Buckling Analysis. Buckling Analysis

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3 Objective of Buckling Analysis: To Find Buckling load factor To Find Buckling mode shape To determine member effective lengths Hands-on Exercise Using SPACE GASS

4 What is : An accurate buckling analysis looks at the interaction of every member in the structure and detects buckling modes that involve one member, groups of members, or the structure as a whole. A buckling analysis is an essential component of every structural design because it: 1. Determines if the loads exceed the structure's buckling capacity and by how much. 2. Calculates the member effective lengths for use in the member design. 3. Determines if the static analysis results are useable or not.

5 Buckling effective lengths: The effective length of a compression member is the length of an equivalent pin-ended strut that has an Euler buckling capacity equal to the axial force Pcr in the member at the point of frame buckling. It can be determined from the formula: It is evident from the formula that because the member actual length is not involved in the calculation, subdividing the member into smaller segments does not change its effective length. Many Structural analysis software allows, Effective lengths calculated by the buckling analysis can be automatically transferred into the steel member design modules

6 Buckling effective lengths: Buckling analysis identifies the portion of the frame that buckles first. This determines the BLF and, consequently, controls the effective lengths of all the members in the frame. The buckled portion of the frame may just involve one or two members and may be remote from many of the members that are having their effective lengths controlled by it. For example, the buckling collapse of the left-hand column of a portal frame due to a heavy load applied to it can control the effective length of the right-hand column which has no such load applied. Consequently, each column would have a different effective length.

7 Buckling effective lengths: During, ensure that node movements that are able to move in the real structure are not restrained. For example, if intermediate nodes restrains translation in out-of-plane direction in the real structure then it will prevent the lateral translations of the nodes. While this may not affect a static analysis (due to no loads in that direction), it may affect a buckling analysis because any out-ofplane buckling modes involving the intermediate nodes would be restricted. A frame buckling failure is triggered whenever a degree of freedom becomes unstable

8 Buckling effective lengths: In particular, when performing a buckling analysis, node movements may occur in directions in which there are no loads and it must be ensured that you don t restrain those movements if they can occur in the real structure. Remember that restraints anchor the structure in space. They should not be confused with member fixities which are used to model internal releases such as pin-jointed members! A frame buckling failure is triggered whenever a degree of freedom becomes unstable

9 Non-Linear Effects: A non-linear analysis considers both P- and P-δ effects. The P- effect occurs as a result of the ends of an axially loaded member moving laterally with respect to each other. A moment of P. is induced which alters the member s equilibrium and causes the relative member end movement to change further. Unless the axial load P exceeds the member s Euler buckling load, a point of equilibrium eventually occurs such that the P- moment is balanced by moments applied by other members or restraints.

10 Non-Linear Effects: The P-δ effect occurs as a result of lateral curvature being induced in an axially loaded member. A parabolic moment distribution is induced along the length of the member which alters the member s effective stiffness and causes the curvature to change further. Unless the axial load P exceeds the member s Euler buckling load, a point of equilibrium eventually occurs such that the P-δ moments are balanced by internal flexural resistance built up within the member.

11 Special buckling considerations: For sway members, limit the effective lengths to a multiple of the actual member length by entering a factor into the "compression effective length ratio limit" field at the start of the design phase. In fact, effective lengths charts in most design codes limit the effective lengths for sway members to not more than 5.0 times the actual member length. For braced members, simply specify them as "braced" in the steel member design data for the direction(s) in which they are braced. This will limit the effective lengths from the buckling analysis to the actual member length.

12 Special buckling considerations: Restraining the structure for buckling - It is important to restrain the appropriate degrees of freedom to prevent buckling modes that can t occur in the real structure. For example, if a plane frame is braced in the out-of-plane direction, you must ensure that the braced nodes are restrained in that direction, otherwise the buckling load factor may apply to an unexpected out-of-plane buckling mode.

13 Special buckling considerations: A linear static analysis of a plane frame is not as sensitive to outof-plane restraints as a buckling analysis because static analysis out-of-plane displacements generally only occur if out-of-plane loads are applied. This is not true of a buckling analysis which can cause buckling in any direction, even if there are no loads in that direction.

14 Special buckling considerations: Buckling analysis with secondary members - Structures are often modelled with the secondary members such as ties or bracing removed. If these members are required to prevent buckling of the major members in the real structure then they should be included in the buckling analysis model, otherwise the buckling capacity of the structure will be underestimated by the analysis. This is particularly true of tower structures that contain large numbers of slender members that prevent buckling of the major support members.

15 Exercise: Exercise using SPACE GASS

16 Key Features: The SPACE GASS buckling analysis module performs a rational elastic buckling analysis of a frame to determine : its buckling load factors, buckling mode shapes and member effective lengths

17 Analysis Procedure: The purpose of this exercise is to illustrate the ease of carrying out buckling analysis using SPACE GASS and to obtain a frame s buckling load factor and member effective lengths. The Frame shown is used for illustration

18 Analysis Procedure: The procedure for the buckling analysis exercise is as follows: 1.Perform Linear Static Analysis using Load case 1 (SW + UDL 30kN/m) Deflections BM Diagram

19 Analysis Procedure: 2. Add a combination load case (load case 2) which factors up load case 1 (SW + UDL 30kN/m) by a factor of Perform a static non-linear analysis on both load cases. Take note of the message at the end of the static analysis that states that Frame buckling occurred in one or more load cases and therefore the results for those load cases should not be used.

20 Analysis Procedure: 4. The deformed geometry for both load cases. Note that load case 2 causes a sway to the left which is opposite to the direction you would expect. This is a clear indication that buckling has occurred and that the frame has moved to a position of unstable equilibrium.

21 Analysis Procedure: 5. Load case 2 come with a warning that states that they should not be used because frame buckling has occurred. From this, you can determine that frame buckling has occurred in load case 2, however you can t tell which members are involved or how close to buckling you are.

22 Running buckling analysis:

23 Running buckling analysis: Buckling modes The number of buckling modes that are required. Normally only the first buckling mode is of interest, because beyond that the structure has usually collapsed and further modes are of academic use only. Solver The "Paradise" solver is a new parallel multi-core sparse solver. The Paradise solver is the recommended setting for all static analyses. This solver doesn't generate buckling mode shapes. The Wavefront solver be used instead.

24 Analysis Procedure: 6. Perform a buckling analysis using a linear Buckling Mode Shape

25 Codes and Recommended Practices Wittrick W.H. and Williams F.W. "Natural Frequencies of Elastic Structures", Quarterly Journal of Mechanics and Applied Mathematics, Vol. XXIV, Pt. 3, Harrison H.B. "Computer Methods in Structural Analysis", pp , Prentice Hall, 1973.

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