MecMovies 4.0 : M5.13: Rod and Post with Temperature Change

scene 8 of 15

The figure shows the free body diagram around the flange at B. The free body diagram cuts across the rod above and the post below. The axial forces on the rod and the post are F subscript 1 directed vertically upwards and F subscript 2 directed vertically downwards respectively. The parameters corresponding to the rod are A subscript 1, L subscript 1, alpha subscript 1 and E subscript 1. The parameters corresponding to the post are A subscript 2, L subscript 2, alpha subscript 2 and E subscript 2.

Substituting

$δ_{1} = \frac{F_{1} L_{1}}{A_{1} E_{1}} + α_{1} ∆ {TL}_{1}$

and

$δ_{2} = \frac{F_{2} L_{2}}{A_{2} E_{2}} + α_{2} ∆ {TL}_{2}$

into

$δ_{1} + δ_{2} = 0$

yields the compatibility equation:

$\frac{F_{1} L_{1}}{A_{1} E_{1}} + α_{1} ∆ {TL}_{1} + \frac{F_{2} L_{2}}{A_{2} E_{2}} + α_{2} ∆ {TL}_{2} = 0$