Principles of Problem Solving

PPS-14s: Translation/Define the System (Statics)

(Adapted from MPS 8, Don Woods 2003)

Pre-class assignment

1. Read sections What is It?, Why Do It?, New Concepts, How to  Do It, and Learning Objectives
2. Take the Translation Pretest
3. Be able to define  Translation and describe how it fits into the Six Step Problem Solving Method

What is It?

Translation is part of the Explore step in the Six Step Method of Engage, Define, Explore, Plan, Do It, and Look Back.

By now you have Defined the Stated Problem and have listed the Goals/Unknowns, Given/Knowns, Constraints, Assumptions, and have perhaps drawn a picture or two describing the situation.

Next we need to define the system that we intend to analyze, and translate the words of the problem statement into engineering symbols and equations.  Definition of the system often goes hand in hand with the principles used to solve the problem, but identification of principles is not the focus of this unit.

New Concepts

System Boundary, Input, Output, Free Body Diagram

Why Do It

In many Mechanical Engineering courses, the critical final step in problem definition is drawing the System, identifying the state of the System, and identifying all inputs and outputs to the System.  This System Diagram is the precursor to applying the principles of Conservation of Mass and Energy and is important for the task of accounting for the flows through the system.

In the Solid Mechanics area (Statics, Dynamics, Mechanics of Materials), these System Diagrams are called Free Body Diagrams.

How to Do It

In this unit we are going to concentrate on translation as applied to Engineering Statics. Using problems from Statics, we will translate words to equations and draw and label Free Body Diagrams.

Words into symbols

Forces and Moments

• Symbols for forces are traditionally the uppercase letters F, T, or P.  Symbols for moments are traditionally uppercase M or T (torque).  I recommend not using T to symbolize both force and torque in the same problem.
• Units of force are N (for Newtons) in the S.I. system and lb. (for pounds) or kip (for kilopounds) in US Customary units.
• To distinguish between forces, use of subscripts is recommended (F1, F2, F3 or Fa, Fb, Fc).
• Force magnitudes have no  arrow, F, but force vectors have an arrow or bar over the letter,  or .

Use my old notes for FBD and book pictures

Learning Objectives

Given a Statics problem statement, you should be able to Define the System by:

1. Identifying the System Boundary on a sketch of the problem situation with a clearly drawn circumscribed line.
2. Selecting the correct combination of Forces and Moments associated with different supports that are removed by the circumscribed line
3. Correctly drawing and labeling a Free Body Diagram

Pretest

Awareness:

How aware are you of what you do when you Draw Free Body Diagrams?             _________

On a scale of 1-10, where

1   is Unaware, I just do it,

5   is Aware of some

10 is Very aware: I can describe the details of how I do it

Skill:

How skilled are you in doing this activity?                               _________

On a scale of 1-10, where

1 is poor, 3 is fair, 5 is good, 7 is very good, and 10 is excellent?

In-Class

Exercise 1 (5 min.): (instructor hands out problem statement)

As an individual

1. Circumscribe the system with a line (the line should clearly show where supports have been cut to “free” the system)
2. Draw and Label the Free Body Diagram, FBD, which results from those cuts
1. show appropriate forces and moments at locations where supports were cut
2. show all external or applied forces and moments on the system
3. using correct notation, label all forces and moments

As a group of 2-4 people

2. note differences
3. try to resolve those differences.

PPS-13  Define the Stated Problem

Assignment 1  Individual

For the problem statement assigned,

1. Circumscribe the system with a line (the line should clearly show where supports have been cut to “free” the system)
2. Draw and Label the Free Body Diagram, FBD, which results from those cuts

a.      show appropriate forces and moments at locations where supports were cut

b.      show all external or applied forces and moments on the system

c.      using correct notation, label all forces and moments

Evaluation:

1. Circumscribe Situation Drawing

Excellent (10)  - continuous line that clearly shows where supports are cut

Mediocre (5)    - some of line is not shown or not clear

Weak (0)         -  line is not continuous, cuts are unclear

2. Appropriate Forces Moments

Excellent (10)  – all applied forces and moments are shown, appropriate forces and moments are shown where supports were removed

Mediocre (5)    - some forces and moments are missing or incorrect

Weak (0)         – most forces and moments are missing or incorrect

3. Labeling

Excellent (10)  – Forces and moments are labeled correctly (correct vector notation, units, directions, subscripts)

Mediocre (5)    - some labels are incorrect or missing

Weak (0)         – most labels are incorrect or missing