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A stairway is set to around 35 degrees, not 45. The stringer by itself(usually a 2x12) is actually weaker because it is notched to accept treads and risers. As a unit a staircase gets its strength from its "shear" values" laterally. This happens because the treads and riser boards add stability to lateral movement. Because a stairway is at an angle the downward force is transferred to the base of the stairs rather than distributing it on a flat surface such as a floor or ceiling, so in that case your less likely to break a stringer due to weight than you are a joist.
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