Deflection thin wall arch
Deflection thin wall arch
(OP)
I am currently designing a project that uses a thin walled cylinder and was asked to come up with the following info.
I started to solve the problem but feel I may be in left field because of the thickness of the cylinder.
I have a thin wall cylinder (.874" I.D. & .020" wall). The I.D. of the cylinder contacts 20 equally spaced .0625 diameter pins. The pins are in a fixed position that are assumed not to move. I will provide a uniform pressure to the O.D. of the cylinder to deflect the arch between the pins .005"
See attachment for illustration.
I need to determine the pressure required to deflect the cylinder or arch .005" between the pins and determine the stress when deflected.
I started to solve this problem by analyzing the cylinder between pins as shown in section Z-Z (see of attached drawing.)
Because of symmetry I was able to divide the section in half and use Castigliano's Method which I plugged in the deflection and solved for the force. I came up with a calculated resultant force of 2,881 lbs. If I use deflections formulas for straight beam with both ends fixed I come up with similar results. I was going to continue by calculating the maximum bending stresses both compression and tension and transverse shear stress.
I was told originally I may be able to solve this by using hoop stress calculations by finding the difference in length and solving. In the segment between pins I come up with .0005" difference before and after compressed. This method gave me a calculated resultant force of 1,044 lbs.
Any info on the proper method to solve this problem or examples would greatly be appreciated.
I have reviewed Roark's and all the engineering books I could find, but do not know enough about the exceptions to rules.
Thanks in advance.
Nickjk
I started to solve the problem but feel I may be in left field because of the thickness of the cylinder.
I have a thin wall cylinder (.874" I.D. & .020" wall). The I.D. of the cylinder contacts 20 equally spaced .0625 diameter pins. The pins are in a fixed position that are assumed not to move. I will provide a uniform pressure to the O.D. of the cylinder to deflect the arch between the pins .005"
See attachment for illustration.
I need to determine the pressure required to deflect the cylinder or arch .005" between the pins and determine the stress when deflected.
I started to solve this problem by analyzing the cylinder between pins as shown in section Z-Z (see of attached drawing.)
Because of symmetry I was able to divide the section in half and use Castigliano's Method which I plugged in the deflection and solved for the force. I came up with a calculated resultant force of 2,881 lbs. If I use deflections formulas for straight beam with both ends fixed I come up with similar results. I was going to continue by calculating the maximum bending stresses both compression and tension and transverse shear stress.
I was told originally I may be able to solve this by using hoop stress calculations by finding the difference in length and solving. In the segment between pins I come up with .0005" difference before and after compressed. This method gave me a calculated resultant force of 1,044 lbs.
Any info on the proper method to solve this problem or examples would greatly be appreciated.
I have reviewed Roark's and all the engineering books I could find, but do not know enough about the exceptions to rules.
Thanks in advance.
Nickjk






RE: Deflection thin wall arch
Also, a 2D or 3D FEM model can give further assurance.
RE: Deflection thin wall arch
Also, upon compression and since seating upon a polygonal array of unyielding supports, hoop stresses are simply not possible, because the reaction supports take out the problem of such solution. Arches or plate arches fixed at the supports are correct, from symmetry. And then everything of what above.
RE: Deflection thin wall arch
In the first site below, under Arches -> Circular -> Fixed-fixed -> Unif.rad.load , you find a sheet for calculating stresses and deflections for such an arch.
However the Roark also has it, it is, in my 5th Ed., case 5h of Table 18; it doesn't provide general stress and deformation equations though.
prex
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RE: Deflection thin wall arch
I would like to thank ishvaaag and prex for your help and support. Yesterday was spent trying to prove how a certain theory would apply to this application. prex I hope to dive into your suggestions this weekend.
This forum is such a powerful tool with brilliant minds on hand. Just wanted to let you know how much your support is appreciated.
Thank you again.
Nickjk