Originally Posted by desconhecido

When you pull on a spoke, it elongates in accordance with the stress-strain relationship of the material that it is made out of. The parameter which ties stress(think of this as tension) to strain (think of this as elongation or compression) is called Young's modulus, or the modulus of elasticiity. So, for a stainless DT spoke, the modulus is a constant. The variables that tie stress to strain are the cross sectional area (pi r^2) and the length of the section you are considering. So, if you are looking at a particular length of 14 gauge spoke from the hub out, the only thing that controls how much it stretches or contracts is how much the tension changes. The length is the same, the area is the same, and the modudlus is the same, so for a given tension change, the length change is the same. If the rate that tension changes is small with respect to the speed of sound in the material, you can consider the tension in an element like a spoke to be constant. That's the case in a bicycle wheel. So, when you pull on a spoke from the ends, tension is constant everywhere within the spoke -- either in the fat sections or the skinny middle section.

Back to the fat section near the hub of the butted spoke: when you pull on that spoke with a force of 100 units, the fat section will lengthen by the same amount that the same length section of a straight gauge spoke will elongate. Just because the middle section stretches more in a butted spoke doesn't change the behavior of the unbutted portion -- if the tension change is the same.