Pressure vessel internal (bottom support grid, support ring, and support beams) 5

[somacast]

Hello,

I hope everyone is doing fine, at first I would like to apologize for not replying on my last post a few months ago, as it seems there was a technical issue at my end preventing me from receiving the notification emails !!! and special thanks for the extremely useful replied.

now for the subject here, with reference to (Pressure Vessel Design Manual, 4th edition, by Moss), I do have some questions please:

I am reading and trying to understand the strength calculation records of an existing vertical vessel which has got a bed of catalyst resting on a mesh tied to a grid, then support ring, and 5 beams below, and although the part of calculations related to internals is referring to the above mentioned book as the reference (the calculations are performed by some excel sheet probably as it had some minor typing errors such as area in m3 etc...), now what is a bit confusing is that they dont follow the book exactly, and even in the book some equations result units dont make sense to me ....

1- for the support grid/grating: in the calculations documents they used a load width (B) of 1000 mm (in the book they suggested a 1 foot length to calculate the area then moment), and they call it max load width, however its different from max span length of 660 mm .. however unlike what the book says that you need to count the number of bearing bars in the panel, they just calculated the entire grid Z and I by multiplying the I and Z of the grid bar section into number of bars in the entire grid, not only the panel area of 1000 x 660 !! and if I follow the book, the bending moment in one bar M4 comes in Kg only not kg-mm or lb-in as it is supposed !! I have attached some screens below for reference ...

2- in the grid calculations as well, the max deflection equation in the book is = [ 5 p Lg (12Lg)^3 ] / 384 E I ... were 12 is the 1 foot (12 inchs) which is width of loading area as suggested by the book, using this equation gives some off values if you cube the number 12, however in the calculations they only used this = [5 p lg^4 x B]/384 E I ... am I missing something here?

3- in the grid attached , what is ng suggested in the book here if I take B as 1000 mm? is it 3 ??

3- the support ring calculations are quite simple, however again in the book page 306 the moment in ring M3 = w3 L , but if you calculate this you get moment units of Kgs only (or lbs) , so in the calculations documents they fixed this by making the unit kg - mm/mm , i.e. multiplying by mm/mm to get it as moment .. and it works fine this way in the thickness equation .. my understanding is this is because the uniform load here is circular so the moment is per mm or circumference ?? not sure though ...

4- for the beams table in the book page 303 , I have 2 questions please: in the equations below there is fT=Tn/AT , what is AT here as it is missing from notations table even ..

Thanks alot & Regards,

 

[somacast]

seriously you dont have to be so angry, you can simply ignore the post, and keep your needless words to your self ... and try to make minimum effort in understanding the questions before answering ..

 

[david339933]

somacast....don't take it personally....he's a jackass to everyone.

 

[somacast]

@david339933 I C ,thnx for letting me know, I just hope a Mod can deal with him to not to spoil such an excellent forum..

 

[HTURKAK]

Dear somacast (Mechanical), I looked to the subject book. There are some contradictions for the use of notations. Each time it may be necessary to use discretion .

I will try to answer to some of your queries..

/ 384 E I ... were 12 is the 1 foot (12 inchs) which is width of loading area as suggested by the book, using this equation gives some off values if you cube the number 12, however in the calculations they only used this = [5 p lg^4 x B]/384 E I ... am I missing something here?]

The max. deflection of simply supported beam for uniform distributed loading is Δmax=( 5 pL^4 ) /( 384 E I). The units SHALL BE CONSISTENT. If the unit of E psi, I in^4 , and if the UDL p is Lb/ ft, you are expected to change the unit of p Lb/ in or, find the total load acting on the beam say W= p*Lg = with units = (lb/ft) * ft = the result is Lb. and use the formula [ 5 p Lg (12Lg)^3 ] / 384 E I .

So, the unit of p (UDL) on the subject formula is Lb/ft.



The book uses unit width foot. What is the reason to change 1000 mm ?. The grid attached has 5 beams and 9 bearing bars. The maximum span of bearing bar for 5 beams 0.16 D = 0.16*4000/305=2.1 ft

Find M= qL^2/8 in this case q = (406/305)*p ( p is uniform load, psf ) and unit of M lb- ft

Find required section modulus Zreq= 12*M/Fb Fb = maximum allowable fiber stress ,psi

Section modlus of proposed or actual bar,Z =ng*b*d^2/6

ng = number of bearing bars per foot in this case ng=304/406 = 0.75

Pls find below , I copied and pasted the relevant page of (Pressure Vessel Design Manual. Illustrated procedures for solving major pressure vessel design problems )

 

[somacast]

Dear HTURKAK (Structural)

Thank you very much indeed for your kind & very informative reply, however if you allow me I do have a few more points to clarify please:

1- Thanks for clarifying the units issue, in fact the page which you have kindly posted is from the third edition of the book, while the one I have posted is from the forth edition, if you go through the procedure in the page I posted I do feel that there is an error in it or I might be confused ... I have posted the page of notations from the forth edition too , in the forth edition he just puts all the notation at the beginning of the section, unlike the third edition which makes more sense to me...

2- I believe if units are used correctly, the equations may be used in both metric and imperial ... correct me if I am wrong please..

2- what they have done in their calculations of the existing vessel is as follows (with their numbers)

the grid is made of a flat bar of 6mm thickness & 90 mm height
they calculated a section modulus Z = 114613.55 mm3 (if you divide by a single bar section modulus that would be approximately 14, which means they have just taken the entire 14 bars making the grid together).
the unit load total = 0.028 kg/mm2
they found a bending moment = unit load x (B) x SL^2 / 8
where they define B as : Max load width , they took it as 1000 mm ( I believe since all units are metric they took a 1 meter unit length instead of the 1 foot used in the book)
SL = 660 mm defined as max span load ( so they did not use the 0.16D the book suggested since it is already known from the drawing that it is 660 mm, and I believe increasing the unsupported length Lg is on the safer side)

then they found the bending stress = bending moment / section modulus Z = 13.4 kg/mm2 , which when compared to allowable value at design temp for this material is 13.85 ... not a good margin but it smaller...

so what do you think of their approach? they did not follow the book exactly although they referred to it as reference of calculations.

3- regarding ng , doesn't this number have to be an integer? so in our case in 1 foot that would be ng=1 ?


Thank you very much again

 

[HTURKAK]

I posted the third edition of the book to draw attention that , sometimes discretion may be necessary .


Not always true. If an equation or formula has some coefficients and / or constants having dimensions , the formula will change for SI units and Imperial units. (e.g. API provides both formulas if necessary)



- Z = 114613.55 mm3 is the section modulus necessary for 1000 mm width. if you provide bars 6mm thickness & 90 mm height, 14 bars will be necessary. If you provide bars 12.5mm thickness & 90 mm height, you will need 6.67 bars for 1000 mm width ..however, the spacing will be bold (1000/6.67 =150 mm.)..So regarding ng , this number is not necessarily to be an integer.

-SL = 660 mm or 0.16D =0.16*4000=640 mm similar figures. If the as-built SL is 660 mm, the use of SL=660 mm is reasonable.

- If 6mm thickness is corroded, yes.. the figures comply with the requirements .There are also other margins for example, Md=gL^2 / 8 is the span moment for simply supported beams. In this case , the bars are continuous beams having 2 to 6 spans.

 

[somacast]

Thank you very much for your replies.