## Diff of /doc/ocframe/manual.tex [000000] .. [347140]  Maximize  Restore

### Switch to side-by-side view

--- a
+++ b/doc/ocframe/manual.tex
@@ -0,0 +1,293 @@
+\documentclass[a4paper]{article}
+\usepackage{graphicx}
+
+\title{Ocframe Manual  \\ {\large  Structural Analysis functions of the Mechanics package}}
+\author{Johan Beke}
+
+\begin{document}
+
+\maketitle
+
+\tableofcontents
+% for F in *.m; do octave -q --eval "get_help_text_from_file(\"$F\")"; done > output.texi +% for F in *.m; do octave -q --eval "disp(get_help_text_from_file(\"$F\"))"; done > ref.texi ; makeinfo --plaintext ref.texi > ref.txt
+
+\section{Introduction}
+	\begin{sloppypar}
+	The structural analysis functions of the \emph{Mechanics} packages where written during a FEM course. The following posibilities are in the package:
+		\begin{itemize}
+			\item The analysis of 2D frames with rigid connections with the function {\emph{SolveFrame}}.
+			The solutions for the reaction forces, displacements and member end forces are given.
+			\item Solution of multiple load cases at once with the function \emph{SolveFrameCases}
+			\item A plot of the frame, with nodal displacements if needed, with the function \emph{PlotFrame}. The nodes and members are numbered.
+			\item Calculation the member internal forces for each member with the function \emph{MSNForces}
+			\item Plot of the internal member forces diagram with the function \emph{PlotDiagrams}
+		\end{itemize}
+	\end{sloppypar}
+\section{Conventions}
+	\subsection{Units}
+		\begin{sloppypar}
+		The user can use any units as long as they are consistent. So if the forces are provided
+		in kN, kN/m and kNm, the geometry and member properties must be in similar units (m, m$^2$, m$^4$ and kN/m$^2$).
+		\end{sloppypar}
+	\subsection{Global and local axis}
+		\begin{sloppypar}
+		For the nodes and the members, care must be taken for the axes.
+		The following images show the used coordinate systems (figure \ref{fig:axis.png})
+		and the conventions for the member forces (figure \ref{fig:dist.png} and \ref{fig:point.png}).
+		The local axes are always from the near node to the far node.
+		\end{sloppypar}
+		\begin{figure}[h]
+			\includegraphics[width=0.50\linewidth]{axes.png}
+			\caption{Local and global axis convention}
+			\label{fig:axis.png}
+		\end{figure}
+		\begin{figure}[tb]
+			\includegraphics[width=0.50\linewidth]{dist.png}
+			\caption{Conventions for a distributed load on a member}
+			\label{fig:dist.png}
+		\end{figure}
+		\begin{figure}[tb]
+			\includegraphics[width=0.50\linewidth]{point.png}
+			\caption{Conventions for a point load on a member}
+			\label{fig:point.png}
+		\end{figure}
+		\begin{figure}[tb]
+			\includegraphics[width=0.50\linewidth]{sign_conv.png}
+			\caption{Sign conventions for internal forces}
+			\label{fig:sign_conv.png}
+		\end{figure}
+
+\newpage
+\section{Example}
+	\begin{sloppypar}
+	An example will clarify the usage of the different functions.
+	\end{sloppypar}
+	\subsection{Forces and geometry}
+
+		\begin{figure}[h]
+			\includegraphics[width=0.75\linewidth]{example5_7.png}
+			\caption{Example frame}
+			\label{fig:example_frame}
+		\end{figure}
+
+		\begin{sloppypar}
+			An example frame, which was taken from the book Matrix Structural
+			Analysis, is shown in figure \ref{fig:example_frame}.
+			The following code snippet is used to enter the geometry:
+		\end{sloppypar}
+
+		\begin{verbatim}
+joints=[0,0,1,1,1;
+		7.416,3,0,0,0;
+		8+7.416,3,1,1,1];
+# first cells of each row are the x and y coordinates
+# next cells are the x, y and z constraints.
+# node 1 and 3 are fully fixed, node 2 is free
+
+# member data
+E = 210.0e3; # N/mm^2 = MPa
+A = 6000;# mm^2
+I = 200.0e6;# mm^4
+
+# convert units to kN and m
+E = E*10^3;
+A = A*(10^-3)^2;
+I = I*(10^-3)^4,
+
+#connectivity data
+members=[1,2,E,I,A;
+		2,3,E,I,A];
+		\end{verbatim}
+
+		\begin{sloppypar}
+			The following code snippet is used to enter the loads:
+		\end{sloppypar}
+		\begin{verbatim}
+			# point load on node 2
+			# Fx = 18.75 kN
+			# Fy = -46.35 kN
+			# Mz = 0 kNm
+
+			loc = 1;
+			glob = 0;
+
+			# distributed load on member 2
+			# Fx = 0 kN/m
+			# Fy = -4 kN/m
+			# same for the end of the load
+			# a = b = 0 m  load on full span
+			dist=[2,0,-4.0,0,-4.0,0.0,0.0,loc];
+			#no point loads on members
+			point=[];
+		\end{verbatim}
+
+	\subsection{Solutions}
+		\begin{sloppypar}
+			The following code snippet is used to find the basic solution:
+		\end{sloppypar}
+		\begin{verbatim}
+		\end{verbatim}
+		\begin{sloppypar}
+			The basic solution are the reactions, the displacements and the member end forces:
+		\end{sloppypar}
+		\begin{verbatim}
+			P =
+
+			   130.497    55.677    13.374
+				   NaN       NaN       NaN
+			  -149.247    22.673   -45.356
+
+			D =
+
+			   0.0000000   0.0000000   0.0000000
+			   0.0009476  -0.0047441  -0.0005088
+			   0.0000000   0.0000000   0.0000000
+
+			MemF =
+
+			   141.8530     2.6758    13.3742  -141.8530    -2.6758     8.0315
+			   149.2473     9.3266    -8.0315  -149.2473    22.6734   -45.3557
+		\end{verbatim}
+		\begin{sloppypar}
+			Each row of the reaction matrix (matrix P in this case) corresponds to the node. (First row to first node, etc.).
+			The columns are R$_x$, R$_y$ and M$_z$. For node 1 the reactions are thus: R$_x$ = 130.497 kN, R$_y$ = 55.677 kN and M$_z$ = 13.374 kNm.
+			In case of a free component without reactions, the value is represented by NaN.\\
+			The same convention holds for the displacement matrix (matrix D in this case). For node 2 the displacements are thus:
+			x = 0.0009476 m, y = -0.0047441 m and rotation = -0.0005088 rad.\\
+			A similar principle holds for the member-end-forces. Each row corresponds to the element. The columns are: F$_x$, F$_y$, M$_z$, F$_x$, F$_y$ and M$_z$ where
+			the first three components are for the first node and the last three components are for the last node.
+
+		\end{sloppypar}
+
+\newpage
+\section{Function reference}
+		\begin{verbatim}
+ -- Function File: [X, M, S, N] =  MSNForces (JOINTS, MEMBERS, DIST,
+          POINT, MEMF, MEMBERNUM, DIVISIONS)
+     This function returns the internal forces of a member for each
+     position x. The member  is divided in 20 subelements if the
+     argument is not given. The used sign convention is displayed in
+     the help file.
+
+     Input parameters are similar as with SolveFrame and PlotFrame with
+     extra arguments:
+
+     membernum = Number of the member to calculate     divisions =
+     Number of divisions for the member
+
+
+ -- Function File:  ocframe_ex1 ()
+     Example of a planar frame.
+
+
+ -- Function File:  ocframe_ex2 ()
+     Example of a beam.
+
+
+ -- Function File:  ocframe_ex3 ()
+     Example of a planar frame.
+
+
+ -- Function File:  ocframe_exLC ()
+     Example of a beam with generation of eurocode ULS  load cases
+
+
+ -- Function File:  ocframe_railwaybridge ()
+     Example taken from a real railwaybridge.
+
+
+ -- Function File:  ocframe_tests ()
+     Various tests for the entire package.   Test 1, 2 & 3 are simple
+     beams (tested for reactions and internal forces)  Test 4 & 5 are
+     frames (tested for reactions)
+
+ -- Function File:  PlotDiagrams (JOINTS, MEMBERS, DIST, POINT, MEMF,
+          DIAGRAM, DIVISIONS, SCALE)
+     This function plots the internal forces for all members. The force
+     to be plotted can be selected with DIAGRAM  which will be "M", "S"
+     or "N" for the moment, shear or normal forces.
+
+     Input parameters are similar as with SolveFrame and PlotFrame.
+
+ -- Function File:  PlotFrame (JOINTS, MEMBERS, D, FACTOR)
+     Plots a 2D frame (with displacements if needed) using  the
+     following input parameters:
+
+     joints = [x , y, constraints ; ...]
+
+     constraints=[x , y, rotation] free=0, supported=1
+
+     members = [nodeN, nodeF, E, I, A; ...]
+
+     	  Optional arguments:
+
+     D = [x,y,rotation;...] Displacements as returned by SolveFrame
+
+     factor= Scaling factor for the discplacements (default: 10)
+
+
+ -- Function File: [RESULTS] = SolveFrameCases (JOINTS, MEMBERS,
+     Solves a 2D frame with the matrix displacement method for  the
+     following input parameters:
+
+     joints = [x , y, constraints ; ...]
+
+     constraints=[x , y, rotation] free=0, supported=1
+
+     members = [nodeN, nodeF, E, I, A; ...]
+
+     loadcases is a struct array with for each loadcase the fields
+
+     - nodeloads = [node, Fx, Fy, Mz; ...]
+
+     - dist = [membernum,FxN,FyN,FxF,FyF,a,b,local ; ...]
+
+     - point = [membernum,Fx,Fy,a,local; ...]
+
+     input is as for the function SolveFrame.
+
+     Output is a struct array with the fields: Displacements, Reactions
+     and MemF
+
+     (output formated as for the function SolveFrame.)
+
+ -- Function File: [REACTIONS, DISPLACEMENTS, MEMF] =  SolveFrame
+          (JOINTS, MEMBERS, NODELOADS, DIST, POINT)
+     Solves a 2D frame with the matrix displacement method for  the
+     following input parameters:
+
+     joints = [x , y, constraints ; ...]
+
+     constraints=[x , y, rotation] free=0, supported=1
+
+     members = [nodeN, nodeF, E, I, A; ...]
+
+     nodeloads = [node, Fx, Fy, Mz; ...]
+
+
+     dist = [membernum,FxN,FyN,FxF,FyF,a,b,local ; ...] for distributed
+     loads     where FxN and FyN are the loads on distance a from the
+     near node     (same with far node and distance b)     local=1 if
+     loads are on local axis, 0 if global
+
+     point = [membernum,Fx,Fy,a,local; ...]      where Fx and Fy are
+     the loads on distance a from the node near     local=1 if loads
+     are on local axis, 0 if global
+
+     Output is formated as follows (rownumber corresponds to     node
+     or member number):
+
+     Reactions = [Fx,Fy,Mz;...] where NaN if it was a non supported dof
+
+     Displacements = [x,y,rotation;...]
+
+     MemF = [FxN, FyN, MzN, FxF, FyF, MzF; ...]
+	\end{verbatim}
+\end{document}