A bar ABC of length L consists of two parts of equal lengths but different diameters. Segment AB has diameter d1 = 100 mm, and segment BC has diameter d2 = 60 mm. Both segments have length L/2 = 0.6 m.
A longitudinal hole of diameter d is drilled through segment AB for one-half of its length (distance L/4 = 0.3 m). The bar is made of plastic having modulus of elasticity E = 4.0 GPa. Compressive loads P = 110 kN act at the ends of the bar.
(a) If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter dmax of the hole? (See figure part a.)
(b) Now, if dmax is instead set at d2/2, at what distance b from end C should load P be applied to limit the bar shortening to 8.0 mm? (See figure part b.)
(c) Finally, if loads P are applied at the ends and dmax = d2/2, what is the permissible length x of the hole if shortening is to be limited to 8.0 mm? (See figure part c.)

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