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PUNCHING SHEAR OF FLAT SLABS: FAILURE AND CAPACITY CALCULATION OVERVIEW OF CURRENT DESIGN PRACTICE PROPOSED STRENGTHENING AND REMEDIAL PROCEDURES EXPERIMENTAL TESTING OF REMEDIAL MEASURES
SCHALK WILLEM MARAIS
THESIS PRESENTED IN PARTIAL FULFILLMENT OF REQUIREMENTS FOR THE DEGREE OF AT THE
MASTER OF ENGINEERING (CIVIL)
UNIVERSITY OF STELLENBOSCH
SUPERVISOR: PROF. G.P.A.G. VAN ZIJL STELLENBOSCH APRIL 2005
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DECLARATION
I, the undersigned, declare that the work contained in this thesis is my own original work and has not been submitted in its entirety or in part for a degree at any other university.
______________
____________
SW Marais
Date
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Opsomming Moderne beton konstruksie maak meestal gebruik van plat blaaie sonder kolomkoppe of blad verdikkings, in plaas van die meer konvensionele balk-en-blad stelsels. Die gebruik van plat blaaie bied aansienlike voordele ten opsigte van koste, relatief maklike konstruksie en meer vryheid met die argitektoniese uitleg van die gebou. Ongelukkig word die volle voordele en kapasiteit van plat blaai nie noodwendig benut nie. Heelwat ontwerpkodes bied onakkurate metodes om ponsskuif weerstand te voorspel. Gepaardgaande hiermee word die gebruik van plat blaaie gepenaliseer in gebiede wat onderhewig is aan matige seismiese aktiwiteit, as gevolg van moontlike moment geïnduseerde ponsskuif swigting.
Hedendaags word al meer bestaande geboue omskep en herbenut. In baie gevalle veroorsaak die nuwe uitlegte en veranderde gebruik dat ekstra strukturele kapasiteit van die bestaande kolom en blad verbindings benodig word. Somtyds is daar reeds skade aan hierdie verbindings as gevolg van ontwerpfoute of ongewenste praktyke tydens konstruksie.
Na aanleiding van die voorafgenoemde spreek hierdie verslag die volgende aspekte aan: Eerstens word „n aantal ontwerpkodes se voorspelling van ponsskuif swigting vergelyk. Uit die vergelyking volg dat weinig van die benaderings in lyn is met moderne betroubaarheidsbeginsels vir die ontwerp van strukture. Op hede is daar slegs een kode wat op alle beskikbare toetsdata gekalibreer is om te voldoen aan 5% moontlikheid van swigting. Hierdie kode is die nuutste DIN 1045-1 (2001) ontwerpkode.
Tweedens word verskeie metodes voorgestel vir die herstel en versterking van bestaande kolom en blad verbindings. Gepaardgaande hiermee word „n universele klassifikasie van skade voorgestel om te sorg dat die korrekte stappe vir remediërende werk geneem kan word. Derdens is „n kolom en blad verbinding eksperimenteel getoets. Hierdie toets het die welbekende, bros gedrag van ponsskuif swigting uitgelig, asook „n groot verskil tussen die
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voorspelde skuif kapasiteit en die getoetse kapasiteit van die model. Meganistiese modellering toon dat die swiglas van die model wel in die regte ordegrootte was.
Laastens is daar gepoog om die beskadigde blad te herstel deur vertikale wapening stawe in die blad te installeer met „n hoë sterkte epoksie. Hierdie stawe is binne die oorspronklike skuifwapening omtrekke geïnstalleer, asook op „n nuwe wapeningsomtrek. Ongelukkig het die herstelde blad nie dieselfde kapasiteit as die oorspronklike blad gehad nie. Ten spyte hiervan kan die sukses van die herstel toegeskryf word aan die feit dat die uiteindelike swigting buite die vegrote bewapening sone geskied het. Die addisionele skuifstaal het die skuifkrake forseer om weg van die kolom te migreer en uiteindelik buite die versterkte sone te swig.
Daar word voorgestel dat verdere toetse gedoen word om die presiese bydrae van die addisionele skuif wapening te bepaal, sowel as die meer akkurate voorspelling van die kapasiteit van herstelde blaaie.
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Synopsis Modern concrete construction favours the use of flat slabs without drop-panels or column capitols as opposed to more conventional slab and beam systems. Flat slabs offer numerous advantages in terms of cost, ease of construction and architectural flexibility. However, more often than not, the full advantage of using flat slabs is not harnessed. Many design codes offer inaccurate formulations to predict punching shear capacity; furthermore, they discriminate against their use in modestly active seismic regions due to potential moment induced punching failure.
Lately, more and more existing structures are being refurbished and renovated. In many cases the change in architectural layouts and altered use necessitate additional load carrying capacity from the existing slab-column connections. In some cases the existing structures already show distress due to under-designed slab-column interfaces or dubious construction methods.
Based on the aforementioned points the aims of this report are the following:
Firstly, a comparison of several current codified design approaches is performed to highlight the fact that some of the favoured codified approaches do not comply with modern reliability-based structural design philosophies. At this stage, there is only one design approach that has been calibrated with virtually all available test data, and scaled to comply with a 5% probability of failure. This is the formulation presented in the latest DIN 1045-1 (2001) design code.
Secondly, numerous methods of strengthening and repair of existing slab-column connections are presented. Accompanying these suggested methods, a universal classification of damage is proposed to aid in the effective repair of damaged connections.
Thirdly, experimental testing shows the well-known brittle behaviour of punching shear failure and the difference between the predicted and actual failure loads measured. Mechanistic modelling of the test panel shows the failure load to be in the correct order of magnitude.
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Lastly, an attempt was made to repair the damaged slab by adding vertically doweled reinforcing bars, bonded with high strength epoxy grout within the original shear reinforced zone, as well as on a new perimeter. Even though the failure load of the repaired test panel did not meet that of the original panel, the effectiveness of the repair was evident in the fact that punching failure did not take place within the extended shear reinforced zone. The additional perimeter of shear reinforcing forced the inclined shear cracks to migrate away from the column, causing failure outside the shear reinforced zone.
It is proposed that further future testing is done to quantify the added benefit of additional reinforcing, as well as the accurate prediction of the punching shear capacity of repaired slab-column connections.
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Acknowledgments: Special thanks go out to the following people for their patience, time, support, ideas and critique:
Gideon van Zijl
University of Stellenbosch
Billy Boshoff
University of Stellenbosch
Wayne Ritchie
Sutherland Associates (Pty) Ltd
Gerrit Bastiaanse
BKS (Pty) Ltd
Ralph Kratz
University of Cape Town
Without the support and enthusiasm of the engineering industry the experimental testing would not have been possible. Very special thanks go out to each of the following companies and their representatives for the supply of construction materials and expertise:
Dave Miles Lafarge South Africa
Grant Pistor HILTI South Africa
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Contents
1.
2.
Overview of Punching Shear Failure 1.1.
Introduction
13
1.2.
Classical Punching Failure
16
1.3.
Punching failure due to lateral loading of the structure
18
Proposed Analytical and Empirical Models 2.1.
Synthesis of Punching Shear Failure, as proposed by Menétrey (2002)
20 20
2.1.1. Experimental results
20
2.1.2. Numerical simulations
21
2.1.2.1. Model description
22
2.1.2.2. Simulation of the punching failure
22
2.1.2.3. Parametric analysis
23
2.1.3. Analytical Model
2.2.
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2.1.3.1. Punching- vs. Flexural capacity
27
2.1.3.2. Tensile force in the concrete
27
2.1.3.3. Contribution of the dowel effect
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2.1.3.4. Contribution of the shear reinforcing
29
2.1.3.5. Contribution of prestressing tendons
33
Proposed Punching Capacity Increase due to the use of Fibre Reinforced Concrete
3.
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33
2.2.1. Experimental testing
34
2.2.2. Prediction of Punching Shear Strength
35
2.2.3. Observations and discussions based on the experiments
36
Current Design Practice
39
3.1.
German design code – DIN 1045-1988
40
3.2.
British Standard 8110-1:1997
42
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4.
3.3.
ACI 318M-02
45
3.4.
Eurocode 2
48
3.5.
DIN 1045-1:2001
49
3.6.
CSA A23.3
53
3.7.
CAN/CSA-S6-00 Canadian Highway Bridge Design Code
54
3.8.
Comparisons of code equations for punching shear with and without shear reinforcing – standardized approach.
56
3.8.1. German design code DIN 1045 (88)
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3.8.2. Eurocode 2 (EC2)
59
3.8.3. British Standard 8110-1:1997
61
3.8.4. ACI 318-95
63
3.8.5. DIN 1045-1 (2001)
65
3.8.5.1. Punching shear resistance of a slab without shear reinforcing
66
3.8.5.2. Maximum punching shear capacity
66
3.8.5.3. Punching shear strength within the shear reinforced area
67
3.8.5.4. Punching shear strength outside the shear reinforced area
67
Accuracy of Modelling and Codified Design Rules 4.1.
Accuracy of Experimental Testing
4.1.1. Single Column Tests
69 69
4.1.1.1. The effect of boundary conditions
70
4.1.1.2. The effect of compressive membrane action
71
4.1.2. Slab subsystems 4.2.
69
Accuracy of Code Predictions
4.2.1. Compilation of databank
72 72 73
4.2.2. Comparisons between Design Code Rules and Experimental Results for Flat Slabs without Shear Reinforcing
74
4.2.3. Comparisons between Design Code Rules and Experimental Results for Flat Slabs with Shear Reinforcing 4.2.4. Discussion of the Comparison of Test Data and Codified Predictions
75 77
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5.
Proposed Repair Methods for Punching Shear Failure and Preventative Measures against Punching Shear Failure 5.1.
Strengthening of Existing Slab-column Connections
5.1.1. Increasing the Effective Slab Depth 5.1.1.1. Slab strengthened with additional concrete and vertical bolts
78 79 79 79
5.1.1.2. Slab strengthened with additional concrete and bonded steel plate80 5.1.2. Increasing the area of load transfer
81
5.1.3. Installation of additional shear reinforcing
82
5.2.
5.1.3.1. Doweling additional bars into the existing slab
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5.1.3.2. Slab strengthened with vertical bolts
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Repairing slab-column connections showing distress due to punching shear failure or near failure
5.2.1. Proposed Classification of Damage
84
5.2.1.1. Damage Level 1 – Minor to medium levels of damage
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5.2.1.2. Damage Level 2 – Medium to severe levels of damage
85
5.2.1.3. Damage Level 3 – Extreme levels of damage
86
5.2.2. Proposed remedial works for the different levels of damage
5.3.
84
86
5.2.2.1. Repair of Damage Level 1
87
5.2.2.2. Repair of Damage Level 2
87
5.2.2.3. Repair of Damage Level 3
88
Retrofitting of slab-column connections for improved behaviour under seismic loading conditions
5.3.1. Fibre reinforced concrete infill panel
88 89
5.3.2. Demolition of part of the existing concrete slab and replacement thereof with fibre reinforced concrete 6.
Experimental Testing of an Undamaged Slab-column Connection
90 91
6.1.
Experimental Test Setup
92
6.2.
Proposed Test Procedure
95
6.3.
Actual Test – Virgin test panel
96
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6.3.1. Material Test Results
96
6.3.2. Load Application
97
6.3.3. Placement and Setting Up of the Test Panel
98
6.3.4. Original Panel – Load Application 1
99
6.3.5. Original Panel – Load Application 2
104
6.3.6. Original Panel – Load Application 3
106
6.3.7. Original Panel – Combination of results – Loads 1, 2 &3
109
6.3.8. Verification of test results with the method proposed by Menétrey (2002) 112 7.
8.
9.
Experimental Testing of Repaired Slab-column Connection 7.1.
Classification of Damage and Proposed Method of Repair
117
7.2.
Repair of the damaged slab
118
7.3.
Testing of the Repaired Panel
121
7.3.1. Material Test Results
121
7.3.2. Load Application
121
7.3.3. Repaired Panel – Load Application 1
122
7.3.4. Repaired Panel – Load Application 2
128
7.3.5. Dismantling of the failed slab panel
135
Conclusions and Recommendations
139
8.1.
Conclusions
139
8.2.
Recommendations
140
Appendix A – Estimation of the experimental model‟s punching shear capacity and the design of the required shear reinforcing
10.
117
142
Appendix B – Calculations using the Mechanistic Model Proposed by Menétrey147 10.1. Virgin Test Panel
147
10.2. Repaired Test Panel
152
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11.
Appendix C – Construction Details
12.
Appendix D – Prediction of Flexural Failure at Slab-column Connections – Yield
155
Line Approach
158
13.
Appendix E – Method for Epoxy Crack Injection
160
14.
References
162
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1. Overview of Punching Shear Failure 1.1. Introduction Building construction with flat plates has become more and more popular lately. This construction method may dominate all modern reinforced concrete construction in conventional buildings. Flat plates – better known as flat slabs – offer numerous advantages:
Architectural flexibility
More clear spaces
Reduced overall building height – equating to lower construction and maintenance cost
Simpler and less costly formwork systems
Shorter construction times
Some of the disadvantages associated with the use of flat slabs systems are the following:
From a serviceability point of view, designs are often governed by deflection criteria. Accurate estimation of deflections in two-way spanning slab systems is debatable.
Flat slab construction is penalised by certain codes in seismic regions, e.g. Eurocode and SABS(SANS).
From an ultimate limit state point of view the greatest limiting factor in the design process is punching shear failure of the flat slab at the column-slab interfaces.
Punching shear failure can be defined for two specific cases. Firstly, flat slabs without shear reinforcing, and secondly flat slabs with shear reinforcing.
Flat slabs without shear reinforcing typically tend to fail in a brittle manner with the telltale signs of failure being a conical concrete plug perforating the slab in
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combination with a fair amount of flexural cracking evident on the top surface of the slab. The brittle behaviour of the slab-column connection at failure is clearly depicted on a load-deflection curve (Fig 1.1), showing a sudden loss in load carrying capacity of the connection.
Flat slabs with shear reinforcing commonly fail in a less spectacular fashion. The addition of shear reinforcing causes increases the toughness of the connection. The failure mode is shifted from pure punching failure towards a more ductile flexural failure mode. This intermediate failure behaviour can be seen on the load-deflection plot (Fig 1.1). Even though the connection is more resilient it still shows a rather steep decline in load carrying capacity. At failure the connection shows more warning of distress by means of a more pronounced flexural cracking pattern originating at the column, and circumferential cracking around the loaded surface. In some cases delamination of the concrete at the level of the tension reinforcing may occur.
Fig. 1.1 Response curves for flexural- and punching failure (Menétrey 2002)
Both failures, with and without punching shear reinforcing, can be considered as brittle failure designated by the sudden reduction in the load carrying capacity of the structure. Due to their sudden nature these failures are more often than not, disastrous. However with shear reinforcement a more acceptable failure can be achieved.
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A number of structural failures and collapses can be attributed to punching shear failure of slab-column connections, of these a few examples are shown in Fig 1.2 and Fig 1.3.
Fig. 1.2 Progressive collapse of the Sampoong department store in Seoul Korea (Gardner et al 2002)
During the years numerous ways of countering punching shear failure of flat slabs have been proposed and used, all with varying rates of success. Some of these methods are:
Drop panels
Column capitals
Additional flexural reinforcing
The use of pre-stress
Pre-fabricated shear heads
Shear reinforcing in the depth of the slab
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Fig. 1.3 Collapse of the upper parking deck at Pipers Row Car Park, Wolverhampton, UK (Wood et al, 1998)
Numerous codified approaches to the design of shear-reinforced slabs exist, as well as number of mechanical and numerical models to predict the punching behaviour and capacity of flat slabs. Most of these methods are based on limited number of tests and formulated in such a way that no clear comparison between the methods can be used, even though most of them are defined by the same parameters.
This report aims to compare the various approaches to predict shearing resistance of slab-column connections. One approach for punching shear enhancement is selected and studied both analytically and experimentally. After initial testing of the undamaged plate a repair will be attempted. The capacity of the repaired slab will be compared with the original capacity and verified with a mechanistic failure model.
1.2. Classical Punching Failure At overloading a typical slab-column connection will fail at a perimeter, proportional to the effective depth of the slab, from the column face.
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Excessive loading, in combination with an unbalanced moment over the column will cause the shear stress on this critical perimeter to exceed the capacity of the structural system.
These shear stresses cause angled cracks to develop from the column face to the upper surface of the slab. In slabs without shear reinforcing the crack growth is rapid resulting in a concrete plug being pushed out of the slab. This behaviour is clearly illustrated in Fig 1.4.
Fig. 1.4 Punching failure of slab without shear reinforcing (Beutel 2002)
When the slab has been reinforced with shear reinforcing in the area around the column the reinforcing stirrups, clips or studs bridge the cracks and prevents the conical concrete plug to separate from the rest of the slab. The behaviour of a slab-column connection with shear reinforcing is illustrated in Fig 1.5. The shear reinforcing also causes cracking to migrate away from the column. If the shear capacity of the concrete outside the shear-reinforced zone is insufficient the failure will be similar to a connection without shear reinforcing.
Fig. 1.5 Punching failure of slab with shear reinforcing (Beutel 2002)
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Fig. 1.6 Punching failure zone evident on top of a failing slab (Wood et al 1998)
In the event that the moment transfer to the column is negligible, the punching failure would typically be similar to the failure pattern shown in Fig 1.6. However, when moment transfer is more significant, the circumferential degradation would only be visible on one side of the column – corresponding to the stress distribution indicated in Fig 1.7.
1.3. Punching failure due to lateral loading of the structure It is common practise to design multi-storey buildings with two independent structural systems. The first for resisting gravity loading and the second to resist lateral loading imposed by wind and earthquake excitations, where applicable. In most cases these two systems are designed independently.
However, due to building drift and the flexibility of the gravity resisting structure (mostly reinforced concrete or post-tensioned slabs) unbalanced moments develop over the columns. The stresses caused by the moment transfer to the columns are additional to the stresses caused by the normal gravity loading –Fig 1.7.
(a)
(b)
Fig. 1.7 Shear due to gravity loading (a) and unbalanced moments (b)
18
Consequently slab-column connections may fail at gravity loads below their intended design scope if significant effects of lateral loading are present.
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2. Proposed Analytical and Empirical Models Various approaches to predict punching shear resistance have been formulated in the available literature and the numerous structural design codes. In this section two interesting approaches will be studied. Firstly the method proposed by Menétrey, a particularly rigorous method, taking different components of resistance into account. Secondly a method proposed to include the beneficial shear properties of fibre reinforcing will be overviewed. In the next chapter the different approaches of various design codes will be compared.
2.1. Synthesis of Punching Shear Failure, as proposed by Menétrey (2002) Menétrey presents a general model for predicting the punching capacity of a slab. The punching resistance of the slab is obtained by integrating the vertical components of the tensile stresses around the punching crack. The contribution of flexural reinforcing, shear reinforcing, prestressing tendons and the inherent resistance of the concrete are accounted for by means of addition of the vertical components of tensile forces of each crossing the punching crack.
2.1.1. Experimental results The tests conducted by Menétrey focused on the difference between flexural- and punching failure of slabs. Flexural and punching failure can be distinguished with the help of a load vs. deflection plot for the test, see Fig 1.1. A steep capacity drop for increasing deflection characterizes punching failure, while flexural failures show a rather steady decrease in load carrying capacity with increased deflection.
The experiments show that increasing the cross-sectional area of the flexural reinforcing can increase the failure loads. However, by increasing the bending steel even more, a transition is made from a flexural, fairly tough failure to brittle punching shear failure at higher loads.
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Another experimental observation was that controlling the shape of the punching cone, i.e. different cone inclinations, it is possible to reveal a transition between punching and flexural failure.
The inclination of a pure punching failure crack is in the order of 30°. This is reported both by Menétrey and Mervitz (1971), who studied a series of flat slab punching experiments. However, Menétrey managed to control the inclination of the punching crack artificially. Placing a reinforcing ring concentrically around the column position and varying the ring radius achieved control of the crack inclination, since the shear crack always crossed the reinforcing ring. By increasing the crack inclination (), see Fig 2.1, the behaviour became less brittle. The most ductile failure was achieved at = 90°. This angle in fact implies flexural failure, as the crack is perpendicular to the flexural stresses in the slab.
Fig. 2.1 Punching cone shape enforced by steel ring reinforcement By denoting the failure load for 30 0 as the punching load Fpun, and the load at flexural failure ( 90 ) as Fflex, these results could be fitted with the following expression:
F fail Fpun F flex Fpun sin 0 2 0
(2.1)
2.1.2. Numerical simulations Finite element analyses were performed by Menétrey (2002) to study the slab column interaction. Thereby insight was gained, leading to the
21
eventual formulation of an analytical expression for punching shear capacity prediction.
2.1.2.1. Model description Axi-symmetry was considered for analysing punching shear in round plates. Finite element analysis enabled the consideration of the complicated stress state in the structure. As failure criterion, the concrete constitutive law developed by Menétrey & William (1995) was considered. The dilatancy observed experimentally is matched to a specific flow rule. Concrete cracking is described using a smeared crack approach with a strain softening formulation. For this softening Hillerborg, et al‟s (1976) fictitious crack model is used for reducing the tensile stresses (t) as controlled by the crack opening (w) and the fracture energy, which is defined as the amount of energy absorbed per unit area in opening of the crack from zero to the crack rupture opening wr. wr
G f t dw 0
(2.2)
The fracture energy is forced to be invariant with the finite element size by adoption of the crack band concept by Bazant and Oh (1983). The connection between the brittleness of failure and the state of stress is reproduced by the introduction of a fictitious number of cracks.
2.1.2.2. Simulation of the punching failure The analyses were done on slabs similar to those of Kinnunen & Nylander (1960). These slabs were chosen because of their perfect axially symmetric geometry. The cracking phenomenon in the vicinity of the column is clearly shown by the simulation, in reasonable agreement with experimentally observed cracking.
The punching crack is initiated by the coagulation of micro cracks at the top of the slab. As the vertical displacement increases, the inclined crack expands towards the corner of the slab-column intersection.
22
Simultaneously the other inclined micro cracks are closing. Failure occurs when the inclined crack reaches the corner of the slab-column connection.
The crack angle is found to be approximately 45°, as opposed to the 30° reported earlier. This phenomenon is ascribed to the effect of the upper layers of flexural reinforcing, which directs the initially 40°-45° shear crack to an eventual 30° by delamination along the longitudinal reinforcing. This observation was also made by Mervitz (1971).
2.1.2.3. Parametric analysis Having found reasonable numerical results, a parametric analysis was performed on a circular slab reinforced with orthogonally placed reinforcing. Partial bond between the concrete and reinforcing steel was simulated by means of rigidly fastening the reinforcing element to the concrete at the end of a fictitious fastening length. This fictitious length allows some cracks to grow, while others close. The fictitious length is related to the observed spacing of cracks in tensile tests of reinforced concrete.
In Fig 2.2 and Fig 2.3 it is shown that the load capacity increases with increased uniaxial tensile strength of the concrete, as well as with increasing fracture energy.
23
Fig 2.2 Influence of tensile concrete strength on response curves (Menétrey 2002)
Fig 2.3 Influence of fracture energy on response curves (Menétrey 2002)
By varying the percentage of flexural reinforcing the following can be shown: Firstly, all the slabs show a similar cracking pattern, regardless of the percentage of longitudinal flexural reinforcing. Secondly, all the slabs show similar initial elastic behaviour. Lastly it is shown that the post-elastic behaviours vary considerably with varying percentages of reinforcing. The higher the reinforcing ratio is, the higher is the failure load, and with increasing reinforcing percentages the ductility of the connection decreases. This is in agreement with the experimentally observed transition from flexural, tough failure to high capacity brittle punching failure.
24
Fig 2.4 Influence of the percentage of flexural reinforcing on response curves (Menétrey 2002)
The size effect was simulated using varying slab thicknesses with similar scaling factors applied to the concrete geometry and reinforcing steel area, while the boundary conditions and material characteristics remained similar. The nominal shear stresses at failure were computed as follows:
n
Pfailure
2 rs d d
(2.3)
d
Effective depth of the slab
Pfailure
Failure load
rs
Column radius
n
Nominal shear stress
Assuming constant fracture energy, the size-effect law by Bazant & Cao (1987) can be used. The experimental data is adjusted using the RILEM recommendations for linear regression yielding the following equation: 1
d 2 n 1.55 f t 1 34
(2.4)
d
Effective depth of the slab
ft
Uniaxial tensile strength of the concrete
n
Nominal shear stress
25
Fig 2.5 Size-effect law obtained by numerical analysis (Menétrey 2002)
2.1.3. Analytical Model The model is based on the assumption that the punching load is influenced by the tensile stress in the concrete along the inclined punching crack. The magnitude of the punching load is obtained by integrating the vertical stress components along the punching crack and summation of the vertical force components of the flexural reinforcing, shear reinforcing and prestressed tendons crossing the punching crack. Thus the general formulation is: Fpun Fct Fdow Fsw Fp
Fct
(2.5) Vertical component of concrete tensile force
Fdow
Dowel force contribution by the flexural reinforcing
Fsw
Vertical components of force in the shear reinforcing
Fp
Vertical components of force in the prestressing tendons
Even though punching failure is sudden it is due to the amalgamation of micro cracks. This formation takes place progressively and consequently the steel forces are activated gradually and can be added to the tensile concrete forces.
26
Fig 2.6 Typical cross-section showing relevant parameters (Menétrey 2002)
2.1.3.1. Punching- vs. Flexural capacity The influence of the inclination of the punching crack can be expressed by equation 2.1, with 30 90 .
The following special cases can be highlighted:
Ffail = Fpun
Ffail = Fflex
Menétrey calculated Fflex using the following equation: F flex
2 mr r 1 s re
(2.6)
mr
Bending moment resistance
rs
Column radius
re
Radius of the slab
2.1.3.2. Tensile force in the concrete The punching crack is assumed to form the border of the punching cone. The bottom radius is defined as r1 and the top radius as r2.
27
r1 rs
d 10 tan
r2 rs
d tan
(2.7) (2.8)
Subsequently the inclined length is:
s
r2 r1 2 0.9 d 2
(2.9)
In order to simplify the formulation, a constant stress distribution is assumed, leading to the vertical component of the concrete tensile force being: Fct r1 r2 s v r1 r2 s f t 3 2
(2.10)
The shear resistance is seen to be proportional to the concrete tensile strength to the power 2/3, i.e. Fct f t
2 3
(2.11)
From the results of the numerical simulations, Menétrey determined the influence of the percentage of longitudinal reinforcing to be approximated by the following relations:
0.1 2 0.46 0.35 for 0 2% 0.87
for 2%
(2.12)
The size effect is incorporated in the formulation with the following expressions : d 1.6 1 da
1
2
da
with
d 3d a
(2.13)
Maximum aggregate size
28
In order to predict the failure load of a slab with shear reinforcing and a failure outside the shear reinforced area the parameter is used. 2
r r r 0.1 s 0.5 s 1.25 0 s 2.5 h h h for rs 2.5 for h
0.625
(2.14)
2.1.3.3. Contribution of the dowel effect According to Menétrey the contribution of longitudinal reinforcing crossing the punching crack can be evaluated as being equal to: Fdow
1 s2 2 bars
f c f s 1 2 sin
(2.15)
s
s
fs
(2.16)
Fpun
(2.17)
tan As bars
s
Bar diameter
s
Axial tensile stress in reinforcing bar
fs
Reinforcing yield strength
Angle between punching crack and reinforcing, in the vertical plane
2.1.3.4. Contribution of the shear reinforcing Different types of shear reinforcing are used to increase the failure load of slabs and to lessen the sudden decrease in load carrying capacity of the slab, i.e. to improved post-peak ductility. Generally systems such as studs, stirrups, bent-up bars and bolts are used.
Three different positions of the punching crack are possible at failure. 1. Punching crack between the column face and the first row of stirrups.
29
The calculation should consider the interaction between the punching load and the flexural capacity in terms of the crack inclination and the bending failure load. rswi rs d
1 arctan
(2.18)
Fig 2.7 Crack position 1.
2. Punching crack outside the shear reinforced area. The capacity of this scenario is calculated in a way similar to a slab without shear reinforcing. Instead of using the column radius (rs), the radius of the outermost row of reinforcement (rsc) should be used. The size effect is to be considered using the parameter .
Fig 2.8 Crack position 2.
3. Punching crack crossing the shear reinforcing.
30
Fig 2.9 Crack position 3.
The ultimate punching load is to be the minimum value calculated from the three cases presented above.
The punching load in scenario 3 can be calculated as follows:
Firstly some distinction is to be made with regard to the bond properties of the shear reinforcing. Reinforcing made of plain bars will be denoted as studs, and those made with high bond (deformed) bars will be denoted as stirrups.
The contribution of injected strengthening bolts, installed after drilling through the slab, will be determined similar to either stirrups or studs, depending on their respective bond properties.
Interestingly Menétrey & Brühwiler (1997) found that noninjected bolts do not interact and consequently the concrete- and shear reinforcing contributions cannot be added.
31
Fig 2.10 Crack formation in a stud-reinforced slab
The failure mechanism is initiated by the formation of micro cracks. Due to the crack formation the slab depth increases and resulting in the reinforcing bars to start taking load. The studs are subjected to displacement controlled loading. The displacement corresponds to the summation of the micro cracks opening.
The stud elongation at failure can be expressed as: l wr cos
(2.19)
Consequently the deformation is: sw
wr cos l
(2.20)
The crack rupture opening (wr) is approximated as: wr
5Gf
(2.21)
f sw
The maximum force can then be expressed as: Fsw
A
sw
studs
E sw
5Gf f sw l cos
sin sw Asw f sw sin sw Fswy
(2.22) Up to a stud length l0 the force is limited by the yield strength. However, if the stud length exceeds l0 the
32
reinforcing contribution decreases at a rate inversely proportional to the stud length.
l0
wr cos E sw f sw
(2.23)
The contribution of high bond bars can be evaluated in a similar way. Due to the micro crack formation and the increased slab depth the generated tensile forces in the bars are distributed beyond the micro crack zone by means of bond stress to the concrete along the transmission length. The transmission length is defined as the length of bar along which slip between the steel bar and concrete occurs. If the necessary length is available the yield stress of the stirrup can be reached. Fsw
A
sw
f sw sin sw Fswy
(2.24)
stirrups
If the required length is not available, the force developed in the stirrup is a function of the anchorage at the stirrup‟s extremity.
2.1.3.5. Contribution of prestressing tendons Taking the contribution of inclined prestressing tendons into account can enhance the punching shear resistance of a slab.
Fp
A
p
p sin p
(2.25)
tendons
2.2. Proposed Punching Capacity Increase due to the use of Fibre Reinforced Concrete Harajli et al (1995) propose a design equation to predict the increased resistance to punching shear failure of flat slabs by using deformed steel fibre reinforcing in the concrete. The equation is based on a number of small-scale test specimens. These tests were also compared to work done by Alexander & Simmonds (1992).
33
Due to the brittle nature of punching shear failure, it should be avoided at all costs. The general design philosophy of the North American codes (ACI & CSA) is to design flexural members in such a way that the structure develops a yield mechanism and therefore fails in a ductile, flexural manner.
From this point of view and the known fact that fibre reinforcing enhances the mechanical properties of concrete, by controlling crack growth, numerous researchers have investigated the influence of fibres on slab-column connections. Fibre reinforcing leads to higher load carrying capacities, improved ductility of shear failure and better energy absorption properties.
However, experimental studies are still limited and there is no established method to predict the contribution of the fibre reinforcement as a function of the fibre parameters. Harajli et al used the following experimental setup to calibrate the capacity enhancement due to fibres:
2.2.1. Experimental testing The panels tested by Harajli et al (1995) consisted of square slabs (650mm x 650mm) with a monolithically cast 100mm x 100mm column. Two slab thicknesses were used, i.e. 55mm and 75mm. The specimens are representative of slabs setups with span-depth ratios of 26 and 18 respectively. Two identical slabs for each different input variable were tested to minimize possible scatter.
The slabs were rather heavily reinforced ( = 1.12%) in order to ensure that they failed by means of punching prior to flexural failure. Fibre reinforcing consisted of one of the following:
Loose 30/50 hooked steel fibres (30mm long, 0.5mm diameter)
Collated 50/50 hooked steel fibres
12.5mm long monofilament polypropylene fibres
The slabs were reinforced with fibres at the following densities:
80kg/m3 – 1% 30/50 fibres
34
160kg/m3 – 2% 30/50 fibres
35kg/m3 – 0.45% 50/50 fibres
64kg/m3 – 0.8% 50/50 fibres
8.8kg/m3 – 1% polypropylene fibres
Fig. 2.11 Typical specimen cross-section showing reinforcing details (Harajli et al 1995)
2.2.2. Prediction of Punching Shear Strength In order to obtain the design capacity of the connection, the capacity of a normal slab setup without fibres is added to the additional capacity provided by the fibres.
The best-fit equation for the prediction of the additional capacity is:
Pu 0.33 0.075 V f b0 d f c'
(2.26)
Adjusted to a zero y-intercept and a reduction factor of 0.9 a reasonably safe equation follows:
Pu 0.096 V f b0 d f c'
(2.27)
The above equations are limited to cases where fibre reinforcing is less than 2% volume fraction and where the reinforcing used is similar to those of the experiments, i.e. hooked-, crimped-, corrugated- and paddle fibres.
35
2.2.3. Observations and discussions based on the experiments Harajli et al (1995) concluded the following: 1. The addition of steel fibres increased the ultimate punching shear capacity of a slab-column connection by ±36% 2. The increased punching capacity is related to the volume fraction of fibres added and not the length or aspect ratio of the fibres 3. Steel fibres cause the failure mode to change from punching to flexuralor combined flexural-punching failure 4. Improved ductility of shear failures 5. The inclination of the shear failure plane decreased with the addition of steel fibres. This causes the failure surface to move away from the column face, resulting in an increased failure load. 6. Polypropylene fibres led to improved ductility and energy absorption in the post-failure portion of the test. However, the polypropylene fibres made an insignificant difference in the ultimate failure loads.
From the experimental results it is clear that the punching capacity increases linearly with an increased volume of steel fibres. This increase is not significantly influenced by the span-depth ratio of the slabs.
Table 2.1 provides a summary of the behaviour of the two groups of slabs tested, accompanying this the load vs. deflection behaviour of the panels are illustrated in Fig 2.12 and Fig 2.13.
36
Slab
Fibre
Volume
Aspect
Failure
Fraction (%)
Ratio
Mode
Test
ACI
Test/ACI
Normalized Strength A1
-
0.0
-
Punch
0.53
0.33
1.61
A2
Steel
0.45
100
Punch
0.57
0.33
1.73
A3
Steel
0.8
100
Flexural
0.64
0.33
1.94
A4
Steel
1.0
60
Flex-
0.64
0.33
1.94
Punch A5
Steel
2.0
60
Flex
0.64
0.33
1.94
A6
Polypr.*
1.0
0.5in
Punch
0.53
0.33
1.61
B1
-
0.0
-
Punch
0.52
0.33
1.58
B2
Steel
0.45
100
Punch
0.60
0.33
1.82
B3
Steel
0.8
100
Punch
0.61
0.33
1.85
B4
Steel
1.0
60
Punch
0.64
0.33
1.94
B5
Steel
2.0
60
Punch
0.79
0.33
2.39
B6
Polypr.*
1.0
0.5in
Punch
0.60
0.33
1.82 * Polypropylene
Table 2.1 Summary of test variables and results (Harajli et al 1995)
Fig. 2.12 Normalized load-deflection behaviour for Series A slabs
(Harajli
et al 1995)
37
Fig. 2.13 Normalized load-deflection behaviour for Series B slabs
(Harajli
et al 1995)
38
3. Current Design Practice The general approach to determine the punching shear capacity of slab-column connections can be summarized as follows: The shear strength of the concrete is determined on a predetermined critical perimeter (u0 – See Fig 3.1) at a specified distance from the loaded area (i.e. column) – this is to cater for the presence of an inclined shear crack in the assumed region. If the capacity of the system is adequate, the connection can be deemed satisfactory. If the resistance is inadequate, either the slab depth or the cross section of the column needs to be increased. If this is not desired, additional shear reinforcing in the slab depth needs to be provided.
The shear reinforcing provides resistance additional to the shear capacity of the concrete and the dowel action of the flexural reinforcing. In order to determine the amount of reinforcing needed, the required area of reinforcing steel is evaluated on consecutive perimeters (u1, u2, u3, etc.) around the loaded area. Reinforcing is needed up to a perimeter such that the following perimeter under consideration does not need any additional shear reinforcing.
Various prescriptions of what the considered parameters, such as the critical perimeters, contribution of the shear reinforcing, as well as other requirements are given by the different codes. In this chapter the requirements of the most important codified approaches are summarized.
Fig 3.1
Basics of evaluating punching shear capacity of a slab-column connection
39
Due to the unavailability of original copies of certain codes a simplified presentation used by Albrecht (2002) is used for codes marked with **. The simplification uses the following notation:
c1 c 2 2h
(3.1)
d 0.85 h
(3.2)
List of symbols:
c1
First sectional dimension of the column
c2
Second sectional dimension of the column
h
Total height i.e. depth of the concrete slab
d
Effective depth i.e. distance from the centroid of the tension reinforcement to the extreme compression fibre
fyd
Design yield stress of steel
u
Control perimeter
VULS
Ultimate load imposed on the connection
f
Common loading factor determined by the weighted average of the load factors for imposed and permanent loads (live and dead loads)
Percentage of longitudinal tension reinforcing in the considered cross-section
Vrc Vmax
Resistance provided by the concrete Maximum allowed punching shear resistance with shear reinforcing
3.1. German design code – DIN 1045-1988 ** According to the 1988 formulation of the German design code the critical perimeter is calculated as a circle concentric to an equivalent circular column cross section. This circle is a distance 0,5d from the equivalent circular column
40
face. Moment transfer to the columns is ignored if the panel spans differ by less than 33%.
Fig 3.2
Critical perimeter and relevant parameters
The calculations are based upon a circular column cross-section. However, rectangular cross-sections are converted to equivalent circles with radius dst.
d st 1.13 c1 c2
(3.3)
From this the critical perimeter can be determined,
u 1.13 c1 c2 d
(3.4)
It should be noted that the ratio of the side lengths of a rectangular column is limited to less than 1.5. c1 1.5 c2
(3.5)
The contribution by the concrete and the longitudinal tensile reinforcing is expressed as
Vrc
f
2.48 1 1.33 h 2
(3.6)
The maximum shear resistance allowed for slabs with shear reinforcing is
Vmax
f
1.4 Vrc
(3.7)
If the shear force is higher than the capacity of the concrete, shear reinforcing is to resist 75% of the force, i.e. Vsd s 0.75 VULS
(3.8)
41
The required cross-sectional area of shear reinforcing is:
Asv
Vsd f yd
(3.9)
The shear reinforcing is to be placed into two consecutive perimeters. The first placed at 0.5d from the column face and the second at 1.0d from the column face.
3.2. British Standard 8110-1:1997 The requirements of the British standard stipulate that the critical perimeter is a rectangle at a distance 1.5d from the column face.
Fig 3.3
Critical perimeter and relevant parameters
Accordingly the control perimeter is: u 2c1 c2 12d
(3.10)
In order to allow for moment transfer to the column the total shear force needs to be factored. In the absence of detailed calculation, internal column loads in braced structures with approximately equal spans; the enhancement is done with a predetermined factor of 1.15. Veff 1.15 Vt
(3.11)
In case moment transfer is calculated in the structural analysis, the shear load enhancement is determined according to the following equation
1.5M t Veff Vt 1 Vt x
(3.12)
42
At corner columns and edge columns bending about an axis parallel to the free edge an enhancement factor of 1.25 can be used. Veff 1.25 Vt
(3.13)
Alternatively the enhanced shear force for edge columns bending about an axis perpendicular to the free edge can be calculated with the following equation.
1.5M t Veff Vt 1 Vt x
(3.14)
Alternatively the shear force should be enhanced with a factor of 1.4. Veff 1.25 Vt
(3.15)
It should be noted that Mt may be reduced by 30% if an equivalent frame analysis with pattern loading was done.
The maximum stress at the column face is not allowed to exceed the lesser value of:
f max MAX 0.8 f cu ,5MPa
(3.16)
The concrete contribution to the shear resistance is derived as follows: 1
1
100 As 3 400 4 1 f cu vc 0.79 bv d d m 25
1
3
(3.17)
The nominal shear stresses on the specific perimeter under consideration can be calculated with the following equation: v
V ud
(3.18)
If the shear stress at the control perimeter is less than vc, no additional shear reinforcing is needed.
43
The shear stress is to be checked on consecutive perimeters, each taken at 0.75d from the former perimeter, until a perimeter is reached where no shear reinforcing is needed. For the perimeters requiring reinforcing the amount of shear steel is determined as follows:
v 1.6 vc
A
sv
sin
v vc u d 0.95 f yv
(3.19)
1.6 vc v 2 vc
A
sv
sin
5 0.7 v vc u d 0.95 f yv
(3.20)
List of symbols:
As
Cross-sectional area of the longitudinal tensile reinforcing
d
Effective slab depth
fcu
Characteristic concrete cube strength
fyv
Characteristic strength of the shear reinforcing
Mt
Design moment transferred to the column
u
Control perimeter
u0
First control perimeter taken at 1.5d
V
Factored shear force
Veff
Effective shear force
x
Length of the side of the considered perimeter parallel to the axis of bending
Asv
Area of shear reinforcement Angle between the plane of the slab and the shear reinforcing
m
Partial material factor (1.5 for concrete)
44
3.3. ACI 318M-02 The ACI recommendations consider a critical perimeter taken at 0,5d from the column face. Moment transfer to the column is assumed to be due to a stress distribution as indicated in Fig 3.4.
Fig 3.4
Critical perimeter, relevant parameters and shear distribution due to
moment transfer
For non-prestressed members Vc should be taken as the lesser value of the following:
24 Vc 1 c
f c' b0 d 6
(3.21)
d Vc s 2 b0
f c' b0 d 12
(3.22)
s
Critical Section with:
40
4 Sides, i.e. internal columns
30
3 Sides, i.e. edge columns
20
2 Sides, i.e. corner columns
Table 3.1 Shear enhancement factors Vc
1 3
f c' b0 d
(3.23)
For prestressed members Vc should be taken as
Vc p f c' 0.3 f pc b0 d Vp
(3.24)
with -
s – As above
45
-
sd 1.5 b p MIN 0.29; 0 12
-
Vp – The vertical component of prestress
-
c is to be taken as the ratio of the longest overall dimension of the
(3.25)
effective loaded area to the largest overall perpendicular dimension of the effective loaded area. The effective loaded area is taken as the area that totally encloses the actual loaded are, for which the perimeter is a minimum.
Shear reinforcement is allowable in slabs where the effective depth is greater than 150mm.
Vn Vs Vc
(3.26)
Vc should be taken as above but not greater than Vc Vs
1 6
f c' b0 d
Av f y d
(3.27)
s
Vn should not exceed Vn
(3.27)
1 2
f c' b0 d
(3.28)
When shear reinforcing is used the yield strength of the reinforcing is limited to 420MPa. The maximum allowable yield strength of the shear reinforcing is an empirical value. The reasoning behind limiting the tensile strength of the reinforcing is that with decreasing slab depth, full yield capacity of the steel is less likely to be reached before punching shear failure takes place.
The required shear reinforcing is placed in the slab similar to shear stirrups in beams – see Fig. 3.5. The control perimeter outside the shear-reinforced zone is taken at a distance 0.5d outside the last line of shear stirrups. However, the shape of the outer control perimeter is quite different from the original control perimeter.
46
When using the ACI recommendations for punching shear design it should be kept in mind that the required integrity steel must be provided and that the tensile reinforcing is adequate to resist bending failure.
Integrity reinforcing is the provision of adequately anchored sagging (bottom) reinforcing that has to be provided through the core of the column.
Fig 3.5
ACI control perimeters and shear reinforcing details (ACI 318M-02)
List of symbols:
Av
Area of shear reinforcing
b0
Critical perimeter
d
Effective depth
fc ’
Characteristic compressive cylinder strength of concrete
fpc
Average pre-stressing stress after losses
fy
Shear reinforcing yield stress
s
Spacing of shear stirrups
Vc
Punching shear capacity of the concrete
Vp
Vertical component of pre-stress force after losses
47
Vs
Punching shear capacity contributed by shear reinforcing
s
Shear enhancement factor
c
Ratio of column dimensions
3.4. Eurocode 2 ** The Eurocode considers a control perimeter with rounded corners at 1.5d from the column face.
Fig 3.6
Critical perimeter and relevant parameters
Moment transfer is considered as a shear force per unit of perimeter.
sd
VULS u
(3.29)
For internal columns the enhancement factor is 1.15
The control perimeter is calculated as:
u 2c1 c2 3d
(3.30)
It should be noted that the ratio of the column side lengths is limited to 2 c1 2 c2
Vrc
f
2.21.2 40 1 0.5 h 2
Vmax 1.6 Vrc
(3.31)
(3.32)
(3.33)
48
If the shear force is higher than the capacity of the concrete, shear reinforcing is used with the total resistance calculated by the addition of the concrete- and steel resistances.
3.5. DIN 1045-1:2001 The latest DIN recommendations are formulated using a critical perimeter taken at a distance equal to1.5d from the column face.
When dealing with rectangular columns or walls the critical perimeters should be taken as indicated in Fig 3.7.
Fig 3.7
Critical perimeter for a rectangular column or wall
a1 MIN a;2b;5.6d b1
b1 MIN b;2.8d
(3.34)
The critical perimeter is selected to be such that it has the shortest length and at a distance 1.5d from the column face – see Fig 3.8.
Fig 3.8
Typical Columns
Penetrations in the close proximity of the column should be taken into account as shown in Fig 3.9.
49
Fig 3.9
Penetrations close to the column
When corner and edge columns are located closer than 3d from edge of the slabs the critical perimeter should be taken according to Fig 3.10.
Fig 3.10
Corner and Edge Columns
The geometrical parameters used in the calculation of the punching shear capacity and the required reinforcing are indicated in Fig 3.11.
Fig 3.11
Calculation Parameters
50
In order to take moment transfer between the slab and the column into account, the enhancement factors given in Table 3.2 are used to increase the shear stress around the column.
Type of Support:
1.05
Internal Column
1.4
Edge Column
1.5
Corner Column
Table 3.2
vEd
Shear enhancement factors
VEd
(3.35)
u
Flat slabs without shear reinforcing should conform to: vEd vRd ,max
(3.36)
Flat slabs with shear reinforcing should conform to the following: The upper limit of the punching capacity is given by
vEd vRd ,max
(3.37)
Within the shear reinforced area vEd vRd ,sy
(3.38)
Outside the shear reinforced area vEd vRd ,ct ,a
(3.39)
Flat slabs without shear reinforcing:
vRd ,ct 0.141 100 l f ck 3 0.12 cd d
1 d
d
x
1
200 2.0 d dy 2
l lx ly 0.40 f cd f 0.02 yd
(3.40) (3.41) (3.42) (3.43)
51
cd
cd , x cd , y
cd ,i
[MPa]
2
N Ed ,i Ac ,i
(3.44) (3.45)
Flat slabs with shear reinforcing:
vRd ,max 1.5vRd ,ct
(3.46)
For the first perimeter of shear reinforcing within 0.5d from the column face vRd ,sy vRd ,c
s Asw f yd u
(3.47)
For the perimeters with reinforcing within spacing sw 0.75d vRd ,sy vRd ,c
s Asw f yd d u sw
vRd ,c vRd ,ct
(3.48) (3.49)
0.7 s 0.7 0.3
d 400 1.0 400
(3.50)
Bent down bars within 0.5d from the column face is considered using the following equation: vRd ,sy vRd ,c
1.3 As sin( ) f yd u
(3.51)
Outside the shear reinforced area the critical perimeter is taken as 1.5d from the last row of shear reinforcing, with vRd ,ct ,a a vRd ,ct
a 1
0.29lw 0.71 3.5d
(3.52) (3.53)
List of symbols:
Ac
Cross-sectional area of concrete under consideration
Asw
Area of shear reinforcing in the considered perimeter
52
d
Effective depth of the tension steel
fck
Design crushing strength of a standard cylinder
fyd
Design yield strength of reinforcing steel
lw
Radial distance from the column face to the last reinforcing row
N
Axial force on the above mentioned crosssectional area
sw
Spacing of the shear reinforcing
u
Critical perimeter
VEd
Imposed axial column load
vEd
Design shear stress
VRd
Design resistance shear load
vRd
Design resistance shear stress
Angle of the bent down bar measured from horizontal. 45o 60o
Factor f moment transfer
Shear enhancement factor
1
1.0 for normal concrete – refer to DIN1045-1 for lightweight concrete
Size effect factor
s
Effectiveness factor of shear reinforcing
cd
Effective pre-stress in the considered crosssection
3.6. CSA A23.3 ** The Canadian building code considers a critical perimeter taken at 0,5d from the column face. Moment transfer between the slab and column is similar to the assumptions of the ACI-318 code – Fig 3.12.
53
Fig 3.12 Critical perimeter, relevant parameters and shear distribution due to moment transfer
The control perimeter is:
u 2c1 c2 4d
(3.54)
The contribution of the concrete and longitudinal reinforcing is given by:
Vrc
f
4.59100 3 1 0.37 h 2 1
(3.55)
The upper limit of resistance is set as:
Vmax 12.82 f h 2
(3.56)
Similar to the ACI recommendations the capacity of the concrete and the shear steel can be added together. In principle the ACI and CSA approaches are similar, but the detailing of the shear reinforcing differs. According to the ACI the shear reinforcing is fixed as beam strips, while the CSA method uses evenly arranged reinforcing on the control perimeters.
3.7. CAN/CSA-S6-00 Canadian Highway Bridge Design Code According to the Canadian Bridge Code the shear resistance of slabs should be the more severe of the following cases: 1.
Beam action, with a critical section extending in a plane across the entire width and located at a distance, d, from the face of the concentrated load or reaction area, or from any change in slab thickness.
2.
Two-way action, with a critical section perpendicular to the plane of the slab and located so that its perimeter, u, is a minimum. This perimeter need not be closer than 0.5d to the perimeter of the concentrated load or reaction area. The shear resistance should also be checked at critical
54
sections located at a distance no closer than 0.5d from any change in slab thickness and should be located such that the perimeter, u, is a minimum.
The shear resistance for two-way action is calculated as follows Vr V f
(3.57)
Vr c f cr 0.25 f pc u d p Vp
(3.58)
List of symbols:
d
Effective depth – distance from the extreme compression fibre to the centroid of the tensile force (mm)
fcr
Cracking strength of concrete (MPa)
fpc
The average of the compressive stresses in the two directions in concrete after all prestress losses have occurred, at the centroid of the cross-section (MPa)
u
Perimeter of the critical section (mm)
Vf
Shear demand (factored applied load) (kN)
Vp
Shear resistance provided by reinforcing (kN)
Vr
Shear resistance (kN)
c
Material resistance factor for concrete (0.75)
p
Material resistance factor for reinforcing (0.95)
55
3.8. Comparisons of code equations for punching shear with and without shear reinforcing – standardized approach. In order to compare the provisions made for punching shear by the various codes the method used by the International Federation of Structural Concrete (fib) will be presented.
The fib has done extensive research on the topic of punching shear and the related performance of available codified approaches to the problem of punching shear failure. In their publication “Punching of Structural Concrete Slabs” (2001) a comparison of the available test data and commonly used design code predictions are presented. In order to compare the different codes standardization was necessary. The results of their standardization and comparisons are overviewed in the following sections. Nominal punching shear stress is taken as a shear force ( F VF ), divided by a control surface around the loaded area. The resistance partial shear factor to avoid punching failure is determined by comparing the nominal shear stress of tests with a strength parameter of the concrete.
To determine admissible punching shear strength, partial safety factors for the actions (imposed loading) and resistances (material characteristics) are used.
VF F
VR
(3.59)
R
This states that the demand is less than the capacity of the system. Standardization of the punching shear capacity or resistance is done by considering the concrete shear resistance and that of the reinforcing steel superimposed as follows:
VRd
R
Vc
c
Vs
s
Vc ,outside
c
Vmax
c
(3.60)
where the concrete shear capacity is
56
Vc c k f ( l ) u d
(3.61)
and the steel shear capacity contribution is Vs Asw s f y sin( )
(3.62)
List of symbols:
Asw d f(l)
Cross sectional area of the shear reinforcing Effective depth Function of the longitudinal tension reinforcing
fy
Yield strength of the shear reinforcing
k
Size effect factor of the effective depth
u
Control perimeter
Vc
Characteristic punching resistance without shear reinforcing, or the contribution of the concrete to the punching shear capacity in the presence of shear reinforcing
Vc,outside
Characteristic shear capacity outside the shear reinforced area
Vf
Characteristic value of the acting force
Vmax
Characteristic maximum shear capacity
VR
Punching shear capacity
Vs
Characteristic shear capacity of the shear reinforcing
l,g
Ratio of the longitudinal tension reinforcing
Inclination of the shear reinforcing
c
Partial material factor for the concrete
f
Partial safety factor for the imposed forces
s
Partial material factor for the reinforcing steel
s
Efficiency of the shear reinforcing
c
Concrete shear capacity
57
In the following sections the standardised fib formulation of the different codified approached are presented.
3.8.1. German design code DIN 1045 (88) The German code considers the cube strength of the concrete and the flexural reinforcing ratio as input parameters. The control perimeter is to be taken at a distance d from the column face. Punching cones inclined at angles between 30 and 45 were considered in the formulation. The concrete contribution was calculated to be 25% of the ultimate load capacity. It should be noted that punching shear failures outside an area of 1.2d was not investigated.
Safety factors:
Resistance without shear reinforcing
c
2.10
s
1.75
2
c c 011; 011 0.056 f cu , 200 3
(3.63)
f ( l ) 1.3 s g
(3.64)
s 0.7 1
fy 500 f cu , 200
0.5% g 25
g
Outside shear reinforcing
Maximum shear capacity
(3.65)
fy
Asl ,beamstrip 100% bbeamstrip d
1.5%
(3.66)
(3.67)
Not investigated
Vmax c 2 02 u d 2
02 0.21 f cu , 200 3
(3.68) (3.69)
58
Within the shear reinforced area
Additional rules
2 s 0.45 g
(3.70)
Vc 0.25 VF
(3.71)
Vs Asw f y sin( )
(3.72)
Slab to be no less than 150mm thick. Stirrups to enclose tension and compression flexural reinforcing. Rectangular columns can be transformed into round columns if
a 1.5 and the cross sectional area b is the same.
3.8.2. Eurocode 2 (EC2) The Eurocode recommendations for punching shear failure consider the following parameters:
Concrete cylinder strength
Flexural reinforcing ratio
Size effect of the effective slab depth
Shear capacity of the shear reinforcing
Safety factors:
Resistance without
c
1.50
s
1.15
2
c c 0.035 f c 3
shear
(3.73)
reinforcing (Vc) k 1.6 d 1
(3.74)
f ( l ) 1.2 40 l
(3.75)
59
l 1.5%
(3.76)
Resistance
Similar to above under consideration of
outside the
an exterior control perimeter
shear reinforced area (Vc,outside) Maximum
Vmax 1.6 Vc
shear
(3.77)
capacity (Vmax) Resistance
Vc Punching capacity without shear
within the
reinforcing
shear reinforced area (Vc + Vs )
Vs Asw f y sin( )
(3.78)
h 200mm
(3.79)
Asw _ MIN 0.6 c
Akrit Aload
(3.80)
sin( )
0.11% c 0.13%
l
Asl ,control_ perimeter
(3.81)
control_ perimeter d
Some authors have criticized the Eurocode formulation and have suggested the following changes. Firstly, the function expressing the influence of the concrete strength should use the power 1
2 3
instead of
3.
Secondly the shear strength c should be increased by 20% and lastly, the
60
efficiency of the stirrups used as shear reinforcing should be changed to 50-60% instead of 100%. 1
c c 1.2 0.09 f c 3
(3.82)
Vs (0.5 _ or _ 0.6) Asw f y sin( )
(3.83)
According to Kordina (1994) the punching shear strength without shear reinforcing in the EC2 control perimeter is 20% more than the uniaxial shear capacity. In order to rectify this discontinuity the following two ways can be used. (1) The punching shear strength is defined as the uniaxial shear strength, while the higher punching shear capacity is judged using a large control perimeter. (2) Using a fixed control perimeter with a transition zone the difference between punching shear strength and the uniaxial shear strength can be incorporated. Kordina (1994) showed that the control perimeter of EC2 could be increased. Due to this increase in control perimeter the local shear stress concentrations diminish and consequently the geometry of the loaded area on the acting shear stress can be neglected for low-level loads. For highlevel loads (i.e. slabs with shear reinforcing) the stress concentrations cannot be neglected and should be limited.
3.8.3. British Standard 8110-1:1997 The BS8110 prescriptions for punching shear design consider the following parameters:
Concrete strength
Flexural reinforcing ratio
Size effect of the effective slab depth
Shear capacity of the shear reinforcing
61
The 1997 revision of the code takes the beneficial membrane forces acting in a cracked flat slab into account. The inclination of the punching shear crack has also been adjusted from 45º to 33º, causing a reduction in the required shear reinforcing by up to 50%.
Safety factors:
Resistance without
c
c
1.25
s
1.15
1 1.5 d 0.27 f cu 3 av
shear
(3.84)
reinforcing (Vct) Where av is the distance from the column face to the control perimeter
k4
400 d
(3.85)
f l 100 l 3
(3.86)
l 3%
(3.87)
1
Resistance outside the shear
Similar to above under consideration of an
reinforced
exterior control perimeter
area (Vc,outside) Maximum shear capacity
5 Vmax 2.0 Vc u0 d MIN 0.8; f cu
(3.88)
(Vmax)
62
Resistance
Vc Punching capacity without shear
within the
reinforcing
shear
Vs Punching capacity provided by shear
reinforced
reinforcing
area (Vc +
Vsf Applied shear force
Vs ) If v f 1.6vc then
Vs 0.95 Asw f y sin( )
(3.89)
If 1.6vc v f 2vc then (3.90)
Vc 1.42Vc
Vs 0.27 Asw f y sin( ) Minimum shear
A
sw
sin( ) 0.4ud
1 0.95 f y
(3.91)
(3.92)
reinforcing
3.8.4. ACI 318-95 The ACI code takes the following parameters into account for estimating the punching shear resistance:
Concrete strength
Column geometry
Length of the control perimeter
The code does not take the influence of the longitudinal tension reinforcing into account.
Safety factors:
c
1.176
s
1.176
Resistance without
The Minimum value of the following:
shear
c 0.33 f c
(3.93)
reinforcing (Vc)
63
4
c
c 0.083 f c 2
(3.94)
0 d c 0.083 f c 2 u resp u ext
(3.95)
Resistance outside the shear reinforced
Similar to above under consideration of an exterior control perimeter
area (Vc) Maximum shear capacity of
Vmax 0.5
fc u d
(3.96)
stirrups (Vmax) Resistance within the shear reinforced
Vc 0.167 f c ud
(3.97)
area (Vc + Vs ) Vs Asw f y
f y 414 MPa
(3.98)
Typical shear reinforcing arrangements according to the ACI recommendations, as seen in practise, is shown in Fig 3.13 and Fig 3.14.
64
Fig 3.13 Shear-stud rails on site – detailed and designed according to the ACI-318 recommendations
Longitudinal Reinforcing
Shear Stirrup (Shape Code 72) Lacing Bar
Fig 3.14 Shear stirrups on site – detailed and designed according to the ACI-318 recommendations
3.8.5. DIN 1045-1 (2001) In principle the new DIN code is based on Model Code 90 (fib 1999), thus using the following parameters to estimate the punching resistance of the slab-column connection:
Concrete strength
The flexural reinforcing ratio, i.e. the longitudinal tensile reinforcing
The size effect of the effective depth
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The shear capacity of the shear reinforcing
This code is regarded as the latest and safest code at the moment. It has been calibrated using all available test data published from over the world to conform to accepted reliability criteria.
The codified formulation will be presented in the following parts. 3.8.5.1. Punching shear resistance of a slab without shear
reinforcing The control perimeter is taken at 1.5d. VRd ,ct v Rd ,ct ucrit
(3.99)
v Rd ,ct 0.12 100 l f ck 3 d 1
(3.100)
l 0.4
f cd 0.02 f yd
(3.101)
1
200 2 d
(3.102)
d
Effective depth [m]
fck
Characteristic compressive concrete strength [MN/m2]
ucrit
Control perimeter [m]
VRd,ct
Punching shear resistance [MN]
vRd,ct
Punching shear capacity stress [MN/m2]
Size effect parameter
l
Flexural reinforcing ratio
3.8.5.2. Maximum punching shear capacity The maximum capacity has been confirmed by testing to correlate with the load level at which crushing of concrete at the column face occurs.
66
VRd . max 1.7 VRd ,ct
(3.103)
3.8.5.3. Punching shear strength within the shear reinforced area Within the shear reinforced area the resistance is provided by a constant concrete contribution and by the shear strength of the shear reinforcing. The level of contribution decreases with increasing distance from the column. Due to stirrup anchorage slip the shear strength of the reinforcing is limited to 70% of yield strength in thin slabs. VRd ,sy,i vRd ,sy ui
v Rd ,sy vcrd
(3.104)
s Asw,i f yd ui
vcrd v Rd ,ct 0.7 0.7 0.3
(3.105) (3.106)
d 400 1.0 400
d
Effective depth [mm]
fyd
Reinforcing design yield strength
ui
Perimeter of each stirrup row [m]
VRd,sy,i
Shear capacity in every stirrup row i
vRd,sy
Shear capacity in every stirrup row per
(3.107)
meter
s Aswi
Effectiveness factor of the shear reinforcing Sum of the stirrup cross-sectional area in each row
3.8.5.4. Punching shear strength outside the shear reinforced area It is assumed that the control perimeter is located at a distance 1.5d from the last row of stirrups.
67
VRd ,cta v Rd ,cta ua
(3.108)
vRd ,cta a vRd ,ct
(3.109)
a 1
0.167 l w 0.83 3.5 d
ua
Exterior control perimeter
lw
Radial distance between the column face
(3.110)
and the last row of stirrups
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4. Accuracy of Modelling and Codified Design Rules In order to formulate the mathematical modelling of punching shear behaviour and prediction of punching shear failure, representative experimental models of structures, or part thereof are needed.
4.1. Accuracy of Experimental Testing Due to the complexity of the punching shear problem, any analytical model has to be based on, or verified with experimental test results to a certain extent. Experimental testing of punching shear presents numerous problems.
Testing of real structures is not feasible due to the tremendous costs involved and the large scale of such a test setup. The only practical option is to test representative parts of the structure either at full scale or scaled down.
Most of the punching shear tests undertaken to date were done using single column tests with little attention given to the boundary conditions of the slab portion used. The validity of this approach is explained in the following sections.
4.1.1. Single Column Tests In most cases the dimensions of isolated slab-column are selected to coincide with the lines of contra flexure in the real structure. In other words, the region of negative moments in the real slab is used for a single slabcolumn test.
These tests are relatively inexpensive and allow full scale testing. However, there are a number of disadvantages in using a single column setup:
Simulation of real boundary conditions is ignored
Confinement of the concrete is ignored
Membrane forces in the slab is not present
Failure shear stresses are not influenced by the size effect (The size effect causes a reduction of shear strength with increasing slab depth)
69
Load redistribution is not possible
Two different configurations of a single column test are possible. The two setups should not be perceived as similar. Firstly the slab can be supported on its boundary with the load applied on the column. This setup allows the forces to distribute along the boundary. Secondly the slab specimen can be supported on the column with the load applied at a fixed distance from the column.
4.1.1.1. The effect of boundary conditions Elstner & Hognestad (1956) tested the effect of different boundary conditions in 1956. They set up three scenarios. Firstly, a square slab with continuous simple supports along all four edges. Secondly, a similar slab with continuous simple supports on two opposing edges and lastly the four corners were simply supported.
A linear elastic finite element analysis on the three scenarios renders similar shear stress distributions for all three cases. However, the actual testing reveals a decrease in the punching shear capacity with decreasing support provided to the slab boundary.
If the failure loads are normalized with respect to
f c' , the capacities
reduce from 100% for a slab with all four edges supported, to 85% for two opposing edges supported, to 60.4% for a slab with corner supports only. It seems that boundary forces develop in slabs supported on all edges. These forces enhance the shear capacity of the slab-column connection.
It should be noted that the effect of the moment to shear ratio is included in these tests. This ratio will be the highest for the slab supported on all four edges and consequently a higher punching shear capacity can be expected.
70
Alexander and Simmonds (1992) reported similar results by using three test scenarios providing rotational restraints with rollers. Firstly they used a slab with rotations of the corners and edges restrained, secondly, rotations of the edges alone restrained and thirdly rotations of the corners alone restrained. The normalized capacities of these tests are 100%, 89.7% and 82.1% respectively. Evidently increasing rotational restraint enhances the punching capacity of the connection.
The punching shear strength of a slab is also influenced by the shear span ratio ( av d ), where av is the shear distance, i.e. the distance from the loaded area to the support, and d the effective slab depth. Although test data on the influence of the shear span ratio is rather limited, it is safe to say that shear strength rises significantly for ratios less than 1.5, but remains fairly constant for higher ratios – fib (2001). Thus if the supports are too close to the applied load, they interfere with the results. According to the fib (2001) it is reckoned that a distance of at least three slab thicknesses is necessary between the loaded area and the slab supports.
4.1.1.2. The effect of compressive membrane action Due to the confinement of the slab-column connection by the adjacent slab it also plays a role in the punching shear capacity of the connection.
Compressive membrane action is considered as a secondary effect, which occurs after cracking of the concrete and yielding of the reinforcing steel. As the slab fails and deflects, the surrounding concrete restrains the sagging portion of the slab by compressing around it.
It has been found that the punching shear capacity increases if the slab specimen extends beyond the nominal line of contra flexure. Testing by Bond, Long, Masterson and Rankin indicate strength
71
increases ranging from 30% up to 50% compared to similar single column setups.
Due to numerous reasons their test is thought to overestimate the capacity enhancement. In addition to these, real slabs undergo restrained shrinkage inducing tensile stresses, which in turn reduces the shear capacity of the slab.
For design purposes compressive membrane action should not be used as an enhancing factor for the predicted failure loads.
4.1.2. Slab subsystems It is believed that a subsystem will render more realistic results than a single column test. Sherif (1996) tested the most realistic subsystem to date.
The slab consisted of a 150mm thick, continuously reinforced slab with realistic boundary conditions along lines of zero shear centred on an exterior column and an adjacent interior column.
Testing of this slab resulted in the conclusion that the punching shear capacity for interior slab-column connections is similar for both single column tests and full slab tests.
4.2. Accuracy of Code Predictions Numerous punching shear tests have been done to date and most of the codified design approaches are based on a limited number of these tests. The biggest complication is that almost each code was developed from a different set of experiments and that the various codes use different parameters to predict the punching shear resistance of slab-column connections.
However, the fib technical report on punching shear - Bulletin 12 (Reineck et al 2001) presents a database of more than 400 punching shear test results as well
72
as a comparison of the prediction performance of the different codified approaches.
4.2.1. Compilation of databank In order to compile a set of data for the neutral comparison of code formulas all available test data went through a rigorous classification and filtering process performed by the fib task group.
150 of the more than 400 available test results were of flat slabs with shear reinforcing. The following significant observations were made:
All tests, except five were done with isolated slab-column connections.
49% of the tests used stirrups and 34% used bent-up bars as shear reinforcing. Hooks and shear ladders account for 17% of the tests.
Some of the older publications give no indication of the mode of failure. The other reports indicated 30% failed outside the shear reinforced zone, 25% failed at the column face and 45% of the slabs failed within the shear reinforced zone.
90% of the tests were done on plates with total depths less than 250mm. This raises some concern, since flat slabs in practise range between 250mm and 350mm in depth, while foundation plates are normally thicker than 500mm.
Due to the fact that only thin plates were tested, the following should be kept in mind. Firstly, there is a beneficial size effect if failure is due to crushing of the concrete. Secondly it should be kept in mind that the anchorage of stirrups and shear ladders in the compression zone was underestimated because the height of the compression zone is in the range of the concrete cover.
Only nine specimens were tested with high strength concrete.
73
4.2.2. Comparisons between Design Code Rules and Experimental Results for Flat Slabs without Shear Reinforcing Modern design codes are driven by reliability principles. It is generally accepted that a characteristic value represented by the 5% fractile is acceptable, i.e.
5% avg 1.645
(4.1)
This approach is based on the methods outlined in Eurocode 1.
Using the mean values of material strengths, 149 tests were used in the statistical analysis of punching tests without shear reinforcing. Some application rules of the specific codes necessitated that some test data were not considered for certain codes. The required 5% fractile of the safety factor, 5%, is 1.0. Comparing the codified capacity predictions with the relevant test results yield the following:
m Vtest Vcode
(4.2)
n/n0
m
v
5%
DIN 1045(88)
84/149
1.22
0.23
0.19
0.84
Model Code 90, FIP
149/149
0.98
0.16
0.16
0.72
BS8110-1:1997
149/149
1.03
0.17
0.16
0.76
Eurocode 2, Part 1 (1992)
112/149
1.28
0.25
0.20
0.87
ACI318-95
149/149
1.29
0.27
0.21
0.85
DIN 1045-1 (2001)
149/149
1.38
0.23
0.17
1.00
Code
Recommendations
Table 4.1 Statistical results of codified capacity predictions on test slabs without shear reinforcing
Model Code 90 (MC90 1999) and the BS8110 recommendations give the best approximation of the mean behaviour, as seen in Table 4.1. In order to meet the 5% design value the shear capacity predicted by MC90 should be
74
decreased by ±27% and the BS8110 predictions should be decreased ±24%.
Eurocode 2 underestimates the beneficial influence of higher ratios of longitudinal reinforcing; on the other hand it overestimates the contribution of higher strength concretes. In order to bring it‟s predictions to a 5% design value, the concrete contribution should be reduced by ±13%.
Due to the fact that the ACI recommendations ignore the contribution of the longitudinal tensile reinforcing the scatter is unacceptably high. The fib strongly recommends that the longitudinal reinforcing be taken into consideration. The acceptable safety level of 5% will only be obtained if the predicted punching strength is reduced by approximately 25%.
The latest German design code, DIN 1045-1, was calibrated using the above mentioned test data bank; therefore it complies with the required reliability criteria.
4.2.3. Comparisons between Design Code Rules and Experimental Results for Flat Slabs with Shear Reinforcing Similar to the predictions for punching failure without shear reinforcing, the fib compared the 5% fractiles of test slabs with shear reinforcing for three different failure modes. The three considered modes being: -
Concrete crushing at the column face, i.e. maximum shear capacity
-
Failure within the shear reinforced area, i.e. failure of the shear reinforcing
-
Failure outside the shear reinforced area
As seen in Table 4.2 the mean values of the predicted concrete crushing failure are all above the required level, however the characteristic values are noncompliant with the 5% fractile criterion.
75
n/n0
m
v
5%
DIN 1045(88)
81/93
1.29
0.26
0.20
0.86
Model Code 90, FIP
42/141
1.31
0.26
0.20
0.88
BS8110-1:1997
85/141
1.15
0.32
0.28
0.62
Eurocode 2, Part 1 (1992)
37/141
1.26
0.31
0.25
0.74
ACI318-95
13/141
1.27
0.30
0.24
0.78
DIN 1045-1 (2001)
39/141
1.34
0.19
0.14
1.02
Code
Recommendations
Table 4.2 Statistical results of codified capacity predictions for the maximum punching shear capacity of slabs with shear reinforcing
Similarly the mean ratios of the predicted capacities within the shear reinforced area with the test results are more than 1.0, but the 5% fractile does not reach the demanded safety level – see Table 4.3. It should be noted that only 10% of the tests evaluated with DIN 1045(88), Eurocode 2, MC90 and BS8110 failed within the shear reinforced area. On the other hand, 86% of tests evaluated with the ACI recommendations failed within the reinforced area.
n/n0
m
v
5%
DIN 1045(88)
12/93
1.47
0.16
0.11
1.29
Model Code 90, FIP
16/141
1.30
0.29
0.23
0.82
BS8110-1:1997
22/141
1.08
0.25
0.23
0.67
Eurocode 2, Part 1 (1992)
12/141
1.27
0.30
0.23
0.78
ACI318-95
122/141
1.73
0.57
0.33
0.80
DIN 1045-1 (2001)
71/141
1.71
0.41
0.24
1.16
Code
Recommendations
Table 4.3 Statistical results of codified capacity predictions for the punching shear capacity within the shear reinforced area
76
In Table 4.4 it is shown that not all codes comply with the required safety levels outside the shear reinforced zone.
n/n0
m
v
5%
n/a
n/a
n/a
n/a
n/a
100/141
1.18
0.20
0.17
0.86
BS8110-1:1997
34/141
0.91
0.14
0.15
0.68
Eurocode 2, Part 1 (1992)
104/141
1.26
0.31
0.25
0.74
ACI318-95
6/141
(1.25)
(0.36)
(0.29)
(0.66)
DIN 1045-1 (2001)
31/141
1.24
0.14
0.11
1.02
Code DIN 1045(88) Model Code 90, FIP Recommendations
Table 4.4 Statistical results of codified capacity predictions for the punching shear capacity outside the shear reinforced area
4.2.4. Discussion of the Comparison of Test Data and Codified Predictions From the above results it is clear that the different codes predict quite different capacities for the same structure. The predictions also show unacceptably high standard deviations, causing the 5% fractile to be below the required value.
The most obvious explanation for both the different values predicted by the different codes and the high variances in the predicted capacities vs. actual capacities can be attributed to the fact that the different codes were formulated using limited test data.
Due to the variability of the predictions the fib decided to present an improved codified formulation based on all the data presented in the punching shear test databank. Taking the required reliability criteria into consideration this process lead to the development of the latest German DIN 1045-1 design code.
77
5. Proposed Repair Methods for Punching Shear Failure and Preventative Measures against Punching Shear Failure Due to the brittle nature of pure punching shear failure it can easily result in progressive collapse of a structure without much warning of structural distress. However in most cases there are clear signs of distress in the structure prior to collapse. Although the structure has failed, collapse does not take place due to the following possible reasons:
Design codes ignore the possible positive contribution of compressive membrane action in slabs
Some structural systems go into a state of catenary action
The slabs are suspended on the columns by means of adequately anchored bottom reinforcing.
A slab-column connection in distress will show some of the following telltale signs of structural deterioration:
Radial cracks on the top surface of the slab originating at the column
Circular cracks around the column
Formation of a flexural yield pattern above the affected column
Possibly excessive slab deflections
It will be beneficial if a fairly easy, non-disruptive and relatively inexpensive method(s) can be used to either repair such a failed slab – without requiring the demolition of the structure, or to increase the punching shear capacity of a slab if required due to change of use or altered loading conditions.
In the following sections the author proposes numerous strengthening measures and remedial measures for damaged slab-column connections.
78
5.1. Strengthening of Existing Slab-column Connections Theoretically, in order to strengthen an existing slab-column interface, three basics can be addressed in order to achieve the required increase in capacity, i.e. (1) increasing the effective depth of the slab and adding flexural reinforcing, (2) increasing the area of load transfer, thus increasing the critical perimeter, (3) the addition of shear reinforcing.
Access to the affected slab-column connection will depend on the specific use of the structure. For instance strengthening of a bridge deck connection would require a method to be implemented from below the slab instead of from above in order to minimize interference with traffic.
5.1.1. Increasing the Effective Slab Depth 5.1.1.1. Slab strengthened with additional concrete and vertical bolts By adding an additional concrete layer onto the existing slab, the effective depth can be increased, along with this the addition of longitudinal reinforcing is possible, both enhancing the punching shear capacity of the slab. In order to prevent delamination vertical reinforcing bars (shear reinforcing) need to be doweled into the existing concrete.
This solution seems fairly simple in principle, but poses numerous disadvantages and complications:
Additional dead weight of concrete – consuming some of the added punching capacity
Doweling vertical reinforcing into the existing slab is rather costly
Proper bonding of the concrete layover to the existing concrete substrate might be problematic
79
Fig. 5.1 Slab strengthened with additional concrete and vertical bolts
Recalculation of the punching shear capacity can now be done, taking the increased slab depth; new longitudinal reinforcing and the additional or new shear reinforcing into account.
5.1.1.2. Slab strengthened with additional concrete and bonded steel plate Similar to the above solution, a concrete layover increases the effective depth of the slab. Additional longitudinal reinforcing is added by means of bonding steel plates on top of the existing concrete.
Possible problems with this strengthening method are:
Additional dead weight of concrete – consuming some of the added punching capacity
Bonding of the steel plate to the existing concrete substrate is often not done to specification. This can be due to the use of unskilled or inexperienced labour, improper use of epoxy bonding agents and/or incorrect preparation of the concrete substrate.
Fig. 5.2 Slab strengthened with additional concrete and bonded plate
80
Recalculation of the punching shear capacity can now be done, taking the increased slab depth and additional longitudinal reinforcing (provided by the steel plate) into account. The contribution of the plate needs to be investigated further. Reasons for concern are the following:
The plate may act as a bond breaker between the existing concrete and the new overlay, causing delamination of the slab
The cross sectional area provided by the plate is not necessarily optimally utilized, mainly due to the fact that it is located quite far from the extreme tension fibre in the slab section
5.1.2. Increasing the area of load transfer By increasing the critical shear perimeter of the slab-column connection, the punching shear capacity can be enhanced substantially. This can be achieved rather easily by increasing the column diameter with shotcrete, conventional concrete or self-compacting concrete – see Fig 5.3 and Fig 5.4.
The use of self-compacting concrete and shotcrete would be suited best for this application. Practically speaking one would not be able to cast conventional concrete to the underside of the existing slab. The only options are one of the following: (1) cast the last portion of the column through the existing slab or (2) grout the last portion of the column with an expanding cementitious grout.
Shotcrete and self-compacting concrete can easily be cast to fit snugly to the existing slab.
If not properly addressed load transfer to the column can be a problem. Due to differential creep the new concrete column will shorten and will consequently not be loaded as envisaged. This can be problematic, especially when casting the column head through the existing slab. Differential shrinkage of the old- and new concrete will cause the new column head to separate from the older slab. 81
This remedial measure is cost effective, durable and reliable. However, it can be time consuming and rather expensive to install.
Fig. 5.3 Punching capacity increased with added column head
Fig. 5.4 Punching capacity increased with increased column cross section
The punching shear capacity of the slab-column connection can now be calculated using the enlarged column cross section, thus resulting in a bigger critical perimeter being considered, rendering a higher shear capacity.
5.1.3. Installation of additional shear reinforcing The slab-column connection can be strengthened by means of installing additional shear reinforcing. The new shear reinforcing would typically consist of short reinforcing bars grouted into holes drilled in the slab.
5.1.3.1. Doweling additional bars into the existing slab This remedial method will be very easy and fast to install, as well as relatively inexpensive.
82
Fig. 5.5 Punching capacity increased with additional shear reinforcing
The increased punching shear capacity can now be calculated taking the additional shear reinforcing into account. If a proper adhesive grout – e.g. HILTI HIT-RE 500® or similar – is used, the bonded bars should be at least as effective as bars cast into the slab during construction. For 450MPa reinforcing bars pullout tests on bars grouted with these grouts mostly result in the bars yielding before concrete pullout failure.
5.1.3.2. Slab strengthened with vertical bolts In the case where an insufficient quantity of shear reinforcing is provided, additional shear reinforcing can be added by merely perforating the slab around the column to install steel bolts into the slab – Fig 5.6.
Fig. 5.6 Slab strengthened with vertical bolts
Due to the fact that micro cracking of the slab takes place during failure, the strength of the bolt is utilised along its length only if it is properly bonded to the concrete – simply assuming that the restraint provided by the bolt heads alone, is not adequate.
83
5.2. Repairing slab-column connections showing distress due to punching shear failure or near failure Similar to the strengthening of a slab-column connection there are certain basic points that need to be addressed when repairing a damaged structure.
It should be kept in mind that most structural repairs are fairly to very expensive and will be disruptive to the normal use of the structure or part thereof. The old adage stating prevention is better than cure is especially true when it comes to the design for punching shear.
5.2.1. Proposed Classification of Damage The risk of collapse and the extent of damage on a structure must be assessed by means of visual inspection. When dealing with punching shear failure the following should be considered (Wood et al 1998): -
Prior to collapse no signs of distress will be evident on the soffits of the slab under question
-
Star / radial cracking on top of the slab is merely an indication of the redistribution of permissible flexural stresses and does not give an indication of the shear behaviour of the slab-column connection
Fig 5.7 Typical Star Cracking
-
Circumferential cracking around the column is usually evident at about 80% of the ultimate punching shear capacity of slabs without shear reinforcing.
84
-
Due to deterioration of the cover concrete and numerous other reasons the shear crack may never extend to the surface of the slab. The shear crack can develop along the longitudinal tension reinforcing causing delamination.
In order to determine the type and extent of remedial works necessary, a system of grading the inflicted damage on the structure is needed. The following grading is proposed:
5.2.1.1.
Damage Level 1 – Minor to medium levels of damage
Minor radial cracking originating from the column corners and concentric cracks forming around the column
Minor deflection of the slab around the column and a possible crack pattern around the column indicative of a flexural failure
5.2.1.2.
Damage Level 2 – Medium to severe levels of damage
Extensive radial and concentric cracking around the column, with the possibility of shear cracks having developed through the full depth of the slab
Crushing of the concrete at the column face
Fig. 5.8
Crushing of concrete at the column face
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5.2.1.3.
Damage Level 3 – Extreme levels of damage o A myriad of diagonal shear cracks, radial and concentric cracking on the slab surfaces and general disintegration of the concrete. o Excessive deflection of the slab surrounding the column o The slab being suspended on longitudinal reinforcing bars going through the column core. In essence the structure / slab could collapse at any instant if additional loading is introduced or if the structure is damaged any further.
5.2.2. Proposed remedial works for the different levels of damage In order to apply the correct remedial measures to a specific structure, quite a number of factors must be taken into account. Some of these factors are: o Age and condition of the structure o The use of the structure – i.e. the ratio of the level of permanent loads to level of live / repetitive loads o The importance of the structure – e.g. is the structure used as a hospital or as a unimportant storage facility o The expected service-life of the repaired structure o Possible alteration in the use of the structure – e.g. conversion of offices into apartments o The extent and severity of the damage to the structure
The interpretation of theses factors, especially the latter one, depends on sound engineering judgement, sufficient understanding of the failure mechanism and sufficient knowledge of the strengthening or structural principles used in the remedial measures.
The proposed remedial works presented in the following sections serve only as a guide and need to be adapted to suit each specific repair or strengthening application using sound engineering judgement.
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5.2.2.1.
Repair of Damage Level 1 Typically the repair of a connection suffering a relatively minor level of damage will be less involved or invasive as for more extreme levels of damage. The repair will most likely consist of methods similar to proposed strengthening procedures:
Epoxy crack injection
Installation of additional shear reinforcing
Plate bonding to provide additional longitudinal reinforcing
Additional drop panels or concrete overlays
Increasing the column cross-section or adding column capitals
5.2.2.2.
Repair of Damage Level 2 Repair of such a structure will at least entail the following procedures:
Removal of all loose and unsound concrete
Cleaning of the concrete substrate and cracks by means of high pressure water jetting
Epoxy injection of all structural cracks, i.e. cracks deemed to impair the structural capacity of the connection
In addition to this, some or all of the following measures could be implemented:
Installation of additional shear reinforcing
Increasing the slab thickness by means of added drop panels or concrete overlays
Increasing the shear perimeter by means of increased column cross-section or the addition of bolt-on steel column heads
Replacing the upper portion of the original concrete with a fibre reinforced concrete infill / overlay portion
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5.2.2.3.
Repair of Damage Level 3 Repair of a structure damaged to this extent will comprise of extreme remedial measures, disruption of use and intervention. The repair process will at least incorporate the following steps:
Propping of the slab adjacent to the damaged slab-column connection(s)
Demolition of the slab surrounding the column, with special care being taken not the damage the existing reinforcing
Jacking of the surrounding intact slab portions to an appropriate level if necessary
Installation of dowels into the edge of the original concrete slab
Epoxy injection of all the remaining visible cracks
Enlarging of the slab-column interface by means of enlarging the column or addition of a column capital
Casting of a new slab with sufficient longitudinal reinforcing, shear reinforcing and/or drop panels to resist the required load capacity
5.3. Retrofitting of slab-column connections for improved behaviour under seismic loading conditions As described earlier, structures subject to lateral loading can show premature punching shear distress due to unbalanced moments transferred to the supporting columns.
Punching shear problems due to seismic or lateral loading can be addressed similar to normal punching shear problems, i.e. increasing the effective depth of the slab and adding flexural reinforcing, increasing the area of load transfer, thus increasing the critical perimeter, and/or the addition of shear reinforcing (see 5.1). Similar methods to increase punching shear resistance have been proposed by Martinez et al (1994) – Fig 5.9.
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Fig 5.9
Proposed retrofitting of a slab-column connection for added seismic resistance to punching shear (Martinez et al 1994)
For dynamic loading there is a need to increase the ductility of the slab-column connection as much as possible. In addition to the conventional methods proposed earlier, the use of fibre reinforced concrete (FRC) can be well suited to this application. In most cases the addition of steel fibres can increase the punching loads by up to 36% (Harajli et al 1995). Even more significant than the increased capacity is the increased toughness of the connections, i.e. the resistance of the connection is maintained over a large deflection range.
5.3.1. Fibre reinforced concrete infill panel
Fig 5.8
Fibre reinforced concrete infill
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The replacement of the upper portion of concrete with FRC renders a tensile zone in the slab with a wholly different behaviour under loading. Failure of this FRC portion will be more ductile than conventional concrete showing more but less pronounced cracks. According to some testing the slab-column connection will tend towards flexural failure instead punching shear failure. Special attention should be given to: -
Shrinkage cracking and possible delamination from the existing concrete substrate due to differential movement
-
Delamination of the two different concrete portions under loading
5.3.2. Demolition of part of the existing concrete slab and replacement thereof with fibre reinforced concrete
Fig 5.9
Concrete replacement with fibre reinforced concrete
Replacing the conventional concrete slab portion surrounding the column with an FRC panel will result in a connection with a totally different behaviour under both dynamic loading and static loading. Given that proper and problem-free joining of the two concrete materials can be achieved, the ultimate punching capacity of the slab can be increased significantly.
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6. Experimental Testing of an Undamaged Slab-column Connection For the proposed experimental testing it was decided that for the purpose of this publication only one test slab would be constructed according to the latest German design code, DIN 1045-1 (2001).
The reasons for following this route were:
Previous punching shear tests in the structures laboratory at the University of Stellenbosch were done in 1971 on a series of slabs differing dimensionally from this publication‟s test slab. Some teething problems with the test set up still need to be resolved, since the support frames used for the previous testing were done away with long ago.
The test would provide a basis on which the performance of the DIN code could be assessed, even though such a judgement may be a hit-and-miss affair.
The test will provide the basis for possible future research both in the updating of the SABS 0100 concrete design code and research into the beneficial use of fibre reinforced concrete for the retrofitting or repair of existing slab-column connections
The damaged slab is to serve as a springboard to judge the performance of some of the proposed repair methods.
The obtained test data can also be used in future studies on punching shear failure using finite element methods
Prediction of the punching capacity of the slab and the evaluation of the required shear reinforcing was done in accordance with the DIN 1054-1 code. The reasons for using a foreign code as opposed to the SABS 0100 code is the following:
The current SABS code is based on BS8110-1:1985.
According to the findings in the technical report “Punching of structural concrete slabs” by the fib (2001) slabs designed according to BS8110 does not comply with acceptable reliability criteria.
The only code conforming to acceptable reliability is DIN 1045-1. DIN 1045-1 has been calibrated using all available test data to render a 5% fractile of safety.
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Punching shear design for the final Eurocode2 will most likely be based on the DIN 1045-1 formulation.
6.1. Experimental Test Setup For the purpose of this publication a single column setup was proposed. It was set out to build and test a slab-column connection consisting of a 2400mm x 2400mm, 220mm thick 30MPa slab and a 200mm x 200mm square concrete column. Longitudinal reinforcing provided would be such that flexural failure does not occur – refer to Appendix A for calculations. Restraint of the slab and load application to the column is illustrated in Fig 6.1.
Fig 6.1
Proposed laboratory setup
The punching shear capacity of the slab is estimated with the latest DIN 1045-1 recommendations and the accompanying shear reinforcement designed to deliver a slab-column connection with an estimated failure load of approximately 375kN (Appendix A).
The construction sequence of the test panel is outlined in Fig 6.2.
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Fig 6.2
Construction of the Test Panel
The decision to repair a slab with shear reinforcing instead of a slab without shear reinforcing is due to the nature of punching shear failure. Testing a slab without shear reinforcing could easily fail in a brittle manner and collapse, thus making the risk too big for not being able to repair the test model.
The available laboratory is equipped with anchoring positions on a square grid spaced at 914mm centre-to-centre, thus eight supports could be used to restrain the slab – Fig 6.3. Effectively a 1828mm x 1828mm slab was tested - the excess
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length of the panel providing ample space to anchor the reinforcing sufficiently and as far away from the supports as possible.
Fig 6.3
Steel rods and hydraulic jack on the laboratory floor
The slab was anchored to the very stiff laboratory floor with 25mm diameter threaded steel rods. The slab was loaded by placing the hydraulic jack(s) in series with a load cell between the column and the laboratory floor – Fig 6.4.
Fig 6.4
Concrete slab lowered onto the steel rods
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Fig 6.5
The test slab set up with all the instrumentation
For the acquisition of raw test data the following instrumentation was used:
5 LVDTs were placed on the top of the slab. A single LVDT placed in the middle of the slab – designated as 1 Four LVDTs placed at the corner supports on the slab – designated as 2, 3, 4 & 5 – Fig 6.5
A load cell between the hydraulic jack and the column stub was used to monitor the applied force
Both the LVDTs and the load cell were linked to a desktop computer via a data acquisition system (Spider 8) for real time data recording
It was decided that no strain gauges were necessary since the focus is more on the global behaviour of punching failure and the practical repair thereof, and not of the fundamentals behind the failure and the modelling of numerous parameters in order to estimate the punching shear capacity of the connection.
6.2. Proposed Test Procedure In a series of tests the total load-deformation behaviour of a slab can be established. Subsequently, on a new slab specimen, one can study repair methods by pre-damaging the specimen with the application of an increasing
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load up to the point where a peak value is reached. Then grouting or another repair method can be applied and it‟s effectiveness tested. In this study, time allowed testing and repair of one slab only.
The repair and strengthening of the slab was envisaged as the installation additional shear reinforcing in the slab. The additional reinforcing consisted of vertical reinforcing bars doweled into the slab using epoxy grout.
From a technical point of view the reasons for using a high strength and flowable epoxy grout are:
The grout is rather free flowing and will penetrate the cracks surrounding the drilled hole to a certain extent to give some degree of epoxy injection to mend the cracked concrete
This grout offers superior bonding strength between reinforcing and concrete, as well as concrete and concrete.
Application of the product is uncomplicated
Rapid curing
After proper curing has taken place a second punching shear test will be done. This time the slab will either be tested to total collapse or tested to a more severe state of damage. If a higher degree of damage is to be repaired, the abovementioned steps will be repeated until the slab is not fit to be repaired any more.
6.3. Actual Test – Virgin test panel 6.3.1. Material Test Results At construction of the test panel numerous 150mm concrete cubes were cast. On the day of testing three (3) of the cubes were crushed, giving the following results: Cube 1:
49.6 MPa
Cube 2:
51.1 MPa
Cube 3:
54.0 MPa
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Average:
51.6 MPa
Standard Deviation:
2.20 MPa
6.3.2. Load Application The load on the concrete column stub was applied using a hydraulic 62.5 ton jack driven by a hand operated hydraulic pump. The jack was placed in series with a digital load cell and a Teflon-coated swivel-head.
Operation of the hydraulic pump was stopped whenever any significant events took place, e.g. audible concrete cracking and/or visible cracks appearing on the concrete surface. When pumping stopped some hydraulic fluid flowed back towards the pump and some creep in the concrete took place. Due to the creep and/or loss of hydraulic pressure there are some points on the load vs. deflection graphs where slight unloading of the test panel takes place. However when pumping resumed, the graph rebounded to the initial slope of the curve.
Due to unforeseen circumstances (as discussed in the following sections) the panel was subjected to three (3) load applications. The three applications are designated as Load 1, Load 2 and Load 3. Loads 1 & 2 were done with a single 62.5 ton jack, while Load 3 was done using two similar jacks in series driven by a more powerful hand operated hydraulic pump.
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Fig 6.6
Column Load vs. Elapsed Time
6.3.3. Placement and Setting Up of the Test Panel When lowering the test panel (Fig 6.7) onto the supporting rods the rods and the penetrations in the slab did not line up properly PVC sleeves were fixed to the shuttering and reinforcing prior to casting to provide the necessary openings for the supporting rods to pass through. During the casting process two of the sleeves moved. The one sleeve was misaligned approximately 15mm and the hole had to be reamed with a concrete drill to get the rod through. Due to the strength of the concrete the hole wasn‟t vertical and the bolt rubbed against the sides of the hole.
Fig 6.7
Test Panel Placement
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Due to the misalignment there was some friction on the rods indicated by the increases in load without any significant deflection of the support (designated with arrows on the graph. This is quite significant for Corner 3 and less pronounced for Corner 4.
6.3.4. Original Panel – Load Application 1
The test slab was only restrained vertically. As the panel deformed the flexible supporting rods would allow the edges to move inwards. The deformation can be visualized as a square piece of paper forced to take a conical shape, which is only possible if the edges move towards the centre as the centre displaces vertically, thus no membrane forces could develop. This also meant that the slab would move horizontally underneath the LVDTs. Since LVDT 2 & 3 were screwed into Perspex plates, the movement of the slab caused the stanchions on the LVDTs to bend – Fig 6.8.
Fig 6.8 Bending of LVDT stanchions
Due to this movement the LVDTs were placed on the concrete. Subsequently the measured deflection values underwent a jump in value and needed some adjustment. The adjustment was done by inspection and adding/subtracting a constant value to the affected measurements to render a more realistic curve. The measured and adjusted behaviours of Corner 1 and Corner 2 can be seen in Fig 6.9 and Fig 6.10 respectively.
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Fig 6.9 Corner 1 – Measured & Adjusted Deflection Values
Fig 6.10
Corner 2 – Measured & Adjusted Deflection Values
Due to the friction on the steel rods and the crushing of little concrete imperfections on the slab, the first loading sequence shows a fairly jumpy load vs. deflection curve – Fig 6.11.
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Fig 6.11
Load 1 – Column Load vs. Corner Support Deflections
From Fig 6.11 it is evident that the deflection behaviours of LVDTs 2 & 3 do not follow the same trend as that of LVDTs 4 & 5. Even though the latter two are more affected by the friction between the supporting rods and the slab, they follow a more acceptable linear behaviour of load vs. deflection. Consequently all further calculations are based upon the average deflections of LVDTs 4 & 5.
Fig 6.12
Load 1 – Column Load vs. Average Relative Middle Deflection
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From Fig 6.12 the following can be concluded:
0mm to ±2.5mm deflection, 0kN to ±350kN column load The stiffness of the slab is initially parabolic and then settles to a linear trend. The first visible cracking took place at approximately 1.5mm deflection and 250kN – Fig 6.13 (a) & (b) The horizontal movements on the graph are due to observers bumping the test panel while inspecting and marking the newly formed cracks.
(a)
(b)
(c)
Fig 6.13
First visible cracking on the concrete surface
From 250kN to 350kN the crack pattern grew into a radial pattern, indicative of flexural cracking – Fig 6.13 (c).
±2.5mm to ±8.5mm deflection, ±350kN to ±550kN column load The panel continued to behave with a linear increase in deflection for the growing load. Once again the horizontal movements on the graph are indicative of the stages where new cracks were inspected and marked on the slab.
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Fig 6.14
Growing flexural cracks
The flexural cracks continued to grow in a radial pattern towards the edges, as seen in Fig 6.14. At approximately 475kN the first shear crack appeared around the column – Fig 6.15.
Fig 6.15
Appearance of first shear cracks at 475kN
Before unloading a distinct radial crack pattern is visible – as can be seen in Fig 6.16. The increased load caused the cracks formed at lower loads to open up more significantly – Fig 6.17.
Fig 6.16
Radial crack pattern prior to unloading 103
Fig 6.17
Increased crack width
Due to behaviour of the LVDTs at Corner 1 & 2, the test was terminated at approximately 550kN.
±8.5mm to ±3mm deflection (unloading) Removing the applied column load caused an approximately linear elastic unloading behaviour of the test specimen – Fig 6.12. The positive residual deflection of the centre of the slab indicates plastic deformation and a certain degree of damage (cracking) already inflicted on the slab.
6.3.5. Original Panel – Load Application 2 Due to the fact that initial cracking had already taken place, the response of the test panel was practically linear with the second load application – Fig 6.19.
Punching shear failure was not yet achieved at the maximum loading capacity of the original test setup. Consequently, it was decided to unload the slab and modify the test equipment to increase its loading capacity.
After unloading, it is clear that further plastic deformation took place. It should be noted that the elastic limit for the bending steel has not yet been reached. Should the slab start yielding due to flexural failure; the Load vs. Deflection curve would form a plateau with increasing deflection, i.e. ductile failure.
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Fig 6.18
Load 2 – Column Load vs. Corner Deflections
With the second load application the effect of the misaligned support at Corner 3 (LVDT 4) can be seen clearly. The friction causes the support to have sudden deflections as the frictional forces are overcome at distinct instances. As seen in Fig 6.18, the load-deflection behaviour of Corner 3 differs considerably from that of the other corners. Subsequently the average value of the corner deflections was calculated using only Corners 1, 2 & 4.
The second load application caused the existing cracks to become more pronounced. As the jack approached the end of its capacity, pumping became more strenuous to the operator. The lower rate of load application seems to cause the response curve to flatten – as seen in Fig 6.19 from ±5mm deflection to unloading.
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Fig 6.19 Load 2 – Column Load vs. Average Relative Middle Deflection
6.3.6. Original Panel – Load Application 3 In order to push the test panel to punching failure, the maximum loading capacity of the setup was increased by introducing a second hydraulic jack (Fig 6.20) and a bigger capacity hydraulic hand pump.
Fig 6.20
New hydraulic jack, load cell and swivel-head arrangement
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Fig 6.21
Load 3 – Column Load vs. Corner Deflections
Once again the measurements taken at LVDT 5 (Corner 3) differed substantially from the other three corner measurements – Fig 6.21. In order to do plot the load-deflection behaviour of the slab panel, the average value of corners 1, 2 & 4 (LVDTs 2, 3 & 5) were used – Fig 6.22.
Fig 6.22 Load 3 – Column Load vs. Average Relative Middle Deflection
For the third load application the following significant stages can be highlighted:
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0mm to ±6mm deflection, 0kN to ±725kN Reloading of the slab shows a fairly linear relation between the applied load and measured deflections. Cracking of concrete was quite audible towards 725kN.
±6mm to ±8mm deflection, 725kN to ±850kN The angle of response started to decrease in this stage of the load application. Between 750kN and 850kN two significant observations could be made. Firstly, crushing of the concrete at the interface of the column and the slab soffit started – Fig 6.23.
Fig 6.23
Concrete crushing at the column face
Secondly, another shear crack appeared on the concrete surface, further away from the column – Fig 6.24.
Fig 6.24
Appearance of the second shear crack
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Fig 6.25
Highlighted possible punching shear cracks
±8mm to ±10.5mm deflection, ±850kN Suddenly, the stiffness of the panel decreased, showing an increased deflection for a fairly constant load. The test panel could be seen deflecting, accompanied by audible cracking inside the concrete.
±10.5mm to ±13mm deflection, ±850kN to ±450kN It was clear that the slab had reached its failure load. The deflection increased dramatically with a lower resistance to the column load.
±13mm to ±5.5mm deflection, unloading Upon unloading the slab once again recovered in a linear fashion; however, the rate of recovery was much lower than for the previous two load applications. The residual deflection is also substantially more than for loads 1 & 2.
6.3.7. Original Panel – Combination of results – Loads 1, 2 &3 Due to the high punching resistance of the slab, the testing produced three sets of data instead of one single series. For most materials a single test from the undamaged state to failure produces an upper bound reaction curve. For a limited number of load repetitions, as in the above tests,
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unloading and reloading of the specimen should render a curve bounded by that of a single test. Thus it is fairly safe to assume that the addition of the three consecutive tests will produce a response curve of which the envelope will be representative of a single test.
Using the data as adjusted previously and adding the residual displacement of each preceding test (Fig’s 6.26 6.27 6.28) one obtains the assumed envelope of response (Fig 6.29).
Fig 6.26
Load 1 – Response Curve
Fig 6.27
Load 2 – Translated Response Curve
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Fig 6.28
Load 3 – Translated Response Curve
Fig 6.29
Combined Translated Response Curves – Load 1, 2 &3
From Fig 6.29 the behaviour of the panel can be summarized as follows: For the first part the slab shows a fairly steep elastic behaviour. After cracking of the concrete takes place the stiffness decreases to a lower, yet constant value. Close to the failure load the deflection starts to increase more drastically at a sustained load level and suddenly the slab loses its load carrying capacity.
Even though the decrease in capacity is rather drastic, it is not typical brittle behaviour. This is confirmed by the crack pattern.
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It can be concluded that a mixed flexural- shear failure occurred, with an intermediate level of ductility between shear failure (brittle) and flexural failure (ductile, with a plateau being reached at the peak resistance).
6.3.8. Verification of test results with the method proposed by Menétrey (2002) Punching shear failure of slabs with shear reinforcing is generally accepted to be in the region of 30°. This same assumption was used in the comparative calculations in the fip Bulletin 12 (2001). At this angle the failure plane will cross both rows of shear reinforcing. Accordingly the ultimate punching shear capacity calculation is as follows: (The following equations are extracted from 2.1.3)
Fpun Fct Fdow Fsw Fp
(eq. 2.5)
Calculation of Fct rs
l1 l2 2
200 200 2 rs 79.788mm rs
d 10 tan 154 r1 79.788 10 tan 30 r1 106.46mm
(6.1)
r1 rs
r2 rs
(eq. 2.7)
d tan
154 tan 30 r2 346.52mm r2 79.788
(eq. 2.8)
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s
r2 r1 2 0.9 d 2
s
346.52 106.462 0.9 1542
(eq. 2.9)
s 277.198
According to the CEB-FIP Committee the tensile strength of is f t 0.24 f cu f t 0.24 50
2
2
3
3
(6.2)
f t 3.257 MPa
2011 9.141103 0.9141% 220 1000
(6.3)
0.1 2 0.46 0.35 0.1 0.91412 0.46 0.9141 0.35 0.687
r h
2
0.1 s 0.5
(eq. 2.12)
rs 1.25 h
2
79.788 79.788 0.1 1.25 0.5 220 220 1.082
(eq. 2.14)
Assuming the maximum aggregate size of 19mm
1.6 1
d d a
1 2
1
154 2 1.6 1 19 0.53
(eq. 2.15)
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Fct r1 r2 s v Fct r1 r2 s f t 3 2
Fct (106.46 346.52) 277.198 3.257
2
(eq. 2.10) 3
0.687 1.082 0.53
Fct 341.56kN
Calculation of Fdow The calculation of Fdow is more complicated, since the ultimate punching load is needed to calculate the tensile stress in the longitudinal reinforcing. In order to obtain the Fpun value the Excel solver is used with two constraining conditions, i.e. Fpun Fct Fdow Fsw Fp and s 450MPa .
As is taken as the total area of longitudinal tensile reinforcing crossing the circle defined by r2.
s
Fpun
tan As
1004.93 103 tan 30 4377.67 s 397.606MPa
s
(eq. 2.17)
s fs
397.606 450 0.884
(eq. 2.16)
The number of bars is estimated by dividing the circumference of a circle with radius r2, with the average spacing of the tensile reinforcing. # _ bars
2 346.52 100
(6.4)
21.77
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1 Fdow s2 f c f s 1 2 sin 2 bars 1 Fdow 21.77 16 2 50 450 1 0.884 2 sin 30 (eq. 2.15) 2 Fdow 97.70kN
Calculation of Fsw Assuming that the yield stress of the shear reinforcing is reached the contribution thereof is: Fsw Asw f sw sin sw Fsw 16
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4 Fsw 565.48kN
450 sin 90
(eq. 2.22)
Failure Load Fpun Fct Fdow Fsw Fp Fpun 341.56 97.7 565.48 0 Fpun 1004.74kN
This calculated capacity is higher than the experimental failure load.
By investigating a scenario with the shear crack originating outside the first perimeter of reinforcing, i.e. rs 175mm and 8 shear stirrups intersecting the failure plane, the results are: Fct
= 410.58kN
Fdow
= 208.61kN
Fsw
= 282.74kN
→
Fpun = 901.94kN
Again the calculated capacity of the system is higher than the experimental failure load.
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Similarly if the shear crack originates outside the second perimeter of reinforcing, i.e. rs 290mm and no shear stirrups intersecting the failure plane, the results are: Fct
= 465.50kN
Fdow
= 304.54kN
Fsw
= 0.00kN
→
Fpun = 770.04kN
The capacity of the slab-column connection outside the shear reinforced area is less than the failure load achieved in the experiment. However it corresponds roughly with the point at which the slope of the load vs. displacement curve started to decrease.
Fig 6.25
Combined Translated Response Curves (Load 1, 2 & 3) and Failure Load Calculated by Menétrey‟s Method.
Further discussion of the slab behaviour and conclusions based on the tests can be found in Chapter 8.
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7. Experimental Testing of Repaired Slab-column Connection The first test inflicted a substantial amount of damage to the slab and caused a rather drastic capacity reduction. Ideally one would like to control the amount of damage inflicted more accurately so that the achieved level of damage suits a predetermined method of repair. This section describes the repair and testing of the damaged slabcolumn connection.
7.1. Classification of Damage and Proposed Method of Repair Using the damage classification proposed earlier, it is safe to say that the test panel falls between Damage Levels 2 & 3. The facts leading to this conclusion are: -
Extensive radial cracking around the column is visible
-
Shear cracks have developed to the surface of the slab
-
Delamination along the tension reinforcing is occurring at certain locations around the column
-
Crushing of concrete is taking place at the column and slab interface
Typically a column-slab connection in this condition would be extensively repaired by removing all unsound concrete, epoxy crack injection, installation of additional shear reinforcing, patching of the concrete slab and possibly increasing the area of load transfer.
The reasoning behind this approach is, firstly, epoxy injection would yield a slab with an unquantifiable amount of capacity added – it is difficult to judge how much of the epoxy pumped into cracks are filling voids and how much of it is actually bonding the disintegrated concrete. Secondly, the mere addition of additional shear reinforcing is by far the quickest and easiest measure to improve the punching capacity of the slab.
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Using the mechanistic method proposed by Menétrey (2002), a calculation similar to that shown in 6.3.8 was used to estimate the amount of new shear reinforcing needed – see Appendix B. The following assumptions were made to achieve a peak load similar to that achieved in the previous test -
The concrete contribution can be ignored for the calculations on perimeter 1 and 2. The contribution to shear resistance of the cracked concrete is uncertain.
-
Due to the ineffective anchorage of shear clips/stirrups in thin slabs, the shear reinforcing has not yielded yet.
-
The bending steel did not yield in the first test.
With the help of Menétrey‟s method is was decided to add eight dowel bars to each of the original reinforcing perimeters and to add a third perimeter of shear reinforcing by means of 24 vertically doweled bars – Fig 11.4. The installation of additional shear reinforcing is similar to Fig. 5.5.
7.2. Repair of the damaged slab The first step in the repair process was to map the position of the existing reinforcing. This was done with the help of a HILTI Ferroscan instrument, which allowed the accurate plotting of the underlying reinforcing relative to a reference grid placed on the concrete surface – see Fig 7.1.
Accurate information on the position of the reinforcing helps to position the holes for doweling the new shear reinforcing and to avoid hitting the existing reinforcing bars during drilling. In addition to this it also gives added insight into the meaning of the observed crack pattern.
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Fig 7.1
Mapping the existing reinforcing with the HILTI Ferroscan
After plotting the positions of the existing longitudinal reinforcing the positions of the shear clips and the control perimeters were superimposed on the slab surface, as shown in Fig 7.2. The positions of the new shear reinforcing dowels were then indicated on the slab and the drilling commenced.
Using the correct equipment drilling the required holes in the slab is fairly easy. Even though the existing reinforcing was mapped (Fig 7.2) some bars were hit during drilling. Some of these were shear clips; some were part of the bottom reinforcing and others were bars that were probably misaligned during the casting of the slab. Some of the bar positions were extrapolated from the data acquired by mapping certain areas on the slab. Consequent to the Ferroscan being unable to scan the Y10 bottom reinforcing bars it was decided to drill only 180mm deep to avoid drilling onto them.
As seen in Fig 7.3(a) the desired positions of the additional shear reinforcing bars were marked on the slab and drilling took place accordingly. Fig 7.3(b) shows the drilled holes in the slab.
During drilling one was able to distinguish from the drill feedback whether the slab was cracked or not as the drill-bit progressed into the slab. In some places in the shear reinforced area one could feel brittle / hollow regions within the slab. This offers some insight on the fact that during testing a great deal of cracking was audible, without the accompanying cracks appearing somewhere on the slab surface. It can only mean that not all the shear cracks developed to the
119
surface. These cracks probably evolved into delaminations along the tensile reinforcing.
Fig 7.2
Shear reinforcing perimeters and reinforcing layout superimposed on the crack pattern
(a)
Fig 7.3
(b) (a) Positions
of new shear reinforcing superimposed on the slab
(b) Positions
of the drilled holes
After drilling, all the holes were properly cleaned, filled with HILTI RE-500 epoxy adhesive and the reinforcing bars inserted in the holes – Fig 7.4. The epoxy was allowed to cure for a weekend. A total of three HILTI RE-500 tubes were used to fill the holes.
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Fig 7.4
Epoxy injection of the holes and the finished product
7.3. Testing of the Repaired Panel 7.3.1. Material Test Results On the day of testing three 150mm concrete cubes were crushed. Cube 1:
51.6 MPa
Cube 2:
53.1 MPa
Cube 3:
53.0 MPa
Average:
52.6 MPa
Standard Deviation:
0.84 MPa
7.3.2. Load Application Similar to testing of the virgin panel two 62.5 ton hydraulic jacks driven by a hand-operated pump were used. The modus operandi was similar to the initial testing of the slab.
Due to migration of the cracking towards the supports, unwanted stress concentration and cracking occurred at the centre supports; consequently the first load application was stopped.
The bearing conditions at the middle supports were modified and a second load was applied. The load evolutions for the two applications are shown in Fig 7.5 and Fig 7.6.
121
Fig 7.5
Load 1 – Column load vs. Elapsed Time
Fig 7.6
Load 2 – Column load vs. Elapsed Time
7.3.3. Repaired Panel – Load Application 1 Having learnt form the initial testing the LVDTs were set up so that the end could move more freely on top of the concrete when in-plane movement of the panel took place – see Fig 7.7. Similar to the load applications on the virgin test panel some of the supports presented problems. This can be clearly seen in Fig 7.8.
122
Fig 7.7
Corner LVDT setup
Fig 7.8
Column load vs. Corner Support Deflections
From Fig 7.8 the following deductions can be made; firstly, Corner 3 shows erratic behaviour due to friction between the supporting rod and the concrete. Secondly, it seems as if there were some interference with the LVDT at Corner 1. This instrument shows a substantial deflection at ±200kN, while the LVDTs at Corners 2 and 4 do not.
In order to calculate an average corner deflection the measurements at Corner 1 was scrutinized and adjusted to remove the unwanted jump in the deflection and the measurements at Corner 3 were ignored.
123
Fig 7.9
Column load vs. Adjusted Corner Support Deflections
Fig 7.10 Column load vs. Relative Middle Deflection
From Fig 7.10 the following can be concluded:
0mm to ±2.0mm deflection, 0kN to ±200kN column load Initially the response of the slab was parabolic, settling to a linear trend. At approximately 200kN the first of the original flexural cracks started to open up – Fig 7.11
124
Fig 7.11 Reappearance of original cracks
±2mm to ±6.0mm deflection, ±200kN to ±400kN column load Due to observers marking cracks on the slab some movement takes place, causing the erratic behaviour seen on the curve at 200kN, 300kN and 400kN. Virtually all the flexural cracks have opened up through the chalk locating on the slab at this stage. The crack pattern at approximately 400kN is shown in Fig 7.12.
125
Fig 7.12
Crack pattern at ±400kN
A very important crack appeared at this stage of the test. A shear crack was starting to appear on the concrete surface outside the newly installed third perimeter of shear reinforcing. This happened without the formation of new shear cracks within the shear-reinforced zone – Fig 7.13.
Fig 7.13
Appearance of new shear cracks outside the perimeter of dowel bars
126
±6mm to ±10mm deflection, ±400kN to ±550kN column load After the appearance of the shear crack outside the last perimeter of shear reinforcing, the angle of response on the load-deflection curve decreased. Cracking was audible inside the slab, without significant new flexural or shear cracks appearing on the concrete surface. However, it seems as if the cracking started to migrate towards the supports along the tensile reinforcing. This probably happened due to stress concentrations at the middle supports between Corners 4 & 1 as well as Corners 1 & 2. Delamination of the concrete at theses supports was clearly evident, as seen in Fig. 7.14.
Fig 7.14 Delamination due to cracking migrating to the supports
±10mm to ±12.5mm deflection, ±550kN to ±450kN column load The load carrying capacity of the slab reached a peak at approximately 550kN and the deflection started to increase accompanied by a lessening load carrying capacity. It was decided to stop the test. The support conditions had to be altered before the panel could be tested to destruction. Up to this point the new shear crack had become significantly visible and the slab seemed to be increasing in thickness.
To get better insight into the behaviour of the repaired slab in comparison with the original, the measurements of the different tests can be added together. Fig 7.15 shows the load deflection behaviour of the repaired slab when it is added to the response of the undamaged specimen.
127
Fig 7.15 Column Load vs. Relative Middle Deflection Original Panel & Repaired Panel
7.3.4. Repaired Panel – Load Application 2 Due to the installation of additional shear reinforcing the shear cracking was forced to migrate away from the column, causing shear cracks to grow to the surface outside the shear reinforced zone.
In essence this proves that the installation of additional reinforcing is an effective way of countering punching shear failure. However, due to the observed migration of cracking, the support conditions of the slab were interfering with the mode of failure. Delamination started to occur at the small bearing plates.
It was thought best to increase the area of load transfer at the supports before any further testing took place – Fig 7.16.
128
(a)
(b)
Fig 7.16 Revised support conditions: (a) Original support, (b) Revised Support
Due to the friction in the supports reloading of the repaired panel caused erratic movements on the load-deflection plots of the corner supports – as seen in Fig 7.17.
Fig 7.17 Column load vs. Corner Support Deflections
In order to calculate the average support deflection the measurements of only Corners 2 and 4 were used. The values measured at Corner 3 are too erratic due to the friction between the tie rod and the slab. The deflection behaviour of Corner 1 is most likely due to the delamination and increased slab thickness observed in that quarter of the panel.
129
Fig 7.18 Column load vs. Corner Support Deflections
Fig 7.19 Column load vs. Relative Middle Deflection
From Fig 7.19 the following can be concluded:
0mm to ±7.0mm deflection, 0kN to ±400kN column load Reloading caused the slab to behave with an initial parabolic curve settling to a linear response from ±100kN onwards. The two most important observations for this portion of the test were; firstly, that delamination of the concrete continued at the supports, despite the enlarged support area – see Fig 7.20. Secondly, extensive cracking within the slab was audible without any major crack appearances or growth on the slab surface. 130
Fig 7.20
Delamination at middle support
±10mm to ±15mm deflection, ±400kN to ±400kN column load At approximately 400kN the slope of the load-deflection curve decreased dramatically. A peak value can be observed at approximately 425kN – Fig 7.19. Post peak the load carrying capacity of the slab started to decrease with increased deflection. On the top surface of the slab, as seen in Fig 7.21, the newly formed shear crack was growing around the last row of shear reinforcing. The direction of growth is indicated with dotted arrows.
Fig 7.21
Development of the outer shear crack
131
On the soffit of the slab punching of the column could be clearly seen as well as concrete spalling below the original shear clips – see Fig 7.22.
Fig 7.22
Concrete spalling and punching of the column
±15mm to ±36mm deflection Punching shear failure of the slab has clearly taken place and it was decided to sustain the load application. With continued pumping of the jacks the slab resistance remained fairly constant with very high and increasing middle deflections. The behaviour of the slab is similar to bending failure behaviour in reinforced concrete. Delamination of the cover concrete became highly defined on the one end of the slab. Accompanying this, the slab thickness started to increase as a cone of concrete was being pushed out of the original slab. This can be clearly seen in Fig 7.23 & Fig 7.24.
132
Fig 7.23
Continued delamination and shear cracking
Fig 7.24
Bulging of the slab
133
Fig 7.24 – continued
Bulging of the slab
Further pumping was stopped and the instrumentation removed. The jacks were kept extended to support the slab in its bulging form.
In Fig 7.25 the compilation of all the load-deflection curves can be seen.
Fig 7.25 Column Load vs. Relative Middle Deflection Original Panel & Repaired Panel
134
7.3.5. Dismantling of the failed slab panel With the jacks extended the loose cover concrete was removed and the slab thoroughly inspected. The following observations were made:
Delamination of the concrete was much worse on the one side of the slab. When the loose concrete was removed it was clear that a very large shear crack developed outside the outer perimeter of shear reinforcing. The concrete surrounding this crack was disintegrating quite badly. It was so loose that it could be removed with bare hands.
Fig 7.26
The shear-reinforced zone remained intact.
Fig 7.26
Removing the cover concrete
Intact shear reinforced zone
The epoxy grout flowed into the cracks wherever the drilled holes intersected inclined shear cracks.
135
Fig 7.27
Epoxy bonding of a shear crack
Due to the fact that the grout was only applied to the drilled holes with the supplied applicator, the epoxy flowed into the cracks only to a limited extent – Fig 7.28.
Fig 7.28
Extent of epoxy crack bonding
Some of the dowel bars did not extend into the slab sufficiently. On Fig 7.28 the bar on the left is clearly the shorter one of the two. When still in the slab it was seen that the shear crack migrated to find a path of least resistance underneath the shorter dowel. The dowel failed due to an insufficient depth of embedment or insufficient filling of the hole with epoxy.
136
Fig 7.29
Shear crack travelling beneath dowel
The longitudinal reinforcing de-bonded outside the shear-reinforced zone. This happened because the shear cracks developed from the slab soffit upwards at an angle and then continued along the top reinforcing causing the observed delaminations.
As the slab increased in thickness the original shear clips started to take load. At some point the increasing slab thickness and consequent axial loading of the shear clip caused the 90° hook at the bottom of the slab to slip and bend open. The result of this opening of the hook is evident in the soffit cover concrete spalling underneath the shear clips – Fig 7.30.
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Fig 7.30 Deformed shear clip and column punching through soffit
Due to either asymmetric support conditions, asymmetric levels of strength around the slab or eccentric loading of the column, the travel of the column was not vertical – see Fig 7.31. This clearly caused a moment on the column, which in turn caused a differential shear stress distribution in the control perimeters. Consequently one side of the slab punched before the other side.
Fig 7.31
Misaligned column
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8. Conclusions and Recommendations 8.1. Conclusions Firstly an overview of the current design practise for the prevention of punching shear failure has been presented. From the extensive work done by the Fédération Internationale du Béton (fib) it is clear that current design codes do not comply with the modern approach of reliability based design.
South African concrete design is based on the recommendations of BS8110-1. The inaccurate and variable estimation of actual failure loads raises concern. In lieu of the findings by the fib, the punching shear design approach in SABS0100:2000 needs to be given attention. It is recommended that further investigations be undertaken to verify the applicability of the new German design code (DIN 1045-1 2001) to our construction and detailing practices.
The experimental testing of the original panel and the repaired panel leads to the following conclusions:
Due to the reliability-based approach in the formulation of codified design formulas it is difficult to estimate the exact failure load of a structural system. Modern code formulations allow a 5% probability of failure. Consequently it is very likely that a slab-column connection will fail at a load much higher than anticipated and calculated.
Due to the fact that shear reinforcing causes failure to move away from pure brittle failure, it would be good practice to detail all slab-column with shear stirrups, regardless whether it is needed or not.
Even though the repaired panel did not reach the failure load of the original panel, repairing of the slab with vertical dowels and HILTI RE-500 epoxy grout, can be judged as successful in principle due to the following reasons: (1) The extended shear-reinforced zone remained intact (2) Punching failure occurred outside the shear reinforced zone (3) The doweled shear reinforcing bridged existing shear cracks and prevented the slab to fail on the failure surface formed with the initial test
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Shear cracking appears to travel along the bottom reinforcing, past dowels not installed to a sufficient depth and then grows at an angle towards the top of the slab.
With the additional testing the slab was most probably damaged further away from the column than anticipated, causing boundary interference.
Due to delamination of the concrete, the anchorage of the tension reinforcing is compromised. Consequently the method of Menétrey (2002) may overestimate the contribution of the doweling effect of the tension reinforcing.
More punching shear tests with high strength concrete are needed. Only nine specimens in the fib databank used high strength concrete.
8.2. Recommendations
Due to cracking within the slab, epoxy injection of all cracks is essential for a more effective repair. This should preferably be done after removing of all unsound cover concrete and other loose concrete. Injection has to be done under pressure.
When installing vertical dowels it would be better to let the bars protrude from the slab soffit. The best option would be to thread the ends of the bars and install nuts and plates at both ends to provide better anchorage in addition to the epoxy grout.
In the view of future testing of repaired models the following need to be considered:
It is essential to manufacture an undamaged panel with a known behaviour under loading, as well as a known point of failure.
If several panels of exactly the same virgin behaviour can be produced, it will be possible to test the effectiveness of different repair methods at varying levels of initial damage.
It is proposed that a proper analysis and parametric study need to be undertaken to quantify the effectiveness of different repair methods.
The influence of the supports on the testing of both an undisturbed and repaired panel need to be investigated and better understood. Other panel layouts should be investigated and tested, i.e. circular, hexagonal, etc.
140
The behaviour of a repaired slab-column connection subject to both vertical loading and unbalanced moments needs to be investigated.
141
9. Appendix A – Estimation of the experimental model’s punching shear capacity and the design of the required shear reinforcing In order to do a proper punching shear experiment, bending failure of the slab needs to be prevented. Since the punching shear capacity is also related to the amount of longitudinal reinforcing provided, it is important that the amount of provided bending reinforcing is such that bending failure does not occur, while punching failure must not be prevented.
According to Mervitz (1971) the ultimate bending capacity can be estimated using a formulation found in ACI318-63. The calculation below is done using the intended concrete crushing strength of the slab as 30MPa with Y16 bars at 100mm spacing. 1 x 8 0.172 1 D L 1 8 0.172 1 200 1828 7.607
(9.1)
3 f y Pbend x f y d 2 1 4 f cu 2011 3 450 2011 2 7.607 450 154 1 154 1000 154 1000 4 50 966kN
(9.2)
The chosen top reinforcing of the slab is sufficient to resist a column load of up to ±966kN without failing in flexure.
142
Column size:
200mm x 200mm
Slab thickness:
200mm
Cover:
30mm
Tension reinforcing :
16mm
Concrete design strength:
30MPa
d d avg h c 200 30 16
(9.3)
154mm
h
Slab thickness
d
Average effective slab depth
fcu
Characteristic concrete cube strength
fy
Characteristic steel yield stress
c
Cover thickness
Tension reinforcing diameter
Ratio of tensile reinforcing
[Refer to 3.5 for clarification of the symbols used below]
Shear capacity without shear reinforcing
VRd ,ct 0.1 100 l f ck 3 0.12 cd d ucrit 1
(9.4)
1.0 for normal concrete l
Asl 0.02 bw d
1 cd
200 2.0 d
N sd - for prestress N < 0 Ac
(9.5)
(9.6) (9.7)
143
Calculation of required punching shear reinforcing
VRd ,sy,i vRd ,sy ui vRd ,sy vcrd
(9.8)
s Aswi f yd
(9.10)
ui
vcrd vRd ,ct 0.1 100 l f ck
1 3
0.12 cd d
(9.11)
A f u 1 P 0.1 100 l f ck 3 0.12 cd d s swi yd i ui 1000
(9.12)
Rearranging (9.12) yields the required area of shear reinforcing
P 103 1 0.1 100 l f c 3 0.12 cd d ui u Aswi i s 0.7 f y
(9.13)
Punching outside the shear reinforcing vRd ,ct ,a a vRd ,ct
a 1
0.29lw 0.71 3.5d
(9.14) (9.15)
Using these design equations a spreadsheet was set up to design the test panel. For the design of the test panel the following parameters were considered to be unity:
The enhancement factor (
Partial material factors (rebar, conc)
144
Table 9.1 Punching Design with 30MPa Concrete
145
Table 9.2 Punching Design with 51.6MPa Concrete
146
10. Appendix B – Calculations using the Mechanistic Model Proposed by Menétrey As extracted from 6.3.8 the capacity calculation of the test panel using Menétrey‟s method is done as follows:
10.1.
Virgin Test Panel Fpun Fct Fdow Fsw Fp
Shear crack originating at the column face
Calculation of Fct rs
l1 l2 2
200 200 2 rs 79.788mm rs
d 10 tan 154 r1 79.788 10 tan 30 r1 106.46mm r1 rs
r2 rs
d tan
154 tan 30 r2 346.52mm r2 79.788
s
r2 r1 2 0.9 d 2
s
346.52 106.462 0.9 1542
s 277.198
According to the CEB-FIP Committee the tensile strength of is 147
f t 0.24 f cu f t 0.24 50
2
2
3
3
f t 3.257 MPa
2011 9.141103 0.9141% 220 1000
0.1 2 0.46 0.35 0.1 0.91412 0.46 0.9141 0.35 0.687
2
r r 0.1 s 0.5 s 1.25 h h 2
79.788 79.788 0.1 1.25 0.5 220 220 1.082
Assuming the maximum aggregate size of 19mm
1.6 1
d d a
1 2
1
154 2 1.6 1 19 0.53
Fct r1 r2 s v Fct r1 r2 s f t 3 2
Fct (106.46 346.52) 277.198 3.257
2
3
0.687 1.082 0.53
Fct 341.56kN
Calculation of Fdow The calculation of Fdow is more complicated, since the ultimate punching load is needed to calculate the tensile stress in the
148
longitudinal reinforcing. In order to obtain the Fpun value the Microsoft Excel solver is used with two constraining conditions, i.e. Fpun Fct Fdow Fsw Fp and s 450MPa . The objective of the solver is to maximize the ratio of Fcalc:Ftest. The calculated value has no real value; it is merely used to comply with the way the solver is set up in Microsoft Excel
As is taken as the total area of longitudinal tensile reinforcing crossing the circle defined by r2.
s
Fpun
tan As
1004.93 103 tan 30 4377.67 s 397.606MPa
s
s fs
397.606 450 0.884
The number of bars is estimated by dividing the circumference of a circle with radius r2, with the average spacing of the tensile reinforcing. # _ bars
2 346.52 100
21.77
1 Fdow s2 f c f s 1 2 sin 2 bars 1 Fdow 21.77 16 2 50 450 1 0.884 2 sin 30 2 Fdow 97.70kN
Calculation of Fsw
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Assuming that the yield stress of the shear reinforcing is reached the contribution thereof is: Fsw Asw f sw sin sw Fsw 16
102
4 Fsw 565.48kN
450 sin 90
Failure Load Fpun Fct Fdow Fsw Fp Fpun 341.56 97.7 565.48 0 Fpun 1004.74kN
Microsoft Excel Calculation
Fig 10.1
Menétrey – Crack from column face
Shear crack originating at the first perimeter of shear clips
By investigating a scenario with the shear crack originating outside the first perimeter of reinforcing, i.e. rs 175mm and 8 shear stirrups intersecting the failure plane, the results are: Fpun
= 901.94kN
Fct
= 410.58kN
Fdow
= 208.61kN
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Fsw
= 282.74kN
Fig 10.2
Menétrey – Crack from first shear perimeter
Shear crack originating at the second perimeter of shear clips
Similarly if the shear crack originates outside the second perimeter of reinforcing, i.e. rs 290mm and no shear stirrups intersect the failure plane, the results are: Fpun
= 770.04kN
Fct
= 465.50kN
Fdow
= 304.54kN
Fsw
= 0.00kN
151
Fig 10.3
10.2.
Menétrey – Crack from second shear perimeter
Repaired Test Panel Using the calculations presented above and assuming a shear crack at 30º a rough estimate of the repaired panel‟s capacity was attempted. Four different cases were considered (1) Shear crack originating at the column face The following assumptions were made: The concrete contribution can be ignored 24 bars cross the shear crack. Only 8 of the bars on the inner perimeter are considered as still effective due to anchorage slip, etc. On the second perimeter the 8 new bars and the 8 existing clips are taken into account.
152
(2)
Shear crack originating at the first perimeter of shear reinforcing The following assumptions were made: The concrete contribution can be ignored 16 bars cross the shear crack. Only the second perimeter is assumed to bridge the shear crack.
(3)
Shear crack originating at the second perimeter of shear reinforcing The following assumptions were made: The concrete contribution can be ignored
153
(4)
24 bars cross the shear crack. Only the third perimeter is assumed to bridge the shear crack.
Shear crack originating at the third perimeter of shear reinforcing The following assumptions were made: The concrete contribution is taken into account No bars are crossing the shear crack.
154
11. Appendix C – Construction Details
Fig 11.1
Test Panel Reinforcing Schedule
155
Fig 11.2
Drawings for Formwork Manufacturing (not to scale)
156
Fig 11.3
Sketch for Placement of Original Shear Reinforcing
Fig 11.4
Sketch for Placement of Additional Shear Reinforcing
157
12. Appendix D – Prediction of Flexural Failure at Slabcolumn Connections – Yield Line Approach (Goodchild 2003) Internal Columns m m' m (1 i)
V 2
n A 1 3 V
(11.1)
Edge Columns m' m
(11.2)
180
(11.3)
n A 5.14 m V 1 3 V
(11.4)
Corner Columns n A 2 m V 1 3 V
(11.5)
General
m 2 m' m 1 i 1.14 i V 1 3
n A V
(11.6)
Extent of yield pattern
r
a b
V n A
(11.7)
158
m
Positive ultimate moment
kNm/m
m‟
Negative ultimate moment
kNm/m
n
Ultimate uniformly distributed load
kN/m2
A
Area of column cross section
m2
V
Ultimate load transferred to the column
kN
from the tributary area
Inscribed angle of the corner
159
13. Appendix E – Method for Epoxy Crack Injection Step 1: Clean the cracks Oil, grease, dirt, efflorescence and concrete particles will prevent desired epoxy penetration and bonding. Mechanical means or appropriate solvents should remove these foreign substances. Acids and corrosives are not permitted. Cracks should be water-jetted to clean out solvents and then blown out with compressed air and allowed to air-dry. Step 2: Seal the surface Surface cracks are to be sealed in order to prevent leakage of the epoxy before it has gelled. Where the crack face cannot be reached, but where there is backfill, the backfill material is often an adequate seal. Where extremely high injection pressures are needed, cracks should be cut out to a depth of about 13mm and about 20mm wide in a V-shape. This groove should then be filled with epoxy and finished flush with the concrete surface. Step 3: Installation of injection ports Three methods are generally used: (a) Drilled holes with a fitting inserted. Commonly a pipe nipple or tire valve is bonded into the hole (b) Bonded flush fitting. These fittings are commonly used when the cracks are not cut before sealing (c) Interruption in seal. With the use of a special gasket epoxy can be injected directly into the crack Step 4: Mixing of epoxy Mixing takes place continuously or in batches. When using the batch mixing procedure, care should be taken that the amount mixed should match the amount that can be used before gel of the epoxy takes place. In the continuous mixing system the two components of the epoxy pass through
160
individual driving and metering pumps before passing through an automatic mixing head. Preferably injection equipment should be equipped with sensors on both the component A and B reservoirs that will automatically stop the machine when only one component is being pumped to the mixing head. Step 5: Injection of the epoxy Hydraulic pumps, paint pressure pots and air-actuated caulking guns can be used. Pressure of injection should be selected carefully. Increased pressure often has no significant increase in filling rate of the crack. Excessive injection pressure may cause propagation of the crack, causing further damage to the structure. Vertical cracks should be filled from the lowest port upwards. When epoxy reaches the upper port, the lower one can be capped and injection continued at the upper one. Horizontal cracks are filled in a similar manner – from one end to the other. A crack can be regarded as filled when the injection pressure can be maintained, if not, epoxy is still filling the crack, or a leak may be present. Step 6: Seal removal The epoxy seal can be removed by means of grinding or other appropriate method. Fitting holes should be patched with an epoxy compound.
161
14. References 14.1. ACI318M-02 & ACI318RM-02, Building Code Requirements for Structural Concrete and Commentary, 2002, American Concrete Institute, Michigan, USA 14.2. Albrecht U, Design of flat slabs for punching – European and North American practices, 2002, Cement & Concrete Composites 24 (2002) pp. 531-538, Elsevier, www.elsevier.com 14.3. Alexander S, Simmonds S, Punching Shear Tests of Concrete Slab-column Joints Containing Fibre Reinforcement, 1992, American Concrete Institute, pp 425-432, Detroit, USA 14.4. Bazant ZP, Cao Z, Size effect in punching shear failure of slabs, 1987, ACI Structural Journal, V.84, pp. 44-53, Detroit, USA 14.5. Bazant ZP, Oh BH, Crack band theory for fracture of concrete, 1983, Materials and Structures, 16(93), pp155-177 14.6. Bazant ZP, Size effect in blunt fracture: concrete, rock, metal, 1984, Journal of Engineering Mechanics, V.110, pp. 518-535 14.7. Beutel R, Hegger J, The effect of anchorage on the effectiveness of the shear reinforcing in the punching zone, 2002, Cement & Concrete Composites 24 (2002) pp. 539-549, Elsevier, www.elsevier.com 14.8. BS8110-1:1997, Structural use of concrete – Part 1: Code of practice for design and construction, 2002, BSI, United Kingdom 14.9. CAN/CSA-S6-00, Canadian Highway Bridge Design Code, 2000, CSA International, Toronto, Canada 14.10. DIN 1045-1, Tragwerke aus Beton, Stahlbeton und Spannbeton, Teil 1: Bemessung und Konstruktion, 2001, Deutsches Institut für Normung, Berlin, Germany 14.11. Elstner RC, Hognestad E, Shearing strength of reinforced concrete slabs, 1956, ACI Journal, V.28 (1956), No.1, July, pp.29-58, Detroit, USA 14.12. Gardner NJ, Jungsuck Hugh, Lan Chung, Lessons from the Sampoong department store collapse, 2002, Cement & Concrete Composites 24 (2002), pp. 523-529, Elsevier, www.elsevier.com
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14.13. Gardner NJ, Relationship of the Punching Shear Capacity of Reinforced Concrete Slabs with Concrete Strength, 1990, ACI Structural Journal V.87 (1990), No.1, January-February, pp. 66-71, Detroit, USA 14.14. Goodchild C, Kennedy G, Practical Yield Line Design, British Cement Association, 2003, pp. 88-92, Crawthorne, United Kingdom 14.15. Harajli MH, Maalouf D, Khatib H, Effect of Fibers on the Punching Shear Strength of Slab-Column Connections, Cement & Concrete Composites, 17 (1995), pp. 161-170, Elsevier, www.elsevier.com 14.16. Hassanzadeh G, Sundqvist H, Strenghtening of Bridge Slabs on Columns, 1999, Royal Institute of Technology, KTH, Stockholm, Sweden 14.17. Hillerborg A, Modeer M, Petersson PE, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite element, 1976, Cement and Concrete Research, pp773-782 14.18. Kinnunen S, Nylander H, Punching of concrete slabs without shear reinforcing, 1960, Transactions No. 158, Royal Institute of Technology, Stockholm, Sweden 14.19. Kordina K, Zum Tragsicherheitsnachweis gegenüber Schub, Torsion und Durchstanzen nach EC 2, 1994, Teil 1: Erläuterungen zur Neuauflage von Heft 425 und Anwendungsrichtlinie zu EC 2. BuStb 89, H.4, pp97-100 14.20. Krüger G, Burdet O, Favre R, Punching Tests on Reinforced Concrete Flat Slabs with Eccentric Loading, 1998, 2nd International Ph.D. Symposium in Civil Engineering, Budapest, Swiss Federal Institute of Technology, Lausanne, Switzerland 14.21. Long AE, Bond D, Punching Failure of Reinforced Concrete Slabs, Proc of the Institution of Civil Engineers, May 1967, V.37, pp. 109-135, London, United Kingdom 14.22. Martinez-Cruzado JA, Qaisrani AN, Moehle JP, Post-tensioned Flat-plate Slabcolumn Connections Subjected to Earthquake Loading, 1994, 5th U.S. National Conference on Earthquake Engineering Proceedings, Vol. 2, pp. 139-148. 14.23. MC90, Bulletin 1 to 3, Structural Concrete. Textbook on behaviour, design and performance – updated knowledge of the CEB/FIP Model Code 1990, 1999, fib, Lausanne, Switzerland 14.24. Menétrey P, Synthesis of Punching Failure in Reinforced Concrete, 2002, Cement & Concrete Composites 24 (2002), pp. 497-507, Elsevier, www.elsevier.com
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14.25. Menétrey P, William KJ, A triaxial failure criterion for concrete and its generalization, 1995, ACI Structural Journal, V.92(2), Detroit, USA 14.26. Menétrey Ph, Brühwiler E, Punching shear strengthening of reinforced concrete: experimental and analytical investigations, 1997, Structural Faults and Repair, Edinburgh, United Kingdom, pp451-458 14.27. Mervitz CP, Ponsskuif, 1971, University of Stellenbosch, South Africa 14.28. Regan PE, Braestrup MW, Punching shear in reinforced concrete – A state-ofthe-art report, CEB Bulletin 168, 1985, International Federation of Structural Concrete (fib), Lausanne, Switzerland 14.29. Reineck K, et al, Punching of structural concrete slabs, Technical Report, Bulletin 12, 2001, International Federation of Structural Concrete (fib), Lausanne, Switzerland 14.30. Sherif AG, Behaviour of reinforced concrete flat slabs, 1996, The University of Calgary, Canada 14.31. Van Zijl GPAG, Wium J, Engineered Cement-Based Composites for Seismic Ductility, 2004, University of Stellenbosch, South Africa 14.32. Wallace JW, Kang THK, Seismic Performance of Flat Plate Systems, 14.33. Wood JGM, Pipers Row Car Park, Woverhampton, Quantative study of the causes of the partial collapse on 20th March 1997, 1998, Structural Studies & Design Ltd., Surrey, United Kingdom
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