Powered by a sophisticated FEM Solver increasing capacity and substantially speeding up solution for large and complex models, spMats v8.12 is widely used for
analysis, design and investigation of concrete mat foundations, footings, and slabs on grade.
spMats, formerly pcaMats and MATS, is equipped with the latest American (ACI 318-14) and Canadian (CSA A23.3-14) concrete codes. spMats is utilized by engineers worldwide to optimize
complicated foundation design,and improve analysis of soil structure interaction.
spMats uses the plate-bending theory and the Finite Element Method (FEM) to model the behavior of the mat or slab. The soil supporting the slab is assumed to behave as a set
of one-way compression-only springs (Winkler foundation). The boundary conditions may be the underlying soil, nodal springs, piles, or translational and rotational nodal restraints.
The model is analyzed under uniform (surface) and concentrated loads. The resulting deflections, soil pressure (or spring reactions), and bending moments are output.
Reinforced Concrete Foundation Systems
Spread and Combined Footings
Office Building Mat Foundation
Tank Pad Foundations
Circular Tank Foundation
Pump Station Building Foundation
Telecommunication Tower Foundations
Telecommunication Tower Foundation
To the top
Analysis & Design
Finite Element Method
spMats Program uses the Finite Element Method for the structural modeling and analysis of
reinforced concrete slab systems or mat foundations subject to static loading conditions. The slab is idealized as a
mesh of rectangular plate finite elements with four nodes at the corners and three degrees of freedom (Dz, Rx and Ry)
per node. This element considers the thin plate theory, which makes use of the following Kirchhoff hypotheses.
Finite Element Meshing - Node Element Numbering
The soil supporting the slab is modeled as a group of linear uncoupled springs (Winkler type)
concentrated at the nodes. The soil element is tensionless, weightless, and has one degree of freedom, which is the displacement
in the Z direction (Dz). The contribution of each element node to the soil spring stiffness is equal to the nodal tributary area
(one-fourth of the element area) multiplied by the soil subgrade modulus, Ks, under the element. Additional nodal springs may be
applied in parallel to the Winkler’s springs. Accordingly, their linear stiffness, Kns, is added to the equivalent spring constant.
Two-way (Punching) Shear Calculations
spMats program checks the punching shear around columns and piles for ultimate load combinations
per American (ACI 318), and Canadian (CSA) concrete codes. Piles are allowed to be embedded into the slab/mat which effectively
decreases the average effective depth of the critical section segments.
To the top
spMats reports the reinforcement quantities per unit length. The base reinforcement ratio can be specified by the user that is taken into account (base reinforcement
shown with blue color in contour views below) by the Program when displaying reinforcement contours.
Required Top Reinforcement Along X-Direction (in2/ft)
Required Bottom Reinforcement Along X-Direction (in2/ft)
Required Top Reinforcement Along Y-Direction (in2/ft)
Required Bottom Reinforcement Along Y-Direction (in2/ft)
spMats reports the extreme positive (top layer) and extreme negative (bottom layer) Wood-Armer design bending moments, Mux, and Muy in X- and Y-directions per unit length.
Top Layer Design Moments Along X-Direction (k-ft/ft)
Bottom Layer Design Moments Along X-Direction (k-ft/ft))
Top Layer Design Moments Along Y-Direction (k-ft/ft)
Bottom Layer Design Moments Along Y-Direction (k-ft/ft)
Design Moment Contour Views – Envelope Values – Pile Supported Industrial Foundation
Contour View – Pressure down Envelope (ksf)
spMats reports displacements, both settlement and uplift, for individual service and ultimate load combinations as well as
envelope values. The user may set a maximum allowable service displacement limit.
During the analysis, if loading/support conditions or the mat shape causes any uplift and induces tension in a
spring (soil, nodal spring, or pile), the spring is automatically removed. The mat is re-analyzed without that or any other tension spring.
The program automatically iterates until all tension springs are removed and equilibrium is reached. The Program allows the user to specify
a positive nodal displacement criteria beyond which a node is considered to be in uplift. Since the supporting soil is assumed to be tensionless,
the default value for this nodal displacement is zero. However, this option can be utilized for pile only supported foundations with piles
that have tension capacity. In this case, the positive nodal displacement input shall enable the pile to take tension as long as the specified
positive displacement limit is not reached.
Soil Contact Area
Minimum ratio of soil contact area with respect to total initial soil-supported area (%) is set to 50% as default by
the Program and. needs to be approved or reentered by the user based on project requirements. Setting this ratio to 100% together with positive
nodal displacement criteria set to zero ensures no uplift in the model as the solution will not be completed and an error message will appear.
For example, a mat foundation for a Nuclear Power Plant may require such a strict criterion to be set in spMats.
Pile Only Supported Foundations
spMats allows the user to model, analyze, design, and investigate pile supported foundations
without the contribution of weak soil under the mat.
Pile reactions (compression or tension) for individual service and ultimate load combinations
as well as envelope can be calculated by spMats Program.
An existing L-shaped foundation slab (supported by Soil 1) will undergo expansion (supported by Soil 2). On the expansion side,
the soil subgrade modulus is 100 kcf because the contractor could not match the soil properties under the existing foundation slab, which is 200 kcf.
spMats software program is utilized to investigate the impact of the dissimilar soils. Read more
Single Layer Reinforcement
Ground supported slabs are frequently designed with a single layer of reinforcing. Such slabs are referred to as membrane slabs,
floating slabs, or filler slabs and range in thickness from as little as 4" to 8" depending on the supported loads. In warehouses and storage facilities such
slabs are subjected to concentrated point loads from storage rack posts or forklift wheel loads. Read more
Finite Element Mesh Density
Structural engineers routinely ask us about the influence of mesh density on the results obtained from spMats models. Read more