Starting with SP LIRA 10.16, full support for floating licenses has been implemented to ensure greater flexibility and efficiency in managing software in teamwork. This approach allows a group of users within a local or corporate network to share a certain number of licenses. These licenses are dynamically allocated upon launching the client application and automatically returned to the shared pool once the application is closed. This functionality is especially important for large design firms and educational institutions, where the number of potential users often exceeds the number of active users at any given time. It enables more efficient use of resources and helps optimize software investment.

To support this functionality, our team has developed a standalone application called the “Floating License Server”. This self-contained module is designed for installation on either a dedicated server or one of the workstations within the network. Its primary purpose is to manage the pool of purchased floating licenses: handling their registration, monitoring their current status (available or in use), and controlling the allocation and return of licenses. This application is designed as a web interface for managing licenses and monitoring their current status.

The SP LIRA 10.16 client application has been supplemented with necessary settings to enable connection to the Floating License Server. To configure the connection, the user must specify the network address (either an IP address or hostname) and port number of the license server, as well as authorization data (user login and password for the license server). During each start, SP LIRA sends a request to the server to obtain an available license. If the license is successfully granted, the application starts with the functionality provided by the corresponding license type. Once the application is closed, the license is released and returned to the shared pool, making it available to other users on the network. Also, the mechanisms for handling network problems and temporary disconnections from the server with built-in support for restoring the connection when possible are provided.

For linear problems, the decomposition of a system of linear algebraic equations by using the Cholesky method (which implies the use of a compressed format of sparse columns) was implemented in SP LIRA 10.10. Starting with SP LIRA 10.16, the applicability of this method was extended to nonlinear and assembly problems. This significantly accelerates the calculation process exactly in those problems where multiple decomposition of the stiffness matrix is performed. In some problems, the time needed for the overall calculation was reduced by three and even more times compared to using the Gaussian method.

It is now possible to specify a list of degrees of freedom that will be considered in the absolutely rigid body. In previous versions of SP LIRA, the absolutely rigid body functioned in the direction of all degrees of freedom available in a specific element of the model. This ARB type remains available, and 13 new types have been added.

One of the most common examples of ARB application is modeling the support of a floor slab on a column, where the compliance of the part of the slab that directly rests on the column body can be neglected. In such cases, the finite element mesh of the slab is created so that the edges of the elements adjacent to the common node of the slab and of the column form a polygon of the projection of the column cross-section outer contour onto the plane of the slab. The nodes located within this polygon and on its boundary are connected by ARB. However, under significant horizontal loads the column body will not influence the membrane group of internal forces in the slab (tension/compression). For this reason, it is recommended to consider this ARB type only for the bending degrees of freedom, in this case, ZuXuY.

In previous versions of SP LIRA, the finite element 55 used to model an elastic link between nodes, functioned (in terms of applying stiffness characteristics and calculating reactions) only in the global coordinate system. Starting with SP LIRA 10.16, the user can assign a local coordinate system to FE 55. This enhancement provides greater flexibility in and design.

In design practice, we use two approaches to determine the most critical load combinations, namely, design combinations of forces (DCF) and design combinations of loads (DCL). In SP LIRA 10.16, support for DCL combinations according to the USA standard ASCE/SEI 7-22 (Minimum Design Loads and Associated Criteria for Buildings and Other Structures) has been implemented.

The following load types provided by the standard are taken into account:

• Dead Loads
  • (D) Dead load
  • (Tp) Prestressing force, permanent
  • (Tv) Prestressing force, variable
  • (N) Load for structural integrity
• Live Loads
  • (L) Live load
  • (Lr) Roof live load
• Environmental Loads
  • (E) Earthquake load
  • (W) Wind load
  • (S) Snow load
  • (R) Rain load
  • (H) Lateral earth pressure
• Flood, Ice & Water Loads
  • (F) Fluid load
  • (Fa) Flood load
  • (Di) Ice weight
  • (Wi) Wind-on-ice (Section 10)
• Special / Accidental Loads
  • (Ak) Load due to extraordinary event
• Service / Technical
  • (-)Inactive (technical method to ignore the load)

To generate DCL automatically, select the USA standards from the list in the Loading States Editor, then add the item Automatic Combination into the Combinations Library.

The Automatic Combination mode allows you to:

• Select the relevant section for load combination;
• Generate a list of combinations automatically.

The algorithm for generating combinations is based on constructing a graph of logical links between loading states and identifying valid combinations by using the Depth-First Search Method. The resulting combinations are automatically applied to the selected design formulas.

Based on the calculation results, the user can obtain design combinations in accordance with ASCE/SEI 7-22, with the ability to analyze the results in both tabular and graphical formats: either for individual combinations or as envelopes of internal forces.

Starting with SP LIRA 10.16, when calculating NCF, the combinations are now generated separately for each of the Eurocode formulas 6.14b, 6.15b, and 6.16b. In previous versions only the maximum value among these formulas was considered. This change affects not only NCF but also Eurocode-based design systems where combinations (NCF or autoNCL) are generated automatically.

Eurocode 0 defines the following load combinations for serviceability state verification:

1. Characteristic combination (formula 6.14b), is generally used for irreversible limit states;
2. Frequent combination (formula 6.15b), is generally used for reversible limit states;
3. Quasi-constant combination (formula 6.16b), is generally used to account for long-term effects and to assess the appearance of the structure.

For the calculation of short-term cracks opening in reinforced concrete elements by using automatic load combinations, only frequent combinations (formula 6.15b) are applied. For the calculation of long-term cracks opening, only quasi-constant combinations (formula 6.16b) are applied.

For the calculation of deflections in steel or timber elements, the user can choose which formula the combinations should be based on. To select the appropriate formula, choose the corresponding option from the drop-down list When calculating deflections for automatic combinations, analyze:

DCF Groups are created when different factors of combination need to be considered for different elements of the model, or when it is necessary to select the most unfavorable combinations for elements by checking two sets of factors.

The number of available DCF columns has been increased to 16, allowing for the definition of up to 4 sets of factors that can be used in different DCF groups.

Important! The tool of DCF Group is only available when you calculate the combinations based on the Soviet school of combination formation.

In previous versions, the tool for assignment of construction axes allowed for the creation of entire blocks of construction axes (rectangular or polar). However, when construction axes do not have a clear layout, this could be inconvenient. Starting with SP LIRA 10.16, users can now define individual construction axes by specifying two points (start and end), with the option to assign a designation to the axis.

In previous versions of SP LIRA 10, one-sided elastic foundation was available only when using linear or physically nonlinear iterative elements. Starting with SP LIRA 10.16, consideration of one-sided elastic foundation is now supported for all types of elements, including geometrically nonlinear, physically and geometrically nonlinear ones.

New element types have been added, enabling simultaneous consideration of physical and geometrical nonlinearity: type 404 – geometrically and physically nonlinear FE “cable”, types 442-444 – geometrically and physically nonlinear FE “membrane”.

A new load type has been implemented for bar elements, automatically accounting for the uniformly distributed weight of an additional material layer on the outer perimeter of the bar cross-section (cladding, insulation, glaze ice, etc.). This load is interactive and does not require reassignment when the bar cross-section is changed.

Common cases of application:

• Pipelines, chimneys, structural and bearing tubular trusses with thermal insulation;
• External utilities, power lines, cables, railings – in cases when icing is possible;
• Any bars with an additional thin-walled material layer along the perimeter.

Controlled by the following parameters:

• Density, thickness, perimeter of the layer – can be set manually or determined automatically;
• X / Y / Z – the axis along which the load is applied.

The load editor now allows sorting the editable load library based on direction or load value. This functionality greatly improves efficiency when analyzing and editing loads in models with a large number of pre-assigned loads.

• The method used for construction of pressure-time graph based on the Kingrey-Bulmash model has been implemented;

• The option to select between a spherical and hemispherical explosion (available in both the Kingrey-Bulmash and Kinney methods) has been added;

• The option to specify the type of explosive material (available in both the Kingrey-Bulmash and Kinney methods) has been added;

The mode Merging of FE has been enhanced with the option to automatically create bar finite elements along the ribs of plate and solid elements, as well as plate elements on the edges of solid finite elements. This significantly accelerates the conversion of solid models into grid structures and supports the rapid creation of a frame system, eliminating the need for manual modeling. Other cases of application include the creation of elements that simulate special boundary conditions for heat exchange or filtration along the edges/faces of base elements, or the instant generation of fictitious elements to model additional surface loads and/or elastic foundations.

A new feature has been introduced that enables intersecting loads with a plane, which can be defined either by three points or by a single point for plane parallel to the global coordinate planes. This is particularly useful when you need to cut off a certain portion of the loads in a model, allowing you to work only with the required segment. Each resulting load fragment can be edited independently, greatly simplifying local adjustments and preparation of models for calculation.

A new feature has been added that allows you to adjust of overall dimensions of architectural elements along a selected global coordinate axis by scaling the selected object. In the corresponding active mode, you simply specify the new dimension along the axis (X, Y, or Z), and the selected fragment will be automatically updated. This functionality is particularly useful for quickly modifying floor heights, slab dimensions, and similar elements, thus, eliminating the need for manual recalculation of coordinates of the required object.

New tools for quick selection of nodes, elements, and loads have been added to the quick access toolbar, allowing you to make selections without switching to corresponding selection mode. This enhancement offers greater flexibility when working with the model and accelerates the editing process.

When working with a large number of tables, finding the required information can be challenging. To facilitate searching for the required table, the list of the table of results is now presented in a tree-like interface. All data are organized into logical groups (model, elements, nodes, loads, etc.), making it easier and more intuitive to work with the results.

When designing multistory buildings, it is often essential to have the information about floor characteristics. This is especially important in seismic design, when we need to determine the parameters of building regularity, mass eccentricities, stiffness centers, etc. To simplify and automate the analysis of floor characteristics, a new summary table containing all the required information has been added in the mode Tilts and Twists. The columns include the following information:

1. Loading state
2. Floor
3. Floor dimensions (Xmin, Ymin, Zmin, Xmax, Ymax, Zmax)
4. Floor mass center (G – mass; Gx – X coordinate; Gy – Y coordinate; Gz – Z coordinate)
5. Floor slab mass center (A – mass; S – area; Fx – X coordinate; Fy – Y coordinate; Fz – Z coordinate)
6. Floor stiffness center (ΣIx – bending stiffness relative to X; ΣIy – bending stiffness relative to Y; Rx – X coordinate; Ry – Y coordinate; Rz – Z coordinate)
7. Stiffness eccentricity (E0x – eccentricity relative to X; E0y – eccentricity relative to Y; E0 – geometric sum of eccentricities)
8. Ultimate displacements (dXmin, dYmin, dZmin, duXmin, duYmin, duZmin, dXmax, dYmax, dZmax, duXmax, duYmax, duZmax)
9. Average displacements generated according to the averaging method selected in the mode Tilts and twists (dX, dY, dZ, duX, duY, duZ)
10. Settlement (Smin, Smax, S – average settlement depending on selected averaging method)
11. Tilt (Kx, Ky)
12. Twist (Hc – floor slab mark; Xhc – twist relative to X; Yhc – twist relative to Y)
13. Inertial forces (Px, Py, Pz)

In previous versions of SP LIRA, editing local axes was only possible through dedicated modes or by manually editing the calculation processor’s text file. Starting with SP LIRA 10.16, a new option allows users to define and edit axes within the table interface. In some cases, this provides a more convenient tool for automating the modeling of complex structures or for documenting the model.

It may happen that a cross-section is specified for some reason, for example, parametrically, but design calculations shall factor in exactly the rolled steel cross-section. For example, this may happen when you import a model from third-party formats, which do not support the creation of the required rolled cross-sections.

When you enter the mode Equivalent cross-section, the program with selection coefficients by default automatically will be searching for the most suitable type of cross-section, and for the most suitable profile from the first table of gauge.

In non-editable zones with tolerances, you can see the final error calculated by using the specified formulas. Also, you can see separate tolerances for the area and for each of the moments of inertia.

The window displays the formula used to calculate the error. You can manually edit the coefficients \( k_1, k_2, k_3, k_4 \) applied respectively to the area \( A \), and to the moments of inertia \( I_y, I_z, I_x \). After editing the coefficients \( k_1, k_2, k_3, k_4 \), the most suitable cross-section is automatically updated from currently active table of the gauge.

If necessary, you can change the type of cross-section, the table of gauge, and the profile. When the type of cross-section or the table of gauge is changed, the most suitable profile will be selected automatically.

When selecting a profile manually, you can view the final error and the errors separately for the area and for the moments of inertia.

When you need to create a new rolled cross-section based on the current profile, click the button Apply. As a result, a new rolled cross-section with the current rolled profile will be created in the Cross-Sections Editor.

Starting with SP LIRA 10.16, a new mode Effective lengths has been introduced, allowing the user to assign effective lengths to each individual finite element.

The assigned effective lengths can be used in subsequent design calculations. To enable this functionality, the user must specify the effective length parameters in the chosen direction and select the checkbox Use effective length assigned to the element.

Effective lengths in this mode can be either calculated automatically (for the frames) or can be entered manually.

To obtain the effective length automatically, switch to the tab Calculation, then select the frame type (sway or non-sway) for each direction, and click the button Calculation.

If effective lengths are specified only for a certain list of elements, the user must first activate the checkbox Only selected structural and finite elements before starting the calculation. Next, select on the scheme the elements for which the effective lengths will be calculated.

Automatic determination of effective lengths generally provides sufficiently accurate results for both moment frames and braced frames. The approach used for determination of effective lengths is based on Appendix 7 AISC 360-16, which provides analytical solutions for non-sway and sway frames, represented by formulas (C-A-7-1) and (C-A-7-2), respectively:

1. Elements are analyzed based on their spatial orientation: vertical elements are identified as columns, horizontal elements as beams, and all others as braces. For beams and braces, the effective length factor is set to 1.

2. For each initial and final node of a column, at the connection points with beams, the relative stiffnesses of the columns and beams adjacent to the node are summed. Stiffnesses of the columns must be recalculated taking into account the local axes Y1 and Z1 of the column.

$$ S_{cy} = \sum \left(\frac{E_c \cdot I_c}{L_c}\right)_y; \quad S_{cz} = \sum \left(\frac{E_c \cdot I_c}{L_c}\right)_z; \quad S_{by} = \sum \left(\frac{E_c \cdot I_b}{L_b}\right)_y; \quad S_{bz} = \sum \left(\frac{E_c \cdot I_b}{L_b}\right)_z $$

Where \( E \) – modulus of elasticity; \( I \) – moment of inertia; \( L \) – length; indices \( c \) and \( b \) indicate the column and beam, respectively.

If an element in the considered node has a rotational hinge in the corresponding direction, it is not analyzed when summing up the stiffnesses.

If an element has a rotational hinge only at the far end, only half of its relative stiffness is considered.

If the beam is not fixed at the far end relative to the considered node (for example, a cantilever), it is not analyzed when summing up the stiffnesses.

If ideal hinges are located at both ends of the column in the considered rotational direction, the effective length factor is assumed to be 1.

3. Dimensionless factors G are determined for the first node of column I and for the last node of column J.

$$ G_y^I = \frac{S_{cy}^I}{S_{by}^I}; \quad G_y^J = \frac{S_{cy}^J}{S_{by}^J}; \quad G_z^I = \frac{S_{cz}^I}{S_{bz}^I}; \quad G_z^J = \frac{S_{cz}^J}{S_{bz}^J} $$

If there are no beams at one end of the column, the effective length factor is assumed to be 1.

If a hinge is located at one end of the column in the corresponding rotational direction, the value of G for that end is assumed to be 10.

If the column is fixed at one end in the corresponding rotational direction, the value of G for that end is assumed to be 1.

4. For sway frames, the effective length factor of an element is calculated using the formula: \( \mu = \pi/\alpha. \), where α is derived from the equation:

$$ \frac{\alpha^2 \cdot G^I \cdot G^J - 36}{6(G^I + G^J)} = \frac{\alpha}{tg(\alpha)} $$

in this case, the resulting value of \( \mu \) must be more or equal to 1.

5. For non-sway frames, the effective length factor of an element is calculated using the formula: \( \mu = \pi/\alpha. \), where α is derived from the equation:

$$ \frac{G^I \cdot G^J}{4} \cdot \alpha^2 + \frac{G^I+G^J}{2} \cdot \left(1 - \frac{\alpha}{tg(\alpha)}\right) + \left(\frac{tg(0.5\alpha)}{0.5\alpha} - 1\right) = 0 $$

in this case, the resulting value of \( \mu \) must be less or equal to 1.

To assign the effective lengths manually, switch to the tab Assign and select on the scheme the elements to which the effective lengths will be assigned.

Next, select the radio button to mark the method of assigning the effective length (Effective length or Element length factor) and click the checkboxes to mark the types of lengths you want to edit. Once you have selected all the necessary parameters, click the button Assign.

Alternatively, you can assign and edit effective lengths by using Table Editing.

In the design of buildings and structures, the standards usually provide a complete set of input data for modeling seismic action using the linear response spectrum method. The main disadvantage of this method is that it cannot be applied when significant nonlinear effects occur in the model during an earthquake. Such effects may arise due to the presence of one-sided and/or nonlinear links, during formation of large plastic zones, at destruction of individual elements, under special seismic isolation conditions, the second-order effects, etc. In such cases, the linear response spectrum method is not applicable, and a direct dynamic analysis using earthquake seismogram or accelerogram is required. However, it raises the issue where we can get these accelerograms. In some cases, ground motion records for a given region may have been accumulated. For example, such data source could be PEER NGA Strong Motion Database (Pacific Earthquake Engineering Research Center, USA), ESM (European Strong-Motion Database), etc. However, in design analyses for a given region, there is often no database of records with such a magnitude that would meet the design requirements. If no realistic ground motion records are available for the design earthquake, it is recommended to use artificial (synthesized) accelerograms that satisfy the design acceleration response spectrum with certain accuracy. The requirements for artificial accelerograms are usually in seismic design standards. For example, see Eurocode 8, item 3.2.3.1.2 Artificial Accelerograms. The most common requirements for artificial accelerograms include:

1. The accelerogram, as required by the standards, shall correspond to the design response spectrum at 5% damping;
2. Accelerograms in the X, Y, and Z directions do not need to be coordinated;
3. Accelerations in the accelerogram must increase at the beginning and damped at the end;
4. The peak acceleration in accelerogram must, within acceptable accuracy, correspond to design PGA (Peak Ground Acceleration);
5. The building must be verified by using several sets of accelerograms.

Depending on the regulatory documents used in different countries, the list of these requirements may be expanded or shortened.

Starting with SP LIRA 10.16, official users of the software have the ability to generate accelerograms based on response spectra. As input data, the user specifies a table with the response spectrum “Frequency-Acceleration” or “Period-Acceleration. For certain standards, you can select a predefined response spectrum shape based on suggested parameters and then multiply the spectrum or the final accelerogram / seismogram by the required coefficient.

Next, the parameters for synthesizing the accelerogram and seismogram are specified.

1. Damping factor, \( \xi \);
2. Number of points in the accelerogram, \( n \);
3. Accelerogram step, per time units, \( dt \);
4. Maximum error in percents \( \varepsilon \). This error is compared with calculation error obtained as the root mean square deviation between the design spectrum and the response spectrum from the synthesized accelerogram, divided into the maximum acceleration at the initial response spectrum and multiplied by 100%;
5. Number of iterations – the number of times the accelerogram is refined to minimize the error;
6. Number of frequencies – the number of points in the response spectrum “Frequency-Acceleration”, obtained from the synthesized accelerogram;
7. Degree of oscillation damping \( \delta \) – a dimensionless parameter, which accounts for the intensity of seismic acceleration increase at the beginning of the earthquake and the damping at the end of the earthquake;
8. Adjustment of displacements – it is possible to specify the method used to generate a seismogram based on accelerogram. When synthesizing a seismogram, it is desirable for both the initial and final displacements to be zero. Since a seismogram is typically obtained via accelerogram integration, it is almost impossible to achieve a zero displacement at the end, and the final displacement remains \( d_0 \). The simplest method is to apply a zero-line rotation, when the equation of seismogram motion \( d(t) \) is subtracted \( d_0 \cdot \frac{t}{T} \), where\( T=(n-1) \cdot dt \) – the duration of accelerogram. Formally, if you double-differentiate a seismogram adjustment in this way, you will obtain the same accelerogram based on which a seismogram was initially generated. The second approach is to adjust the accelerogram itself until the final displacement in the seismogram obtained via accelerogram integration becomes zero. The disadvantage of this algorithm is that the accelerogram adjustment may reduce its agreement with the target response spectra, thus to improve the accuracy, it is necessary to increase the number of motion synthesis attempts.

By clicking the button Synthesize the synthesized accelerogram and earthquake seismogram are automatically determined.

This data is available in tables and can also be saved in special formats for the use in SP LIRA. Once the motion equation is synthesized, the spectrum graph will display the design spectrum as a green line, and the response spectrum of the synthesized accelerogram as a red line according to the user-defined number of frequencies.

It is assumed that the accelerogram record, within its duration, can be approximated with acceptable accuracy by a Fourier series. At the first stage, the Fourier series coefficients are assigned random values, which will be adjusted to match the target spectrum.

1. The initial spectrum is re-sampled by using linear interpolation into \( k \) points with a constant frequency step \( d\omega = \frac{\omega_{\max}}{k} \). As a result, we obtain a set of interpolated points of the basic response spectrum “Acceleration-Frequency” \( [a_{s0,i}, \omega_i] \).
2. The initial acceleration equation is generated based on the following expression: $$ a_0(t) = \sum_{i=0}^{k} A_i \sin(\omega_i \cdot t + \phi_i) $$ where: $$ \omega_i = i \cdot \frac{\omega_{\max}}{k} $$ \( A_i \) – the amplitude of the i-th acceleration component at this stage is defined as a random value; \( \phi_i \) – the initial phase of the i-th acceleration component at this stage is defined as a random value.
3. The acceleration response spectra are generated for the specified damping based on accelerogram \( a_0(t) \). The response spectrum will be taken as a set of points \( [a_{spec.i}, \omega_i] \).
4. The amplitude will be adjusted for each frequency: \( A_i = \frac{a_{0i}}{a_{spec.i}} A_i \)
5. After adjustment, a new accelerogram will be obtained: $$ a_0(t)=\sum_{i=0}^{k} A_i \sin(\omega_i \cdot t + \phi_i) $$
6. Evaluate the error as: $$ \frac{\sum_{i=0}^{k} (a_{0i}-a_{spec.i})^2}{a_{s0,\max}} \cdot 100\% $$ and compare it with \( \varepsilon \).
7. If the error exceeds \( \varepsilon \), the steps 3-6 will be repeated until the error becomes less than specified value or the predefined number of iterations is reached.
8. Adjust the accelerogram to ensure the required increase at the beginning and damped at the end.
9. Generate a seismogram from the accelerogram.

The advantage of using random numbers in accelerogram synthesis is that each time we obtain a different result. This makes it possible to satisfy the requirement that a structure must be evaluated using multiple accelerogram records. If the user is not satisfied with obtained result, then re-synthesis can be performed until a satisfactory response spectrum graph is achieved. Additionally, this approach allows us to take into account the requirement that accelerograms in different directions should not be consistent. Since random numbers are used for each acceleration component, the consistency is practically excluded. It is important to understand that the number of frequencies during synthesis should be sufficiently large. If the frequency step is too large, the peak accelerations at intermediate points may be significantly lower than those at reference points, therefore, the calculation based on accelerogram will not provide a sufficient conservatism.

In addition to the aforementioned capabilities, several minor improvements have been implemented to simplify the work of design engineers:

• Text messages from the have been converted from ANSI to UNICODE;
• Rigid inserts in plates are taken into account when collecting internal forces into equivalent bar;
• Added the ability to switch between loading states by using keyboard arrows (Shieft+Up or Shieft+Down);
• It is now possible to enter the Loading States Editor while in the calculation results mode;
• Performance of user result scripts has been improved.

Proportioning and checking of steel structures in SP LIRA 10.16 shall be carried out in accordance with the following chapters of the AISC 360-16 standard: Chapter D – Design of Members for Tension, Chapter E – Design of Members for Compression, Chapter F – Design of Members for Flexure, Chapter G – Design of Members for Shear, Chapter H – Design of Members for Combined Forces and Torsion. There is also an option to activate checks for deflections and slenderness. The calculation is performed for the following cross-section types: rolled I-beam, rolled channel bar, bent-welded RHS, round pipe, rolled T-beam, angle, welded symmetrical I-beam, welded channel bar, welded RHS, welded T-beam.

In the structural design parameters, you can select the design approach based on ultimate internal forces: LRFD (Load and Resistance Factor Design) or ASD (Allowable Strength Design).

The LRFD approach implies that loads are increased by load safety factors (load factors), while the element resistance is reduced by material safety factors (\(\Omega\)).

The ASD approach implies that characteristic (non-increased) loads are used, while the element resistance is reduced by strength factor (\(\varphi\)).

When designing structures based on strength criteria, the use of LRFD approach typically results in lower material consumption, therefore this method is preferable.

It is possible to assign the user-defined factors to check each of the criteria: tension, compression, bending, shear, and torsion.

For the analysis of overall stability, specify the effective lengths of elements relative to the Y1 and Z1 axes, as well as the effective lengths for torsional and flexural buckling modes. Effective lengths can be specified as absolute values, as coefficients of the actual length of structural element, or as effective lengths assigned to the element in the mode Effective lengths or Table Editing.

For shear analysis of certain cross-section types, you can also specify the presence of stiffeners and their spacing.

Important! When checking the elements upon bending, the bending moment diagram in the span of a structural element will be determined automatically in order to define the coefficient for flexural-torsional buckling mode Cb. If disbracings for deflections are assigned to the element, then it will be analyzed only the segment between these disbracings of deflections, which contains the finite element being analyzed, not the entire structural element.

Flexibility check can be activated for compressed or tensile elements.

Deflection checks can be activated during serviceability analysis.

For deflection calculations, it is recommended to use ASD from ASCE/SEI 7-22, or the combinations from Appendix CC2, Subsection СС2.2.1 Vertical Deflections.

To ensure accurate deflection analysis, it is recommended to specify the bracing for deflections in the elements being checked.

Deflection limits are defined according to project requirements. User can find the recommended reference values in ASCE/SEI 7-22, Subsection СС2.2.1 Vertical Deflections.

To view the results of structural design checks, the AISC standards are selected along with the factor used for calculation (Internal forces/DCF/DCL). If needed, results can be displayed for strength checks (tension, compression, bending, shear, torsion, combinations of various factors), as well as flexibility check results for each local axis of the bar, and deflections.

Table of results showing calculation trace data for each factor is also available for viewing.

In general, support sections in a beam can have different configurations. For example, end supports may be designed with additional stiffening ribs, while central sections may only have a single stiffening rib per support.

In previous versions of SP LIRA 10, users could only define a general view for all support sections. As a result, designing of a continuous span required creating several sets of structural design parameters and dividing the element into separate sections. Starting with SP LIRA 10.16, it is now possible to specify the parameters of supporting elements at the beginning, end, and intermediate points of a span. This functionality is available when support zones are analyzed based on the bending moment diagram or deflection bracing.

When designing steel structures according to Eurocode 3, shear delay effects are considered in accordance with Section 3 of EN 1993-1-5. In previous software versions, the user was required to define the span type and size in order to identify it according to the Table 3.1 of EN 1993-1-5. The capability to define span zones based on bracings of deflections was implemented at one of the stages of SP LIRA 10.14. The method was based on the diagram shown in Fig. 3.1 of EN 1993-1-5, which did not provide a general solution, since this diagram is only applicable when adjacent spans differ by no more than 50%, or the cantilever length does not exceed 50% of the adjacent span.

For the general case, the span length \( L_e \) is evaluated as the distance between two zero points of acting moments. Starting with SP LIRA 10.16, it became possible to automatically identify span lengths. To determine the effective flange width reduction factor \( \beta \) were used the recommendations from the publication [B. Johansson, R. Maquoi, G. Sedlacek, C. Müller, D. Beg. Commentary and worked examples to EN 1993-1-5 “Plate structural elements”]. This guide, Section 3 Effective width approaches in design covers the general case of the span subjected to uniformly distributed and concentrated forces. The parameter \( \beta \) is determined according to the Fig. 3.13 given in the table of the aforementioned guide.

$$ \beta = \left[1 + 4\left(1 + \Psi\right)\frac{b}{L} + 3.2\left(1 - \Psi\right)\frac{b^2}{L^2}\right]^{-1} $$

It depends on the span length \( L \), flange width \( b \) and coefficient of the shape of bending moment diagram \( \varPsi \), which is defined as four times the ratio \( \frac{\Delta M}{M_{max}} \), where: \( \Delta M \) – the maximum deviation between the actual bending moment and a linearly varying moment from 0 to \( M_{max} \), and \( M_{max} \) – the maximum moment within the span.

The presence of a support within a span is determined according to the following rule:

If the segment is at the end and a transverse force is present in it, a support is assigned at that point. If the segment is a point having the maximum moment within the span and the coefficient \( \varPsi > 0 \), support is also assigned at that point. In all other cases, the segment is considered to be a part of the span.

To ensure that spans are recognized based on the actual bending moment diagram, you must select the corresponding radio button in span parameters.

Eurocode 8 defines two main approaches to the linear response spectrum method for seismic resistance evaluation. The first approach is based on the actual expected elastic response spectra, according to Eurocode 8, subsections 3.2.2.2 Elastic response spectrum for the horizontal components of the seismic action and 3.2.2.3 Elastic response spectrum for the vertical component of the seismic action. The second approach is based on the use of fictitious reduced response spectra according to Eurocode 8, subsection 3.2.2.5 Design spectrum for elastic analysis, which accounts for energy dissipation in the dissipative zones of the building. When using the first approach, we obtain very large seismic loads with a margin of safety. At that we can design the building without meeting special requirements for the formation of dissipative zones. However, if we use the second approach, we must determine the behavior factor q and ensure that, under seismic action, the oscillations were damped in specially designed zones. Typically, in moment-resisting frames, these zones are located in the beams near the connections to columns. Table 6.3 of Eurocode 8 states, that when the factor of behavior is 1.5 < q < 2, you can use the cross-section classes 1, 2, 3; when the factor of behavior is 2 < q < 4, only classes 1 and 2 are allowed; and for q > 4 only cross-sections of class 1.

The requirements for limiting the use of cross-section classes 3 and 4 in SP LIRA 10.16 can be met by selecting an appropriate option from the drop-down list Minimum allowable class of cross-section under seismic loads.

Plastic zones must be formed in beams, while plastic strains must not occur in columns. Eurocode 8 contains recommendations in subsection 4.4.2.3 Conditions for global and local ductility that ensures compliance with this principle. According to these recommendations, the total load-bearing moment of the columns at beam-to-column joints must exceed the total load-bearing moment of the beams by 1.3 times. To meet this requirement for columns, activate the checkbox Implement the principle of seismic resistance “weak beam - strong column” in the structural design parameters and, if necessary, specify the coefficient with which the moment from the beams will be taken into account in the additional seismic combination.

In the calculation, this principle is implemented as follows:

1. It is checked whether the element is a column. If it is not located vertically, then ignore this principle;
2. At the element nodes, adjacent horizontal and inclined elements are searched for. They must have design parameters of steel elements according to Eurocode. If no such elements are found, then ignore this principle.
3. For each local direction y and z of the column element, the sum of projected plastic ultimate moments \( M_{yb} \), \( M_{zb} \) that can be accumulated in beams/braces is calculated. If the beam is adjacent by a hinge in the corresponding rotational direction, its ultimate moment is not included in the sum. For RC elements, the positive and negative ultimate moments in beams may have different absolute values.
4. The ultimate moment at the node is distributed among the adjacent columns at the node proportionally to column stiffnesses.
5. For all seismic load combinations, the maximum and minimum axial internal forces \( N_{min}, N_{max} \) are determined.
6. The column is checked against the following additional fictitious load combinations:
   $$ \begin{array}{|c|c|c|} \hline N_{min} & M_{yb} & 0 \\ \hline N_{min} & -M_{yb} & 0 \\ \hline N_{min} & 0 & M_{zb} \\ \hline N_{min} & 0 & -M_{zb} \\ \hline N_{max} & M_{yb} & 0 \\ \hline N_{max} & -M_{yb} & 0 \\ \hline N_{max} & 0 & M_{zb} \\ \hline N_{max} & 0 & -M_{zb} \\ \hline \end{array} $$

The LIRA 10 software package provides functionality for defining variable cross-sections in structural bar elements. This enables accurate modeling of beams, columns, and other elements whose cross-sectional dimensions vary linearly along their length. Starting with SP LIRA 10.16, this feature supports the calculation of symmetrical I-beams, asymmetrical I-beams, and welded rectangular hollow sections (RHS) in accordance with Eurocode 3. Calculations are performed for the cross-section corresponding to the dimensions at a given point along the element, similarly to constant-size cross-sections, but with several important distinctions. First, the calculation for the flexural buckling mode is not considered. Second, the shear delay effect is not taken into account. Third, when determining the element effective lengths, additional transformations are performed. These adaptations are necessary because the effective length varies continuously along the span of an element with a variable cross-section. If the value of element effective length lef.bas (base) is known for a given moment of inertia Ibas, the element effective length at any other point with a current coordinate x (in the local axes of the bar) can be determined based on the following expression:

$$ l_{efx} = l_{ef.bas} \cdot \sqrt{\frac{I_x}{I_{bas}}} $$

The user can select the criterion used to define the base effective length. Available options are shown in the figure below. If the effective length is assigned directly to the elements, it is recommended to select the parameter Use the effective length constant.

In SNiP II-23-81 and other national standards derived from it, the local buckling checks for the webs of centrally compressed symmetrical I-beams (as defined in Table 27) impose strict limitations on web slenderness. These checks do not take into account the actual stress state of the web. Such requirements are based on the assumption that local buckling must not occur before global buckling. However, in practice, this approach can result in an excessive and unjustified safety margin. As a result, applying these provisions rigidly can often result in unacceptably high utilization ratios for local buckling, even in cases involving moderate or low loads. Starting with SP LIRA 10.16, in such cases the calculation is performed using the following algorithm:

$$ \frac{|N| \gamma_n}{\gamma_c \varphi_z A} \le \frac{3,6152 \chi R_y}{\bar{\lambda}_w^{-2}} $$

$$ \chi = \begin{cases} \frac{167\psi^5 - 995.75\psi^4 + 991.45\psi^3 - 398.0875\psi^2 + 75.24334\psi}{9} + 1, & \text{if } 0 < \gamma \le 4 \\ 0.08 \psi + 1.643, & \text{if } 4 < \gamma \le 10 \\ \frac{0.1 \psi + 15.407}{9} \le 1.8, & \text{if } \gamma > 10 \end{cases} $$

Here, the \( \chi \) coefficient is obtained by approximating Table 1 from the article: B.M. Broude, V.I. Moiseev, “Stability of rectangular plates with elastic restraint along longitudinal edges”, Structural Mechanics and Structural Analysis, No. 1, 1982, pp. 39–42.

$$ \Psi = \frac{\gamma}{10} $$

$$ \gamma = \frac{G I_{fx}}{h_w D} $$

$$ I_{fx} = \frac{b_f t_f^3}{3} $$

$$ D = \frac{E t_w^3}{12(1-\mu^2)} $$

The load type is used to determine the coefficient \( \varPsi \) in accordance with the Tables N.1, N.2, and N.5 of DBN V.2.6-198:2014; Tables 77-79 of SNiP II-23-81; and Tables J.1, J.2, and J.5 of SP 16.13330.2017. The load type can be specified manually from the listed tables. At that, starting with SP LIRA 10.16, the load type can be selected automatically based on the bending moment diagram.

In the case of automatic load type recognition, it is determined according to the following procedure:

1. The structural element is divided into individual spans, taking into account bracing of deflections;
2. The span containing the analyzed element is selected;
3. For each checked load (internal forces/DCF/DCL), the bending moments M and snapping coordinates \( X \) are determined along the span points of the structural element;
4. The maximum moment within the span \( M_{max} \) shall be identified;
5. Basis diagrams are generated by using data from the Tables N.1, N.2, N.5 of DBN V.2.6-198:2014; Tables 77, 78, 79 of SNiP II-23-81; and Tables J.1, J.2, J.5 of SP 16.13330.2017, based on the coordinate X and the maximum moment \( M_{max} \):
   1. Concentrated load in the center of a beam hinged at the edges: $$ M_1(x) = \begin{cases} 2 \cdot M_{\max} \cdot \frac{(L-x)}{L}, & x \ge \frac{L}{2} \\ 2 \cdot M_{\max} \cdot \frac{x}{L}, & x < \frac{L}{2} \end{cases} $$
   2. Concentrated load at 1/4 of a beam hinged at the edges: $$ M_{21}(x) = \begin{cases} 4 \cdot M_{\max} \cdot \frac{x}{L}, & x \le \frac{L}{4} \\ \frac{4}{3} \cdot M_{\max} \cdot \frac{x}{L}, & x > \frac{L}{4} \end{cases} $$
   3. Concentrated load at 3/4 of a beam hinged at the edges: $$ M_{22}(x) = \begin{cases} \frac{4}{3} \cdot M_{\max} \cdot \frac{x}{L}, & x \le \frac{3L}{4} \\ 4 \cdot M_{\max} \cdot \frac{L-x}{L}, & x > \frac{3L}{4} \end{cases} $$
   4. Two concentrated loads: at 1/3 and 2/3 on a beam hinged at the edges: $$ M_3(x) = \begin{cases} 3 \cdot M_{\max} \cdot \frac{x}{L}, & x \le \frac{L}{3} \\ M_{\max}, & \frac{L}{3} < x < \frac{2L}{3} \\ 3 \cdot M_{\max} \cdot \frac{L-x}{L}, & x \ge \frac{2L}{3} \end{cases} $$
   5. Concentrated load in the center of a beam rigidly supported at the edges: $$ M_{41}(x) = \begin{cases} M_{\max} \cdot \left(1 - \frac{4x}{L}\right), & x < \frac{L}{2} \\ M_{\max} \cdot \left(\frac{4x}{L} - 3\right), & x \ge \frac{L}{2} \end{cases} $$ $$ M_{42}(x) = -M_{41}(x) $$
   6. Uniformly distributed load on a beam hinged at the edges: $$ M_5(x) = 4M_{\max} \cdot x \cdot \frac{L-x}{L^2} $$
   7. Uniformly distributed load on a beam rigidly supported at the edges: $$ M_{61}(x) = M_{\max} \cdot \left(1-8x \cdot \frac{L-x}{L^2}\right) $$ $$ M_{62}(x) = -M_{61}(x) $$
   8. Linear bending moment diagram, the coefficients k and c are determined using the least squares method relative to the actual diagram: $$ M_7(x) = k \cdot x + c $$
   9. Concentrated load at the end of the cantilever: $$ M_{81}(x) = M_{\max} \cdot \frac{x}{L} $$ $$ M_{82}(x) = M_{\max} \cdot \frac{L-x}{L} $$
   10. Uniformly distributed load along the cantilever: $$ M_{91}(x) = M_{\max} \cdot \frac{x^2}{L^2} $$ $$ M_{92}(x) = M_{\max} \cdot \frac{(L-x)^2}{L^2} $$
6. For each basis diagram \( M_i(x) \) the sum of squared deviations between the basis diagram and the actual diagram is calculated for beams or cantilevers.
7. The basis diagram for which the minimum sum of squared deviations is obtained will be used for further analysis taking into account the data from the Tables N.1, N.2, N.5 of DBN V.2.6-198:2014; Tables 77, 78, 79 of SNiP II-23-81; and Tables J.1, J.2, J.5 of SP 16.13330.2017 to determine the coefficient \( \varPsi \).

The SOIL module has been supplemented with a capability to calculate piles for the combined action of vertical and horizontal forces and moment according to DBN V.2.1-10:2009 standards (the calculation is based on SNiP 2.02.01-83*).

To perform this calculation, you need to assign the design horizontal forces and/or moments to the pile, and then activate the checkbox Calculate stability of the foundation surrounding the pile.

Calculation results in Soil Editor contain the following parameters for each pile: coefficients of deformation \( \alpha_{\varepsilon} \), reduction factors \( dK \), conditional restraint depth of the pile tip \( l_{1} \), ultimate and design pressure on soil along pile skin \( \sigma_z \), design depth (pile cross-section depth in soil) \( z \), horizontal displacement \( u \) and angle of pile rotation \( \varPsi \) the for the X and Y axes.

Also, user can view the graphs of transverse force \( Q \), design bending moment \( M \), design pressure on soil along pile skin \( \sigma_z \) and ultimate soil bearing pressure along pile skin \( \sigma_{zu} \) depending on the depth of the pile cross-section in soil \( z \).

For a general assessment of foundation stability the Model Analysis provides mosaics of the utilization coefficient \( K_h \) and the degree of lateral plasticity \( K_{pl} \).

The utilization coefficient is defined according to the formula: \( K_h = \frac{\left| \sigma_z \right|}{\left| \sigma_{zu} \right|} \), and the degree of lateral plasticity is defined according to the formula: \( K_{pl} = 1 - dK \).

• The algorithm for generating soil layers based on borehole data has been optimized;
• The calculation of screw pile bearing capacity according to Eurocode 7 has been updated to comply with the Recommendations on Piling (EA-Phäle) issued by the German Geotechnical Society;
• The capability to edit the local coordinate system has been implemented for the piles specified by using architectural elements.

In SP LIRA 10.16, the plugin for integration with Revit 2025 has been redesigned. Compared to the plugins for previous versions of Autodesk Revit, both the functionality and interface have been significantly improved.

Export of the analytical model is performed by using the intermediate file (*.2lira format). To transfer calculation results to Revit, this intermediate file is supplemented with data from SP LIRA 10.16, which is then read by the plugin within the Revit environment.

When exporting cross-sections, you can select the dataset to be extracted from the Revit based on:

1. Comparison library (the user can choose the corresponding profiles from the SP LIRA library);
2. Parametric characteristics (the cross-section type and its geometric characteristics are extracted from the Revit model);
3. Stiffness characteristics (design characteristics of cross-section are extracted from the Revit model, and a cross-section specified by numerical description will be generated in the SP LIRA).

When exporting materials, you can select the dataset to be extracted from the Revit based on:

1. Comparison library (the user can choose the corresponding materials from the SP LIRA library);
2. Numerical characteristics of material physical parameters (modulus of elasticity, Poisson’s ratio, coefficient of thermal expansion, etc.).

Displaying the results – the Revit supports displaying the results of reinforcement proportioning for both slabs and bar elements.