Bending stresses at base of tapered padeye/beam 1

[tnteng]

I uncovered something that I may have overlooked in past design calculations. The question comes up when analyzing the stresses on a tapered padeye (with a long base to hole dimension) or on a tapered beam. The tapered member is loaded perpendicular to the longitudinal axis of the member. For the padeye, what I have done in the past is calculated the radius needed around the hole of the padeye (based on allowable tearout stress) and calculated the section height needed at the base of the padeye (based on allowable bending stress). Then I simply would make the taper line from the base to the tangent of the radius around the hole. My assumption was that the max bending stress was always going to be the largest at the base of the padeye. I have now found that not to be the case - that there are sometimes bending stresses that are higher at some intermediate point between the base and the hole. The same problem holds true for tapered beams.

Can anyone let me know have they have handled that issue in calculations? Is there a formula that will give the taper angle (as a function of the height of the section) that is needed in order to assure that the max stress is at the base of the padeye/beam? I saw a formula in appendix F of the ASD spec that possibly could be used. How would I use that formula to determine "dL" the depth at the larger end of the member?

Thanks in advance for any help with this problem.

Tony Billeaud
Mechanical Engineer



Tony Billeaud
Mechanical Engineer

 

[Heckler]

Tony,

You might want to pick up a copy of Roark's Formulas for Stress & Strain. I have the sixth addition, section 7.8 covers beams of variable section and section 8.0 covers curved beams.

Best Regards,

Heckler
Sr. Mechanical Engineer
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[vonlueke]

tnteng: If you want the maximum bending stress to be located at the tapered cantilever fixed end, then you would need to have a taper angle (relative to a horizontal line) on each edge (top and bottom edge) less than or equal to alpha = atan(0.5*ho/L), where ho = beam depth at cantilever tip (or lug width at hole centerline), and L = beam length.

 

[tnteng]

Vonlueke,

Can you provide any info on the orgin or derivation of the formula you have provided? If the top of the beam is horizontal and only the bottom has the taper then the height of the base would need to be no taller than twice the height of the beam at the tip - correct?

Thanks,

Tony Billeaud
Mechanical Engineer

 

[vonlueke]

tnteng: That's correct; well said. There's no requirement that it be perfectly symmetric. Unfortunately I don't have time to derive it here, but since you have my answer, you can plot it and otherwise prove to yourself whether or not the answer is correct.