MecMovies 4.0 : M5.3: Deformation of a Compound Axial Member

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The figure shows a compound axial member consisting of a larger cylindrical segment A B which is marked 1 having a length of 1800 millimeters flanged to another cylindrical segment B C which is marked 2 having a length of 800 millimeters. Segment 1 is fixed to a wall at the point A. The x axis is taken along the common axis of the two cylindrical members and the y axis is taken perpendicular to the x axis along the wall. The tension load at the free end of segment 2 is P which equals 50 kilo newtons oriented in the positive x direction.

The maximum elongation that is acceptable for segment $(2)$ is $δ_{2} = 2.14 mm$ . Rearrange the axial force-deformation equation to solve for the minimum acceptable area $A_{2}$ .

$A_{2} = \frac{π}{4} d^{2}$

$∴ d^{2} = \frac{4}{π} A_{2} = \frac{4}{π} (267.02 {mm}^{2}) = 339.98 {mm}^{2}$

$d = 18.44 {mm}^{}$