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Unexpected moment forces from Frame

Consider the Frame example in Figure 1.

analysis img_01
Figure 1: Frame model under consideration.

The following applies to the model in Figure 1:

  • Full 3D Domain.
  • Supports resisting translation only (i.e. simply supported beams).
  • Equal loading of 20kN/m on the beams.
  • Linear analysis type is used.
  • Beam length = 4.5m.
  • Own weight is excluded from analysis.

The analysis generates two different moments in the main beams, although the two beams
have identical length and loading.

analysis img_02
Figure 2: Moments in X-Direction.

One would expect a moment in the beams to be similar to the equation:

analysis img_03
When the diagonal members are removed and the analysis is done, the moments in the
beams are equal to the result in the above equation (50.6 kNm).
analysis img_04
Figure 3: Moments in X-direction (no diagonal members).

When the diagonal members are added, a transfer of moments occurs between the beams
and the diagonal members. The transfer occurs for the following reasons:

  1. The diagonal members have fixed end connections.
  2. There is a difference in the moments at each of the two nodes of the diagonal
    members. For equilibrium to be reached, a moment transfer occurs between the two
    nodes. (The amount of moment that is transferred depends on the stiffness of the
    elements.)

Note the results for the analysis without the diagonal members (see figure 3). The moments
are equal, even though there are struts in between the two beams. The reason for this is
that the moment at each of the two nodes of each strut is equal. Therefore, no transfer is
required for equilibrium.

To minimise the transfer of moments, the diagonal members should be pinned.

analysis img_05
aFigure 4: Moments in X-direction (Pinned diagonal members).