Determination of the design moments

In the case of reinforced foundations, the design moments for the bending reinforcement of the slab must be determined from the soil pressure. There are two pairs of design moments:

• Design moment pair for the bottom reinforcement of the plate
• Design moment pair for the top reinforcement of the slab

These design moment pairs consist of the design moments for the respective reinforcement in the direction of the principal axes of the support coordinate system.

Concrete foundations | Determination of design moments

The figure shows a simply loaded foundation. A straight-line stress distribution arises below the foundation block. The program ensures that the exact stress is determined under the four corner points of the foundation as well as in the foundation center, and that the distribution of a gaping joint is determined, if necessary. As soon as the distribution of the stress below the foundation block is known, the design moments for the bottom reinforcement of the slab can be determined in the x- and y-directions.

design sections

The determination of the design moments is based on the so-called "design sections". The execution depends on how the column is connected to the foundation plate. For the individual connection types, the program automatically determines the appropriate design sections (some foundation types are still in preparation).

Column Without Bucket or Block Foundation

Concrete foundations | Design section of the exterior of columns

The design sections are run along the faces of the column. Thus, the distances Δ_x and Δ_y of the respective design sections from the corresponding parallel axes of the support coordinate system are obtained as follows:

Bucket Foundation with Smooth Bucket Inner Walls

Concrete foundations | Pile foundation with smooth pile inner walls: Design section along the outer side of the columns

The design sections are guided along the external sides of the column as in the case of a column without a bucket.

Bucket foundation with rough bucket walls

Concrete foundations | Pocket foundation with rough pocket inner walls: Design section through the center of the pocket wall

The design sections are taken through the center of the bucket walls. We obtain the following distances:

Design moments

First, the resultant of the compression stress is determined as the volume of the compression stress body beyond the design section. The program determines the distance of the centroid of this compression stress body perpendicular to the design section. The product of the resulting compression force multiplied by the distance to the design section results in the compression moment M_d.

Thus, the compressive moment M_d is determined from a compressive stress that also includes components of loads that load the soil directly in their direction of action, and thus do not cause any bending of the foundation plate. These compressive stress components occur due to the self-weight of the foundation plate, the earth covering, and, if necessary, an additional uniformly distributed surface load. These components must be subtracted from the compressive moment. This is done by multiplying the foundation area up to the design section by the distance of the centroid, then multiplied by the corresponding area loads. In this way, the component M_G is calculated of the compression moment that does not cause bending and must, therefore, be subtracted from M_d. The remaining difference then results in the design moment_Mbottom.

Calculation of design moments for the bottom reinforcement

In this way, the design moments for the reinforcements are determined in the x- and y-directions.

The design moment for the upper plate reinforcement is calculated analogously from the difference of the moments from soil pressure and loading.

Calculation of design moments for the bottom reinforcement