[347140]: doc / ocframe / manual.tex  Maximize  Restore  History

Download this file

294 lines (223 with data), 9.7 kB

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
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}
\subsection{Loads}
\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
nodeloads=[2, 18.75,-46.35, 0.0];
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
# local load
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}
[P,D,MemF]=SolveFrame(joints,members,nodeloads,dist,point);
\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,
LOADCASES)
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; ...]
loads on members:
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}

Get latest updates about Open Source Projects, Conferences and News.

Sign up for the SourceForge newsletter:





No, thanks