Determination of the ideal spring stiffness for lateral supports of buckling members
Technical Article
If a member is laterally supported due to a compressive axial force to prevent buckling, it must be ensured that the lateral support is actually able to prevent buckling. Therefore, the aim of this article is to determine the ideal spring stiffness of a lateral support using the winter model.
According to George Winter, the ideal spring stiffness is that which is at least necessary to completely prevent the lateral buckling of the main member with regard to the critical load and to act accordingly as a full support. Winter speaks of "full bracing". Accordingly, the zero crossing of the buckling line should be located at the location of this support spring, so that the buckling line itself has two or more waves instead of one.
In the winter model, an ideally straight compression member hinged on both sides is considered, which is held in the middle by a support spring. To determine the ideal spring stiffness, Winter developed the idealized model shown in Figure 01.
The fictitious hinge is based on the assumption of an inflection point in the bending buckling line with the same span. Is as a normal force the buckling load Pe recognized and the rod in the region of the support spring displaced by the dimension w, obtained by cutting-free at the notional hinge and positioning of the moment equilibrium ideal spring stiffness Cideal.
| Cideal | Ideal spring stiffness |
| Pe | Critical load |
| L. | Span between support and support spring |
This correlation between spring stiffness and critical load results in the function shown in Figure 02. Accordingly occurs in spring stiffness less thanideal C a buckling shape with lateral displacement in the region of the support spring.
Thecritical load P e can be determined with the add-on modules RSBUCK and RF-STABILITY or manually as follows.
| Pe | Critical load |
| E | modulus of elasticity |
| I | Moment of inertia |
| L. | Span between support and support spring |
Determination of the ideal spring stiffness using an example
In the model (Figure 03), a compression member (IPE 400) hinged on both sides with the parameters E = 21,000 kN/cm², Iz = 1,318 cm 4 and L = 5 m is held in the middle by a support spring.
This results in acritical load P e of 1,089 kN, whichresults in an ideal spring stiffness C ideal for the support spring defined in the center of the member of 436 kN/m.
Determination of the stabilizing force in the support spring using the example of a buckling member with imperfection
After performing ultimate load tests on buckling columns in addition to the theoretical considerations mentioned above, it was found that the theoretically ideal spring stiffness is not sufficient for columns with geometric imperfections.
Accordingly, the deformation w from Figure 01 is supplemented by the pre -deformation w0 to wtot .
wtot = w + w0
After setting up the moment equilibrium about the fictitious hinge (Figure 01), the result is:
P ⋅ (w + w0 ) = C ⋅ w ⋅ L/2
This results in:
| wtot | Total deformation from buckling deflection and precamber |
| w0 | Pre -deformation from precamber due to geometric imperfection |
| P. | Existing compression axial force in the buckling member |
| C | Spring stiffness of the lateral support spring |
| L. | Span between support and support spring |
And for Cideal = 2 ⋅ Pe/L:
| wtot | Total deformation from buckling deflection and precamber |
| w0 | Pre -deformation from precamber due to geometric imperfection |
| P. | Existing compression axial force in the buckling member |
| Pe | Critical load in the buckling member |
The stabilizing force Fc results from these equations:
| Fc | Lateral stabilization force |
| C | Spring stiffness of the lateral support |
| w | Lateral deflection of the buckling member in the middle |
| P. | Compression axial force in the buckling member |
| L. | Span between support and support spring |
| w0 | Pre -deformation from precamber due to geometric imperfection |
| Pe | Critical load of the buckling member |
The stabilizing force Fc can thus be determined from the following parameters:
Existing compressive force P = 500 kN
Span between support and support spring L = 5.00 m
Precamber from imperfection w0 = Ltotal/300 = 10/300 = 0.0333 m
Critical load Pe = 1,089 kN
This results in a stabilization load Fc = 12.3 kN. RFEM determines 11.7 kN.
Summary
To check the correctness of the determined spring stiffness, you can look at the results from RF-STABILITY. The first mode shape is a double -wave buckling line with zero crossing at the level of the support spring, while the second mode shape is a single -wave buckling line supported by the support spring (Figure 04). Both have approximately the same critical load.
Keywords
Ideal Spring stiffness Buckling member Lateral Support
Reference
Links
Write Comment...
Write Comment...
Contact us
Do you have questions or need advice?
Contact our free e-mail, chat, or forum support or find various suggested solutions and useful tips on our FAQ page.
Recommended Events
Videos
Models to Download
Knowledge Base Articles
Steel Frame Considering Connection Stiffness
This technical article analyzes the effects of the connection stiffness on the determination of internal forces as well as the design of connections using the example of a two-story, double-spanned steel frame.Screenshots
Product Features Articles
Material Database with Steels According to the Australian Standard AS/NZS 4600:2005
The material database in RFEM, RSTAB and SHAPE-THIN contains steels according to the Australian standard AS/NZS 4600:2005.Frequently Asked Questions (FAQ)
- How can I create a twisted beam in RFEM?
- For which programs is the STEEL Warping Torsion add-on module available?
- In the RF‑/STEEL EC3 add-on module, I obtain an extremely high design ratio for a member in the case of "Biaxial bending, shear and axial force." Although the axial force is relatively high, the design ratio seems to be unrealistic. What is the reason?
- I have just noticed that the STEEL EC3 add-on module also calculates with γM0 = 1.0 when designing a tension member, although it should actually be γM2 = 1.25. How can I perform the design correctly?
- Is it possible to design intermittent welds in the CRANEWAY add-on module?
- I design a cross-section created in the SHAPE‑THIN program by using the RF‑STEEL EC3 add-on module, but the program shows the error message "ER006 Invalid type of c/t-part for cross-section of type General." What can I do?
- For a buckling analysis, FE‑BUCKLING determines the governing shear stress of τ = 7.45 kN/cm², while RF‑/STEEL gives the result of the maximum shear stress of τ = 8.20 kN/cm². Where does this difference come from?
- Why do I get a design ratio for the stability analysis according to 6.2.9.1 in the STEEL EC3 add-on module? Why is a * added to Equation (6.36)?
- I design a frame with a taper (docked cross-section). STEEL EC3 classifies the taper in Cross-Section Class 3. Accordingly, the elastic resistances are taken into account, which is very unfavorable. According to the standard, the taper should be categorized in Class 1, and thus the plastic reserve should also be usable.
- When modeling a beam connection to a continuous column, I have the problem that the column flange fails under bending. If I add backing plates in the FRAME‑JOINT Pro add-on module, nothing changes for all design ratios. Why?
Customer Projects
Associated Products
Main Program
Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements
3,540.00 USD
Add-on Module
Stability analysis according to the eigenvalue method
1,030.00 USD
Main Program
The structural engineering software for design of frame, beam and truss structures, performing linear and nonlinear calculations of internal forces, deformations, and support reactions
2,550.00 USD
Add-on Module
Stability analysis according to the eigenvalue method
670.00 USD
