Fig. 146 - Cutting up a beam

to make an arch

(visualization model)



of the beam must span.  And it shifts the internal stresses to compression mainly, which
stone is especially capable of resisting due the nature of its atomic structure.  The arch
design facilitates this by enabling the vertical loads to be collected and displaced laterally
around the curved mass of the arch so that they are concentrated at the base.  There the
legs of the arch must be prevented from spreading apart from the thrust of the weight by
the abutments against which they rest.  For the most efficient displacement of the load the
rise of the curved section of the arch should be equal to about one-half of its span.  Many
examples of arched Roman aqueducts survive to this day attesting to the extraordinary
stability of the arch design.




Fig. 147 - Roman aqueduct

(scale visualization model)

click image to enlarge

Both the post and lintel, and arch designs rely on the mass of the structural members to
resist the stresses of their loads.  To repeat, this is a very inefficient use of material which
contributes substantially to the dead weight of the structure itself. Modern designs optimize
the shape and arrangement of members to build more efficient structures.
As with columns, increasing the moment of inertia of a beam to increase its stiffness can be
achieved by placing as much of the beam's material at the outer edges of the beam's cross-
section, and eliminating as much material from the center, as is practical.  A modern beam
(or column) design that permits this is the I-beam, so named for its cross sectional shape.




a) Steel

b) Reinforced concrete

click image to enlarge

Fig. 148 - Typical I-beam designs  (demonstration models)


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Page 97 - Building stability - Arched beam, I-beam

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