Problem 4: A tapered structural steel rod varies linearly from one inch to ½ inch diameter. It is subjected to a 1.5 kip axial force as shown. Determine the change in length.
Solution: From Appendix B, the elastic
modulus is 29 x 106 psi. Because the diameter varies, the area
is a function of y. Replacing the usual summation (of PL/EA) by an integral,
where the 1.5 kips force acts on each element of length dL on a cross-sectional
area A, and noting that the equation of the right edge of the taper is 
,
