Problem: I want to calculate the stress in the walls of a hexagonal pressure vessel but I can't manage to get coherent results. For long vessels, cylinders are supposed to have the lowest hoop stress but I obtain out-of-wall stresses with close or lower magnitudes with my method, which is wrong...
Wrong method: 1) I cut the cross section where I assume the max stress will be 2) drew a free body diagram where $\sigma$ is the unknown and $F_p$ is the outward force that the pressure generates on each wall. I considered 2 options, one where the pressure is always normal to the walls (not represented), and one where it's omnidirectional coming from the center (represented). I am not sure about which one applies. 3) Respectively, $F_p=p*h*a$ and $F_p = 2\int^{30°}_{0°}p*h\frac{a}{2}cos(\theta)d\theta$ ; $F_{\sigma}=\sigma *h*t$ 4) When projecting on X and Y, $\sigma$ appears to be out-of-wall (no Y component), and considering only $2*\sigma_x*cos(30°)*h*t=2F_p$, I end up with 87MPa and 38MPa at the corners (lower elsewhere) compared to 75MPa for a cylinder (t=1mm,a=375mm)) - which does not sound right at all.
a is the length of a side, h the height of the vessel (flat ends), p the internal pressure, t the thickness of the walls and $\theta$ the angle between the pressure vector and the normal to the considered face.
Question What is the right method?