## Existing Wood Beams

Calculate the maximum span for a built up beam consisting of 4-2x8 wood sections. The actual size of the 2x8’s is 1-7/8” x 8” which is larger than the 2x8’s considered in the OBC Part 9 tables which are 1 ½” x 7 ¼”. The beams actual size is used to calculate the section modulus (S) and the species of the wood (Douglas fir) is used to determine the extreme fibre bending stress (fb). This information can now be used to calculate the beams maximum load carrying capacity.

Figure 1   Section through a built up wood beam

Use the excel sheet below to make various calculations. The red shaded numbers are meant for input. You should just be able to tap on the cell you want to change or click it with a mouse. The numbers in black are formulas. Unfortunately, because the online version of this sheet cannot be locked, the sheet is unprotected. This means that all or none of the cells are protected. In this case, in order to allow the user to make calculations, all cells can be changed, including the ones with formulas. If you do this simply reload the page to start over. Changes are not saved.

Wood type is Douglas fir. Use extreme fibre bending stress from tables and multiply by repetitive use factor (Cr) of 1.15 to obtain a design value for extreme fibre bending stress [1]

## Old and New Lumber

Figure 2 Compare Old and New lumber

The size of an old piece of lumber may be larger than the sizes that are indicated in the current building code which are based on newer sizes. In the example above, compare an old 2x8 with a new one. In common language, we call both of these things a 2x8 and this refers to its nominal dimension. When doing structural calculations, the actual size needs to be considered. In this case, use the actual dimensions of the 2x8 pieces shown above to calculate the Section Modulus of each shape.

The Section Modulus for the old 2x8 is larger than one might have thought. Take a 75 lb design load and see how each joist performs under similar conditions

Figure3  Compare spanning capabilities of old an new floor joist

The old 2x8 can span approximately 2 feet further under than the new 2x8 joist under similar loading conditions spaced at 16 inches on centre

[1] From Canada Wood Council publication on design values for visually graded lumber. Listed values show 1620 psi for select structural Douglas fir and 1380 psi for no. 1 and better. Repetitive use value (Cr) of 1.15 is used for beams consisting of 3 plies or more