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Beam Bending Safety
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This directory contains a single Notation3 file that encodes a 
structural case study about the bending safety of simple rectangular 
beams. Each beam design is described by its span, a mid-span point 
load, cross-section dimensions (width and height), and an allowable 
bending stress. Using standard beam formulas for a simply supported 
beam under a central load, the theory computes the maximum bending 
moment, the section modulus of the rectangular section, the resulting 
bending stress, and a safety factor given by allowableStress / 
bendingStress. A design is classified as safe if its bending stress 
does not exceed the allowable value and failing otherwise. Four example 
beams illustrate typical situations: a short, lightly loaded shelf, a 
base floor beam under design load, the same beam under an overloaded 
case, and a taller beam that carries the same load more comfortably.

On top of this mechanical core, the file adds an ARC layer that 
produces three kinds of derived information. An `:answer` node 
summarises which of the four designs are safe or failing and highlights 
that doubling the load on a fixed section roughly doubles the stress, 
while increasing the height of the section (and thus its section 
modulus) significantly reduces stress. A `:reason` node explains in 
mathematical English why these relationships hold, referring directly 
to the formulas σ = M_max / S with M_max = P·L/4 and S = b·h²/6. 
Five `:check` nodes act as a small harness: they confirm that all 
designs have derived stresses and safety factors, that the overloaded 
case has higher stress than the base design, that the taller beam has 
lower stress than its shorter counterpart, that safe designs have 
safety factors ≥ 1 while the failing design has a factor < 1, and 
that the taller beam has the largest safety margin. All of these ARC 
conclusions are computed from the same equations and input data, so if 
you modify the beam dimensions, loads or allowable stress, the Answer, 
Reason and Checks adapt automatically—making the file a small, 
self-documenting example of quantitative structural reasoning in N3.

