CALCULATION OF MULTI-STORY BUILDINGS FOR LANDSLIDE DAMAGE

УДК 624.046.012.45

Abstract

This article investigates the design and analysis of multi-story frame buildings with a frame-braced structural system constructed using monolithic reinforced concrete technology, taking into account the possibility of progressive collapse. The study considers an accidental scenario involving the failure of the central column and the stiffness diaphragm on the first floor, which may initiate the redistribution of internal forces and lead to local damage propagation. Numerical calculations were performed to evaluate the stress-strain state and load-bearing capacity of the remaining structural elements after local failure. Particular attention was paid to changes in bending moments, axial forces, and reinforcement requirements in beams and columns adjacent to the damaged zone. The obtained results demonstrate that local damage does not necessarily lead to complete structural collapse, provided that sufficient structural redundancy and continuity are ensured. Recommendations aimed at preventing progressive collapse and improving the robustness, reliability, and survivability of multi-story reinforced concrete buildings are proposed. The findings may be used in the design of buildings subjected to accidental and extreme loading conditions..

Аннотация

В статье рассматриваются вопросы расчета многоэтажных каркасных зданий с каркасно-связевой конструктивной системой, возводимых из монолитного железобетона, с учетом возможности прогрессирующего обрушения. Исследован аварийный сценарий, связанный с выходом из строя центральной колонны и диафрагмы жесткости первого этажа, приводящий к перераспределению внутренних усилий и развитию локальных повреждений. Выполнен анализ напряженно-деформированного состояния и несущей способности оставшихся элементов конструкции после возникновения локального разрушения. Особое внимание уделено изменению изгибающих моментов, продольных сил и потребности в дополнительном армировании балок и колонн, расположенных вблизи поврежденной зоны. Установлено, что локальное повреждение не всегда приводит к полному разрушению здания при наличии достаточной конструктивной избыточности и непрерывности несущей системы. Предложены рекомендации по повышению надежности, живучести и устойчивости многоэтажных железобетонных зданий к прогрессирующему обрушению при аварийных воздействиях.

Keywords: progressive collapse, multi-story frame building, monolithic reinforced concrete, frame-braced system, central column, stiffness diaphragm

Ключевые слова: прогрессирующее обрушение, многоэтажное каркасное здание, монолитный железобетон, каркасно-связевая система, центральная колонна

Introduction

Currently, there is a significant increase in natural, man-made, and even terrorist-related impacts that were not previously considered in design standards but can lead to the collapse of individual components or, in some cases, entire structures. Consequently, many countries, including Russia, have developed and implemented regulatory documents into their design practices to prevent the progressive collapse of buildings and structures from such impacts, thereby increasing their structural safety and preserving the lives and health of their occupants. However, in our country, there are still only a few scientific publications dedicated to studying the specific characteristics of the stress-strain state of building and structural components under such impacts that cause limit state conditions. Furthermore, no regulatory documents have been developed for designing buildings that account for progressive collapse.

In the article in view caught main The goal is a frame- linked structural system according to designed many multi-storey of buildings mobile phone of the violation ahead take design issues considered .

Methods

Unity reinforced concrete technology according to building 9 floors residence the frame of the building is connected first  two in the case outside loads to the effect considered taken results (concrete and steel reinforcement consumption) each other with compared to . First in the case what is it everyone elements to work suitable , second in the case and one first on the floor brand name pillar and virginity diaphragms to work unsuitable because reception done .

The building geometric dimensions in Table 1, effect to do cargo amounts are in Table 2 quoted .

Table 1. Building geometric

Table 2. Effect to do cargo amounts

First in the version one in the elements defect and injuries absence for in the accounts everyone elements to work suitable accept done. Calculation simplified in the method done .

Building first floor central to the pillar impact to do loads calculation is presented in Table 3 .

Table 3. Building first floor central to the pillar impact to do loads calculation

Total load affecting column:

normative  N _{n , mark} = 2257.64 kN; calculated           N _mark = 257 9 .4 kN.

Column private due to weight N _columns = 108.5 kN; crossbars private heavy ­gypsy N _rig =475.2 kN; celibacy diaphragms due to the weight N _diafr = 540 , 1 kN.

Building "V" and "3" axes in the center intersected located first floor central to the pole impact to do total permanent load - N _center ( g) = 2986.8 kN, temporary cargo - N _centers ( v+ s ) = 716.4 kN. Total : N _center ( q )=3703.2 kN.

Central pillar for  .

Reception reinforcement Æto be made 8 28 (A _s = 4926 mm ² > 4916.9 mm ²).

Beam account . Beam impact to do loads quantity In table 4 cited

Table 4. Beam impact to do loads

Figure 1. To the avalanche failure of the frame-linked frame calculation: a – transverse diaphragm frame; b – transverse frame; v is the change in wind pressure along the height of the building; g - alignment of columns and diaphragms in plan; d - "V" and the central column at the intersection of the "G" axes the load-bearing surfaces of the columns (S=9 m2); e - after failure the load acting on the outer columns (S=36 m2) and the beam (S=36 m2)

Total normative accounting cargo : .

Total normative accounting cargo : .

Bending of moments approximately values following from formulas calculation possible : middle on a stick bender - ; the roofs ­are - ; ; . .

Height 40 см was crossbar thickness 16 см was with a solid plate together preparation for of the crossbar height 56 см, h ₀ =52 cm.

Medium on the support M=211.46 kNm . Coefficient ; z=0.927; . Reception reinforcement Æto be made 4 20 ( A _s = 1256 mm ² > 1202 mm ² ).

From the wind to the building impact to do horizontal cargo ( space type B):

, this on the ground .

.

Virginity to the diaphragm impact to do stress .

The force of the coil Q _d = 206.7 kN ( base) at the level of ).

Torque M _d = Q _d Z = 3648.25 kNm .

To the foundation impact to do load . Thickness 80 см planned from ­a slab of size 6 ´13.8 m pressure G _f =22.0 kN / m ² . Calculated "3" bullets from the cargo according to foundation underneath to the ground pressure p _m = 186 kN / m ² .

Thickness 16 см was virginity Diaphragm from the constructive point of view­ two layer net with a ­grain is equipped . Net of sturgeons diameter 12 мм, cell  Size 200x200 mm.

Thickness 80 см was foundation plate both constructive from the point­ two layer net with a ­grain is equipped . Net of sturgeons diameter 20 мм, of the cell Size 200 x 200 mm.

9 floors building for materials expense following to the table we enter

Table 5. Floors building for materials

Calculation when the central column at the intersection of the "B" and "3" axes on the first floor fails. In this case, the building must be designed for avalanche destruction.

When the central column on the first floor fails, the design scheme of the frame changes (Fig. 3). The arch between the columns changes from 6 meters to 12 meters, and the knot connecting the first floor to the column of the second floor hangs. The frame is calculated for the action of normative loads, and the accumulation coefficient is taken as 1=1 for constant loads and 2=0.5 for temporary loads.

Figure 2. Defects and injuries of frame elements for the calculation of the frame in the case of: a, b - frame views; c - load on end columns impact surfaces (S=9 m2); g-first floor central column failure

Assembly of loads that take into account the avalanche-like destruction of the building as a result of the destruction of the central column and diaphragms of the first floor.

When calculating for landslide failure, taking into account standard loads, the load factor for permanent loads is taken as = 1, and for temporary loads as = 0.5.

Side pillars for permanent , useful temporary and snow from the load stress

. Columns private due to weight . Beams private due to weight .

First floor edge column impact to do total cargo

.

First floor central pillar from work when it comes out simple to a very static (quasistatic) style suitable to the load dynamic coefficient. At that time central to the pole extendable cargo

.

Sidebar strength provision for demand reinforcement section to be made surface . Acceptance fittings to be made

4 Æ32+4 Æ36 A400 ( A _s =3217+4072=7289 >7221 mm ² ) .

Beam account . First floor pillar from work from the source later beams length increases twice . First and second floor the nights of the night twisted knot point is considered .

Beam in the section bender of torque approximately value .

Thickness 16 см was with a solid plate together working  beams height 56 см, h ₀ =52 c m. Coefficient . .

  that it was for crossbar section excessive hard time Compressed zone concrete strength enough not. Central pillar from work until it comes out compressed in the zone reception made armature 4 Æ20A400 ( .

Coefficient . .  condition is doing ­it ­. Coefficient . .

Stretching per zone 4 Æ20 +4 Æ22 ( A _s = 2776 mm ² > 2733.0 mm ² ) rods two row will be placed .

Column account . From work came out central to the pole impact to do cargo edge to 4 columns  is distributed . Har to one end column impact to do additional cargo

To the side pillar impact to do total cargo

,

The way increased (from 6 meters to 12 meters ) rafters one side by side from loading  neighbor on the pillars  both additional moments ( about 150-200 kNm ) to the body comes .

First on the floor virginity of the diaphragm existence of the building to move virginity in providing plays an important role . His breakdown  of the building  to move was virginity sharp reduces . This in the case wind and from the earthquake into existence coming horizontal of goods only accept rama does Shifter the tensions first upstairs remaining eight pillar reception does In columns cutter forces sharp increases. Calculation stresses are presented in table 5.

Table 6. Calculation stresses

Table 7. First floor for materials expense collection

* First upstairs out of a total of 9 columns central pillar from work What's up ­? for to account not received .

Table 8. Building first to the floor expense to be done materials

Discussion

Discussion. As a result of the failure of the central column on the first floor of the building, the loads on the columns adjacent to the central column increase depending on the load-bearing surface. The design length of the beam will double.

To ensure the viability of the building, beams must be equipped continuously along the entire length, and columns must be calculated based on double the load.

The failure of the central diaphragm in the building requires additional reinforcement of the peripheral columns against wind and seismic forces.

The failure of central columns on the first floors of buildings leads to an increase in reinforcement consumption while maintaining the geometric dimensions of the building elements. An approximately twofold increase in reinforcement consumption is shown in Table 6 using the example of the first-floor column and rail.

Designing without considering avalanche destruction leads to an increase in the initial estimated cost of building construction. This is due to the consequences of the avalanche disruption. When a building is completely unusable, the construction of a similar building in its place (due to inflation, the removal of demolished buildings, etc.) becomes several times more expensive. Furthermore, it is necessary to take into account the immeasurable human losses and the destruction of spiritual and material values resulting from the avalanche-like collapse of a building. Therefore, when designing unique buildings of high responsibility, it is necessary to take into account their avalanche-like destruction from anthropogenic or natural impacts.

Conclusion

Above cited accounts based on following conclusions to do possible :

1. When designing high-responsibility multi-story reinforced concrete buildings, the condition of progressive collapse must be taken into account.

2. As a result of the failure of the central column of the first floor, the design stresses on adjacent columns and beams increase significantly, which negatively affects the reliability and safety of the structure.

3. When the central column fails, bending moments increase sharply as a result of doubling the design arc of the beam and additional reinforcement is required.

4. Failure of the first-floor stiffening diaphragm reduces the horizontal stiffness of the building and leads to the redistribution of forces from wind and seismic impacts to the remaining columns.

5. When designing for landslide failure, the concrete consumption remains practically unchanged, but a significant increase in reinforcement consumption is observed.

6. To ensure the viability of the structure, it is advisable to ensure continuous reinforcement on the ridges and to check the columns for emergency loading.

7. The results obtained show that it is economically and socially expedient to take into account protective measures against avalanche destruction when designing high-responsibility buildings.

References:

1. Asmanova Ch.A., Ibragimov Kh.M., Usmanov V.F. Modeling of a multi-story reinforced concrete frame building for experimental investigations. In: Innovations in Construction and Seismic Safety of Buildings and Structures. Proceedings of the International Scientific and Practical Conference. Namangan, November 27–28, 2025. P. 131–134.
2. Asmanova Ch., Usmanov V., Ibragimov H., Madatov I. Calculation of building load-bearing structures according to the second group of limit states. Academic Journal of Science, Technology and Education. 2026;2(3):16–21. Available at: https://integrumpublication.org/index.php/ajste/article/view/171
3. Feng D.C., Shi H.R., Parisi F., Brunesi E., Wang C.L. Efficient numerical model for progressive collapse analysis of prestressed concrete frame structures. Engineering Failure Analysis. 2021;129. DOI: 10.1016/j.engfailanal.2021.105683.
4. Fu F. Progressive Collapse Analysis and Design of Building Structures. 2nd ed. Boca Raton: CRC Press; 2021.
5. GOST 27751–2014. Reliability of Building Structures and Foundations. Basic Principles. Moscow: Standartinform; 2015.
6. Kiakojouri F., De Biagi V., Chiaia B., Sheidaii M.R. Progressive collapse of framed building structures: Current knowledge and future prospects. Engineering Structures. 2020;206. DOI: 10.1016/j.engstruct.2019.110061.
7. Qian K., Li B. Experimental investigation of the progressive collapse of reinforced concrete structures: An overview. Structures. 2020;25:881–900. DOI: 10.1016/j.istruc.2020.03.018.
8. QMQ 2.01.03–19. Construction in Seismic Regions. Tashkent; 2019.
9. QMQ 2.03.01–96. Concrete and Reinforced Concrete Structures. Design Standards. Tashkent; 1996.
10. SP 385.1325800.2018. Protection of Buildings and Structures against Progressive Collapse. Design Rules. Moscow: Ministry of Construction of the Russian Federation; 2018.
11. Starossek U. Progressive Collapse of Structures. 2nd ed. London: ICE Publishing; 2023.
12. Yi W.J., Yi F., Zhou Y. Experimental Studies on Progressive Collapse Behavior of RC Frame Structures: Advances and Future Needs. International Journal of Concrete Structures and Materials. 2021;15. DOI: 10.1186/s40069-021-00469-6.