Limits to Deflected Shape Assumptions of the SDOF Methodology for Analyzing Structural Components Subject to Blast Loading

This paper examines the deflected shape assumptions built into the single-degree-of-freedom (SDOF) methodology used for analyzing structural components subject to blast loading. Design professionals use the SDOF models to analyze blast effects on components. It is common knowledge that the SDOF method is an approximation, and is not suitable for large charges with short distances (lower scaled distance $-Z$). Current design guidelines establish the limit of $Z=1.2\mathrm{m}/{\mathrm{kg}}^{1/3}$ for using SDOF methodologies for blast-loaded components, which is equivalent to a peak pressure of 5,000 kPa; however, this paper shows that the limit may be significantly higher in $Z$ value (or lower in peak pressure). Higher air-blast pressure and impulse combinations cause hinges to form before the assumed deflected shape dominates the response. Because transformation factors for SDOF are derived using static deflected shapes and the static collapse mechanism, the factors may not produce accurate or conservative responses for blast loading at lower scaled distances. Using the finite element multi-degree-of-freedom (FE-MDOF) model, the paper validates the accuracy of SDOF shape factors for large scaled distances, and shows that the static deflected shape assumptions do not apply at lower scaled distances with higher impulses. Limits to SDOF are established based on the equivalent shape factors, and the variability in the limits based on damping and mass are also discussed.