<content> <p>Equations with symbolic substitutions</p> </content>

bba46783-e94a-4e5e-8b9d-3b0ef7353de7 44 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

The \[REGION[7fbe9f218b5a4741b04a34b217cdb4f9]]\ equations serve the purpose of displaying a numeric value symbolicly WITHOUT fractions, and to desired units. Supports Multiple input Parameters as shown:

# var_expand

_var_unit_showVar_placeholder var_expand // Author: Kenny Lemens, P.E. ᵂᴵ   Date: 2024-05-31 // Parses param ((2)) to determine number of decimal digits to include in results digit 0_unit . findstr 1 - ≡_unit . strsplit 2 el strlen_unit' findstr 1 - ≡_unit' strsplit 1 el * strrep \ strrep . strsplit 2 el strlen cases cases : // Parses param ((2)) to determin the desired unit to display results in (MUST be a string, else SMath WILL simplyl fo base units....) rawUnit 1_unit' findstr 1 - ≡'_unit' strsplit 2 el concat cases : // Release Param ((1)) from Absolute Variable to local variable to retrieve actual value varValue_var num2str ~ strrep str2num eval : // Returns decimal values as SYMBOLIC values, with the units and decimal places calculated above.  if param ((3)) = True; will include the name of the variable  in the system of equations_var num2str *'꞊꞊ concat str2num varValue rawUnit str2num 10 digit -^* / 0 round 10 digit -^* digit var2str 110 / var2str 21 substr ․ strrep ﻿ concat str2num * rawUnit''﻿ strrep str2num * ﻿_showVar varValue rawUnit str2num 10 digit -^* / 0 round 10 digit -^* digit var2str 110 / var2str 21 substr ․ strrep ﻿ concat str2num rawUnit''﻿ strrep str2num * ﻿ cases 91 line :

_var_unit_showVar var_expand help Exands a given Variable into a Symbolic Format, custom unit and supports decimal places_var [Absolute Variable] Used as a symbolic placeholder; to be converted to the locally defined variable of simliar name (~b --> b)_unit [STRING] If Unitless, whold number,  if unitless and to the nearest ten-thousandths (  if  to the 2 digits, etc.) 
- NOTE: function will only consider adding additional decimal places (e.g., 0.99*'in will only result in consideration of 2-digits, identical to 0.00*'in)_showVar 1 if True, 0 if False Default: 0 (False); will not show _var name as the assignment to the variable value at hand 33 mat Source: Custom Equation (displayEquations.sm), Written by Kenny Lemens 31 mat :_var_unit_showVar 0 var_expand 21 line :

_var_unit var_expand help Exands a given Variable into a Symbolic Format, custom unit and supports decimal places_var [Absolute Variable] Used as a symbolic placeholder; to be converted to the locally defined variable of simliar name (~b --> b)_unit [STRING] If Unitless, whold number,  if unitless and to the nearest ten-thousandths (  if  to the 2 digits, etc.) 
- NOTE: function will only consider adding additional decimal places (e.g., 0.99*'in will only result in consideration of 2-digits, identical to 0.00*'in) 23 mat Source: Custom Equation (displayEquations.sm), Written by Kenny Lemens 31 mat :_var_unit 00 var_expand 21 line :

_var var_expand help Exands a given Variable into a Symbolic Format, default unit, as a whole number_var [Absolute Variable] Used as a symbolic placeholder; to be converted to the locally defined variable of simliar name (~b --> b) 13 mat Source: Custom Equation (displayEquations.sm), Written by Kenny Lemens 31 mat :_var_var num2str ~ strrep str2num UnitsOf num2str 00 var_expand 21 line :

The \[REGION[7fbe9f218b5a4741b04a34b217cdb4f9]]\ equations serve the purpose of displayig an equation with some variables substituted with their current contents. Supports Multiple input Parameters as shown:

# # # Equ

_equName_equation_mat_resultUnit_placeholder Equ // Author: Kenny Lemens, P.E. ᵂᴵ   Date: 2024-05-31 // LastEquResult will be declared a as a GLOBAL Variable, all other variables will be treated as local. LastEquResult_equation : tmpAssignVal_equation : // For each item in param ((3), generate formatting to be used for each variable і 1 : і_mat rows ≤ і і 1 + : tmpVar_mat і 1 el : tmpUnit_mat і 2 el : // Replace Variable with LastEquResult LastEquResult num2str tmpVar num2str * tmpVar var_expand num2str concat_mat і 2 el strtoupper SKIM ≡ tmpVar num2str_mat і 2 el strtoupper SKIP ≡ * tmpVar tmpUnit 1 var_expand num2str concat cases strrep str2num : //Release variable to evaluate numerically, apply to Numeric Container tmpAssignVal tmpAssignVal num2str tmpVar num2str tmpVar num2str ~ strrep strrep str2num : 61 line Do Nothing... try for //Final numeric Evaluation, removes symbolic grouping (i.e., undefined 'unit' function of no-name) to allow complege evalaution; Assign as Global Variable!_equName : tmpAssignVal num2str'' strrep'﻿ strrep concat str2num // Clear temp variables out, else they will remain as Global Variables! tmpAssignVal tmpVar tmpUnit і Clear // Construct final symbolic value to return;  will display vairable, the defined equation, and the equation with inline substitutions ﻿_equName *'꞉⚌*'﻿(_equation num2str)*'⚌('﻿(LastEquResult num2str))*'⚌(﻿ ~_equName concat var_expand (num2str concat str2num_resultUnit strtoupper SKIM ≡ ﻿_equName *'꞉⚌*'﻿(_equation num2str)*'⚌('﻿(LastEquResult num2str)) concat str2num_resultUnit strtoupper SKIP ≡ ﻿_equName *'꞉⚌*'﻿(_equation num2str)*'⚌('﻿(LastEquResult num2str))*'⚌(﻿ ~_equName concat_resultUnit var_expand (num2str concat str2num cases 121 line + :

_equName_equation_mat_resultUnit Equ_tmpReturnVal_equName_equation_mat_resultUnit 0 Equ : help Equ(_equName,_equation,_mat,_resultUnit)   - Exands a given Variable into a Symbolic Format, custom unit and supports decimal places_equName [STRING] Name of the variable that will contain the FINAL evaluated numeric value;_equation [math] Target equation; actual variables replaced with Absolute Variables equivalent._mat [ ~▮ , "▮" ] Variables to be subsituted out:
 - 1) Varaibles to be declared as 'absolute', will be evaluated as a local variable equivalent for numeric eval
 - 2) STRING,  to report unit in terms of units and decimal places  (e.g., 0.99*'in will only result in consideration of 2-digits, identical to 0.00*'in)
        a) keyword 'SKIM' to just report variable in base units w/ zero decimal places; 'SKIP'  to leave variable in place._resultUnit [STRING] STRING,  to report unit in terms of units and decimal places  (e.g., 0.99*'in will only result in consideration of 2-digits, identical to 0.00*'in)
        a) keyword 'SKIM' to just report variable in base units w/ zero decimal places; 'SKIP'  to leave variable in place. 43 mat Source: Custom Equation (displayEquations.sm), Written by Kenny Lemens 31 mat :_tmpReturnVal 31 line + :

_equName_equation_mat Equ tmpReturnVal_equName_equation_mat SKIP 0 Equ : help Equ(_equName,_equation,_mat)   - Exands a given Variable into a Symbolic Format, custom unit and supports decimal places_equName [STRING] Name of the variable that will contain the FINAL evaluated numeric value;_equation [math] Target equation; actual variables replaced with Absolute Variables equivalent._mat [ ~▮ , "▮" ] Variables to be subsituted out:
 - 1) Varaibles to be declared as 'absolute', will be evaluated as a local variable equivalent for numeric eval
 - 2) STRING,  to report unit in terms of units and decimal places  (e.g., 0.99*'in will only result in consideration of 2-digits, identical to 0.00*'in)
        a) keyword 'SKIM' to just report variable in base units w/ zero decimal places; 'SKIP'  to leave variable in place. 33 mat Source: Custom Equation (displayEquations.sm), Written by Kenny Lemens 31 mat : tmpReturnVal 31 line + :

The \[REGION[83e3dd0f94dd4ecc9a79219f2065fc1d]]\ equations serve the purpose of displayig an equation with some variables substituted with their current contents. Supports Multiple input Parameters as shown:

NOTE:
- Some functions will get 'disolved' through symbolic evaluation, such as \[REGION[1116619da36549bba6a43c818df3d528]]\ which will report in terms of its definition: \[REGION[7f5ff2a13bda478ba7d56ab6f435c442]]\.
- There are also some limits to multiple units ('lbf * 'in will not work, but a custom 'lbf·in will work).
- The user should evaluate symoblic, and then right-click and unchkeck "Display input data" to hide inputs
- If variable is not being defined at the end, verify that said variable it is not being defined to a bad value within the Equation itself.
- These functions work on the assumption the absolute variables in the equations are not defined! if they are defined, those variables will be substitued in directly and botch the whole premise of this exercise.

Param (1): as STRING Target Variable for assignment; this would be the variable that will contain the evaluated numeric value;
- In order for the math to work, the corresponding variables to the absolute SHOULD BE DEFINED! (e.g,. if \[REGION[a079caec4539403296d833dbdbb67c84]]\ is referenced, \[REGION[43ce00e8ad854b379f071ea330c5a9b8]]\ must be declared.);
Param (2): as math,
- variables to be subsituted to be prefixed with \[REGION[774c46af005649fea937878e79815dd2]]\; varaibles to be declared as 'absolute', will be evaluated as a local variable for numeric eval
- \[REGION[4a53ceed5e65444981e6e5137a8e52a2]]\ this funciton (\[REGION[c4416bbe31614258835630ee81b811e2]]\) will keep terms grouped for symbolic; advanced users can use special code \[REGION[0f574f8841d547f4926902dbcbf9ac7a]]\ for a seamless grouping
Param (3): as a matrix of terms to subtitue; first column 'absolute' variables, the second column to be the terms to report as:
- \[REGION[72eeaf1fd69f4655a1e833583d251412]]\ to leave the variable as is
- \[REGION[6b9edf413ea242518291958814e2e13f]]\ to evaluate the variable and report in terms of base units
- \[REGION[565362edd426411189fdfaea779080d7]]\ if Unitless, whold number, \[REGION[021f3985ef544db1b1132de443960ea0]]\ if unitless and to the nearest ten-thousandths ( \[REGION[65570b5cc05847c48578d362919312d8]]\ if \[REGION[1188c98f31254b30a32b44cf3720998e]]\ to the 2 digits, etc.)
- NOTE: function will only consider adding additional decimal places (e.g., 0.99*'in will only result in consideration of 2-digits, identical to 0.00*'in)

# # # Equ

# # # lele

~1 ~2 ~3 lele ~2 ~1 ≤ (~1 ~3 ≤ (&

~a

a # ≡

~

#'

''(#)

# \005C\FEFF\005C\

SKIP

SKIM

1

0.01

0.01*'mm

mm

EXAMPLES:

a 200.22 mm * :

Variable \[REGION[df0fe955dc8842bfad221a223d156675]]\ is defined, so pass absoluteVariable as \[REGION[ed819f32e2cb4c3a8ab5a791f65e7cfa]]\ (i.e., prefilx variable with ~); and symbolic Evaluate:

a

~a

~a var_expand 0﻿ ﻿m * ﻿

Base unit, whole Number

~a 0.00*'cm var_expand 20․02﻿ ﻿cm * ﻿

Value is parsed to 2 Digits, for centimeters

~a 0.0000*'m 1 var_expand ~a ꞊꞊ * 0․2002﻿ * ﻿m * ﻿

4 Decimal Places for Meters, display variable in result

Define variables (Normal SMath):

Symbolic Evaluation:

a 22 mm * :

c 1.23 m * :

d 20 :

Call Equation, type equation in terms of AbsoluteVariables (~)

b ~a ~c + ~d / ~c 0.1*'in ~a 2.000*'ft ~d 0.0000 32 mat Equ ﻿b ꞉⚌ * ~a ~c + ~d / ﻿ * ~a ꞊꞊ * 0․072﻿ * ﻿ft * ﻿ ~c ꞊꞊ * 48․4﻿ * ﻿in * ﻿ + ~d ꞊꞊ * 20․0000﻿ * ﻿ / ﻿ ⚌ *

b 0.06 m *

d 0.2 :

Explore the Use of "SKIM" and "SKIP"

b ~a ~c + ~d / ~c SKIM ~a 1.00*'in ~d SKIP 32 mat Equ ﻿b ꞉⚌ * ~a ~c + ~d / ﻿ * ~a ꞊꞊ * 0․87﻿ * ﻿in * ﻿ 1﻿ ﻿m * ﻿ + ~d / ﻿ ⚌ *

b 6.26 m *

c 2 a * :

b ~a ~c + ~d / ~c 0.1*'in ~a 2.000*'ft ~d 0.0000 32 mat 2.000*'ft Equ ﻿b ꞉⚌ * ~a ~c + ~d / ﻿ * ~a ꞊꞊ * 0․072﻿ * ﻿ft * ﻿ ~c ꞊꞊ * 1․7﻿ * ﻿in * ﻿ + ~d ꞊꞊ * 0․2000﻿ * ﻿ / ﻿ ⚌ * 1․083﻿ ﻿ft * ﻿﻿ ⚌ *

FINALLY: hide inputs

Equation WILL assign the actual variable 'b'

b ~a ~c + ~d / ~c 0.1*'in ~a 2.000*'ft ~d 0.0000 32 mat 2.000*'ft Equ ﻿b ꞉⚌ * ~a ~c + ~d / ﻿ * ~a ꞊꞊ * 0․072﻿ * ﻿ft * ﻿ ~c ꞊꞊ * 1․7﻿ * ﻿in * ﻿ + ~d ꞊꞊ * 0․2000﻿ * ﻿ / ﻿ ⚌ * 1․083﻿ ﻿ft * ﻿﻿ ⚌ *

b 33 m * 100 /

b 0.33 m *

A more advanced equation (uses a dummy function to effectively serve as a "grouping" factor.

Default Symbolic:

Default Numeric:

Use of "Equ()"

abc.12 abc.12

abc.12 ~a abs (2^2 * 12 ~d + / \005C\FEFF\005C\ ~c 2^\FEFF\ + ~c 0.2*'mm ~a 1*'ft ~d SKIP 32 mat Equ ﻿abc.12 ꞉⚌ * 2 ~a abs 2^* 12 ~d + / \FEFF\ ~c 2^﻿ + ﻿ * 2 ~a ꞊꞊ * 0﻿ * ﻿ft * ﻿ abs 2^* 12 ~d + / ﻿ ~c ꞊꞊ * 44․0﻿ * ﻿mm * ﻿ 2^﻿ + ﻿ ⚌ *

abc.12 0 m 2^*

Applied to Section Modulus Calcluations:

L.eff 12 in * :

t 0.125 in * : 0 m *

S.x ~L.eff ~t 2^* 6 / ~L.eff 0.0*'in ~t 0.000*'in 22 mat Equ ﻿S.x ꞉⚌ * ~L.eff ~t 2^* 6 / ﻿ * ~L.eff ꞊꞊ * 12․0﻿ * ﻿in * ﻿ ~t ꞊꞊ * 0․125﻿ * ﻿in * ﻿ 2^* 6 / ﻿ ⚌ *

S.x mm 3^512.1

S.x ~L.eff ~t 2^* 6 / ~L.eff 0.0*'in ~t 0.000*'in 22 mat 0.000*'in^3 Equ ﻿S.x ꞉⚌ * ~L.eff ~t 2^* 6 / ﻿ * ~L.eff ꞊꞊ * 12․0﻿ * ﻿in * ﻿ ~t ꞊꞊ * 0․125﻿ * ﻿in * ﻿ 2^* 6 / ﻿ ⚌ * 0․031﻿ ﻿in 3^* ﻿﻿ ⚌ *

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