2.3 Mathematical Functions

2.3.1 Trigonometric and Logarithmic Functions

VCmaster is proficient in all mathematical functions of the scientific calculator including all parenthesis levels and exponentiations.  The function descriptions are either entered directly or called up via the menu.

When using the menu VCmaster assists by inserting predefined functions e.g. SIN(). The cursor is automatically positioned in the brackets for the function value to be entered, which can either be a numerical value or a variable. 
All functions can be linked, i.e. a function value can also contain a function call (for nesting: See examples). 

The VCmaster TechEditor can interpret super scripted characters so that the expression X² , written with (ALT GR+2 ) is equivalent to the representation X² (written with super scripted 2). X^1/3 will also be correctly evaluated, rendering special exponential functions unnecessary. 

Naturally all current mathematical rules apply. If an equation is unsolvable, VCmaster shows a relevant error message. Calculation then continues with the number of decimal places specified. Meaning, if a higher calculation accuracy is required, the number of places after the decimal point has to be increased.

MENU:

Calculate-Angular function/Logarithm

Examples

Trigonometric function:
	Width b =				200.	00 mm
	Angle α =				45.	00 °
	Height h =		b * SIN( α )		= 141.	42 mm
Exponentiation (automatic interpretation of superscripted fields):
	χ =		1/(φ+(φ²-λ²)0,5)		0.	8083
Exponentiation (ALT GR+2 * or ALT GR+3 key * ):
	Width b =				10.	00 mm
	Height h =				20.	00 mm
	I =		b * h3 / 12		6666.	67 mm4

Note: Depending on the specific charset

2.3.2 Logical functions

Functions such as ABS(), MAX(), MIN(), IF(), AND, OR are realized. Arguments are separated by semicolons.

The IF function consists of three elements: The condition, the formula or the value that is to be used if the condition is fulfilled, and the formula or the value that is relevant if the condition is not fulfilled.

In the IF function all common operators "=" , "≠" , ">" , "<" , “≥" and “≤"" are allowed. Text variables can be compared although only numerical values are allowed as a result.

The IF function is resolved from right to left. Hence, it makes sense to utilize brackets in operations.

Examples

IF function (read: if; then; else):
	D =		55.00 mm
	k =		IF( D≤32; 1; 1 - 0.26*LOG(D/32)))					= 0.	939
IF function (nested):
	d =		20 cm
	b =		IF( d>25; 1;IF( d>17.5 ; 0.9 ; 0.75) )					= 0.	90
Example with text variables:
	Steel =		"S355"
	Re =		IF( Steel="S235" ; 235 ; 355 )					= 355.	00 N/mm2
Example with text variables:
	FEd =		45.00 kN
	FRd =		50.00 kN
	Re =		IF( FEd / FRd ≤ 1; "valid"; "invalid" ) =						admissible
	Re =		IF( FEd / FRd ≤ 1; FEd / FRd ; "invalid" ) =						0,90
	Exception: If an if () function, that usually returns a number, returns a text in case of an error, this variable will no longer be used for calculations.
Example showing different brackets (red) and the results:
	A =		15
	b =		30
	IF( A < 10 AND B < 20 OR B > 25; 1; 0.80 )							= 1.	00
	IF( (A < 10 AND B < 20) OR B > 25; 1; 0.80 )							= 1.	00
	IF( A < 10 AND (B < 20 OR B > 25); 1; 0.80 )							= 0.	80
Examples of MIN()- / MAX() function:
	F1 =		150 N
	F2 =		200 N
	FMAX =		MAX( F1; F2 )					= 200.	00 N
			MIN (F1; F2 * 0.50 )					= 100.	00 N
	Note: The IF() call can be hidden in the printout. For details, see Chapter 2.9

2.3.3 Summation and Absolute value function

Both functions are entered in the graphic formula editor.
The entry of a total corresponds with the mathematical rules.

Note: The index must be identical with the mathematical rules.

Rules:




Example:


The example shows the following summation:

Iy = Iy₁+ Iy₂ + Iy₃

2.3.4 Conversion of Units of Measurements

On generating a formula, every variable can be allocated the unit of measurement expected by the formula. Alternatively the shortcut CTRL + # is available. This function calls for the use of a graphic formula, which will be generated automatically after text input. The target unit of measurement is hidden during this operation. It can be modified later in the Formula Editor.


The fact that formulae are always calculated correctly regardless of the underlying variable is a major advantage of allocating target units of measurements.

Using B= 8,00 dm as shown in the example would generate the identical value for the area. Using target units of measurements, errors while copying formulae and templates are avoided. If a unit of measurement can not be converted, an error message is shown instead. For validation purposes the converted value can be displayed. Working with target units of measurements is especially recommended in countries working with various units and not only with SI-units. VCmaster is able of working with and converting e.g. British Units.

MENU:

Calculate- Other functions-Target unit

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