Should be easy structures problem Help Axial Load on wall

This should be super easy but I'm having a hard time:

Find total axial load at the midheight of the wall:

Wall is 12' High with dead load of 54psf. has a roof dead load of 54psf and a roof snow load of 40 psf.

The answer simply multiplies the 12' (54 + 40) + 6' (45) ... but why? I'm inclined to take the moment of the corner of the wall and roof which would be 12(54+40)+ P(6) and then solve for P, but this is obviously incorrect.

This is a 'tributary area' concept problem. When the roof loads are specified as 54 and 40 psf, that 1 square foot area is in the horizontal plane (of the roof). So, to convert this area load to a line load acting on the wall footing, you need to to multiply the area load by plan dimensions - one of these will be half the spacing between the walls, assuming half the load goes to one wall and the other half to the other wall. The other plan dimension will be along the length of the wall. If you take the latter as 1 ft, you will find the load per unit length of the wall.

On the other hand, when the wall dead load is specified as 54 psf, that 1 square foot area is in the vertical plane (of the wall). So, to convert this area load to a line load acting on the wall footing, you need to to multiply the area load by the wall thickness. The other dimension (in the vertical plane) will be along the length of the wall. If you take the latter as 1 ft, you will find the load per unit length of the wall.

Hope this helps.

The way you wrote the moment equation, you are treating the load P as a horizontal force (because you multiplied by the vertical distance of 6 ft). Such a force would be a shear for the wall, not axial.

thanks!! I really found a way to make that problem hard!!

One way that I found helpful for me to visual this problem is by turning it into a simply supported beam with a uniformly distributed load (the dead load) and placing a point load on both ends and making the point load equal to the wall weight * distance to axial load in question. Then I can just solve for the reaction by summing all forces to zero. (i know thats a little overkill on a problem this simple, but it helps to visualize) thanks again!