To sum up, the strength of a simply supported solid beam to resist bending due to a load

applied to its middle (the simplest case) is a function of its:

     - height squared -  e.g. height doubled, strength quadrupled, stresses reduced by four;

     - span - e.g. span doubled strength halved;

     - width - e.g. width doubled strength doubled;  and

     - modulus of elasticity - e.g. modulus doubled strength doubled.


Post and lintel construction


Wood has been a preferred material for making beams because of its good compressive

and tensile strength, provided that the beam is cut parallel to the wood's grain.  However,

wood can rot, burn, and be attacked by insects.  Ancient builders preferred to use stone for

building structures that were meant to last for the ages.  A popular design for masonry

structures comprised of simply supported, hewn stone beams is called post and lintel

construction.  Ancient Egyptian, Greek, and Roman architects made extensive use of this





Fig. 145 - Post and

lintel construction

(scale visualization model)

click image to enlarge



type of construction to support the roofs of temples and public places.  However, while

stone has high compressive strength, it is comparatively weak in tension.  The fact that the

greatest tensile stresses are concentrated in the midpoint of the bottom edge of a beam

causes a disproportionate reliance on the tensile strength of this small area.  This grossly

underutilizes most of the beam's other mass.  As a result the lintels had to be made

especially thick and wide in order to increase the amount of mass they had to resist these

tensile stresses.  This increased their own dead weight, which significantly reduced the

distance they could reliably span to about eight feet on average.  As a consequence, Greek

temples, like the Parthenon, were so crowded with columns that there was not much room

for crowds to gather inside.  One solution to using stone beams to span longer distances

was the to arch them.


Arched beams



The Romans used the stone arch extensively to provide for open

areas in buildings as well as to bridge obstructions and channel

water across valleys.  An arch can be imagined as being

assembled from wedge shaped sections of stone, called

voussoirs, that are cut out of a beam and then rearranged into

the shape of an arch.  This reduces the distance any one section

click to enlarge


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Page 96 - Building stability - Lintels and arches

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