Calculation for the progressive collapse of the steel frame based on the shutdown of an element of the structural scheme

. Reliability of a building object - the ability of a building object perform the required functions during the estimated service life. In this case, the structure may experience a special limit state after exceeding the limit of the bearing capacity in the first and deformability in the second limit states, in which they do not fully comply with the functional requirements; further increase in loads and impacts leads to their destruction. The assumed initial local destruction implies the removal of a bearing structural element, simulating the loss of bearing capacity and stability, as well as leading to a change in the structural design of the structure. As a result of the damage received, a progressive avalanche collapse can occur in the form of the destruction of load-bearing building structures, leading to the collapse of the entire building or structure or its parts due to the initial local destruction.


Introduction
The calculation for each selected design scheme [1,2] should be carried out in compliance with a number of requirements. It is necessary to specify the most probable mechanisms for the destruction of structural elements that have lost their support. To specify the destruction mechanism means to determine all destructible bonds, including the formed plastic hinges, and find possible generalized movements in the direction of efforts in these connections.
In this case, the most probable failure mechanism corresponds to the minimum potential energy [3] of the structure on possible generalized displacements. For each of the selected fracture mechanisms, it is necessary to determine the limiting forces that can be perceived by the sections of all plastically fractured elements, bonds. and plastic hinges. It is necessary to determine the resultant of external forces applied to the individual links of the mechanism, as to separate indestructible elements or their parts, and displacements in the direction of their action. It is necessary to determine the work of internal forces and external loads on possible movements of the mechanism under consideration to check the fulfillment of the equilibrium condition.
If, for any design scheme, the equilibrium condition is not met, then structural elements should be strengthened or with the help of other measures. For example, it is allowed [4,5] to take into account the work of non-load-bearing elements in the design scheme and thereby achieve the fulfillment of the equilibrium condition. In addition, in load-bearing vertical elements that are not located above the zone of local destruction, the impact from local destruction leads to an increase in stresses and efforts. It is necessary to check the bearing capacity of these elements.

Materials and Methods
The workshop for the production of energy-efficient glass coating is a one-story building with complex dimensions. The dimensions of the building include a group of rooms for technical purposes, a two-story building was made to accommodate administrative, amenity and technical rooms. By design solutions, the frame of the production building was developed according to a single-span scheme. Overhead cranes are located in the building. Based on the results of the calculation, the following main dimensions and sections of the elements were adopted. Thus, the foundation of the structure is taken as a pile, united by monolithic grillages under the columns. The frames are hinged to the foundation. Fachwerk structures, ties and braces, frame columns, truss crossbars, runs between trusses are made of steel profiles of various sections. Frames are placed in the plan taking into account technological, design and economic requirements. The overall dimensions of the process equipment, its location and the direction of cargo flows are taken into account. From the unification conditions for industrial buildings, spans in the form of a distance between columns across the building are assigned in accordance with the enlarged module, a multiple of 6 meters. The step of largespan frames in the form of the distance between the frames in the longitudinal direction is taken as a multiple of 12 meters.
A static calculation of the supporting structures of the building was performed for the first and second groups of limit states. The calculations were performed using a spatial calculation model that takes into account constant, short-term, snow, wind, crane and brake loads. Calculations were performed by the finite element method. Spatial bar finite elements are used to model columns, trusses, braces, ties. The calculation model was developed in accordance with the architectural and construction drawings. General view of the design scheme is shown in fig. 1. The computational stability analysis against progressive collapse is performed in a quasistatic or dynamic setting and should include a number of procedures [6,7,8]. According to the primary and secondary design schemes adopted at the initial stage, the stress-strain state in the elements of the structural system is determined under normal operation conditions. In the primary design scheme, one of the vertical or horizontal load-bearing elements or sections, and secondary design schemes are built with the element of the first and second levels excluded. The instantaneous removal of an element to be switched off [9] is modeled by the efforts defined in this element in the calculation according to the primary calculation E3S Web of Conferences 389, 06023 (2023) https://doi.org/10.1051/e3sconf/202338906023 UESF-2023 scheme, applied in the secondary calculation scheme with the opposite sign. If under all possible scenarios of a special emergency impact in the form of removal of one of the structural elements, the additional loading of the structural system of the structure is of a gradual static nature, for example, the subsidence of the base during soaking caused by a break in communications, the forces that acted in the switched off element when calculating according to the primary design scheme, in the secondary design scheme can be taken equal to zero [10]. The structural system with the removed element is calculated according to the secondary design scheme and the stress-strain state in the elements of the structural system is determined, which occurs when the carrier element is locally destroyed or switched off. It is necessary to conduct a criterion verification of the bearing capacity of structural system elements for a special limit state of structures along normal and inclined sections, as well as for interface nodes of structural system elements with each other. In the case of large deflections, the work of the floors above the removed column should be considered as the work of the elements of the hanging system. At the same time, the possibility of perceiving emerging horizontal forces should be structurally ensured.

Results
In design and research calculations for progressive collapse, a certain number of approaches to the formation of design schemes are used [11,12]. A spatial design scheme of the entire building is being built. As a rule, columns and beams are modeled with bar finite elements, slabs and walls with shell finite elements. This approach retains an advantage in claims for greater accuracy. From the previous approach, everything is discarded except for the spatial section of the object, which includes structures that perceive and are able to redistribute loads when the column is removed. Boundary conditions are imposed at fragment clipping points, such as pliable bonds, displacements, modeling the mutual influence of the remaining fragment and the cut-off part of the 3d fragment. A further simplification is performed with respect to the previous approach. All floors located above the failure site are represented as a single continuum section of horizontal structures, where the 3d fragment is brought together into a horizontal 2d fragment oriented. For the frame and beam analogies, the entire building is modeled by the equivalent space frame as a 3d diagram with 2d beams. The fail-safe part of the building is reduced to one flat vertical 2d frame. From the previous approach, everything is discarded except for the section that includes structures that redistribute loads when the column is removed. All structures that redistribute loads are reduced to one cantilever beam in case of failure of the corner column, two-span with pinching along the edges in case of failure of the internal or external non-corner column, where the vertical fragment in 2d is reduced to one beam.
To calculate for progressive collapse, one supporting or bracing element is removed, and forces are applied in the removed element with the opposite sign, which decrease to 0 in a short time. Thus, the problem of calculating for progressive collapse in the ideal representation is a non-linear dynamic one. The calculation is carried out only for the first group of limit states, and all loads are accepted as standard. In large-span buildings and structures, local destruction of a number of elements should be considered. The calculation case should include one of the supporting structures of columns, truss elements or bar structures, support and compression rings, main beams, support nodes. Also, for the calculation, one should consider a structural element that unfastens the load-bearing element, which leads to an increase in its estimated length or span.
The list of structural elements of the design scheme that are subject to removal with a description of their serial number and functional affiliation within the design scheme are presented in Table 1. The location of the removed elements in the design scheme of the building frame is indicated in Fig. 2.

Discussions
The calculation has established that all the considered situations of failure of specific elements do not lead the design scheme beyond the limits of the structural provision of the sections with the required strength. The results of the calculations, indicating the number of the structural element of the scheme, the purpose of the element, as well as the percentage of use of the strength of the sections, are shown in Table 2. The analysis of the obtained results made it possible to establish that the system has the greatest margin of safety when removing elements with numbers 3570 -support brace and 1954 -truss vertical brace. The usage percentage was 32.8% and 34.4% respectively. The system has a minimum safety factor when removing elements 1580 -lower belt element and 686 -internal post of the column. The percentage of use in case of failure of these elements was 97.8% and 99.7% respectively. The percentage of section strength utilization for the case with element number 1580 is shown in

Conclusion
The calculation of the steel frame for progressive avalanche collapse made it necessary to identify more than ten calculated cases of failure of the elements of the bearing purpose, or the elements of the fastening, the shutdown of which leads to an increase in the estimated length. The calculation was carried out only for the first group of limit states, and all loads were accepted as standard. The percentage of use of assigned sections, depending on the type of element, lies in the range of 32.8% -99.7%. The minimum safety factors for the sections were obtained for the elements of the supporting column and the lower chord of the truss structure.
In calculations of this kind, one supporting or bracing element is removed, and forces are applied in the removed element with the opposite sign, which decrease to zero in a short time. The utilization factor of 99.7% allows us to make a conclusion about the correctness of the circuit element selected for shutdown, as well as the effectiveness of the assigned steel sections for the supporting structures of the structure frame.