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CUTWP by Andrew Sarawit*
Global Buckling Analysis of
Thin-walled Members
The global buckling analysis
(flexural-torsional, lateral-torsional, etc) of thin-walled members can
be an involved task. CUTWP provides the thin-walled cross-section
properties necessary in such analysis and provides classic stability
solutions as well. After all Pcr2 =
((Pe1+Pe3)-sqrt((Pe1+Pe3)^2-4*B*Pe1*Pe3))/(2*B); is not a calculation
you want to do by hand every day. The December 2006 release of CUTWP has
provided corrections to b1
and b2
which are used in lateral-torsional buckling calculations
and CUTWP has been modified to read CUFSM input
files.
Introduction
Global buckling, such as flexural-torsional
buckling in columns or lateral-torsional buckling in beams can sometimes
be an involved calculation for the engineer. First, the section
properties can be onerous to calculate, and second, the elastic
stability itself requires the solution of a cubic equation. For
thin-walled members the preceding is all the more true, as the
unsymmetric nature of many sections requires that the more complicated
global buckling modes such as flexural-torsional buckling always be
considered. Andrew Sarawit wrote a small piece of code along with an
interface for making these section property calculations and global
buckling calculations, and this code is made available in open source
form for your use here. The program CUTWP was written in Matlab, and
includes a full graphical interface.
What does the CUTWP
interface look like?
CUTWP uses a single page interface, and
reports the section properties as well as the buckling mode shapes for
the three global modes of the cross-section. A screen shot of CUTWP in
action is given below. CUTWP has been modified to read CUFSM input
files.
What is the
difference between CUTWP and CUFSM?
CUTWP only calculates global buckling
properties. The classical formulas that you find in Timoshenko's
Theory of Elastic Stability (or more correctly the work of Pekoz
from the late 1960's) are used for generating the solution.
CUFSM can calculate local, and distortional buckling modes in addition
to global buckling. CUFSM is closer to a general purpose finite element
type of software, as opposed to CUTWP which is closer to analytical
solutions, i.e., calculate section properties and then solve the
standard beam theory differential equations. As of version 3.0 of CUFSM,
the reported section properties in CUFSM use the same base code as CUTWP.
Can CUTWP
and CUFSM work together?
CUTWP was modified in November of 2005 to be
able to read CUFSM files as input. This allows a CUFSM user to perform
traditional global buckling solutions without recourse to hand formulas.
In particular, approximate solutions when Kx, Ky, and Kt are not equal
can be handled readily in CUTWP -- and the formula involved are the same
as those typically used in civil engineering design specifications.
Further integration of the two programs is being considered.
What's
underneath the hood / how does CUTWP work?
Some incomplete snippets of code are provided
to give you a sense of the nature of the CUTWP calculation:
% compute the flexural buckling and
torsional buckling
...
Pe1 = pi^2*E*I1/KL1^2;
Pe2 = pi^2*E*I2/KL2^2;
...
Pe3 = (G*J+pi^2*E*Cw/KL3^2)/rob^2;
...
Pcr1 = Pe2;
B = 1-(a1/rob)^2;
Pcr2 =
((Pe1+Pe3)-sqrt((Pe1+Pe3)^2-4*B*Pe1*Pe3))/(2*B);
Pcr3 =
((Pe1+Pe3)+sqrt((Pe1+Pe3)^2-4*B*Pe1*Pe3))/(2*B);
...
"..." indicates intermediate code left out - the
code for a traditional flexural-torsional buckling calculation is
provided above, just to indicate to the user what manner of calculations
are performed in CUTWP. The mode shapes are also generated and provided.
Matlab
open source version of CUTWP (requires the user have Matlab)
The matlab files necessary for running CUTWP
are provided here.
download matlab
Installation instructions are as follows.
Click on download above. Unzip the files to a directory of your
choosing. In Matlab change your working directory to the same directory
as where you unzipped the files. At the command line, type "cutwp". The
program will initiate. (download
November 2005 version)
Standalone version of CUTWP (runs on Windows machines)
The libraries and executable files necessary
for running CUTWP are provided here.
download standalone for PC
Installation instructions are as follows.
Click on download above. Save the exe file, double-click on
cutwp_pkg.exe - this will expand all the files and install a Matlab
runtime engine after that run (double-click) cutwp.exe and the
program will initiate.
How do I
reference CUTWP? CUTWP is open source?
| CUTWP is
open source,
Academic Free License v 1.2. Please provide a reference to the
author (Andrew Sarawit) and note the version you are using.
For example: Sarawit, A. (2006). "CUTWP Thin-walled section
properties" December 2006 update <www.ce.jhu.edu/bschafer/cutwp>
and add the date you referenced this web page |
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*Andrew Sarawit, Ph.D. is the developer of
CUTWP. He is currently employed at Simpson, Gumpertz & Heger Inc. and
may be reached at atsarawit@sgh.com.
Ben Schafer performed the modification to CUTWP to allow it to read
CUFSM input files and made corrections to
b1
and
b2
in December 2006. Also, Ben Schafer maintains this web site, page, and
all the commentary above. Send comments, questions, etc. to
schafer@jhu.edu.
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