When a slab is subjected to a gravity-directed load, can I find the bending moment of the slab using the Local Direction Force Sum function?
Yes, you can use the Local Direction Force Sum (L.D.F.S.) function to calculate the bending moments in a slab.
I will explain this for two cases: when a beam is modeled with plate elements (with in-plane loads) and when a slab is modeled (with out-of-plane loads).
[Image 1] Beam subjected to in-plane loads (Case 1)
[Image 2] Slab subjected to out-of-plane loads (Case 2)
[Image 3] Table results for the beam subjected to in-plane loads
[Image 4] Table results for the slab subjected to out-of-plane loads
In Case 1, where in-plane loads act, the node forces and moments for the plate elements result in in-plane forces only, as shown in Image 1. Therefore, you can use the L.D.F.S. function to calculate the in-plane bending moment (My) from the in-plane force (Fx) as follows
My = -(44.594 + 43.166)*0.75 + -(30.744 + 7.769 + 6.340 + 29.316)*0.25 = -84.362kN*m
In Case 2, where out-of-plane loads act, the node forces and moments for the plate elements result in out-of-plane forces only, as shown in Image 2. Therefore, you can use the L.D.F.S. function to calculate the out-of-plane bending moment (Mz) from the out-of-plane force (Mx) as follows
Mz = -3.129 - 3.126 - 3.120 -3.120 - 3.126 - 3.129 = -18.75 kN*m
[Image 5] Bending moments calculated using L.D.F.S. for Case 1 & Case 2 & Case 3
In Case 3, when both in-plane (inplane load) and out-of-plane (outplane load) loads are simultaneously applied, the results are obtained by summing the results of the cases with only in-plane loads and only out-of-plane loads.