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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

5

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.