ME 101:

Forces & Moments(Continued)

Chapter 4

ME-1011

Particle/Rigid Body

• Particle – A very small amount of matter assumed to

occupy a single point in space

• Rigid Body – A combination of a large number of

particles that are fixed relative to one another

ME-1012

Newton’s 3 Fundamental Laws

• First Law – If the resultant force acting on a particle

is zero, the particle will remain at rest (if originally at

rest) or will move with constant speed in a straight

line (if originally in motion)

• Second Law:

• Third Law – The forces of action and reaction

between bodies in contact have the same magnitude,

same line of action, and opposite sense

ME-101

amF

3

Equilibrium

ME-101

0 FR

0 FrMM

1F

2F 3F

3r

2r

1r

4

Equilibrium (in 2-D)

ME-101

0xF

0yF

0oM

Particle is in

equilibrium if forces balance (zero

resultant)

Rigid body is in

equilibrium if forces and

moments balance

5

Free Body Diagram (FBD)

Forces and moments acting on a body are applied to a

simplified version of the body

ME-101

W

Fchair

W

Fchair

6

How to Draw a FBD

1. Isolate the body from its surroundings and draw a simplified version of it

2. Use an appropriate coordinate system (Usually Cartesian) and include it with your FBD

3. Add the loads to the body in appropriate locations with proper direction and magnitude

4. Label all known quantities

ME-1017

T

Example

ME-101

WB

TWA

NA

A

B

Fapp

Pulley

θ

Assume surface is smooth – no friction

What is FBD of Block A? Block B?

Fapp

Use the free body diagram to evaluate the system

y

x

θ 3

4

5

8

Example

The mass center G of the 1400 kg rear engine car is

located as shown in the figure

Determine the normal force under each tire when the

car is in equilibrium

ME-1019

Example

ME-10110

Example

• Determine the pull P on the rope

exerted by the man to hold the

crate in the position shown

• Also find the tension T in the

upper rope

ME-10111

Example

Compute the moment about point O

ME-10112

Design Applications

ME-10115

Hyatt Regency Hotel in Kansas City

• July 17, 1981

• Killing 114

• Injuring 200+

• Worst structural disaster in U.S. history

• The engineering firm that approved the final

plans was stripped of its license

• http://www.onlineethics.org/CMS/

profpractice/ppcases/texindex/

hyatt_walkway.aspx

ME-10116

Why?

ME-10117

The initial plan and final deviation

ME-101

http://azurebrooke.com/

18

Beam Failure

ME-10119

Design Application: Bearings

Two types of bearings

– Rolling-Element • Balls or rollers between inner and outer race

• Very common

– Journal• Shaft in lubricated sleeve

• Rotates on film of oil

• Examples – Engine crankshafts, pumps, and compressors

ME-10120

Radial Ball Bearing

ME-10121

Ball and Roller Contact Stress

ME-101

Max shear stress occurs below the surface, failure appears as cracks, pits, or flakes

22

Roller Bearings

Higher Loads – Axial or Radial

ME-10123

How to Size Component

• Create FBD

• Determine loads acting on component

• Determine size of component– Consider Non-Traditional Solutions

– Factor of Safety

– Consider Dimensional Constraints

– Cost

– Manufacturability

– Ease of Assembly

ME-10124

Bearing Selection

ME-10125