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4. Linear Static and Buckling Analysis

# Linear Static and Buckling Analysis

Linear Static and Buckling Analysis are some of the analysis methods that SkyCiv offers to solve your structure.

This analysis considers the buckling of members which is flexural instability due to axial compression, also known as Euler Buckling. The main result determined by the analysis is the buckling load factor which is the factor that the loads need to increase in order for the buckling load to occur. A factor of less than 1.0 indicates that the structure is buckling. Buckling will be more common for long, slender members undergoing high compression loads.

SkyCiv users often enquire about why the software only returns a single buckling factor, thinking that there should be a factor for each member. However, SkyCiv performs a rational elastic buckling analysis via an eigenvalue analysis, meaning that buckling is considered for the entire structure, groups of members, and individual members. This way, the entire stiffness of the model is factored into its buckling susceptibility.

This analysis method is important because a linear static analysis alone is not enough to indicate failure due to buckling. In fact, if a structure is found to be buckling then the results of the static analysis are not correct or applicable. Performing this extra analysis will however increase the solve time.

The critical load of each member is also determined during the analysis. This is the load at which a certain member will buckle. The critical load is proportional to Young’s Modulus and Moment of Inertia, and inversely proportional to the length of the member. The critical load is not a function of Yield Strength.

## Extra Notes and Considerations

• This buckling analysis only considers Euler Buckling due to axial compression. Torsional buckling is not considered.
• If an extremely low buckling load factor is found by the software (i.e. less than 0.05) then this could be due to the model being unstable. Hence, you should look at the stability of the model as it could be the problem rather than buckling. Check your member-end fixities and supports. Often excessive deflections can be a hint that these instabilities exist too.
• This buckling analysis only applies to members, not plates.

## Example: Buckling of a Vertical Column

1) Consider a vertical member that is 3 feet tall with a rectangular cross-section that is 1 inch by 2 inches made from the default Structural Steel material in SkyCiv Structural 3D. It is fully fixed at the base of the column and experiencing a 1 kip compressive point load.

2) To solve the structure with a linear static and buckling analysis, hover over Solve and click Linear Static + Buckling as shown above. When the structure has finished solving, you’ll notice that a warning appears to indicate that the buckling load factor is less than 1, indicating that buckling is occurring and needs to be checked.

3) View the buckling results by clicking the ‘Buckling’ button on the left. The buckling shape of the structure is drawn and a pop-up will appear to inform you of the buckling load factor. A load factor less than 1, as in this case, indicates that buckling is taking place.

4) More buckling result details can be viewed in the Analysis Report. Click ‘Report’ in the set of results on the left and generate a report. Open the report and find the ‘Member Buckling Results’ checkbox. Results are given for the critical load (the load at which buckling begins), actual length, and theoretical effective lengths in the z and y axes.