In creating automotive structures, larger section sizes are desired to provide a stiffer body, yet wall thickness is typically decreased to offset the increase in mass. There is a temptation to throw as strong a material as possible into the design to compensate for this strength compromised structure. In compression-dominated members, any local buckling of the surface will reduce load-carrying capability. They are further compromised by the myriad holes and features needed for integration reasons, shown here :

Pillar Structures
By calculating the critical buckling stress for the section, we can better refine our choice of material parameters. Shown below is the equation to determine the critical buckling stress of a simple section. Please note that in this equation, geometry is the main factor with no influence of material strength.

First, the edge boundary conditions and the aspect ratio (a/b) of the compression surface(s) are needed to determine the buckling coefficient kc.
Buckling Coefficient
Using the buckling coefficient chart

we observe that as the aspect ratio (a/b) approaches 2, the buckling coefficient (kc) can be considered constant for a defined edge boundary condition.
Depending on the section, the edge boundary conditions can fall between fully constrained (Curve A) and simply supported (Curve C). For this example we will assume a balance between simple supported (kc = 4) and fixed (kc = 7), so kc will be 5.5
Poisson’s Ratio
Assuming Poisson’s Ratio for steel is 0.3 and Young’s modulus of elasticity is 29.6×106 psi, the critical buckling stress is:

By plotting the critical stress against the t/b ratio we can then narrow down our material parameters. For a given t/b ratio, there is a critical stress above which
the material is no longer effective in resisting local buckling. Increasing the material grade will get you very little performance as the structure is “geometry-limited”.
Any improvements will need to be focused on section shape before reconsidering material grade.
Another way to interpret is to consider the typical yield strengths of common steel grades. For a t/b ratio that falls to the right of the critical stress curve, a material upgrade could improve performance. However, for those ratios that fall to the left of the curve, the shape of the section (compression side) will drive performance.
Example:
A t/b ratio of 0.02 is a likely ratio in automotive structures (such as a 1.2mm thick surface (t) with a width of 60mm (b)). Using Figure 6, for 0.02, the critical buckling stress is approximately 420MPa. A BIW engineer could specify up to a DP780 material and be confident the material is working efficiently. Anything more than that will fall to the left of the critical stress curve and provide little strength benefit.