Buckling Analysis

Buckling Analysis

Buckling Analysis

Objective of Buckling Analysis:

• To Find Buckling load factor

• To Find Buckling mode shape

• To determine member effective lengths

• Buckling Analysis Hands-on Exercise Using SPACE GASS

Buckling Analysis

What is Buckling Analysis:

An accurate buckling analysis looks at the interact ion 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 b uckling 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 us eable or not.

Buckling Analysis

Buckling effective lengths:

The effective length of a compression member is the length of an equivalent pin-ended strut that has an Euler buckli ng capacity equal to the axial force “P cr” 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

Buckling Analysis

Buckling effective lengths:

Buckling analysis identifies the portion of the fra me that buckles first. This determines the BLF and, consequently, c ontrols the effective lengths of all the members in the frame. The buckled portion of the frame may just involve one or two me mbers and may be remote from many of the members that are hav ing 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 ef fective length.

Buckling Analysis

Buckling effective lengths:

During Buckling Analysis, ensure that node movemen ts that are able to move in the real structure are not restrained. F or 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-of-plane buckling modes involving the intermediate nod es would be restricted.

Buckling Analysis

A frame buckling failure is triggered whenever a degree of freedom becomes unstable

Buckling effective lengths:

In particular, when performing a buckling analysis, node movements may occur in directions in which there ar e no loads and it must be ensured that you don’t restrain thos e movements if they can occur in the real structure.

Remember that restraints anchor the structure in sp ace. They should not be confused with member fixities which a re used to model internal releases such as pin-jointed members !

A frame buckling failure is triggered whenever a de gree of freedom becomes unstable

Buckling Analysis

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.

Buckling Analysis

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.

Buckling Analysis

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 th ey are braced. This will limit the effective lengths from the buck ling analysis to the actual member length.

Buckling Analysis

Special buckling considerations:

Restraining the structure for buckling - It is impor tant to restrain the appropriate degrees of freedom to prevent buckl ing 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 ar e restrained in that direction, otherwise the buckling load fact or may apply to an unexpected out-of-plane buckling mode.

Buckling Analysis

Special buckling considerations:

A linear static analysis of a plane frame is not as sensitive to out-of-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 c ause buckling in any direction, even if there are no loads in tha t direction.

Buckling Analysis

Special buckling considerations:

Buckling analysis with secondary members -

Structures are often modelled with the secondary me mbers such as ties or bracing removed. If these members are re quired to prevent buckling of the major members in the real s tructure then they should be included in the buckling analysis mo del, otherwise the buckling capacity of the structure wi ll 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.

Buckling Analysis

Buckling Analysis Exercise:

Exercise – Buckling Analysis using SPACE GASS

Buckling Analysis

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

Key Features:Buckling Analysis

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

Analysis Procedure:Buckling Analysis

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

Analysis Procedure:Buckling Analysis

2. Add a combination load case (load case 2) which factors up load case 1 (SW + UDL 30kN/m) by a factor of 4.0.

3. 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”.

Analysis Procedure:Buckling Analysis

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.

Analysis Procedure:Buckling Analysis

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.

Analysis Procedure:Buckling Analysis

Running buckling analysis:Buckling Analysis

Running buckling analysis:

Buckling modes

The number of buckling modes that are required. Normally only the first buckling mode is of interes t, 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.

Buckling Analysis

6. Perform a buckling analysis using a linear

Buckling Mode Shape

Analysis Procedure:Buckling Analysis

Wittrick W.H. and Williams F.W."Natural Frequencies of Elastic Structures", Quarterly Journal of Mechanicsand Applied Mathematics, Vol. XXIV, Pt. 3, 1971.

Harrison H.B."Computer Methods in Structural Analysis", pp 248-251, Prentice Hall, 1973.

Codes and Recommended Practices

Buckling Analysis

Q & A

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