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Advances in Continuous
and Discrete Models
Duan and Zhang Advances in Continuous and Discrete Models (2025) 2025:40
https://doi.org/10.1186/s13662-025-03865-4
R E S E A R C H Open Access
Analysis of monolithic collapse resistance of
reinforced concrete column-steel beam frame
structures
Kaimin Duan1* and Guofeng Zhang2
*Correspondence:
dkm0610@163.com;
kaimin_duan34@outlook.com
1Changjiang Institute of
Technology, Wuhan 430212, Hubei,
China
Full list of author information is
available at the end of the article
Abstract
To analyze the monolithic collapse resistance of reinforced concrete column-steel
beam frames, adjustments were made to the layout, and the design was optimized to
meet relevant regulations and codes. Concrete and steel beam strengths were
determined, reinforcement details finalized, and a physical model was constructed in
the laboratory following applicable standards. Different load levels were applied to
the model using a mixed force-displacement controlled loading method.
Displacement and strain data were collected at various measurement points under
these loads to evaluate the collapse rate through simulation and experimental
measurements. The results reveal that measuring point 7 was the first to exhibit
failure due to external loading. However, other areas, including the concrete and steel
reinforcements, showed only minor damage, preserving the frame’s integrity.
Compared to frames made solely of concrete or steel, the reinforced concrete
column-steel beam configuration demonstrated superior safety, with an overall
collapse rate not exceeding 35%.
Keywords: Reinforced concrete; Column-steel beams; Frame structures; Monolithic
collapse resistance; Concrete strength; Displacement measurements
1 Introduction
The combined frame system of reinforced concrete columns and steel beams is a unique
hybrid structural design that skillfully integrates reinforced concrete and steel qualities.
The combined frame system of reinforced concrete columns and steel beams offers key
advantages in structural integrity, including high compressive strength, improved seismic
resistance,enhanced safety,and efficient construction. It effectively combinesthe strength
and flexibility of both materials to achieve stability and cost-effectiveness. The reinforced
concrete columns in this system act as vertical support structures, which carry vertical
and horizontal loads and provide stable support with their excellent lateral stiffness [1].
Thesteel beams areused asthehorizontalload-bearing to ensurestability and, at thesame
time, increase the effective use area of the building. This combined structure fully utilizes
the performance advantages of the two materials. Reinforced concrete columns provide
strongsupport by their excellent compressive properties and fire and corrosionresistance.
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At the same time, steel beams reduce the weight and improve the construction efficiency
by the excellent tensile properties of steel [2]. In the combined frame system, the ten-
sile properties of the steel beams complement the compressive strength of the reinforced
concrete columns. The concrete columns act as vertical supports, providing stability and
bearing vertical and horizontal loads.
Meanwhile, the steel beams offer excellent tensile strength, which enhances the system’s
flexibility and ability to resist bending. This combination improves the structure’s overall
load-bearing capacity and stability while reducing weight. Compared with the all-steel
structure, reinforced concrete columns must comprehensively consider the force perfor-
mance, stability, durability, and other factors, especially the node design and connection,
to ensure safety and stability. Key factors include force performance, stability, durability,
and careful design of node connections to handle loads, maintain stiffness, and prevent
corrosion or fire damage. The strength grade of concrete and steel reinforcement of rein-
forced concrete columns should be carefully selected based on design requirements and
actual conditions. Steel beams should be made of steel with excellent tensile properties,
and fire protection should be considered. During the construction process, construction
safetymanagement should bestrengthenedtoensure the safetyof construction personnel.
After the completion of the project, detailed acceptance and testing must be carried out to
ensure the structural dimensions, appearance quality, bearing capacity, and other aspects
align with the design requirements and relevant standards [3]. The reinforced concrete
column-steel beam frame has good seismic performance and is easy to construct. The ac-
tual project’s characteristics and advantages should be fully considered, and the construc-
tion program should be reasonably designed to ensure safety and economy. In the design
process, the overall stability of the building needs to be considered, including geometry,
material strength, and position of the center of gravity. In addition, by designing according
to relevant national norms and standards, scientific calculations, and mechanics analysis,
the dynamic stability and resistance to continuous collapse of the building can be ensured
[4]. In the seismic design, it is necessary to determine the seismic and use the complete
nonlinear dynamic analysis method to adjust the safety coefficient of the durability design
strength to 1.0, as well as the comparison of the two design methods of static or dynamic
and take the worst value as the final design results. Steel reinforcement’s strength, plastic-
ity, and strain-hardening properties influence the frame’s bearing capacity, stiffness, and
flexibility. The strength class, durability, and shrinkage creep of concrete also affect the
design of frame member dimensions and long-term performance [5].
The reinforced concrete column steel beam frame structure is a relatively important
building, and considerable research results have been obtained from many studies in re-
lated fields. Andreotti R and other scholars evaluated the seismic response of the steel-
concrete moment resisting frame (MRF), that is, the seismic performance analysis of the
steel-concrete moment resisting frame. It adds dissipative replaceable components in the
design phase to reduce energy consumption while improving the seismic performance,
providing technical support for the functional recovery after a major earthquake event.
However, the hysteretic performance of the joint is affected by many factors, and the un-
certainty of these factors may lead to the fluctuation and uncertainty of the joint perfor-
mance. At the same time, the steel-concrete composite itself is complex. In this strength
steel-concrete composite, the strength, stiffness, and other parameters of steel and con-
crete are different, leading to increased complexity [6]. Al Jelawy H M and other scholars
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researched using fiber-based models to analyze reinforced concrete column-steel beam
frame structures. To evaluate their performance, these models simulate the working con-
ditions of individual structural components, particularly under cyclic loading. The ap-
proach aimed to enhance understanding of each element’s efficiency and response to load
conditions, emphasizing identifying adverse factors and reducing overall structural costs.
However, challenges were noted in accurately modeling node connections and simulat-
ing the complexities of cast-in-place column construction, which can impact the stress
distribution and final structural performance. Through this model, the working condi-
tions of the component elements are analyzed, and the working efficiency of each element
under cyclic load is simulated to eliminate the structure’s adverse factors and reduce the
use cost. However, the connection between precast columns is usually achieved through
nodes. At the same time, the fiber model is used to simulate this kind of node connection;
it is difficult to accurately reflect the stress distribution and transmission mechanism at
the nodes, which leads to a certain deviation between the simulation results and the actual
situation. The pouring process of cast-in-place columns involves multiple stages, such as
concrete flow and vibration, which have an important impact on the final performance of
the columns. Fibre mold has certain difficulties in simulating these processes; it is diffi-
cult to accurately reflect the influence of the pouring process on column performance [7].
Prajapati G N and other scholars use GFRP polymer to protect concrete and improve the
seismicperformance of theoverall building. Throughanalysis, it isfound that although the
seismic performance has been improved after strengthening, the key influencing factors
of the seismic performance are related to the reinforcement situation. Through analysis,
this study meets the design requirements of North America. However, further analysis
found that the design method of reinforced concrete columns with mixed reinforcement
underreverse cyclic load in this studywas not perfect, the rationality of actual engineering
demand was not considered in the design process, and the proportion, layout, and other
parameters of mixed reinforcement did not pay attention to reducing costs based on ra-
tionality [8]. Hosseini et al. studied wavy steel fiber-reinforced concrete (WSFRC) and
showed that steel fibers enhance fracture behavior and load-bearing capacity by control-
ling crack propagation, which could similarly improve fracture and collapse resistance in
concrete column-steel beam hybrid structures under seismic or cyclic loading [9].Perceka
W and other scholars studied the shear strength of reinforced concrete under cyclic load,
analyzed the seismic performance, determined that the shear strength was high, and pre-
dicted the future development of seismic performance with high accuracy and reference.
However, in this study, steel fiber is used to enhance the strength of concrete, and the
existing shear strength model of steel fiber-reinforced concrete columns cannot provide
high-precision prediction in all cases. This is mainly because the mechanical properties
of concrete and steel fiber will be affected by various factors such as material type, fiber
content, fiber length, etc. In future research, it is necessary to develop a universal High-
precision shear strength model [10].
In this paper, the reinforced concrete column-steel beam frame model is constructed
concerning the relevant building construction standards by selecting concrete and steel
beams with excellent performance and determining the reinforcement parameters. By ap-
plying actual loads, the overall collapse resistance of the model is analyzed under different
load conditions to guide the optimization and performance improvement of the building.
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Thepaper is organizedasfollows: Sect.2coversmaterialsand methods,includingstruc-
tural reinforcement design, specimen preparation, model design, and loading setup. Sec-
tion 3details test results, focusing on displacement, strain in concrete and reinforcement,
crack distribution under load, and collapse probability. Section 4concludes with findings
onthe stability and seismic resilience of thereinforced concrete column-steel beam frame.
2 Material methods
2.1 Design of structural reinforcement
The reinforced concrete column steel beam frame studied in this paper needs to use many
reinforcement materials to design the overall collapse resistance of the associated struc-
ture. The reinforcement used is HPB300 [11], and the longitudinal reinforcement is gen-
erally full-length. HPB300 reinforcement was chosen to design the reinforced concrete
column-steel beam frame due to its excellent mechanical properties, including a favor-
able yield and tensile strength balance. This reinforcement enhances the structure’s abil-
ity to resist external loads, improving overall stability and collapse resistance. The stirrup
used in the column is an overall dense structure. Stirrups play a crucial role in enhancing
the collapse resistance of the column structure by providing lateral support to the lon-
gitudinal reinforcement, helping to prevent buckling and shear failure. These reinforce-
ments can be extended to the inside of the cast-in-place slab for the outer longitudinal
reinforcement of the column outside the beam width. The length that extends into the
cast-in-place slab shall be consistent with the length it extends into the beam. Maintain-
ing consistent reinforcement lengths when expanding into the slab and beam is essential
for proper load transfer and structural integrity. It creates a continuous load path, reduces
stress concentrations, and enhances bonding between concrete and reinforcement. When
the longitudinal reinforcement of the frame beam passes through the column reinforce-
ment, it will extend fromtheinsideof the column reinforcement tothe node.Thediameter
of steel bars varies with the arrangement of steel bars. HPB300 is selected for its high yield
strength of approximately 300 MPa and good ductility, allowing significant deformation
before failure. This combination ensures substantial load-bearing capacity and energy ab-
sorption, making it suitable for withstanding dynamic loads during seismic events while
maintaining structural safety and stability. The diameters of steel bars are 5 mm, 7 mm,
and 9 mm, respectively, when preparing structural specimens in this paper. The details of
the mechanical properties of each steel bar material are shown in Table 1.
2.2 Test specimen preparation
When preparing the test specimen of reinforced concrete column steel beam frame, to
make the test results more accurate, complete the steps of steel bar binding, plate instal-
lation, concrete pouring, etc., in the laboratory. Due to the need to analyze the overall
collapse resistance, the concrete pouring strength is selected as Grade C40 [12], and the
Table 1 Mechanical properties of rebar materials
Mechanical property type 5mmDiameter bar 7mmDiameter bar 9mmDiameter bar
Yield strength/MPa 428.1 465.2 444.7
Tensile strength/MPa 552.5 651.4 638.9
Modulus of elasticity/MPa 2.23*1052.66.1052.36*105
Elongation/% 0.31 0.29 0.30
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Table 2 Parameters of the concrete foundation
Mechanical property First column Secondary column
Overall compressive strength/MPa 31.59 22.93
Axial compressive strength/MPa 24.27 17.69
Axial tensile strength/MPa 2.69 2.26
Modulus of elasticity/MPa 29853.35 26481.58
pouring is completed two times. The first concrete pouring is mainly for pouring the first
layer of foundation concrete columns, and the second pouring is for pouring the second
layer of concrete columns. After each pouring, attention should also be paid to installing
steel beams.
Refer to the GB/T50152-2012 standard [13]for concrete pouring. Afterpouring,usethe
same concrete materials to pour 30 mm ×30 mm ×30 mm concrete samples in the mold
to test the mechanical properties of the concrete. The so-called material data input and
the test results of various concrete parameters during subsequent model construction are
showninTable2.
2.3 Model design scheme for reinforced concrete column-steel beam frame
structures
When designing the reinforced concrete column steel beam frame, refer to the standards
listed in the relevant codes GB50010-2010 and GB50011-2010 [14] and design the rein-
forced concrete column steel beam frame model for experimental analysis. The height of
each floor of the model is designed as 1.5 m, and the number of spans is designed as 3
×2. Compared with the actual building, the model is reduced by 1/3. In the indoor test
setup, anchor bolts are used to securely fix the reinforced concrete column-steel beam
frame model within the trench of the test site. This ensures the stability of the model dur-
ingtesting by preventing unwanted movement ordisplacement. The framestructure must
remain stationary as external loads are applied to simulate real-world forces and analyze
structural responses. The placement of anchor bolts is crucial for maintaining the model’s
integrity throughout the experiment, allowing for precise measurement of displacement,
strain, and other structural behaviors under various loading conditions. This setup con-
tributes to the accurate simulation of collapse resistance and seismic performance. The
frame structure model is shown in Fig. 1.
In Fig. 1of the paper, different colors are utilized to visually differentiate the materials
used for beams and columns in the reinforced concrete column-steel beam frame struc-
ture. Specifically, the columns are made of concrete, which is known for its excellent com-
pressive strength, while the beams are constructed from steel, chosen for its superior ten-
sile properties. This combination leverages the strengths of both materials: the concrete
columns provide stable vertical support and high compression resistance, and the steel
beams contribute flexibility, tensile strength, and a reduction in overall structural weight.
This hybrid approach enhances the stability and load-bearing capacity of the structure
while allowing for efficient construction [15].
2.4 Arrangement of the loading device and setting of the loading regime
(1) Loading device arrangement
To facilitate the test, the frame model is constructed without adding floor slabs to the
model. This frame will be subjected to internal stress redistribution due to the upper steel
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Figure 1 Geometric diagram of frame structure
beams under the influence of pile loads during the test, resulting in safety hazards in the
whole structure. So, in this paper, when designing the loading device, the top load borne
by the actual building is converted into the vertical load that needs to be borne by the test
model. The vertical loading device is arranged atop the concrete [16].
The vertical loading device consists of two 300t hydraulic jacks, two 50t manual jacks,
and one 100t manual jack. Two 50t manual jacks are arranged on the leftmost and right-
most concrete columns of the frame, and 100t manual jacks are arranged on the middle
concrete columns, 300t jacks are arranged respectively at the center of beam C [17]tore-
alize the earthquake level simulation. At the same time, a sensor is arranged at the center
and top of each concrete column, through which the deformation and possible collapse
changes of each concrete column affected by the jack can be obtained. To simulate the
impact of earthquake action, it is also necessary to keep the applied vertical load constant
to avoid deviation of test results and select a manual jack to realize axial force compensa-
tion. During the test, the vertical load is always maintained. When the entire frame model
collapses, it is concluded that the collapse is global.
It is also necessary to keep the low cycle horizontal load repeatedly loaded in vertical
load, achieved using a 100t electro-hydraulic servo actuator. Maintaining low-cycle hor-
izontal loading while applying vertical loads in structural testing is crucial for simulating
real earthquake conditions. This testing method helps assess how structures, like rein-
forced concrete column-steel beam frames, respond to the dynamic forces experienced
during seismic events. Low-cycle repeated loading replicates the stress caused by earth-
quakes, which are characterized by repeated cycles of loading and unloading that can lead
to significant damage. By applying these loads, researchers can study how a structure re-
distributes forces andwithstands damagewithoutcollapsing. This approachhelps identify
howlocalized damageat critical points impacts thestructure’soverallstability and ensures
it remains safe and intact under severe conditions. This method is essential for evaluating
the seismic resilience of hybrid structures and their ability to prevent total failure despite
damage.
(2) Loading system setup
The load was applied to the model using force-displacement mixing and control loading
methods [18]. The electro-hydraulic servo actuator applies a low-cycle repeated load to
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the middle of the second-floor steel beam. Applying low-cycle horizontal loads with an
electro-hydraulic servo actuator is crucial for evaluating the seismic performance of hy-
brid structures like reinforced concrete column-steel beam frames. These loads replicate
the fluctuating forces during seismic events, helping assess the structure’s resilience un-
der dynamic conditions. When the load is loaded, the horizontal lateral force generated is
realized by the displacement on the top area of the frame model. In the loading process,
load step by step according to the provisions of relevant standards on the limit value of
displacement angle between horizontal lower layers, and stop loading when the structural
model loses its bearing capacity. When loading the equipment, it is necessary to simulate
the limit change of displacement angle between the lower floors under different natural
actions of the real building frame structure as far as possible. The closer the difference in
displacement amplitude is, the better. The limit point will be missed if there is a large dif-
ference between the displacement amplitude and the actual limit. When the frame model
does not yield,the displacement amplitudeincreases by 3.5 mm [19]foreachloading level,
and each loading level needs to cycle on the frame structure model once. When the frame
model is loaded to yield, the loading amplitude needs to be increased, and the number of
cycles needs to be increased to 3 times until the frame model collapses and the loading
stops. However, according to research experience, it will not lose its overall bearing capac-
ity even if the frame collapses. During the test and analysis, the actual building conditions
need to be considered, and the loading displacement can be set at 1/25 of the vertex dis-
placementangle. Stop loading whenthe model is significantlydamaged andtherisk is high
[20].
2.5 Test point arrangement
The arrangement of test points on the frame model is designed to provide a more intu-
itive and accurate understanding of the numerical changes in displacement, strain, de-
flection, and other factors under load. This helps determine the structural model’s varia-
tions in strength and the strength reserve. In this paper, to analyze the monolithic collapse
resistance of reinforced concrete column-steel beam frame, it is necessary to start from
the perspective of the relationship between the vertical displacement change of concrete
columns and the displacement change of steel beams at the angle of failure [21,22]. The
improved monolithic collapse resistance in hybrid frame structures arises from the syn-
ergy of concrete’s compressive strength and steel’s tensile strength, enhanced ductility and
energy dissipation, effective load redistribution, increased lateral stiffness, and reduced
stress concentrations, all contributing to superior seismic resilience and stability com-
pared to traditional all-concrete or all-steel systems and the location of the test points of
the frame model is shown in Fig. 2.
Strain gauges and displacement transducers are arranged at each measurement point in
Fig. 2. The strain gauges obtain the changes in displacement and strain at each measure-
ment point, which can also capture the order and number of changes at each position,
determining the frame model’s performance in resisting the monolithic collapse under
the influence of external loads.
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Figure 2 Location of measuring points
3Results
3.1 Displacement change of each measurement point of the frame structure
under different load ratings
During the test, each jack equipment was used to apply external loads to the frame model.
The 300t jack simulated different earthquake levels (2.5, 5.5, 9.5), and the remaining three
jacks simulated local loads, respectively, with load levels of 1–6. Figure 3shows the dis-
placement value changes of each measuring point under different earthquake levels.
It can be seen from Fig. 3that increasing the seismic load will cause the displacement
of each measuring point on the frame model to rise significantly, and the greater the seis-
mic load, the more serious the displacement of each measuring point. In Fig. 3(a), the
seismic load is small. Each measuring point in Fig. 3(b) is under moderate seismic load,
and the maximum displacement value also occurs at measuring point 7, with a displace-
ment value close to 9 mm. In Fig. 3(c),theframestructuremodelbearsalargeseismic
load. At this time, the cyclic low cycle repeated load will easily lead to the collapse of the
frame. At this time, it can be seen that under the influence of various loads, the location
of the frame model test point 7 is the first to be damaged, and the location of the concrete
column and steel beam where the test point is located is also more likely to be damaged.
By comparison, the displacement changes of measuring point 7 and measuring points 1
and 2 adjacent to measuring point 7 are large. The displacement changes from measuring
point 3 to measuring point 6, which is far away from measuring point 7, is not large, which
means that even in the same frame model, under the same load, the displacement change
in the severely damaged area is quite different from that in the nondamaged area, which
also makes the nondamaged area not easy to collapse.
3.2 Relationship between displacement changes in the damaged region of the
frame structure
After the above test, it was found that the location of measurement point 7 was the first
concrete column to fail after being subjected to external loads. The displacement relation-
ship between the remaining measurement points of the frame and measurement point 7
isshowninFig.4.
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Figure 3 Displacement changes of each measuring point of the frame structure under different load levels
As shown in Fig. 4(a), the displacement of point 7 on the concrete column that is the
first to experience performance failure increases after being subjected to external loads,
resulting in the displacement of test point 1 and test point 2 also showing a uniform up-
ward trend, which indicates that beam and column 3 will fail at the end of the column
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Figure 4 Relation between displacement of frame and displacement of failed concrete column
when affected by external loads, and the failure angle will continue to increase with the
increase of displacement, The corresponding concrete columns and steel beams also have
obvious displacement changes at each measuring point, the maximum displacement is
close to 70 mm, which is very easy to cause collapse of the frame structure. In Fig. 4(b),
the displacement changes of measuring point 3 - measuring point 6 are positive and neg-
ative values, respectively. The positive value represents the displacement change of the
measuring point toward the upper part of the frame, and the negative value represents
the displacement change toward the lower part of the frame. Although the displacement
changes the direction of measuring points 3 and 6 is different from that of measuring
points 4 and 5, the displacement of each measuring point shows an increasing trend with
the displacement change of measuring point 7; however, the displacement change value is
small, and the maximum displacement value is close to 1.2 mm. This change trend may be
because measuring points 1 and 2 are relatively close to measuring point 7 on the failed
column, so after the failure of the measuring point, measuring points 1 and 2 are seriously
affected, and the displacement rise changes greatly. However, under the same load, the
measuring points that are a certain distance from the failed column do not show a large
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Figure 5 Strain relationship between the concrete column and failure column
displacement, which indicates that the overall bearing capacity of the structure is high and
the stability is strong; the overall collapse resistance is considerable.
3.3 Analysis of strain changes in concrete columns
A mixture of concrete columns and steel beams constructs the frame structure studied in
this paper. The displacement change of the whole frame structure under external loading
is analyzed above. The strain change of concrete under external loading is also analyzed
in detail in this test. The test results are shown in Fig. 5.
It can be seen from Fig. 5(a) that the strain values of column 1 and column 2 on beam
A and column 1 and column 2 on beam B, which are far from the test point 7 on the
failed column, are small. The strain value of beam-column 1, closest to test point 7, is the
largest, and the maximum value is close to 300 με. The strain value of beam-column 1 far
from test point 7 does not exceed 150 με. It can be seen that the strain of the concrete
column, which is a small distance from the failure point, is not seriously affected, so it will
not collapse integrally under the load. In Fig. 5(b), two concrete columns near the failure
measuring point have relatively serious strain changes. Among them, the strain value of
beam-column 3, where failure occurs, has a large change, with a maximum value close to
24000 με, indicating that this area is likely to collapse seriously under external loads.
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Figure 6 Strain analysis of reinforcement
3.4 Analysis of strain changes in reinforcement
Reinforcing steel is one of the key components of the frame model constructed in this
paper. It is affected by external load. Figure 6shows the detailed changes of reinforcement
strain in the frame structure model.
Since each steel bar is distributed in the concrete column, testing the strain change of
the steel bar under different loads must be obtained by measuring the concrete column.
The reinforcement in beam column 1 of A and B in Fig. 6(a) is affected by the load and
has a downward strain change, but the change value is small, which proves that the rein-
forcement in this area has no obvious strain change due to the external load, A. Although
the strain of the reinforcement in connecting column 2 of beam B shows a significant up-
ward trend, the strain value of each reinforcement has a small upward change, so it can
be seen that the reinforcement materials have small changes. In Fig. (b), column 3, con-
nected by beam A and beam B, bears a large external load, and the failure measurement
point of beam A and column 3 occurs directly. Therefore, the steel strain change value at
this location is large, indicating that under the influence of external load, not only may the
concrete be damaged, but the steel strain value is also high, and deformation and fracture
may occur.
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Figure 7 Crack distribution of damaged concrete columns under different load levels
3.5 Distribution of damage cracks in specimens under different loads
The above analysis shows that when the whole frame model is affected by the external
load (small load imposed by 100t manual jack), beam-column A 3 appears to be a failure
behavior, and the damage is the most serious. Therefore, field test and record the crack
changes in this area under different load levels, as shown in Fig. 7.
It can be seen from Fig. 7that as the load on the frame model increases, the failure at
the location of test point 7 becomes more pronounced. In Fig. 7(a), the frame model only
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bears a 10N load; at this time, only a few cracks appear at the location of test point 7, and
the failure of the concrete column has not changed. The load is increased step by step. The
frame model in Fig. 7(d) bears 70N load, the concrete column has obvious material falling
off, and the corners have obvious breakage. The frame model in Fig. 7(f) bears a load of
110N. At this time, the concrete column is seriously damaged. The concrete column has
failed and can no longer play a supporting role in the frame model. Based on the above
test results, despite the failure of test point 7 and the concrete column position, the rest of
the concrete structures will not be seriously affected; that is, even if the tested position in
Fig. 7has serious failure, other positions of the entire frame model will not have serious
damage, with strong collapse resistance.
3.6 Integral collapse probability analysis
In this paper, a steel beam system combined with concrete columns was employed to en-
hance the monolithic collapse resistance of the designed frame. The above tests were con-
ducted to analyze the changes in the frame model under loading conditions. To compare
the overall collapse resistance intended in this paper, the probability of overall collapse
was analyzed using the frame constructed with concrete alone and the frame constructed
with steel alone in the testing process. The basic parameters of each frame were inputted
into the model collapse software, and the external load was increased step by step. At the
same time, the laboratory applied the external load force to the actual model to compare
the simulation results with the actual test results and to further determine the accuracy of
the test. The test results are shown in Fig. 8.
ItcanbeseenfromFig.8that the actualtestresults are relativelycloseto the results from
software simulation analysis in each test group. This indicatesthat the testmethod used in
this paper is highly accurate and has a strong reference value in actual construction. From
thetestresultsin Fig. 8(a), it can be seen that the overall collapse performance is gradually
rising due to the continuous effect of external load when the concrete component frame
is used alone. In actual use, the overall collapse is very easy to occur in the face of possible
earthquake disasters in the natural environment. In Fig. 8(b), the steel structure is used
alone to build the frame. Although this structure has high strength, its cost is high. When
it is disturbed by external loads due to the insufficient strength of the steel, the overall
collapseresistance of themechanism is reduced.Figure8(c)showsthereinforcedconcrete
column combined with the steel beam frame used in this paper. This structure has a low
cost and significantly lower overall collapse probability after being affected by the load.
The maximum collapse rate does not exceed 35%. It is suitable for application in actual
buildings and can resist the impact of seismic action in the natural environment.
4Conclusion
The reinforced concrete column-steel beam frame structure, leveraging the high com-
pressive strength of concrete columns and the bending capacity of steel beams, demon-
strated significant stability and resilience under seismic loads. The study highlighted that
although A-beam column 3 was the first to fail due to external loads, the rest of the struc-
ture exhibited minimal damage and retained overall stability, showcasing an impressive
ability to resist complete collapse. This indicates the effectiveness of this structural design
for withstanding seismic events. However, this research focused on symmetric structures,
which are simpler than the complex, irregular structures often found in real-world appli-
cations. The study’s methodology, while accurate, may not fully reflect these complexities.
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Duan and Zhang Advances in Continuous and Discrete Models (2025) 2025:40 Page 15 of 17
Figure 8 Overall collapse probability analysis
Additionally, using standardized standardized models and loading scenarios may limit the
generalizability of the results.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Duan and Zhang Advances in Continuous and Discrete Models (2025) 2025:40 Page 16 of 17
4.1 Limitations and future work
The limitations include using simplified structural models, primarily regular, symmetric
framemodels, whichlimit the applicabilitytoreal-world, irregulardesigns. The controlled
static loading conditions may not capture all dynamic variables encountered in practical
scenarios. Moreover, the specific types of reinforcement and concrete used in the study
may not represent the full range of variations in construction. To advance this research,
future studies should explore irregular structures by investigating complex, nonsymmet-
ric frame systems to enhance the applicability of the findings. Implementing advanced
simulations that replicate varied seismic conditions more accurately would be beneficial.
Utilizing high-fidelity numerical models and simulations could help predict performance
across a broader range of materials and construction methods. Additionally, conducting
field tests on real structures would confirm the simulated findings and improve predictive
accuracy.
Abbreviations
HPB, High-Performance Beam; MPa, Megapascal; ACI, American Concrete Institute; GB, Guobiao (National Standard of
China); MRF, Moment Resisting Frame.
Acknowledgements
The authors would like to sincerely thank those techniques who contributed to this research.
Author contributions
Kaimin Duan and Guofeng Zhang contributed to the design and methodology of this study, the assessment of the
outcomes, and the writing of the manuscript. All authors read and approved the final manuscript.
Funding
There is no specific funding to support this research.
Data availability
The experimental data used to support the findings of this study are available from the corresponding author upon
request.
Declarations
Competing interests
The authors declare no competing interests.
Author details
1Changjiang Institute of Technology, Wuhan 430212, Hubei, China. 2China South-to-North Water Diversion Jianghan
Water Network Construction and Development Co., Ltd, Wuhan 430040, Hubei, China.
Received: 26 September 2024 Accepted: 30 December 2024
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