 # Medeek Truss

Version 2.3.4 - 04.24.2019

• Enabled the “Edit Roof Assembly” function for gable and hip rafter roofs (imperial and metric units).
• Corrected an issue with H2.5A hurricane ties when utilized with raised heel trusses.

This is a fairly substantial upgrade for the plugin and now gives the user the ability to edit stick framed roofs. Previously only certain truss roofs could be edited.

I still need to enable editing for the other rafter roof types (shed roofs, I-Joist, rafter roofs with glulam beams etc…), but at least I’ve now got the two most common roof types with full parametrics enabled.

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This brings me back to some topics I was exploring last year at about this time regarding asymmetric rafter roofs. I will set aside the hip roof for a minute and look at the simple gable roof in continuation of this discussion.

Each side of the roof may have a different pitch. Additionally the top plate height may differ as well as the birdcut. Things tend to get a little complicated when the symmetry is broken.

Basically one can boil it down to a symmetric or asymmetric gable roof. The asymmetric variant will have the following additional parameters:

Roof Type: Symmetric Gable, Asymmetric Gable
Pitch2 - Roof pitch of right side roof
Birdcut2 - Birdcut length of right side of roof
Delta Height - Difference in height between left and right bearing walls (left side is reference)

One could even go so far as to define a different rafter depth for the opposite side, as its length may be more or less than its opposite side:

Rafter Depth 2 - Rafter depth on right side of roof.

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With the asymmetric variant the secondary pitch and bearing height cause the location of roof peak to be off center. In order to draw the roof one must first solve for the location of the roof peak (x direction). The solution is given by:

I won’t really know if the math is correct until I drop it into the ruby code and test it.

I will also need to check for null solutions, where certain combinations of pitches and delta h create impossible geometry.

I kind of miss the rigor of the math often required with the development of the truss plugin. Asymmetric hip roofs are going to be even more math intensive.

I’m not exactly sure on what to do with the ridge board. I can either bevel it or drop it to the same height as the lower side rafters.

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Couldn’t you just calculate the ridge to come to a peak and let the builder determine whether to drop or bevel? I just did a roof like this and because it was an outbuilding, I dropped the ridge. I probably wouldn’t in a residential roof however.
Another quirk of this roof is that the overhang rafter’s miter is not plumb.

Shep

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Version 2.3.5 - 04.28.2019

• Fixed the show_modal bug for macOS in the Materials tab of the global settings.

First look at an asymmetric roof:

Note the addition of “Asymmetric Options” in the edit menu (4 parameters).

Also note that the rafter depth is different for each side of the roof as well as the birds mouth cut.

If the delta height is non-zero (can be either negative or positive) then I have the ceiling joists disabled for now. I will need some more direction with regard to that possible configuration.

I now just need to focus on the advanced options and bring them up to speed for an asymmetric gable roof (ie. gutters, hip and ridge, rake boards, sheathing, cladding etc…)

I’ve also spent some considerable time cleaning up the rafter roof module and re-organizing the file structure where it seemed prudent. The thing about these plugins is there is always more to do.

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Version 2.3.6 - 05.01.2019

• Enabled asymmetric gable rafter roofs (imperial and metric units).

Tutorial 14: Asymmetric Gable Roofs

Sometimes you just never know until you dig into it. This latest update required a virtual rewrite of the entire rafter roof module. Asymmetric roofs literally change everything up. I’m glad to get this one wrapped up and behind me.

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The asymmetric roof addition beat me up pretty hard for about three days, but in the end I won out. Now I need to look at the hip roof and how best to deal with multi pitches…

With the hip roof we are now talking about four different possible top plate heights with four different possible pitches, birdsmouth cuts, and rafter depths.

If one is to assume that the fascia boards all line up (gutters), then the top plates heights are actually driven by the roof overhang and the pitch of each roof plane. Only one roof plane (Plane A) will actually have its plate height set (the zero or base height of the roof), the other roof planes’ top plate heights will be automatically calculated.

I suppose there is always the possibility where the fascia don’t line up but I think this is more the exception than the rule, correct me if I am wrong.

As I’ve given this some more thought it occurred to me that typically the designer will set the roof pitches from the outset. Then, in order to get the fascia to line up, he/she can either adjust the overhang or the top plate height (assume that the birdsmouth cut is set to some value). So depending on the situation the user may want the plugin to calculate either the overhang (same top plate height) or the top plate height (same overhang). I will need to give this some more thought.

If the user keys in a numeric value for the overhang (roof planes B, C or D) then the edit menu can automatically set the delta height (top plate heights) for each respective roof plane to “AUTO”. Likewise if a value is keyed in for the delta height the HTML form can set the respective overhang(s) to “AUTO”.

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I don’t normally post on the boards regarding price changes in the plugins however I thought it might be worth noting that I have decreased the renewal price on the Truss plugin to \$10.00. The idea being that once you have paid your initial license fee ongoing renewals are mostly a token payment.

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Continuing on with regards to multi pitch hip roofs we need to be very clear about what point on the roof lines up when we talk about lining up the fascia. Do we mean the sub-fascia, rafter tail or the fascia?

Since I currently don’t have the fascia and soffit added yet I can probably ignore these for now and state that the top of the fascia board must line up with other fascia boards on other roof planes.

Once we know that fascia_top_y = fascia_top_y2 then we can calculate the location of the top of the rafter tail for rafter2 given the pitch2. This same algorithm can then be used for the other two roof planes. Its a little bit backwards compared to the usual way of crunching the numbers for a roof but it should get us there.

Once I’ve established the overhang/plate height auto configuration then it is simply a matter of utilizing the previous equation for gable roofs to calculate the rest of the rafters geometry.

I’ve got the asymmetric options added to the edit menu and the common rafters and fascia are calculating correctly:

Note that all four pitches are different values, however the fascia lines up all the way around the roof as it should (in this case I have the overhangs auto calculating).

Next I will work on the hip rafters and jack rafters. As we can see in this example, all symmetry is broken, each hip rafter will be unique (x4) as well as each set of jack rafters (x8). Luckily we can program this sort of thing, drawing this type of roof manually would be a real headache.

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First look at the sheathing and labels for an asymmetric hip roof:

Pitch and SQFT callouts/labels are now working:

Hip and Ridge Cap is now working:

This chunk of code is just for the ridge cap geometry:

``````@Phi1_3 = atan(sin(@Phiplane13) * tan(@Phi) * cos(@Phihip13))
@Phi3_1 = atan(cos(@Phiplane13) * tan(@Phi3) * cos(@Phihip13))

@Phialpha1_3 = acos(cos(@Phihip13) * sin(@Phiplane13))
@Phialpha3_1 = acos(cos(@Phihip13) * cos(@Phiplane13))

@Psi1_3 = asin(0.70710678118 * sqrt(1.0 - cos(@Phi)*cos(@Phi3)))

@Phi2_3 = atan(sin(@Phiplane23) * tan(@Phi2) * cos(@Phihip23))
@Phi3_2 = atan(cos(@Phiplane23) * tan(@Phi3) * cos(@Phihip23))

@Phialpha2_3 = acos(cos(@Phihip23) * sin(@Phiplane23))
@Phialpha3_2 = acos(cos(@Phihip23) * cos(@Phiplane23))

@Psi2_3 = asin(0.70710678118 * sqrt(1.0 - cos(@Phi2)*cos(@Phi3)))

@Phi1_4 = atan(sin(@Phiplane14) * tan(@Phi) * cos(@Phihip14))
@Phi4_1 = atan(cos(@Phiplane14) * tan(@Phi4) * cos(@Phihip14))

@Phialpha1_4 = acos(cos(@Phihip14) * sin(@Phiplane14))
@Phialpha4_1 = acos(cos(@Phihip14) * cos(@Phiplane14))

@Psi1_4 = asin(0.70710678118 * sqrt(1.0 - cos(@Phi)*cos(@Phi4)))

@Phi2_4 = atan(sin(@Phiplane24) * tan(@Phi2) * cos(@Phihip24))
@Phi4_2 = atan(cos(@Phiplane24) * tan(@Phi4) * cos(@Phihip24))

@Phialpha2_4 = acos(cos(@Phihip24) * sin(@Phiplane24))
@Phialpha4_2 = acos(cos(@Phihip24) * cos(@Phiplane24))

@Psi2_4 = asin(0.70710678118 * sqrt(1.0 - cos(@Phi2)*cos(@Phi4)))

@Ridgex = (cos(@Phi)*@HRthk*tan((@Phi + @Phi2)*0.5)) - sin(@Phi) * @HRthk
@Ridgey = (sin(@Phi)*@HRthk*tan((@Phi + @Phi2)*0.5)) + cos(@Phi) * @HRthk

if @Sheathing_option == "YES"
if @Roofbatten == "YES"
if @Cboption == "YES"
thtot = @Cbheight + @Battenheight + @Sheathing_thickness + @Roofcladding_thickness
else
thtot = @Battenheight + @Sheathing_thickness + @Roofcladding_thickness
end
else
end
else
if @Roofbatten == "YES"
if @Cboption == "YES"
thtot = @Cbheight + @Battenheight + @Roofcladding_thickness
else
end
else
end
end

# Extension at Peak

@Wa3 = PI - (@Phialpha3_1 + @Phialpha3_2)
@Beta23 = atan(sin(@Wa3)/(tan(@Psi1_3)/(tan(@Psi2_3)) + cos(@Wa3)))
@Beta13 = @Wa3 - @Beta23

ext13 = (thtot * tan(@Psi1_3))/(tan(@Beta13))
ext23 = (thtot * tan(@Psi2_3))/(tan(@Beta23))

@Wa4 = PI - (@Phialpha4_1 + @Phialpha4_2)
@Beta24 = atan(sin(@Wa4)/(tan(@Psi1_4)/(tan(@Psi2_4)) + cos(@Wa4)))
@Beta14 = @Wa4 - @Beta24

ext14 = (thtot * tan(@Psi1_4))/(tan(@Beta14))
ext24 = (thtot * tan(@Psi2_4))/(tan(@Beta24))

# Ridge Length and Extensions

ridgedx = (cos(@Phi)*thtot*tan((@Phi + @Phi2)*0.5))
ridgedy = (sin(@Phi)*thtot*tan((@Phi + @Phi2)*0.5))

length_sq = thtot**2 + ridgedx**2 + ridgedy**2

rext3 = sqrt(ext13**2 + (thtot/(cos(@Psi1_3)))**2 - length_sq)
rext4 = sqrt(ext14**2 + (thtot/(cos(@Psi1_4)))**2 - length_sq)

phicheck3 = atan(ext13*cos(@Psi1_3)/thtot) + PI - @Phihip13
phicheck4 = atan(ext14*cos(@Psi1_4)/thtot) + PI - @Phihip14

if phicheck3 > PI
rext3 = -1.0 * rext3
end

if phicheck4 > PI
rext4 = -1.0 * rext4
end

@Ridgecaplength = @Arraylength - @Hipf - @Hipb + rext3 + rext4
``````

Two months from now I’m not going to have any idea what all of this means, its a good thing I keep a binder of all my notes and diagrams.

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Gutters and Downspouts are now functional for the Asymmetric Hip Rafter Roof:

Even with the different overhangs and top plate heights the gutter height (fascia) is the same height all the way around. However the downspouts on opposite sides of the roof are customized per the overhang on each respective side.

Tomorrow I will jump back into the hip and jack rafters and see if we can wrap this one up.

The good news is that the required code for the asymmetric hip and jacks already exists. I will be borrowing from the roof return module where I handled dissimilar pitches. The bad news is that after a cursory review of this block of code I have absolutely no idea how it actually works anymore (I haven’t looked at it in about 2 years). It’s just a matter of reverse engineering my own code for about an hour and it will all come back to me.

I’m actually still working on the hip rafters. The complexity of a multi-pitch roof took another unexpected turn with the realization that when roof planes A and B are different pitches it causes an offset in the rafters at the peak which requires some additional logic to account for this fact with the placement of the hip rafters and their geometry.

I’m also still a bit conflicted on how to best handle the birdsmouth cut of the hip rafters when they walls have different top plate heights. In some cases the hip rafter misses the corner entirely and is askew on one of the walls, this is the simple case. In other cases the hip rafter technically rests at the “corner” but since there are two different wall heights possible it is not clear how the birdsmouth cut should be constructed exactly. I’m assuming that the higher plate height will govern.

Does anyone have any photos or details of actual construction where a hip rafter bisects a corner where the top plate heights vary?

Take a look at this thread from last march.

When the hip roof is asymmetric across the ridge you end up with a situation like what is shown below:

The common rafter in the upper right is a 7:12 pitch and the common rafter in the lower left is a 10:12 pitch. Normally with a symmetric hip or gable roof the common rafters would be flush with the top of the ridge board.

However in the asymmetric case the steeper pitched side is flush and the lesser pitched side overshoots the ridge board just slightly as shown. This additional asymmetry causes further complications in the calculations of the hip rafter that is adjacent to the overshooting common.

Also note that the seams in the sheathing (edges of the roof planes) do not center up on the ridge board or hip rafters. This is not a flaw or an error it is just the way the asymmetric roof goes together.

It appears that I have the hips correctly calculating now (after nearly two days of intense debugging and about 10 sheets of engineering pad) however tomorrow I will continue with further testing, to see if I can break anything, and then begin attacking the jack rafters.

A further look at the bird mouth cut question in shown in the example below:

So in reality I am still missing the birds mouth cut for the hip rafters and the implementation of the soffit cut for trimming the tails of the hip rafters. Always too much to do and never enough time to get it all done.

I’m really hoping that the jack rafter piece is a lot less trouble than the hip rafters, I would really like to get this roof type wrapped up by the end of the weekend.

Since each hip rafter is potentially unique each one requires the following calculations (for those that are interested):

``````@Returnext = @HipendX + @Overhang3_num
@Returnext2 = (@Pitch3/@Pitch) * @Returnext
@Returnexthip = sqrt(@Returnext * @Returnext + @Returnext2 * @Returnext2)

@Zeta = acos(@Returnext/@Returnexthip)

@Tcy4mod = 0 - @Fascia_width * (tan(@Phi) - tan(@Phi3))
@Returnext2mod = @Tcy4mod/(tan(@Phi))

@Zeta_a = atan((tan(@Zeta))/(cos(@Phihip13)))
@Zeta_b = atan(tan(@Zeta)*cos(@Phihip13))
@Iota = atan(sin(@Zeta)*tan(@Phihip13))
@Kappa = atan(cos(@Zeta)*tan(@Phihip13))

@Term1 = (cos(@Zeta_a))/(cos(@Iota)) + ((sin(@Zeta_b))/(cos(@Kappa))) * ((tan(@Phi) - tan(@Iota))/(tan(@Phi3) - tan(@Kappa)))
@Abar = @Ply/@Term1
@Hipoffsetx = (@Returnexthip - @Ply) * sin(@Zeta)
@Bbar = @Abar * ((tan(@Phi) - tan(@Iota))/(tan(@Phi3) - tan(@Kappa)))
@Ebar = @Returnext - ((@Returnext2 + @Returnext2mod - @Abar)/(tan(@Zeta)))
@Fbar = @Returnext2 + @Returnext2mod - (tan(@Zeta))*(@Returnext - @Bbar)

if @Phi2 > @Phi
@Zbar = @Ry4 - @Ry4r
@Xbar = @Zbar/(tan(@Phi))
@Bbarmod = ((@Abar+@Xbar) * (tan(@Phi) - tan(@Iota)) - @Zbar) / (tan(@Phi3) - tan(@Kappa))
else
@Zbar = 0
@Xbar = 0
@Bbarmod = @Bbar

end

@Exthip13 = ((@Xbar+@Abar)*cos(@Phihip13)/tan(@Zeta))/(cos(@Phialpha1_3)) - @Zbar/(tan(@Phihip13))
``````

Term1 of the Abar equation is really interesting. If I took the time I could probably condense down some of the variables and reduce the amount of algebra but then in the future it would be harder for me to follow, so it is best left as verbose as possible for myself and future generations.

The terms Abar, Bbar, EBar and Fbar specify the compound bevel cuts at the peak and eave of the hip rafter.

Actually I stand corrected. The sheathing does center up on the ridge board provided that you do vertically offset the opposing common rafters as shown in the previous images. A top down view shows the result:

If you don’t vertically offset the commons and the pitch on plane A and B differ then the ridge board will not center up on the sheathing. For now I have it centering and a vertical offset, for future work I may provide an option to toggle between these two possible configurations.

Here is a view of the other side of the roof, note the different top plate heights and where the hip rafters land on them and the corners:

Better yet, go ahead and download my test model that was most recently generated by the new asymmetric module: