# Performance of Punching Shear Reinforcement under Gravity Loading: Influence of Type and Detailing

TL;DR: In this paper, the performance of 11 different shear reinforcement systems against punching of inner slab-column connections under gravity loading was compared on the basis of experiments on 12 full-scale specimens, 8 of them newly reported.

Abstract: The performance of 11 different shear reinforcement systems against punching of inner slab-column connections under gravity loading was compared on the basis of experiments on 12 full-scale specimens, 8 of them newly reported. The slab geometry and flexural reinforcement ratio (1.5%) were kept constant. The shear reinforcement systems included different layouts of double-headed studs, individual links, bent-up bars and bonded post-installed reinforcement. All the systems were found to increase both the strength and the deformation capacity of the members but exhibited varying performances. The factors influencing the maximum punching strength of different systems, such as the layout and the anchorage conditions of the transverse reinforcement units, are described and analyzed. The mechanical model of the Critical Shear Crack Theory is used to explain the observed differences and provide design guidance. Comparisons to the codes of practice (ACI 318, Eurocode 2 and Model Code 2010) are also presented.

## Summary (3 min read)

Jump to: [INTRODUCTION] – [Gravity Loading: Influence of Type and Detailing] – [RESEARCH SIGNIFICANCE] – [EXPERIMENTAL PROGRAM] – [Parameters] – [Test setup] – [Main results] – [INTERPRETATION OF TEST RESULTS] – [Efficiency of shear reinforcement] – [INTERACTION BETWEEN FLEXURAL AND] and [CONCLUSIONS]

### INTRODUCTION

- Punching failures around columns often govern the design at the ultimate limit state of flat plates and footings.
- Post-installed shear reinforcement can also be used to strengthen existing slabs with insufficient punching shear capacity.
- Several different shear reinforcement systems are currently used, including bent-up bars, single- or multiple-leg stirrups, double-headed studs, and other kind of preor post-installed reinforcing bars, vertical or inclined (Fig. 1).
- Some codes of practice acknowledge these differences (such as ACI 318-143 and Model Code 20104), whereas others (Eurocode 25) do not explicitly account for them.
- Also, the influence of placing the shear reinforcement in a cruciform or a radial pattern13,14 and the efficiency of postinstalled shear reinforcement15-17 have been studied.

### Gravity Loading: Influence of Type and Detailing

- By Jürgen Einpaul, Fabio Brantschen, Miguel Fernández Ruiz, and Aurelio Muttoni ACI Structural Journal, V. 113, No. 4, July-August 2016.
- The reduction of the shear strength with increasing slab deformation is justified by the presence of wider cracks that weaken the diagonal shear-carrying strut around the column.
- It is also available in hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.
- This failure mode (and its associated factor ksys) is thus instrumental to determine the applicability of a given system to a particular case.
- The normalized punching shear capacity depends on the type of shear reinforcement only in the case of reaching the maximum strength for a given system (stirrups or studs in Fig. 3).

### RESEARCH SIGNIFICANCE

- This paper presents new experimental evidence of the performances of different shear reinforcement systems.
- The full-size test specimens were provided with high amounts of flexural and transverse reinforcement to avoid flexural failures and to achieve the maximum possible strength and deformation capacity of each system.
- The results are easily comparable as the other properties of the specimens were kept constant.
- The experiments provide clear evidence that the punching performance and strength of flat plates depends significantly on the type of shear reinforcement.
- This can be explained by the differences in detailing and properties of the transverse reinforcement units.

### EXPERIMENTAL PROGRAM

- The experimental program included testing of eight new punching specimens equipped with different types of shear reinforcement.
- All slabs had identical geometries and flexural reinforcement as well as similar material properties (common European reinforcing steel and normal-strength concrete).
- The thickness and slenderness ratios of the specimens were selected to model typical slab-column connections in buildings.
- Four specimens with similar properties from previous test campaigns of the authors are also included in the comparison.

### Parameters

- The main parameters of the tested slabs are presented in Table 1.
- The nominal concrete cover both on the top and on the bottom face of the slabs was 20 mm (0.8 in.).
- The investigation focused on comparing the maximum performance of reinforcement systems with different anchorage conditions, inclinations and layouts of the shear units, and extents of the shear-reinforced area.
- PM1 was reinforced with radially arranged noncontinuous bent-up bars (Fig. 5(g)), with double the number of bars in the first perimeter than in the second; 2. PT42 was reinforced with traditional bent-up bars on one perimeter (Fig. 5(h)); 3. PA31 was reinforced with inclined studs (Fig. 5(i)), otherwise similar to PL7; and 4.

### Test setup

- Load was applied on specimens at eight points located 120 mm (4.7 in.) from the slab edge by tension rods passing through cylindrical holes (Fig. 7).
- The oil pressure in the jacks was increased by shear reinforcement.
- More information about the test setup can be found elsewhere.
- The self-weight of the slab and the loading system was later added to the measured force.
- Rotations of the slabs were measured with four inclinometers placed on the top face of the slab on main axes 100 or 120 mm (3.9 to 4.7 in.) from the slab edge.

### Main results

- The failure of all specimens with shear reinforcement occurred either in the vicinity of the edge of the column plate (in all the cases with steeper failure cones than in the reference slab without shear reinforcement) or outside the furthermost perimeter of shear reinforcement units.
- Figure 8(b) shows a comparison of the achieved punching strengths.
- Systems with inclined shear reinforcement also showed enhanced performance compared to similar systems with vertical shear reinforcement, as can be seen by comparing the two systems with post-installed reinforcement (PS2 and PV15) or the two slabs reinforced using double-headed studs (PL7 and PA31).
- That said, all failures occurred as a separation of a central cone by an inclined cracking zone, with a sudden drop of force to only approximately 30% of the maximum load and a penetration of the column plate into the slab (the post-punching residual capacity23 was not investigated further in the present research).
- Closer examination revealed however that the inclination of the crack steepened closer to the studs and the crack did not cross shear reinforcement (Fig. 9(b)).

### INTERPRETATION OF TEST RESULTS

- Failure outside shear-reinforced area Failure outside of the shear-reinforced area occurs when the extent of such area is not sufficiently large.
- Anchorage of shear reinforcement units Observing the cracking patterns on the saw-cuts of the slabs with post-installed shear reinforcement (PS2 in Fig. 9(a)), the failure crack appears to develop through the transverse reinforcement (concrete screws ø19 mm [0.75 in.]) although the low level of load indicates that the screws had not reached yielding.
- This failure mode still demands additional investigation, as the bond conditions are influenced by transverse stresses and cracking due to bending of the specimen.
- This strut has to transfer the force from the first transverse element to the column.

### Efficiency of shear reinforcement

- As shown by the experimental results, the performance of various shear reinforcement systems can be quite different.
- The punching provisions of Model Code 20104 are based on the CSCT1 and thus acknowledge the differences between various systems through factor ksys that modulates the maximum punching capacity criterion governing for large shear reinforcement ratios19 (Fig. 2(c)).
- The calculated values of ksys are given in Table 3 and in Fig. 8(b).
- The tests presented in this paper suggest that values around 2.6 may be suitable for stirrups, whereas ksys can even be larger than 3.6 for studs when the spacing rules regarding the distance from the first stud to the column are respected.
- Again, the efficiency of post-installed shear reinforcement may vary significantly.

### INTERACTION BETWEEN FLEXURAL AND

- In the cases when punching governs the strength, the slab-column connections usually show limited deformation capacities unless very low amounts of flexural reinforcement or fairly large support areas are used.
- Thus, the design methods that are based on the theory of plasticity can only be applied with careful evaluation of the possible differences between assumed and actual distributions of internal forces.
- In a study on axisymmetric continuous slabs, Einpaul et al.28 have shown that considerable redistribution between hogging and sagging moments may occur before a punching failure.
- Thus, the local bending moment concentrations that appear in the vicinity of the columns according to elastic distribution of internal forces can be redistributed within the slab, provided that the slab has sufficient deformation capacity.
- This effect cannot appear in isolated specimens.

### CONCLUSIONS

- This paper presents the results of one slab without shear reinforcement and 11 slabs with identical geometrical param- eters but different systems of shear reinforcement tested to failure by punching.
- This is consistent with the approach followed by ACI 318 and Model Code 2010.
- The factor kmax, recently introduced in Eurocode 2 to account for the influence of punching shear reinforcement on the maximum punching shear strength, is also observed to depend on the type of transverse reinforcement.
- The calculated values of this parameter for the present tests varied between 1.4 and 1.9 with higher values associated again to slabs with headed studs.
- For uneven spacing of shear reinforcement close to the column, the failure crack may obtain a lower angle in the areas too far from the transverse elements.

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ArticlepubliéparleLaboratoiredeConstructionenBétondel'EPFL

PaperpublishedbytheStructuralConcreteLaboratoryofEPFL

ArticlepubliéparleLaboratoiredeConstructionenBétondel'EPFL

PaperpublishedbytheStructuralConcreteLaboratoryofEPFL

Title: Performanceofpunchingshearreinforcementundergravityloading:Influenceof

typeanddetailing

Authors: EinpaulJ.,BrantschenF.,FernándezRuizM.,MuttoniA.

Publishedin: ACIStructuralJournal

DOI 10.14359/51688630

Volume:

Pages:

Vol.113,No4

pp.827-838

City,country: FarmingtonHills,USA

Yearofpublication: 2016

Typeofpublication: Peerreviewedjournalarticle

Pleasequoteas: EinpaulJ.,BrantschenF.,FernándezRuizM.,MuttoniA.,Performance of

punching shear reinforcement under gravity loading: Influence of type and

detailing,ACIStructuralJournal,Vol.113,No4,FarmingtonHills,USA,2016,

pp.827-838.

[Einpaul16a]Downloadedbyinfoscience(http://help-infoscience.epfl.ch/about)128.178.224.97on25.07.201612:57

827ACI Structural Journal/July-August 2016

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

The performance of 11 different shear reinforcement systems

against punching of inner slab-column connections under gravity

loading was compared on the basis of experiments on 12 full-scale

specimens, eight of them newly reported. The slab geometry and

exural reinforcement ratio (1.5) were kept constant. The shear

reinforcement systems included different layouts of double-headed

studs, individual links, bent-up bars, and bonded post-installed

reinforcement. All the systems were found to increase both the

strength and the deformation capacity of the members but exhib-

ited varying performances. The factors inuencing the maximum

punching strength of different systems, such as the layout and the

anchorage conditions of the transverse reinforcement units, are

described and analyzed. The mechanical model of the Critical

Shear Crack Theory is used to explain the observed differences

and provide design guidance. Comparisons to the codes of practice

(ACI 318, Eurocode 2, and Model Code 2010) are also presented.

Keywords: critical shear crack theory; interior slab-column connections;

punching shear; shear reinforcement.

INTRODUCTION

Punching failures around columns often govern the design

at the ultimate limit state of at plates and footings. The

ways to enhance the punching capacity under gravity loads

include enlarging the supported area or slab thickness (for

instance, adding column capitals or drop panels), increasing

the concrete strength (or using ber-reinforced materials),

or using shear reinforcement.

1,2

The rst methods are not

always feasible due to practical or architectural consider-

ations, and using high-performance materials in the whole

slab may not be economically justied; thus, shear reinforce-

ment has been established as a common solution that allows

constructing slender slabs by avoiding local punching prob-

lems. Post-installed shear reinforcement can also be used to

strengthen existing slabs with insufcient punching shear

capacity. Several different shear reinforcement systems are

currently used, including bent-up bars, single- or multi-

ple-leg stirrups, double-headed studs, and other kind of pre-

or post-installed reinforcing bars, vertical or inclined (Fig. 1).

The performances of these systems, especially the maximum

punching strength in the case of large amounts of shear rein-

forcement, have been reported quite different depending on

the anchorage properties and detailing of the shear units.

2

Some codes of practice acknowledge these differences (such

as ACI 318-14

3

and Model Code 2010

4

), whereas others

(Eurocode 2

5

) do not explicitly account for them.

The crucial issue in designing and assembling shear

reinforcement is nding a compromise between efcient

anchorage and the ease of installation of the transverse

reinforcement units. A considerable amount of research

has been performed in the eld and several shear rein-

forcement systems have been experimentally investigated.

Other-than-conventional solutions composed of vertical

stirrups or headed studs, unusual systems, such as stirrups

that do not embrace main reinforcement,

6-8

combinations of

continuous stirrups and bent-up bars,

9,10

inclined stirrups,

11

as well as offcuts of steel I-sections

12

have been studied.

Also, the inuence of placing the shear reinforcement in a

cruciform or a radial pattern

13,14

and the efciency of post-

installed shear reinforcement

15-17

have been studied. The tests

have shown that all types of shear reinforcement improve the

punching capacity, but, on the basis of available experimental

Title No. 113-S71

Performance of Punching Shear Reinforcement under

Gravity Loading: Inuence of Type and Detailing

by Jürgen Einpaul, Fabio Brantschen, Miguel Fernández Ruiz, and Aurelio Muttoni

ACI Structural Journal, V. 113, No. 4, July-August 2016.

MS No. S-2015-142.R2, doi: 10.14359/51688630, received September 1, 2015, and

reviewed under Institute publication policies. Copyright © 2016, American Concrete

Institute. All rights reserved, including the making of copies unless permission is

obtained from the copyright proprietors. Pertinent discussion including author’s

closure, if any, will be published ten months from this journal’s date if the discussion

is received within four months of the paper’s print publication.

Fig. 1—Examples of punching reinforcement systems.

828 ACI Structural Journal/July-August 2016

data, it is difcult to compare the efciency of different systems

because of the different parameters (slab thickness and

span, column size, exural reinforcement, load introduction

system) used in the tests. In addition, many of the tests have

been performed on thin slabs and therefore cannot be consid-

ered representative of real structures. This paper presents an

experimental campaign on full-scale slab specimens equipped

with different types of shear reinforcement, whereas all the

other parameters are kept similar or constant. The results are

discussed and analyzed on the basis of the mechanical model

of the Critical Shear Crack Theory (CSCT).

1

The CSCT states that the punching shear strength of slabs

without shear reinforcement is a function of the opening of

critical crack w, which is assumed to be proportional to the

product of slab rotation ψ and effective depth of the slab d

(Fig. 2(a); refer to Appendix A

*

for design formulas). The

reduction of the shear strength with increasing slab defor-

mation is justied by the presence of wider cracks that

weaken the diagonal shear-carrying strut around the column.

Considering the slab rotation as the governing parameter

allows directly accounting for the reduced strength of more

slender slabs that show larger deformations for the same

level of applied shear force.

18

The CSCT failure criterion

also directly accounts for the size effect (reduced unitary

shear strength for thicker slabs).

1

The CSCT was extended by Fernández Ruiz and Muttoni

19

to be applicable on slabs with shear reinforcement. Different

failure modes that may occur in such slabs are summarized

in Fig. 2(b) to (e). Placing shear reinforcement that intersects

the critical crack allows for carrying part of the shear force

with transverse reinforcement. The total punching capacity

V

R

can thus be found by summing the concrete contribution

(V

R,c

in Fig. 2(b)—note that it decreases with increasing slab

rotation) and the forces in shear reinforcement units. These

latter forces depend on the strains in the transverse rein-

*

The Appendix is available at www.concrete.org/publications in PDF format,

appended to the online version of the published paper. It is also available in hard copy

from ACI headquarters for a fee equal to the cost of reproduction plus handling at the

time of the request.

forcement units, which increase for increasing slab rotation

due to larger openings of the critical shear crack that these

elements intersect (Fig. 2(b)). The steel contribution is also

limited by the yield strength of shear reinforcement, as well

as anchorage conditions of transverse reinforcement units

for some reinforcing systems.

19

The failure occurs when the

slab rotation reaches a critical value (ψ

R,within

) with a sudden

loss of concrete capacity and subsequent anchorage failure of

transverse reinforcement units or steel rupture. This failure

mode is referred to as failure within the shear reinforced area

and it is usually governing for low or moderate amounts of

shear reinforcement.

In slender slabs, if a large amount of shear reinforcement

is provided, punching may also occur before shear rein-

forcement reaches yielding due to a failure of the diagonal

compression struts developing between the edge of the

supported area and the top anchorage zones of the shear

reinforcement units (Fig. 2(c)).

2,19

According to the CSCT

1

(and the punching provisions of Model Code 2010

4

that are

based on this model), the punching capacity in this failure

mode is inuenced by the same parameters as for punching

without shear reinforcement. This is justied because both

failure modes are governed by the capacity of concrete to

carry shear forces (that is, governed by its cracking state).

It should be noted that the maximum punching capacity

is assumed to be independent of the amount of shear rein-

forcement (no strength increase above a certain amount

of provided shear reinforcement). However, positioning,

detailing, and anchorage properties of shear reinforcement

units inuence the capacity by controlling the locations and

transverse strains of the concrete struts. This is accounted for

in the CSCT by multiplying the concrete contribution failure

criterion (V

R,c

) with factor k

sys

(Fig. 2(c)) that depends on the

performance of the shear reinforcement system. The value of

k

sys

should be determined by specic testing for each system.

If a relatively large amount of shear reinforcement is

provided in a rather small area, punching failures may also

occur outside of the shear-reinforced zone (Fig. 2(d)). In this

case, that zone can be considered a supported area with a

Fig. 2—Punching failure modes of at slabs.

829ACI Structural Journal/July-August 2016

control perimeter outside of the last perimeter of transverse

reinforcement units.

Design for punching shear should be performed by consid-

ering all the above-mentioned failure modes. Failure within

the shear-reinforced area governs for selecting the amount

of shear reinforcement (the diameter and the number of rein-

forcement units on a perimeter), and failure outside of the

shear reinforced area dictates the required number of perim-

eters. Failure of the concrete struts (the maximum punching

shear strength) limits the maximum achievable punching

strength for each system. This failure mode (and its associ-

ated factor k

sys

) is thus instrumental to determine the appli-

cability of a given system to a particular case. Therefore, this

failure mode was targeted in the design of the test specimens

of the present campaign.

The predicted inuence of the amount of shear reinforce-

ment on the punching strength of a at plate is shown in Fig.

3. According to the provisions of Model Code 2010,

4

three

regimes depending on the shear reinforcement ratio can be

distinguished corresponding to failures within the shear-re-

inforced area without full activation of shear reinforcement,

failures within the shear-reinforced area with full yielding of

shear reinforcement (Fig. 2(b)), and the maximum punching

capacity (Fig. 2(c)). The normalized punching shear capacity

depends on the type of shear reinforcement only in the case

of reaching the maximum strength for a given system (stir-

rups or studs in Fig. 3). Also, in ACI 318,

3

the type of shear

reinforcement has an inuence on the maximum achievable

punching strength (stirrup and stud shear reinforcement as

well as structural steel shearheads are distinguished).

RESEARCH SIGNIFICANCE

This paper presents new experimental evidence of the

performances of different shear reinforcement systems. The

full-size test specimens were provided with high amounts

of exural and transverse reinforcement to avoid exural

failures and to achieve the maximum possible strength and

deformation capacity of each system. The results are easily

comparable as the other properties of the specimens were

kept constant. The experiments provide clear evidence that

the punching performance and strength of at plates depends

signicantly on the type of shear reinforcement. This can be

explained by the differences in detailing and properties of

the transverse reinforcement units.

EXPERIMENTAL PROGRAM

The experimental program included testing of eight new

punching specimens equipped with different types of shear

reinforcement. All slabs had identical geometries and ex-

ural reinforcement as well as similar material properties

(common European reinforcing steel and normal-strength

concrete). The thickness and slenderness ratios of the spec-

imens were selected to model typical slab-column connec-

tions in buildings. Four specimens with similar properties

from previous test campaigns of the authors are also included

in the comparison.

Parameters

The main parameters of the tested slabs are presented in

Table 1. All the slabs were square with a thickness of 250 mm

(9.8 in.) and a side length of 3 m (9.8 ft). The size of the square

support region was 260 mm (10.2 in.). Concrete cylinder

strength (measured on 160 x 320 mm [6.3 x 12.6 in.] samples)

was kept between 28.1 and 36.8 MPa (4070 and 5340 psi) for

all slabs except PT42 (where 51.7 MPa [7000 psi] concrete

was used). The maximum size of the aggregate (mainly

limestone alluvial gravel) was d

g

= 16 mm (5/8 in.) for all

slabs. The nominal exural reinforcement ratio for the inves-

tigated slabs was 1.50 with ø20 mm (0.79 in.) reinforcing

bars with a spacing of 100 mm (3.9 in.). The measured effec-

tive depths varied from 197 to 211 mm (7.8 to 8.3 in.) (refer

to Table 1 for details). The yield strength of the tensile rein-

forcing steel (between 515 and 709 MPa [74.7 and 103 ksi])

was determined experimentally for all specimens. Compres-

sion reinforcement consisted of ø10 mm (0.39 in.) bars

with spacing equal to that of the tension reinforcement. The

nominal concrete cover both on the top and on the bottom

face of the slabs was 20 mm (0.8 in.).

Table 1—Main parameters of test specimens

Slab d, mm (in.) f

c

, MPa (psi) ρ

ex

, % ρ

t

, % f

y

, MPa (ksi) Shear reinforcement

PV1

17

210 (8.3) 34.0 (4930) 1.50 — 709 (103) —

PS2 200 (7.9) 35.2 (5100) 1.57 1.03 583 (84.5) Fig. 5(f)

PF2

2

208 (8.2) 30.4 (4410) 1.50 0.79 583 (84.5) Fig. 5(d)

PB3 205 (8.1) 35.9 (5200) 1.53 0.79 576 (83.5) Fig. 5(b)

PR1 210 (8.3) 31.0 (4500) 1.50 0.63 515 (74.7) Fig. 5(e)

PL7

2

197 (7.8) 35.9 (5200) 1.59 0.93 583 (84.5) Fig. 5(e)

PB2 197 (7.8) 34.9 (5060) 1.53 0.79 590 (85.6) Fig. 5(c)

PE1 200 (7.9) 36.0 (5220) 1.57 0.73 590 (85.6) Fig. 5(e)

PV15

17

210 (8.3) 36.8 (5340) 1.50 0.95 527 (76.4) Fig. 5(j)

PA31 211 (8.3) 28.1 (4070) 1.49 1.03 576 (83.5) Fig. 5(i)

PM1 200 (7.9) 28.4 (4120) 1.57 1.48 515 (74.7) Fig. 5(g)

PT42 200 (7.9) 51.7 (7500) 1.57 0.19 551 (79.9) Fig. 5(h)

Note: Shear reinforcement ratio for radial and cruciform layout is dened as ρ

t

= A

v

/[b

0,rnd

∙ max(s

0

+ s

1

/2; s

1

)], where ΣA

v

is the total cross-section area of shear reinforcement units

in the innermost perimeter; b

0,rnd

is dened in Fig. 8; and s

0

and s

1

are dened in Fig. 6.

830 ACI Structural Journal/July-August 2016

Eleven specimens (eight slabs tested within the present

research and three previously published specimens) were

equipped with different types of shear reinforcement. The

investigation focused on comparing the maximum perfor-

mance of reinforcement systems with different anchorage

conditions, inclinations and layouts of the shear units, and

extents of the shear-reinforced area. An overview of the

campaign is shown in Fig. 4. Specimen PV1

17

(Fig. 5(a))

was a reference slab with no shear reinforcement. In the

series of slabs with vertical shear reinforcement:

1. PB3 was reinforced with individual hooked links

(Fig. 5(b));

2. In PB2, the anchorage of the individual links was enhanced

by enclosing the end hooks in blocks of ultra-high-perfor-

mance ber-reinforced concrete (UHPFRC)

20

(compressive

strength 150 MPa [21,800 psi], tensile strength 10 MPa

[1450 psi], and 3% ber content [ø0.16 mm (0.006 in.); ber

slenderness ratio 80)] (Fig. 5(c));

3. PF2 was reinforced with continuous cages of stirrups

(Fig. 5(d));

4. PL7 was reinforced with double-headed studs with

deformed shafts, and PR1 with studs with smooth shafts

(Fig. 5(e)); and

5. PS2 had post-installed shear reinforcement—vertical

screws were screwed into pre-drilled holes that were lled

with two-component epoxy adhesive (Fig. 5(f)).

Fig. 5—Details of shear reinforcement. (Note: dimensions in

mm; 1 mm = 0.039 in.)

Fig. 4—Overview of test program.

Fig. 3—Inuence of amount of shear reinforcement on

punching strength (parameters: slab span 7.3 m [24 ft.]; d =

210 mm [8.3 in.]; column size 260 x 260 mm [10.2 in.]; ρ

ex

= 1.5%; f

y

= 550 MPa [80 ksi]; f

yt

= 450 MPa [65 ksi]; f

c

=

35 MPa [5080 psi]; d

g

= 16 mm [5/8 in.]).

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TL;DR: In this article, the performance of different actual anchorage types (straight, hooked, U-shaped and headed bars) is analyzed and compared to the test results. But the results show a very significant influence of in-plane cracking on both strength and bond-slip stiffness, with decreasing mechanical performance for increasing crack openings.

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31 citations

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TL;DR: In this article, a two-parameter kinematic theory for punching shear in reinforced concrete slabs without shear reinforcement is developed taking into account the aforementioned observations, and the punching strength is calculated by summation of the contributions of compression ring, aggregate interlock, residual tensile stresses, and dowel action.

26 citations

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TL;DR: In this article, a failure criterion for punching shear based on the rotation of a slab is proposed, which correctly predicts the size effect (decreasing nominal shear strength with increasing size of the member).

Abstract: A mechanical explanation of the phenomenon of punching shear in slabs without transverse reinforcement is presented on the basis of the opening of a critical shear crack. It leads to the formulation of a new failure criterion for punching shear based on the rotation of a slab. This criterion correctly describes punching shear failures observed in experimental testing, even in slabs with low reinforcement ratios. Its application requires the knowledge of the load-rotation relationship of the slab, for which a simple mechanical model is proposed. The resulting approach is shown to give better results than current design codes, with a very low coefficient of variation (COV). Parametric studies demonstrate that it correctly predicts several aspects of punching shear previously observed in testing as size effect (decreasing nominal shear strength with increasing size of the member). Accounting for the proposed failure criterion and load-rotation relationship of the slab, the punching shear strength of a flat slab is shown to depend on the span of the slab, rather than on its thickness as often proposed.

490 citations

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TL;DR: In this paper, a new theoretical model based on the critical shear crack theory is presented to investigate the strength and ductility of shear-reinforced flat slabs and its application to various punching shear reinforcement systems is also detailed in the paper and its results are compared to available test data.

Abstract: The traditional approach of codes of practice for estimating the punching strength of shear-reinforced flat slabs is based on the assumption that concrete carries a fraction of the applied load at ultimate while the rest of the load is carried by the shear reinforcement. Concrete contribution is usually estimated as a fraction of the punching strength of members without shear reinforcement. The ratio between the concrete contribution for members with and without shear reinforcement is usually assumed constant, independent of the amount of shear reinforcement, flexural reinforcement ratio, and bond conditions of the shear reinforcement. The limitations of such an approach are discussed in this paper and a new theoretical model, based on the critical shear crack theory, is presented to investigate the strength and ductility of shear-reinforced slabs. The proposed approach is based on a physical model and overcomes most limitations of current codes of practice. Its application to various punching shear reinforcement systems is also detailed in the paper and its results are compared to available test data.

180 citations

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TL;DR: In this article, the authors investigated the influence of a set of mechanical and geometrical parameters on the punching shear strength and deformation capacity of flat slabs supported by interior columns.

Abstract: This paper presents the results of an extensive experimental campaign on 16 flat-slab specimens with and without punching shear reinforcement. The tests aimed to investigate the influence of a set of mechanical and geometrical parameters on the punching shear strength and deformation capacity of flat slabs supported by interior columns. All specimens had the same plan dimensions of 3.0 x 3.0 m (9.84 x 9.84 ft). The investigated parameters were the column size (ranging between 130 and 520 mm [approximately 5 and 20 in.]), the slab thickness (ranging between 250 and 400 mm [approximately 10 and 16 in.]), the shear reinforcement system (studs and stirrups), and the amount of punching shear reinforcement. Systematic measurements (such as the load, the rotations of the slab, the vertical displacements, the change in slab thickness, concrete strains, and strains in the shear reinforcement) allow for an understanding of the behavior of the slab specimens, the activation of the shear reinforcement, and the strains developed in the shear-critical region at failure. Finally, the test results were investigated and compared with reference to design codes (ACI 318-08 and EC2) and the mechanical model of the critical shear crack theory (CSCT), obtaining a number of conclusions on their suitability.

121 citations

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TL;DR: In this paper, an innovative system overcoming most of the previous difficulties is presented, which consists of inclined shear reinforcement installed within existing flat slabs by drilling holes only from the soffit of the slab and by bonding it with high-performance epoxy adhesive.

Abstract: A significant number of existing flat slabs currently require strengthening against punching shear for safety reasons (the increase of applied loads and deficiencies during design or construction) or to comply with more stringent code requirements. Available strengthening methods are, however, not completely satisfactory, or they cannot be applied in many cases (depending on the possibilities to enlarge column sizes or to intervene on the upper face of slabs). In this paper, an innovative system overcoming most of the previous difficulties is presented. It consists of inclined shear reinforcement installed within existing slabs by drilling holes only from the soffit of the slab and by bonding it with high-performance epoxy adhesive. The results of a test program on 12 full-size slabs 3.0 x 3.0 x 0.25 m (118 x 118 x 9.8 in.) show that such reinforcement is an efficient way to increase both the strength and deformation capacity of flat slabs. Finally, the design of the reinforcement based on the critical shear-crack theory (CSCT) is presented.

102 citations

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TL;DR: Fernandez et al. as mentioned in this paper proposed a critical crack theory based on the armature de poinconnement, dalle and the theory of the fissure critique of the critical crack.

Abstract: Keywords: armature de poinconnement ; dalle ; poinconnement ; theorie de la fissure critique ; punching shear reinforcement ; slab ; punching ; critical crack theory Reference EPFL-ARTICLE-174480 URL: http://ibeton.epfl.ch/util/script/sendArticle.asp?R=Fernandez11 Record created on 2012-01-26, modified on 2017-11-16

100 citations