Support Lug Calcs per Bednar 1

[julesomar]

I am trying to check some support lug calcs using Pressure Vessel Design Handbook, 2nd Ed. by H. Bednar.

On page 156, there is a "maximum stress in base plate" equation which has a variable Beta. This is followed later by a line with "For 15/12 = 1.25, Beta = 0.72", where 15 is the radial width of the base plate, and 12 is the corresponding width of the support member beneath.

Can someone advise on this 'Beta' variable and how it is calculated / found?

Thanks.

 

[doct9960]

The "beta" is found in Roark's Formulas for Stress and Strain, Table 11.4 (Formulas for flat plates w/ straight boundaries & constant thickness), Case 2a.

 

[julesomar]

Thanks doct9960.

Can anyone elaborate on this? I don't have access to that book, will have to try and borrow it. Is it a formula or just tabulated values of 'Beta' to choose from?

 

[doct9960]

On page 156 of Bednar's book, did you notice [46] beside "maximum stress in base plate"? Go to Appendix A9 of Bednar and see what is listed under #46...the Roark's book.

On page 154 of Bednar, read the second sentence at the top of the page. I don't have the Bednar book at the moment, but if recall it, I think it says that to check for the stress on the base plate, consider a uniformly loaded flat plate with one edge free and three edges supported.

Roark's (7th Edition) Table 11.4, Case 2a shows formulas and coefficients for a rectangular plate (three edges simply supported, one edge free) with a uniform loading over the entire plate.

I will try to post that particular page from Roark's.

 

[doct9960]

See Case 2 (Rectangular plate; three edges simply supported,
one edge (b) free) and Case 2a (Uniform under entire plate).

By interpolation, you will get a moment coefficient "beta" of 0.72 for a/b=1.25

 

[julesomar]

Thanks doct9960.

I am still not clear on one item. The example uses "12" for the value of b, which lest I am mistaken, is the the bearing width of the support.

Now referring to Roark, Table 11.4, case 2a, this would mean the 'free' end is along the bearing support. Am I making sense here? I would have thought it was the other way round so that a = 12 (bearing support width), b = 15 (bottom plate circumferential length).

 

[warrenw]

julesomar

I agree with you. It looks like the example is wrong, the free edge "b" dimension should have been 15".

 

[doct9960]

Or maybe the Roark's book is incorrect. Maybe Case 2 should have read "Rectangular plate; three edges simply supported, one edge (a) free" and the sketch should have shown "Free" along dimension "a". This is just my gut feeling.

If you read Roark's Preface to the First Edition, it says that the book was derived "almost wholly from the work of
others". It would be best to check Roark's original source of information to verify correctness.

 

[LSUME]

I got the same result as Doct9960. See attached

 

[chicopee]

I have my bednar which may be a prior edition since the same example is on my pg 146.
First of all the equation for max stress is a bending stress equation whereby the uniform load between the two gussets is on the bearing plate and the two supports are from the two welded (gussets)plates. In essence the reverse of the beam diagrams. The beta value appears to be a modifier due to the type of support(probably simple supports with end moments)from the gussets.

 

[julesomar]

Anyone else have any experience / input on this?


According to the efunda.com page on this (

http://www.efunda.com/formulae/solid_mechanics/plates/calculators/FSSS_PUniform.cfm),

doct9960 is right and there is an error in Roark 7th Ed. (the 'a' and 'b' should be reversed).

a/b = length of free edge / length of simply-supported edge

The Bednar support lug example refers to Roark 4th edition....I presume the formula is correct in that version.