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 deflection of $C$ relative to the support is the sum of the deformations in segments $(1)$ and $(2)$ :

$u_{c} = δ_{1} + δ_{2}$

The deformation in segment $(1)$ is $δ_{1} = 2.86 mm$ . Set $u_{c} = 5 mm$ and solve for the allowable deformation in segment $(2)$ .

$5 mm = 2.86 mm + δ_{2} ∴ δ_{2} = 2.14 mm$