### Section Strength – 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 shown here, 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 the graph 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.