The diameter-changing section of a tower-type container is conical. Which end of this cone, the larger one or the smaller one, experiences greater stress?
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Interview questions for auditors in Changsha, October 27–28, 2015: The reduction section of a tower-type vessel is in the form of a cone. Which end of this cone, the larger one or the smaller one, is subjected to greater stress? And explain the reason?
Which end of the cone, the larger one or the smaller one, bears more stress? And explain the reason? ——Pressure and stress: assuming the pressure is the same, the object with a larger surface area experiences greater force. ——The change in diameter is necessary due to variations in load. It’s not the same amount of traffic; it has nothing to do with the saying that one person can hold off thousands of others.
Of course, the larger end bears more stress; since the pressure inside the tower is the same, the larger end has a greater area.
F=PA; when the pressure P remains constant, the greater the area A, the greater the force F； The wall thickness of the pipe elbow is determined based on the larger end.
The question the teacher asked was which end has greater stress. The stress on the smaller end is higher. When designing a tower, the moments generated by seismic and wind loads must be taken into consideration. For conical shells, they are generally not very tall; the bending moment values at the large and small ends of such shells are similar, but the area is proportional to the square of the diameter. Consequently, the axial stress resulting from bending moments is clearly greater at the smaller end than at the larger end. The axial stress values caused by internal pressure and vertical force are similar; it can be seen that for the combined axial stress, the value at the smaller end is higher.
It’s not just stress; there are also wind loads and seismic loads!
It’s large over long sections; the reason is first the circumferential stress of pd/2t, as the circumferential stress is high over such long sections； The axial stress is pd/4t; when converted to the conical shell, it becomes pd/4t cosα, so it is also quite large ； The bending moment is the same as well
When it comes to towers, does one also need to consider axial forces resulting from bending moments and the weight of the equipment itself? How to overlay? Should the issues of secondary stresses at the large and small ends as well as at the cylinder body also be considered? I’ve thought about this question for a long time and really don’t know how to answer it.
Regarding the stress on a regular conical shell that I mentioned earlier, when it is part of a tower structure, it is necessary to take into account the bending moment M/W, where W∝d³. When the bending moments are similar, the sections should be larger in those areas. As for the axial force F/S, where S∝d², the sections there should also be larger； Additionally, the internal pressure can be ignored in comparison to the external torque and gravity; therefore, at this point, it should be a short segment with a large value
Can the internal pressure be ignored compared to the external torque and gravity? ? ? What’s the reason for this sentence? When there is an axial force, it is also necessary to consider whether it is compressive stress or tensile stress.
Indeed, this statement may not be very specific; for specific issues, you can do the calculations by yourself. The pressure on ordinary towers isn’t very high (it’s quite low in simple calculations). As for tension and compression, it’s not something that can be determined easily, as bending moments also play a role. You might want to look up information on towers on your own, taking into account principles of mechanics of materials! It’s pointless to keep fixating on one thing.