Structural Ridge Beam & Statics? 1

[Wheels77PE]

I am designing a cathedral ceiling and having a difficult time wrapping my head around the structural ridge beam concept. If we look at the statics of the sloped rafter member and draw a free body diagram, there is a vertical (Fy) and horizontal (Fx) component to the reaction. I understand the ridge beam is designed for the vertical component. How is the horizontal accounted for? Many articles talk about the outward thrust not being present if the rafters don't move but even if the structure doesn't move, the load is applied. If the load is applied the forces are there internally. To be in static equilibrium the reactions have to support the internal forces. Thoughts?

 

[JAE]

You can't get horizontal reactions from just vertical loads on a simple span sloping beam.
I assume your horizontal reaction is coming from wind forces acting orthogonal to the sloping roof plane, correct?

If so, then you might have some offset lateral force at the ridge beam (due to differences in widnward slope force vs. leeward slope force).

The sloping beam might be sheathed either on the top with roof sheathing or on the bottom with ceiling sheathing which has some shear resistance to take some of this lateral load to end walls.
Mostly, though, we ignore that effect and design for the beam loads taking everything. Maybe with a strap connection over the ridge perhaps.



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[1freewun]

In my 1st year of my degree course the structures lecturer showed us a very simple demonstration of the forces involved with a rafter and ridge support.
One rafter had a birdsmouth cut at both ends thus theoretically ensuring vertical support only, the lower end was supported on a roller and the upper end on a vertical "spring support" and the loaded rafter remained stationary. The second rafter had a vertical cut at the upper end thus tending to lean on the support and a similar roller support at the lower and the rafter moved horizontally at the lower end due to "lean" effect @ the the upper end.
Thus a ridge beam to be effective should essentially provide a vertical support only to a rafter @ the top end. Practically of course it is difficult to avoid all horizontal contact and when the ridge essentially acts as a ridge board a couple of skew nails can also provide a degree of vertical support.

 

[Wheels77PE]

To JAE
I am referring to the horizontal reaction from a vertical load on a sloped beam. The outward thrust that ceiling joists usually tie together seems to just magically disappear because the ridge beam is adequate to support the vertical loads. I don't see how.
To 1freewun
This concern of mine spawns from my 1st statics homework problem in college - inclined beams. If the beam is inclined, the reaction is perpendicular to the beam (thus on an angle) and must be broken down into X & Y components using trigonometry or geometry. Regardless of how the rafter is supported, whether it is an A frame truss or a structural ridge beam, I believe there is still a horizontal force to account for.

 

[JAE]

I am referring to the horizontal reaction from a vertical load on a sloped beam.

Per my comment above -there is no horizontal reaction from vertical loads.

No magic here, just statics.



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[CANPRO]

Wheels, see attached for diagram.

If you do not have a structural ridge beam, then you cannot have a vertical reaction at the ridge (F[sub]r,y[/sub]). If you don't have a reaction at the ridge, then all of the vertical load goes to the wall. If this is the case then you need to have a horizontal reaction at the ridge (F[sub]r,x[/sub]) to remain stable (sum the moments at the wall). This creates the horizontal reaction at the wall. If you don't have a collar tie to provide that reaction, the roof will sag and the walls will spread.

If you do have a structural ridge beam, you can have a vertical and horizontal reaction at the ridge. The magnitude of the horizontal reaction will depend on the stiffness of the ridge beam and if there is anything that can provide a horizontal reaction at the wall (F[sub]w,x[/sub]). If there are no means of providing a reaction at the base of the rafter then basic statics says there cannot beam a horizontal reaction at the ridge beam (in the case drawn in the attached).

If you're designing a ridge beam with no horizontal reactions, remember that the horizontal displacement of the wall is going to be proportional to the deflection of your ridge beam. The rafter is your hypotenuse (which for all practical purposes is not changing length) and as the peak comes down the horizontal distance has to increase accordingly.

 

[msquared48]

What JAE stated regarding basic principles of statics is correct.

However for the condition of a sloped rafter sitting on a double top plate of the wall and also resting on a ridge beam there is a horizontal component for a vertical load,, but not due to that load. It is due to the end condition. The corners of the ridge beam and the wall plate are rounded. When you apply a sloping plane to that rounded surface there is a reaction down and parallel to the joists as well as a vertical reaction to the joist that causes in it this is the end. That causes a tendency for the joist to want to slide down hill that is the reason we secure it to the ridge beam and to the wall those nails are needed or the strap over the top of the ridge beam.

Mike McCann, PE, SE (WA)

 

[msquared48]

Sorry for the garbled post. My I phone still does not do well with the voice option.

Mike McCann, PE, SE (WA)

 

[JAE]

CANPRO,
Your diagram isn't correct. There is no horiz. component from the sloping beam as you show.
From pure statics there is zero horizontal response to a sloping beam with ONLY vertical loads.

If you sum forces in the Y direction you will get vertical reactions of 1/2 of the total load (wL) at each end.
Then if you sum moments about the left end you will get wL^2/2 in one direction and wL^2/2 in the other ... all from the vertical reactions only.

Thus, there would be no horizontal reactions at either end since if there were the sum of moments wouldn't add up.

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[CANPRO]

JAE, I showed the forces on the diagram to help clarify my written explanation. There are cases where the horizontal force = 0. If the ridge beam isn't structural (maybe just a 1x6 board), then I believe there is a horizontal force.

 

[msquared48]

If I lay a sloping rafter across a ridge beam and wall top plate, if the slope is great enough, the rafter WILL slide off the roof. That fact is due to the generated horizontal force at the bearing points. Plain as day to me.

Mike McCann, PE, SE (WA)

 

[JAE]

Well yes - a 1x6 is not a structural beam taking the reaction out to the ends. That, of course wasn't the description of the original post.

With a 1x6 "rim board" there needs to be a competing opposite sloping beam on the other side...different statics then.

I re-read your post and understand what you were indicating. Thanks.

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[dhengr]

I think several of you guys, JAE and/vs. almost everyone else, are kinda talking past each other. JAE is simplistically and technically correct that the sloped rafter can be resolved/reacted by two vertical reactions of wl/2. This works best if there are horiz. bearing seat cuts on the rafters at both the ridge beam and also at the top of the ext. wall pls., which is usually typical anyway. You can really visualize two vert. reactions taking care of the load transfer in this case. Even then, you have the deflection of the ridge beam which will cause a trust at the ext. wall top pls., suggested by MikeMcC and CANPRO and an opposite thrust at the ridge beam, maybe from an opposite rafter. A ridge board depends upon equal and opposite horiz. thrusts of opposing rafters and then ceiling joists to pick up this thrust at the ext. wall top pls.; or collar ties which are significantly less effective at this effort since they are generally too high and induce significant bending moments in the rafters. A vertical bearing cut on the rafter, at the ridge beam almost screams some lateral/trust loading in the rafter. You might improve this detail by using one of several different pieces of hardware (Simpson or USP/Mitek, etc.) to attach the vert. cut on the rafter to the ridge beam, but you still can’t get away from the deflection of the ridge beam and some settlement of the rafter in the nailed connection of each piece of sloped seat hardware at the ridge beam, both adding-up/summing to some thrust or outward movement of the rafter at the top pls. of the ext. wall. The best solution for minimizing this thrust is a stiff enough ridge beam to minimize deflection and then birds-mouth/horiz. seat cuts at each end of the rafters. That means that the rafters should sit on top of the ridge beam, sometimes architecturally objectionable. And, that horiz. seat cut/birds-mouth cut is not acceptable if it is too deep into the rafter. It becomes a horiz. shear/lengthwise splitting problem on the rafters. I’ve seen this horiz. thrust problem many times on long/narrow buildings. Stretch a string at the top of the ext. walls, under the rafter bearings and/or top pls. and you will see the top of the walls bowing outward at the mid-lengths of the walls. Then again, a good plywd. or osb sheathing diaphragm will minimize some of this in-plane movement (thrusting movement) of the rafters.

 

[msquared48]

To all:

1 free one mentioned the example his or if demonstrated. I was just trying to explain why the force existed and why the joist moved. That force exists irrespective of joists on both sides of a ridge beam.There are other reasons why lateral movement presents itself.

As for the ridge board condition, collar ties are required in order to form a beam with the rafters taking the compression element and the collar ties the tension. This is a total different condition.

Mike McCann, PE, SE (WA)

 

[msquared48]

"or if" = "PROF"


Mike McCann, PE, SE (WA)

 

[desertfox]

Wheels77PE

I'm not a structural engineer but I was curious about your post and did some digging and what I found was this:-

https://mathscinotes.wordpress.com/2010/11/29/the-mathematics-of-rafter-and-collar-ties/

not sure if this might help or not.

desertfox

 

[1freewun]

I design my rafters as per the sketch attached.
As I said previously with a designed ridge beam rather than a ridge board due to practicalities there will be some tendency for horizontal forces to develop and deflection of the ridge beam will be mirrored according to the roof pitch by attempted horizontal movement at the lower support.
If it is a simple ridge board it will also provide some vertical support due to friction and nailing.
With the ridge board condition, horizontal force only at the top, the total vertical rafter load is transferred to the bottom support by axial and shear forces.

 

[JAE]

1freewun - I think your attached sketch clearly and correctly shows the difference between having a ridge beam and just having a non-structural rim-board.

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[Wheels77PE]

Got it! Thank you to all. As I mentioned many of the articles on the topic talk about movement or deflection but the rafter framing seems just as important & critical. As it happens the architect I am working with wants to face mount the rafters. Thanks again!

 

[KootK]

I feel that, for commonly used details, the nature of the connection (bird's mouth / face mount) has relatively little impact on whether or not a horizontal / vertical reaction component exists. Rather, it is the flexibility of the potential horizontal / vertical reaction that determines the load that it attracts. Two specific examples include:

1) Low end bird's mouth connections. They often have vertical toe-nails and can thus transfer a horizontal reaction. Were this not true, the supporting walls would cave in under wind load.

2) High end face mount connections. They often have horizontal toe nails capable of transmitting a vertical reaction. Were this not the case, the roof would cave in.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.