----------------| | NOTE.--Two specimens of each were tested. All were fairly seasoned and | | without defects. The piece sheared off was 5/8 in. The single circular | | area of each pin was 0.322 sq. in. | |-----------------------------------------------------------
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TRANSVERSE OR BENDING STRENGTH: BEAMS
When external forces acting in the same plane are applied at right angles to the axis of a bar so as to cause it to bend, they occasion a shortening of the longitudinal fibres on the concave side and an elongation of those on the convex side. Within the elastic limit the relative stretching and contraction of the fibres is directly[9] proportional to their distances from a plane intermediate between them—the neutral plane. (N_{1} P in Fig. 15.) Thus the fibres half-way between the neutral plane and the outer surface experience only half as much shortening or elongation as the outermost or extreme fibres. Similarly for other distances. The elements along the neutral plane experience no tension or compression in an axial direction. The line of intersection of this plane and the plane of section is known as the neutral axis (N A in Fig. 15) of the section.
[Footnote 9: While in reality this relationship does not exactly hold, the formulae for beams are based on its assumption.]
[Illustration: FIG. 15.—Diagram of a simple beam. N_{1} P = neutral plane, N A = neutral axis of section R S.]
If the bar is symmetrical and homogeneous the neutral plane is located half-way between the upper and lower surfaces, so long as the deflection does not exceed the elastic limit of the material. Owing to the fact that the tensile strength of wood is from two to nearly four times the compressive strength, it follows that at rupture the neutral plane is much nearer the convex than the concave side of the bar or beam, since the sum of all the compressive stresses on the concave portion must always equal the sum of the tensile stresses on the convex portion. The neutral plane begins to change from its central position as soon as the elastic limit has been passed. Its location at any time is very uncertain.