Beam on elastic foundation analysis of TIMOSHENKO

[401laurent]

Dear All,
I'am designing a Presssure vessel, with conical head with
angle greater than 30 deg., ASME code doesntgive formulas for Head calculations,it refer to Beam elastic foundation analysis of TIMOSHENKO on Appendix L.
Could some one give me reference and explanation for this issue,
Thanks.

 

[TomBarsh]

Briefly, you must equate the displacements and rotation of the end of the cone and the end of the cylinder so that there is continuity of the structure. The local bending and membrane stresses are distributed over regions in the cone and cylinder determined by the "beam on elastic foundation" principle.

"Pressure Vessel Design Handbook" by Henry Bendar has a good numerical example of this calculation. See "Formulas for Stress and Strain" by Roark and Young for a more extensive, detailed numerical example.

 

[JStephen]

See Timoshenko's "Theory of Plates and Shells" for another reference. I'm not familiar with the cone design, but the elastic-foundation equation is used for cylindrical shells as well. I think Timoshenko's Strength of Materials books had a good bit on the actual beam-on-elastic-foundatioon problem.