Introduction to Engineering Mechanics

Introduction to Engineering Mechanics Dr. Wayne Whiteman Director of the Office of Student Services and Senior Academic Professional School of Mechanical Engineering

This course is an introduction to learning and applying the principles required to solve engineering mechanics problems.

School of Mechanical Engineering

Module 12 Learning Outcomes Define the moment (or torque) of a couple  Define how to calculate a moment due to a couple using the scalar method and the vector method  Solve a problem determining the moment do to a couple 

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Moment of a Couple -Tendency of a pair of forces to cause rotation of a body -Forces are: - Equal in magnitude - Opposite directions - Act along parallel LOAs -Couples are a “Free Vector” – same rotation effect anywhere on the body Scalar approach: M C  M D  C  F d  Vector approach: M B  C  rBA  F 3

Given the pair of forces F, each with a magnitude of 50 lbs: a) Determine the total moment about point A b) Determine the total moment about point O c) Is the moment caused by the couple the same for any point on the system?

Scalar approach: M C  M D  C  F d 

y 6 in

F

2 in 4

3

A 4

O

x

B

3

F

4

Given the pair of forces F, each with a magnitude of 50 lbs: a) Determine the total moment about point A b) Determine the total moment about point O c) Is the moment caused by the couple the same for any point on the system?

Vector approach: M A  C  rAB  F

y 6 in

F

2 in 4

3

A 4

O

x

B

3

F

5

Given the pair of forces F, each with a magnitude of 50 lbs: a) Determine the total moment about point A b) Determine the total moment about point O c) Is the moment caused by the couple the same for any point on the system?

F  12iˆ  16 ˆj lb Vector approach: M A  C  rAB  F

y 6 in

F

2 in 4

3

A 4

O

x

B

3

F

6