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.
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 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. 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. 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'#. For live load, the reaction is 3,000 pounds. Accordingly, there can be no horizontal force applied to the supports.Īnother way to calculate the tie force is to consider the bending moment divided by the height. Your calculation of tie force is based on the assumption that the ends of the rafter are supported on hinge and roller. RE: Rafter w/ raised ceiling ties rafter tail deflection thrust msquared48 (Structural) 17 Jun 14 13:18 I have attached my calculations so you can see better what I am talking about. 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. At this point my rafters can't cause wall spreading until I am past the rafter tie point. I have sized the rafter tie to by summing the moment about the ridge and solving for the rafter tie horizontal force. Because my rafter is sloped, I have both a vertical and horizontal components at the column. 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. 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 outward movement that occurs as the rafter tails bend to transfer the load to the columns. Number 2 of Mike's response is what I am referring to. RE: Rafter w/ raised ceiling ties rafter tail deflection thrust SteelPE (Structural) 17 Jun 14 08:28 This seems like it should be easy, what am I missing? Here is a link for rafters with raised ties. 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.
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. 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. Here is a link that shows what I am talking about. 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. 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. 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. The roof will be framed with rafters and rafter ties. I am designing a barn framed with structural steel.