Strength of cast-in-place slabs for rectangular cross-section columns punching

. Flat slabs in contemporary buildings are most commonly supported by rectangular cross-section columns. Research of slabs supported by rectangular cross-section columns for punching is rather narrow. The purpose of this work was the experimental research of slabs punching by rectangular cross-section columns and adjustment of their design method. Reinforced concrete slabs 6 cm in thickness without transverse reinforcement were used as testing specimens. During tests load on the slab was transferred using stamps. Side ratios for stamps varied from 1 to 5 in experiments. Strength and strain properties of concrete were determined before slabs testing for punching. Ultimate loads, that resulted in slab punching, were acquired from test results. Formulae for punching load are suggested for rectangular cross-section columns punching based on obtained results. Generalized analysis of experimental research results shows that slab strength for punching is also influenced by short side of rectangular cross-section to slab thickness ratio.


Introduction
Cast-in-place reinforced concrete buildings with beamless frame represent significant portion in nowadays construction. Flat floor slabs most commonly are supported by rectangular cross-section columns. Most experimental and theoretic studies associate with research of punching behavior of slabs supported by square cross-section columns [1][2][3][4][5][6][7]. Thereat research for slabs supported by rectangular cross-section columns is rather narrow [8][9][10][11][12]. Punching design for cast-in-place floor slabs according to SP 63.13330.2018 leads to overstatement of load bearing capacity by up to 40% in relation to experimental data [10,13]. Analysis of numerical investigations for stress condition of cast-in-place slabs at punching loads showed that increase in rectangular cross-section columns sides ratio leads to significant non-uniformity in stress and strain distribution across column perimeter [14][15][16]. Most propositions for accounting of non-uniformity in strain and stress distribution across the long side of rectangular columns cross-section come down to artificial reduction of design cross-section perimeter.
Research purpose -experimental research of slab strength for rectangular cross-section columns punching and adjustment of its design methods.

Methods and materials
Reinforced concrete slabs 100x100 cm in plan sizes and 6 cm in thickness were used as testing specimens. Slabs were reinforced using wire reinforcement grid 5 mm in diameter with steel grade Vr500, which was placed near the bottom edge of slab. There was no transverse reinforcement in slab. Figure 1 shows structure of reinforced concrete slabs. Weight proportion concrete composition was 1 : 1.2 : 2.2 with W/C=0.32. Composition of concrete mix included superplasticizing agent С-3 in a quantity of 0.7% and organosilicon fluid GKZh-94 in a quantity of 0.15% of cement mass. Cement content on 1 m3 of concrete mix was 500 kg. Granite ballast stone of 5-10 mm fraction, river sand, Portland cement of grade 400 were used for preparation of concrete mix.
Concrete casting for test specimens was done in wooden collapsible form. Compaction of the concrete mix was done on vibration table. After 3 days of curing collapsible forms were removed. Specimens were kept in humid sawdust for 28 days. After that specimens were stored at temperature of +15±5°C at relative humidity of 60-65% in conditions of production space.
Concrete cubes 10x10x10 cm in sizes and prisms 10x10x40 cm in sizes were made for determination of strength and strain properties of concrete simultaneously with reinforced concrete specimens using the same concrete mix. Prism concrete strength, tension strength and elasticity modulus were determined according to [11].
Testing method for slab punching was as follows. Slabs were laid on supports in the form of metal frame situated in the center of load application area. Testing slab specimens were loaded using jack (Q = 25 t). Load on slab was transferred through reinforced concrete stamps. Distance from stamp edges to internal contour of supports was set equal to 10 cm at each side. Thus bending of slabs was excluded. Figure 2 shows the scheme of force rig for testing slabs for punching.  Table 1 shows stamps marking and their sizes. During tests we recorded concrete strain using strain gauges and load at which the punching of slab occurred.

Test results and discussion
Prism strength ( b R ) and initial elasticity modulus for concrete (E b ) were acquired after concrete prisms tests for axial compression. Concrete tension strength ( bt R ) was determined after concrete prism tests for bending. Reinforcement bar strength ( s R ) and elasticity modulus ( s E ) were defined after bar tests for tension. Table 2 shows average values of strength and strain properties of concrete and reinforcement bars.  from edges of loading area was calculated using PK LIRA based on acquired test data. Shear stress curve completeness factors at fracture moment (ω) were calculated using shear stress curves across design contour. Table 3 shows test and calculation results.
where b , h -width and length of column cross-section respectively.
Upper and lower bounds of confidence limit for shown experimental data equal respectively:  Figure 3 shows that practically all test data lies in range of confidence limit for shown data. Data variation can be caused by influence of scale factor (ratio of column cross-section short side to slab thickness). This ratio for tests of b , h -width and length of column (stamp) cross-section respectively; 1 h -slab thickness.
It should be noted that formula (4) is true subject to: 1,43≤ Value of respective bound is used in design for values of outside the range of specified interval. Figure 4 shows values of shear stress curve completeness factor calculated using formula (4) for respective test values of column cross-section short side to slab thickness ratio

Fig. 4. Influence of on factor of shear stress curve completeness factor
Ultimate load born by slab concrete for rectangular cross-section columns punching is recommended to calculate using formula: where Z -shear stress curve completeness factor calculated using formula (1).
Dependency for lower bound of confidence limit should be used for engineering calculations (formula (3)).

Conclusions
Conveyed research showed that design of cast-in-place floor slabs in the absence of bending moments according to recommendations of SP 63.13330.2018 for punching by E3S Web of Conferences 263, 02035 (2021) FORM-2021 https://doi.org/10.1051/e3sconf/202126302035 rectangular cross-section columns leads to overstatement of load bearing capacity by up to 67% in relation to experimental data.
Non-uniformity in stress and strain distribution across rectangular cross-section column perimeter can be taken into account using shear stress curve completeness factor.
Suggested dependencies for shear stress curve completeness factor allow to decrease divergence between design and experimental values of slab strength for rectangular crosssection columns punching (in average understatement of load bearing capacity was 9% in relation to experimental data).
Article shows research results for one slab thickness. Further research is expected to investigate influence of scale factor (ratio of column cross-section short side to slab thickness) on slab punching strength.