CAE SETS (Structure Engineering Turnkey System): True #1

ADVANCED ALGEBRAIC OPERATION DATA INPUT GUIDE Copyright (C) 1996 by CAEINC, U S A
This FREE dissemination of info NOT for CAEinc competitors

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1) ALGEBRAIC EXPRESSION INPUT DATA ITEM

1-1) AN INPUT DATA ITEM

An item of input data can be:
1-1-1) A simple numerical constant, which is conventionally accepted,
1-1-2) An ALGebraic expression that can contain variables, numerical
constants and algebraic operators.
1-1-2-1) Algebraic Variables: X Y Z A B C ....
A single-letter from 26 alphabets, such as A B C .. X Y Z.
(Lower case is the same as upper case)
As many as needed that are defined currently or previously.
1-1-2-2) Algebraic Numerical Operators: = ** * / + -
6 operators: = ** * / + -
As many as needed with only ONE "=" as FIRST operator with
top priority if any.
Others, namely ** * / + -, are according conventional
algebraic convention.

Each item and every item of numeric data may be input as a form of
ALGebraic expression in one contiguous item. For example, the numeric
number 8. can be any one of them as shown below: (with (Y=2.))

8. | Y=2.**2+2.**3_2.*2. | Y*4.**3/4./Y**2 | 2.**4/2.

The operation priority for the expression Y=2.**2+2.**3_2.*2. is
(Y=2.)**2+2.**3_2.*2.. However, in input the open parenthesis "(" and
the close parenthesis ")" must be omitted.

Each item and every item must be contiguous including "+" and/or
"-", which is used as sign of positive and/or negative numbers
respectively.

Blanks are used as item separator along with commas "," as separator.
It is highly advisable not to use commas "," due to third party
compiler problem. This situation may be corrected in the future.

Use the under line "_" as subtraction operator, not minus "-", due to
conflict in some input notations. The "-" is used for the sign of a
negative number only. In time this situation will be corrected.

1-1-3) INPUT DATA SPACE LIMITATION

In an original input line, there are allocated 110 (or 80) total
column spaces for input.

Each and every input data item, if needed, is converted to form a
simple nominal data item. This way, an internal input line is obtained.

The TABLE below shows their maximum allowable column spaces currently.

Input line that has converted data	256
Algebraic expression	32
Numerical constant	16
Variable	1

There are 6 ALGebraic operators in all to use and 26 single-letter
variables that you can assign a numerical constant.

The 6 operators : = ** * / + -
The 26 variable : A B C D E ... X Y Z (lower case same as upper case)

1-2) PRIORITY OF OPERATION

The priority of algebraic operation is the same as that in
conventional mathematics for ** * / + -. The Program adds the
sign "=" as additional operator with top priority.

1-2-1) = An item can only have ONE equal sign in the form Y=xxx.xx
Y, any one of 26 single-letter variables.

The "=" must be, if any, the FIRST algebraic operator.
xxx.xx, which is assigned as value for Y, must be a
numerical constant.
A variable is considered DEFINED with this numerical
constant and it continues to have the same value until
it is redefined by another Y=yyy.yy in any OPERATION in
the Articles 1-2), 2) and 3).

Y=xxx.xx** means (Y=xxx.xx)** in priority.
However, (Y=xxx.xx)** is INCORRECT input syntactically.

1-2-2) ** To raise to a power

1-2-3) * / The priority between * and / is according to input order.

1-2-4) + - The priority between + and - is according to input order.

Each numerical number associated with an algebraic operator must
be in floating point except a number which is raised to the power of
whole digit. (some computers may take fixed point for floating point.)

For example, all below are good.

X=2.54**2 better (means (X=2.54)**2)
X=2.54**2.0 good
X=3600.**0.5 good and must be.


1-3) INVOCATION SYNTAX

1-3-1) ALGebraic 6 ...

ALG 6 : The Program scans all 6 operators, namely = ** * / + _.
ALG 4 : The Program scans only 4 operators, namely = ** * /.
If there is + and/or - in expression, Program will treat
it as an input error and stops.
ALG 0 : Defaults to ALG 4 (Otherwise it is meaningless.)
ALG ON: The Program is to default currently to ALG 4.
ALG OFF: Program is disabled from such capability.

2) DATA CONVERT/MODIFY COMMAND: MUL, DIV, ADD & SUB

O P E R A T I O N    P R I O R I T Y

1	2	3	4
MULtiplier	DIVisor	ADDer	SUBtracter

There are times when various data are mixed in use, when several
sets of data with different reference points of datum are merged
and/or when it is desired to output in different unit systems, then
it can be highly advantageous to invoke the data converting/modifying
commands, namely, MULtiplier, DIVisor, ADDer and SUBtracter.
For example, raw data base of different unit systems for section
properties, material properties and so on are mixed in use. This is
a powerful capability to handle various data from verious sources and
also to convert competitors' data for checking by CAESETS.

2-1) MULtiplier

MULtiplier 6	xxxx	xxxx	xxxx	xxxx	xxxx	xxxx
MUL 6	xxxx	xxxx	xxxx	xxxx	xxxx	xxxx
MUL 4	xxxx	xxxx	xxxx	xxxx	xxxx	xxxx
MULtiplier 0	xxxx	xxxx	xxxx	xxxx	xxxx	xxxx
MULtiplier ON	xxxx	xxxx	xxxx	xxxx	xxxx	xxxx

MULtiplier OFF : The capability is disabled. (Values asigned to VARIABLES retained for future use.)

MUL N xxxx xxxx xxxx xxxx xxxx xxxx,

Where N is 6, 4, 0 or ON for enabling and OFF for disabling.

When N is 6, it is to scan 6 operators, = ** * / + _.
When N is 4, it is to scan 4 operators, = ** * /.
When N is 0, it is to scan 0 operator; namely all xxxx....
must be simple numerical constants if any.
When N is ON, it is to default value for ON, currently 0.

Where xxxx xxxx .... .... are input data items as multipliers.
Number of multiplier items between 0 to 40.

Zero (0.) multiplier will not perform any operation.
If a multiplier item is NOT input, it defaults to 0.
Each NONE ZERO (not 0.) multiplier as an item is to modify the
corresponding item of the raw data of input file respectively.

A non-zero input data is retained as a simple numerical constant after ALGebraic operations. After MUL OFF, it will NOT be wiped out and just be inactive. Under Article 3, it can become active again when MULtiplier Command that is ENABLING is invoked IMPLICITLY.
However, an EXPLICITLY input MULtiplier Command that is ENABLING (not MUL OFF Command) will clear all existing numerical constants with 0. and start a new set of its own data items if any.

Note: The above four commands are independent from one among another.
Each can only be applied to all original raw data in input file but not to data of these four input lines themselves.

2-1-1) Taking from the SECT.DAT file for illustration, For example:

	ITEM 1	ITEM 2	ITEM 3	ITEM 4
MUL 6	0.	Y=2.**2+2.**3_2.*2.	Y*4.**2/Y**2	1.

The line above shows 4 multiplier items.

2-1-1-1) The 1ST item is a 0., which indicates NOT to modify EACH and
EVERY 1ST corresponding ITEM of the raw data of the SECT.DAT File
as shown below. In this case, the data item is an input data of
NOT numerical number but of characters, namely, STELW36X230.

$ SECT.DAT FILE
$ SECTION PROPERTIES OF MEMBERS

$	ITEM 1	ITEM 2	ITEM 3	ITEM 4	ITEM 5	ITEM 6	ITEM 7
$	ID NAME	AREA	IY	IZ	J	DY	DZ
MUL 6	0.	Y=2.**2+2.**3_2.*2.	Y*4.**2/Y**2	1.
ALG 6
	STELW36X230	67.6	9.4*10.	15.*10.**3	28.6	35.9	16.47
	...
	...
	ALG OFF
	MUL OFF
	END DATA

2-1-1-2) The 2ND item is Y=2.**2+2.**3_2.*2., which is an ALGebraic
expression data item evaluated as (Y=2.)**2+2.**3_2.*2. to be 8..
As a multiplier to its corresponding 2ND item 67.6 is to give:

67.6 times 8 equaling 540.8.

2-1-1-3) The 3RD item is Y*4.**2/Y**2, which is an ALGebraic
expression data item evaluated with Y predefined as 2. to be 8. too.
As a multiplier to its corresponding 2ND item 9.4*10. is to give:

firstly, "ALG 6" operating on 9.4*10. to yield 940.,
secondly, 8. as multiplier to 940. resulting in 7520.

2-1-1-4) The 4TH item is 1. as a multiplier,
"ALG 6" operating on 15.*10.**3 gives 15.*1000., namely 15000.

2-1-1-5) Remaining Unmodified Items:
Items 5 through 7 are unmodified since MUL 6 Command has only 4
items. The trailing items must be 0. by default.

The file above after the operation is equivalent to the one below.

$ SECT.DAT FILE
$ SECTION PROPERTIES OF MEMBERS

$	ITEM 1	ITEM 2	ITEM 3	ITEM 4	ITEM 5	ITEM 6	ITEM 7
$	ID NAME	AREA	IY	IZ	J	DY	DZ
	STELW36X230	540.8	7520.	15000.	28.6	35.9	16.47
	...
	...
	END DATA

2-1-2) Practical Situations

2-1-2-1) METRIC SYSTEM Computation Using a British DATA BASE
2-1-2-1-1) STRAIGHT DATA BASE
2-1-2-1-1-1) EXAMPLE NO. 1: SECT.DAT IN BRITISH SYSTEM

$ SECT.DAT FILE
$ SECTION PROPERTIES OF MEMBERS
$ Unit is inch.

$	ITEM 1	ITEM 2	ITEM 3	ITEM 4	ITEM 5	ITEM 6	ITEM 7
$	ID NAME	AREA	IY	IZ	J	DY	DZ
MUL 6	0.	Y=2.54**2	Y**4	Y**4	Y**4	Y	Y
	STELW36X230	67.6	940.0	15000.	28.6	35.9	16.47
	...
	...
MUL OFF
END DATA

In computation for S I System, the above British System File is
used and equivalent to the S I File below.

$ SECT.DAT FILE
$ SECTION PROPERTIES OF MEMBERS
$ Unit is centimeter

$	ITEM 1	ITEM 2	ITEM 3	ITEM 4	ITEM 5	ITEM 6	ITEM 7
$	ID NAME	AREA	IY	IZ	J	DY	DZ
	STELW36X230	436.13	39125.8	624347.1	1190.4	91.19	41.83
	...
	...
	END DATA

2-1-2-1-1-2) EXAMPLE NO. 2: MAT.DAT IN BRITISH SYSTEM

$ MAT.DATA FILE

$ METRIC COMPUTATION USING MATERIAL PROPERTY FILE IN BRITISH SYSTEM

$ I D	E	G	ALPHA	RHO	FY	FU
$ NAME	K/In**2	K/In**2	In/In/Deg_F	K/In**3	K/In**2	K/In**2
$ NAME	T/Cm**2	T/Cm**2	Cm/Cm/Deg_C	T/Cm**3	T/Cm**2	T/Cm**2
MUL 4	K=0.454	I=2.54
MUL OFF
MUL 4 0	K/I**2	K/I**2	1.8	K/I**3	K/I**2	K/I**2
STEL	29000.	11200.	0.0000065	0.000283565	36.0	60.0
MAT2	29000.	11200.	0.0000065	0.000000000
STELWT9X38	29000.	11200.	0.0000065	0.000283565
STELPIPE2	29000.	11200.	0.0000065	0.000000000
STELPIPE6	29000.	11200.	0.0000065	0.000283565
ALUMGIRDER	10000.	3850.	0.0000128	0.000095486
CNC8COLUMN	3620.	1360.	0.0000055	0.000086806

$ FOR PLOT: NO NON-LINEAR ALLOW BELOW; FOR USP: O K

NLINmateri	10000.	3750.	0.0000128	0.0000
MUL OFF
MUL 4 0	0 K/I**2	0 K/I**2	0 K/I**2
NONLcontin	0.002 20.	0.0044 24.	0.010 26.77	$ (Epsilon Sigma)Pair
NONLcontin	0.020 30.65			$ (Epsilon Sigma)Pair
MUL OFF

$ MATERIAL NON-LINEARITY PROPERTY NEXT ABOVE

$ FOR PLOT: NO NON-LINEAR ALLOW ABOVE; FOR USP: O K

END DATA

END DATA

2-1-2-1-2) MIXED DATA BASE
METRIC COMPUTATION WITH MAT.DAT PARTLY IN BRITISH SYSTEM and PARTLY IN METRIC SYSTEM

$ MAT.DATA FILE

$ METRIC COMPUTATION USING MATERIAL PROPERTY FILE IN MIXED SYSTEMS

$ I D	E	G	ALPHA	RHO	FY	FU
$ NAME	K/In**2	K/In**2	In/In/Deg_F	K/In**3	K/In**2	K/In**2
$ NAME	T/Cm**2	T/Cm**2	Cm/Cm/Deg_C	T/Cm**3	T/Cm**2	T/Cm**2
MUL 4	K=0.454	I=2.54
MUL OFF
MUL 4 0	K/I**2	K/I**2	1.8	K/I**3	K/I**2	K/I**2
STEL	29000.	11200.	0.0000065	0.000283565	36.0	60.0
MAT2	29000.	11200.	0.0000065	0.000000000
STELWT9X38	29000.	11200.	0.0000065	0.000283565
STELPIPE2	29000.	11200.	0.0000065	0.000000000
STELPIPE6	29000.	11200.	0.0000065	0.000283565
ALUMGIRDER	10000.	3850.	0.0000128	0.000095486
CNC8COLUMN	3620.	1360.	0.0000055	0.000086806

$ FOR PLOT: NO NON-LINEAR ALLOW BELOW; FOR USP: O K

MUL OFF

NLINmateri	705.	265.	0.0000230	0.0000
NONLcontin	0.002 1.41	0.0044 1.692	0.010 1.887	$ (Epsilon Sigma)Pair
NONLcontin	0.020 2.161			$ (Epsilon Sigma)Pair

$ MATERIAL NON-LINEARITY PROPERTY NEXT ABOVE

$ FOR PLOT: NO NON-LINEAR ALLOW ABOVE; FOR USP: O K

END DATA

END DATA

2-2) DIVisor The same logic as that of multiplier is applied.
2-3) ADDer The same logic as that of multiplier is applied.
2-4) SUBtracter The same logic as that of multiplier is applied.