Design forces in Wall Modules

This wiki describes the procedure to calculate a section cut resultant forces of a surface divided into shell finite elements (FEM), using corner forces that are in equilibrium. The procedure is as follows:

1.    Define the Section Cut Plane

First, define the location and orientation of the section cut plane. This would be a vertical for wall models.

For FEM models in a Cartesian coordinate system, define the plane mathematically (e.g., by its normal vector and a point on the plane) or by specific geometry lines if you're performing a 2D cut along certain shell edges.

For each segment to design bearing walls or shear walls we get three sections, the top, bottom and maximum moment (in-plane for shear and out-of-plane for bearing) section.

 Wall section cuts for design

 
Lintel section cuts for design

2.    Identify Shell Elements Crossing the Section Cut

Determine which shell elements intersect the defined section cut plane. These elements contribute forces to the section cut.
If necessary, find the precise intersection points on the shell element edges. This step can be simplified if the cut is aligned with the shell mesh.

 Shell elements that intersect with Section Cut

3.    Extract Corner Forces

Extract the nodal (corner) forces from each shell element that intersects the section cut. In FEM analysis, these forces at each node typically include six degree-of-freedom (6 DOF) axial, in-plane shear, out-of-plane shear, in-plane moment, out-of-plane bending forces and torsion, given as resultants from equilibrium.

Corner forces should be in equilibrium, meaning that the total force and moment vectors for each shell element should sum to zero. This ensures that forces are balanced, respecting the principles of static equilibrium.

4.    Resolve Corner Forces to the Section Cut

For each shell element crossing the cut, resolve the nodal forces to the section cut plane.

Decompose forces at each node into components parallel and perpendicular to the cut plane. This step may involve transforming the force vectors from the global coordinate system to the local coordinate system of the section cut.

This transformation helps isolate shear, axial, and bending contributions along the section cut direction.

Corner Forces that are above Section Cut

5.    Calculate Resultant Forces and Moments

Sum the force components (shear, axial, and normal) and moments from each shell element along the section cut to find the resultant forces and moments.

Moment contributions can be calculated by multiplying the resolved forces by their perpendicular distance to a chosen reference point on the section cut (often the centroid of the cut line or a chosen origin).

Ensure that the equilibrium equations hold, confirming that your resultant forces accurately represent the internal load transfer along the section cut.

To have an accurate resultant, the internal pressure forces applied to the element should be considered in the equilibrium. So, the pressure on the upper shell polygon should be calculated and the gravity center. Consider that the pressure could be uniform and variable.

Resultant force at middle point

6.    Verify Equilibrium

Check that the sum of the resolved forces and moments along the section cut satisfies equilibrium, which means the sum of the forces in all directions and the sum of the moments should balance to zero.

Any discrepancy indicates potential issues with the force data or the cut definition. Small numerical errors are normal, but significant discrepancies may require revisiting the extraction and transformation steps.

7.    Interpret and Apply Resultant Section Cut Forces

Use the resultant forces and moments to understand the load-carrying behavior across the section cut. These results can reveal information about internal stresses, structural performance, and safety margins.

For design or analysis, the resultant section forces may be compared to material strengths, safety requirements, or serviceability limits as part of a larger structural evaluation.

This process relies on accurate force extraction, precise alignment of the section cut, and careful transformation of forces to the cut plane. This approach ensures that the internal load paths and equilibrium of the FEM surface are maintained and properly reflected in the section cut analysis.