Chapter 7.7 of "Chemical and Process Equipment Design" by Azbel & Cheremisinoff has a method where the head takes half the load & the ribs take half the load.
Rib stiffened flat heads are not allowed by Div.1.
Also radial stiffeners are not necessarily the best choice, as the center portion, with highest stresses, will require the ribs to be heavily welded together.
The italian code for pressure vessels has a method for that.
First check is that the thickness of the flat wall satisfies the rules for unreinforced flat heads with a diameter equal to the largest circle that may be inscribed between the ribs, and, using the method of UG-34, with C=0.2.
Then one has to calculate the ribs, but the detailed method is too complex to be repeated here.
However you can simply calculate the ribs with the participation of the flat wall as an equivalent T beam, by taking the following limits (t is wall thickness):
-width of participating flat wall not higher than 20t (and of course you can't account the same material for separate ribs, this holds for the central portion of your radial ribs)
-height of ribs between 5 and 15 times their thickness
-rib thickness between 0.75t and 1.5t
UG-34 and UG-39 govern the design of flat heads. I would think it would be more economically feasible from a material and welding perspective to just make the head thick enough to take the loading rather than add reinforcement to a thinner flat head.
When you want to keep the t down, there is no choice. ribs act as stays and can cut t in half, not even radially but crosssectional as well. radially are most difficult to calc.
look in sec VIII-1 vessels of rectangular configurations, calcs for stiffeners on the flat surface.
ER
Sometimes that thickness increase you are suggesting might be for an expensive material, while ribbing can be plain old (formerly) cheap carbon steel.
we used to do flat side side and flat head designs for evaporator equipment made of CU/NI material, and it was obviously much more cost effective to make the CU/NI thickness minimal, and pour on the ribbing.
Secondly, now-a-days, some head and covers are limited in maximum weight by specifications so that they can be lifted by a single person without the aid of lifting devices, in which case, ribbing would produce a lighter piece than thickening.
If thickness and Ribbing proves difficult on can think of Doming the head, some thing like floating head of Exchanger. This would reduce the thickness (As compared to flat head) and unnecessary complicated calc could be avoided.
For a rib stiffened flat head, you need to look to U2g, which states basically that for configurations for which the code design rules (i.e. the thickness sizing formulas in the code) do not specifically apply, do something just as safe as other code construction. Perhaps you may find a suitable hand calculation procedure; if not, FEA is an appropriate evaluation method. This is typically done using the Div 1 allowable stresses, but the evaluation methodology of Section VIII, Div 2, Appendix 4.
You can check on the calculations use to analyze FT power boiler tubesheets w/ welded diagonal stays. I do not believe that calculations can be significantly different.
FT staying calcs. will not work on bar stiffeners.as stays.
the area of staying will be part of the stiffeners calcs.,
the needis the same.
I am looking into the calculations myself and it is not easy. I will keep looking.
ER
Two parts must be calculated. first the stiffener itself and if stiffener is right then plate.
Stiffeners for crossectional areas as previously stated by prex are in Italian Codes RACCOLTA VSR and VSG for vessels and boilers respectively.
Plate between stiffeners are also in these codes but in others too because in its crossectional versión is a tipicaly boiler used construcction. Out of my head is UNE 9300, new EN (12935?)for pirotubular Boilers, TRD perhaps.
It's based in calculate thicknes with the major circle diameter with three supporting points, a factor for other auxiliar circles of 0,75D with two supporting points which center are off the main circle (thats forms a oval area)and another factor for the stiffening method. Rectangular areas must be also considered with a factor for the rectangular form.
During one of my interactions with ASME code committee, I was informed that ASME Section VIII div 1 permits the use of stiffeners in the design of flat circular heads, bolted covers or flanges. The requirements of U-2g are to be satisfied.
Stiffened heads do not function very well due to unequal deflection. The sealing is a headache, so be warned in advance to stiffeners very liberally and check the differential deflection.
