Program: Torsion
By: Ben Axelrod

   This program will find the angular displacements and reactions at the support of a 
torsionally loaded beam.  This is the second program of a set of finite element modeling 
programs.  This program is great for classes like Statics, Strength of Materials, any 
Finite Element Modeling class, and other similar engineering classes.  It can even do 
statically indeterminate members.  To use, follow the main menu.  First select materials,
then nodes, then elements, and so on.  Detailed instructions are below.

MATERIALS:
   First enter the number of different materials you have.  A material is anything with a
different cross-section, or sheer modulus.  If you have a member with two materials in 
parallel (like concrete with steel rebar in it,) enter each one individually, as it’s own
material.  This topic will be covered in more detail below.  Then just enter the 
material’s sheer modulus and polar moment of inertia.  It is important to remember the 
numbering of you materials, you will need this information later in the program.

NODES:
   First enter the number of nodes you have.  You should put a node every where you have 
a torque acting on the member, a support, at the ends of the member, or a change in cross
section.  You should not put more than one node at the same location.  Then you will have
to enter the coordinates of each node.  It is important to remember how you numbered your
nodes.

ELEMENTS:
   The program will now ask you how many elements you have between each node.  Most of 
the time this will just be 1.  But in the example above with the concrete with rebar in 
it, you now have two elements between the two nodes.  So enter 2.  Then the program will 
ask for which materials are between the two nodes.  Enter the proper material numbers.  

FORCES:
   First enter the number of forces you have acting on the member.  Then enter at which 
node the force acts, and in what direction.  

CONSTRAINTS:
   First enter the number of constraints you have.  This program can even do statically 
indeterminate members.  Enter the node that the constraint is at and then enter the 
amount that that node can move.  Most of the time this will be 0 for a fixed support.  
But if you have some problem where the end of the member can only move a specified 
amount, enter it there.  

SOLVE:
   Once you have completed all of the steps above, this will solve the problem.  The 
nodal angular displacements are saved in the list ROTAT and the reactions at the supports
are saved in the list REACT.  The angular displacements are in radians.  To access these 
lists, press [2nd], [STAT].  The displacements and reactions are listed in the order of 
the node numbering.  (node1, node2, node3, …)  After the solution is complete, the 
program exits.  The matrices used for the program are not deleted.  This way you can 
reenter the program, change some parameters, and re-solve the system.  There are 
instructions below on reentering data.

EXIT:
   You can either choose to SAVE AND EXIT, or to CLEAR AND EXIT, or to go back to the 
main menu.  Clear and exit deletes matrices A through G and deletes the ROTAT and REACT
lists.  Save and exit, quits the program without clearing the matrices used by the 
program.  Important, if you quit the program and wish to reenter it to solve the system 
later.  You must not save any values to the real numbers (A through Z).  This might cause
the program to screw up.

NOTE:
   All numberings in this program start with the number 1.  (You can’t have a node 0)  If
you mess up entering your data, you can always go back and reenter it.  However, if you 
have moved on to the next entry in the main menu, you should redo that one too.  (If you 
messed up with your nodes, and have already moved on to elements and forces.  You should 
redo nodes, elements and forces.)   

If you have any questions or comments, please email me at: bmaxelro@syr.edu