1

Spreadsheet Problem Solving

syntax for Excel formulas one-way case studies:

using formula copy using the TABLE function

2

Syntax for Excel formulas

formulas must start with =, + or - ( leftover from 1-2-3)

expressions are evaluated left-to-right

parentheses are used to establish order for calculations

precedence for arithmetic operators is:negation unary –exponentiation ^multiplication & division * and /addition & subtraction + and -

functions are evaluated first and the result is insertedat the position of the function in the expression

3

Examples

algebraic format Excel syntax

2

y 2 x 2

x xy y

=(y+2)*(x-2)/(x^2+x*y+SQRT(y))

Order of evaluation:

1) put y into SQRT function, return answer to that position2) compute y+2 result3) compute x-2 result4) multiply y+2 result times x-2 result to get numerator result5) compute x^2 result6) compute x*y result7) add up x^2, x*y and SQRT(y) to get denominator result8) divide numerator result by denominator result

4

Examples

algebraic format Excel syntax

2D

4L

=pi()*D^2/(4*L)

or =pi()*D^2/4/L

L

H L

T T

a T T

=(T-TL)/a*(TH-TL)

or =(T-TL)/(a*(TH-TL))

or =(T-TL)/a/(TH-TL)

5

Examples

Negation – unary minus

algebraic format Excel syntax

23 -3^2

Result

9 or –9 ???

2yx =x^y^2 ??? or =x^(y^2)

Repeated exponentiation

algebraic format Excel syntax

[test it!, if you’re not sure]

[What do you really want tohave happen?]

6

Examples

algebraic format Excel syntax

2h 3R h

3

=PI()*h^2(3*Radius-h)/3

What’s wrong with this?

forgot the * operator

sin 45 =SIN(45)

What’s wrong with this?

=SIN(45/180*PI())

arguments to trig functionsmust be in radians

7

Examples

Logarithms and exponents Remember!

ln y x xy e exp x

10

Blog P A

T C

BA

T CP 10

a

ln xlog x

ln a

LN(y) EXP(X)

LOG10(P) 10^(A-B/(T+C))

=LN(x)/LN(a)

=LOG(x,a)

8

Examples

for3x

do not use=x^3.

but=x^3

This is ok

23 =(-3)^2

This is not

=(-3)^2.0

When Excel (and other computer programs) see anexponent with a decimal sign, it computes the resultas follows:

aAnswer x aln Answer ln x a ln x

a ln xAnswer e

calculates (-3)*(-3)

2.0 ln( 3 )e ?? Nope!

9

One-way case studies

Example Problem

Deflection of cantilever beam

d

bL

F

3F L

3 E I

3b dI

12

E modulus of elasticity I moment of inertia

10

Deflection of cantilever beam

Basic data: F = 100 N L = 3 ft

E = 30 x 106 psi

b = 1 in d = 2 in

Find in mm

Case study 1: How does change as L varies?

Case study 2: How does change as d varies?

Case study 3: How does change as b and d vary?

11

Deflection of cantilever beam

Find in mm

12

Deflection of cantilever beam

Find in mm

13

Deflection of cantilever beam

Case study 1: How does change as L varies?

Use formula copy

Single formula with only oneparameter changing

Range of parameter valuesin adjacent column

14

Case Study 1

0.00

0.20

0.40

0.60

0.80

1.00

1.20

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Beam Length -- ft

Bea

m D

efle

ctio

n -

- m

m

15

Case study 2: How does change as d varies?

Deflection of cantilever beam

Use one-way data table[ Data Table ]

Multiple formulas

One input variable, d, in adjacentcolumn

One output variable, delta

“pointer”formula:where toget answeron spread-sheet

where valuefrom adjacentcolumn getsplaced onspreadsheet

16

Case Study 2

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Beam vertical dimension -- in

Def

lect

ion

--

mm

17

Case study 3: How does change as b and d vary?Deflection of cantilever beam

row input: B11

column input: B9

pointer formula to delta

deflection in mm for allcombinations of b and d

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

S1

S3

S5

S7

S9S11

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

d categories

bcategories

Def

lect

ion

in m

m