I Googled it and came up with this from;
Required thickness for a cylindrical body is less than a rectangular in a similar design condition. A round body with less thickness makes welding easier and also the production will be cheaper, but sometimes advantages of shape makes rectangular vessels more attractive.
Generally if the ratio of (thickness/diameter) increases then the noncircular vessels will become an alternative for cylindrical equipment. Mostly in case of "Air heater/cooler header" it is the case.
In contrary of manufacturing the design and calculation of such construction is not easy one. The occurred stress on construction involves two parts;
1- membrane stress
2- bending stress
Most codes just take membrane and handheld the tube-holes and plug-holes as a simple Opening!
But ASMEVIII div 1 appendix 13 takes both stresses in account and EN13445 adapts in most case this appendix of ASME.
Hence in the most case the bending dominates the occurred stress on a rectangular construction, usually the middle of long side is the most critical point. The reasons behind this fact are:
1- the bending moment in middle is maximum
2- ligament efficiency at the corner is not smaller than joint efficiency but at the middle it is under the influence of tube-holes and plug-holes and usually less then joint efficiency.
(if there is no hole in long side then it will be 1).
The total stress in each side is equal to sum of membrane and bending. There is no need to employ the "Von mises" or "Tresca" equivalent stress. The reason is simple, membrane is a Tensor phenomenon! It means that in contrary of Vector, the strain occurs in any directions in plate which is perpendicular to load.
Considering reinforcement and partition makes such calculation more complex. In order to reduce the concentration factor at the corner, sometimes (usually for thickness less than 20 mm) the corners are rounded (see sketch 3 and 5).
The calculation of stress at such section differs from a flat section. At the conjunction-point actually discontinuity exists, which is ignored by code.
For calculation of noncircular vessel except appendix 13, many other parts of ASME VIII div.1 must be employed, e.g.:
- end plate (closure) UG-34
- for reinforcement UG-47
- for Tube thickness appendix 1.
But in case of nozzle load only one option is available, which is API-661 namely (Air cooled rectangular Heat exchanger), section 6.1.10. More discussion hereabout is placed in "Help Nozzle load".
In this program the next 6 kind most employed noncircular vessels of ASME and EN13445 are presented;
1-Rectangular with equal tube-sheet and plug-sheet thickness (13-2a sketch1 of ASME).
2-Rectangular with nonequal tube-sheet and plug-sheet thickness (13-2a sketch2 of ASME).
3-Corner rounded vessel (13-2a sketch3 of ASME).
4-The first type but with continuous reinforcement (13-2a sketch 4 of ASME).
5-Corner rounded with noncontinous reinforcement(13-2a sketch 5 of ASME).
6-Obround vessel (13-2b sketch1 of ASME)