Hand calculations for the bending & radial stresses in the base plate.

[niteshahuja]

thread507-292170

I am using Roark's formula for Stress And Strain Table 24 case 21b to calculate the bending & radial stresses. Can I extrapolate the values above 0.8 for b/a ? Do you think that bending goes to zero for b/a > 0.8 ? Am I thinking right?

 

[rb1957]

maybe look over the test related to the table, and see if there's an underlying formula or a specific reference.

 

[JedClampett]

My book is an old edition and doesn't have a case 21b, just 21. But 21 references "Theory of Plates and Shells" by Timoshenko. They solve it in Chapter 9, but it looks like b/a is limited to .8 in there, also.
Bending might not be zero for b/a greater than .8, but it can't be too much. Why don't you just use the .8 case to be conservative?

 

[niteshahuja]

Thanks JedClampett & rb1957 for the reply.
For my design, b/a is 0.909. Based on this b/a value, combined stresses are within the allowable limit but if I use 0.8 my design doesn't work.
I am thinking of extrapolating beta value based on b/a 0.909.What do you say?

 

[rb1957]

what b/a do you need ?

 

[niteshahuja]

rb1957
I want to calculate Bending stress for b/a=0.909?
Roark's table gives us the Beta numbers for a given b/a value upto 0.8 but my b/a number is above 0.8 which is 0.909. What will be the correct approach to calculate the bending stress?

 

[dhengr]

What kind of base plate is fixed at its outer edges, and has and upper member (column, with moment) which is 91% of the size of the base pl.? When the column size (dia.?) is that close to size (dia.?) of the base pl., this is no longer just a plate bending problem, more and more it is a shear stress problem btwn. the col. and the fixed edge support, through the pl.; that’s why beta is going to zero so quickly at larger b/a. This looks to me like a fixed end moment plate on a cantilever beam. Is the beam and the end pl. circular, and how is it attached, and to what? Some sketches and more details might help you get better help, instead of just debating the value of beta when this may not even apply.

 

[niteshahuja]

The plate looks very much similar to the link below.

http://www.fhwa.dot.gov/bridge/images/sign36.jpg

Thanks a lot dhengr. I totally agree with your explanation of shear stress problem with no bending between the column & the fixed edge support. Can you please suggest me a good reference book or article for this kind of scenario?
I really appreciate your help.

Thanks again.

 

[rb1957]

the column will be applying a moment to the base plate.

the moment will be reacted by tension in the 2 bolts and a distributed compression (as the plate bears up against the concrete foundation).

i'd've imagined that this had been analyzed in the past and a design rule created.

if not, and if you need an accurate answer, use FEA. roark and the like will give you something close, but doesn't look like it closely matches your geometry.

 

[BAretired]

Have you checked out this reference?

BA