Concept explainers
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
(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 “lean on” the material any more than the proven design, set σm/σ = 1. Express Fm in terms of the scale factors and F, and comment on what you have learned.
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Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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