MecMovies 4.0 : M5.10: End-to-end Rods with Misfit

The figure shows a 6 inches long horizontal post labeled 1 on the left fixed to a rigid support on the left at A. A cylindrical rod B C of length 18 inches and labeled 2 is fixed to a rigid support on the right at C. A flange is shown at B. The gap between the post and the flange is one sixteenth of an inch.

Substituting the properties of the axial members into the equation:

Brass post $(1)$
$A_{1} = 0.60 {in.}^{2}$
$E_{1} = 16, 000 ksi$

Aluminum rod $(2)$
$A_{2} = 0.20 {in.}^{2}$
$E_{2} = 10, 000 ksi$

$F_{1} = \frac{0.0625 in .}{\frac{L_{1}}{A_{1} E_{1}} + \frac{L_{2}}{A_{2} E_{2}}} = \frac{0.0625 in .}{\frac{6 in .}{(0.60 {in.}^{2}) (16, 000 ksi)} + \frac{18 in .}{(0.20 {in.}^{2}) (10, 000 ksi)}} F_{1} = 6.49351 kips = F_{2}$