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1 INTRODUCTION
Flat slabs are two way spanning slab directly supported by columns. Their thickness is typically governed by deflection control or punching shear resistance. The latter is influenced by many different factors, from concrete and reinforcement parameters, to more complex issues like size effect, slenderness, and boundary conditions (test set up). It is somewhat understandable that even after more than 100 years of research, and 50 years since the first rational model [1], there is still no consensus regarding a general theory.
The number of models available developed from different backgrounds, such as those described in the literature review of fib [2] (empirical control surface approaches, plasticity approaches, Kinnunen and Nylander [1]-like models, etc.), and dating as early as the 1910s [3], and as late as the 2010s [4], [5], shows that it is a very active field of research, and attempts are still being made in this regard.
The complexity of the phenomenon is reflected in the conflicting opinions expressed by researchers. For instance, depending on the test arrangement, conclusions can become conflicted regarding the influence of continuity, with works such as Sherif and Dilger [6] observing no difference between isolated and continuous specimens, whereas Chana and Desai [7] found an increase of around 40% on punching resistance from extending the panel beyond the line of contraflexure. The compressive membrane action is well recognized for contributing to punching resistance, which is influenced by a great number of factors leading to difficulties in quantifying the increase in resistance due only to continuity.
fib [2] states that when analyzing isolated specimens, the compressive membrane action is not considered, however in real slabs restrained shrinkage induces tensile stress which reduces the punching resistance. fib [2] also mentions that based on experimental results developed by Sherif [8] it can be concluded that the punching shear strength of an interior slab-column connection in a realistic slab is almost the same for a single column test specimen. Issues like this one led fib [2] to remark that, for design purposes, it is still not recommended to rely on compressive membrane action.
Another example is related to the shear reinforcement layout. Einpaul et al. [9] observed that cruciform and radial arrangements showed comparable performances regarding the punching strength as oppose to Vollum et al. [10], who concluded that stirrups in a cruciform layout increases the shear strength of flat slabs by a multiple up to 1.5, in comparison to multiples of 2.0 or more for well anchored radial arrangements.
Some of the assumptions of the different mechanical models differ significantly, while presenting reasonable predictions for punching shear capacity. Even models based on similar backgrounds such as the Critical Shear Crack Theory (CSCT) by Muttoni [11] and the Tangential Strain Theory (TST) by Broms [4] can present some discrepancy, like the impact of time dependent effects such as creep and drying shrinkage. The CSCT assumption that the critical shear width is proportional to the slab rotation implicates that punching capacity decreases with time due to the increased rotation resulting from concrete creep and drying shrinkage. However, Broms [4] stated, based on the experimental tests under sustained loading developed by Moe [12], that a slight enhancement of punching capacity (around 4%) can be observed even though both the width of flexural cracks and deflection increased by 80%. The TST can account for that minor increase by employing a creep factor (1+φ) over the critical strain and Young’s modulus of its model.
The CSCT by Muttoni [11] and Fernández Ruiz and Muttoni [13] was chosen as the physical theory behind the latest MC2010 [14]. Since its introduction, the model has been tested in many different situations (non-axis-symmetric slabs, steel fibre reinforced slabs, prestressing, post-installed shear reinforcement, continuity, etc.). However, the model is still not universally accepted, and works such as Ferreira et al. [15] and Broms [4] have already identified and discussed a few issues with the theory.
For instance, MC2010 Levels of Approximation (LoA) I to III do not consider the effect of moment redistribution on punching resistance. Consequently, they can give very conservative estimates of the shear resistance of slabs designed in accordance to UK practice using the equivalent frame method, where moments are typically redistributed downwards by 20% over columns. Both tests and the CSCT suggest that this inward movement of the line of radial contraflexure should lead to an increase in shear resistance. This increase is not accounted for in levels I to III of MC2010 which consequently underestimate the punching resistance of such slabs.
The interpretation of the size effect is also a subject that presents different approaches in normative codes and consequently divergences between researchers. Brazilian and European codes, for example, characterize the size effect through an empirical formulation, whereas MC2010 adopted the size effect equations based on the CSCT. However, Dönmez and Bažant [16] suggest that the CSCT derivation and calculation procedure obfuscates the mechanics of failure not leading to consistent results, based on their experimentally calibrated finite element simulations of crack path and width, of stress distributions and localizations during failure, and of strain energy release.
This paper addresses some of the theoretical issues regarding the punching shear resistance of flat slabs, while giving and comparing the amount of punching shear reinforcement required based on predictions of Brazilian’s NBR 6118 [17], Eurocode 2 [18], and MC2010. The discussion is focused on a realistic flat slab according to the model developed by Sherif and Dilger [6], without shear reinforcement, in order to evaluate how the codes of practice consider the influence of in-plane restraint and flexural continuity in punching shear resistance and design. The analysis concentrates on edge columns. Punching at edge columns is much less researched than at internal columns, despite the fact that buildings typically have more edge than internal columns. Furthermore, practical experience shows that design for punching shear is frequently more critical at edge than internal columns.
This study also presents an evaluation of the directions of critical rotations for practical slabs, since MC2010 bases the shear resistance on the greater of the rotations about axes normal and parallel to the slab edge. As noted by Soares and Vollum [19] for example, different specimens such as those tested by Regan [20] and El-Salakawy et al. [21] all have shown critical rotations over the longitudinal direction. It also aims to discuss a few modelling assumptions adopted which are relevant on the interpretation of the results, such as the consideration of elastic columns in the numerical analyses required by MC2010 LoA III and IV in order to calculate the punching shear.
2 CODES OF PRACTICE
This paper includes comparisons of punching shear requirements between three codes of practice: Eurocode 2 (EC2), NBR6118, and MC2010. This section will provide the equations and general assumptions used in the studies extracted from the codes aforementioned.
2.1 Eurocode 2
BS EN 1992, Eurocode 2: Design of concrete structures, commonly abbreviated to EC2, is the current code adopted by the majority of European countries and by a few countries outside Europe. It allows flat slabs to be designed using a proven method of analysis such as Finite Element, Yield Line, Grillage, or Equivalent Frame. The analysis with Equivalent Frame divides the slab in both plane directions into frames consisting of columns and sections of the slab. The panels are divided into column and middle strips. The bending moment should be apportioned for the Column strip as 60-80% for negative, and 50-70% for positive moments and as 40-20% and 50-30% for negative and positive moments, respectively, in the middle strip. This code locates the control perimeter at a distance 2d from the column face and must be calculated in accordance with 6.4.2 section of EC2 [18]. The punching shear resistance without shear reinforcement is given by Equation 1
where
EC2 multiplies the design shear force by
EC2 also allows fixed values for
where
2.2 MC2010
MC2010 punching shear recommendations are based on the CSCT [11], [13], and so it relates punching resistance to the rotation in the so-called critical shear crack. The basic control perimeter
MC2010 reduces the design shear resistance by the multiple
where
in which
where
where
The maximum punching resistance is limited by crushing of the concrete struts near the support region, according to Equation 9.
The coefficient
LoA II calculates the rotations as Equation 10
where
Level IV of approximation allows the rotation
2.3 NBR 6118
Punching shear requirements according to Brazilian code NBR 6118 are very similar to those of EC2, previously described in section 2.1. Like EC2, the Brazilian code allows the use of equivalent frame method for the design of flat slabs when it is a reinforced concrete slab, in which the columns are arranged in regular orthogonal rows and with slightly different spans. The Brazilian code also locates the control perimeter at a distance 2d from the column face, as presented in section 19.5.2 of NBR 6118 [17]. The proportion of punching shear assumed to be resisted by concrete is calculated according to Equation 1. This portion is also reduced when shear reinforcement is considered, leading to Equation 11.
However, the size effect term of
Where
3 GENERAL ASPECTS
In order to assess the impact of continuity, a representative flat slab was designed using the equivalent frame method. The floor plate is 250 mm thick and consists of 9 square bays spanning 7500 mm between column centrelines. The internal columns are 400 mm square in cross section. Edge and corner columns are 250 mm x 400 mm in cross section. Figure 1 shows a plan view of the slab which, although not shown, is considered to be braced with shear walls or steel bracing. The slab was designed for a single load case of all spans fully loaded as permitted by the UK National annex to EC2 [24]. The resulting support bending moments were redistributed downwards by 30% at the edge columns and 20% at internal columns as required by the UK National annex to EC2 when designing for a single load case.
The characteristic concrete cylinder and reinforcement yield strength were taken as
The resulting uniformly distributed design ultimate load, calculated with load factors of 1.35 for dead load and 1.5 for imposed load, is 14.21 kN/m2. The hogging flexural reinforcement was designed for the peak bending moments at the centreline of the columns. The slab was divided into column and middle strips and the design bending moments were proportioned between the strips in percentage as 75:25 for hogging, and 55:45 for sagging moments as allowed by the EC2 and NBR 6118. The additional reinforcement required by the cladding load was distributed across the entire edge column panel width in the same proportion as the UDL (Uniformly Distributed Load).
Surplus span rebar was provided for deflection control in accordance to EC2 span-to-effective-depth rules, which, for instance, increased the column strip sagging reinforcement ratio between columns A2 and B2 (refer to Figure 1) from 0.51% to 0.73%, or its middle strip sagging from 0.41% to 0.45%. Two thirds of the hogging reinforcement within the column strip was placed within a band over the columns of ¼ of the panel width. Details of the flexural reinforcement can be found in Soares [25]. The reinforcement effective depths were
4 CONTINUOUS SLABS OF SHERIF AND DILGER [6]
Sherif and Dilger [6] tested two continuous flat slabs with a novel setup in which the panel extended to the points of zero shear, as shown in Figure 2. Further details of the test set up are given in Sherif [26]. The slabs measured 5000 mm x 7500 mm on plan and were 150 mm thick. Both slabs had the flexural reinforcement depicted in Figure 3, with No. 15 bars (200 mm2) with
The load was applied to the specimen at 16 points on the full panel and 8 points on the half panel to simulate an UDL. The columns extended 1.5 m (around half of the story height) above and below the slab and were heavily reinforced with six No. 25 (500 mm2) deformed bars. Table 1 gives more details of the specimens.
Table 1 Details of specimens tested by Sherif and Dilger [6].
| Slabs | Column size (edge and internal) (mm) | h (mm) | d (mm) |
|
fc (MPa) | Failure Load (kN/m2) | Failure Mode and Location | Failure Shear Force (kN) | Remarks |
|---|---|---|---|---|---|---|---|---|---|
| S1 | 250x250 | 150 | 114 | 1.41 | 28 | 15.54 | Punching at internal column | 399 | No Shear Studs |
| S2 | 250x250 | 150 | 114 | 1.41 | 33 | 19.97 | Punching at edge column | 164 | Studs at edge and internal column |
*Reinforcement ratio within the width c2+3h
4.1 Numerical Modelling
The Sherif and Dilger [6] slabs were analysed with TNO Diana version 9.6 [27] using the following modelling assumptions: the slab was modelled with the eight-node quadrilateral isoparametric curved shell element. Reinforcement bars were modelled as embedded elements. The Von Mises yield criterion was adopted for reinforcement with no hardening. The integration scheme was 3 x 3 in plan with 9 points through the slab thickness as recommended by Vollum and Tay [28]. Concrete was modelled using the ‘total strain fixed crack model’ of Diana. Following the suggestion of Vollum and Tay [28], the concrete tensile was taken as 0.5
Diana adopts the concept of a shear retention factor in its Total Strain Fixed crack models to account for the reduction in shear stiffness after cracking. Suidan and Schnobrich [29] suggests that it should lie around 0.1~0.2, which gives good results for shear dominant failure cases as shown in Sagaseta [30]. Trautwein [31], also using the commercial software Diana, developed analyses in axisymmetric models of slabs used in experimental studies, with a shear retention factor equal to 0.2. The value adopted for the shear retention factor in this analysis was also 0.2.
For behaviour in compression, the Thorenfeldt model [32] was adopted along with the four-parameter Hsieh-Ting-Chen failure surface to simulate the increase in concrete compressive strength with increasing isotropic stress. Concrete compressive strength reduction due to lateral cracking was modelled in accordance with Vecchio and Collins [33]. A Quasi-Newton iterative solution procedure was adopted in conjunction with an energy-based convergence criteria with 10-4 tolerance. The main aim of the NLFEA was to capture the deflected shape of the slab, allowing the punching resistance to be calculated with MC2010 LoA IV.
Around the columns, the mesh was refined using 50 mm square eight-node quadrilateral curved shell elements compared with 100 mm square elements elsewhere. The connection between the refined and coarse mesh was made with six-node triangular curved shell elements, shown in Figure 5. The final mesh is presented in Figure 5. The columns were modelled with the twenty-node brick and element size of 100 x 50 x 50 mm.
Figure 6 compares deflections from test data of Sherif [26] and NLFEA. The deflected shape was extracted along the slab centreline in the 7500 mm direction (Longitudinal), and the displacement was extracted at midway between the edge and internal column. Both slabs are reported to have failed in punching shear. The NLFEA gave very good estimates of the measured slab deflections up to failure. The analysis of S1 stopped fairly close to the flexural capacity as indicated by the yield line capacity in Figure 6.
Figure 6 Comparisons between NLFEA results and experimental data from Sherif’s (1996) slab (a) S1 and (b) S2.
Sherif and Dilger [6] reports that specimens S1 and S2 failed in punching at the internal and edge column, respectively. Figure 7 shows the prediction of MC2010 LoA IV, with resistances calculated from Equations 5 (
Figure 7 Column reaction-rotation relative to the column for the slabs of Sherif and Dilger [6] and resistance according to the CSCT.
In Figure 7, rotations relative to the column for both perpendicular directions on plan are depicted as ‘Longitudinal’ when calculated from the longitudinal deflected shape, and ‘Transverse’ (in this case, the transverse rotations are equal to either side of the column due to symmetry), when calculated from the deflected shape along the slab edge (see Figure 5). Previous analysis has already shown that there is no significant difference between extracting the rotations from the shell elements or calculating them from the corresponded deflected shape [25].
The CSCT is seen to give reasonable predictions for punching failure for the slabs of Sherif and Dilger [6] when adopting a fixed
5 SUBASSEMBLY OF DESIGNED SLAB
A parametric analysis of the flat slab designed in Section 3 was carried out with Diana. The slab was modelled in a series of subassemblies similar to that tested by Sherif and Dilger [6]. The subassembly shown in Figure 8 includes edge column 2A and internal column 2B (refer to Figure 1).
The slab was modelled with eight-node quadrilateral curved shell elements with a size of around 50 mm square near the slab/column connection, and 150 mm square elsewhere. Six-node triangular curved shell elements were used to connect the refined mesh to the coarse mesh. The columns were modelled with elastic twenty-node brick elements measuring 150 x 50 x 50 mm, and were fully fixed at each end. Although unrealistic, this assumption has no significant influence on the NLFEA results since the columns were modelled elastically, which is representative of the lower levels of a tall building in which the axial column load is sufficient to prevent cracking.
The analysis modelled the full column height of 3.75 m above and below the slab. The adopted characteristic concrete compressive strength was 30MPa. Symmetry was simulated with only rotational fixities as done for the analysis in Soares and Vollum [34] to avoid any additional in-plane forces.
5.1 Influence of Reinforcement arrangement
A parametric study was carried out to investigate the influence of varying the reinforcement in the slab of the subassembly shown in Figure 8. Columns were modelled as elastic and extended 3.75 m above and below the slab. The ends of the columns were fully fixed. Figure 8 gives further details on the slab dimensions and adopted boundary conditions. The objective was to determine whether the influence of varying the flexural reinforcement in the subassembly was similar to that predicted for slabs with the geometry tested by Regan [20], discussed in Soares and Vollum [19].
Figure 9 and 10 show the baseline reinforcement arrangement used in the subassembly which was determined from analysis of the full slab shown in Figure 1 using the procedure described in Section 3. A minimum reinforcement area of 377 mm2/m was provided where no reinforcement is shown, calculated according to EC2. Loads were applied as shown in Figure 8. Both UDL and cladding loads were increased proportionately until failure. This load case is critical for the internal column, but not the edge column where pattern loading consisting of the full factored load on the end of span and factored dead load on the internal span is more critical. The all spans fully loaded load case was adopted since the main objective was to compare the punching resistances given by EC2, NBR 6118 and MC2010 Levels II to IV.
In Figure 9, the support reinforcement ratio, normal to the free slab edge, is ρsup = 0.8% over a width of c2 + y (where y is the perpendicular distance from the slab edge to the inner column face and c2 is the parallel column dimension). Analyses were also carried out with ρsup doubled to ρsup = 1.0% and halved to ρsup = 0.5%. The span reinforcement ratio was also doubled from ρsup = 0.6% in to ρspan = 1.2%, and halved to ρspan = 0.3%. All nine slabs were loaded with a line load along the short external edge representing cladding. An additional analysis was carried out with reinforcement ratio of ρsup = 0.8% and ρspan = 0.6% and no cladding load, making a total of ten analyses. Table 2 gives more details of the slabs.
Table 2 Details on the parametric study varying the reinforcement arrangement.
|
|
30 MPa |
|
|
1.5 |
|
|
500 MPa |
|
|
200 GPa |
|
|
1.15 |
|
|
212 mm |
|
|
196 mm |
| Self-weight | 6.25 kN/m2 |
| Superimposed dead load | 1.5 kN/m2 |
| Imposed load | 2.5 kN/m2 |
| Cladding load | 10 kN/m |
| Edge Column (2A) | 250 mm x 400 mm |
| Internal Column (2B) | 400 mm x 400 mm |
|
|
0.7 |
|
|
0.89 |
aTop and Bottom bars in the transverse direction. b Top and Bottom bars in the longitudinal direction.
Figure 11 shows the resulting longitudinal rotations relative to the column, calculated from the longitudinal deflected shape (such as that presented in Figure 6), and the design shear force at the external column extracted from LFEA. The rotations were calculated as previously described.
Figure 11 shows that, as for Regan’s [20] slabs (Soares and Vollum [19]) , longitudinal span reinforcement is predicted to have significantly greater influence on the longitudinal rotation at edge columns than longitudinal hogging reinforcement at the edge column. Figure 11 also shows the shear resistance provided by the concrete calculated according to MC2010 with
Figure 12 shows that the calculated eccentricity M/V at the edge column increased with load. A similar outcome was observed in the specimens by Regan [20] (Soares [25]) where the increase in eccentricity for the elastic column is explained by its increased stiffness compared to the column in Regan’s tests. In MC2010, the basic control perimeter is reduced by a multiple
6 CODE PREDICTIONS
This section is used to compare predictions of levels II, III, IV of MC2010, NBR 6118, and EC2, for the slabs considered in the parametric study previously described.
6.1 Critical direction for rotations
According to MC2010, the punching resistance depends on the greater of the slab rotations relative to the column in the longitudinal and transverse directions. Soares and Vollum [19] show that longitudinal rotations (i.e. rotations calculated from longitudinal deflections) are critical for the specimens of El-Salakawy et al. [21] and Regan [20] in all cases. This finding is not true in general, and is partly a consequence of the specimen geometry and loading arrangement. Longitudinal rotations are also critical for the tests of Sherif and Dilger [6], but the difference between longitudinal and transverse rotations is much less than for Regan’s [20] slabs, since the specimens have slightly more realistic dimensions ratio. The subassembly shown in Figure 8 realistically models the direction of span in both the longitudinal and transverse directions as for the Sherif and Dilger’s [6] tests.
For practical slabs, the critical direction can vary and depends on parameters including the reinforcement arrangement and magnitude of the cladding load. Figure 13 compares the longitudinal and transverse rotations with and without cladding load for slab ρsup = 0.8% and ρspan = 0.6%. The reinforcement is the same for both cases and is designed for the case with cladding. Interestingly, the critical direction for rotations in Figure 13 changes from longitudinal to transverse when the cladding load is included. The resistances in Figure 13 are calculated with Equation 5 and
Figure 13 Comparison between longitudinal and transverse rotations with and without cladding loads for ρsup = 0.8% and ρspan = 0.6%.
Table 3
| Slabs | VRd,c (kN) |
|
|---|---|---|
| Longitudinal | Transverse | |
| With Cladding Load | 290 | 257 |
| Without Cladding Load | 240 | 260 |
Figure 14 compares longitudinal and right-hand side transverse rotations (greater than the left-hand side transverse rotation for all cases due to asymmetric transverse reinforcement), relative to the column, for all 9 slabs with cladding load. Also shown is the MC2010 punching resistance provided by the concrete calculated with Equation 5 for
Figure 14 Comparison between longitudinal and transverse rotations for the edge column of the subassembly parametric study.
It can be seen in Figure 14 that transverse direction is critical for all cases. Neither the span nor the support longitudinal reinforcement seems to have a significant impact on these transverse rotations, as shown in Figure 15. Longitudinal flexural reinforcement (span/support) have no influence on transverse rotations, as can be seen in Figure 15, though it can still influence punching resistance owing to shear redistribution around the control perimeter, as stated by Sagaseta et al. [35], which suggests that the boundary conditions adopted in punching shear tests could have a greater influence than considered up to now.
6.2 Comparisons between MC2010 Levels II, III, IV, EC2 and NBR6118 for edge columns
The following section compares the areas of punching shear reinforcement required by the different levels of MC2010, NBR 6118 and EC2 for edge column A2 (refer to Figure 1). The effects of uneven shear were accounted for using the simplified
For Level III,
Figure 16 Longitudinal and Transverse rotations of the subassembly slabs from the parametric study. Note: Slabs with ρspan = 0.3% didn’t reach the design load as would likely fail in flexure, therefore they are not shown in the figure.
MC2010 requires a minimum area of reinforcement to satisfy
Table 4
| MC2010 | EC2 | NBR 6118 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| ke = 0.7 | |||||||||||
|
|
|
||||||||||
| LoA IV | LoA III | LoA II | LoA IV | LoA III | LoA II |
|
|
|
|
|
|
| ρsup = 1.0% |
|
|
|
- | 1358.52 | 1364.83 | 267.98 | 1107.72 | 313.97 | 1091.32 | 424.77 |
| ρspan = 0.3% | |||||||||||
| ρsup = 1.0% |
|
788.18b | 546.37 | ||||||||
| ρspan = 0.6% | |||||||||||
| ρsup = 1.0% |
|
778.33b | 759.68 | ||||||||
| ρspan = 1.2% | |||||||||||
| ρsup = 0.8% |
|
|
|
- | 1358.52 | 1488.67 | 260.09 | 1132.20 | 301.81 | 1126.4 | 420.69 |
| ρspan = 0.3% | |||||||||||
| ρsup = 0.8% |
|
802.96b | 542.29 | ||||||||
| ρspan = 0.6% | |||||||||||
| aρsup = 0.8% |
|
|
886.70b | 1218.97 | 542.29 | ||||||
| ρspan = 0.6% | |||||||||||
| ρsup = 0.8% |
|
|
778.33b | 1358.52 | 755.61 | ||||||
| ρspan = 1.2% | |||||||||||
| ρsup = 0.5% |
|
|
|
- | 1358.52 | 1676.90 | 252.21 | 1153.62 | 279.71 | 1190.19 | 414.34 |
| ρspan = 0.3% | |||||||||||
| ρsup = 0.5% |
|
812.81b | 535.95 | ||||||||
| ρspan = 0.6% | |||||||||||
| ρsup = 0.5% |
|
778.33b | 749.25 | ||||||||
| ρspan = 1.2% | |||||||||||
aWithout Cladding Load. b Smaller than the minimum reinforcement by MC2010 corresponding to
Interestingly, the rotations in the transverse direction calculated with LoA III are slightly greater than LoA II. This is believed to be the result of the elastic shell elements overestimating torsion at the side of the column, which led to a greater
As can be seen in Figure 16 and Table 4, the critical direction varies with the level of approximation. Figure 13 and Table 3 shows that the omission of cladding load in the NLFEA swapped the critical direction from transverse to longitudinal, which led to a slightly greater amount of shear reinforcement required according to MC2010 LoA IV (refer to Table 4).
In most of the LoA II and III designs, the design shear force is very close to the maximum possible shear capacity which is limited by crushing of concrete near the support region according to MC2010’s limit of
Though slabs with ρspan = 0.3% would likely fail in flexure as suggested by
Figure 17 compares the amount of shear reinforcement within a zone of 1.5d around the column in relation to the longitudinal span reinforcement for all slabs with cladding load. According to MC2010 LoA II, III, NBR 6118, and EC2, the required area of punching shear reinforcement is independent of the span reinforcement ratio. However, Figure 17 shows that even though LoA IV captures the influence of span reinforcement, the impact on required shear reinforcement is minimal, especially for slabs with ρsup = 1.0%. This is so since transverse rotations are critical for the considered slabs, which is not always the case.
The impact of longitudinal support reinforcement is significantly greater for LoA II of MC2010 than LoA III and IV, NBR 6118, or EC2. Both LoA II and III, which are intended for design, required significantly more punching shear reinforcement than NBR 6118, and in some cases double the reinforcement required by LoA IV, which is intended for assessment. LoA IV requirements are very close to those of EC2 when the minimum reinforcement rule of MC2010 is implemented.
7 CONCLUSIONS
This paper investigated the impact of slab continuity through modelling assumptions, critical directions of rotations and code comparison on the punching resistance of an edge column from realistically proportioned flat slab floor plates. Elastic columns were considered in the punching shear assessments of the full-scale slab to simplify the analysis. The effect of this was to increase the moment transferred to the edge column but also to reduce longitudinal slab rotations calculated with NLFEA which were generally not critical for the considered slabs.
The increase in M/V with load, due to moment redistribution from span to support, presented in Figure 12 has little impact on the reactions at edge columns, as stated by Soares [25]. The reason being that edge column moment is relatively small compared with that at internal support. The parameter that characterizes the eccentricity by the MC2010,
For the modelled full-scale flat slabs, longitudinal span reinforcement has a significantly greater impact on longitudinal rotations than longitudinal support reinforcement at the slab edge (Figure 11) as for Regan’s [20] specimens. The direction of greatest rotation varies with reinforcement arrangement and between the LoA in MC2010. However, the longitudinal reinforcement could still affect punching resistance due to shear redistribution around the control perimeter of the type proposed by Sagaseta et al. [35] for slabs with non-axis-symmetrical reinforcement. The impact on punching resistance was significantly less than observed for Regan’s specimens [20], partly because transverse rotations are critical for all cases. The analyses carried out in accordance with EC2, NBR 6118 and MC2010 LoA II and LoA III showed that results for punching shear reinforcement are independent of the longitudinal span reinforcement, unlike the results obtained with MC2010 LoA IV, which is capable of capturing the influence of continuity and flexural reinforcement ratio in the span. For the considered full-scale slab, the area of shear reinforcement required within 1.5
