How the resultant forces on groups of walls are represented in Advance Design?

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The resultant forces on groups of walls are expressed in the Global System. They are computed by the composition of the contributing individual resultant forces expressed in the Global System. In turn, each individual wall resultant force expressed in the Global System, is obtained from the individual wall resultant force computed relative to the conventional local axes system (see “How the resultant forces on walls are represented in Advance Design?”). This way, the resultant forces on the group will be independent from the local axes of the walls included in the group.

Model description

The composition of the resultant forces on group of walls is explained below in steps.
First of all, the results on each wall are computed relative to the resultant forces axes convention. The results are summarised in Table 1.

Mz - Resultant bending moment on walls, about the local conventional axis z

Table 1 - Resultant Forces on walls in local conventional system

The resultant forces of walls cannot be expressed about the Global system accessing the option in the Results display window – see picture below. To do this, it is necessary to select one wall and choose to display the resultant force for group – see picture below. The results are summarised in Table 2.

Results display settings

MX / Group - Resultant bending moment about the global X axis for selected wall 2 

MY / Group - Resultant bending moment about the global Y axis for selected wall 2 

Table 2 - Resultant Forces on walls relative to the global system

The resultant forces on the group of walls are available only relative to the global system, since local axes of the walls are not consistent.

The resultant forces on the group of walls are displayed and computed in the centre of gravity of the walls as follows:

MY/Group = MY/Group_wall1 + MY/Group_wall2 + NZ_wall1*x_w1 + NZ_wall2*x_w2

MX/Group = MX/Group_wall1 + MX/Group_wall2 + NZ_wall1*y_w1 + NZ_wall2*y_w2

TY/Group = TY/Group_wall1 + TY/Group_wall2

TX/Group = TX/Group_wall1 + TX/Group_wall2

NZ/Group = NZ/Group_wall1 + NZ/Group_wall2

Where:

x_w1 = (-1) and is the projection on X of the distance between the resultant axial resultant N on wall 1 (NZ_wall1) and the geometrical centre of the group

x_w2 = 0.5 and is the projection on X of the distance between the resultant axial resultant N on wall 2 (NZ_wall2) and the geometrical centre of the group

y_w1 = (-2) and is the projection on Y of the distance between the resultant axial resultant N on wall 1 (NZ_wall1) and the geometrical centre of the group

y_w2 = 1 and is the projection on Y of the distance between the resultant axial resultant N on wall 2 (NZ_wall2) and the geometrical centre of the group

See picture below to identify the axial resultant forces lever arms.

Lever arms of axial resultant forces

The results are computed at the top (up) of the walls and at the bottom (down) and are summarised in Table 3.
 

Table 3 - Resultant Forces on group of walls (relative to the global system) 

MY / Group - Resultant bending moment about the global X axis for selected walls 1 and 2