Beam Loading

When a load is applied to a simple beam, the beam tends to bend. As the beam bends or flexes, the fibers along the bottom surface of the beam are stretched (put in tension), and the fibers along the top surface of the beam are pressed together (compressed). It is important to remember that the opposite is true for a cantilever beam. with a cantilever beam, the top stretches and the bottom is compressed.

As the fibers of a beam stretch, a stress is set up in the fibers. When beam loading and fiber stretching proceed to a point where the fibers yield, the maximum allowable fiber stress (S) has been exceeded. Estimates for maximum allowable stress are available for most materials, and values for maximum allowable fiber stress of wood can be found in Appendix XI.

The shape of a beam and the way that it is positioned to carry a load greatly affect its load-carrying ability. The common sawing method for boards results in boards that are flat sawn, the grain of the wood tends to be parallel with the long dimension, Figure 24.2. A flat sawn beam will support more weight on edge than when placed flat.

The dimensions of a beam (width and depth) are used to determine the section modulus, which provides an index of the relative stiffness or load-carrying ability of the member.

FIGURE 24.1. Two types of beams and two types of loads.

Two Load Bearing Beams Side Side
FIGURE 24.2. Relative strength of lumber oriented with the shortest dimension parallel to the load (on its side) and the shortest dimension perpendicular to the load (on its edge).

For a rectangular cross-section member, the section modulus is determined by using the following equation:

where K = Section modulus (in3); a = Width of member, horizontal dimension (in); b = Depth of member, vertical dimension (in).

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