wood rafter thrust problem 5

[structuralnerd]

I have a wood framed building with a very tall and steep pitched roof. Unfortunately, the client wants the ceiling vaulted, so we cannot use trusses to frame the roof, only rafters with one intermediate brace toward the top of the roof. This results in quite a bit of thrust force at the bottom of these rafters. To take this thrust force out, I was thinking about resolving it into the sill. By analysis, this results in a really big sill plate. I was thinking of the sill plate as a simply supported beam. Is this the right way to go about this thrust problem? Would I need a pretty substantial connection at the end of this sill plate? Any other suggestions? Thanks in advance.

 

[miecz]

Hemifun-

It's true there is not a roller support at the top of the wall. but it's not a moment connection either. If you think of the wall as a member pinned top and bottom, then any horizontal movement at the bottom of the rafter simply tilts the wall slightly. The wall acts like a strut with axial force. Since the wall tilts, the force at the joint is technically not vertical, but it's close enough.

 

[csd72]

UcfSE,

If the rafter was set in concrete each end then it would resemble the pinned-pinned models and would therefore have very significant horizontal thrust even if it had a ridge beam.

But in a real situationwith a ridge beam and where the bottom end of a rafter ends at the top of a stud wall, then the wall will tend to yield outward slightly therefore giving closer to the pinned-roller model which has no horizontal thrust. This wall does not have to move much to make a massive reduction in the horizontal force - 1/16" each side would make a big difference.

My point was that it doesnt 'require' horizontal reactions to be stable. There are reactions, but they get reduced down to very small values.

csd

 

[Hemifun]

So, I guess the rafter would act like it is pinned at the ridge beam and a roller support at the wall? How does one determine that "movement" at the top of the wall will eliminate the horizontal force? Say you had a steep roof with 6/12 slope, this would give a sizeable horizontal force which I don't think would disappear with a minute amount of wall movement. Also, when would the movement stop?

 

[bylar]

I really can’t believe all this discussion among structural engineers.
Like I stated previously get a “real” structural engineer.

Take a ladder and lean it against the wall and place a skateboard under each side leg of the ladder and climb the ladder and see what happens.

Now take an anchor like a Simpson LSSU and attach the ladder top to the wall
Now climb the ladder and see what happens.

Do the same thing but with a LVL (as ridge beam) instead of the wall and see what happens.

Now go back and design your ridge beam.

By the by if you have scissor trusses look at the cut sheet and note the disclaimer as to the horizontal load and who has to account for it.

 

[UcfSE]

You don't need a horizontal reaction at the top of the wall necessarily, if that is your roller end, but you do need some horizontal reaction to balance the internal axial force in the rafter. bylar has a very good example of this. The only time you get no horizontal reaction under gravity load is when the roof angle [θ] is zero or 90 degrees. So even with no thrust on the walls, you still end up designing the rafter itself for axial load as well as the connection.

 

[miecz]

UcfSE

The internal axial force in the rafter is offset in the horizontal direction by the internal shear. Net horizontal reaction is small. You get little horizontal reaction under gravity load no matter what the roof angle.

 

[Lion06]

Is there really this much discussion (typically) over a ridge beam? I thought it was a long settled discussion that as long as you design the ridge beam to take the vertical reaction of the sloped rafters that you don't need to worry about whatever minor thrust may occur at the walls. It seems to me that the majority of the thrust in this situation would occur as a result of the deflection of the ridge beam allowing the "pinned" end to translate down, which in turn allows the "roller" end at the wall to translate out (or create thrust).
This is illustrated well by bylar with his example. The reason the ladder will fall out from under you in the first situation is that the friction is not enough to keep the ladder (the end against the wall) from translating down. Once you add the LSSU that he mentions, the ladder (the end against the wall) can not translate down and the skateboards will not translate outward. If, however, you get a little give in the connection and the ladder (the end against the wall) drops by say 0.5" (this would be comparable to the deflection in the ridge beam) then the skateboard (or the end bearing on the wall) will translate out just slightly causing the thrust.
Please help me out if I have missed something.

 

[csd72]

UcfSE,

The small axial force in the rafter will be taken out by the roof diaphragm and will not end up in the wall.

csd

 

[UcfSE]

jmiec,

If you have uniform transverse load and uniform axial load, the axial load isn't taken out by the shear. Where did you get that information, or how do you prove it mathematically? Whether the thrust has a diaphragm that can resist it is another matter.

 

[apsix]

Ignoring lateral loads, the only reason that there is a horizontal reaction (or displacement) is due to the deflection of the ridge beam.
As jmiec said, the vector sum of the internal shear and axial force is resisted by the vertical reaction (assuming an infinitely stiff ridge beam OR a roller support at the lower end).
Diaphragm action will of course stiffen up the whole structure.

 

[miecz]

UcfSE

Ignoring the diaphragm, which admittedly, changes the picture;

For a rafter with a horizontal projection L at an angle "a", from the horizontal, with a uniform vertical load w;

The vertical reaction at the ridge and at the sill is R=.5wL

The shear at each end of the rafter due to this reaction is V=R*cos(a).

The axial force at each end of the rafter due to this reaction is A=R*sin(a). Tension at the ridge, compression at the sill.

The horizontal force at the sill is: H=V*sin(a)-A*cos(a)=R*cos(a)*sin(a)-R*sin(a)*cos(a)=0.

Same thing at the ridge.

I have a RISA model that gives the same result.

 

[dodson]

Anyone thought of using an exposed collar tie instead of a ridge?? The connection of the collar tie to the rafters will take care of your thrust force.

 

[jechols]

dodson,

The rafters would have to be quite stiff to minimize the thrust. The collar tie acts similar to the rafters being moment connected at the center and now having to span from bearing wall to bearing wall. If the rafters deflect, the walls bow out. Does that sound accurate to you?

j

 

[JLNJ]

If the loads applied are all vertical the reactions need only be vertical - regardless of the geometry. Those vertical loads will induce some internal axial load in a sloping member but this does not result in a horizontal resultant force.

 

[apsix]

JLNJ
You said "If the loads applied are all vertical the reactions need only be vertical - regardless of the geometry."

That's only true if there is no vertical displacement of the roof structure (whether using a ridge beam or collar ties above eaves level), or there is no horizontal restraint at eaves level. Neither one of those conditions is very realistic.

 

[bylar]

JLNJ
Try it set up two rafters with no ridge with the ends of the rafters on a smooth surface and then go stand on the apex of the two rafter and tell me how long it take you to hit the ground.

Dodson you apparently don't understand the function of collar ties. They are to be in the upper third and if you take the moment at the junction of the rafter and the collar tie you will see how large a section you need.

 

[csd72]

JLNJ,

what you say is strictly not true, but is not too far off.

Equilibrium of forces requires 2 things.

1. Sum of Moment reactions = Sum of applied moments
(or in cases like this center of reaction = center of applied loads)
2. Sum of Force Reactions = Sum of applied forces.
In this case it means:
Vertical reactions = applied load, but in the horizontal direction it does not necessarilly mean that there are no reactions only that the sum is equal to zero. You can also have equal and opposite horizontal reactions on both sides!.

csd

 

[apsix]

"collar ties. They are to be in the upper third "
That must be a local definition, not a global one.

By the definition I use collar ties are located higher than the lower rafter support.

 

[DRC1]

The rafter is best modeled as a pin and roller member. Reactions will resolve themselves at right angles to the rafter. Thus there will be a horizontal reaction due to vertical load at the base of the rafter that should be easy to calculate. It needs to be dealt with and can not be wished away. Ties, steel framing or external bracing are ways to deal with it.

 

[Lion06]

DRC1-
Are you suggesting that if you had a roller-roller support on a sloped beam that the beam would just roll away with vertical-only loads?