Post on 05-Jun-2017
transcript
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2nd International Student Competition on Cold-Formed Steel Design
Design Example
Revised on June 10, 2012
Task
To design an open section shape for a 48-inch (1219-mm) long cold-formed
steel truss member which yields the highest possible nominal compression
strength. Distortional buckling is ignored.
Requirements
1. The original steel sheet is 50 ksi (344.7 MPa), 10-inch (254-mm) wide, 0.0451-inch (1.1455-mm) thick, 48-inch (1219-mm) long.
2. The section shall have a minimum 1.5-inch (38.1-mm) wide flange to
accommodate screw-fastened sheathing attachments
3. The cross-section shall be an open shape.
4. Sharp corners (zero radius) can be assumed.
5. Pin-end boundary conditions
6. Cold-formed steel properties: elastic modulus E=29500 ksi (203.4 GPa), Possion's ratio v=0.3.
7. Students shall submit the design individually, team work will not be
accepted.
Note: English units (inches, kis, kip, etc) are used in this design example
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Step 1 – Design the cross-section shape
Basically you are given a 10 inches (254 mm) wide 48 inches (1219 mm) long flat steel sheet,
and you want to fold or bend the sheet to create a 48 inches long member with an optimal
cross-section shape that gives the highest possible compression nominal strength.
The shape has to be an open section and has to have a 1.5 inches (38.1 mm) wide flange for
screw connections to sheathing. Keep in mind that the sheathing is a long panel, the shape
shall be suitable to be attached to an infinitely long panel.
Here are some valid cross section shapes:
Here are some invalid cross section shapes:
1.5-inches wide flange
Can not be a closed section
There is no 1.5-inches flange
The flange can not be attached to a deck
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We take a C section shape as an example.
Make sure the total length of the section = 10 inches.
Step 2 – Create the cross section model in CUFSM 3.12, link for downloading
2.1 Install and open the CUFSM software
Click “Input” to enter the geometric input modulus.
6”
1.5”
1.5”
0.5”
0.5”
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2.2 Define the nodes and update the “Nodes” entry
We need to assign nodes to all corners, intersections, and end points. For the C section, we can
define 6 nodes and assume the origin of the Z-X coordinate system is at node #3.
According to the required Nodes entry format in CUFSM, the
following node entry can be established.
1 1.5 0.5 1 1 1 1 1
2 1.5 0 1 1 1 1 1
3 0 0 1 1 1 1 1
4 0 6 1 1 1 1 1
5 1.5 6 1 1 1 1 1
6 1.5 5.5 1 1 1 1 1
(hint: you only need to specify the node #, x and z coordinates, leave 1 for the other entries)
2.3 Define the elements and update the “Elements” entry
We will need to assign an element # to each flat portion which is defined by two end nodes.
According to the format, the element entry can be established as follows
1 1 2 0.0451 100
2 2 3 0.0451 100
3 3 4 0.0451 100
4 4 5 0.0451 100
5 5 6 0.0451 100
(hint: 0.0451 is the steel thickness (in inches) required
by the competition. 100 is the material #, the default
material properties in CUFSM are accepted, no change is
needed. If you use SI units, you will need to change the
material properties’ units)
1
23
4 56
(0,0) x
z
1
23
4 56
(0,0) x
z1
2
3
4
5
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2.4 Update the Nodes and Elements entries in CUFSM and click “Update Plot” button
2.5 Increase the element number by keeping clicking “Double Elem.” button.
(hint: more elements may result in accurate results, we double the elements twice here.)
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2.6 Check the “Lengths” entry, and make sure number 48 are included.
The “Lengths” are the half-wave lengths to be analyzed, since the member is 48 inch long, we
need to add 48 in the box.
2.7 Focus the analysis on Global buckling and local buckling only.
The Competition requires the distortional buckling mode to be ignored. The analysis shall be
focused on the lateral-torsional bucking (also called global buckling) and local buckling.
Click the “On/OFF” button to initiate the buckling constraint function. Uncheck “Dist.” and
“Other”. Select “Natural modes”
Step 1click button
Step 2Uncheck “Dist.” and “Other”
Step 3Select Natural modes
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Step 3 – Perform elastic buckling analysis in CFUSM
3.1 Click “Properties” to determine yield load Py
First check the cross section A, since the member length and cross-section total width are fixed
numbers, the cross section A is also a fixed number, A=0.451. If the number is 1% different
than 0.451, you shall modify your design to meet the geometric requiments.
Secondly, input 50 in for “Generate P and M based on max (yield) stress =”. (the Competition
requires the yield stress = 50 ksi)
Then click “Calculate P, M and B”. The result for P is the axial yield compression load for the
section.
Py = 22.55 kips (the default force unit in CUFSM is kip = 1000 lbs)
Step 1: input 50
Step 2: click
Step 3: write down result for Py
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3.1 Generate uniform applied compression stress
Check “P” (axial force), and input P =1 (initial uniform load = 1 kip). Uncheck the other items.
Then click “Generate Stress using checked P and M” to generate the initial compression stress.
3.2 Click “Analyze” tab to perform the analysis
The finite strip results are automatically shown after the analysis.
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From this plot, we can determine the critical elastic lateral-torsional buckling load Pcre, and the
critical elastic local buckling load PcrL.
3.3 Determine the critical elastic lateral-torsional buckling load Pcre
In CURSM’s result plot, change the “half-wavelength = 48” and then click “Plot Shape” to
update the plot. Check the buckling mode. Make sure the lateral-torsional buckling mode is
shown. In the lateral-torsional buckling mode, the entire cross section moves and/or rotates
without element bending.
In this example, the mode 1 can be regarded as a lateral-torsional buckling mode because the
entire section moves horizontally, small element deformation occurs on the web, but it can be
ignored.
The load factor = 18.1729. Since we gave an initial load P = 1 kip,
The elastic lateral-torsional buckling load
Pcre = load factor X initial load P = 18.1728 x 1 (kip) = 18.1729 kips.
Hint: if the 1st mode is not the lateral-torsional buckling mode, you can increase the “mode” to
until the desirable shape is reached. Make to click the “Plot Shape” button to update the result
every time when you change the mode # or the half-wave length.
Step 1,Change to 48
Step 2, update plot
Step 3,Get results
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Hint: the CFSUM only gives you the first 10 buckling modes. If you could not find the lateral-
torsional buckling mode within the first 10 modes, it is allowed and also conservative to use the
results of the 10th mode for the Pcre.
3.4 Determine the critical elastic local buckling load PcrL
This Competition defines the critical elastic local buckling load, PcrL, as the minimum buckling
load for the half-wave length range between 1 inch to 48 inches including 1 inch and 48
inches.
This example, the minimum buckling load is located at half-wave length 4.0 inches. Move the
“half-wavelength = 4”, update the plot, and get the results.
PcrL = load factor X initial load P = 4.0126 x 1 (kip) = 4.0126 kips.
Summary of the results in Step 3
Pcre = 18.1729 kips
PcrL = 4.0126 kips
Py = 22.55 kips
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Step 4 – Save the CFSUM model to a .mat file
Save the file name as first name _ last name.mat
Step 5 – Calculate the nominal compression strength of the 48-in long member using the
Direct Strength Method, Pn
We will use the AISI S100 North American Specification for Cold-Formed Steel Structural
Members – Appendix 1 to determine the nominal compression strength. The specification can
be downloaded from the Competition website, here is the link.
Pn = minimum ( Pne , PnL ) (Note: the distortional buckling is ignored in this Competition)
Where Pne is the nominal lateral-torsional buckling strength, PnL is the nominal local buckling
strength.
The AISI S100 provisions for Pne , PnL is listed below.
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Calculation for this example:
114.11729.18/55.22P/P creyc
5.1c 414.1355.22658.0P658.0P2114.1
y
2c
ne
kips
828.10126.4/414.13P/P crLneL
776.0L
511.7414.13414.13
0126.4
414.13
0126.415.0115.01
4.04.04.04.0
ne
ne
crL
ne
crLnL P
P
P
P
PP kips
7.5117.511) ,414.13(min,min imumPPimumP nLnen kips
Step 6 –Repeat above steps until the optimal cross section shape is sought.
Step 7 - Fill out the Information Form
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Step 8 – Write a design essay
A brief essay (in English), limited to maximum 5 letter-size pages, is required as part of the design package. The essay shall describe the concept of the design, the methodology used for optimization, and the detailed calculation of the nominal compression strength.
Step 9 – Compressed three files into one single .zip or .rar file
Email the single file to CFS_Competition@unt.edu before June 30, 2012, 6:00pm student
entrant’s local time.