Tutorial of CUFSM4 Objectives - Introduce the basic methods of modeling thin-

walled structures and calculating elastic critical buckling load (Pcr) or elastic critical distortional buckling moment (Mcr)

- Some discussion about the effect of boundary condition and modal decomposition and identification (cFSM)

Example - C-section with lips

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Tutorial General procedure

- Input the coordinates of each node on the cross-section

- Divide structural elements

- Set material properties

- Specify the boundary conditions, number of eigenvalues, and a series of half-wave lengths

- Choose the basis vector and base vectors of various modes in cFSM (Optional)

- Define loads on the cross-section

- Calculation and the post-process of results

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Example 1 – C-section with lips Welcome interface

- On the left side: load an existent file or save your work

- In the middle: input data, set boundary conditions, add constraints on modes (cFSM) and half-wavelengths, submit your work for calculation, show curves of the results

- On the right side: zoom in, zoom out, reset the amplification, print, copy the screen, reset, info & close the program

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Example 1 – C-section with lips

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Example 1 – C-section with lips Main interface

- Choose which properties you would like to be shown on the screen by tick them out and click ‘Update Plot’ (here we choose no#, constrains, springs and origin)

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Example 1 – C-section with lips

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Example 1 – C-section with lips Input coordinates of nodes

- For a concrete section, specify the coordinates of each node, and input them respectively.

- A dof is given the value of zero for constraint; while one for free movement (normally one).

- If you are not sure with the stress, just assume them as uniform one. (We will do with them later)

- For some cross-section (like C and Z), template can be used.

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Example 1 – C-section with lips

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Example 1 – C-section with lips Divide structural elements

- Mat# is the material that will be defined (there are default values).

- The division of elements near the round corner should be more refined.

- Some buttons (like Double Elem. and Divide Elem.) helps, like to double your mesh or refine your mesh further. A doubled mesh is shown in the next slide.

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Example 1 – C-section with lips

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Example 1 – C-section with lips Set material properties and element connections

- Material properties include Mat#, Young’s modulus, Poisson’s ratio and Shear modulus (Usu. Young’s modulus is 29500 ksi for CFS, and Poisson’s ratio is 0.3).

- The software also allows different Young’s moduli for two principal axes.

- Elements should numbered and start and end nodes, thickness and material number of each element should be given.

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Example 1 – C-section with lips Set boundary conditions and a series of half-wave

lengths (traditional signature curve)

- After clicking “boundary condition”, “traditional signature curve” means only one term of triangular series will be used for a specified half-wave length (m is locked to 1 for (mπy/L)). This is the only possible value of m in past editions.

- The user are free to choose the boundary conditions, and the curve of longitudinal shape functions are shown at the lower-right corner. (Only pin-pin are available in the past.)

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Example 1 – C-section with lips Set boundary conditions and a series of half-wave

lengths (traditional signature curve)

- The number of eigenvalues is exactly the number of buckling load factors you would like the software to solve for each half-wave length. For those who interested in higher modes, you can choose a larger number.

- The number of half-wave lengths should be enough, or you may miss some critical loads (can be modified after a trial). Remember local, distortional and global bucklings differ in half-wave lengths.

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Example 1 – C-section with lips

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Example 1 – C-section with lips Set boundary conditions and a series of half-wave

lengths (general boundary condition solution)

- “General boundary condition solution” means a certain number of terms of triangular series will be used for a specified half-wave length (m can be larger than one for (mπy/L)). Note that we choose m from 1 to 20 for 92 inch half-wave length, and the shape functions are shown in slide 17 with m = 2 highlighted by red line.

- The user are also free to choose the boundary conditions, number of eigen-values and half-wavelengths (like explained in slide 12 and 13).

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Example 1 – C-section with lips Set boundary conditions and a series of half-wave

lengths (general boundary condition solution)

- One key is that if you use m = 2 for half-wave length 2L, with other conditions the same , you will get the same results with m = 1, half-wave length L, since m and half-wave length are both doubled. Wisely choose them.

- The “recommend m” means a traditional signature curve analysis will be run automatically, and the software will suggest you the m which resolves the half-wave lengths close to the critical half-wave lengths of local, distortional and global modes.

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Example 1 – C-section with lips

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Example 1 – C-section with lips Define loads on the cross-section

- Press “Sect. Prop.” the software will automatically calculate the properties of the cross-section.

- In, “Applied Load”, input the yield stress, the software will automatically calculate the axial force and moment on the cross-section.

- Note that only the checked axial force or moment will be used in calculation. Make sure before press “Generating Stress”. Then there will be a stress distribution at every node.

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Example 1 – C-section with lips

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Example 1 – C-section with lips Calculation and the post-process of results

- Click “Analyze” will start the calculation.

- Then, click “Post” to show the results.

- The curve of buckling load-factor vs. half-wavelength contains all the information.

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Example 1 – C-section with lips About the curve of buckling load-factor vs. half-

wavelength

- Critical buckling load of a certain buckling mode (local, or distortional) is the local minimum on the curve. While the global buckling half-wave length should be the physical length of the member.

- There are cases where we have only one local minimum (like on slide 23) or multiple local minima.

- Generally, we tell the modes apart by their half-wavelengths and mode shapes. A more physical way is to use cFSM (we will explain later).

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Example 1 – C-section with lips About the curve of buckling load-factor vs. half-

wavelength

- The “Plot Shape” button will let you see the mode shape of buckling (2D or 3D) at a specific point on the curve. Use the scroll bar to see every mode (less than your number of eigenvalues) of every half-wavelength.

- You may also load another curve for comparison by clicking “load another file”.

- This edition allow you to dump your results into documents and can do modal classification and decomposition.

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Example 1 – C-section with lips

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Example 1 – C-section with lips cFSM - constrained fininte strip method, modal

decomposition and identification (details are in the paper posted on Dr. Schafer’s website)

- If you click “classify” under “cFSM Model classification” at the lower-left corner, their will be a pop-out informing you to initiate cFSM.

- After choosing “yes”, you will be directed to “cFSM” page. The first thing is to choose the base vector (natural or orthogonal)

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Example 1 – C-section with lips cFSM - constrained fininte strip method, modal

decomposition and identification

- Select the categories of mode base (L, G, D, O), and click “on/off”. You selection will be effective. You can also see the 2D or 3D figures of each mode below.

- Go back to “Post” and click “Classify”.

- One way to understand the result is the color distribution on the load vs. length curve. The dominant color portion (also see the numbers below the mode figure) at a the mode of certain half-wavelength corresponds with the dominant mode.

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Example 1 – C-section with lips cFSM - constrained fininte strip method, modal

decomposition and identification

- You can also look at the load factor vs. node number curve. The will let you know the modal participation of each mode (less than the total number of eigenvalues) at a fixed half-wavelength (supplemental participation plot tells the same thing).

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Example 1 – C-section with lips cFSM - constrained fininte strip method, modal

decomposition and identification

- Advanced users can go to “cFSM” page and select the mode set before submitting for analysis. This will find the buckling loads of specified modes at the half-wavelengths. An example of this is limiting the mode to “G” only to solve the global buckling loads of stocky members which are much higher than local buckling loads.

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Example 1 – C-section with lips

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Example 1 – C-section with lips

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Example 1 – C-section with lips

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Example 1 – C-section with lips

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Example 1 – C-section with lips Boundary condition and higher modes

- In fact, at a given half-wavelength in our code, there are infinite buckling modes. However, the one with the lowest critical load are most possible to happen. We only solve designated number of eigenvalues.

- Constraints affect the buckling load since some buckling mode will not happen if the component is properly constrained.

- CUFSM allows you to add constraints: either by adding springs at nodes or imposing equations (master-slave) as constraints. (See the front panel)

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Example 1 – C-section with lips Boundary condition and higher modes

- Due to the constraints, some buckling mode will not appear. However, the buckling load will point to a certain higher mode. After all, the buckling load indeed increases. This buckling load will be used if necessary in our design.

- For example, after the torsion is restrained, the distortional buckling would result in a local minimum.

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Conclusion This tutorial is intended to show how CUFSM4

works.

You should be able to calculate the buckling load of common cross-section and recognize the critical ones with respect to their modes.

You can get an idea on more advanced functions like using cFSM and adding spring or multi-point-constraint to nodes on the section to model things like sheathing stiffness.

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