iemisc: secprop Example (R and GNU Octave)
In iemisc: Irucka Embry's Miscellaneous Functions

\bigskip

secprop Example (R style)

Example 1 (Caprani Reference)

library("iemisc")
import::from(ramify, mat)

vo <- mat("0, 0; 600, 0; 630, 580; 1200, 650; 1200, 920; 900, 920; 900, 845; 0, 845")
vo

vi <- mat("0, 300; 300, 300; 300, 695; 0, 695")
vi

# The following will plot both the original and the final (transformed plot)
SP <- secprop(outer = vo, inner = vi, original_plot = 1, final_plot = 1)
SP

\bigskip \bigskip \bigskip \bigskip

secprop Example (GNU Octave style)

```{octave eval = FALSE} % % Copyright (C) 2008 Colin Caprani - www.colincaprani.com % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see http://www.gnu.org/licenses/.

function SP = secprop(outer,inner,plotflag) % Section Properties Calculator % outer is a matrix of outer coordinates (x,y) % inner is a matrix of coordinates for a void % SP is a vector of A,I,yt and yb properties of the section

[nOC n] = size(outer); [nIC n] = size(inner);
outer(nOC+1,:) = outer(1,:);
inner(nIC+1,:) = inner(1,:);

propsOC = zeros(1,3); propsIC = propsOC;
propsOC = algor(outer);
if(nIC > 2); propsIC = algor(inner); end;
A = propsOC(1) - propsIC(1);
I = propsOC(2) - propsIC(2);
ybar = propsOC(3) - propsIC(3);

ybar = ybar/A;
I = I-A*ybar^2;   
A = 2*A; I = 2*I;
yt = max(outer(:,2)) - ybar;
yb = ybar;
SP = [A,I,yt,yb]; SP = SP';

if plotflag == 1
    outer(nOC+1:2*nOC-1,1) = -outer(nOC:-1:2,1);
    outer(nOC+1:2*nOC-1,2) =  outer(nOC:-1:2,2);
    inner(nIC+1:2*nIC-1,1) = -inner(nIC:-1:2,1);
    inner(nIC+1:2*nIC-1,2) =  inner(nIC:-1:2,2);
    h = fill(outer(:,1),outer(:,2),'r'); hold on;
    fill(inner(:,1),inner(:,2),'w'); axis equal;

    s1 = sprintf('Area = %d mm2 | Height to N-A = %3.1f mm',A,round(ybar*10)/10);
    s2 = sprintf('Second Moment of Area = %d mm4',I);
    s3 = sprintf('Elastic Moduli, t = %d mm3; b = %d mm3',I/yt,I/yb);
    annotation1 = annotation('textbox',[0.15 0.12 0.4 0.14],
    {s1,s2,s3});

% annotation1 line modified by Irucka Embry to avoid the error message associated with % set: unknown hggroup property FitHeightToText end end

function props = algor(vc) A = 0; ybar = 0; I = 0; x = vc(:,1); y = vc(:,2); n = length(x); for i = 1:(n-1) A = A + 0.5(x(i)-x(i+1))(y(i)+y(i+1)); ybar = ybar + (1/6)(x(i)-x(i+1))(y(i)^2 + y(i)y(i+1) + y(i+1)^2); I = I + (1/12)(x(i)-x(i+1))(y(i)^3 + y(i)^2y(i+1)+y(i)*y(i+1)^2 + y(i+1)^3); end props = [A,I,ybar]; end

% check against GNU Octave

vo = [0, 0; 600, 0; 630, 580; 1200, 650; 1200, 920; 900, 920; 900, 845; 0, 845]; vi = [0, 300; 300, 300; 300, 695; 0, 695]; SP = secprop(vo, vi, 1)

print("file.png")

% Results warning: annotation: couldn't parse PROP/VAL pairs, skipp warning: called from annotation at line 218 column 7 secprop at line 36 column 21

SP =

1.1175e+06 8.6279e+10 4.1937e+02 5.0063e+02

\bigskip
\bigskip

```r
linguisticsdown::include_graphics2("secprop_gnu-octave_figure.png")

\bigskip \bigskip \bigskip \bigskip

Works Cited

Colin Caprani, "Section Properties Calculator", https://www.colincaprani.com/programming/matlab/.

\bigskip \bigskip

EcoC²S Links

EcoC²S Home -- https://www.ecoccs.com/
About EcoC²S -- https://www.ecoccs.com/about_ecoc2s.html
Services -- https://www.ecoccs.com/services.html
1 Stop Shop -- https://www.ecoccs.com/other_biz.html
Products -- https://www.questionuniverse.com/products.html
Media -- https://www.ecoccs.com/media.html
Resources -- https://www.ecoccs.com/resources.html
R Trainings and Resources provided by EcoC²S (Irucka Embry, E.I.T.) -- https://www.ecoccs.com/rtraining.html

\bigskip \bigskip

Copyright and License

All R code written by Irucka Embry is distributed under the GPL-3 (or later) license, see the GNU General Public License {GPL} page.

All written content originally created by Irucka Embry is copyrighted under the Creative Commons Attribution-ShareAlike 4.0 International License. All other written content retains the copyright of the original author(s).

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.