While a perpendicular line defines the position of the stiffeners within the element faces, the stiffener's perpendicularity is normal to the line between the cross-section element face's beginning and end nodes. Therefore, there is always the assumption of a straight line, highlighted in red, as the dotted lines between the arrows, for the stiffener's perpendicularity. For stiffeners at a linear face this is not an issue; but, for curved face elements, it could be, as undesired shapes might arise from this assumption. It depends on the element face angle, or, the ratio between the circular sector length and the radius.
Θ = s / r = 2 { arccos [ (r - d ) / r ] }
When the user considers this assumption not good enough, the best practice is to subdivide an element into more elements and have a smaller circular segment with this reference line closer to the desired local orthogonal desired shapes.
For the curved element division, a radial line and a tangential line are needed to create the element's extreme nodes references.
A simple example is shown in the images below for a circular open channel sector with one and two cross-section elements:
- with one cross-section element, at the left, there is only one perpendicular line from the element face beginning to end
- with two cross-section elements, at the right, by adding one subdivision, there will be two perpendicular lines, one from each element's face beginning to end
Note that the central stiffener is quite similar for both cases, even a better approximation in the first one; though, for all other elements, there are improvements in creating the subdivision, with significant differences in the most lateral ones. Therefore, for circular elements, it is advisable to subdivide one element into several smaller elements when adding stiffeners.
It requires the user engineering evaluation, in this simple example, for only one cross-section element only the central stiffener is correct and the extremes are quite wrong. When adding one more element, the two central stiffeners are now correct and the three others could still be improved.
The previous Wiki article addresses the basics of steel stiffeners creation: