MecMovies 4.0 : M5.12: Temperature Effects in Axial Member

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The figure shows a rigid bar A B C pinned at A and supported at B by a wire labeled 1 of length 600 millimeters. The separation between A and B is 400 millimeters and the separation between B and C is 800 millimeters. A weight W is shown attached to the bar at C. The parameters listed on the top left are A subscript 1 which equals 2 square millimeters, E subscript 1 which equals 200 giga pascals and alpha subscript 1 which equals 12 times 10 to the negative 6 per degree Celsius. The right end of the rod marked C is deflected downward by 2.52 millimeters and the elongation of the wire at point B is v subscript B.

Only a portion of the elongation in wire $(1)$ is due to the force in the wire. Part of the elongation results from the temperature increase.

The relationship between internal force, temperature change, and deformation for an axial member is given by:

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