MecMovies 4.0 : M5.5: Rod and Post in Series

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The figure shows a vertical rod A B labeled 1 attached to a vertical post B C labeled 2 by a flange at B. The length of member 1 is 1500 millimeters and the length of member 2 is 1000 millimeters. The load at B is P which equals 110 kilo newtons directed vertically downwards. The parameters corresponding to member 1 are A subscript 1, L subscript 1 and E subscript 1. The parameters corresponding to member 2 are A subscript 2, L subscript 2 and E subscript 2. The rod is attached to a rigid support at A and the post is attached to a rigid support at C.

Compute the deformation of member $(1)$ from the relationship between force and deformation:

$δ_{1} = \frac{F_{1} L_{1}}{A_{1} E_{1}} = \frac{(27, 500 N) (1, 500 mm)}{(800 {mm}^{2}) (200, 000 N / {mm}^{2})} = 0.258 mm$

The positive deformation means that member $(1)$ gets longer. Since member $(1)$ is attached to a fixed support at $(A)$ , it can only get longer if flange $(B)$ moves downward. Therefore, flange $(B)$ deflects downward by $0.258 mm$ .