Displaying the resultant in the section across a slab

When displaying the results in sections across slabs, you may select between two options. Either the distribution over the section is displayed or the resultant for that section is calculated and shown.

Procedure to display the resultant in the section across a slab

  1. Have the project calculated.

  2. Open service Results.

  3. Call a function that displays the results in slabs in sections, i.e.:

    1. 2D members > Deformation of nodes,

    2. 2D members > Member 2D – Internal forces,

    3. 2D members > Member 2D – Stresses.

  4. Set the Drawing to Resultant.

  5. Select the quantity to be displayed.

  6. If required, adjust other display parameters.

  7. Refresh the screen.

Behaviour and features

Direction of the resultant

If the resultant of force in some section on a 2D member (in this example slab) is being plotted (in this example force F_z), there are two options of the coordinate system (CS) to choose: "LCS - Member 2D" (LCS) and "Global" (GCS). For some cases, even if the direction of the z-axis of the LCS is the same as the GCS, the direction of the resultant might be the opposite (as in the picture below). This is a feature, and the meaning of this is explained in this chapter.

In order to understand the reason, fist let's discuss what is being actually considered for the "resultant of the force in a section".

Consider a beam loaded by a self-weigh as in the figure below. For a considered convention, the internal force V (V_z) would have a sign and a distribution as depicted below.

However, that is given for the internal force. But, what is the resultant of forces in the considered section? Depends which part of section (from left, or right) is to be considered. The total resultant in a single point is always = 0 (static equilibrium of forces). Therefore, if in a given section a resultant is desired, it must be somehow defined which part of the section is required to consider. In SCIA Engineer, it is possible to model a section on 2D anywhere (also through the 2D FEM elements), and the results are interpolated. However the "selection" of either the left or right part of the section is automatic, not to be altered, and it is based on the CS x-axis direction - explained below.

There are 5 types of rectangular slabs, each 1 m wide and 4 m long, mesh size 0,5 m. Slabs are noted as #A1 - 3 , #B2 and #B3.

Case #A1 = edges aligned with the GCS.

Case #A2 =slightly rotated anticlockwise, LCS of the slab (and also mesh elements) is parallel with GCS.

Case #A3 =slightly rotated clockwise, LCS of the slab (and also mesh elements) is parallel with GCS.

Case #B2 =slightly rotated anticlockwise, LCS of the slab is rotated the same angle as well (x-axis of the LCS is still parallel with slab edge).

Case #B3 =slightly rotated clockwise, LCS of the slab is rotated the same angle as well (x-axis of the LCS is still parallel with slab edge)

If the sections are defined in a distance of 0,1 m from the slab ends, the resultant F_z in the sections are as below:

For case #A2, the direction of resultant is opposite from the other cases. For this case #A2, the direction of the section itself is slightly rotated clockwise from the #x-axis.

#x-axis is parallel with the LCS of the mesh elements (and for this case coincident with the GCS as well).

For cases #A1 and #A3, the #x-axis is parallel or rotated slightly anticlockwise respectively. For cases #B2 and #B3, the axis is parallel as well (the LCS there are rotated as well).

If the direction of the section is exactly parallel with the #x-axis, or rotated clockwise from this #x-axis, one part of the "section" is considered for the evaluation, and the resultant is "minus" (therefore in this example this force would represent the action on the little cut-out-part). If the direction of the section is rotated anticlockwise from this #x-axis, the other sign is considered, and the force would in such case represent for example a reaction on the larger cut-out-part.

If the results are to be considered in the GCS, the direction of the resultant changes for the case #B2, as depicted in the figures below. The same logic is being respected, but now the x-axis for evaluation, the "#x-axis " is considered to be parallel with the GCS. Otherwise analogical conditions are applied.

Notes:

The "correct" direction in this case cannot be determined by the software. It depends on the purpose and the angle of view of the user, therefore it is necessary to adapt the expected sign accordingly.

The same applies for F_y and F_x resultants - the directions might be and will be exactly the opposite in some cases. The #x-axis defines the direction of the right-handed Cartesian CS, the y and z axis are hence defined.