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Engineering Stress on utility pole from weight on line?

I have a wooden 4"x4" pole that is 13' above ground to the attachment point of a service wire, and the wire is 60' long to the attachment point on the utility company's pole. Assuming the wire is more or less level, and weighs about .25 lb/foot, how much force is being applied to the 4"x4" pole at the attachment point? If a 50 lb. limb falls 20 feet onto the line 10 feet from the attachment point and catches on the line, how much is the force at the attachment point. What size pole would be necessary (pine) for it not to fail under these conditions? I don't know if I have included enough info to calculate this, but I am just trying to get a general idea of how this works.

Update:

Thanks Bill, I meant to say the ends were level and the wire would have some droop. I wouldn't install it without a guy wire, but was just trying to find out what types of forces would have to be countered. Does your calculation just find the force at the top of the pole, or how does it translate to the bottom at ground level?

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  • 9 years ago
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    If the wire is level, it is exerting a huge force on the pole. Better to have it droop a few feet, that lessens the force.

    The wire weighs 60 x 0.25 = 15 pounds.

    The force it exerts on the pole is something like 15 / sinθ where θ is the angle the wire makes with the horizontal. If it is at a 30º angle, sin 30 = 0.5, and the force is 30 pounds. If the angle is 10º, sin 10 = 0.17, and 15/0.17 = 86 lb.

    Adding the force of the limb, the weight is 15+50 = 65, and the force is 130 pounds, again assuming 30º angle. 10º and the force is 65/0.17 = 380 lb. Getting large.

    You need a guy wire, a wire from the opposite side of the pole to the ground, about 60 feet away.

    edit

    Bottom line, I don't think the strength of the pole is what is important, what matters is how it is set in the ground, as you will have a steady force pulling it in one direction. Over time, most any method will tend to allow the pole to tilt. Which is why you need an opposing guy wire.

    edit2:

    force at the bottom is a torque, a turning moment. if the force at the top is 200 lb and the height is 13 feet, the torque is 2600 foot-pounds.

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