Analysis and design of mats is based on finite element method (FEM) coupled with slab-on-elastic-subgrade principles.

First, you will create a finite element model of the proposed mat foundation. This may be accomplished in many ways:

Importing a STAAD.Pro file of the superstructure, thus providing reference points for initial mat set-up and load information, and defining boundaries of the mat, or by creating the foundation slab from scratch and inputting loading information manually or copy-pasting coordinates from MS Excel.

Any shape of mat (raft) can be modeled in STAAD Foundation Advanced. Various methods to create mat (raft) model are explained in Quick Tour and STAAD Foundation Advanced graphical environment. Any shape of hole or control region can be added to the mat (raft boundary).

STAAD Foundation Advanced follows physical modeling concept for mesh generation. By which you only have to specify the boundary for mat (raft) and program will generate plate mesh based on boundary geometry, loading, pile locations etc.

Program will also convert finite elements analysis results to global axis irrespective of plate orientations.

Modeling of foundation involves choosing meshing type (quadrilateral, triangular, or mixed), Internal Nodes Spacing Factor, Optimization Level.

As with any FEM project, the denser the grid (smaller elements), the more precise results will be obtained. In addition to the slab, the raft may include a number of beams between the column locations. Since the beams would normally be part of the foundation, the slab polygonal meshing algorithm accounts for the presence of the beam and ensures that they become continuously integrated with the slab. New nodes are purposely created on the centerline of the beam and the beam is split between those points into a number of segments.

Meshing setup can be further refined using Optimization Level and Internal Nodes Spacing Factor. Higher optimization level implies program will try to precise the mesh with higher number of iterations. For larger mats higher optimization level will lead to substantially large computer processing time. Internal Nodes Spacing Factor is inversely proportional to node density inside the mesh.

Once the mat is defined and all material/soil properties are input, the program may proceed with the analysis of the structure. It is performed by the STAAD Analysis Engine. Realistic soil response is achieved by employing non-linear (compression only) spring supports to model subgrade reactions. Pile reactions, if present, are proportional to linear displacements of the supported node and include both compression and tension (uplift).

Using control regions different soil properties can be assigned a single mat model. Also mat can be partially resting on soil and pile supports.

The program calculates internal forces and deflections for all slab and beam elements of the foundation. This information is then used in the design stage of the program to:

Establish the required top and bottom flexural reinforcing in two orthogonal directions, check punching shear capacity at column locations.

The flexural design is done in accordance with ACI 318 Chapter 10 of the Code (for US jobs). The reinforcement areas are computed for a notional band one unit of length wide.

The program allows the designer, as an option, to use the Wood-Armer equations for reinforcement calculations, as follows:

Mx, My, and Mxy are fetched or calculated, as described above. They are used to compute the values of design moments, Mxd and Myd.

For top reinforcement, the program computes:

Mx1 = Mx + abs(Mxy)

My1 = My + abs(Mxy)

Mx2 = Mx + abs(Mxy2 / My)

My2 = My + abs(Mxy2 / Mx)

If both Mx1 and My1 are positive, Mxd = Mx1 and Myd = My1.

If both Mx1 and My1 are negative, Mxd = 0 and Myd = 0.

If Mx1 is negative and My1 positive, Mxd = 0 and Myd = My2.

If My1 is negative and Mx1 positive, Mxd = Mx2 and Myd = 0.

For bottom reinforcement:

Mx1 = Mx - abs(Mxy)

My1 = My - abs(Mxy)

Mx2 = Mx - abs(Mxy2 / My)

My2 = My - abs(Mxy2 / Mx)

If both Mx1 and My1 are positive, Mxd = 0 and Myd = 0.

If both Mx1 and My1 are negative, Mxd = Mx1 and Myd = My1.

If Mx1 is negative and My1 positive, Mxd = Mx2 and Myd = 0.

If My1 is negative and Mx1 positive, Mxd = 0 and Myd = My2.

Mxd and Myd are then used in lieu of Mx and My for calculations of the required reinforcing. Use of the modified bending moments brings about more accurate distribution of the reinforcing, better matching critical areas of the slab.