In spMats, reference is often made to objects, members, and elements. Objects represent the physical structural members in the model. Elements, on the other hand, refer to the finite elements used internally by spMats to generate the stiffness matrices. In many cases, objects and physical members will have a one-to-one correspondence, and it is these objects that the user draws in the spMats interface. Objects are intended to be an accurate representation of the physical members.

Physical Model

Analytical Model

Templates is an option for creating new models in the spMats program. It enables the user to select from a set of pre-defined templates and edit them for quick model generation.

The structural grids can be created or imported in order to facilitate the input of structural elements such as columns, walls, and piles in a specific structural plan view.

In spMats, the objects, or physical members drawn by the user, are automatically meshed internally prior to the analysis, into the greater number of finite elements needed for the analysis model, without user input. Because the user is working only with the physical member-based objects, less time is required both to create the model and interpret the results. The user, however, can dictate several meshing criteria after examination of the automatic mesh proposed by the program.

spMats 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

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.

spMats features a sophisticated FEM 64-bit Solver that analyzes large and complex models with speed.

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.

The minimum ratio of soil contact area with respect to total initial soil-supported area (%) is set to 50% as default by spMats 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.

The Principal of Minimum Resistance is used by spMats to obtain values for the design moments, which include the effects of the twisting moment. Then, the equivalent design bending moments, Mux and Muy, for the design of reinforcing steel respectively in the X and Y direction are computed.

spMats offers two options for the computation of the required flexural reinforcement under Solve Options. These are:

• Compute required reinforcement based on maximum moment within an element.
• Compute required reinforcement based on average moment within an element.

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)

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 calculates the soil pressures at all four nodes of an element for both service load and ultimate load combinations. The calculated soil pressures are compared with the allowable pressure values during the analysis. If the calculated soil pressure exceeds the allowable pressure specified by the user, the Program displays a warning message when analysis is completed and elements with this condition are indicated in the graphical pressure contours view.

Pressure Down Contour Views – Envelope Values – Construction Crane Foundation Pad

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.

Displacement down (settlement)

Displacement up (uplift)

The Tables Module enables the user to view program inputs and outputs in tables and export them in different formats.

The Reporter Module enables the user to view, customize, print and export reports in different formats.

• Support for ACI 318-14/11/08/05/02 and CSA A23.3-14/04/94 design standards
• Object-based modeling of foundation slab systems with a full featured graphical interface
• Structural grids may be utilized to facilitate structural member placement from plan
• Export of column and/or pile sections as CTI files to be analyzed by spColumn
• Import of grids, loads, and load cases & load combination information from text files to facilitate model generation
• Export of grids, loads, and load cases & combination information from text files to facilitate model generation
• Four-noded, prismatic, thin plate element with three degrees-of-freedom per node
• Material properties (concrete and reinforcing steel) may vary from slab object to slab object
• Soil may be applied uniformly over slab objects or concentrated and applied at nodes using nodal spring supports
• Default definitions and assignment of model properties are provided to facilitate model generation
• Nodes may be restrained for vertical displacement and/or rotation about X and Y axes
• Nodes may be slaved to share the same displacement and/or rotation
• Applied loads may be uniform (vertical force per unit area) or concentrated (Pz, Mx, and My)
• Load combinations are categorized into service (serviceability) and ultimate (design) levels
• The self-weight of the slab is automatically computed and may optionally be included in the analysis
• Result envelopes (maximum and minimum values) for deflections, pressures, and moments
• Design moments include contribution of twisting moments via Wood-Armer formulas
• Isometric (3D) view of the modeled slab with ability to view grids, loads and other typical model features in typical CAD environment in multi view ports with up to 6 concurrent views
• Contour plots to visualize results of analysis and design
• U.S. Customary or SI (metric) units
• Checking of data as they are input for validation
• User-controlled screen display settings including a full color pallet
• Ability to save defaults and settings for future input sessions
• 26 Load cases
• 255 Load combinations (service plus ultimate)
• 64,500 Mesh elements

spMats provides the options to export column and/or pile sections, used in the foundation model, as spColumn Text Input (CTI) files for analysis by spColumn. The loads coming on the sections after analysis are also included in the exported files. This export can only be done with the model had been executed and results generated.

spMats Program

Automation & Integration

spColumn Program

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

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

Structural engineers routinely ask us about the influence of mesh density on the results obtained from spMats models. Read more