QUESTION 5 Figure below depicts a tapered elastic bar subjected to an applied tensile load P at one end and attached to a fixed support at the other end. The cross-sectional area varies linearly from A, at the fixed support at x = 0 to A/2 at x = L. Calculate the displacement of the end of the bar (a) by modeling the bar using three bar elements of equal length having cross-sectional area equal to the area at the midpoint along the element length, (b) using four bar elements of equal length and similarly evaluating the area at the midpoint of each, and (c) compare displacements and stresses against the exact values defined as: the displacement of the end: 8-1.386- PL A.E VITE A(X) = A (1-2) the stress distribution in the bar: (a) A= 0.74 σ(x)=- (b) (a) tapered axial bar, (b) one-element model, (c) two-element model (c) P 2L

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