Suitable for natural finishes Practically clear Generally clear and of high quality Suitable for paint finishes Adapted to high-quality paint finishes Intermediate between high-finishing grades and common grades, and partaking somewhat of the nature of both Common. Lumber suitable for general construction and utility purposes, often given various commercial designations. For standard construction use Suitable for better-type construction purposes Well adapted for good standard construction Designed for low-cost temporary construction For less exacting purposes Low quality, but usable Structural lumber is assigned modulus of elasticity values and working stresses in bending, compression parallel to grain, compression perpendicular to grain, and horizontal shear in accordance with ASTM procedures. These values take into account such factors as sizes and locations of knots, slope of grain, wane, and shakes or checks, as well as such other pertinent features as rate of growth and proportions

FIGURE 5.27 Unit shearing stresses on a beam cross section. 5.5.13 Shearing Stresses in a Beam The vertical shear at any section of a beam is resisted by nonuniformly distributed, vertical unit stresses (Fig. 5.27). At every point in the section, there is also a horizontal unit stress, which is equal in magnitude to the vertical unit shearing stress there [see Eq. At any distances y from the neutral axis, both the horizontal and vertical shearing unit stresses are equal to V v  Ay (5.59) It where V  vertical shear at the cross section t  thickness of beam at distance y from neutral axis I  moment of inertia about neutral axis A  area between the outermost fiber and the fiber for which the shearing stress is being computed y  distance of center of gravity of this area from the neutral axis (Fig. For a rectangular beam with width b and depth d, the maximum shearing stress occurs at middepth. Its magnitude is 12V bd2 3 V v  bd3b 8 2 bd That is, the maximum shear stress is 50% greater than the average shear stress on the section. Similarly, for a circular beam, the maximum is one-third greater than the average. For an I beam, however, the maximum shearing stress in the web is not appreciably greater than the average for the web section alone, if it is assumed that the flanges take no shear. 5.5.14 Combined Shear and Bending Stress For deep beams on short spans and beams made of low-strength materials, it is sometimes necessary to determine the maximum stress on an inclined plane caused by a combination of shear and bending stressv and , respectively. This stress , which may be either tension or compression, is greater than the normal stress. Its value may be obtained by application of Mohrs circle (Art. 5.3.6), as indicated in Fig. 5.10, but with y  0, and is 2   v2 
 (5.60) 2 2 5.5.15 Beam Deflections When a beam is loaded, it deflects. The new position of its longitudinal centroidal axis is called the elastic curve. At any point of the elastic curve, the radius of curvature is given by

Grades Width, in Thickness, in 2 and 3 4 Ft Fc 2, 3, and 4 1.5 1.5 1.5 1.15 Select 5 1.4 1.4 1.4 1.1 Structural, 6 1.3 1.3 1.3 1.1 No. 1 and better, 8 1.2 1.3 1.2 1.05 No. 1, No. 2, 10 1.1 1.2 1.1 1.0 No. 3 12 1.0 1.1 1.0 1.0 14 and wider 0.9 1.0 0.9 0.9 Stud 2, 3 and 4 1.1 1.1 1.1 1.05 5 and 6 1.0 1.0 1.0 1.0 Construction and Standard 2, 3 and 4 1.0 1.0 1.0 1.0 Utility 4 1.0 1.0 1.0 1.0 2 and 3 0.4 0.4 0.6 C
(12/d)1 / 9 (10.8) F 10.5.5 Beam Stability Factor Design values Fb for bending should be adjusted by multiplying by the beam stability factor CL specified in Art. 10.7.2. For glulam beams, the smaller value of CL and the volume factor CV should be used, not both. See also Art. 10.5.6. 10.5.6 Volume Factor Design values for bending Fb for glulam beams should be adjusted for the effects of volume by multiplying by 1 / x 21 12 5.125 C
K
      (10.9) V L L d b where L
length of beam between inflection points, ft d
depth, in, of beam b
width, in, of beam
width, in, or widest piece in multiple piece layups with various widths (thus, b  10.75 in) x
20 for southern pine
10 for other species KL
loading condition coefficient (Table 10.9) For glulam beams, the smaller of CV and the beam stability factor CL should be