Enhancing punching shear and post-punching behavior of flat slabs using wire mesh, integrity bars and fibers

Abstract

Punching shear failure is a common issue in the connection between flat slabs and reinforced concrete columns. Once failure occurs, a supplementary load-carrying mechanism is necessary to prevent the progressive collapse of the connections. This study presents an experimental program and a theoretical model to investigate the punching shear and post-punching behavior of seven flat slabs with different concrete types and reinforcement configurations. The effects of wire mesh, fiber-reinforced concrete, and integrity bars on punching shear failure and post-punching behavior in internal slab-column connections were analyzed. The results indicate that incorporating integrity bars and fibers into the concrete enhances both punching and post-punching shear strength. The experimental findings demonstrated a significant enhancement in both punching strength and maximum post-punching load, exhibiting respective increments of 32% and 28% relative to the specimen without fiber reinforcement. Furthermore, fiber integration within the wire mesh matrix substantially improved the structural ductility of the slab. Notably, the synergistic combination of fiber reinforcement and wire mesh demonstrated a 103% greater energy dissipation capability compared to the baseline configuration lacking both components. This substantial enhancement underscores the influence of optimized material composition and reinforcement strategies in mitigating deformation and improving structural resilience.

Introduction

In recent decades, numerous structural collapses worldwide have been attributed to punching shear failure¹. When punching shear failure occurs at a single connection, the applied loads redistribute to adjacent connections, which may then fail due to overloading. This chain reaction can cause the slab to collapse onto the one below, ultimately leading to the progressive failure of the structure^{2,3,4,5,6,7,8,9}. However, implementing a secondary load-carrying mechanism can help prevent such failures. One such mechanism is the dowel action of flexural tensile bars, which enhance shear strength when intersected by diagonal cracks.

Flat slab-column structures, vulnerable to progressive collapse due to punching shear failures and lack of redundancy, have been extensively studied through experimental, analytical, and numerical approaches. Experimental investigations employ quasi-static and dynamic protocols, including alternate column removal scenarios (corner, edge, interior), to assess load redistribution and strength mechanisms like tensile/compressive membrane actions. Numerical models, validated via full-scale tests, utilize multi-scale finite element analyses to simulate collapse behaviors, while theoretical frameworks incorporate strain-hardening and deformation compatibility. Strengthening strategies—perimeter beams, shear walls, or their combination—reduce vertical displacements and demand-capacity ratios by up to 81% and 67%, respectively. Post-punching strength, influenced by in-plane constraints and reinforcement detailing, is enhanced by continuity of bottom rebars. Recent codes emphasize robust design: edge beams, shear walls, improved column configurations, and anchorage detailing to mitigate risks. Emerging technologies, including machine learning and physics engines, further advance predictive modeling and prevention strategies^{10,11,12,13,14,15,16,17,18,19}.

Two primary failure modes for dowel action are illustrated in Fig. 1. The first mode (Mode I) occurs when the steel bar yields while the surrounding concrete is simultaneously crushed (Fig. 1a). The second mode (Mode II) involves concrete cracking (Fig. 1b)²⁰. Experimental research suggests that Mode II failure is more likely when the concrete thickness is less than 6–7 times the diameter of the steel bar in the direction of the shear force. In contrast, greater concrete thicknesses typically lead to Mode I failure^20,21.

Fig. 1

Failure modes: (a) Yielding bar, (b) Concrete cracking²³.

Experimental observations revealed a significant reduction in post-punching strength, with decrements of 21% and 43%, as the diameter of flexural tensile bars increased incrementally from 8 to 10 and 12 mm, respectively, under a constant reinforcement ratio. This inverse correlation underscores the critical influence of flexural bars geometry on structural performance, wherein smaller-diameter bars demonstrated a proportional enhancement in shear strength attributed to the amplified efficacy of dowel action mechanisms²².

Additionally, when punching shear failure occurs, integrity bars deform, contributing to shear strength through the dowel action of flexural tensile bars and the membrane effect of the integrity bars. Flexural tensile bars also enhance post-punching shear strength^23,24.

The overall behavior of a model flat slab under a monotonic load, with all edges fully restrained, is illustrated in Fig. 2. The slab’s response can be divided into three stages. Initially, it exhibits linear elastic behavior. As the load increases, nonlinear behavior begins due to concrete cracking or reinforcement yielding. This phase continues until point A, where failure occurs due to either punching shear or flexural failure^25,26.

Fig. 2

Load–displacement behavior for flat slab²⁵.

Up to point A, compressive membrane action develops as a result of lateral constraints, enhancing the slab’s load-carrying capacity. Beyond this point, the load decreases as deflection increases until reaching a minimum at point B. After point B, the slab’s behavior is primarily governed by its deformation capacity, continuity, redundancy, and structural integrity. At this stage, the slab restraints resist inward edge movements, causing in-plane membrane forces to shift from compression to tension. Additionally, high tensile strains at the slab’s surface often led to cracks propagating through its full depth. As a result, the concrete becomes fully fractured, and the integrity bars contribute to load strength through tensile membrane action^25,26.

Fiber-reinforced concrete (FRC), famous for its higher mechanical properties and durability, has seen increasing use in fluffy elements and strengthening applications. However, gaps persist in understanding its punching shear behavior and design guidelines. Recent studies address these limitations through experimental analyses of FRC slabs, proposing methodologies to predict flexural and punching strengths. Concurrently, high-ductility concrete has been explored to reinforce thin-walled steel tubes, overcoming bond-strength challenges via interface treatments and axial tests, with design equations developed to enhance load strength and ductility. Computational frameworks integrate multi-scale models—from single-fiber pullout mechanics to meso-scale finite element simulations—to optimize fiber-reinforced concrete performance, bridging material design and structural crack-propagation analysis. These advancements collectively advance performance-based design for FRC and composite systems^{27,28,29,30,31,32,33,34,35}.

This research combines an experimental program and a theoretical model to investigate the punching shear and post-punching shear behavior of seven specimens with different reinforcement configurations and concrete types. The study aims to examine the effects of integrity bars, various types of flexural tensile bars, and fiber-reinforced concrete on the punching and post-punching shear behavior of slabs.

Materials and details of specimens

Materials

The experimental framework included normal concrete, fiber-reinforced concrete, and a consistent water-to-cement ratio of 0.45. The design compressive strength of both types was 30 MPa, while the experimental compressive strength was 31 MPa and 34 MPa for normal and fiber-reinforced concrete, respectively. Tensile strength evaluations yielded values of 3.35 MPa for normal concrete and 5.54 MPa for fiber-reinforced concrete. Figure 3 illustrates the materials utilized in this investigation. The maximum particle size of the aggregate in the concrete mixture was 25 mm. Two concrete mix designs for the specimens are provided in Table 1. Hybrid fibers (steel and polypropylene) were used in the fiber-reinforced concrete, with steel and polypropylene fiber contents of 1% and 0.4% of the cement weight, respectively. The properties of the fibers are detailed in Table 2. Two flexural tensile bars—steel bars and wire mesh—were incorporated into the specimens. The properties of these bars are presented in Table 3. The stress–strain behavior of the steel bar (with a yield strength of 430 MPa) and the wire mesh (with a yield strength of 300 MPa) are shown in Fig. 4.

Fig. 3

Material used in this study.

Table 1 Concrete mixture in $1{\text{m}}^{3}$.

Table 2 Properties of polypropylene and steel fibers.

Table 3 Mechanical properties of reinforcing bars.

Fig. 4

Strain–stress behavior for steel bars and wire mesh.

Details of specimens

Three groups of half-scale specimens were fabricated for the experimental investigation to examine the effects of wire mesh, integrity bars, and fiber-reinforced concrete on the punching shear and post-punching behavior of slabs. The specifications of the specimens and experimental protocols are elaborated in Figs. 5, 6, and Table 4. As shown in Table 4, the specimens were categorized into three groups. The concrete cover for both the integrity and flexural tensile bars was 20 mm, and the flexural tensile reinforcement ratio was maintained at 0.402% across all specimens.

Fig. 5

Specimen and testing details: (a) Reinforcement and fabrication, (b) Planar layout, (c) Experimental configuration.

Fig. 6

Reinforcing Steel Details for specimens.

Table 4 Specification of Reinforcing Steel in Concrete Specimens.

The design of the flexural tensile bars and slab thickness was based on ACI 318–19³⁶, assuming an original flat slab span length of 6.8 m. The concrete cover was 40 mm. In the half-scale specimen, the slab length is 3.4 m and concrete cover is 20 mm. Live and superimposed dead loads were considered to be 2 kPa and 5 kPa, respectively. Since ACI 318–19 does not provide specific design guidelines for integrity bars, these were designed according to CSA A23.3–04³⁷.

According to Muttoni³⁸, lines of contraflexure occur at a radial distance of approximately 0.22L from the supports, where L is the center-to-center span of the slab. Based on this, the supports in this experimental study were positioned at a distance of 0.22L from the center of the column. Given that the specimens were scaled to half of the original structure, the support spacing was set at 1500 mm.

This experimental program examined seven square flat slabs, each with a nominal total thickness of 150 mm and a total width of 1600 mm.

In Table 4: SP refers to Specimen, W, S and Ib stand for wire mesh, steel bar and integrity bar, respectively, FC is fiber-reinforced concrete.

Details of group 1

Group 1 consisted of two specimens. Specimen SP-S included only flexural tensile bars, while specimen SP-S-4Ib incorporated both flexural tensile bars and two integrity bars in each direction. As illustrated in Fig. 6, the details of this group.

Details of group 2

Group 2 consisted of two specimens. Specimen SP-W-4Ib included flexural tensile bars and two integrity bars in each direction, while specimen SP-W-10Ib incorporated flexural tensile bars and five integrity bars in each direction. The flexural tensile reinforcement ratio in this group was the same as that of specimen SP-S-4Ib. However, in Group 2, wire mesh was used as the flexural tensile reinforcement instead of traditional bars. As illustrated in Fig. 6, the details of this group.

Details of group 3

Group 3 consisted of three specimens, all made with fiber-reinforced concrete. Specimen SP-W-FC included only flexural tensile bars, while specimen SP-W-FC-4Ib incorporated flexural tensile bars along with two integrity bars in each direction. Specimen SP-W-FC-10Ib contained flexural tensile bars and five integrity bars in each direction. The flexural tensile reinforcement ratio in these specimens was the same as that of specimen SP-S-4Ib. In this group, wire mesh was used as the flexural tensile reinforcement. As illustrated in Fig. 6, the details of this group.

Test setup

The main components of the test setup included a Linear Variable Displacement Transducer (LVDT), a load cell, a hydraulic jack, a steel frame, and a computer-based data acquisition system (Fig. 5). The slab was simply supported along its edges by a steel frame. A hydraulic jack with a maximum capacity of 800 kN applied a concentrated load at the center of the slab through a square concrete pedestal. During testing, the loading rate was approximately 500 N per second. The load cell measured the applied load at the slab’s center, while the LVDT recorded the slab’s vertical displacements. Both the load cell and the LVDT were connected to a data acquisition system for real-time data collection.

Test results and discussion

This section presents the laboratory results of seven specimens, summarized in Table 5. The load–displacement responses for these groups are illustrated in Fig. 9. The displacement and applied load were measured at the center of the slabs.

Table 5 Test results of laboratory work.

Results of group 1

The load–displacement responses for this group are shown in Fig. 9. The ratio of the maximum post-punching load to the punching shear strength was 0.43 for SP-S and 0.59 for SP-S-4Ib. The punching shear strength and maximum post-punching load were 242 kN and 105 kN for SP-S, and 254 kN and 151 kN for SP-S-4Ib, respectively. The higher post-punching strength observed in specimen SP-S-4Ib compared to specimen SP-S is attributed to the inclusion of integrity bars in the former.

Results of group 2

The load–displacement responses for this group are shown in Fig. 9. The punching shear strength was 177 kN for SP-W-4Ib and 229 kN for SP-W-10Ib, while the maximum post-punching load was 153 kN and 181 kN, respectively. Increasing the number of integrity bars from 2 to 5 in each direction resulted in a 29% increase in punching shear strength and a 18.5% increase in post-punching load for SP-W-10Ib.

The enhanced punching shear strength of SP-W-10Ib can be attributed to two key factors:

• Concrete confinement Increasing the number of integrity bars improves concrete confinement in the compression region at the bottom of the slab. This lateral compression effect enhances the shear strength of the concrete, as illustrates in Fig. 7.

• Shear crack control A greater number of integrity bars helps limit shear crack openings, thereby improving overall shear strength, as illustrates in Fig. 8.

Fig. 7

Contribution of integral bars to the concrete confinement.

Fig. 8

Crack width mitigation by integral bars: (a) With integral bars. (b) Without integral bars.

Several studies have also highlighted the influence of integrity bars on punching shear strength. For instance, Mirzaei and Muttoni³⁹ demonstrated that increasing the diameter of integrity bars enhances a slab’s ability to resist punching shear loads. The improvement in the maximum post-punching load is due to the increased number of integrity bars from 2 to 5 in each direction (Fig. 9).

Fig. 9

Load–displacement behavior of Groups.

Comparison between SP-S-4Ib and SP-W-4Ib specimens

As discussed in “Introduction” Section, reducing the diameter of flexural tensile bars can enhance the shear strength of dowel action. The load–displacement responses of these specimens are shown in Fig. 10. The punching shear strengths for SP-W-4Ib and SP-S-4Ib were 177 kN and 254 kN, respectively, while their maximum post-punching loads were 153 kN and 151 kN.

Fig. 10

Load–displacement behavior of SP-S-4Ib and SP-W-4Ib.

Reducing the flexural tensile bar diameter from 10 to 4.2 mm resulted in a 30% decrease in punching shear strength for SP-W-4Ib, while improving post-punching ductility. (Note: The total ratio of flexural tensile bars remained constant.) The reduction in punching strength for SP-W-4Ib is likely due to differences in yield strength between the 10 mm steel bars and the wire mesh, as illustrates in Table 3.

Additionally, SP-W-4Ib exhibited improved post-punching ductility due to a greater concrete spalling area, as seen in Fig. 11. The 35° failure angle was adopted in alignment with ACI 318-19 (Section R17.7.2), which stipulates the concrete breakout strength criteria for anchors under shear loading, ensuring compliance with standardized failure mechanisms in structural design, as illustrates in Fig. 11. This enhancement can be attributed to the higher number of flexural tensile bars, which distribute shear forces more effectively. Consequently, reducing the diameter of the flexural tensile bars strengthens the concrete cover, enhancing its post-punching shear strength (Figs. 10 and 11).

Fig. 11

Behavior of flat slab using wire mesh or fiber-reinforced concrete.

Results of group 3

Previous studies have demonstrated that fibers significantly enhance the ductility of structural members^40,41. Fibers primarily improve initial crack strength, maximum element strength, and shear strength. In this study, hybrid fibers are used as randomly dispersed staples within the cementitious matrix.

The load–displacement responses for this group are shown in Fig. 9. The punching strengths for SP-W-FC, SP-W-FC-4Ib, and SP-W-FC-10Ib were 202 kN, 233 kN, and 293 kN, respectively, while their maximum post-punching loads were 88 kN, 196 kN, and 269 kN.

Increasing the number of integrity bars from 2 to 5 in each direction resulted in a 26% increase in punching shear strength and a 37% increase in maximum post-punching load for SP-W-FC-10Ib.

Comparison between SP-W-4Ib and SP-W-FC-4Ib specimens

The limitations of conventional reinforced concrete, particularly its susceptibility to cracking that cannot be fully controlled by reinforcement alone, can be mitigated using fiber reinforcement. By incorporating randomly oriented fibers into the concrete matrix, crack formation is bridged and restrained under applied loads. This enhances the ductility and energy absorption capacity of the concrete. Once cracking initiates, the bridging fibers absorb stresses, improving the overall structural performance.

The load–displacement responses for these specimens are shown in Fig. 12. The punching shear strengths for SP-W-4Ib and SP-W-FC-4Ib were 177 kN and 233 kN, respectively, while their maximum post-punching loads were 153 kN and 196 kN. The use of fiber-reinforced concrete in SP-W-FC-4Ib led to a 32% increase in punching shear strength and a 28% increase in post-punching load capacity compared to SP-W-4Ib. This increase in punching shear strength is attributed to the reduction in shear crack width. During the post-punching stage, fiber reinforcement significantly delays the separation of the concrete cover from the flexural tensile reinforcement, as shown in Figs. 11 and 13. In contrast, SP-W-4Ib, which lacks fiber reinforcement, exhibited early concrete cover separation, as shown in Figs. 11 and 13. The punching failure shape formations of SP-W-4Ib and SP-W-FC-4Ib are illustrated in Figs. 13 and 14.

Fig. 12

Load–displacement behavior of SP-W-4Ib and SP-W-FC-4Ib.

Fig. 13

The upper failure plane of flat slabs under punching shear in specimens SP-W-4Ib and SP-W-CF-4Ib.

Fig. 14

The bottom failure plane of flat slabs under punching shear in specimens SP-W-4Ib and SP-W-CF-4Ib.

Comparison between SP-W-10Ib and SP-W-FC-10Ib specimens

Figure 15 shows the load–displacement relationships of the experimented specimens. The maximum punching shear strengths of SP-W-10Ib and SP-W-FC-10Ib were 229 kN and 293 kN. while their maximum post-punching loads were 181 kN and 269 kN, respectively. Including steel fiber-reinforced concrete in SP-W-FC-10Ib improved its punching shear strength by 28% (from 229 to 293 kN). It enhanced its maximum post-punching load by 49% (from 181 to 269 kN) compared to the normal concrete specimen (SP-W-10Ib). This performance improvement highlights fiber reinforcement’s critical role in punching shear strength and maximum post-punching load. During punching, the fibers reduced shear crack propagation through crack-bridging effects. Also, Increasing the integrity bars enhances concrete confinement in the compression part at the bottom of the slab. In the post-punching phase, fiber reinforcement mitigated concrete cover spalling and delayed debonding of the flexural tensile reinforcement.

Fig. 15

Load–displacement behavior of SP-W-10Ib and SP-W-FC-10Ib.

Comparison between SP-S-4Ib and SP-W-FC-4Ib specimens

Figure 16 illustrates the load–displacement behavior of the tested specimens. Specimen SP-S-4Ib exhibited a punching shear strength of 254 kN, whereas SP-W-FC-4Ib achieved 233 kN. Maximum post-punching loads for SP-S-4Ib and SP-W-FC-4Ib were 151 kN and 196 kN, respectively. As detailed in “Comparison between SP-S-4Ib and SP-W-4Ib specimens” Section, the smaller yield strength of wire mesh contributed to a 30% decrease in punching strength. However, integrating fibers in SP-W-FC-4Ib alleviated 73% of this reduction compared to SP-W-4IS, highlighting their role in shear strength. Post-punching evaluations further demonstrated that the hybrid system (steel fibers + wire mesh) in SP-W-FC-4Ib enhanced shear capacity by 30% relative to the control specimen (SP-S-4IS), confirming synergistic reinforcement effects. The hybrid system also displayed superior ductility, as evidenced by Fig. 16, which depicts sustained load behavior beyond peak strength. These outcomes underscore fibers’ dual functionality in mitigating wire mesh-related deficiencies and augmenting structural resilience under shear-driven failures. Collectively, the findings advocate for hybrid reinforcement systems in scenarios demanding optimized strength-deformability balance, particularly in shear-critical applications.

Fig. 16

Load–displacement behavior of SP-S-4Ib and SP-W-FC-4Ib.

Energy absorption during post-punching phase

Energy absorption is the mechanism by which a system takes energy from an external source. Progressive collapse typically occurs when a concrete column is suddenly removed. During such an event, a dynamic load factor must be applied to determine the loads transferred to adjacent columns. This dynamic factor decreases as energy absorption during the post-punching phase increases. The energy absorption can be quantified by calculating the area under the load–displacement curve in the post-punching phase, as illustrated in Fig. 17. In Fig. 17:

• A represents the initial of the post-punching stage.

• B represents the post-punching failure.

• C refers the displacement at the post-punching failure.

• D refers to the displacement corresponding to the initial of the post-punching stage.

Fig. 17

Energy absorption during the post-punching stage.

Table 6 shows the energy absorption of specimens during the post-punching shear stage. For instance, specimen SP-W-4Ib (containing normal concrete and wire mesh as flexural tensile bars) exhibits 68% higher energy absorption compared to specimen SP-S-4Ib (which contains flexural tensile bars with a 10 mm diameter and normal concrete). Also, specimen SP-W-FC-4Ib (incorporating fiber-reinforced concrete and wire mesh) demonstrates 103% higher energy absorption than specimen SP-S-4Ib. Additionally, specimen SP-W-FC-10Ib (consisting of fiber-reinforced concrete, wire mesh, and five integrity bars in each direction) shows 18% higher energy absorption compared to the SP-W-FC-4Ib specimen (consisting of specimen fiber-reinforced concrete, wire mesh, and two integrity bars in each direction).

Table 6 Area of energy absorption of specimens during post-punching shear stage (EA,_PP).

A theoretical model to predict maximum post-punching shear strength

This section presents a theoretical model for predicting the contribution of concrete cover strength and integrity bars to post-punching shear resistance. The model consists of the following values:

• ${\text{V}}_{{{\text{pp}},{\text{t}}}}$: Maximum post-punching shear strength contributed by flexural tensile bars.

• ${\text{V}}_{{{\text{pp}},{\text{Ib}}}}$: Maximum post-punching shear strength contributed by integrity bars.

• ${\text{V}}_{{{\text{pp}},{\text{M}}}}$: Maximum post-punching shear strength predicted by the theoretical model.

• ${\text{V}}_{{{\text{pp}},{\text{L}}}}$: Maximum post-punching shear strength obtained from laboratory experiments.

The theoretical post-punching shear strength (${\text{V}}_{{{\text{pp}},{\text{M}}}}$) is determined as the sum of ${\text{V}}_{{{\text{pp}},{\text{t}}}}$ and ${\text{V}}_{{{\text{pp}},{\text{Ib}}}}$, representing the combined contributions of flexural tensile bars and integrity bars. Different theoretical values of ${\text{V}}_{{{\text{pp}},{\text{t}}}}$ and ${\text{V}}_{{{\text{pp}},{\text{Ib}}}}$ are discussed in “Maximum post-punching shear strength contributed by flexural tensile bars (V_pp,t)” and “Maximum post-punching shear strength contributed by integrity bars (V_pp,Ib)” Sections.

Maximum post-punching shear strength contributed by flexural tensile bars ${\text{(V}}_{{{\text{pp}},{\text{t}}}} )$

In this section, Eq. (1) from ACI 318-19 is applied to determine the shear strength of the concrete cover against post-punching shear forces³⁶. In ACI 318-19, Eq. (1) is typically used to evaluate the shear strength of the concrete cover in anchor groups subjected to shear force.

$${\text{V}}_{{{\text{pp}},{\text{t}}}} = \frac{{{\text{A}}_{{{\text{Vc}}}} }}{{{\text{A}}_{{{\text{Vc}}0}} }}\Psi_{{{\text{ed}},{\text{V}}}} \Psi_{{{\text{ec}},{\text{V}}}} \Psi_{{{\text{c}},{\text{V}}}} \Psi_{{{\text{h}},{\text{V}}}} {\text{V}}_{{\text{b}}}$$

(1)

In Eq. (1):

• ${\text{A}}_{{{\text{Vc}}}}$ is the projected area of the failure surface on the side of the concrete member at its edge for a group of bars, and ${\text{A}}_{{{\text{Vco}}}}$ is the projected area for a single bar in a deep member.

• The breakout edge effect factor $\left( {{\uppsi }_{{{\text{ed}},{\text{V}}}} } \right)$, modification factor for single or bar groups loaded in shear and is calculated using Eqs. (2) and (3):

  $${\text{If d}}_{2} { } \ge 1.5{\text{d}}_{1} ,{\text{ then }}\;\Psi_{{{\text{ed}},{\text{V}}}} = { }1.0$$

  (2)
  $${\text{If}} {\text{d}}_{2} < 1.5{\text{d}}_{1} ,{\text{ then}}\;{ }\Psi_{{{\text{ed}},{\text{V}}}} = 0.7 + 0.3\frac{{{\text{d}}_{2} }}{{1.5{\text{d}}_{1} }}$$

  (3)

  where ${\text{d}}_{1}$ is distance from the center of a flexural tensile bar shaft to the edge of concrete in one direction and ${\text{d}}_{2}$ is distance from center of a flexural tensile bar shaft to the edge of concrete in the direction perpendicular to ${\text{d}}_{{1{ }}}$, as illustrated in Fig. 18.

  Fig. 18

  

  Shear force near a corner.

• The eccentricity modification factor (${\uppsi }_{{{\text{ec}},{\text{V}}}}$) accounts for shear load eccentricity in bar groups and is computed via Eq. (4):

  $$\Psi_{{{\text{ec}},{\text{V}}}} = \frac{1}{{\left( {1 + \frac{{{\text{e}}_{{\text{v}}}^{\prime } }}{{1.5{\text{d}}_{1} }}} \right)}} \le 1.0$$

  (4)

  where ${\text{e}}_{{\text{v}}}^{\prime }$ denotes shear load eccentricity relative to the bar groups centroid. Eccentric shear loading induces uneven stress distribution, increasing shear forces on specific bars and elevating concrete breakout risk near edges.

  This study focuses on interior flat slab-column connections, where shear eccentricity is absent; thus, ${\uppsi }_{{{\text{ec}},{\text{V}}}} = 1$. For edge or corner columns, this factor is critical to quantify breakout capacity.

• The cracking effect modification factor, ${\uppsi }_{{{\text{c}},{\text{V}}}}$, quantifies the influence of concrete cracking around bars. Experimental observations of flat slab tests revealed that concrete outside the punching shear cone remains uncracked during initial shear failure but develops progressive cracking during the post-punching phase, culminating in full breakout. ACI 318-19 designates ${\uppsi }_{{{\text{c}},{\text{V }}}}$ = 1.4 for bars in uncracked concrete regions, as validated by empirical data.

• The thickness effect modification factor, ${\uppsi }_{{{\text{h}},{\text{V}}}}$, is applied to bars embedded in concrete members where the effective embedment length ${\text{l}}_{{\text{e}}}$ is less than $1.5{\text{d}}_{1}$ and is calculated via Eq. (5):

  $$\Psi_{{{\text{h}},{\text{V}}}} = \sqrt {\frac{{1.5{\text{d}}_{1} }}{{{\text{l}}_{{\text{e}}} }}} \ge 1.0$$

  (5)

  Eligehausen et al. demonstrated that for bars with ${\text{l}}_{{\text{e}}} < 1.5{\text{d}}_{1}$, concrete breakout strength under shear does not scale linearly with member thickness⁴². In flat slabs, however, ${\text{l}}_{{\text{e}}}$ (effective tensile reinforcement length) typically exceeds $1.5{\text{d}}_{1}$(concrete cover), rendering ${\uppsi }_{{{\text{h}},{\text{V}}}} = 1.0$ for slab-column connection analyses.

• The concrete shear failure strength of the flexural tensile bar in cracked concrete, denoted as ${\text{V}}_{{\text{b}}}$, must not exceed the lesser value obtained from Eqs. (6) and (7) ³⁶.

  $${\text{V}}_{{\text{b}}} = 0.66{ }\left( {\frac{{{\text{l}}_{{\text{e}}} }}{{{\text{d}}_{{\text{a}}} }}} \right)^{0.2} \sqrt {{\text{d}}_{{\text{a}}} } {\uplambda }_{{\text{a}}} \sqrt {{\text{f}}_{{\text{c}}}^{\prime } } \left( {{\text{d}}_{1} } \right)^{1.5}$$

  (6)
  $${\text{V}}_{{\text{b}}} = 3.7 \lambda_{{\text{a}}} \sqrt {f_{{\text{c}}}^{\prime } } \left( {{\text{d}}_{1} } \right)^{1.5}$$

  (7)

  here ${\text{l}}_{{\text{e}}}$ represents the effective length of the flexural tensile bar that resists shear forces and is determined through laboratory testing. ${\text{d}}_{{\text{a}}}$ is the diameter of the flexural tensile bar, while ${\uplambda }_{{\text{a}}}$ is the modification factor for lightweight concrete, which is equal to 1. ${\text{f}}_{{\text{c}}}{\prime}$ denotes the compressive strength of concrete. In this research, the ratio $\frac{{{\text{A}}_{{{\text{VC}}}} }}{{{\text{A}}_{{{\text{Vc}}0}} }}$ is represented by n, which depends on the depth of the concrete cover and the spacing between two adjacent flexural tensile bars. The value of n is determined using Eq. (8) ³⁶.

  $${\text{n}} = \left\{ {\begin{array}{*{20}c} {{\dot{\text{n}}}} & {S \ge 3{\text{d}}_{1} } \\ {\frac{{\text{S}}}{{3{\text{d}}_{1} }}{\dot{\text{n}}}} & {S < 3{\text{d}}_{1} } \\ \end{array} } \right.$$

  (8)

  here ${\dot{\text{n}}}$ represents the number of flexural tensile bars in both directions, S is the spacing between two adjacent flexural tensile bars, and ${\text{d}}_{1}$ is the depth of the concrete cover measured from the center of the flexural tensile bar. The values of ${\dot{\text{n}}},{\text{ n}},{\text{ V}}_{{\text{b}}} ,{\text{ l}}_{{\text{e}}} ,{\text{ d}}_{{\text{a}}} ,{\text{ f}}_{{\text{c}}}^{\prime } ,{\text{ and d}}_{1}$ are provided in Table 7.

Table 7 Basic parameters of concrete cover strength during post-punching shear stage.

According to the information’s above, Eq. (1) is converted to Eq. (9).

$${\text{V}}_{{{\text{pp}},{\text{t}}}} = 1.4{\text{ n V}}_{{\text{b}}}$$

(9)

Maximum post-punching shear strength contributed by integrity bars (${\text{V}}_{{{\text{PP}},{\text{Ib}}}}$)

Figure 19 illustrates the contributions of integrity bars and flexural tensile bars to post-punching shear strength. The flexural tensile bars contribute through dowel action, while the integrity bars enhance the load-carrying capacity via tensile action. When slab deflection (δ) occurs, the integrity bar bend at an angle (θ) (Fig. 19), generating two force components that resist shear:

Fig. 19

Deformation behavior of flexural tensile and integrity bars with explaining basic parameters.

• Post-punching shear strength contributed by the tensile strength of integrity bars ${\text{(V}}_{{{\text{PP}},{\text{Ib}},{\text{t}}}} {)}$, calculated using Eq. (10):

  $${\text{V}}_{{{\text{PP}},{\text{Ib}},{\text{t}}}} = {\text{N}}_{{{\text{b}},{\text{i}}}} \sin \theta$$

  (10)

• Post-punching shear strength contributed by the shear strength of integrity bars (${\text{V}}_{{{\text{PP}},{\text{Ib}},{\text{s}}}}$), calculated using Eq. (11):

  $${\text{V}}_{{{\text{PP}},{\text{Ib}},{\text{s}}}} = {\text{V}}_{{{\text{b}},{\text{i}}}} \cos \theta$$

  (11)

  where ${\text{N}}_{{{\text{b}},{\text{i}}}}$ is the tensile strength of integrity bars, ${\text{V}}_{{{\text{b}},{\text{i}}}}$ is the shear strength of integrity bars, θ is the inclination angle of the integrity bar.

Equation (12) is used to calculate the contribution of integrity bars to post-punching shear strength.

$${\text{V}}_{{{\text{PP}},{\text{Ib}}}} = {\text{N}}_{{{\text{b}},{\text{i}}}} \sin {\uptheta } + {\text{V}}_{{{\text{b}},{\text{i}}}} \cos {\uptheta }$$

(12)

where ${\uptheta }$ is the inclination angle of the integrity bar, as shown in Fig. 19, which is taken as $26^{^\circ }$¹. According to Habibi et al.⁴³ and Paulay et al.⁴⁴, Eqs. (13) and (14) are used to determine the tensile and shear strengths of the integrity bars.

$${\text{N}}_{{{\text{b}},{\text{i}}}} = \sum {\text{A}}_{{{\text{s}},{\text{i}}}} {\text{ f}}_{{\text{y}}}$$

(13)

$${\text{V}}_{{{\text{b}},{\text{i}}}} = \sum \frac{{{\text{M}}_{{{\text{p}},{\text{i}}}} }}{{2{\text{l}}_{{\text{i}}} }}$$

(14)

where ${\text{A}}_{{{\text{s}},{\text{i}}}}$ represents the cross-sectional area of a single integrity bar, ${\text{f}}_{{\text{y}}}$ is the yield strength of the bars, and ${\text{M}}_{{{\text{p}},{\text{i}}}}$ is the plastic moment capacity of a single bar, determined using Eq. (15). The parameter ${\text{l}}_{{\text{i}}}$ denotes the distance between two plastic hinges, as illustrated in (Fig. 19) .

$${\text{M}}_{{{\text{p}},{\text{i}}}} = \frac{{2{\text{d}}_{{\text{i}}} {\text{A}}_{{{\text{si}}}} {\text{f}}_{{\text{y}}} }}{{3{\uppi }}} = \frac{{{\text{d}}_{{\text{i}}}^{3} }}{6}{\text{f}}_{{\text{y}}}$$

(15)

To derive an equation for calculating ${\text{l}}_{{\text{i}}}$ in Eq. (16), the statistical analysis software SPSS was used. SPSS (Statistical Package for the Social Sciences) is a software program used for statistical analysis, data management, and reporting. it is widely used by researchers⁴⁵. This program analyzed the data presented in Table 8 to formulate Eq. (16).

$${\text{l}}_{{\text{i}}} = 1.72 \times 10^{4} \left( {({\text{f}}_{{\text{c}}}^{{\prime - 0.3207{ }}} { } + {\text{d}}_{{\text{a}}}^{1.047} )/{\text{f}}_{{\text{y}}}^{1.167} } \right)$$

(16)

Table 8 Initial parameters of the deflection length of integrity bars.

In Table 8: ${\text{f}}_{{\text{c}}}^{\prime }$ refers to compression concrete, ${\text{da}}$, ${\text{d}}$, ${\text{fy}}$ and ${\text{l}}_{{\text{i}}}$ stand for diameter of the integrity bar, depth effective, yield strength and distance between two hinges, respectively.

Subsequently, Eqs. (15) and (16) were substituted into Eq. (14), leading to the formulation of Eq. (17). The parameter values ${\text{A}}_{{{\text{S}},{\text{i}}}} ,{\text{ f}}_{{\text{y}}} ,{\text{ M}}_{{{\text{p}},{\text{i}}}} ,{\text{ l}}_{{\text{i}}} ,{\text{ f}}_{{\text{c}}}^{\prime } {\text{ and d}}_{{\text{a}}}$ are presented in Table 9.

$${\text{V}}_{{{\text{b}},{\text{i}}}} = \sum \frac{{{\text{d}}_{{\text{a}}}^{3} {\text{ f}}_{{\text{y}}}^{2.267} }}{{5.16 \times 10^{4} \left( {{\text{f}}_{{\text{c}}}^{\prime - 0.3207} + {\text{d}}_{{\text{a}}}^{1.047} } \right)}}$$

(17)

Table 9 Basic parameters of the integrity bars strength during post-punching shear stage.

To derive the final Eq. (18) for calculating the post-punching shear strength contributed by integrity bars, Eqs. (13) and (17) were substituted into Eq. (12).

$$V_{{{\text{pp}},{\text{Ib}}}} = \sum {\text{A}}_{{{\text{s}},{\text{i}}}} {\text{f}}_{{\text{y}}} \sin \theta + \sum \left( {\frac{{{\text{d}}_{{\text{a}}}^{3} {\text{f}}_{{\text{y}}}^{2.267} }}{{5.16 \times 10^{4} \left( {f_{{\text{c}}}^{\prime - 0.3207} + {\text{d}}_{{\text{a}}}^{1.047} } \right)}}} \right)\cos \theta$$

(18)

Table 10 presents all values of ${\text{V}}_{{{\text{pp}},{\text{t}}}}$, ${\text{V}}_{{{\text{pp}},{\text{Ib}}}}$, ${\text{V}}_{{{\text{pp}},{\text{L}}}}$, ${\text{V}}_{{{\text{pp}},{\text{M}}}}$ and the ratios of predicted over experimental post-punching shear strengths $\left( {{\text{V}}_{{{\text{pp}},{\text{M}}}} /{\text{V}}_{{{\text{pp}},{\text{L}}}} } \right)$. The mean, median, standard deviation and variance of ${\text{V}}_{{{\text{pp}},{\text{M}}}} /{\text{V}}_{{{\text{pp}},{\text{L}}}}$ values for the specimens are 1.12, 1.08, 0.34, and 0.12, respectively, as shown in Table 11. These values indicates that the analytical model can predict post-punching strength almost acceptable.

Table 10 The results of a model.

Table 11 Statistical parameters for values ${\text{V}}_{{{\text{PP}},{\text{M}}}} /{\text{V}}_{{{\text{pp}},{\text{L}}}}$.

Conclusions

This research used seven half-scale slabs to examine the behavior of flat slab-column connections, focusing on punching shear strength and maximum post-punching load. The effects of wire mesh, integrity bars, and fiber-reinforced concrete on punching shear strength and post-punching behavior were studied. The experimental results were compared with the values calculated using the proposed analytical model.

Based on the experimental results, the following conclusions were drawn:

• The test results demonstrated that the use of wire mesh enhances the ductility of the slab. This improvement can be attributed to the delayed separation of the concrete cover from the flexural tensile reinforcement.

• Increasing the number of integrity bars from 2 to 5 in each direction increased the punching shear strength and the maximum load post-punching by 29% and 18.5%, respectively. Therefore, the integrity bars can improve the post-punching shear strength by developing substitutional load paths to carry loads.

• Combining fibers in the concrete mixture with wire mesh as tensile reinforcement increased energy absorption by 103%. This enhancement is primarily due to the fibers delaying the separation of the concrete cover from the flexural reinforcement, thereby maintaining structural integrity under dynamic loading conditions. The hybrid system (fibers + wire mesh) enhances crack strength and improves stress distribution, enabling enhanced energy dissipation mechanisms prior to ultimate failure. Fiber reinforcement within the cementitious matrix restricts crack propagation by reducing crack aperture development and suppressing microcrack formation under mechanical stress. Furthermore, the wire mesh component demonstrates increased post-punching ductility through expanded concrete spalling regions, maintaining residual load strength beyond initial structural failure.

• The use of fiber-reinforced concrete increased punching strength and the maximum post-punching load by 32% and 28%, respectively. By incorporating randomly oriented fibers into the concrete matrix, crack formation is bridged and restrained under applied loads. Therefore, fibers can improve punching shear strength and the maximum load post-punching.

• The proposed model demonstrates almost acceptable accuracy in predicting post-punching strength.

Recommendation for future research

Future investigations should explore critical parameters such as the influence of different slab thicknesses with wire mash and alternative fiber materials (e.g., Glass, carbon, or hybrid fibers) to quantify their effect on punching shear strength and post-punching residual capacity. Further research must assess the optimization of reinforcement layouts by varying bar diameters, tensile strengths, and density to establish balanced strength-ductility relationships.