9. Consider a tapered bar of circular cross-section. The length of the bar is 1 m, and the radius varies as r(x) = 0.050 - 0.040a:, where r and x are in meters. Assume Young's modulus = 100MPa.

Both ends of the bar are fixed, and F = 10,000 N is applied at the center. Determine the displace¬

ments, axial force distribution, and wall reactions using four elements of equal length.

F= 10,000N-

• L = 1 m -

Hint: To approximate the area of cross-section of a bar element, use the geometric mean of the end areas of the element, i.e. = ^/AjAj = nrtrj.