Framed Knee Walls and Sloped Ceilings.
By Joseph Fusco.
December 18, 2002

Such is the condition when you have a framed wall that the “cuts” must follow the sloped roof line. This condition is found most often in the attic space. The type wall that is most commonly framed is the “knee” wall.

If the wall runs parallel or perpendicular to the roof slope it’s a simple affair to determine the proper cut of the studs. If the wall is parallel to the roof slope the studs will be cut on a “bevel” through the thickness of the stud and that bevel is equal to the roof slope pitch angle.

If the wall is perpendicular to the roof slope the stud will be cut on a “miter” across the face (width) of the stud and that miter is equal to the roof slope pitch angle.

These type of cuts are single cuts or (simple) because they only cut through one plane of the stud. Whenever a cut is made across two planes the cut is called a compound miter cut. These types of cuts consist of both a miter and bevel cut.

If the wall that is to be framed is at any orientation other then parallel or perpendicular the cut across the stud will be a compound miter cut. In this case you will need to know how to determine both the miter and bevel setting on the saw to make the correct cut. Luckily, this is not out of reach and is only a mildly complicated procedure.

Using a scientific calculator follow these steps:

1. Mark/layoff or determine the angle that the wall will make in relationship to the sloped ceiling on the floor.
2. Determine the angle of the roof pitch.
3. The relationship of the miter and bevel cuts will change depending on what face is perpendicular to the angle of the wall.
4. Use these formula to determine the “miter” and “bevel” angles:
a. Miter setting = Tan-1 ( tan (roof angle) * cos (plane angle))
b. Miter setting = Tan-1 ( tan (roof angle) * cos (90-plane angle))
c. Bevel setting =Tan-1 ( sin (miter setting) * tan (plane angle))

An example would be a wall at 30° to a roof pitch of 45° commonly known as a 12/12 roof. This example also assumes that the “width” of the wall is perpendicular to the wall angle.

5. Miter setting = Tan-1 ( tan (45) * cos (30))= 40.89°
6. Miter setting = Tan-1 ( tan (45) * cos (60))= 26.57°
7. Bevel setting = Tan-1 ( sin (40.89) * tan (30))=20.70°
8. Bevel setting = Tan-1 ( sin (26.57) * tan (60))=37.77°

If you have a Construction Master™ calculator you can use these steps to find the miter and bevel sets.

The first thing you’d need to do is to understand how the parts work in this calculation. If you are framing with say a 2x4 then width is 3-1/2" and the thickness 1-1/2". Where you see “width” you enter that value and where you see “thickness” you enter that value. Plan Angle refers to the angle the wall makes with the roof. Roof Pitch Angle is the slope of the roof. In reality you can use any value for either width and thickness as long as you use the same value for both of them.

Miter Settings

Short Side
Enter [Thickness (1-1/2")] [Diag]
Enter [Plan Angle ( (90- Plan Angle))] [Pitch]
Press [Rise] Returns the value equal to the “Run” of the roof slope angle: 1-5/16"
Press [=] [Run]
Enter [Roof Pitch Angle (45.00°)] [Pitch]
Press [Rise] returns 1-5/16" [=] [Rise]
Enter [Thickness (1-1/2")] [=] [Run]
Press [Pitch] Returns 40.89°

Long Side
Enter [Width (3-1/2")] [Diag]
Enter [ (Plan Angle (30°))] [Pitch]
Press [Rise] Returns the value equal to the “Run” of the roof slope angle: 1-3/4"
Press [=] [Run]
Enter [Roof Pitch Angle (45.00°)] [Pitch]
Press [Rise] returns 1-3/4" [=] [Rise]
Enter [Width (3-1/2")] [=] [Run]
Press [Pitch] Returns 26.57°

 

 

Bevel Settings

Short Side
Enter [40.89°] [Pitch] [Pitch] (the idea here is to get 10-13/32" to display)
Enter [M+]
Enter [26.57°] [Pitch] [Pitch] (the idea here is to get 6" to display)
Enter [=] [Rise]
Press [Rcl] [M+] [=] [Run]
Press [Diag] returns 12"
Enter [=] [Run]
Press [Diag] returns 13-13/32"
Enter [=] [Run]
Enter [10-13/32"] [Rise]
Press [Pitch] returns 37.78° which is the saw bevel angle for the short side.

Long Side
Since you now know both inch rises you can just enter them directly for the long side.
Enter [10-13/32"] [Rise]
Enter [6] [Run]
Press [Diag] returns 12"
Enter [=] [Run]
Press [Diag] returns 15-29/32"
Enter [=] [Run]
Enter [6"] [Rise]
Press [Pitch] returns 20.70° which is the saw bevel angle on the long side.

 

©JOSEPHFUSCO.ORG
1997-2010

All written, photographic and drawn materials property of and copyrighted by josephfusco.org 1997-2010.

No materials may be used in any way without the written permission of Joseph Fusco