ca05 review - problem solving
Problem Statement #1: A cable of length l0 is needed to
suspend an object of mass mobj from the ceiling. The load, T
= mobjg, is the force that the mass exerts on the cable. The
deflection (elongation) of the cable under the load must be
less than lmax. Ignoring the mass of the cable (mcable, which
adds to the load), what cable mass is required to just support
the load without permanent deformation?
step 1: draw a sketch!!!
ceiling
l0
mobj
T = mobjg
Engr 0012 (04-1) LecNotes 06-01
needs
l0
mobj
lmax
step 2: review relevant engineering
strain
stress-strain problem: S = Ee
stress
elastic (Young’s) modulus
permanent deformation when S > Sy
looking for mass of cable
mcable   V
need equation for volume
A0
material property
look it up
add to needs list
Engr 0012 (04-1) LecNotes 06-02
l0
step 2: review relevant engineering
V  A0 l 0   d l 0 / 4
2
already on needs list
need equation
T
S
A0
needs list
l0
mobj
lmax

Sy
Engr 0012 (04-1) LecNotes 06-03
4T
S 
2
d
can calculate
T = mobjg
4T
d
S
need value
use Sy
add to needs list
step 3: restate problem
Design a MATLAB script to find the minimum mass of a
cable required to support an object hanging from a ceiling
given the mass of the object, initial length of the cable,
maximum deflection, cable density, and cable yield stress.
step 4: algorithm
1. Ask user for mass of the object, initial length of the cable,
maximum deflection, cable density, and cable yield stress.
2. Compute mass of cable.
3. Report mass of cable.
Engr 0012 (04-1) LecNotes 06-04
step 5: expand step 2 of algorithm
2. Compute mass of cable.
a. Compute tension.
b. Compute cable diameter.
c. Compute cable volume.
d. Compute cable mass.
Engr 0012 (04-1) LecNotes 06-05
ca05 review - problem solving
Problem Statement #2: My boss at the Internal Revenue
Service (IRS) has asked me to develop a program that will
determine how much taxes are due based upon a taxpayer’s
annual salary. The tax due is based upon a provided table.
step 1: draw a sketch!!!
Can’t - not applicable.
step 2: review relevant information
Percentage
Salary Range, $ Base Tax, $
on Excess, %
0 - 14,999
0
15
15,000 - 29,999
2,250
18
30,000 - 49,999
5,400
22
50,000 - 79,999
11,000
27
80,000 & above
21,600
33
Engr 0012 (04-1) LecNotes 06-06
needs list
salary
Need to find where salary
falls in table.
Compute tax due as base
+ % time amount in
excess of minimum in
range
step 3: restate problem
Design a MATLAB script to find the tax due based upon a
taxpayer’s salary.
step 4: algorithm
1. Ask user for salary.
2. Compute tax due.
3. Report tax due.
step 5: expand step 2 of algorithm
2. Compute tax due.
a. Use salary and if/elseif/else structure to
find appropriate row in table
b. Compute appropriate excess.
c. Compute appropriate tax due.
Engr 0012 (04-1) LecNotes 06-07
decision making - design issues
Whenever you need to make a decision, make a decision table
condition
action
Raining
Take umbrella
Cloudy
Take hat
Sunny
Take sunblock and hat
A decision table is a simple listing of conditions and actions
that result if the condition is met.
Engr 0012 (04-1) LecNotes 06-08
decision making - design issues
Two types of decision conditions
Mutually exclusive conditions
Conditions have no overlap, i.e., only one of the
conditions can be true
Nonexclusive conditions
Conditions can overlap, i.e., one or more of the
conditions can be true at same time
Example
Condition
Action
Raining
Take umbrella
Cloudy
Take hat
Sunny
Take sunblock and hat
Engr 0012 (04-1) LecNotes 06-09
Nonexclusive - Why?
decision making - design issues
Example
Condition
Score < 60
Score >= 60
Score >= 70
Score >= 80
Score >= 90
Action
Earned F
Earned D
Earned C
Earned B
Earned A
Nonexclusive - Why?
score of 84 satisfies
conditions 2, 3, and 4
Important because we will use an if/elseif command
structure to find proper condition and action
Engr 0012 (04-1) LecNotes 06-10
if/else if/else command structure
first conditon from table
if
(condition 1)
perform condition
elseif (condition 2)
perform condition
elseif (condition 3)
perform condition
else
perform “default”
end
if none of the
conditons are met
Engr 0012 (04-1) LecNotes 06-11
first conditon actions
1 actions from table
2 actions
3 actions
actions
perform
these
actions
default is
frequently omitted
decision making - MATLAB syntax
Example
Condition
Score < 60
Score >= 60
Score >= 70
Score >= 80
Score >= 90
(score < 60)
grade = ‘F’;
elseif (score >=
grade = ‘D’;
elseif (score >=
grade = ‘C’;
elseif (score >=
grade = ‘B’;
elseif (score >=
grade = ‘A’;
end
Action
Earned F
Earned D
Earned C
Earned B
Earned A
if
Engr 0012 (04-1) LecNotes 06-12
60)
70)
80)
90)
MATLAB moves through
structure looking for first
condition that is satisfied.
MATLAB then executes
the “action statements”
under the condition.
When the last “action
statement” is finished,
MATLAB goes to the end.
decision making - nonexclusive conditions
nonexclusive conditions are a problem - can either rearrange
table to make sure order of execution is appropriate
Condition
Score >= 90
Score >= 80
Score >= 70
Score >= 60
Score < 60
Action
Earned A
Earned B
Earned C
Earned D
Earned F
note use of default
rather than condition
Engr 0012 (04-1) LecNotes 06-13
if (score >= 90)
grade = ‘A’;
elseif (score >= 80)
grade = ‘B’;
elseif (score >= 70)
grade = ‘C’;
elseif (score >= 60)
grade = ‘D’;
else
grade = ‘F’;
end
decision making - nonexclusive conditions
nonexclusive conditions are a problem - can either rearrange
table to make sure order of execution is appropriate or make
Condition
Action
conditions mutually exclusive
if
(score < 60)
grade = ‘F’;
elseif (score >= 60 & score < 70)
grade = ‘D’;
elseif (score >= 70 & score < 80)
grade = ‘C’;
elseif (score >= 80 & score < 90)
grade = ‘B’;
else
grade = ‘A’;
end
Engr 0012 (04-1) LecNotes 06-14
Score < 60
Score >= 60 and Score < 70
Score >= 70 and Score < 80
Score >= 80 and Score < 90
Score >= 90
Earned F
Earned D
Earned C
Earned B
Earned A
Order of execution of
mutually exclusive conditions
not important because only
one condition can be true
decision making operators
comparison (relational) operators
greater than
less than
greater than or equal
less than or equal
is the same as
is not the same as
logical (set) operators
and
or
not
Engr 0012 (04-1) LecNotes 06-15
&
|
~
>
<
>=
<=
==
~=
example function using decision making
grade_earned.m
how do you know it is working properly?
test it!!!
Engr 0012 (04-1) LecNotes 06-16
programming assignment 03
due Wed 17 Sep
class activity 06 : ca06_e12(04-1).pdf
Engr 0012 (04-1) LecNotes 06-17