Beams are the horizontal members used to support vertically applied loads across an opening. In a more general sense, they are structural members that external loads tend to bend, or curve. Usually, the term beam is applied to members with top continuously connected to bottom throughout their length, and those with top and bottom connected at intervals are called trusses.

There are many ways in which beams may be supported. Some of the more common methods are shown in Figs. 5.11 to 5.16.

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.

Related post


Post a Comment