## Question

**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?**

## Answer

**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.