Rafter w/ raised ceiling ties rafter tail deflection thrust 1

[jeffhed]

I am designing a barn framed with structural steel. The roof will be framed with rafters and rafter ties. The roof pitch is very shallow, so although the roof ceiling ties are not very high off the bearing elevation, they are in about 3'-3" from the end of the end of the rafters. My question is this, the rafter ties prevent spreading, but with the rafter tails "cantilevering" from the point of the rafter tie connection, any deflection of the cantilevered rafter seems like it will have to push the columns outward. Everything I have about rafter ties never shows anything about this force, just a free body diagram of the rafter with both rafter ties and raised rafter ties. Here is a link that shows what I am talking about. My rafter is statically determinant without this force, is it negligible? Because of the rafter tie are my rafter tails working in bending only with no axial component? This structure will have these roof rafter "trusses" on each column line and the columns will be cantilevered columns in the direction parallel with the rafters. As I said before, the roof is really shallow so my rafter tie force is quite large, so I am thinking that this secondary deflection thrust force could be significant. But when I go through the free body diagram I have horizontal forces at the peak and the rafter tie that are equal and opposite and the rafter reaction is equal and opposite to the loading on the rafter. This seems like it should be easy, what am I missing? Here is a link for rafters with raised ties.

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

 

[SteelPE]

I'm not exactly sure what you are talking about, maybe a sketch would help?

If you are talking about the deflection of the system (two rafters and a tie) pushing the exterior wall out, or in this instance your column. You are correct, you will end up with some lateral movement of the wall system with this configuration. I don't don't know how often this deflection is checked for residential structures, but if you are running a system on a commercial building where you have rafters and ties only at column locations (20'-0" o.c. or so) I would definitely make sure you check the deflection/outward movement of the system.

 

[msquared48]

If the rafter tie is at the plate line, the only lateral deformation is the elongation of the rafter tie due to the axial tension.

If the rafter tie is higher, two things happen:

1. the effect of the tie at reducing lateral spreading diminishes due to less leverage, plus

2. the rafters are subjected to increased bending and shear, increasing their vertical deflection and increasing the lateral spreading.

The deep beam action of any structural roof diaphragm should help to mitigate the lateral spreading though, which is not included in your model.

Mike McCann
MMC Engineering

 

[jeffhed]

Mike and SteelPE,
Number 2 of Mike's response is what I am referring to. The outward movement that occurs as the rafter tails bend to transfer the load to the columns. The roof is extremely flat 1.5:12 or so, so my rafter tie force is large, which is why I am concerned that the lateral spreading force will be larger than typical. The rafter tie is only up about 6" from the bearing point, but because of the flat pitch, the rafter tie ties into the rafters at about 3'-3" away from the column. Because my rafter is sloped, I have both a vertical and horizontal components at the column. I have sized the rafter tie to by summing the moment about the ridge and solving for the rafter tie horizontal force. At this point my rafters can't cause wall spreading until I am past the rafter tie point. Once I am past the rafter connection point, I have solved for the horizontal thrust force the same way, however, the forces are larger than what I expected. I have attached my calculations so you can see better what I am talking about.

 

[msquared48]

Well, I get your tension force being about 18.8 kips, and based on 1.6:12, that yields a normal force to the rafter of 2.5 kips to induce bending in the rafters.

Personally, I would not be concerned with lateral spreading here so long as you can develop the 18.8 kip tension in the connection of the tie to the rafter. If it helps, double up on the rafters at the tie allowing double shear if you are using bolts. It will also cut down any vertical deflection in the rafter by .5.

Mike McCann
MMC Engineering

 

[BAretired]

If the columns are hinged top and bottom, the system is statically determinate without a horizontal force between rafter and column but wind or seismic loads would need to be carried by the roof diaphragm. The rafter will be primarily stressed in bending, but it will carry a small axial and shear component where it meets the column. The net horizontal force in the rafter is zero where column and rafter meet. Horizontal deflection can be calculated in the usual manner.

If the columns are cantilevered from the base, the structure is indeterminate. There will be a horizontal force between rafter and column. Deflections can be checked using a frame analysis.

BA

 

[jeffhed]

Mike,
My tension number is the same as yours, but my normal force is higher. If my reaction is 3757 that is the hypotenuse of the triangle and my components are perpendicular and parallel to the rafter. So my normal force would be 3757*12/sqrt(12^2+1.6^2) = 3724 lbs. The client wants to weld the rafter ties to the rafters rather than bolting, so I don't have to worry about the bolts. Are you choosing to not be worried about the lateral spreading because the rafter tie is in the bottom third of the roof height?

 

[jeffhed]

BA,
The front and back of the barn are open and the sides are solid walls. Columns are fixed at the base and provide lateral resistance parallel with the rafters (transverse direction). The longitudinal direction is handled with shear walls. The cantilevered columns are the reason I am concerned about the horizontal thrust.

 

[msquared48]

18.8(1.6/12.11) = 2.5 K

As for my relative lack of concern regarding any spreading, I just do not think it will be much of an issue due to the position of the rafter tie.

Mike McCann
MMC Engineering

 

[BAretired]

I looked at your calculations. I agree with the tie force calculation. The calculation of Rx(D) and Rx(L) is completely wrong.

I tend to agree with Mike. Under gravity load, the force is pretty close to zero. If you want an accurate assessment, you must do a frame analysis because the structure is indeterminate.

Design the columns as fixed at the base and free at the top.

BA

 

[jeffhed]

BA,
I was not sure if the RxD and RxL was right or not. The forces seemed really high to me, but I was unsure where my statics error was and with the extremely flat roof, it seemed to me like there would be some horizontal force. The columns are designed as fixed at the base and free at the top and I was trying to get the columns to support this large thrust force which was giving me some problems so I posted the questions.

Mike,
Yes. I was calculating from the cantilevered tail not at the point of the rafter tie.

 

[BAretired]

jeffhed,

Your calculation of tie force is based on the assumption that the ends of the rafter are supported on hinge and roller. Accordingly, there can be no horizontal force applied to the supports.

Another way to calculate the tie force is to consider the bending moment divided by the height. For live load, the reaction is 3,000 pounds. The total live load on both rafters is 6,000 pounds and the bending moment M at the ridge is W*L/8 = 6,000*30/8 = 22,500'#. This moment must be resisted by the tension T in the tie operating over a distance of 1.5' so T = M/1.5 = 15,000# which agrees with your calculation.

If you want to take into account the stiffness of the columns, there will be a small horizontal reaction at the outer end of each rafter which would reduce T slightly, but it is conservative to ignore it.

If Rx(L) was 9,600# in each column, tie force T would be reduced by 9,600*2/1.5 = 12,800# leaving only 2,200# tension in the tie which would require extremely stiff columns. If, instead of columns the rafter ends are considered pinned, the horizontal reaction at each pin would be 22,500/2 = 11,250# and the horizontal deflection at each pin would be zero.

The statics of this problem are not difficult and you should stay with it until you thoroughly understand it.

BA

 

[jeffhed]

BA,
I went back and broke the the forces up into axial and shear components and I think I've got it. Before I was trying to keep them in x and y directions and trying to do most of it in my head, but I think I must have made a mistake with my sines and cosines and probably a had a sign flip flopped. Using my free body diagram to step through it slower I broke up the loads into axial and shear components on the rafter. The shear component of the Rx and the axial component of the Rx end up being equal and opposite and cancel each other out leaving a net horizontal force of zero. The vertical components of the shear and axial components are equal to my previously calculated vertical reactions.

 

[BAretired]

Jeffhed,

Good. Sounds as if you have it.

As for the horizontal force on top of the columns, you can't calculate it by statics alone. The deformation of the tied rafter must be compatible with the deformation of the column.

BA

 

[jeffhed]

BA,
Yes. I realized that it could not be calculated by statics once I ran through it. Thank you for your help.