Figure 6-17.—Layout of lower end of cutout stringer.risers. For the stairway shown in figure 6-15, there are15 risers and 15 complete treads. Therefore, the total runof the stairway is equal to the unit run times 15, or 12 feet11 5/8 inches.In view B, only part of a tread is at the top of thestairway. If this method were used for the stairwayshown in figure 6-15, the number of complete treadswould be one less than the number of risers, or 14, Thetotal run of the stairway would be the product of 14multiplied by 10 3/8, plus the run of the partial tread atthe top. Where this run is 7 inches, for example, the totalrun equals 152 1/4 inches, or 12 feet 8 1/4 inches.In view C, there is no tread at all at the top of thestairway. The upper finish flooring serves as the toptread. In this case, the total number of complete treadsis again 14, but since there is no additional partial tread,the total run of the stairway is 14 times 10 3/8 inches, or145 1/4 inches, or 12 feet 1 1/4 inches.When you have calculated the total run of thestairway, drop a plumb bob from the header to the floorbelow and measure off the total run from the plumb bob.This locates the anchoring point for the lower end of thestairway.As mentioned earlier, cutout stringers for mainstairways are usually made from 2 by 12 stock Beforecutting the stringer, you will first need to solve for thelength of stock you need.Assume that you are to use the method of upper-endanchorage shown in view A of figure 6-16 to lay out astringer for the stairway shown in figure 6-15. Thisstairway has a total rise of 8 feet 11 inches and a totalrun of 12 feet 11 5/8 inches. The stringer must be longenough to form the hypotenuse of a triangle with sidesof those two lengths. For an approximate lengthestimate, call the sides 9 and 13 feet long. Then, thelength of the hypotenuse will equal the square root of 9^{2}plus 13^{2}. This is the square root of 250, about 15.8 feetor 15 feet 9 1/2 inches.Extreme accuracy is required in laying out thestringers. Be sure to use a sharp pencil or awl and makethe lines meet on the edge of the stringer material.Figure 6-17 shows the layout at the lower end of thestringer. Set the framing square to the unit run on thetongue and the unit rise on the blade, and draw the lineAB. This line represents the bottom tread. Then, drawAD perpendicular to AB. Its length should be equal tothe unit rise. This line represents the bottom riser in thestairway. You may have noticed that the thickness of atread in the stairway has been ignored. This thickness isnow about to be accounted for by making an allowancein the height of this first riser. This process is called“dropping the stringer.”As you can see in figure 6-14, view B, the unit riseis measured from the top of one tread to the top of thenext for all risers except the bottom one. For the bottomriser, unit rise is measured from the finished floorsurface to the surface of the first tread. If AD were cutto the unit rise, the actual rise of the first step would bethe sum of the unit rise plus the thickness of a tread.Therefore, the length of AD is shortened by thethickness of a tread, as shown in figure 6-17, by the6-13