These are usually placed 16 inches from centers, except for floors which are to carry very heavy weights. In these the joists are frequently placed 12 inches from centers. To estimate them 12 inches from centers add 1 to the number of feet in length of one wall on which the joists are placed. For example, suppose a building is 32 feet long, and the joists are placed 12 inches from centers. We simply add 1 to 32, which makes 33 the number of joists required for one span. If there are similar spans it will only be necessary to multiply by the number of spans. If the spans are unlike, then estimate each span separately. If the joists are placed 16 inches from centers, then multiply the length of wall by ½ and add 1. This will give the required number. Thus if the wall is 32 feet long, then 32 x ½ + 1 = 25, he number required for one span. The reason for adding 1 is because the first operation, that of multiplying by ½ gives the number of spaces between joists, and one joist more than there are spaces is always required, except in cases where the sills serve the place of a joist. In such a case the exact number will be one less than the number of spaces. A few extra joists are usually required for doubling and framing headers around stairways, chimneys, etc. A little attention given to a plan will show the number required for this purpose. Ceiling joists, collar beams and rafters may be estimated in the same manner.