The Roman method for addressing uncertainty in design was to build a copy of a design that was satisfactory and had proven durable. Although the early Romans did not have the intellectual tools to deal with scaling size up or down, you do. Consider a simply supported, rectangular-cross-section beam with a concentrated load F, as depicted in the figure.

(a) Show that the stress-to-load equation is
F = σbh2l/6ac
(b) Subscript every parameter with m (for model) and divide into the above equation. Introduce a scale factor, s = am /a = bm /b = cm /c etc. Since the Roman method was to not

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