Bending of a curved beam to protect a tank nozzle

[dave319]

In the tank building industry some pressure vessels use curved pieces of flat bar, welded to the tank, to protect nozzles in the event that the tank rolls. I'm trying to determine how thick the flat bar should be for a given length so that it won't bend too much and allow a nozzle to be damaged (this could result in a leak). I initially made a lot of simplifying assumptions using simple beam bending equations but the amount of deflection I got didn't make any sense.

The 500 gal tank when full has a total mass of about 4000 kg. I decided to be more conservative and be a little easier on myself by assuming that the tank is actually being dropped from the height of its diameter instead of rolling. The diameter is about 1 m. This results in a velocity of about 4.43 m/s at the point of impact with the ground. The kinetic energy is 39250 J.

Next I accounted for a maximum allowable deflection of about .1 m (roughly 4 inches) and the cage will experience a force of 392500 N. This will provide enough clearance for the nozzle and is about 30 g's.

Since my background is chemical engineering not structural or mechanical, the next step of determining how thick the piece of flat bar needs to be is a little beyond my expertise being that I don’t believe it can be treated as a simple beam. I have attached a picture to help illustrate what I've written above. I appreciate your input.

 

[Travis_King]

Unless I'm mistaken, you don't have just a flat piece of metal, you have a structure. At least, if I'm reading the drawing correctly.

In that case, you'll have to do some more math to determine the reactions at the various points along the structure.

 

[dave319]

Yes you are correct. I'm interested in the behavior of the flat bar that has been curved and welded to the tank to create a type of cage. A simplifying assumption would be that the force is directed at the center of the curved bar (L/2). This is a little beyond the statics/dynamics class I took so if you can point me in the right direction I'd really appreciate it.