Deflection is related to curvature right? I need to calculate the deflection of a plated wood roof truss if the bottom chord splice slipped 1/8". Any ideas?
1) If the bottom chord splice slipped 1/8” than the splice has failed. I would jack up the truss till the gap is closed and place a add-on to one face and nail for the maximum tension force.
2) If the truss was built with a 1/8” gap, under normal loads (as all the trusses were built on the same table) it will have no addition deflection. For this, I would recommend to wedge/shim the gap or add an add-on to one face for the code maximum wind condition.
As for additional deflection due to a increase in lenght of the bottom chord of 1/8", there will be only be a non-measurable amount due to the tension force in the bottom chord holding the truss up.
I do not dispute what woodman88 has said, but the question asked is a matter of straightforward geometry.
If the splice has slipped 1/8", the angle change (call it [φ]) in the truss at that point is 1/(8*D) where D is the depth of truss.
If it happened at midspan, the rotation at each end is [φ]/2, so the deflection at midspan is (L/2)*[φ]/2.
If it happened a distance 'a' from the left support, the rotation at the left support is [φ](L-a)/L, so the deflection at the splice is [φ](L-a)a/L.
In other words, you can treat a concentrated angle change as a point load on a beam.
