Mat foundation

A rectangular mat under many columns, analysed by the conventional rigid method (ACI 336.2R approach) and designed to ACI 318-19 (13.3.4, Chapter 8, 22.6) with ASCE 7-22 loads. The strip design is approximate, as the method is; the chapter says where it stops.

Inputs of the mat foundation #

• Mat: Lx, Ly, thickness h, soil cover and unit weights.
• Columns: each column's centre (from the mat's lower-left corner), size and unfactored gravity loads (D, L, Lr, S). Overturning moments of the wind or seismic system at the mat base (W, E; both directions are checked).
• Column line tolerance: columns closer than this in one coordinate form one column line (one strip).
• Soil: allowable pressure and basis; the modulus of subgrade reaction ks for the rigidity check only (0 skips it).
• Reinforcement: bottom and top bars each way (size, spacing), covers, λs option (13.2.6.2 lets you neglect it).

Auto-design (editor toolbar) varies the thickness (2-in. steps) and the bottom and top mats (bar size and spacing, each way). Objectives: lowest cost index (concrete, formwork, reinforcement); least concrete, then cost. Every other input is kept; see Auto-design.

Checks performed #

The drawings (screen, report, DXF and PDF sheet) show the mat plan with the columns, the column lines and their dimensions, section A along x through the column line of the strip with the largest moment (columns, top and bottom bars each way at their spacing, covers, soil cover) and that strip's factored moment diagram under it. The smallest sheet scale is 1/16" = 1'-0" (1:200): a mat longer than about 55 ft (17 m) needs the 11 × 17 sheet. Cut-offs, splices, added column-strip bars and dowels are not part of the calculation and are not drawn.

Limitations #

• Rigid method only: partial contact, flexible mats (plate on springs) and irregular mats need a plate analysis.
• Strip moments are spread uniformly over the strip width; the concentration at the columns is not modelled. Provide continuous top and bottom bars both ways (R13.3.4.4).
• Column moments are not entered; the edge and corner punching checks use the shear's eccentricity (conservatively added to any moment).
• The edge rule for punching (an edge or corner section where a column face is within d of the edge) and the rigidity criterion follow common practice (ACI 336.2R, ACI 421.1R); they are marked for verification against those documents.

Verification examples #

Published worked example (backend/tests/test_verify_mat_foundation.py): Das, Principles of Foundation Engineering, mat by the conventional rigid method (16.5 m × 21.5 m, 12 columns, 11,000 kN, resultant 0.44 m and 0.1 m off the centre), as reproduced in free university lecture notes. The published pressures are those of the column loads (the mat's weight is uniform and is subtracted for the comparison).

Das's strip moments are not compared: they are taken at the column centrelines under a uniform average pressure, the program takes them at the column faces under the planar pressure. No free published example of the punching or strip design of a mat to ACI 318-19 was found (ACI 336.2R and the CRSI Design Handbook would provide one).

Hand calculation of the default design: 54 ft × 54 ft × 42 in, 3 × 3 columns at 24 ft.

The strip moment differs by 0.05 % because the diagram is sampled at 100 stations.