Thorny Construction Math Problem I Need Help Solving

[oneway]

Anyone who can lend some insight into this problem please do...

Preface:

I am a building contractor and this problem relates directly to my trade and a real world mathematical puzzle...

I have roof (plane) that is clipped by a curved wall (cylinder)...the roof is actually comprised of 2 planes in a sense as it has a top and bottom plane and forms a 3D solid...consider this to be an inclined slab. The roof clips into the cylinder at a pitch of 5 and 12 or approximately 22.5 degrees (atan(5/12)).

Of course when a simple plane intersects a cylinder at any angle other than perpendicular to the axis of the cylinder, the shape can be described as an ellipse on a 2D plane coplanar with the intersecting plane.

What I need to figure out is how can I mathematically represent the intersection of the inclined slab and the 3D solid wall (cylinder), such that if I was to cut plywood or other flexible material and bend it around around my wall (cylinder)...I could in essence laminated it to the wall, and form a band or ledger around the wall whereby roof framing members would be hung from this band..

The shape required is an ellipse, but it is not the ellipse formed by the simple intersection of the single plane and cylinder...its an ellipse with a greater major radius and I am stumped on how to figure this out...

Any help or links or ideas on this?

Respectfully

Oneway

[Sandman]

Draw a picture?

[Meatwad]

use duct tape

[Stoney]

Anyone who can lend some insight into this problem please do...

Preface:

I am a building contractor and this problem relates directly to my trade and a real world mathematical puzzle...

I have roof (plane) that is clipped by a curved wall (cylinder)...the roof is actually comprised of 2 planes in a sense as it has a top and bottom plane and forms a 3D solid...consider this to be an inclined slab. The roof clips into the cylinder at a pitch of 5 and 12 or approximately 22.5 degrees (atan(5/12)).

Of course when a simple plane intersects a cylinder at any angle other than perpendicular to the axis of the cylinder, the shape can be described as an ellipse on a 2D plane coplanar with the intersecting plane.

What I need to figure out is how can I mathematically represent the intersection of the inclined slab and the 3D solid wall (cylinder), such that if I was to cut plywood or other flexible material and bend it around around my wall (cylinder)...I could in essence laminated it to the wall, and form a band or ledger around the wall whereby roof framing members would be hung from this band..

The shape required is an ellipse, but it is not the ellipse formed by the simple intersection of the single plane and cylinder...its an ellipse with a greater major radius and I am stumped on how to figure this out...

Any help or links or ideas on this?

Respectfully

Oneway

I'm not going to solve it directy.  However, what I'd suggest, if you can get the engineer to buy off on it, is to block inside the radius, and use a Simpson hanger nailed into the face of the sheathing over the exterior radius wall.  So, In essence, your ledger is inside the radius, instead of outside.  I would think that with all the kerfing necessary to make a solid ledger conform to the shape of the ellipse, the ledger isn't going to have much left to supply the structural strength necessary to carry a roof load.  I can't remember the exact designator of the Simpson connector we used, but we had a floorplan with a ski-jump type roof over the entry.  The framers cut the rafters out of 2X12 in order to get a curved "2X6" rafter.  Since the curve was built into the rafters, we needed a rafter hanger that would allow the angle of the bottom of the rafter.  The engineer specified the hanger which basically face-nailed into the vertical wall, and had a tab that bent to accept the angle of the bottom of the rafter.  It was bent, then nailed into the bottom of the rafter, and the face of the sides of the rafter.  This way all you'll need to do is figure out where the rafters intersect the radius wall, place the hangers there, and then hang the rafters.  It will help you avoid the nasty math you described.

I will recommend you do a search for Solid Edge 2D.  Its a free CAD program distributed by Siemens that you can use to put drawings together, if you don't already have something.

[Shuffler]

Swinging circles in a cad program you can lay out any shape in a flat. I've laid out cones, troughs and square to rounds for years in cad. I make the shape in a flat and cut it on my laser and the guys will roll, bend, or weld it as needed.

[oneway]

I'm not going to solve it directy.  However, what I'd suggest, if you can get the engineer to buy off on it, is to block inside the radius, and use a Simpson hanger nailed into the face of the sheathing over the exterior radius wall.  So, In essence, your ledger is inside the radius, instead of outside.  I would think that with all the kerfing necessary to make a solid ledger conform to the shape of the ellipse, the ledger isn't going to have much left to supply the structural strength necessary to carry a roof load.  I can't remember the exact designator of the Simpson connector we used, but we had a floorplan with a ski-jump type roof over the entry.  The framers cut the rafters out of 2X12 in order to get a curved "2X6" rafter.  Since the curve was built into the rafters, we needed a rafter hanger that would allow the angle of the bottom of the rafter.  The engineer specified the hanger which basically face-nailed into the vertical wall, and had a tab that bent to accept the angle of the bottom of the rafter.  It was bent, then nailed into the bottom of the rafter, and the face of the sides of the rafter.  This way all you'll need to do is figure out where the rafters intersect the radius wall, place the hangers there, and then hang the rafters.  It will help you avoid the nasty math you described.

I will recommend you do a search for Solid Edge 2D.  Its a free CAD program distributed by Siemens that you can use to put drawings together, if you don't already have something.

Its exposed...the ledger will be made out of custom laminated Western Red Cedar. The idea is to use the wall as a form, laminate the cedar, remove it, finish and touch up, reinstall laminated ledger, frame decorative ceiling, etc

[oneway]

Swinging circles in a cad program you can lay out any shape in a flat. I've laid out cones, troughs and square to rounds for years in cad. I make the shape in a flat and cut it on my laser and the guys will roll, bend, or weld it as needed.

What do you mean "Swinging circles"...what do you mean "make the shape in a flat"?

[Stoney]

Its exposed...the ledger will be made out of custom laminated Western Red Cedar. The idea is to use the wall as a form, laminate the cedar, remove it, finish and touch up, reinstall laminated ledger, frame decorative ceiling, etc

In this case, I would definitely throw the drawing on a CAD program.  You can create the cylinder of the radius wall, and then draw the roof at the proper pitch.  Once you have both objects drawn, you can pull the dimensions of the ellipse formed at the transition.  Otherwise, I don't know off the top of my head how to determine this one for you.

[Shuffler]

What do you mean "Swinging circles"...what do you mean "make the shape in a flat"?

I have a fabrication and machining facility. What works for us might not for you. When we have parts to make like your talking about, we lay it out on cad so we can get the material in the flat. We then cut it on our laser and roll, bend, and form as needed.

In our business it works for making a cone in the flat for forming. Making Square to Rounds and saddle on or saddle in pipe tees. Swinging circles refers to triangulating. Without postig a pile of drawings it would be hard to explain. There are so many other things involved such as material type and thickness.

[rpm]

use duct tape

Rookie mistake. This obviously requires baling wire.

[Talon07]

Rookie mistake. This obviously requires baling wire.

You forgot cableties and silicone gel.
Sorry oneway
Kind Regards FBClaw

[Shuffler]

You can get decorative duct tape now too with everything from stripes to checks.