Nodal unknowns, stiffness and mass matrices, local loads and internal forces defined are the same as in the bar of a plane spatial truss. Viscous damping matrix is defined based on the functionality of possible work with the use of the basis functions of the truss element.

$$ \int_{0}^{L}(C_{x}\cdot \frac{\partial u_{1}}{\partial t\cdot \partial x} \cdot \frac{\partial \nu_{1}}{\partial t\cdot \partial x} + C_{yz}(\frac{\partial u_{2}}{\partial t\cdot \partial x}\cdot \frac{\partial \nu_{2}}{\partial t\cdot \partial x}+\frac{\partial u_{3}}{\partial t\cdot \partial x}\cdot \frac{\partial \nu_{3}}{\partial t\cdot \partial x}))dx $$

Here \( C_{x},~C_{yz} \) – the coefficients of viscous damping proportional to the velocity gradient.

Input data specifies the linear weight, axial stiffness and two coefficients of viscous damping: in axial and orthogonal directions. The element can be used in problems DYNAMICS+ for modeling seismic isolators or damping properties of soil and supporting structure.

Fig. P1. Elasto-viscous seismic isolator

In addition to elasto-viscous seismic isolators, there are others for which nonlinear damping models may be more appropriate. These include, for example, rubber-metal supporting parts with a lead core, or pendulum supporting parts. Such seismic isolators would be best modeled based on their realistic nonlinear behavior model.

Fig. P2. Model of damping devices of a building based on supporting parts with a lead core

Single-noded elements are suitable for modeling buildings which have their dampers fixed to a conditionally rigid foundation – only superstructure is taken into account, while the substructure remains fully rigid. Two-noded elements are suitable for more detailed calculations, taking into account the modeling of the combined behavior of substructure and superstructure.

Single-noded and two-noded elements (## 257, 257) of non-elastic links are developed. For each nodal unknown, its own nonlinear strain diagram is specified, at that a linear strain diagram is also allowed. The law of nonlinear strengthening is set for nonlinear diagram. For elastoplasticity at unloading, the initial modulus of elasticity is used; for isotropic strengthening, the elastic work (using the initial modulus) will continue until the maximum value (tension or compression) is exceeded throughout the load history.

This FE allows to take physical and geometrical nonlinearity into account simultaneously during the calculation of bar systems. The main characteristics are set as for physical nonlinear element. The calculation is performed by a step method. At each step, the stiffness matrix is formed in the “new position” coordinate system with a change of tangent modulus of elasticity; the structure geometry is changed according to the Cauchy-Green strain tensor, namely:

$$ \varepsilon_{ij}=\frac{1}{2}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u_{j}}{\partial x_{i}}+\sum_{l}^{}\frac{d u_{l}}{d x_{j}}\frac{d u_{l}}{d x_{i}}) $$

The main difference of these elements compared to the previously implemented elements of type 410 is that under reverse loading state their unloading is carried out according to the initial modulus of elasticity (elastoplasticity phenomenon). It better corresponds to the actual behavior of most structures compared to the nonlinear elasticity model. Also, such elements can work with material according to the Laws 12 and 16, where there is a descending branch in the compression tension-stain curve.

This FE is used for strength calculation of thick hollow shells. The Reisner functional is used. Each FE node has six degrees of freedom, namely:

U – horizontal displacement, the positive direction of which coincides with direction X1;

V – horizontal displacement, the positive direction of which coincides with direction Y1;

W – vertical displacement (deflection), the positive direction of which coincides with direction of axis Z1;

UX and UY – angles of rotation relatively to the axes X1 and YI, the positive direction of which is exactly opposite to the clockwise direction of rotation if you look from the end of these axes;

UZ – angle of rotation relatively to the axis Z of the general coordinate system.

The degrees of freedom U, V correspond to membrane ones, and W, UX, UY correspond to bending strains. The angle of rotation UZ is not one of the nodal parameters which determine the element strains and it is equal to zero in the local coordinate system. This degree of freedom appears when joining the elements lying in different planes and is necessary to consider a spatial work of the structure.

It can be either triangular (FE 346 of thick shell) or quadrangular (FE 347).

This FE is used for strength calculation of thick hollow shells. The Reisner functional is used. Each FE node has six degrees of freedom, namely:

U – horizontal displacement, the positive direction of which coincides with direction X1;

V – horizontal displacement, the positive direction of which coincides with direction Y1;

W – vertical displacement (deflection), the positive direction of which coincides with direction of axis Z1;

UX and UY – angles of rotation relatively to the axes X1 and YI, the positive direction of which is exactly opposite to the clockwise direction of rotation if you look from the end of these axes;

UZ – angle of rotation relatively to the axis Z of the general coordinate system.

The degrees of freedom U, V correspond to membrane ones, and W, UX, UY correspond to bending strains. The angle of rotation UZ is not one of the nodal parameters which determine the element strains and it is equal to zero in the local coordinate system. This degree of freedom appears when joining the elements lying in different planes and is necessary to consider a spatial work of the structure.

It can be either triangular (FE 446 of thick shell) or quadrangular (FE 447).

These FE allow to take physical and geometrical nonlinearity into account simultaneously during the calculation of bar systems. The main characteristics are set as for physical nonlinear element. The calculation is performed by a step method. At each step, the stiffness matrix is formed in the “new position” coordinate system with a change of tangent modulus of elasticity; the structure geometry is changed according to the Cauchy-Green strain tensor, namely:

$$ \varepsilon_{ij}=\frac{1}{2}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u_{j}}{\partial x_{i}}+\sum_{l}^{}\frac{d u_{l}}{d x_{j}}\frac{d u_{l}}{d x_{i}}) $$

This FE is used for strength calculation of hollow shells. Each FE node has six degrees of freedom, namely:

U – horizontal displacement, the positive direction of which coincides with direction X1;

V – horizontal displacement, the positive direction of which coincides with direction Y1;

W – vertical displacement (deflection), the positive direction of which coincides with direction of axis Z1;

UX and UY – angles of rotation relatively to the axes X1 and YI, the positive direction of which is exactly opposite to the clockwise direction of rotation if you look from the end of these axes;

UZ – angle of rotation relatively to the axis Z of the general coordinate system.

The degrees of freedom U, V correspond to membrane ones, and W, UX, UY correspond to bending strains. The angle of rotation UZ is not one of the nodal parameters which determine the element strains and it is equal to zero in the local coordinate system. This degree of freedom appears when joining the elements lying in different planes and is necessary to consider a spatial work of the structure. It can be either triangular (FE 642 of thick shell) or quadrangular (FE 644).

These FE allow to take physical and geometrical nonlinearity into account simultaneously during the calculation of spatial systems. The main characteristics are set as for physical nonlinear element. The calculation is performed by a step method. At each step, the stiffness matrix is formed in the “new position” coordinate system with a change of tangent modulus of elasticity; the structure geometry is changed according to the Cauchy-Green strain tensor, namely:

$$ \varepsilon_{ij}=\frac{1}{2}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u_{j}}{\partial x_{i}}+\sum_{l}^{}\frac{d u_{l}}{d x_{j}}\frac{d u_{l}}{d x_{i}}) $$

The main difference of these elements compared to the previously implemented elements of type 442, 444 is that under reverse loading state their unloading is carried out according to the initial modulus of elasticity (elastoplasticity phenomenon). It better corresponds to the actual behavior of most structures compared to the nonlinear elasticity model. Also, such elements can work with material according to the Laws 12 and 16, where there is a descending branch in the compression tension-stain curve.

This FE is used for strength calculation of thick hollow shells. The Reisner functional is used. Each FE node has six degrees of freedom, namely:

U – horizontal displacement, the positive direction of which coincides with direction X1;

V – horizontal displacement, the positive direction of which coincides with direction Y1;

W – vertical displacement (deflection), the positive direction of which coincides with direction of axis Z1;

UX and UY – angles of rotation relatively to the axes X1 and YI, the positive direction of which is exactly opposite to the clockwise direction of rotation if you look from the end of these axes;

UZ – angle of rotation relatively to the axis Z of the general coordinate system.

The degrees of freedom U, V correspond to membrane ones, and W, UX, UY correspond to bending strains. The angle of rotation UZ is not one of the nodal parameters which determine the element strains and it is equal to zero in the local coordinate system. This degree of freedom appears when joining the elements lying in different planes and is necessary to consider a spatial work of the structure. It can be either triangular (FE 646 of thick shell) or quadrangular (FE 647).

These FE allow to take physical and geometrical nonlinearity into account simultaneously during the calculation of bar systems. The main characteristics are set as for physical nonlinear element. The calculation is performed by a step method. At each step, the stiffness matrix is formed in the “new position” coordinate system with a change of tangent modulus of elasticity; the structure geometry is changed according to the Cauchy-Green strain tensor, namely:

$$ \varepsilon_{ij}=\frac{1}{2}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u_{j}}{\partial x_{i}}+\sum_{l}^{}\frac{d u_{l}}{d x_{j}}\frac{d u_{l}}{d x_{i}}) $$

Under reverse loading state the unloading of these elements is carried out according to the initial modulus of elasticity (elastoplasticity phenomenon).

The equation of non-stationary thermal conductivity taking into account nonlinear thermal and physical properties of material can be written as follows:

$$ \rho\cdot c(T)\frac{\partial T}{\partial t}= k(T)\nabla T+Q $$

where T – the current temperature;

\( \rho \) – material density;

c(T) – specific heat capacity of material, generally changes with body temperature;

k(T) – thermal conductivity factor of material, generally changes with body temperature;

\( Q \) – power of the external heat source.

The boundary condition of surface heat exchange is as follows:

$$ \alpha(T)(T-T_{c})+\sigma\cdot \varepsilon(T^{4}-T_{0}^{4})+Q=0 $$

\( Q \) – heat flow.

\( \alpha(T) \) – surface heat transfer coefficient, generally changes with body temperature at the boundary;

Tc – temperature of the environment;

\( \sigma \) – Stefan-Boltzmann constant;

\( \varepsilon \) – emission coefficient, sometimes called the degree of blackness.

For a mirror surface it approximates to zero, and for a black surface it approximates to 1.

If we accept that time derivative in the equation is equal to zero, we will obtain a stationary thermal conductivity equation:

$$ k(T)\nabla T+Q=0 $$

Release of SP LIRA 10.14 allows to take into account all the above mentioned parameters in stationary and non-stationary thermal conductivity equations. Consideration of nonlinear properties of heat transfer coefficient and specific heat capacity has been added compared to the previous version. The law can be preset in the SP LIRA 10 mode in the Material editor. At that, thermal conductivity factor should decrease with temperature rise and specific heat capacity should increase with temperature rise. Nonlinear properties can significantly influence the thermotechnical calculation for steel and reinforced concrete structures at temperature differences up to several hundred degrees, which is typical, for example, for fire conditions.

Fig. P3. Development of nonlinear thermal and physical properties of material in SP LIRA 10

For the elements of surface heat exchange the SP LIRA 10 added for consideration the nonlinear change of the convective heat exchange coefficient, and the term of radiation heat exchange, for which the emission coefficient (so-called body blackness degree) should be set in the input data of nonlinear thermal conductivity.

Fig. P4. Formation of nonlinear characteristics in the elements of surface heat exchange

For complex shapes of ribbed columns, walls or floor slabs, it is expedient to use equivalent elements. Although the basic part was implemented in previous SP LIRA 10 version, it is worth to mention the improvements in the program which resulted from upgrading from version 10.12 to 10.14.

Firstly, the developers managed to optimize and speed up significantly the work with the table of equivalent elements. Some users previously complained that on large models and a huge table of equivalent elements the program slowed down and the work became uncomfortable. We are glad to inform you that this problem is almost solved in version 14.

Secondly, for the mode of automatic generation of equivalent bars, the possibility of creating segments by the chain of nodes has been extended. If in the last version it was possible to do this only by two nodes, now the program will try to build a set of bars by all selected nodes. If the chain is set adequately, it is possible to build curvilinear beams, take into account intermediate nodes, etc.

Fig. P5. The process of generating the bar equivalent element chain

Finally, the third and the most important improvement is the ability to collect internal forces into equivalent bars from the bar elements. Previously, the SP LIRA 10.12 version allowed to collect internal forces only from plates and spatial elements, now this range is not limited any more. Thus, it is now possible to model a ribbed beam from a set of plates + bars + rigid inserts. And then, if necessary, transfer the obtained internal forces into equivalent element with T-section, and calculate the reinforcement.

Fig. С6. Equivalent elements collect internal forces from plates and bars

In some cases, it is not enough to know the internal forces in element and its displacements in its nodes, but it is important to know how the element impacts the structure at the connection points. Some of the most common examples in which a nodal reaction is needed are finding the total reaction on a span support, the reactions from pylon or column to calculate pushover, the slab foundation pressure on a soil foundation that is modeled by spatial elements, etc. The SP LIRA 10 provides an easy way to obtain this data. The calculation results include a Nodal Reaction mode, where the user can specify the nodes and elements from which the total reaction should be collected into a node. And then display 3 linear and 3 rotational components, and deplanation reaction. Also, the node reaction is available in the tables of results. In previous versions, it was possible to view the reactions only for linear static problems. Starting from version 10.14, the user is able to obtain reactions in nonlinear static problems. Therefore, the user will have more possibilities to analyze the results.

In previous versions, for the problems with assemblage, it was possible to collect masses only from loading states, if a modal problem is solved in the loading state or direct integration in dynamics is performed. The SP LIRA 10.14 allows to collect masses also from element densities, which in some cases will give a certain flexibility in the design.

Elastic basis in the form of subgrade reaction coefficients to geometrically nonlinear elements was not possible to assign in previous versions. In SP LIRA 10.14 this possibility has been implemented.

In previous cross sections the SP LIRA 10.14 implemented a single-noded finite element of reinforcement insert for modeling the reinforcement inserts. It is assumed that this finite element has the area of reinforcement insert and it is possible to set a linear or physically nonlinear law of material deformation for it.

Fig. S1. Adding the area of reinforcement insert

The possibility to set pre-tensioning is implemented for a single-noded finite element of reinforcement insert.

Fig. S2. Assignment of pre-tensioning

Important: Pre-tensioning must be set taking into account all losses. In nonlinear problem, incorrect setting of the reinforcement position and values of the reinforcement pre-tensioning can result in destruction of the cross section at the stage of concrete pre-stressing.

The material library for setting nonlinear laws of deformation includes the following dependencies \( \sigma-\varepsilon \) :

• Law 11 – Exponentially Dependent Material;
• Law 13 – Trilinear Dependence;
• Law 15 – Exponentially Dependent Concrete;
• Law 14 – Piecewise Linear Description;
• Law 12 – Nonlinear Law of Concrete Deformation (EuroCode 2);
• Law 16 – Nonlinear Law of Concrete Deformation (DBN V 2.6-98:2009).

Setting the nonlinear laws of material deformation allows to model nonlinear behavior of a cross section and determine the stresses non-linearly dependent on deformations.

Fig. S3. Stresses in concrete in linear and nonlinear formulation

Implementation of the ASSEMBLAGE module allows to model the multi-stage work of cross section with changing geometry at each stage. For example, a steel reinforced-concrete span bridge structure is usually characterized by two-stage work:

the first stage of work of the span structure is characterized by accommodation of the loads from the weight of steel structures, formwork, reinforcement and grouting concrete by steel bearing beams;

Fig. S4. The first stage of work

at the second stage, the combined loads from reinforced concrete slab and other existing loads are transmitted to the steel structures (weight of waterproofing, roadway pavement, railings, sidewalk blocks, lighting poles, communications, temporary loads from rolling stock and pedestrians, etc.).

Fig. S5. The second stage of work

One of the variants of steel reinforced-concrete span bridge structure is beam deck (Filler Beam Decks), so let’s consider a two-stage work on its example.

Fig. S6. Modeling of two-stage work for beam deck structure

The first stage of erection is usually characterized by linear work of the structure, and the second stage is characterized by nonlinear work effects.

For two-noded elements of thin-walled cross section the Stress-strain Behavior (hereinafter refer to as SSB) can be shown by means of mosaics or diagrams.

Fig. S7. Different methods for depicting stresses for two-noded elements

The ASSEMBLAGE module offers a wide range of possibilities for modeling cross sections. For example, dismantling of cross section parts allows to assess defects and internal stresses in damaged cross section, or to forecast the strengthening of such cross sections.

Fig. S8. Initial cross section of a column and cross section of the column with concrete chips in one corner and change in the SSB of this column

Fig. S9. Cross section strengthening with a metal cage made of angles

In previous versions while calculating the user-defined or automatic DCL, both normative and design internal forces (by using the coefficients set for the loadings) were calculated for each combination.

Starting from the version 10.14, when setting the user-defined design combinations it is now possible to specify which internal forces for this combination should be calculated: design, normative or both design and normative.

For automatic DCL this field will be completed automatically.

Automatic generation of design combinations array is performed in 2 stages:

• Generating the graph for logical links of loadings;
• Finding of all possible combinations of loadings by passing the graph for logical links of loadings.

For a large number of loadings with many logical links the generation of the graph and combinations could take too much time. During the development of SP LIRA 10.14 the algorithms generating automatic DCL were significantly accelerated and reliability of their operation at a very large number of resulting combinations was improved.

Two similar but fundamentally different methods of solving the same problem – calculations of the most dangerous combinations of loadings: design combinations of internal forces (DCF) and design combinations of loads (DCL) are used in calculation practice.

When implemented in SP LIRA 10.12 the requirements set forth in normative documents EN 1990:2002, SP RK EN 1990:2002+A1:2005/2011 and DSTU-N B V.1.2-13:2008 (hereinafter referred to as Eurocode 0) the DCL were considered. In SP LIRA 10.14 the accounting of Eurocode 0 requirements is also added to DCL.

Eurocode 0 provides for consideration of the following limit states:

• critical (combinations of actions specified in expressions (6.10) - (6.12b) must be used in calculations by Ultimate Limit State);
• serviceability (combinations of actions specified in expressions (6.14b) - (6.16b), must be used in calculations by Serviceability Limit State).

SP LIRA 10.12 version added EN 1990:2002 for the selection of normative documents for DCF/DCL.

When you click on the button Variable action coefficients according to EN 1990:2002, you will activate a dialog for the correction/setting of the coefficients \( \Psi \) for buildings, for choosing between the formulas (6.10) or (6.10a) and (6.10b) for the Group B (while formula (6. 10) is always used for Groups A and C), the use of \( \Psi \) 1,1 or \( \Psi \) 2,1 for emergency design situations, the selection of tables for the main combinations (permanent or transient design situations), and whether only permanent loads should be used in the formula (6.10a).

The selected tables are marked with checkboxes to make it possible to design structural elements for which geotechnical impacts and interaction with soil must be taken into account (one of the three approaches described in Eurocode 0 must be used).

To select the EN 1990:2002 norms for DCF/DCL, the following must be specified in the loadings:

- for permanent and pre-tensioning – type of impact, coefficients to normative and design loads for limit states of bearing capacity for permanent and transient design situations;

- for temporary and vertical impact caused by crane – impact type, coefficients to normative and design loads for limit states of bearing capacity for permanent and transient design situations, coefficients \( \Psi \) s for buildings;

- for emergency situations and seismic actions – impact type, coefficient for normative loads.

The Automatic combination must be added to the library of combinations to generate an automatic DCL.

The interface Automatic combination consists of 2 tabs.

The tab Generation displays an automatically created graph for logical links of loadings, which can be edited and the list of formulas to be used for combination.

Once you click the button Generate Combinations, the tab Combinations will be opened. It will display the generated combinations resulting from the combining.

In order to find possible combinations of loadings, it is necessary to learn the graph by search in depth method, and afterwards the found combinations will be entered into the given list of formulas. As a result, 328 combinations were generated for this problem.

Once the calculation is completed, the results of calculation will be available in tabular and graphical form in the mode of analysis both for each combination separately and as summary results for all combinations at once.

Rounding of architectural elements is one of the new features added in version 10.14. To round a pair of elements, you need to set the rounding radius and the number of steps in the edit mode of architectural elements. After that, by sticking the cursor, select a common node of two edges (the junction of two bars or the junction of two sections of an architectural plate polygon), or a common edge (for two plates) on the main view. Then, in the context menu, select the Round the contour command.

Rounding can be applied to any architectural elements, but it will be applied if it is possible to create it. Among the problems of creating a contour, for example, may be the following:

• the length of the edge is not enough to build an arc;
• the element becomes invalid after the rounding is built;
• the beginning and the end of faces of a pair of plates that are rounded do not completely coincide;
• when two plates are rounded, the area being rounded falls on an opening.

Fig. А1 Rounding of architectural elements

The ability to separate architectural elements at the places of their pairwise intersection has been added. For example, you need to cut off a triangular element from a roof wall using the Intersection command. At the intersection, the elements are divided into several ones, and new points appear, to which you can stick the cursor during further model construction.

Fig. А2 Removal of AE created by pairwise intersection

You can easily delete the cut off polygon using the context menu. Such functions facilitate the design of architectural structures. You can also delete points on the polygon of architectural elements.

Fig. А3 Deleting a point and the polygon itself

Unit vector in dynamic input mode. Another way to enter Unit vector coordinates has now been added to the architectural object construction mode. It works similarly to coordinate increments. The difference is that in the Unit vector mode, only the direction, in which the entered absolute value is maximum, is taken into account. At the same time, increments along other axes are ignored. To switch between these methods, use the “up” and “down” arrow keys, and to move between input columns - the “Tab” key.

Fig. А4 Entering coordinates using “Unit vector”

The program has a new functionality that allows you to smooth grids of finite elements using various algorithms. This functionality improves the shape of finite elements, which affects the accuracy of calculations.

Why is it necessary to smooth the grid?

Finite elements must have the regular shape to avoid peak stresses in the model. Regular shape means that the elements are close to a square or an equilateral triangle.

During automatic grid generation or in places of transition from a smaller to a larger grid, strongly elongated elements may be formed. Many triangular elements are also generated (when generating a square grid on a curvelinear plate).

Grid smoothing helps align elongated elements and merge triangular elements into square ones where possible. Thereby the shape of the elements is improved and their number is reduced, which facilitates the development of the correct stiffness matrix and calculation without peak values.

How to use the new functionality?

The program offers four different methods of grid smoothing, which are based on different algorithms for moving the internal nodes of the model. Each method has its advantages and disadvantages, therefore, when choosing a method, you should focus on the visual improvement of the shape of the elements.

Grid smoothing methods can be applied to the entire plate or to individual parts or elements. For this purpose, you need to select the desired elements with their nodes, choose one of the four smoothing methods and press the Smooth button, the program will rebuild the grid.

Fig. А5 Different algorithms for smoothing FE grid

The function of pasting a copied element via the clipboard has been added at the request of many users. Model elements can be pasted both in one task and between tasks.

Fig. А6 Copying via clipboard

When you work in Copy fragment or Move fragment mode, coordinate dynamic input mode is now available using insertion points.

Fig. А7 Dynamic editing of coordinates

The function of saving model fragmentation on created views has been added. You can now save model fragmentation on any created view. This allows you to show only the part of the model you are interested in by clicking “fix fragment”. You can also hide and show other elements of the model without losing the fixed fragment. To return to the fixed fragment, simply click “show fixed fragment”. You can create different groups of visible elements on each additional view. This function makes working with large models easier, allowing you to focus on the details you need.

Fig. А8 Model fragmentation on the created views

The possibility of automatic applying the selected checks, not pressing the “Assign” button each time, was added in the representation properties.

Fig. А9 Automatic applying of representation properties

The group creation function has been extended. If earlier we could only create groups of elements, now you can also add nodes to groups.

Fig. А10 Adding nodes to groups

The Absolutely rigid bodies (ARB) function has been added to the table editing, which allows you to set and change the parameters of rigid bodies. The ARB order number is recorded in the table. The basic ARB node is specified using a special symbol *.

The abilities for Unifications of displacements has been increased. You can create groups of unified displacements and assign them group numbers in the table. By default, the created groups of unified displacements are set in all 6 directions. Displacement directions are not specified in the table.

Fig. А11 ARB Table editing and Unifications of displacements

In SP LIRA 10.14, you can specify hinges for architectural and finite elements in the form of a table. This allows you to quickly and conveniently configure the types of hinges and their parameters. For elastic and non-linear hinges, you can specify a stiffness value or a non-linear law.

Fig. А12 Table editing of hinges

Rigid inserts for plates and bars can now be added and edited in tabular form. In the table, the type of insert is specified, and the coordinate system (for bar inserts) and the displacement value are selected.

Fig. А13 Table editing of rigid inserts

Moreover, the numbers of assembly stages can be entered in the table, which allows you to control the sequence of objects assembly.

Fig. А14 Table editing of assembling/disassembling stages

Editing and specifying in tabular form of bars’ local axes, axes for calculation of internal forces in bars, orthotropy axes and stress alignment axes for plates and solid elements are now available.

Fig. А15 Table editing of axes of bars, plates and solid elements

Where possible, the developers of SP LIRA10 improve the product, in terms of calculation speed as well. In the new 10.14 version, the work of the program with RC elements has been speeded up. Thus, thanks to new algorithms, the selection and verification of reinforcement has been accelerated - for large models by 1.1 - 2 times. Therefore, the engineer will have to wait less for results and will have more time to prepare documentation or search for a more optimal reinforcement solution. The procedure for reading reinforcement tables from files has also been improved. This, in return, will speed up the work on large diagrams when fragmenting elements with reinforcement mosaics.

Ribbed floors allow achieving the optimal ratio of stiffness, dead load, strength and rational consumption of construction materials. For residential buildings, for example, floor slabs with oval openings are often used; for roofs of industrial buildings, slabs with ribs in one or two directions can often be encountered. All this allows saving materials and reducing the weight of the structure. On the other hand, many engineers have difficulties with the selection of reinforcement in such slabs. In the previous version of SP LIRA 10, we already demonstrated how to calculate such structures using equivalent elements and plates, the stiffness of which is reduced to the stiffness of ribbed plates. In version 14, we managed to optimize the program for simpler calculations of ribbed plates. Namely, now you can create reinforcement directly, in two mutually perpendicular directions, as it was done for regular plates; the only difference will be in the visualization of the plate geometry. The reinforcement area is also specified with the running meter of the final element size in mind.

Important: The stiffness of a plate with ribs is analyzed in the axes of orthotropy, and the selection of reinforcement is made in the axes of stress equalization. Thus, during design calculations, the orthotropy axes and the stress equalization axes must coincide.

Fig. С1. Custom reinforcement of a T-shaped slab with ribs in one direction

In version 10.14, for design calculations, the calculation of a T-shaped slab with ribs in one and two directions, a cross slab with ribs in one and two directions, a box-like slab with ribs in one and two directions, a slab with circular or oval openings, a beam grillage is available.

Fig. С2. Types of plates

To design slabs with ribs, a separate type of design is specified, the contents of which is similar to the parameters of the bar.

Fig. С3. Types of design of reinforced concrete elements

Fig. С4. Design parameters for a plate with ribs according to EN

As a result of selecting/verifying the reinforcement, the plate element is considered as two bars in two mutually perpendicular directions. The internal forces Nx, Ny, Mx, My, Qx, Qy are adapted to the internal forces in the bar. The resulting selected reinforcement should be interpreted identically to regular plates – with allowance for a running meter. The only significant drawback in the implemented approach is that the effects of shear in the plane of the plate and torsion (internal forces Txy, Mxy) are ignored. However, in real objects, with hinged support, this factor is often not decisive and can be neglected.

For a while now, the ability of transferring selected reinforcement to the input data has been implemented in SP LIRA 10. This is useful both for subsequent verification of reinforcement and obtaining the utilization coefficient for various factors, and for understanding what each inclusion is in which section. This algorithm was built on the following preconditions:

• All elements of the same section, in which the selection was made, are selected;
• We go through each individual reinforcement inclusion for each element, searching for the maximum one;
• We assign the maximum value of each inclusion to the new section.

This approach had one significant drawback. Namely, several elements with bulky reinforcement influenced the elements, where almost no reinforcement was required. Because of this, the user had to distribute dangerous elements into new sections by himself, so as not to reinforce the entire floor according to the maximum value. SP LIRA 10.14 combats this problem using conversion ranges.

Fig. С5. Reinforcement ranges for transferring selected reinforcement to input data

For each inclusion name in the mode of conversion to the input data, we can specify an integer number of ranges between the maximum and minimum selected areas. As a result, not one new section for the entire set of elements will be created for one section, and in the general case there can be many different new sections with a unique set of reinforcement inclusions. Thereat, the area will be closer to the required. However, you should not get carried away with too many ranges, since their number in the worst case scenario can reach the product of all the numbers of ranges.

A new opportunity has appeared for those cases when an engineer uses the same type of reinforcement for bars and plates - bindings, names of inclusions, areas, etc. Having saved such a template once, it can be used in other sections and tasks. The template can be transferred between different computers. The file containing them is stored in the templates folder (default file path "C:\Users\Public\Documents\LiraSoft\Lira10.14\Templates\ArmatureTemplateContainer.atc").

Templates can be saved, renamed, loaded, and also canceled by resetting to the default template. After downloading the template, local editing of reinforcement inclusions is also available; the template file will not change.

Fig. С6. Reinforcement templates

According to p.5.3.1.7 DBN V.2.6-98:2009, a column is an element, whose depth of cross section does not exceed the width by more than 4 times, and the height of the element does not exceed the depth of cross section by more than 3 times. Otherwise, the column should be treated like a pylon or a wall.

Starting from version 10.14, in punching calculations we can consider a column of plate elements. Several criteria are checked:

• A column of plate elements is perpendicular to the floor slab with which it shares common nodes;
• The length of the wall along the interface nodes does not exceed 4 wall thicknesses;
• All nodes of the punching group lie on the same straight line;
• Wall elements have the same thickness.

If the above conditions are met, the junction point of the wall and the slab can be considered the point at which the column adjoins the slab. When calculating punching, the reactions of the contact points will be collected in the same way as would be done for an equivalent bar. The punching contour can be automatically built based on the location of slabs, just as it would be built for a rectangular bar. If necessary, as well as for junction with bars, the punching contour can be manually corrected by the user. Further, the calculation and operational procedure are similar to what it was for slab punching from the column in the form of a bar.

Fig. С7. Punching by a wall

According to p.6.4.2(2) of EN 1992-1-1-2009 and 4.8.2.2 of DSTU V.2.6-156:2010, control perimeters within less than 2d shall be reviewed, considered if the concentrated force is resisted by high pressure (e.g. soil pressure on a foundation) or impacts of load, or reactions within 2d distance from the edge of the force application area.

Fig. С8. Distances from the column edge to the punching contour

To implement this item, a field was added to account for the changed punching contour. First, for punching by a column, the program checks whether there is at least one slab element inside the punching contour, in which an elastic base С1 is specified. If this is punching by a pile, which is calculated in the SOIL module, then the presence of contact between the grillage and the soil is analyzed. If this condition is not met, then parameter a is ignored. Otherwise, it is considered that bearing pressure of soil is present, and the default contour may not be the most dangerous. In this case, more dangerous contours are sought. If the value а is specified manually, then it will be used instead of 2d according to Eurocode and DSTU. In this case, the user takes responsibility for indicating the most dangerous contour, according to which a new punching contour is generated, if this contour has not been created before this user. If Determine automatically is checked, then а is taken equal to d, and then the calculation proceeds in the same way as described above. Also, when taking into account parameter a, according to the Eurocode and DSTU standards, the check is carried out using the following formulas instead of the formula (6.47 EN)/(4.86 DSTU):

$$\begin{flalign}\begin{aligned}V_{Rt.c}=&C_{Rd.c} \cdot k\ \cdot \left(100 \cdot \rho_{1} \cdot f_{ck}\right)^{\frac{1}{3}} \cdot \frac{2d}{a} \\ V_{Rt.c}\le&V_{min}\cdot \frac{2d}{a}\end{aligned}&&&\end{flalign}$$

In SP LIRA 10.14 the user can calculate the punching force of the joint between the pile and the grillage. If the pile was calculated in the SOIL module, then, when calculating according to Eurocode and DSTU standards, clarifications may occur that depend on the geological section of the pile reviewed.

Fig. С9. Determination of contact between soil and grillage using a section of a geological model

If the grillage does not come into contact with the soil, then the calculation of punching by a pile is identical to punching by a column. If the grillage is in contact with the soil, then instead of the formula (6.47 EN)/(4.86 DSTU) the check is carried out according to the formulas:

$$\begin{flalign}\begin{aligned}V_{Rt.c}=&C_{Rd.c} \cdot k\ \cdot \left(100 \cdot \rho_{1} \cdot f_{ck}\right)^{\frac{1}{3}} \cdot \frac{2d}{a} \\ V_{Rt.c}\le&V_{min}\cdot \frac{2d}{a}\end{aligned}&&&\end{flalign}$$

For nonlinear calculations, we try to use those nonlinear deformation models that most accurately approximated to the real situation and do not contradict regulatory documents. In EN 1992-1-1-2009 and DBN V.2.6-98:2009, as the most accurate stress-strain diagram, it is proposed to use thereof formulas (3.14)

\(\sigma_{c} = f_{cm}\frac{k\eta-\eta^{2}}{1+\left( k-2 \right)\eta}\)

and (3.5)

\(\sigma_{c} = f_{cm}\sum_{k=1}^{5}\alpha_{k}\cdot\eta^{k}\)

where

$$\begin{flalign}\begin{aligned}\eta=&\frac{\varepsilon_{c}}{\varepsilon_{c1}} \nonumber \\ k=&1.05E_{cm}\frac{\varepsilon_{c1}}{f_{cm}}\end{aligned}&&&\end{flalign}$$

\(\alpha_{k}\) - coefficients, specified in Appendix D to DBN.

These dependencies are close. For both laws, physical and elastoplastic parameters are set. The strength theory for physically non-linear plates, accounting of plastic hinges and consideration of creep (for reinforced concrete) can be specified as well.

Fig. С10. Nonlinear law of concrete deformation according to EN

Fig. С11. Nonlinear law of concrete deformation according to DBN

Version 10.14 contains an extended list of possible cross sections for structural calculations according to Eurocode, at that asymmetrical I-beam, RHS with flange overhangs \( \left(if ~~ b_{f} \gt d_{y}+t_{w}\right) \), rolled T-beam and welded T-beam have been added. A complete list of possible cross sections for structural calculation according to Eurocode is given below.

Rolled Symmetrical I-beam
Welded Symmetrical I-beam
Welded Asymmetrical I-beam
Rolled RHS
Welded Rectangular HS
Welded RHS with Overhangs
Rolled Channel Bar
Welded Channel Bar
Rolled T-Beam
Welded T-Beam
Angle
Round Pipe

It is known that limit strength of metal under seismic actions is higher than under static actions. Consideration of seismic strengthening factor is regulated by EN 1998-1:2004 (p.6.2) norms. The user specifies a strengthening factor in SP LIRA 10.14, and a separate control for such a factor is provided in Design Editor. If the combination or loading state includes a seismic load, then the material strength will be multiplied by this coefficient.

The plastic hinge coefficient α is used to determine a class of the cross section. This coefficient is calculated automatically in the SP LIRA 10 by using a nonlinear strain model. In previous versions, the coefficient α characterized the ratio of a compressed and tensioned area of the cross section part under consideration. In SP LIRA 10.14 version, this coefficient is defined by the strains of the median line of the studied area. Often the results of both approaches are similar, but in certain cases the difference can be evident. Since the work of this algorithm amounts to about 2/3 of the time required to perform the structural calculation, in the new version this procedure is not performed when the section cannot be of class 3-4 even if \( \alpha=1 \). This allows accelerating significantly the calculation of proportioning and checking of steel structures according to EN norms.

For the cross sections where warping is possible (I-beam, Channel Bar, Z-profile, Σ-profile...), the distribution of torque moments caused by pure (\( M_{xt} \)) and restrained (\( M_{xw} \)) torsion moments makes a considerable influence on shear stresses. Bimoment Mw contributes to the normal stresses. Such internal forces are calculated in SP LIRA 10 for the bars of type 7. Starting from the version 10.14, they are taken into account in structural calculations according to Eurocode. If the user takes the FE type which is different from type 7, then at proportioning and checking it will be assumed that the total torque moment does not include \( M_{xt} \) component. Since the “strength reserve” is usually not taken into account in this approach, the user must make sure that in case of significant torsion, the warpings in cross sections of channel bar and I-beam are limited. Therefore, it is recommended to use the 7th feature of the model in SP LIRA 10.14 and to assign type 7 to the cross sections with significant warping. The regulations do not contain universal guidelines how to take bimoment into account at plastic strains availability. Therefore, it is taken into account in structural calculations only for the cross sections of class 3 and 4, as only elastic work is allowed for them. If the cross section is of class 1-2, the engineer should independently determine how dangerous the bimoment is for such an element.

A number of Eurocode requirements for proportioning and checking the cross sections of lightweight thin-walled steel structures (hereinafter refer to as LTSS) are implemented in SP LIRA 10.14. Geometric characteristics both while proportioning and checking the cross sections are determined according to EN 1993-1-3-2009, Annex C. The cross section is calculated as an open contour that runs along the median line of the plate, without taking into account roundings.

The strength calculation of in SP LIRA 10.14 is based on the fact that the load-bearing capacity is determined by elastic work. That is, when the yield strength is exceeded by equivalent stresses, it is considered that cross section cannot bear the load. The SP LIRA 10.14 does not take into account shear delay, elastic-plastic work and losses of stability in cross section shape. Also, due to the difficulty in identifying the flanges and walls, the check for the combined action of axial force, shear and bending moment according to formula (6.27) is not performed. The local loss of stability is taken into account by reducing the compressed areas of the cross section according to EN 1993-1-5-2009 recommendations.

The strength is checked by tangential and equivalent stresses, and it is required that the maximum stress does not exceed a certain limit (formula 6.11b). The tangential stress components are calculated by using the following formulas:

$$\begin{aligned} \large \tau_{Edy} &= \frac{Q_{y} \cdot S_{z}}{I_{z} \cdot b_{z}} \\ \tau_{Edz} &= \frac{Q_{z} \cdot S_{y}}{I_{y} \cdot b_{y}} \\ \tau_{_{Tw}} &= \frac{M_{xw} \cdot S_{w.ost}}{I_{w} \cdot t} \\ \tau_{_{Tt}} &= \frac{M_{xt} \cdot t}{I_{x}} \end{aligned} $$

where \( Q_{y}, Q_{z} \) – respectively transverse forces along the main axes of the cross-section Y, Z;

\( S_{y}, S_{z} \) – respectively static moments of the cut-off part of the cross-section, cut off by a line parallel to the axes Y, Z;

\( I_{y}, I_{z} \) – respectively moments of inertia of the cross section with respect to the axes Y, Z;

\( I_{w}, I_{x} \) – respectively sectoral moment of inertia and the moment of pure torsion of inertia;

\( b_{y}, b_{z} \) – respectively width of the cross section in the place where stresses are determined in the direction of axes Y, Z;

\( t \) – thickness of the plate used to bend a profile;

\( S_{w.ost} \) – sectoral static moment of the cut part of the cross section where tangential stresses are calculated.

Tangential stresses are calculated at the tops of the cross section and in the middle of the segments of its contours.

The tangential stresses due to Saint-Venant torsion and warping torsion moment are calculated in the direction perpendicular to the cross section boundary. SP LIRA 10.14 structural calculation assumes that the tangential stresses caused by transverse forces reach a maximum in the same direction. When determining the cross section width \( b_{y}, b_{z} \) at the intersection points of two areas of a thin-walled profile, it is assumed that the thickness equals the arithmetic mean of the thicknesses of these areas.

The equivalent Mises stresses are also calculated at the tops of the cross section and at the midpoints of segments of its contours. Compared to the tangential stress check, if there are reduced areas formed due to local loss of stability, the reduced cross section characteristics are used for the calculation of normal stresses. At that the tangential stresses and sectorial coordinates at these points are calculated as if there were no reduction.

The loss of plane stability (longitudinal bending) is checked in accordance with EN 1993-1-3-2009, p.2.2. The torsional and flexural-torsional buckling is checked in accordance with EN 1993-1-3-2009, p.6.2.3. Combined effect of axial force and bending moment is checked in accordance with EN 1993-1-1-2009, p.6.3.3.

If the user specifies in Structural design parameters that the element is on a support, it will be checked for loss of wall stability due to shear forces. Since for the cross sections with an arbitrary contour it is not possible to specify unambiguously which element is a wall and which is a longitudinal stiffener, it is assumed that all areas except for the edge overhangs can be walls. Each area is analyzed for the sum of transverse forces in each direction. Generally, if transverse forces are available along both axes of cross section of the element, we obtain an extended interpretation of formula (6.8) of EN 1993-1-3-2009, according to which the wall stability condition is met if:

$$ \left| Q_{z} \right| \cdot \sin(\phi) + \left| Q_{y} \right| \cdot \cos(\phi) \lt \frac{h_{w}\cdot t\cdot f_{bv}}{\gamma_{_{M0}}} $$

In accordance with the requirements set forth in DBN V.2.6-198:2014, p.5.3.6, the structural elements can be divided into 3 classes depending on the type of stress-strain state. These classes determine the admissibility of plastic strain development in the design cross section. Plastic strains are considered by the coefficients \( c_{y},c_{z},c_{w} \), and by the exponent n in accordance with instructions given in DBN V.2.6-198:2014, pp.9.2.3, 10.1.1, 10.2.10. The values \( c_{y},c_{z},n \) are given in Table M.1, and the value \( c_{w} \) is given in Table 10а, but it is not indicated for which class to use them (it is assumed that for the class 2). SP LIRA 10.14 specifies these coefficients in comparison with those proposed in the norms.

The influence coefficients \( c_{y},c_{z} \) for the elements of class 2 can be calculated under the condition that the residual strain in the element after full unloading should not exceed \( 3\frac{R_{y}}{E} \). This condition can be reformulated after simple transformations as follows: at bending in one of the main planes of the cross section, the full strain should not exceed \( 4\frac{R_{y}}{E} \).

To obtain the elastic-plastic bending moment for class 2, it is necessary to add together the elastic core resistance moment of the cross section and the plastic resistance moment of the area where plastic strains occur. Assuming that the maximum strain at the point most distant from the mass center of the cross section is \( 4\frac{R_{y}}{E} \) , the dimension of elastic core will be equal to \( \frac{1}{4} \) of the full cross section dimension. These areas are easily defined, so based on general considerations, it is possible to derive accurate analytical formulas to determine the elastic-plastic moments of resistance to bending.

For certain symmetrical cross sections, the coefficients cy, cz can be easily derived, as the ratio of elastic-plastic and elastic moments of resistance along the corresponding axis.

For doubly symmetrical I-beams of class 2 in classical orientation the coefficient \( c_{y} \) is determined by the following dependency:

$$ \large c_{y2}=\begin{Bmatrix} \frac{2S_{y}-\frac{t_{w}h^{2}}{192}}{W_{y}}, ~if~ \frac{h}{4}\le h_{ef} \\ \frac{10}{7} \approx 1.42857, ~if~ \frac{h}{4}\gt h_{ef} \end{Bmatrix} \le c_{y~max}=1.15\frac{M_{y}}{M_{yn}};\quad \left( C_{y2} \gt 1\right) $$

The coefficient \( c_{z} \) for I-beams without a slope of flanges is determined by the following dependencies:

$$ \large c_{y2}=\begin{Bmatrix} 4- \frac{27t_{f}b_{f}^{2}}{32w_{z}}, ~if~ t_{w} \lt \frac{b_{f}}{4} \\ \frac{47}{32} \approx 1.46857, ~if~ t_{w} \ge \frac{b_{f}}{4} \end{Bmatrix} \le c_{z~max}=1.15\frac{M_{z}}{M_{zn}};\quad \left( C_{z2} \gt 1\right) $$

The coefficient \( c_{z} \) for I-beams with a slope of flanges is determined by more complicated dependencies, which are not published here as they are cumbersome. You will get only the final result in the report protocol.

For the rolled rectangular hollow sections of class 2 the coefficient \( c_{y} \) is determined by the following dependency:

$$ \large c_{y2}=\frac{2S_{y}-\frac{t\cdot h^{2}}{96}}{W_{y}}~~if~~R\lt \frac{3}{8}h $$

Otherwise, the coefficient is determined by more complicated dependencies, which are not published here as they are cumbersome. You will get only the final result in the report protocol.

The coefficient \( c_{z} \) is determined similarly to the coefficient \( c_{y} \).

For round pipes and round timber of class 2, the coefficients \( c_{y},c_{z} \) are determined by the following dependency:

$$ c_{y}=c_{z}=\frac{2}{3\pi}\cdot \frac{ 8(\cos^{3}\alpha - \nu^{3} \cos^{3}\gamma) + 3 \cdot \left[ 4\alpha-\sin4\alpha-\nu^{4}(4\gamma-\sin4\gamma) \right]}{1-\nu^{4}}\le 1.15\frac{M}{M_{n}}\ge 1 $$

where \( \nu = \frac{d}{D} \) – ratio of internal and external diameters;

\( \alpha=\arcsin(0.25) \)

\( \gamma= \begin{cases}\begin{matrix} \arcsin(\frac{1}{4\nu}), ~~ if ~~ 0.25 \lt \nu \le 1 \\ \frac{\pi}{2} ~~if~~ \nu\le 0.25 \end{matrix}\end{cases}\)

For doubly symmetrical I-beams, rolled rectangular hollow sections, pipes and round timber of class 3 the coefficients \( c_{y},c_{z} \) are determined based on creation of a complete plastic hinge by the following formula:

$$ c_{y}=\frac{2\cdot S}{W} \le 1.15 \frac{M}{M_{n}} \ge 1 $$

Usually the coefficients \( c_{y},c_{z} \) obtained in SP LIRA 10.14 differ from those specified in the norms by no more than a few percent in favor of more economical consumption of metal. But in some cases the amount of savings is significant. For example, for a pipe 127х12 mm, \( c_{y}=c_{z}=1.3781 \) , the norms provide 1.26, the difference is 9.4%, for RHS 80х6 (r=9 mm, R=15 mm) \( c_{y}=c_{z}=1.2355 \), the norms provide 1.12, the difference is 10.3%.

In previous versions of SP LIRA 10, one value of the modification factor \( k_{mod} \) was used for all combinations when calculating wooden structures according to EN 1995-1-1 and DBN V.2.6-161:2017. Nevertheless, if \( k_{mod} \) value is too small, an excessive wood consumption may occur, and if \( k_{mod} \) value is too large, the structure may be overloaded. The SP LIRA 10.14 implements automatic identification of the most short-term load in the loading state or in combination of DCF/DCL.

Fields for the modification factor for all duration degrees have been added to the structural design parameters. Duration of loading states shall correspond to the values of factor \( k_{mod} \) given in table based on the following considerations:

The normative document EN 1997-1:2004 does not contain specific guidelines for the pile settlement calculation. There are general requirements and it is up to the Engineer to control their implementation by using the methods available to him. Fortunately, the Eurocode manual recommends using Poulos’ works as one of the calculation variants (Book Poulos, H. G. et. Davis, E. H.: Pile Foundations Analysis and Design. New York: John Wiley and Sons, 1980). Exactly his provisions were used in pile settlements calculation performed in SP LIRA 10. The settlement of a single pile was implemented in version 10.12, and a new version enables to perform the pile clusters calculation. Compared to the norms of SNiP, DBN and so on, the Poulos approach provides the possibility to include piles with different dimensions (both pile shaft and widening) in one pile cluster, which is a significant advantage. An example of such pile clusters is shown in the figure below.

Fig. G1. Example of pile clusters with different piles

The Poulos model assumes many factors that influence the final settlement of each pile. SP LIRA 10.14 contains, the most essential refinements, in our opinion, which include:

• Consideration of pile widening in the cluster;
• The effect of finite compressibility of the bearing layer;
• Consideration of interaction between different piles for standing piles and friction piles;
• Intergroup impact between pile clusters.

Consideration of pile widening

The refined influence factor between piles is calculated by the formula:

$$\alpha=N_{db}\cdot \alpha_{F},$$

where \(N_{db}\) – correction factor depending on the shaft diameter and widening of each pile, length, distance between piles. The dependence for incompressible piles is shown in Figure G2;

\(\alpha_{F}\) – influence factor for similar piles without widening.

Fig. G2. Dependence of the factor \(N_{db}\) on the shaft diameter \(d\), widening diameter \(d_{b}\), shaft length \(L\), and distance between piles \(s\)

The effect becomes more significant as the base diameter increases and is particularly evident for short piles.

Effect of finite compressibility of the bearing layer

The interaction factor \(\alpha\) for the piles installed on a compressible foundation is between the interaction factor for friction piles in homogeneous soil \(\alpha_{F}\) and for standing piles resting on a completely rigid layer \(\alpha_{E}\). This factor is determined by the following dependency:

$$\alpha = \alpha_{F} - F_{E}\left( \alpha_{F} - \alpha_{E} \right),$$

where \( F_{E} \) – influence reduction factor, which depends on the modulus of strain of the base soil of the pile \( E_{b} \), the modulus of soil strain \( E_{s} \) (soil above the base soil), the length \( L \) and shaft diameter \( d \), and the pile stiffness coefficient \( K \). The value \( F_{E} \) is determined based on the graphs shown in Figure G3 below.

Fig. G3. Interaction reduction factor \( F_{E} \)

Consideration of interaction between different piles for standing piles and friction piles

In general, piles can have different dimensions, but even in this case, their interaction must be taken into account. Additional settlement \( \Delta\rho_{ij} \) of the pile \( i \), caused by the pile \( j \) is determined by the following formula:

$$\Delta\rho_{ij}=\rho_{j}\cdot \alpha_{ij}$$

where \( \rho_{j} \) – settlement of a single pile \( j \); \( \alpha_{ij} \) – factor of interaction between piles \( i \) and \( j \), depending on the distance \( s_{ij} \) between them and the geometric parameters (length \( L \), diameter \( d \)) of the pile \( i \).

For a friction pile:

$$\alpha_{ij}=\alpha_{F}\cdot N_{h}\cdot N_{\nu}$$

where \( N_{\nu} \) – correction factor for effect of Poisson’s ratio. The user defines this value, it can be determined based on Figure G4.

Fig. G4. Correction factor for effect of Poisson’s ratio

\( N_{h} \) – correction factor of interaction, takes into account the depth of the compressible thickness \( h \), which is defined as a distance from the absolute ground level to a hard soil layer. The hard layer is searched for within the depth \( h \), which the SP LIRA 10 determines based on the parameter Maximum depth from the pile tip to search for hard soil layer in fractions of the pile length. If there is no hard layer within the compressible thickness, then \( N_{h} \) is equal to 1. The graph for determining \( N_{h} \) see below in Figure G5.

Fig. G5. Interaction correction factor \( N_{h} \) depending on \( h, s, d, L \)

\( \alpha_{F} \) – interaction factor between a pair of piles in a semi-finite space with the Poisson’s ratio of the soil equal to 0.5. It depends on the ratios of \( s/d \), \( L/d \) and \( K \). It can be determined based on the graphs shown in Figure G6 below.

Fig. G6. Interaction coefficient \( \alpha_{F} \) between a pair of piles in a semi-finite space with the Poisson’s ratio of the soil equal to 0.5

Intergroup impact between pile clusters

For large buildings resting on many groups of pile clusters, each pile cluster may often be useful, therefore it must be assumed as some equivalent single pile. This assumption allows taking into account an additional settlement of each pile cluster caused by a group of neighboring clusters.

Fig. G7. Equivalent pile in the cluster

SP LIRA 10.14 defines the plan area \( A \) for each pile. Here the plan is understood as a polygon described around the contours of the piles in cluster. The conditional width \( B \) of the foundation is determined by the following formula:

$$B=\sqrt{A}$$

The average step between the piles is determined by the following dependency:

$$s=k\sqrt{\frac{A}{n}}$$

where \( n \) – number of piles in the cluster; \( k \) – correction factor, in which the number of piles in the cluster is taken into account, this factor is determined according to the table given below:

$$\begin{array} {|r|r|}\hline n & k \\ \hline 2 & 3.464102 \\ \hline 3 & 2.44949 \\ \hline 4 & 2 \\ \hline 9 & 1.5 \\ \hline 16 & 1.333333 \\ \hline 25 & 1.25 \\ \hline 36 & 1.2 \\ \hline 49 & 1.166667 \\ \hline 64 & 1.142857 \\ \hline 81 & 1.125 \\ \hline 100 & 1.111111 \\ \hline 1000 & 1.001001 \\ \hline 10000 & 1.0001 \\ \hline \end{array}$$

Then, the mean diameter \( d_{e} \) is determined based on the nomograms given in Figure G8.

Fig. G8. Ratio of arithmetic mean of pile diameter and conditional width depending on reduced step between piles and the average diameter of piles in cluster

So, for each pile cluster we obtain a virtual pile with the given geometry and loads. Then for each cluster we add additional settlements resulting from the impact of each of these reduced piles similarly as we do it for real piles.

Since SNiP and Eurocode are based on fundamentally different approaches and limits to the calculation of pile clusters, the SP LIRA 10 interface in tab Piles Group was supplemented with parameter Euro cluster, which is used only for the EU norms. At the same time, the parameter Pile cluster remains for use in accordance with DBN and SP.

This mode iterates to the required convergence while calculating the coefficients of sub-grade reaction of plates and bars, and pile stiffnesses which must be recalculated in the SOIL system. It allows minimizing the human participation in several calculations of the same type, unless, of course, during iterations there are no cases not subjected to calculation.

Fig. G9. Refinement of loads for the SOIL system

To start iterations for calculation of the coefficients of sub-grade reaction or pile stiffnesses automatically, it is necessary to choose the tab Refinement of loads for the SOIL system in the batch calculation mode and indicate the following information:

• task file;
• the coefficient to the loads by which the reactions of the elastic foundation will be multiplied to transfer them to the SOIL module;
• the calculation results from which reactions must be transferred to the SOIL (loading state/DCL and its number);
• the maximum number of iterations;
• the percentage of load changes from iteration to iteration (if this percentage is less during calculations, the iterations will be stopped);
• the maximum distance of displacement of the reaction application center from iteration to iteration (if this change is less during calculations, the iterations will be stopped).

Once the parameters are entered and the process is started, the program will automatically perform finite element calculation, transfer the reactions into input data, and again perform the calculation with new stiffnesses until one of the entered limiting factors is worked out.

The new SP LIRA 10 version extends the list of pile types. Now, screw piles are also available for calculation according to DBN and SP. The calculation of bearing capacity and settlement is performed for single-bladed piles with a blade diameter of no more than 1.2 m and a length of no more than 10 m. In other cases, these values must be entered manually based on the results of static load testing of the pile.

Screw pile parameters are set in the cross sections/stiffnesses editor. Parameters of a tubular metal pile shaft are available in the same named opening area at the bottom of this window.

Size designations used are as follows:

\( D \) – pile shaft outer diameter;

\( t_{w} \) – wall thickness of the metal pile shaft;

\( d \) – diameter of the pile blade;

\( h_{1} \) – pile shaft length to its blade;

\( L \) – pile length.

Fig. G10. Scheme of the screw pile

Bearing capacity of a screw pile according to DBN V.2.1-10-2009, revision #1, p. N.5 is determined by the following formula:

$$F_{d}=\gamma_{c}\left[ \left( \alpha_{1}c_{I} + \alpha_{2}\gamma_{I}h \right)A_{d} + u f_{i} \left( l-d \right)\right],$$

where \( \gamma_{c} \) – conditions of use factor which depends on the type of load applied to the pile and soil conditions determined according to the Table N.5.1 DBN V.2.1-10-2009;

\( \alpha_{1} \), \( \alpha_{2} \) – Dimensionless coefficients taken from the Table N.5.2 DBN V.2.1-10-2009 depending on the calculated value of the angle of internal friction of the soil in working area \( \varphi_{I} \) (working area is understood as a layer of soil adjacent to the blade with a thickness \( d \));

\( c_{I} \) – design value of specific cohesion of clayey soil or linearity parameter of sandy soil in the working area;

\( \gamma_{I} \) – averaged design value of the specific weight of soils lying above the pile blade (in case of water-saturated soils, taking into account the suspension effect of water);

\( h \) – pile blade depth with respect to the natural relief, and when leveling the territory by shearing − with respect to the leveling mark;

\( A_{d} \) – projection of the blade area, counting along the outer diameter, when a screw pile operates under compressive load, and the projection of the blade working area, that is, minus the cross-sectional area of the shaft, when a screw pile operates under extraction load;

\( f_{i} \) - design resistance of soil on the lateral surface of the screw pile shaft, accepted according to the formula N.2.2 or Table N.2.2 DBN V.2.1-10-2009 (averaged value for all layers within the depth of pile driving);

\( u \) – perimeter of the pile shaft cross-section;

\( l \) – length of the pile shaft in the soil;

\( d \) – diameter of the pile blade.

Settlement of a single screw pile according to the norms of DBN V.2.1-10-2009, revision # 1, p.P.1.2 is determined by the following formula:

$$s=2\left( 1+v \right)\frac{Nc}{Eh}+\frac{Nh\left( 1+b \right)}{2E_{0}A},$$

where \( v \) – Poisson’s ratio of the soil;

\( N \) – vertical load on the pile;

\( c \) – coefficient of settlement, determined by the Table P.1.1 DBN V.2.1-10-2009;

\( E \) – reduced modulus of soil deformation, is determined according to the formula P.1.3 DBN V.2.1-10-2009;

\( h \) – depth of the pile blade relatively to the natural relief, and in case of the area leveling by shearing − relatively to the leveling mark;

\( b \) – coefficient determining the part of the load transmitted by the pile toe is defined according to the Table P.1.2 DBN V.2.1-10-2009;

\( E_{0} \) – modulus of the pile shaft material elasticity;

\( A \) – cross section area of the pile shaft.

Settlement of the screw pile cluster according to the norms of DBN V.2.1-10-2009, revision # 1, p. P.1.4, is determined by the following formula:

$$s_{j}=s_{1}+\sum_{j=1}^{n}p_{j}s_{ij},$$

where \( s_{1} \) – proper settlement of a single i-th pile caused by the load \( N \);

\( p_{j} \) – load on the j-th pile in foundation;

\( s_{ij} \) – settlement of the i-th pile caused by a single load applied to the j-th pile in foundation is determined by the following formula:

$$s_{ij}=2\left( 1+v \right)\frac{w_{j}k_{b}}{Eh},$$

where \( w_{j} \) – coefficient is determined according to the Table P.1.3 DBN V.2.1-10-2009 depending on the reduced pile radius \( r \) and the distance between the i-th and j-th piles;

\( k_{b} \) – coefficient is determined according to the Table P.1.4 DBN V.2.1-10-2009.

Calculation of a screw pile field as a conditional foundation is performed similarly to other pile types. The SP LIRA 10.14 according to the norms set in DBN V.2.1-10-2009 (revision # 1) defines the boundaries of conditional foundation in the following way:

above – by the soil leveling surface;

below – by a plane passing through the top of the screw at the depth of the pile blade \( h \);

on sides – by vertical planes remoted from the outer surfaces of the extreme rows of vertical piles at a distance \( h\boldsymbol{\cdot}tg\left( \frac{\varphi_{II,mt}}{4} \right) \), but not less than \(0.5d\), and not more than \(2D\) in cases when clay-bearing soil with ground flow index \( I_{L} \gt 0.6 \) is lying under the pile toes;

here \( \varphi_{II,mt} \) – averaged design value of the soil internal friction angle within the depth of the pile blade \( h \), \( D \) – diameter of the pile shaft, \( d \) – diameter of the pile blade.

SP LIRA 10.14 implements the piles calculation for combined action of vertical and horizontal forces and moment according to DBN (SNiP) and SP. The calculation is available for single piles in the Calculation of single pile utility from the general list of utilities, and in the cross sections/stiffnesses editor, Pile (Elastic Restraint) cross section.

If DBN V.2.1-10-2009 (revision # 1) is chosen, the calculation of stability of the foundation surrounding the pile will be performed in accordance with SNiP 2.02.03-85, Appendix 1.

Calculation of stability of the foundation surrounding the pile is performed under the condition of limiting the design pressure \( \sigma_{z} \) applied to the soil by lateral surfaces of the pile:

$$\sigma_{z} \le \eta_{1} \cdot \eta_{2}\frac{4}{\cos\varphi_{I}}\left( \gamma_{I}\cdot z\cdot \tan\varphi_{I}+\xi\cdot c_{I} \right).$$

If the calculated horizontal soil pressures do not satisfy the stability condition, but at the same time the material bearing capacity of the pile is not fully used and the pile movement is less than the maximum permissible value, then, at reduced pile depth \( \bar{l}\gt 2.5 \), the calculation must be repeated with a lower value of the proportionality factor \( K \) until the stability condition is met. You can find the Reduction factor \( \boldsymbol{dK} \) (the value by which the proportionality factor must be multiplied to meet the stability condition) in the Result tab of this utility

Calculation results also contain the values of strain factors \( \alpha_{\varepsilon} \), depth of conditional restraint of the pile tip \( l1 \), design and ultimate pressure on soil along the lateral surface of the pile \( \sigma_{z} \), design depth (depth of the pile cross section in soil) \( z \), horizontal movement \( u \) and pile rotation angle \( \Psi \) for the X and Y axes.

Fig. G11. Tab Result

Tab Soil stability graphs contains such values as graphs of transverse force \( Q \), design bending moment \( M \), design soil pressure along the lateral surface \( \sigma_{z} \) and ultimate soil pressure along the lateral surface \( \sigma_{zu} \) depending on the depth of the pile cross section in soil \( z \).

Fig. G12. Tab Soil stability graphs

Tab Table of soil stability forces contains the parameter values from the graphs presented in the form of table.

Fig. G13. Tab Table of soil stability forces

SP LIRA 10 is one of the tools for solving geotechnical design problems. The program provides two approaches for calculating soil massifs: according to norms and solving non-linear problems with soil elements. Calculations according to the norms are applicable for slab and pile foundations on the bases, the conditions of which are specified in the normative documents. One of the advantages of calculations based on algorithms set in norms is that they are “consistent with the law”, so you will have fewer difficulties with passing the expert examination of the object. As well, the calculation itself usually takes less than a minute for medium-sized objects, and its results can be used in elastic problems. One of the disadvantages is that they are mainly relevant only for a limited set of slab and pile foundations. Also many design cases with non-standard situations are not available. These calculations are often performed with reserve for stiffness and the real stress-movement picture is not evident.

To avoid these difficulties, a nonlinear soil model is made, which allows solving many problems by modeling the situation close to the real one. Such problems can mainly include:

• Calculation of retaining walls of slopes and excavations;
• Stages of soil excavation and backfilling (assembly problems);
• Soil pressure on basement walls;
• Calculation of tunnels and underground structures;
• Soil resistance to landslides;
• Dynamic calculation of a building on a soil foundation taking into account nonlinearity and by using a direct integration;
• Filtration calculation;
• Special calculations of slab foundations;
• Special calculations of pile foundations.

Now let’s discuss the practical component of soil calculation based on nonlinear models. Usually, a geologic soil model is built on the basis of several geological exploration boreholes. If each of the boreholes has different thicknesses of soil layers, then one of the most problematic stages in creating the model is the application of soil materials to each element forming part of the soil massif. The SOIL module of SP LIRA 10 allows you to automate this process to the maximum extent possible. Once the boreholes are specified, you can automatically build a three-dimensional model of the soil in 3D or its section in 2D. This possibility was also available in previous versions, but there were limitations in attaching the geologic model to the base model and in taking into account the nonlinear characteristics of the soil. The new version allows the user to attach a geologic model to the base model, taking into account the materials, as well as to take into account the nonlinear properties of the materials.

Fig. G14. Functionality for building a soil 3D model

Fig. G15. Soil 3D model attached to a base model

When nonlinear characteristics are taken into account, such properties as soil name, modulus of deformation, Poisson’s ratio, density, specific cohesion and angle of internal friction will be automatically transferred from the Soil Editor tables to the Materials Editor.

Fig. G16. Transfer of soil properties to the material editor

For flat soil models, built from a cross section, it is added a possibility to build a model considering nonlinear properties of the soil. For this you should use the context menu on the cross section.

Fig. G17. Export of soil cross section with nonlinear properties to a file

Calculation of single pile

The cross sections/stiffnesses editor for the cross-section Pile (Elastic Restraint) is supplemented with new functionality for single pile calculation.

Many parameters unique to a particular regulation have been added due to the expansion of regulations in different countries. Extra parameters can be misleading or lead to additional questions. Therefore, the pile cross section parameters are now set according to the selected norms.

A separate tab has been added for loads, with the option of specifying characteristic loads with conversion factors, or design and standard loads directly.

Fig. G18. Tab Loads

Soil Editor

Parameters of selected pile cross section depending on standards are now set in SOIL editor in the window Establish standards and properties of the calculation in the tab Piles. List of available pile cross sections corresponds to the cross sections/stiffnesses editor and includes only those cross sections that have been assigned to the piles involved in the calculation.

Fig. G19. Tab Piles

SP LIRA 10.14 provides local calculation results for piles directly in the Soil editor. This facilitates the control of the foundation calculation and correction of input data, if necessary. To view the results, once the calculation has been performed in the Soil editor, click on the pile of interest and a panel with load properties and calculation results will be displayed on the left side of the window.

Fig. G20. Results in Soil Editor

Elastic Foundation mode

Elastic Foundation mode now allows copying of previously calculated boreholes. To do this, select the line in the table with the borehole to be copied and click the button Copy Current Borehole. A new line with an exact copy of the original borehole will appear in the table. This can be useful if you need to create multiple boreholes with insignificant differences in soil layers.

The Elastic Foundation mode now allows setting design and normative transverse forces and bending moments for elastic pile elements. The mosaics of these loads are available in the Visualization tab of the current mode and in the Piles and Springs tab of the Model Analysis mode.

Fig. G21. Elastic pile elements

Transfer of reactions into the input data for the SOIL system

In versions 10.12 and below, the user could transfer reactions in plates and piles into the input data used for the calculations in SOIL module for Limit State I and Limit State II. At that, it was possible to choose which reactions were transferred: normative or design reactions. It created some confusion for inexperienced users. Therefore, to provide all calculation nuances, the engineer had to calculate the scheme twice: by normative loads to calculate the stiffness of the slab or pile foundation, and by design loads to calculate the pile bearing capacity for compression and extraction, as well as bearing capacity along lateral surface. Starting from version 14, a simultaneous transfer of both sets of loads has been implemented. This significantly accelerates the user's work and reduces the probability of errors in iterative calculations because of human factor.

https://gmsh.info/ is a freely distributed generator of finite element meshes from CAD models. Although previously the model file with a format of this program was available in SP LIRA 10 for import and export, but only version 2 of the *.msh file was supported. Now the latest mesh generator has version 4. It allows you to re-save the file into version 2; however, the difficulties caused by import of version 4 sometimes make the engineer to perform additional manipulations. Currently the version 10.14 allows importing both version 2 and version 4 of *.msh format. Writing (export) of the file from SP LIRA 10 is generated into version 4.

SAF (https://www.saf.guide/) is an initiative of the Nemetschek Group aimed to improve collaboration between civil engineers by developing an open format for data exchange between structural calculation programs based on the Excel format. The focus is on a practical, easy-to-use format which civil engineers can use in their daily practice. This is designed as an open format. Currently the SCIA manages the coordination. In other words, this is an architectural model format which includes geometry of the model, cross section, materials, loads, etc. Partially or fully this format is supported by such complexes as SCIA, FRILO, Risa, Graphisoft (Archicad), Allplan, Radimpex, AxisVM, FEM-Design, Sofistik, Dlubal, ConSteel, mbAEC StrukturEditor, D.I.E, InfoGraph, IDEA, MINEA, NextFEM, MasterSap, Prota Structure, and, of course, by SP LIRA 10.

Version 2.1.0 of the format is implemented in SP LIRA 10.14. Information analyzed during import into LIRA 10.14 is as follows:

SAP2000 is one of the world leading software for finite element modeling of civil structures, in many aspects it is an analogue of SP LIRA 10. It is especially widely used in America, Turkey and the European Union. During calculation SAP2000 can generate a file in text format *.s2k. Depending on what the user has ordered for the text file before calculation, this file can include the information about model geometry, materials, loads, hinges in the scheme, etc. Starting from SP LIRA 10.14 version, a lot of information of this format, which has its analog in SP LIRA 10, became available for import. Thus, the engineer will have tools for transferring his old projects from SAP2000 into SP LIRA 10 for the purpose of cross-validation of calculations, or complete transfer to another program. The full list of *.s2k, format parameters available for transfer to SP LIRA 10 is given in the table below.

Tables *.s2k	Readable parameters
PROGRAM CONTROL	CurrUnits (measurement units)
OBJECTS AND ELEMENTS JOINTS Nodes	JointElem, GlobalX, GlobalY, GlobalZ
OBJECTS AND ELEMENTS FRAMES Bars	FrameElem, ElemJtI, ElemJtJ
OBJECTS AND ELEMENTS – AREAS Plates	AreaElem, ElemJt1, ElemJt2, ElemJt3, ElemJt4
OBJECTS AND ELEMENTS – SOLIDS Solid elements	SolidElem, ElemJt1, ElemJt2, ElemJt3, ElemJt4, ElemJt5, ElemJt6, ElemJt7, ElemJt8
MATERIAL PROPERTIES 02 - BASIC MECHANICAL PROPERTIES Material properties	Material, UnitWeight, E1, U12, A1
FRAME SECTION PROPERTIES 01 – GENERAL Sections and material of the bars	Parametric rectangle Transfer of the following parameters is implemented: SectionName, Material, Shape, t2, t3 Parametric T-Beam Transfer of the following parameters is implemented: SectionName, Material, Shape, t2, t3, tf, tw Parametric Angle Transfer of the following parameters is implemented: SectionName, Material, Shape, t2, t3, tf, tw Parametric Channel Bar Transfer of the following parameters is implemented: SectionName, Material, Shape, t2, t3, tf, tw CHS Transfer of the following parameters is implemented: SectionName, Material, Shape, t3, tw RHS Transfer of the following parameters is implemented: SectionName, Material, Shape, t2, t3, tf, tw Parametric I-Beam Transfer of the following parameters is implemented: SectionName, Material, Shape, t2, t3, tf, tw, t2b, tfb Circle Transfer of the following parameters is implemented: SectionName, Material, Shape, t3
AREA SECTION PROPERTIES Material and section of the plates	Section, Material, Thickness
SOLID PROPERTY DEFINITIONS Solid elements materials	Material
FRAME SECTION ASSIGNMENTS Snap to the bar of section and material	Frame, DesignSection
AREA SECTION ASSIGNMENTS Snap to the plate of material and section	Area, Section
SOLID PROPERTY ASSIGNMENTS Snap to the solid element of material	Solid, SolidProp
JOINT LOCAL AXES ASSIGNMENTS 1 – TYPICAL Local axes of the nodes	Joint, AngleA, AngleB, AngleC
FRAME LOCAL AXES ASSIGNMENTS 1 – TYPICAL Local axes of the bars	Frame, Angle
AREA LOCAL AXES ASSIGNMENTS 1 – TYPICAL Local axes of the plates	Area, Angle
FRAME RELEASE ASSIGNMENTS 1 – GENERAL Ideal hinges in the bars	Frame, PI, V2I, V3I, TI, M2I, M3I, PJ, V2J, V3J, TJ, M2J, M3J, PartialFix
FRAME RELEASE ASSIGNMENTS 2 - PARTIAL FIXITY Elastic hinges in the bars	Frame, PI, V2I, V3I, TI, M2I, M3I, PJ, V2J, V3J, TJ, M2J, M3J
JOINT RESTRAINT ASSIGNMENTS Restraints in the nodes	Joint, U1, U2, U3, R1, R2, R3
JOINT SPRING ASSIGNMENTS 1 – UNCOUPLED Elastic foundation of the nodes	Joint, CoordSys, U1, U2, U3, R1, R2, R3 Only parameter Local is implemented for CoordSys
FRAME SPRING ASSIGNMENTS Elastic foundation of the bars	Only parameter Frame, Stiffness, Dir=2 (read as C1y), Dir=3 (read as C1z) are taken into account
AREA SPRING ASSIGNMENTS Elastic foundation of the plates	The parameters Area, Stiffness (as stiffness C1z) are taken into account by default. If VecX, VecY, VecZ, are set, then the elastic foundation of the plates Cx, Cy, С1z is considered as the multiplication of the Stiffness parameter by the corresponding guide cosine.
LOAD PATTERN DEFINITIONS Names of load cases	LoadPat
LOAD CASE DEFINITIONS Names and types of load cases	Only Case and partially Type are taken into account If Type=LinStatic, then the load case is taken into account. Otherwise it is ignored.
COMBINATION DEFINITIONS DCL tables	ComboName, CaseName, ScaleFactor
JOINT LOADS – FORCE Nodal loads (forces and moments)	Joint, LoadPat, CoordSys, F1, F2, F3, M1, M2, M3
JOINT LOADS - GROUND DISPLACEMENT Nodal displacements	Joint, LoadPat, CoordSys, U1, U2, U3, R1, R2, R3
FRAME LOADS – DISTRIBUTED Distributed bar loads	Frame, LoadPat, CoordSys, Type, Dir, DistType=RelDist RelDistA, RelDistB, AbsDistA, AbsDistB, FOverLA, FOverLB
SOLID LOADS – GRAVITY Dead weight of spatial elements	Solid, LoadPat, MultiplierX, MultiplierY, MultiplierZ
SOLID LOADS – TEMPERATURE Temperature load on spatial elements	Solid, LoadPat, Temp
AREA LOADS – GRAVITY Dead weight of the plates	Area, LoadPat, MultiplierX, MultiplierY, MultiplierZ
AREA LOADS – UNIFORM Uniformly distributed load on the plate	Area, LoadPat, CoordSys, Dir, UnifLoad
FRAME LOADS – TEMPERATURE Temperature load on the bar	Frame, LoadPat, Type
FRAME LOADS – GRAVITY Dead weight of the bars	Frame, LoadPat, MultiplierX, MultiplierY, MultiplierZ

SP ABAQUS is one of the most famous in the world software packages in the field of finite element modeling, belongs to the French company Dassault Systemes. Quality of the program and the range of its capabilities rank the SP ABAQUS in the same level as ANSYS and NASTRAN. Among the obvious advantages of the SP ABAQUS over the line of FEM programs developed for civil engineering, it a high-quality mesh generator and a shell for creating spatial and plane schemes, an API (the ability to write scripts for importing and creating a model in a graphical CAE shell), a calculation processor with a wide range of capabilities, including the option to change the model during calculation by means of user subroutines in the Fortran programming language. The program has its own text file of the processor with *.inp file extension. In its turn, the SP LIRA 10.14 has more possibilities and better adaptivity for structural calculations taking into account normative documents. To use the strong points of both software packages there was developed an exchange of mutually readable part of the data on geometry, materials, loads, etc. via *.inp format.

Format import is fully or partially supported by such programs as Dassault Systemes (ABAQUS, CATIA, SolidWorks…), SP LIRA 10, ANSYS, GMSH, SCAD, and others. Model export is available from ABAQUS, and partially from SP LIRA 10, SCAD, etc.

Model geometry. Since the SP Abaqus does not specify the measurement units and they are user-controlled, while importing the model into SP LIRA it is proposed to select a measurement unit system to consider the scale of dimensions, loads, masses and time.

Fig B9. Dialog box for the units of measurement accounting

In SP Abaqus, an assembly can consist of several details. The SP LIRA 10, in its turn, provides for assembly consisting of only one detail. Taking into account that assembly is packed in one detail, in a general case the indexing of nodes after import/export of the model may not coincide. Furthermore, in SP LIRA the elements with mid-side nodes are generated during the calculation, therefore, when importing *.inp format model, the information about the mid-side nodes in the element is ignored. Neglecting these limitations, the rest of the information from the block *Node is transferred.

For the block *Element, the following types of elements are transmitted:

Single-nodded:

SPRING1

Bars:

T2D2 T2D2H, T2D3, T2D3H, T3D2, T3D2H , T3D3, T3D3H, T2D2T, T2D3T, T3D2T, T3D3T, T2D2E, T2D3E, T3D2E, T3D3E, B21, B21H, B22, B22H, B23, B23H, PIPE21, PIPE21H, PIPE22, PIPE22H, B31, B31H, B32, B32H, B33, B33H, PIPE31, PIPE31H, PIPE32, PIPE32H, B31OS, B31OSH, B32OS, B32OSH, SPRINGA, R2D2

Plane elements:

CPE3, CPE3H, CPE6, CPE6H, CPE6M, CPE6MH, CPS3, CPS6, CPS6M, CPEG3, CPEG3H, CPEG6, CPEG6H, CPEG6MH, CPE3T, CPE6MT, CPE6MHT, CPS3T, CPS6MT, CPEG3T, CPEG3HT, CPEG6MT, CPEG6MHT, DC2D3, DC2D6, DC2D3E, DC2D6E, CPE6MP, CPE6MPH, AC2D3, AC2D6, CPE3E, CPE6E, CPS3E, CPS6E, CPE4, CPE4H, CPE4I, CPE4IH, CPE4R, CPE4RH, CPE8, CPE8H, CPE8R, CPE8RH, CPS4I, CPS4, CPS4R, CPS8, CPS8R, CPEG4, CPEG4H, CPEG4I, CPEG4IH, CPEG4R, CPEG4RH, CPEG8, CPEG8H, CPEG8R, CPEG8RH, CPE4T, CPE4HT, CPE4RT, CPE4RHT, CPE8T, CPE8HT, CPE8RT, CPE8RHT, CPS4T, CPS4RT, CPS8T, CPS8RT, CPEG4T, CPEG4HT, CPEG4RT, CPEG8T, CPEG8HT, CPEG8RHT, DC2D4, DC2D8, DC2D4E, DC2D8E, CPE4P, CPE4PH, CPE4RP, CPE8P, CPE8PH, CPE4RPH, CPE8RP, CPE8RPH, AC2D4, AC2D4R, AC2D8, CPE4E, CPE8E, CPE8RE, CPS4E, CPS8E, CPS8RE, STRI3, S3, S3R, S3RS, STRI65, S4, S4R, S4RS, S4RSW, S4R5, S8R, S8R5, S9R5, DS3, DS4, DS6, DS8, S3T, S3RT, S4T, S4RT, S8RT, SC6R, SC8R, SC6RT, SC8RT, R3D3, R3D4

Spatial elements:

C3D8, C3D8H, C3D8I, C3D8IH, C3D8R, C3D8RH, C3D20, C3D20H, C3D20R, C3D20RH, C3D27, C3D27H, C3D27R, C3D27RH, C3D8T, C3D8HT, C3D8RT, C3D8RHT, C3D20T, C3D20HT, C3D20RT, C3D20RHT, DC3D8, DC3D20, DC3D8E, DC3D20E, C3D8P, C3D8PH, C3D8RP, C3D8RPH, C3D20P, C3D20PH, C3D20RP, C3D20RPH, C3D8PT, C3D8PHT, C3D8RPT, C3D8RPHT, AC3D8, AC3D8R, AC3D20, C3D8E, C3D20E, C3D20RE, FC3D8, C3D4, C3D4H, C3D10, C3D10H, C3D10I, C3D10M, C3D10MH, C3D4T, C3D10MT, C3D10MHT, DC3D4, DC3D10, DC3D4E, C3D10MP, C3D10MPH, AC3D4, AC3D10, C3D4E, C3D10E, FC3D4, C3D6, C3D6H, C3D15, C3D15H, C3D15V, C3D15VH, C3D6T, DC3D6, DC3D15, DC3D15E, AC3D6, AC3D15, C3D6E, C3D15E.

Materials. For the block *Material the following parameters will be analyzed: name, *Elastic (modulus of elasticity and Poisson's ratio), *Density, (density), *Damping (alpha and beta parameters), *Expansion (coefficient of thermal expansion). All parameters must be specified regardless of dependence on temperature, strain rate or other sub-parameters. Otherwise, correct parameter transfer is not guaranteed.

Cross sections. For a plate, the thickness and the name of cross section will be transferred. For bars (*Beam Section), the name will be read and transfer of the following types of parametric cross sections is implemented: PIPE (pipe), RECT (rectangular), L (angle), I (T-beam or I-beam) – with the condition that mass center displacement from attachment points is not transferred, CIRC (circle), BOX (RHS) – with the condition that thicknesses walls and flanges must coincide. Turn of local axes of the bar is also implemented.

Springs. For SpringA and Spring1 types, the stiffness value and the axis along which it is assigned will be transferred (local axes and damping will not be analyzed).

Rigid Bodies. For *Rigid Body, a transfer of the ref node (base node) parameter and the following types of node set is implemented:

• elset – all nodes belonging to the element set will be selected;
• pin nset – a group of nodes;
• tie nset – a group of nodes;
• as well solid body transfer via MPC BEAM (analysis of base node and surface consisting of nodes) is also available.

Important! In SP LIRA 10, a rigid body can include maximum 500 nodes in the calculation. Try to take this feature into account when exporting your model, or edit it later!

Boundaries. If *Boundary are preset in the INITIAL step, they can be transferred as links along selected directions. In SP LIRA 10, at the stage of load cases you cannot edit or cancel the boundaries (the user can implement such actions in the ASSEMBLAGE system by using assembly/disassembly of elastic link elements with high level of rigidity). If boundaries at the stage of load cases are set as zero displacements, then such limits will be collected from all stages, and applied to the model in general, as links. If the boundary conditions are set at the stage of load cases as non-zero displacements, they are transferred as forced displacements in the selected load cases.

Load cases (import only). Only load cases of the type *Static will be imported, the name parameter will be transferred.

Loads (import only). Important! All loads are read without taking into account amplitude, local axes and types of distribution. If such additional parameters are used, the correct transfer of loads is not guaranteed.

*Dload GRAV. Gravitational acceleration, which is converted in SP LIRA as dead weight. It can be set both for the model as a whole and for a set of selected elements.

*Cload. Concentrated forces or bending moment for a group of nodes.

*Dsload. Pressure on a surface: plate or edge of a spatial element. In this case the identifier P is used as the load identifier. For example:

*Dsload
Surf-1, P, 22.4

*Dsload. Uniformly distributed load along line on the plate rib. As load identifiers you can use EDNOR (in the direction along normal to the rib, along normal to the element normal), EDTRA (in the direction along normal to the rib, along the element normal), EDSHR (in the direction along the rib), EDMOM (bending moment around the rib). For example:

*Dsload
Surf-2, EDNOR, 26.14
*Dsload
Surf-7, EDMOM, 0.144

*Dload. Uniformly distributed load on the bar. A uniformly distributed load on the bar. Load identifiers analyzed were as follows: P1 (uniformly distributed load on the bar along Y in the local coordinate system of the bar), P2 (uniformly distributed load on the bar along Z in the local coordinate system of the bar), PX (uniformly distributed load on the bar along X in the global coordinate system), PY (uniformly distributed load on the bar along Y in the global coordinate system), PZ (uniformly distributed load on the bar along Z in the global coordinate system)

In some cases, it is required to provide cross section characteristics in reports, such as, area, moments of inertia, etc. Although you could see them in the cross section editor, but still the engineer had to perform some manual work to transfer them into the table. In SP LIRA 10.14, the table of cross sections is supplemented with this information in the “Comment” column. Values of area, bending moments under inertia, core distances, shear areas, and torsional moment under inertia are available. These characteristics can be displayed for parametric, steel, wooden and user-defined cross sections. You can obtain these data in LiraAPI from the table RTT_SECTIONS_INFO, column RCT_COMMENT.

Fig. B10. Geometric characteristics of cross sections

Contours of cross sections can be useful for advanced users involved in the model export processes, defining specific geometric characteristics of the cross section, and many other activities for which perimeter points are useful In LiraAPI mode, the table RTT_SECTIONS_INFO is supplemented with the column RCT_GEOMETRY_SECTION which contains information about cross section contour. If a contour has several contours (one inner and one or more outer contour), such as, for example, RHS, the contours will be separated by a newline character ‘\n’. Example of the contour visible from Debug mode (Microsoft Visual Studio environment, C# programming language) see in the figure below.

Fig. B11. Code from the Microsoft Visual Studio environment