The nonprismatic cantilever circular bar shown has an internal cylindrical hole of diameter d/2 from 0 to x, so the net area of the cross section for Segment 1 is (3/4)A. Load P is applied at x, and load P/2 is applied at x = L. Assume that E is constant.
(a) Find reaction force R1.
(b) Find internal axial forces Ni in segments 1 and 2.
(c) Find x required to obtain axial displacement at joint 3 of δ3 = PL/EA.
(d) In (c), what is the displacement at joint 2, δ2?
(e) If P acts at x = 2L/3 and P/2 at joint 3 is replaced by βP, find β so that δ3 = PL/EA.
(f) Draw the axial force (AFD: δ(x), 0 ‰¤ x ‰¤ L) and axial displacement (ADD: δ(x), 0 ‰¤ x ‰¤ L) diagrams using results from (b) through (d) above.

Transcribed Image Text:

Segment 1 Segment 2 Ri 3p 2 2 AFD 0 ADD 0