Free way Sign Problem - Statics

[Naeem]

Q. The base of the freeway sign is attached to its foundation with four bolts.The four bolts must be able to resist the twisiting of the pole that is caused by the wind. Assume each bolt carries the same force. If the diameter of the bolt circle is 0.9m, calculate the horizontal (shear) force on each of the bolts due to the twisitng moment about the y - axis.

Let me describe, the measurements in the figure :

12.6 kN is the force of the wind on the sign.

10.5 k N is the weight of the sign acting downward

Distance from O to the positive direction of the x - axis is 5 m. (not indicated in the attached file )

Distance from O to positive direction of z is 9.75 m.

Please help me how to start this problem.

I hope the attached sketch helps you folks.

Thanks

 

[JoAuSc]

I don't quite understand the problem; I've taken physics classes but no engineering classes, so I haven't talked much about these types of problems. The sketch you attached is pretty unclear. The situation seems to be this: This freeway sign is like a stop sign in that it sticks straight up rather than sticking out. The base is circular and pretty large, being 0.9 m wide. Four bolts bolt down the edge of the circular base, each 90 degrees from its neighbors. A wind blows at the sign, producing a torque that gets transferred down to its base, causing a shear stress to be felt by the bolts. I don't know, though, how the wind would produce a torque seeing as the force on all parts of the sign is equal. I feel I'm missing important details here. What am I missing?

 

[Naeem]

I just typed out the question from the textbook as is.

The sign is hanging straight up in the x - z plane.

The wind blowing on the freeway exit sign and the weight of the sign are represented by point loadings acting at the center of the sign, as shown in the sketch. The force of the wind is 12.6 kN and the sign weighs 10.5 kN.

 

[Naeem]

yes, the 4 bolts on the circular base are 90 degrees from each other.

 

[JoAuSc]

I think I get what I was missing. The sign is 9.75 meters high, and it sticks out 5 m from the post. I'm still not sure what the size of the sign is, or if it matters. Because that information is not given in the problem, I'll assume you can treat the sign as a point particle.

First, you need to find the torque produced by the wind. Torque = lever arm * force. Now, the torque at the top of the post is transferred to the bottom of the post, so the bolts feel the same torque the post at the top does. For equilibrium (i.e., so the post doesn't start spinning around), a counter-torque needs to be exerted by the bolts. Equate the torque to the counter-torque, then find an expression for the counter-torque, then solve for the force on each bolt. Is this what you need to know?

 

[Naeem]

Well, this is what I found :

You can take a look at the attached file. Will this help us in finding the force on each bolt.