## Dimensioned Lumber

The lumber industry uses two different sizes, nominal size and actual size. The nominal size is the dimensions of the lumber after it is sawed. The actual size is the size of the lumber after the surfaces have been finished. Finishing removes material, therefore the actual size is smaller than the nominal size, Table 24.1. Lumber is purchased using the nominal size, but the actual size must be used for beam calculations. An additional term may also be used and that is rough sawed or unfinished. When calculating beams using rough sawed or unfinished lumber, the actual size is the nominal size.

Problem: What is the section modulus for a 2 x 4 standing on edge? Solution: Section modulus is calculated on actual size. Therefore:

To save time and eliminate one step in the calculations, Table 24.1 lists values for the section modulus of several common sizes of 2-inch (thick) lumber. Note that

Table 24.1. Section modulus of rectangular members.

Section modulus for position (in3)

 Nominal size (in) Actual size (in) On edge Flat 2 ; 2 1.50 > 1.50 0.56 0.56 2 ; < 3 1.5 > 2.50 1.56 0.94 2 < 4 1.5 > 3.50 3.06 1.31 2 < 6 1.5 > 5.50 7.56 2.06 2 < 8 1.5 > < 7.25 13.14 2.72 2 x : 10 1.5 < 9.25 21.39 3.47 2 x : 12 1.5 < 11.25 31.64 4.22 2x 14 1.5 > 13.25 43.89 4.97

in Table 24.1, the section modulus for a 2 x 4 on edge is 3.06. The nominal size (what one asks for at a lumber yard) and the actual size (the actual dimensions of the lumber) are shown. The section modulus is calculated for the actual size. Two columns of values are shown for the two possible positions of a memberâ€”standing on edge and lying flat. Notice that the values for the section modulus are much greater when the member is standing on edge, as it is much stiffer in this position.

The amount of weight that a beam can support is determined by the section modulus, allowable fiber stress, beam span or length, type of load, and type of support. For the two types of beams and loads being considered in this chapter, the following equations apply:

Cantilever beam, uniform load: W =-

j where W = Maximum allowable load on the beam (lb); S = Allowable fiber stress (lb/in2); L = Length or span of beam (in); K = Beam section modulus (in3).

Problem: What is the maximum point load that can be supported in the middle of a

4 x 6-inch, rough sawed (dimensions are the actual dimensions of the board) simple beam 120 inches long when the allowable fiber stress is 1,500 lb per square inch?

Solution:

4SK 4 x U00-224in

L 120 in

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