Here be dragons. Or, to paraphrase a hadith of the Prophet Mohammed, "There are seventy ways to compute element stresses, and all of them are wrong."
The naive approach is to differentiate the element shape functions to find the strain at a point, and then use the stress-strain relationship for the material.
The problem is that since the shape ...
A shell element is similar to the plate element that having both in-plane and out-plane stiffness (note that membrane has the in-plane stiffness only), and have different bending theories:
Mindlin Theory for thick shells, and
Kirchhoff-Love Theory for thin shells.
Here is a good book to read, "Theory and Analysis of Elastic Plates and Shells", by ...
First of all some geometry, and some simplifications:
The horizontal bars (from the wall to point A) is going to rotate and extend.
The extension of each horizontal will be equal to $\Delta L$. From the detail of AKD (right angle at K) we see that $\Delta L = \delta_A \sin\theta$ (so $\Delta L \le \delta_A $)
angle with the horizontal will be equal to $\...
The illustration below is in response to your comment on alephzero's answer.
I think you are confused with the stress on an inclined plane, after ddelection/rotation, that will have the force components $N $&$ S$ as shown. Assume a finite strip with unit width,
in direction of $"Z", A_X = 1 * \Delta L = \Delta L$,
$\sum \delta_Z = N cos\theta/\Delta L + ...