ARMA 2D
Version 3.0
Author: German Flores Jarquín
USER'S MANUAL
All the images shown in this manual were taken from a TI-92 Plus. For the TI-89 the visualization should vary.
First of all my apologies of my bad english (I speak spanish), but I hope you understand everything in this manual.
This manual contains the following sections:
- Supports
CopyRight and Warranty
All the subroutines included in the group of programs Arma2d are intellectual property of German Flores Jarquin.
Arma2d is protected against writing using prot92p by C Prgm Software; it can be found in www.ticalc.org, DOS section.
The program Arma2d can be distributed waiting hopefully that it will be useful for those people that use it; especially for the students of Analysis of Structures and subjects related with the career of Civil Engineering.
This version of Arma2d is totally free and it can be used as much as it is wanted, whenever it is for personal and not commercial use. The modification of the program in total or partial form is prohibited.
The author provides this program "as it is", without guarantee of any type, included commercial guarantees of any case in particular. The author will not even take responsibility for any material damage caused by the wrong handling of this program.
This program was conceived mainly with educational ends, for what doesn't offer guarantee of its use in the professional field.
Instalation
Just send the file arma2d.9xg (or arma2d.89g) to your calculator making sure of check the retain folder box in the TI Graph Link Software.
You have to make sure that the files: arma2d, ayuda, backs, cargas, conect, editar, esf, grafanim, grafdesp, grafica, lcar1, lcar2, lcar3, lcar4, leemat, nodos, resor1, resort, rigeb and tria are kept in a folder called ARMA2D.
The program uses approximately 32K of RAM.
Description
Arma2d is a program that can be used in the Texas Instruments graphing calculators TI-89, TI-92 Plus and Voyage 200 (I think). This program was created for the structural analysis of two dimensional trusses.
Arma2d can calculate nodal displacements, axial forces, elements stresses and support reactions of any truss type, whenever it is statically determinated or indeterminated; using matrix methods. The only limit for this program is the amount of RAM available in the calculator.
Arma2d was designed in such way that the necessary steps are continued for the analysis in a sequential form but in the simplest way possible, giving the user the opportunity to correct errors after each step and before carrying out the calculations.
Among other characteristics, Arma2d allows to plot the following graphics: geometry of the structure, structure loaded (under punctual external forces), displaced structure and displacements animation. Before beginning the calculations you can review the introduced data and if you want, you can do the convenient changes if there was an error. Once carried out the calculations it is possible to see the matrixes used by the program in the analysis.
Arma2d is written completely in TI-Basic, due to the advantages that it gives for variable dimensions matrixes; this of course in sacrifice of the speed.
History
Beta version, November 2001 (Just personal use, spanish)
-Only punctual forces as load condition
-Extremately slow
-Lots of errors
Version 1.0, March 2002 (First public release, spanish)
-Only punctual forces as load condition.
-A little speed up.
-Some bugs corrected.
Versión 2.0, April 2002 (spanish)
-The analysis for forced displacements is included.
-Code improvement.
-Speed improvement.
-Graph of the truss under punctual forces conditions.
-Allows to see the main matrixes used in the analysis
-Allows to kept the matrixes to use them outside the program.
Version 3.0, Augost 2002 (spanish), October 2002 (english)
-Allows the analysis for different load combinations, including: punctual forces,
Forced displacements, Changes of temperature and incorrect dimensions of elements.
-Exhaustive improvement of the code (I believe that better impossible).
-Improvement of speed when calculating displacements through LU function (Thanks to Scott Pollock).
-Displacements graph.
-Animation of the truss subjected to the loads.
-New routine that allows to edit introduced data before carrying out the analysis.
Coordinates System
The program Arma2d uses the system of coordinates in the XY plane where X is the horizontal direction and Y is the vertical direction.
It is important that all the truss is defined completely in the first quadrant, that means that has positive coordinates. To introduce negative coordinates won't produce erroneous results but it will cause problems with the graphs because the routine to graph the truss considers that all the coordinates should be positive.
Next is the convention of signs presented in the positive sense, considered by the program:
Units System
This program doesn't regulate the use of some units system in particular, this means that you can use any unit. Therefore, it is necessary to have caution in the units to use to obtain consistent results.
Next are some examples of the most used units systems:
| Force | Longitud | Stress |
| N | m | N/m2 |
| kN | m | kN/m2 |
| Kg | cm | Kg/cm2 |
| Kips | inch | Kips/in2 |
| Kips | foot | Kips/ft2 |
Beginning
It is very important that is counted with a draw labeling elements before beginning to run the program: nodes, supports, etc. This will facilitate the agility in the introduction of the data and it will also avoid many errors.
To run the program it should be written in the input line of the Home Screen, arma2d\arma2d (), or you can call the program from the menu of the VAR-LINK. It is also advisable to create a small program for quick launching by means of abbreviated keys, if you don't know how, consult the calculator's manual.
When beginning, a message will always be presented remembering that this is a free software. Next the main screen is presented and it should look this way:
Inicially you will see three options in the menu bar:
New: Start to introduce data for a new truss.
Help: Divided in Help: a little help file about the considerations taken by the program; and About...: an information message about the program and the author.
Exit: Exits the program.
In general form, after it has been introduced the data in each step, the program will show them so that you can check them and it will ask if you want to do any change. In case your answer is no, you will continue normally; but in case your answer is yes, then, you will have the opportunity of correct any error.
This program doesn't carry out tests of confirmation of any error of the inputed data, since it would mean a considerable increase of code, if in some case mistaken data were introduced, as for example geometries impossible to build, the most probable thing is that inconsistents results are obtained or inclusive to cause the program to "crash", in this case it is advisable to erase all the variables that were stored in the ARMA2D directory before running the program again. The best tool to check errors is visualizing the graph and revising the input data in the edit option.
Data Input
General Data
Once you've selected new in the main menu, you will be asked to input the number of nodes and the number of elements of the truss, as shown in the picture:
After you input the number af nodes and elements, arma2d will start to call the routines to introduce the truss characteristics.
Nodes Coordinates
For every node you'll have to input its coordinates in the XY plane. It is important to remember that all coordinates should be positives.
Elements Conections
For every element you'll have to input its initial node and its final node. The introduction order won't change the results, for example: initial node 1 and final node 2, will be the same thing as initial node 2 and final node 1.
Supports
First you will be ask to input the number of nodes in which there are any kind of supports.
Next for each one of the nodes that has supports, the program will ask to indicate in what node is the support, as well as the codes corresponding to the reaction in the X direction and to the reaction in the Y direction.
The codes are the following:
1 = fixed (it means that there is a reaction).
0 = free (it means that there is no reaction but a free movement or displacement).
Above are shown the three posibilities of upports:
Articulated
Support:
X Code
= 1
Y Code = 1
Vertical Roller Support: X
Code = 0
Y Code = 1
Horizontal Roller Support:
X Code
= 1
Y Code = 0
Section Properties
Inicially the program will ask for the number of different sections among the elements of the truss.
For example, if the truss has constant areas and elasticities among its elements or if the structure is statically determinted, then, the section will be unique.
Next, for each section, the program will ask the magnitude of the area and elasticity. If the magnitudes of both are constants on all elements or if its values are not given in the problem (EA=constant), then you can input area=1 and elasticity=1 as their representative values. However, if this is the case it is important to remember that the displacements shown in the results are not the real ones, but, each one has to be divided by the constat EA.
After you input the section area and the elasticity; te program will ask the number of elements with that section. If there is only one section, then, the number of elements will be displayed automatically and logically it will be the total number of elements of the structure.
Once you've input the number of elements with a section, the program will ask to enumerate in brackets [] and separated by a comma, each one of the elements that posses this section. As in the previos step, if there is only one section, then, the total number of elements will be displayed atomatically to speed up the data input.
Loads Conditions
Once you've input all the necessary data to determine the geometry of the structure, the program continues with the load condititions.
Arma2d allows the user to introduce any possible combination of loads among four possibilities: Punctual forces, Forced displacements, Temperature changes and Incorrect dimensions. This means that a single truss can be subjected to one, two, three or the four kind of loads at the same time.
After you input the loads conditions of your structure, you must select DONE in the menu, as is shown in the next picture:
Punctual Forces
Once you've selected this option the program will ask the number of nodes with punctual forces on them.
Next for each node, the program will ask which node is subjected to punctual forces and the magnitude of the force in the X direction and in the Y direction. If the force acting on the node is inclinated, then, it must be decompose in a horizontal force and in a vertical force as mentioned previosly. In the same way if a distributed load exists, then, it must be transformed to its nodal punctual force equivalent.
Forced Displacements
Initially the program will ask the number of nodes with forced displacements, which should be of course, nodes with supports on them.
For each node with a displacement, the program will ask the number of the node, the magnitude of the displacement in the X direction and in the Y direction. Nodes can only have displacements in the same direction of a reaction.
Temperature Changes
The first thing to do is to input the number of elements that are subjected to any temperature change.
Then, for each element subjected to a change, you must identify this element, input the thermal dilation coefficient (linear) of the material and the magnitude of the change in the temperature. If the sign of the change is (+) positive, then, it is considered as an increase of temperature, but if the change is (-) negative, then, it is considered as a decrease of temperature.
Incorrect Members Dimensions
If you selected this option, then, the program will ask the number of elements with any incorrect dimension (also known as misfits or fabrication errors).
Next for each member with an incorrect dimension, you must input the number of the element and the magnitude of the error in the dimension. If the error is introduced (+) positive, then, the element is considered larger, but, if the error is intruduced (-) negative the element is considered shorter.
Truss Analysis
Once you have selected DONE! in the menu of loads combinations, the program will display another menu as shown below:
Graph
Shows the truss graph. In case that it is subjected to punctual loads, the program also shows the directions of them. This option is useful if you want to check the correct introduction of data.
Run
With this option the program will start the necessary calculations. Meanwhile, a screen showing the analysis progress is displayed, when a step is already done, a "check mark" will be displayed.
Edit
This is a new option that will allow the user to return to a specific part of the introduction of the data to carry out some change and to correct possible errors. It is very important to know that when selecting to return to some step, the current data will be displayed and te program will ask if you want to make a change; in case your answer is affirmative, you'll have to change all the data corresponding to that step. For example if you select to change the Coordinates, then, you will have to input the coordinates for each one of the nodes in the truss over again.
To go back to the analysis screen, you must select RETURN.
New
It lets you return to the main screen.
Viewing the Results
Once the analysis is finished, the program will display a message. Then the results screen will be displayed, as follows:
Results
This option lets you view the results as tables. The program results are: Nodal displacements, Supports reactions, Elements forces and stresses.
As I've mentioned before, the displacements and rections are positive in UP and RIGHT direction. And for Elements Axial Forces, positive (+) means Tension and negative (-) means compression.
Graph
Geometry: Lets you visualize the truss geometry
Displacements: Lets you visualize the displaced truss.
Animation: Lets you visualize the truss movement once it is subjected to the loads conditions (or at least give you an idea of it). It is necessary to graph the truss geometry and displacements to this option to be available.
Matrixes
It lets you visualize all the matrixes used by the program. You can view the elements matrixes and the main matrix divided in its four principal parts.
Exit
When selecting this option, the program will ask if you want to kept the matrixes in the RAM to be used outside of the program; if your answer is yes, then the main matrixes will be kept in memory, but you should remember that they must be erased manually since they occupy space in the memory; in case the answer is not, then, the progran will delete all the variables, a general message will be shown and the program will return to the main screen.
Recommendations
Greetings
Author
German Josué Flores Jarquín
National University of Engineering (UNI)
Managua, Nicaragua
2002
http://www.geocities.com/ingenieria8992 (this is my web page but in spanish only)
If you find useful this program, I would like to thank you to let it me know and that you gave me an opinion of it.
If you have some comments, recommendations,
ideas, or you simply want to report
an error or you need help, you can
contact me to any of the following emails:
german_josue_flores_jarquin@hotmail.com