Your diagrams seem to indicate a light load above the arch. As much as the height of the arch is a factor, the thrust, or outward force, of the arch needs to be considered. In masonry, a triangular area of brick above the span is all that you need to calculate for weight. However, there seems to be little load above the door unless the entire gable face is to be brick also. The portal frame, as you describe it, appears to be sufficient for such a light load.
I have attached a technical bulletin by the Masonry Advisory Council (a great organization) which will give you a good qualitative approach as well as formulation if you need to go that route.
To be perfectly honest, a non-technical approach can be utilized talking to a seasoned bricklayer. Do not underestimate their expertise.
Charles Roig Thank you so much for your comprehensive explanation.
Actually, basically I deal with wood structure. The only time we use arch action is when there is brick load above Garage lintel.
Specifically my concern is when we do not have uniform load above the triangle (let's say we have a window outside of triangle but it's close to it), in this case can we use arch action?
The only thing I found is we should have at least 8" uniform load above APEX but it does not mention any limitation about the sides of triangle.
I attached a picture to this message showing the location of window in red.