can only PUSH, and NOT PULL

2D Support ReActions

• Only the Supports (9) & (10) Can Generate a Couple-Moment ReAction

Center of Gravity

• If the Weight of the Rigid Body

is Not Negligible, then the

Entire Weight of the Body can

be concentrated at a Single

Point Called the Center of

Gravity (CG)

• Many times the CG location is Given - Can Calculate using Centroid Methods which will be covered later

2D Free-Body Diagram cont

1. Select the extent of the free- body and detach it from the ground and other bodies
2. Indicate for external loads:
   • Point of application
   • Magnitude & Direction Of External Forces

• Including The Body Weight.

3. Indicate point of application and ASSUMED direction of UNKNOWN applied forces

2D Free-Body Diagram cont.

• The Unknown Forces Typically Include REACTIONS through which the GROUND and OTHER BODIES oppose the possible motion of the rigid body

4. Include All dimensions Needed to Calculate the Moments of the Forces

Example: Truss – Draw FBD

RA (^) W RBy

RBx

RB

 This Dwg is,

in fact, a Full

Free Body

Diagram

φ

3D Support ReActions

• Same as 2D ReActions of this Type

3D Support ReActions

• This configuration is Commonly Known as a “ Pillow Block Bearing ”.
• Type of support is (obviously) designed to allow the shaft to SPIN FREELY on its AXIS

3D Support ReActions

• The Sq-Shaft Bearing System does NOT Allow the shaft to spin completely freely, Thus the M y