I need to build a stairway down a slope between terrace levels in my back yard. The major dimensions are 103" rise and 239" horizontal run. I have downloaded an excellent software tool to calculate the proper rise and run per step. The software calls for cutting the steps in a 2" X 12" and results in leaving 5 1/8" of the 2x12 at the bottom. I plan to use 3 stringers. Does this cut leave enough web to safely support the stairs? Must there be a support pier in the middle of the run?