The tension in a single strand of wire

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Question from Gene:

Seeking an equation that calculates the tension in a single strand of wire or rope. Conditions: the wire is fixed at both ends, A known weight is suspended from the center of the span. The weight will displace the strand downward some distance Y. Let the distance between the fixed ends be X= 500mm. Weight W=0.5kg. Original tension in the strand is T= 10 newttons.Your help sincerely appreciated.

Gene,

The angle of declination of the wire is arctan(2Y/X) = arctan(Y/250).

If we can assume that the elasticity of the wire/rope obeys Hooke's Law, then the displacement triangle will be similar to the force vector triangle. So the hypotenuse of the force triangle can be calculated via the original tension and the cosine of this angle.

Hope this helps,
Gabe and Stephen.

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