where m is the total number of truss members, j is the total
number of joints and r is the number of reactions (equal to 3
generally) in a 2-dimensional structure.
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the American River. At that time, some said it was the finest bridge in
the country. For the first few years there were few automobiles that
needed to cross its narrow span and it was not designed to carry the
weight but after the turn of the century the need for a bridge for
automobiles became more evident. The Truss Bridge was abandoned in 1917
when the 
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Why the
diagonals
The Pratt
(and Howe) trusses
It is now
possible
Structurally, the main problem for any building is how to keep the roof from falling. Most early buildings were simple domes, with roof and walls a single entity. It was not clear where the walls stopped and the roof began. Probably this method started in imitation of huts built by tying together bent saplings rather than as a conscious engineering choice, but it was still effective. All buildings must contend with outward forces on walls, but forces on domed buildings are at an angle instead of directly outward. As domes grow larger, the outward component tends to overwhelm the downward component that is holding the wall together.
One-roomed domed houses were eventually abandoned in most cultures for buildings with vertical walls and flat roofs. The first rectangular buildings were sized by the length of available wooden beams that could be used as the basis of the flat roof. The force of the roof was directed down on the walls, which could be joined to the roof for greater security. Several rooms could also be built adjacent to each other to make a larger building.
Later, builders introduced columns in the interiors of rooms to hold up the ends of some beams, allowing construction of larger rooms. Horizontal beams above windows and doors that support walls are called lintels, so construction that relies on beams held up by columns is often called post-and-lintel construction. Post-and-lintel construction was the basis of most Egyptian and Greek architecture, even the famous Greek temples. It is still used today, along with other construction techniques.
Early dome houses built from bricks had each layer of brick run in a circle of a somewhat smaller radius than the one below it, with each brick resting partly on the lower course and partly cantilevered off into space. A section (slice) across such a building is called a corbeled arch. A true arch uses wedge-shaped bricks or blocks; the result in its simplest form is a semicircle. Although both the corbeled arch and the true arch were known to the builders of the earliest civilizations, a devotion to mass-produced rectangular solids for most construction meant that the corbeled version was much more common. The Romans, on the other hand, preferred the greater structural strength of the true arch, and also tended, even for rectilinear structures, to use bricks and stones that were wedge shaped.
The arch is one of the hallmarks of Roman architecture. Even after concrete replaced brick and stone as the basic building material, Roman builders favored arches. Most Roman arches have semicircular or curved tops placed on vertical columns. Because the curved top directs some force laterally, as well as vertically, such arches often need some support from the sides. While this can be supplied in many ways by one sort of buttress or another, Roman builders often used additional arches for support, resulting in several arches in a row (called a course). The columns on the outside of such a course still needed some sort of buttress to withstand the lateral forces.
A relief picture on a column raised to honor Emperor Trajan's victory over the Dacians in 105 ce reveals that the Romans also knew another construction method, that of the truss. The truss is a brace that forms a triangle, the only rigid polygon. Trusses eventually became a major feature of construction. Frameworks of trusses hold up many older bridges still in use today and are part of the construction of all houses with peaked roofs. The truss does more than simply support the roof in such houses, for it also spreads the stresses in different directions.