Building Design and Construction Handbook - Merritt - Ventech!

STRUCTURAL THEORY 5.31
FIGURE 5.11 Simple beam. FIGURE 5.12 Cantilever beam.
FIGURE 5.13 Beam with one end fixed. FIGURE 5.14 Fixed-end beam.
FIGURE 5.15 Beam with overhangs. FIGURE 5.16 Continuous beam.
The beam in Fig. 5.11 is called a simply supported, or simple beam. It has
supports near its ends, which restrain it only against vertical movement. The ends
of the beam are free to rotate. When the loads have a horizontal component, or
when change in length of the beam due to temperature may be important, the
supports may also have to prevent horizontal motion. In that case, horizontal restraint
at one support is generally sufficient.
The distance between the supports is called the span. The load carried by each
support is called a reaction.
The beam in Fig. 5.12 is a cantilever. It has only one support, which restrains
it from rotating or moving horizontally or vertically at that end. Such a support is
called a fixed end.
If a simple support is placed under the free end of the cantilever, the propped
beam in Fig. 5.13 results. It has one end fixed, one end simply supported.
The beam in Fig. 5.14 has both ends fixed. No rotation or vertical movement
can occur at either end. In actual practice, a fully fixed end can seldom be obtained.
Some rotation of the beam ends generally is permitted. Most support conditions
are intermediate between those for a simple beam and those for a fixed-end beam.
In Fig. 5.15 is shown a beam that overhangs both is simple supports. The overhangs
have a free end, like cantilever, but the supports permit rotation.
When a beam extends over several supports, it is called a continuous beam
(Fig. 5.16).
Reactions for the beams in Figs. 5.11, 5.12, and 5.15 may be found from the
equations of equilibrium. They are classified as statically determinate beams for
that reason.
The equations of equilibrium, however, are not sufficient to determine the reactions
of the beams in Figs. 5.13, 5.14, and 5.16. For those beams, there are more
unknowns than equations. Additional equations must be obtained on the basis of
deformations permitted; on the knowledge, for example, that a fixed end permits
no rotation. Such beams are classified as statically indeterminate. Methods for
finding the stresses in that type of beam are given in Arts. 5.10.4, 5.10.5, 5.11, and
5.13.