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Dimensional analysis

Added March 16, 2018 by Tekla User Assistance tekla.documentation@trimble.com

Software version: 
Tekla Tedds 2018

Dimensional analysis

Dimensional analysis

Dimensional analysis allows you to verify that your calculations are dimensionally correct. The following paragraphs explain how to switch on dimensional analysis, and detail the dimensions of variables that can be used with mathematical operators or functions.

Switch on dimensional analysis ( the Tedds Application )

  1. On the Home tab , click Options.

    The Options - Default dialog appears.

  2. In the side pane, click Calculating.

  3. Select the Perform dimensional checks option.

Switch on dimensional analysis ( Tedds for Word )

  1. In the Tedds ribbon group, click More > Tedds Options.

    The Options - Default dialog appears.

  2. In the side pane, click Calculating.

  3. Select the Perform dimensional checks option.

Operators

Tip:

For Tedds for Word users:

You can access most of the operators in the Library Access System. Go to Writing your own custom calculations > Calculation writing documentation > Math symbols.

Dimensional analysis operators
Function Input dimensions Result dimensions Example

x + y = z

x - y = z

x and y must have identical dimensions z has the same dimensions as x and y (1m) + (1m) = 2m

x × y = z

x ÷ y = z

x and y may have any dimensions Dimensions of z result from those of x and y being multiplied and divided according to × or ÷ function (1m) * (1m) = 1m 2
(((...))) Any No change to dimensions None

y x = Z

10 x

x has to be dimensionless, y may have any dimension z's dimension exponent is y's dimension altered by exponent x (1m) 5 = 1m 5

Functions

Tip:

For Tedds for Word users:

You can access most of the operators in the Library Access System. Go to Writing your own custom calculations > Calculation writing documentation > Maths functions.

General dimensional analysis functions
Function Input dimensions Result dimensions Example
sqrt(x) = z x may have any dimension z's dimension exponent is x's halved sqrt((1 m)) = 1 m 0.5

abs(x) = z

int(x) = z

int(x,"unit") = z

round(x,y) = z

round(x,y,"units") = z

mod(x, y) = z

quotient(x,y) = z

x may have any dimension, y has to be dimensionless z has the same dimension as x abs((-1 m)) = 1 m
sum(x,y,z,…) = z max(x,y,z,…) = z min(x,y,z,…) = z average(x,y,z,…) = z median(x,y,z,…) = z All items being considered in the list (x,y,…) must have identical dimensions z has the same dimensions as x and y sum((1 m),(1 m)) = 2 m
rand() = z None z is dimensionless None
Logarithmic and exponential dimensional analysis functions
Function Input dimensions Result dimensions Example

ln(x) = z

log(x) = z

exp(x) = z

x has to be dimensionless z is dimensionless None
Trigonometric dimensional analysis functions
Function Input dimensions Result dimensions Example
degrees(x,y,z) = a

x, y and z have to be dimensionless.

x can be in degrees or radians because those units are dimensionless.

a is dimensionless, but may be in degrees or radians since they are dimensionless degrees((1,30,0) = 1.5 °

sin(x) = z

cos(x) = z

tan(x) = z

cosec(x) = z

sec(x) = z

cot(x) = z

x has to be dimensionless because degrees and radians are dimensionless z is dimensionless sin (90 °) = 1
asin(x) = z acos(x) = z atan(x) = z x has to be dimensionless z is dimensionless - but may be in degrees or radians since they are dimensionless asin (1) = 90 °
Hyperbolic dimensional analysis functions
Function Input dimensions Result dimensions Example

sinh(x) = z

cosh(x) = z

tanh(x) = z

asinh(x) = z

acosh(x) = z

atanh(x) = z

x has to be dimensionless z is dimensionless None
Logical dimensional analysis functions
Function Input dimensions Result dimensions Example

if(condition,x,y) and(x,y,z,...)

(x && y) or (x,y,z,...)

(x || y)

x > y

x >= y, x ≥ y

x == y

x <> y, x ≠ y

x <= y, x ≤ y

x < y

All logical comparisons must be between values with identical dimensions No change to dimensions, true and false are dimensionless None
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