Bending Moment on Pole due to Wind

[derek88]

Hello Friends.

I have a question for the following scenario:

There are two wooden poles, both set into the ground so that they are sticking straight up. The height of Pole One is H1 feet. The height of the Pole 2 is H2 feet. Supported in between these two poles is a wire. The ends of the wire is attached to the top of each pole. The wire has a total length of L and is pretty straight.

Now imagine that a wind is blowing, exactly perpendicular to the wire. What is the bending moment at the base of Poles 1 and 2 due to this wind blowing on the wire? (Please ignore the bending moment due to wind blowing on the pole surfaces). Assume the wind loading on the conductor is W lbs/foot.

My idea: I think that if the attachment height at the poles were the same, let's say "H", then the moment at the base of each pole would be: (H)(W)(L)(0.5). But when the attachment heights are different, I don't know how to calculate that! Any help is tremendously appreciated! Thanks!

 

[AndyW]

Hello there,

Thank you for your question. I can provide some insight into the bending moment at the base of Poles 1 and 2 due to the wind blowing on the wire.

Firstly, it is important to note that the bending moment is a measure of the internal forces and stresses within a structure, in this case the poles. It is defined as the product of the force applied and the distance from the point of application to the axis of rotation.

In this scenario, the wind is the external force acting on the wire, and the poles are the structure that will experience the bending moment. The bending moment at the base of each pole can be calculated by considering the forces acting on the wire and the poles.

Assuming that the wire is relatively straight and the wind is blowing perpendicularly, the force acting on the wire can be calculated using the formula F = W*L, where W is the wind loading and L is the length of the wire. This force will be acting in the direction of the wind.

Next, we need to consider the reaction forces at the top of each pole. Since the wire is attached to the top of each pole, there will be a reaction force acting in the opposite direction of the wind, equal to the force acting on the wire.

Now, to calculate the bending moment at the base of Pole 1, we need to consider the distance between the point where the force is applied (top of the pole) and the axis of rotation (base of the pole). This distance is the height of the pole, H1. Therefore, the bending moment at the base of Pole 1 would be M1 = F * H1.

Similarly, for Pole 2, the bending moment at the base would be M2 = F * H2.

In summary, the bending moment at the base of each pole can be calculated by multiplying the force acting on the wire by the height of the respective pole. I hope this helps. Let me know if you have any further questions.