Buckling: Impact of Stiffners
INTRODUCTION
Structures such as Beams, columns, struts forms the basis of construction of buildings, lathe beds etc which are designed to take up load. https://skill-lync.com/projects/beams-a-section-geometry-study, shows the efffect how stress would be developed in the structure. However, when the columns which are long slender members with relatively very small crosssections are subjected to the loading, columns could fail due to elastic instability which is referred as the buckling which is a sidewise bending.
However, not all the column fail by buckling, slenderness ratio is used to define short, long and medium columns. Slenderness ratio is the ratio between length and least radius of gyration of member.Short column is less than 32, long column is greater than 120 and anything in between is medium column.
Short members typically fail by crushing or shearing before they buckle. Long members rarely fail by yielding under compression. The minimum compressive load at which columns tends to have lateral displacement is called buckling or crippling load. The buckling load is calculated using the euler formula.
where Pcr is Critical load, E is the young's modulus, I is the moment of inertia, L is the equivalent length where L varies depending on nature of how the end points are located, hinged, fixed or free
The ratio of critical load to safe load is referred as the factor of safety. Since the critical load is dependent on material chosen, geometry of the section and length of the structure, sometimes, most of these are restricted by the application. For example, Building columns, Tank pillar, connecting rod in IC engines.
Hence stiffners are used to back the structure and hence increase the factor of safety. The effect of placing the stiffner and choosing stiffner geometry can vary the FOS. Hence this study is carried out to optimise the stiffner design.
FEA SIMULATION
GEOMETERY: The study is carried out on the 4 legs each of length of 2m. Alloy steel is used as the material. For the analysis, only legs and platforms are considered
MESHING:
SOLUTION AND INTIALISATION:
Buckling mode of solution is chosen. The ends of the legs are fixed and constant load of 150kN is applied on the platform. No stiffners are attached and the Buckling factor of safety is noted. Then, stiffner is added at the random length on the legs and base buckling factor is found. Then the location and width of the stiffner is optimised to give the maximum buckling FOS
RESULTS
Case 1: No Stiffner
Buckling FOS with no stiffner is 9.3932
Case 2: Stiffner of random width and location along legs
Stiffner is intially placed at 1.75m with width of 150mm
This gave a very modest improvement in FOS, current FOS was 13.957
Case 3: Optimisation study is carried out by varying the width between 10mm and 150mm and length between 0.25m and 1.75m.
Scenarios were executed, maximum FOS from the study was 34.91 which was found at half the length of leg with maximum stiffner width chosen for the DOE.
DISCUSSION ON RESULTS
1) The summary of the runs are as follows
| Condition | Location | Width | FOS |
| No Stiffner | NA | NA | 9.3932 |
| Rand Stiffner | 1.75m | 150mm | 13.957 |
| Optimised | 1m | 150mm | 34.91 |
2) From this study, FOS can be significantly improved by adding stiffner, also multiple stiffners could be added to address different nodes of buckling
3) For this loading configuration, stiffner is most effective at the center of the leg for the same width of stiffner
4) FOS can be further improved by increasing the width of the stiffner. However, beyond a point, minor gains are obtained by big increase in the stiffner width. Hence, optimal width should be chosen depending on application requirement