AR T I C L E

Enhancing shear capacity of thin slabs with CFRP shearreinforcement: Experimental study

Jan Bielak | Josef Hegger

Institute of Structural Concrete, RWTHAachen University, Aachen, Germany

CorrespondenceJan Bielak, RWTH Aachen University,Institute of Structural Concrete, Mies-VAN-DER-Rohe-Str. 1, 52074, Aachen, Germany.Email: jbielak@imb.rwth-aachen.de

Funding informationFederal Ministry of Education andResearch, Grant/Award Number:03ZZ0380

Abstract

Employing non-metallic reinforcement made of fiber-reinforced polymers (FRPs)

as textile grids is one promising extension of the utilization range of FRP in con-

crete construction, and thin planar elements reinforced in this manner have high

application potential in bridge or parking garage decks, in façades, or in webs

and flanges of hollow core cross-sections. Existing models for predicting the shear

resistance of such elements were derived for solid cross-sectional dimensions sim-

ilar to conventional steel-reinforced structures, and their application to thin slabs

is debatable. This paper presents the results of an extensive experimental program

on the one-way shear capacity of slabs without and with carbon FPR textile shear

reinforcement. A variation of member height, shear slenderness, and shear rein-

forcement ratio allowed for analysis of the most relevant influencing factors on

shear resistance. Both planar and preformed C-shaped grids enhance the shear

capacity and are suitable as shear reinforcement in thin slabs. The experimental

results are the foundation for the extension of shear models to thin slabs with

FRP reinforcement and for derivation of new unifying shear models that are

applicable to a wider range of reinforcement materials and member dimensions.

KEYWORD S

CFRP, shear, shear slenderness, size effect, slabs, textile reinforcement

1 | INTRODUCTION

With a high tensile strength and excellent resistance tocorrosion, non-metallic reinforcement made of fiber-reinforced polymers (FRPs) is perfectly suited as rein-forcement for concrete constructions exposed to severeenvironmental conditions. Concrete cover, member

thickness, and thus self-weight can be reduced while pro-viding better load-bearing capacities. Extensive researchwas performed in the past to adapt existing models andto derive new specifications for constructions with FRPreinforcement.1–6 These adaptions aimed at a replace-ment of steel (e.g., References 7,8), and most FRP rein-forcement products that are available and actually usedin practice nowadays are similar in shape to steel rebar(e.g., Reference 9). Existing guidelines and code provi-sions are typically limited to such reinforcement and tosimilar dimensions as in steel-reinforced concrete.10–12

The collapses of thin carbon fiber-reinforced polymer

Discussion on this paper must be submitted within two months of theprint publication. The discussion will then be published in print, alongwith the authors’ closure, if any, approximately nine months after theprint publication.

Received: 20 May 2021 Revised: 28 July 2021 Accepted: 16 August 2021

DOI: 10.1002/suco.202100325

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any

medium, provided the original work is properly cited and is not used for commercial purposes.

© 2021 The Authors. Structural Concrete published by John Wiley & Sons Ltd on behalf of International Federation for Structural Concrete

Structural Concrete. 2021;1–17. wileyonlinelibrary.com/journal/suco 1

(CFRP)-reinforced parking deck structures described inReference 13 underline that the transfer of these designrules without adaption to thin slabs pose great risk.

The simple replacement of steel does not exploit thetrue potential of the radical innovation in terms of reduc-tion of concrete cover and reduction of self-weight, sincethe cover depth remains defined by the diameter of thebars and bond requirements. New construction and rein-forcing strategies are called for: One promising concept isthe arrangement of fibers in textile fabrics or grids as lon-gitudinal reinforcement of planar elements or as shearreinforcement for linear members. Such elements havehigh application potential, for example, as bridge orparking garage decks,14–17 as façade elements,18–20 or aswebs or flanges in hollow-core cross-sections and profiledlinear members.21–23 The distribution of reinforcementreduces local stress concentrations and better activatesthe concrete, especially for transfer of bond-induced ten-sile stress. This allows for reduction of the concrete coverrequired for bond and leverages the benefits of the corro-sion resistance of nonmetallic reinforcement. Productiontechniques for such grids are long known and commer-cial products are available since 30 years.24,25 However,while for the flexural design of thin slabs with nonmetal-lic reinforcement design models are established, and par-tial safety factors have been proposed26 accurate andgeneral models to predict the shear capacity of elementsin the range of 30–200 mm member thickness withoutshear reinforcement are amiss. Consequently, for con-struction with non-metallic reinforcement in this particu-larly promising range, tedious, and cost-intensive project-specific experiments and approval processes are stillrequired.14,27 For typical reinforced concrete slabs,designers try to avoid the arrangement of shear reinforce-ment as its installation is labor and cost intensive. Yet inspecific situations, it might be required to enhance shearcapacity when increasing concrete strength or addinglongitudinal reinforcement are not sufficient. This callsfor engineering and design models also for thin shear-reinforced slabs. This paper presents the results of alarge-scale experimental program filling this research gapand providing the basis for the derivation and validationof models that are applicable to a wider range of memberheights and various reinforcement types.

2 | EXPERIMENTAL PROGRAMAND MATERIALS

2.1 | Test setup and test matrix

The experimental investigation of the one-way shear capac-ity of slabs comprised of 72 slab segments with a width of

200 mm. It is known from steel-reinforced concrete that themember width has either no influence on the relative shearstrength28,29 or that testing slab segments is conservativedue to inner redistribution of loads in case of local fail-ure.30,31 Thus, the relative shear capacity determined onslab segments can be assumed to be representative for widerslabs. All specimens were tested in a three-point single spansetup with one concentrated load spread over the entirewidth of the member with a steel roll (Figure 1). One fixedand one free steel roll provided vertical support. The longi-tudinal reinforcement ratio and strength, the shear slender-ness, and the projecting length of 100 mm at the supportswere selected in such a way that premature flexural oranchorage failure could be prevented. The vertical displace-ments were measured with two LVDTs at the axis of loadintroduction. For a subset of the tests, a digital image corre-lation (DIC) system was employed to trace crack propaga-tion throughout the experiment. All specimens were loadedmonotonically and deformation-controlled with 1 mm/mincrosshead or cylinder velocity.

The experimental program featured different rein-forcement configurations: Reference tests without shearreinforcement, specimens with planar vertical CFRPgrids (CR1), and specimens with C-shaped preformedCFRP grids (CRP1–CRP3) (Figure 2). The memberheight, shear reinforcement ratio, and shear slendernesswere varied systematically (Table 1). These parametersreflect the dimensions of examples from practice.14 In thecore series with 100 and 145 mm member height, threerepetitions per configuration were performed. In themajority of the tests, the concentrated load was appliedin mid-span; only for the largest height of 200 mm, three

a2

h

b

elastomerstrip

Ø 30 mm steel roll

fixed roll free roll

d

Anm: longitudinalreinforcement

F

F

LVDT

A

A

section A-A

side view

a1e1=100 e2=100

LLtot

warp 0°

direction of casting

LVDT

anm,w: shearreinforcement

FIGURE 1 Test setup for slab segments subjected to one-way

shear in three-point loading (Adapted from Bielak et al.,32

Bielak et al.33)

2 BIELAK AND HEGGER

54

1

57

d0

21

=

00

1

planar grid C-shaped preformed grid

4 layers +2 yarns CR1

Anm = 79.6 mm2

3 layers CR1= 54.3 mm2Anm 4 layers +

2 yarns CR1Anm = 79.6 mm2

3 layers CR1= 54.3 mm2Anm

we

ft 9

0°

weft 90°

b = 200

09

weft 90°

CR1 95 mm2/m

50

[mm]

51

1

95 mm2/m

d0

8=

53

1

we

ft 9

0°

d3

71

=

5 layers +2 yarns CR1

Anm = .7 mm297

00

2

06

1

5 layers +2 yarns CR1

Anm = .7 mm297

CRP1 CRP2 CRP3

09

1

d0

21

=

reference tests

4 layers +2 yarns CR1

Anm = 79.6 mm2

3 layers CR1= 54.3 mm2Anm

weft 90°

b = 200

d0

8=

d3

71

=

5 layers +2 yarns CR1

Anm = .7 mm297

FIGURE 2 Reinforcement configurations in single span slab segments

TABLE 1 Test matrix

# tests

h = 100 h = 145 h = 200

λ = 4 λ = 5 λ = 4 λ = 5 λ = 3 λ = 4

Reference 3 3 3 3 - 1

Two planar 3 3 3 3 2 4

Four planar 3 3 3 3 - -

Two C-shaped 3 3 3 3 1 4

Four C-shaped 3 3 3 3 - -

FIGURE 3 Reinforcement variants

utilized as longitudinal and shear

reinforcement (Photos: Jan Bielak)

BIELAK AND HEGGER 3

specimens were tested with eccentric loading in two par-tial tests: First with a shear slenderness of four and subse-quently with a slenderness of three.

2.2 | Reinforcement

A symmetric epoxy-impregnated biaxial carbon-fiber grid(CFRP textile) was employed for all specimens as longitu-dinal reinforcement, with the warp direction (0�) alignedto the member axis. The planar shear reinforcement wascut from the same grid, with the weft direction (90�) ori-ented vertically, much like a shear ladder known fromsteel-reinforced concrete. Three different heights of C-shaped preformed grids were utilized as alternative shearreinforcement variant: 75, 115, or 160 mm. They consist ofthe same base material, a carbon textile with grid spacing38 mm � 38 mm, but the yarn dimensions in impregnatedhardened state vary due to the different production tech-nique: The vertical direction is less tensioned and thus lessstraight, and the yarns are wider in the corners, whichresults in a locally smaller yarn cross-sectional height(Figure 3). The outer width of the preformed elementsincluding the tails was 50 mm. In Table 2, the characteris-tics for all reinforcement variants are given. The tensileproperties of CR1 were taken from Reference 34, but theywere validated with own uniaxial tensile tests using thesame concrete as in the shear tests and employing thesetup described in Reference 35. Results of these tests aregiven in Reference 36. For one subset of tests, additionalbatch-dependent material tests from the manufacturerwere available. The properties of CRP1 and CRP2 weredetermined with yarn pullout tests (YPO) on yarns cut

from the preformed grid embedded 15 or 25 mm in twoconcrete blocks.33 All yarns failed in the free length or inthe transition zone to the concrete and not in the bend.36

The modulus of elasticity of the preformed reinforcementwas determined with a different profile height of 410 mmto allow for an undisturbed strain measurement in the freelength. These elements had the same yarn titer, samematerials, and were produced with the same technique.All reinforcement was purchased from one manufacturer(solidian GmbH) in hardened or preformed state.

The grid openings of the multilayered longitudinal rein-forcement were aligned, and each layers' weft and warpyarns were stacked without spacers other than the trans-verse yarns. The preformed grids had a slight offset in longi-tudinal direction to allow the transverse yarns of thelongitudinal reinforcement to be inserted in the grid open-ings. The longitudinal yarns of the shear reinforcementwere considered in the calculation of the longitudinal rein-forcement ratio and the effective depth up to mid-depth ofthe cross-section. In those specimens with four C-shapes asshear reinforcement, all but one layer of the longitudinalreinforcement had to be separated to allow for mutual inter-section. Cut-out yarns were arranged in an additional layeror in between the other layers (Figure 2).

2.3 | Concrete

All specimens were cast with the same concrete mixC3-HF2-165-4 given in Table 3. It has been adapted froma high-strength concrete proposed in the coordinatedresearch initiative carbon concrete composites (C3).37 Themaximum aggregate size 4 mm was adapted to the grid size

TABLE 2 Reinforcement characteristics for impregnated planar and preformed grid

Axialspacing ofyarns

Cross-sectionalarea per yarna

Cross-sectionalarea per metera

Modulus ofelasticity

Mean ultimatestress

Anchoragelength

Inner radiusof bend

(mm) (mm2) (mm2/m) (N/mm2) (N/mm2) (mm) (mm)

Planar CFRPgrid (CR1)

(0�) 38 3.62 95 244,835 3221b (n = 204)c 79 -

(90�) 243,828 3334b (n = 218)c 113 -

PreformedCRP1

(0�) - - - -

(90�) 175,601 1969d - 8.2 (n = 26)c

PreformedCRP2

(0�) - - - -

(90�) 175,601 1969d - 8.2 (n = 26)c

PreformedCRP3

(0�) - - - -

(90�) 175,601 1969b - 4.1 (n = 13)c

afilament cross sectional area without epoxy impregnation.bfor the reference tests without shear reinforcement, the batch-dependent material strength of the reinforcement was 3624 N/mm2 for 0� and 3599 N/mm2 for

90�, tested on n = 6 yarns per direction by the manufacturer.cn = number of tests.dmean of CRP1 (n = 6) and CRP2 (n = 7).

4 BIELAK AND HEGGER

of the reinforcement. No internal or external vibration wasrequired due to the self-compacting properties of the freshconcrete. The binder compound BMK-D5-1 was developedby Deuna Zement GmbH in subproject B2 of C3.38

According to the new EN 197-5, it classifies as CEM VI(S-LL).39 The content of Portland cement is 41%; granulatedblast furnace slag (42.6%) and limestone powder (16.4%) arethe other major components. The fines content of the com-pound has been optimized with an ultrafine blast furnaceslag powder. For production, the aggregate and cementi-tious binder were mixed for 1 minute in dry state. Afteradding the water, each batch was mixed for another 3 min.

The concrete compressive strength was determinedon the day of testing of the respective experiments withcubes (150 � 150 � 150 mm3,41), cylinders (d = 150/h = 300 mm,41), or prisms (40 � 40 � 160 mm3)according to References 42,43. A database evaluation ofall batches cast at IMB of this concrete mix revealed amean conversion factor of 1.19 between compressivestrength of cubes and cylinders of age 7–60 days.36 Themodulus of elasticity Ec was determined on cylindersaccording to DIN EN 12390–1340 and the flexural tensilestrength fct,fl on prisms according to References 42,43.

3 | RESULTS AND DISCUSSION

3.1 | Failure mechanisms

The reference tests without shear reinforcement failed inshear compression or in diagonal tension or a

combination of both. These are the typical shear failuremechanism anticipated for slender rectangular one-wayelements and occur also for steel-reinforced orFRP-reinforced members.44 However, in international lit-erature, different terms and names for such failure exist.Here, the following definition applies: In the event ofshear-compression failure, the compression zone wasdiminished by growth of the shear crack, and in manycases, the constricted concrete bursts out upward at fail-ure. A secondary tension crack from the upper specimenface sometimes facilitated the burst-out (Figure 4). Alter-natively, the specimen halves rotated and slid along adiagonal shear crack, and the longitudinal reinforcementwas sheared off or the bottom concrete cover spalled,which represents the diagonal tension failure mode. Bothmechanisms are also depicted in Figure 5. Previous testswith the same reinforcement but a smaller reinforcementratio showed similar failure mechanisms.45 The forma-tion of a critical shear crack leads usually to a suddenshear failure of the slab segments. In most cases, thiscrack was formed from existing flexural shear cracks,which rapidly extended into the compression zone andsimultaneously along the longitudinal reinforcement asdowel crack. This dowel crack splat off the bottom con-crete cover. In the case of multilayered reinforcement,often the dowel crack occurred in the uppermost layerand a cantilevering dowel block containing the longitudi-nal reinforcement was formed. Generally, the cracks ranthrough the aggregate grains.

All shear-reinforced specimens also failed in shear.The flexural reinforcement remained intact up to failureand distinct shear cracks which ran through the aggre-gate were present. This failure manifested in differentpatterns, that is, shear compression failure through blow-

TABLE 3 Composition of C3-HF2-165-4

Ingredient

Density Content

(kg/m3) (kg/m3)

Cementitious binder compound BMK-D5-1 CEM VI (S-LL)

2962 707

Fine quartz sand F38 S 2650 294

Quartz sand 0.1–0.5 mm 2630 243.2

Quartz sand 0.5–1.0 mm 2630 201.4

Quartz sand 1.0–2.0 mm 2630 148.9

Quartz fine gravel 2.0–4.0 mm 2630 593.5

Superplasticizer (polycarboxylatether-basis) MC-VP-16-0205-02

1070 15a

Water 1000 165

aDepending on ambient temperature and humidity at the day of casting, the

content of superplasticizer has been reduced to prevent aggregatesegregation. Batches for specimen heights 100 and 145 mm had reductionsbetween 0% and 10%. All batches for 200 mm specimen height had 30%–40%reduction, as the supplier of the quartz sand and gravel (aggregate sizes 0.1–4 mm) changed and a new batch of the superplasticizer was used.

(a)

(b)

d0

8=

failure

97% Fmax

4 = 0.34%= l

secondary crackburst-out

FIGURE 4 Failure of reference specimen SH-3PT-3C-4C-84-V1

without shear reinforcement: (a) last image prior to failure and

(b) after failure (Adapted from Bielak36)

BIELAK AND HEGGER 5

up of the compression zone or diagonal tension failurewith a linear shear crack and rotation and sliding of thespecimen halves along this crack line (Figure 5). Mostinteresting is the role of the shear reinforcement and towhat extent it contributed to shear resistance. After itscontribution failed, the specimens reacted similar to non-shear-reinforced members in their post peak-load behav-ior. In some specimens, the longitudinal reinforcementwas sheared off in the aftermath of shear failure.

28 of 30 specimens with planar shear reinforcementhad vertical splitting cracks in the plane of shear reinforce-ment at failure (Figure 6). These cracks split either thecompression zone above the critical shear crack (Figure 6a) or could be observed in the lower specimen part belowthe shear crack (Figure 6b). Such cracks can clearly beattributed to bond action of this type of reinforcement.46,47

Many specimens failed suddenly and without residualcapacity. The vertical yarns of the planar grid remainedintact and were pulled out from the split concrete. This isplausible with regard to the anchorage length required torupture the yarns (Table 2). Even in optimal conditions forthe specimens with 200 mm height and shear reinforce-ment height of 190 mm (Figure 2), when the shear crackcrosses a vertical reinforcement element in mid-depth, ananchorage length of merely 95 mm on either side is avail-able. This is below the extrapolated value of 113 mm forthe weft direction of the grid in the same concrete. In somespecimens, the rotation along the shear crack and the sud-den shift at collapse sheared off the vertical yarns, but thiswas not the initial cause of failure.

From this observation, first conclusions on the role ofplanar vertical reinforcement can be drawn:

• The shear reinforcement transfers vertical loads, as itsability to split the concrete indicates.

• The shear reinforcement cannot be fully activated upto its rupture strain.

• The suddenness of failure and the noises that occurredduring testing indicate toward a coincidence of ulti-mate resistance with the formation of splitting cracksand consequently the loss of anchorage of verticalyarns.

The preformed C-shaped reinforcement elementsbehaved to some extent differently from the planar grids,and a variation of failure mechanisms could be observeddepending on the member height and reinforcementratio (Figure 7). In the smaller slab segments withh = 100 mm, the vertical yarns remained predominantlyintact (Figure 7a). Only for two specimens with two verti-cal C-legs, a rupture in the bend could be identified afterfailure. Whether this rupture occurred as primary or sec-ondary failure could not be distinguished. A similarbehavior was observed for specimens with h = 145 mm:Again, sporadic ruptures in the bend were identified afterfailure. Extensive cracking in the plane of the verticalpart of the C in combination with splitting cracks frombond and dowel action in the layer of longitudinal rein-forcement enabled a lateral pullout of the undamaged C-shapes at failure for 100 and 145 mm high specimens(Figure 7b). Essentially, this was also an anchorage fail-ure like for the planar grids, at least after surpassing ulti-mate load. Closing the C-shapes in a stirrup or helix typewould probably have not increased ultimate resistancefor the own specimens, due to the following reason: Thelateral pull-out in the compression zone occurred in

compression zone blow-up

rotationpart Brotation

part A

rotation

slidingspallingof cover

(a)

(b)

FIGURE 5 Failure kinematics for shear-reinforced specimens

after failure of contribution of shear reinforcement: (a) shear

compression failure and (b) diagonal tension failure (Reproduced

from Bielak36)

FIGURE 6 Failure mechanism for members with planar shear

reinforcement: (a) vertical splitting cracks in compression zone

indicating anchorage failure of shear reinforcement and (b) intact

pulled-out vertical shear reinforcement formerly crossing the shear

crack and vertical splitting crack in direction of the tension zone

(Adapted from Bielak36)

6 BIELAK AND HEGGER

the horizontal branch of the shear crack. A shear-compression failure with blow-up of the compressionzone or a diagonal tension failure with displacementalong the shear crack could not have been preventedbecause the compression zone is situated above the hori-zontal leg of the shear reinforcement for this memberheight. Choosing a smaller concrete cover for the stirrupsto better confine the compression zone is no option, as aminimum cover for anchorage is required. The ownobservations are quite similar to those in References48,49 where a closed stirrup/helix was utilized. The crackpattern reported there was quite similar to the owndespite the different shear reinforcement form, and theauthors report also “shear-compression crushing failure.”

In contrast to the smaller heights, all members withh = 200 mm showed rupture in the bend portion of thevertical C-shapes after failure (Figure 7c,d). This rupturemight partially be explained by the smaller bend radiusof the reinforcement CRP3, probably a result from therelative position of the longitudinal yarns to the bend.

Both types of shear reinforcement, planar and C-shaped, were symmetric grids and contained longitudinalyarns. These yarns also crossed the shear crack. Theirweak connection to the vertical yarns by resin, and thepolypropylene knitting thread was simply sheared off, aswas observed in many specimens. Neither the verticalnor the longitudinal yarns were damaged by this process.The vertical bond cracks in the plane of the shear rein-forcement allowed for a nearly free rotation of theseyarns and consequently also of the specimen halves alongthe shear crack. The yarns might play a significant role in

the formation of the vertical splitting cracks. Their dowe-lling action, which is activated by potential sliding of theshear crack faces, in combination with the wedge-shapeof the yarns also induces splitting stress in the concrete.Whether their presence is detrimental or beneficial forshear resistance remains an open question, as all speci-mens were equipped with the same symmetric reinforce-ment. The longitudinal yarns certainly lower theundisturbed area of concrete in lateral specimen direc-tion, which resists the splitting stresses.

Table 4 lists the results of all reference tests and therespective concrete strength at the day of testing. Allresults for the shear-reinforced specimens are given inTable 5. The nomenclature denotes the type of test (SH:shear test, 3PT: three-point loading), amount, and type oflongitudinal reinforcement (3C/4,5C/5,4C: number oflayers and C for carbon), amount and type of shear rein-forcement (2I/2C/4I/4C: number and shape of shearreinforcement elements, I for planar, C for C-shaped),total specimen length in centimeter, and number of repe-tition (V1–V3). The crack patterns and load-deflectioncurves of each test can be found in Reference 36.

3.2 | Load-deflection behavior

Between each of the three repetitions per configuration,only small scatter was observed. Despite their differentanchorage mechanism, the two shear reinforcementtypes led to similar load-deflection behavior and compa-rable ultimate loads (Figure 8). Members with C-shaped

)b()a(

)d()c(

secondary kink

yarns inbend intact

lateral pullout

rupturein bend

rupturein bend

secondary kinks

h = 100 mmSH-3PT-3C-2C-100-V2

h = 145 mmSH-3PT-4,5C-2C-140-V1

h = 200 mmSH-3PT-5,4C-2C-160-V2

h = 200 mmSH-3PT-5,4C-2C-230-V1a

FIGURE 7 Failure mechanisms for

members with C-shaped reinforcement: (a) and

(b) lateral pullout of intact yarns after shear-

compression failure; (c) and (d) rupture of yarns

in the bend at failure (Reproduced from

Bielak36)

BIELAK AND HEGGER 7

TABLE

4Overviewof

experimen

talresultsforreference

testswithou

tshearreinforcem

ent

Specim

enno

Lb

hd

a/d

M/

(V�d)

ρ lEnm,l

f nm,l

Ec

f c,cyl

f c,cu

f c,pr

f ct,fl

Fail.

Vu

Vu,exp

(-)

(mm)

(mm)

(mm)

(mm)

(-)

(-)

(%)

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(-)

(kN)

(kN)

SH-3PT

-3C-84-V1

639

201

9979

4.03

4.04

0.34

244,835

3624

39,814

110.5

119.1

116.0

10.1

S28.5

28.5

SH-3PT

-3C-84-V2

640

200

100

774.14

4.14

0.35

244,835

3624

39,814

110.5

119.1

116.0

10.1

S23.8

23.9

SH-3PT

-3C-84-V3

640

200

100

774.14

4.14

0.35

244,835

3624

39,814

110.5

119.1

116.0

10.1

S25.8

25.8

SH-3PT

-3C-100-V1

800

200

100

785.10

5.11

0.35

244,835

3624

39,814

110.5

119.1

116.0

10.1

S22.6

22.6

SH-3PT

-3C-100-V2

800

200

100

795.05

5.06

0.34

244,835

3624

39,814

110.5

119.1

116.0

10.1

S25.1

25.2

SH-3PT

-3C-100-V3

800

200

101

804.98

4.99

0.34

244,835

3624

39,814

110.5

119.1

116.0

10.1

S26.9

26.9

SH-3PT

-4,5C-

116-V1

960

201

146

116

4.14

4.15

0.34

244,835

3624

39,814

110.5

119.1

116.0

10.1

S30.5

30.6

SH-3PT

-4,5C-

116-V2

960

200

146

117

4.12

4.13

0.34

244,835

3624

39,814

110.5

119.1

116.0

10.1

S30.5

30.6

SH-3PT

-4,5C-

116-V3

960

201

145

115

4.17

4.18

0.35

244,835

3624

39,814

110.5

119.1

116.0

10.1

S27.3

27.3

SH-3PT

-4,5C-

140-V1

1200

200

146

117

5.13

5.15

0.34

244,835

3624

41,451

107.8

126.1

115.2

11.5

S28.6

28.7

SH-3PT

-4,5C-

140-V2

1198

200

147

119

5.03

5.05

0.33

244,835

3624

41,451

107.8

126.1

115.2

11.5

S30.2

30.3

SH-3PT

-4,5C-

140-V3

1200

200

147

118

5.09

5.11

0.34

244,835

3624

41,451

107.8

126.1

115.2

11.5

S26.6

26.7

SH-3PT

-5,4C-

160-V1

1399

201

200

173

4.04

4.06

0.28

244,835

3221

40,715

106.6

126.9

107.2

10.6

S27.7

27.9

8 BIELAK AND HEGGER

TABLE

5Overviewof

experimen

talresultsof

shear-reinforced

specim

ens

Specim

enno.

Lb

hd

a/d

M/(V�d)

ρ lEnm,l

f nm,l

TW

ρ nm,w

f nm,w

Enm,w

Ec

f c,cyl

f c,cu

f c,pr

f ct,fl

Fail.

Vu

Vu,exp

(-)

(mm)

(mm)

(mm)

(mm)

(-)

(-)

(%)

(N/m

m2 )

(N/m

m2 )

(-)

(%)

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(-)

(kN)

(kNm)

SH-3PT

-3C-2I-84-V1

640

201

9976

4.18

4.19

0.40

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

116.5

11.2

A/S

30.7

30.7

SH-3PT

-3C-2I-84-V2

639

200

101

784.07

4.07

0.39

244,835

3221

I0.10

3334

243,828

42,891

106.5

124.6

116.5

11.2

A/S

29.7

29.8

SH-3PT

-3C-2I-84-V3

639

201

102

764.22

4.22

0.40

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

116.5

11.2

A/S

30.6

30.7

SH-3PT

-3C-2I-100-V1

800

201

100

805.03

5.04

0.38

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

120.0

11.6

A/S

29.9

30.0

SH-3PT

-3C-2I-100-V2

798

200

100

775.18

5.19

0.40

244,835

3221

I0.10

3334

243,828

42,891

106.5

124.6

120.0

11.6

A/S

28.1

28.2

SH-3PT

-3C-2I-100-V3

799

201

100

805.01

5.02

0.38

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

120.0

11.6

A/S

27.5

27.6

SH-3PT

-4,5C-2I-116-V1

959

201

145

117

4.10

4.11

0.37

244,835

3221

I0.09

3334

243,828

45,380

107.5

121.5

126.9

12.4

A/S

40.7

40.7

SH-3PT

-4,5C-2I-116-V2

959

201

147

118

4.05

4.05

0.37

244,835

3221

I0.09

3334

243,828

45,380

107.5

121.5

126.9

12.4

A/S

44.7

44.8

SH-3PT

-4,5C-2I-116-V3

958

201

147

117

4.07

4.08

0.37

244,835

3221

I0.09

3334

243,828

45,380

107.5

121.5

126.9

12.4

S41.3

41.4

SH-3PT

-4,5C-2I-140-V1

1201

201

144

117

5.14

5.15

0.37

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

113.5

9.8

A/S

43.3

43.4

SH-3PT

-4,5C-2I-140-V2

1200

201

144

114

5.25

5.27

0.38

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

113.5

9.8

A/S

40.0

40.1

SH-3PT

-4,5C-2I-140-V3

1199

201

144

111

5.38

5.40

0.39

244,835

3221

I0.09

3334

243,828

42,891

106.5

124.6

113.5

9.8

A/S

44.0

44.1

SH-3PT

-4,5C-4I-140-V1

1197

201

146

121

4.96

4.97

0.39

244,835

3221

I0.19

3334

243,828

45,380

122.1

-126.7

12.5

A/S

58.7

58.8

SH-3PT

-4,5C-4I-140-V2

1200

202

144

118

5.09

5.10

0.40

244,835

3221

I0.19

3334

243,828

45,380

122.1

-126.7

12.5

A/S

60.8

60.8

SH-3PT

-4,5C-4I-140-V3

1200

200

145

117

5.13

5.14

0.40

244,835

3221

I0.19

3334

243,828

45,380

122.1

-126.7

12.5

A/S

58.3

58.4

SH-3PT

-4,5C-4I-116-V1

960

201

147

118

4.06

4.07

0.40

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

119.8

10.6

A/S

67.4

67.5

SH-3PT

-4,5C-4I-116-V2

961

200

147

118

4.08

4.09

0.40

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

119.8

10.6

A/S

67.5

67.6

SH-3PT

-4,5C-4I-116-V3

957

201

146

119

4.01

4.01

0.39

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

119.8

10.6

A/S

63.0

63.0

SH-3PT

-3C-4I-100-V1

800

200

101

705.67

5.68

0.49

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

119.8

11.7

A/S

32.8

32.8

SH-3PT

-3C-4I-100-V2

800

200

101

705.72

5.73

0.49

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

119.8

11.7

A/S

35.6

35.6

SH-3PT

-3C-4I-100-V3

800

200

100

755.31

5.32

0.46

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

119.8

11.7

A/S

39.1

39.1

SH-3PT

-3C-4I-84-V1

640

201

100

744.35

4.35

0.46

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

113.5

10.7

A/S

37.3

37.3

SH-3PT

-3C-4I-84-V2

640

200

102

704.55

4.55

0.49

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

113.5

10.7

A/S

36.1

36.1

SH-3PT

-3C-4I-84-V3

642

201

101

734.40

4.41

0.47

244,835

3221

I0.19

3334

243,828

42,327

104.9

123.5

113.5

10.7

A/S

34.6

34.7

SH-3PT

-3C-2C-84-V1

640

200

100

774.15

4.15

0.45

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

20.5

S28.9

29.0

SH-3PT

-3C-2C-84-V2

642

200

100

784.10

4.11

0.44

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

20.5

S/RV

30.2

30.2

SH-3PT

-3C-2C-84-V3

642

200

102

764.21

4.21

0.45

244,835

3221

C0.09

1969

175,601

43,978

107.5

115.6

107.5

20.5

S28.2

28.2

SH-3PT

-3C-2C-100-V1

800

200

101

824.87

4.88

0.42

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

13.4

S/A

28.2

28.3

SH-3PT

-3C-2C-100-V2

800

200

100

795.04

5.05

0.43

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

13.4

S/A

27.5

27.5

SH-3PT

-3C-2C-100-V3

800

201

100

765.25

5.26

0.45

244,835

3221

C0.09

1969

175,601

43,978

107.5

115.6

107.5

13.4

S/A/R

V27.2

27.2

SH-3PT

-4,5C-2C-116-V

1959

200

148

120

3.99

4.00

0.39

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

13.4

S/A

42.5

42.6

SH-3PT

-4,5C-2C-116-V

2960

200

145

119

4.04

4.05

0.40

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

13.4

S/A

38.8

38.9

(Con

tinue

s)

BIELAK AND HEGGER 9

TABLE

5(Con

tinued)

Specim

enno.

Lb

hd

a/d

M/(V�d)

ρ lEnm,l

f nm,l

TW

ρ nm,w

f nm,w

Enm,w

Ec

f c,cyl

f c,cu

f c,pr

f ct,fl

Fail.

Vu

Vu,exp

(-)

(mm)

(mm)

(mm)

(mm)

(-)

(-)

(%)

(N/m

m2 )

(N/m

m2 )

(-)

(%)

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(N/m

m2 )

(-)

(kN)

(kNm)

SH-3PT

-4,5C-2C-116-V

3960

200

146

120

4.00

4.00

0.39

244,835

3221

C0.10

1969

175,601

43,978

107.5

115.6

107.5

13.4

S/RV

43.7

43.8

SH-3PT

-4,5C-2C-140-V

11200

201

145

118

5.07

5.09

0.40

244,835

3221

C0.09

1969

175,601

41,894

110.0

124.5

112.1

10.2

S/A

43.6

43.7

SH-3PT

-4,5C-2C-140-V

21195

201

146

118

5.03

5.05

0.40

244,835

3221

C0.09

1969

175,601

41,894

110.0

124.5

108.3

8.6

S/RV

43.8

43.9

SH-3PT

-4,5C-2C-140-V

31200

200

146

115

5.21

5.22

0.41

244,835

3221

C0.10

1969

175,601

41,894

110.0

124.5

108.3

8.6

S/A

45.1

45.2

SH-3PT

-3C-4C-84-V1

640

200

100

764.17

4.17

0.54

244,835

3221

C0.19

1969

175,601

41,894

110.0

124.5

112.1

10.2

S/A

43.9

43.9

SH-3PT

-3C-4C-84-V2

640

200

101

764.19

4.20

0.55

244,835

3221

C0.19

1969

175,601

41,894

110.0

124.5

112.1

10.2

S/A

41.5

41.6

SH-3PT

-3C-4C-84-V3

638

201

100

764.20

4.20

0.55

244,835

3221

C0.19

1969

175,601

41,894

110.0

124.5

112.1

10.2

S/A

43.4

43.5

SH-3PT

-3C-4C-100-V1

800

200

100

804.98

4.98

0.52

244,835

3221

C0.19

1969

175,601

41,894

110.0

124.5

108.3

8.6

S/A

40.4

40.4

SH-3PT

-3C-4C-100-V2

800

200

101

785.14

5.14

0.53

244,835

3221

C0.19

1969

175,601

41,894

110.0

124.5

119.3

9.3

S/A

38.9

38.9

SH-3PT

-3C-4C-100-V3

800

200

101

765.23

5.24

0.54

24,4835

3221

C0.19

1969

175,601

41,894

110.0

124.5

119.3

9.3

S/A

36.9

37.0

SH-3PT

-4,5C-4C-116-V

1960

200

145

115

4.16

4.17

0.47

244,835

3221

C0.19

1969

175,601

42,435

107.0

125.0

110.6

7.7

S/A

60.3

60.3

SH-3PT

-4,5C-4C-116-V

2960

200

144

114

4.21

4.21

0.48

244,835

3221

C0.19

1969

175,601

42,435

107.0

125.0

110.6

7.7

S/A

57.7

57.7

SH-3PT

-4,5C-4C-116-V

3960

201

147

115

4.19

4.19

0.47

244,835

3221

C0.19

1969

175,601

42,435

107.0

125.0

110.6

7.7

S/A

63.1

63.2

SH-3PT

-4,5C-4C-140-V

11200

201

146

116

5.16

5.18

0.47

244,835

3221

C0.19

1969

175,601

42,435

107.0

125.0

110.6

7.7

S/A

54.5

54.6

SH-3PT

-4,5C-4C-140-V

21200

201

145

118

5.09

5.10

0.46

244,835

3221

C0.19

1969

175,601

42,435

107.0

125.0

110.6

7.7

S/A

56.5

56.6

SH-3PT

-4,5C-4C-140-V

31200

201

146

119

5.04

5.05

0.45

244,835

3221

C0.19

1969

175,601

42,435

107.0

125.0

110.6

7.7

S/A

59.2

59.2

SH-3PT

-5,4C-2C-160-V

11401

200

195

165

4.24

4.25

0.34

244,835

3221

C0.10

1969

175,601

40,137

106.2

126.4

105.9

11.7

RV

63.0

63.2

SH-3PT

-5,4C-2C-160-V

21401

201

199

170

4.13

4.14

0.33

244,835

3221

C0.09

1969

175,601

40,137

106.2

126.4

105.9

11.7

RV

62.5

62.7

SH-3PT

-5,4C-2C-160-V

31400

200

197

168

4.17

4.18

0.33

244,835

3221

C0.10

1969

175,601

40,137

106.2

126.4

105.9

11.7

RV

64.4

64.6

SH-3PT

-5,4C-2I-160-V1

1400

200

200

171

4.10

4.11

0.31

244,835

3221

I0.10

3334

243,828

40,715

106.6

126.9

107.2

11.3

A58.8

59.0

SH-3PT

-5,4C-2I-160-V2

1400

200

201

170

4.12

4.13

0.31

244,835

3221

I0.10

3334

243,828

40,715

106.6

126.9

107.2

11.3

A59.0

59.1

SH-3PT

-5,4C-2I-230-V1a

2097

201

201

174

4.02

4.03

0.30

244,835

3221

I0.09

3334

243,828

43,362

101.7

113.9

112.3

12.6

A59.3

59.8

SH-3PT

-5,4C-2I-230-V2a

2100

201

202

171

4.09

4.10

0.30

244,835

3221

I0.09

3334

243,828

43,362

101.7

113.9

112.3

12.6

A56.8

57.3

SH-3PT

-5,4C-2C-230-V

1a2100

200

200

169

4.14

4.15

0.31

244,835

3221

C0.10

1969

175,601

43,362

101.7

113.9

112.3

12.6

RV

55.8

56.3

SH-3PT

-5,4C-2I-230-V1b

1403

200

200

172

3.06

3.06

0.31

244,835

3221

I0.10

3334

243,828

43,362

101.7

113.9

112.3

12.6

A62.7

63.0

SH-3PT

-5,4C-2I-230-V2b

1400

200

200

169

3.11

3.11

0.33

244,835

3221

I0.10

3334

243,828

43,362

101.7

113.9

112.3

12.6

A62.0

62.3

SH-3PT

-5,4C-2C-230-V

1b1401

201

200

170

3.09

3.09

0.33

244,835

3221

C0.09

1969

175,601

43,362

101.7

113.9

112.3

12.6

RV

62.5

62.8

10 BIELAK AND HEGGER

shear reinforcement exhibited slightly stiffer behavior atlower load levels, which can be easily explained with thenumber of additional longitudinal yarns provided bythe shear reinforcement: In the lower leg of the C, twoextra yarns per element were situated in the tension zoneclose to the concrete surface; for the planar reinforce-ment, there was only one yarn above the last layer of lon-gitudinal reinforcement (see Figure 2). This is, in next tovariations of effective depth d, one reason for the slightlydifferent geometrical reinforcement ratios ρl denoted inFigure 8. Two tests with four-legged C-shaped shear rein-forcement (4C-116-V1 and 4C-116-V3) in Figure 8 experi-enced a loss of stiffness at approximately 40 kN shearload. This can be attributed to connecting longitudinalcracks, which formed at the level of the overlapping hori-zontal legs of the C-profiles. Their coverage of concretewas large, and the remainder of concrete was no longer

able to transmit the vertical splitting stresses. Hence, thebottommost layer of longitudinal reinforcement was nolonger bonded to the specimen, which explains well tothe loss of stiffness. The identically reinforced specimen4C-116-V3 had no connecting longitudinal cracks, andthus, no decline of stiffness of the same magnitude wasobserved.

All failure types (anchorage failure, shear-compressionfailure, rupture of yarns) manifest similarly in the load-deflection curves as sudden and drops of load, oftencatastrophic without any residual capacity. This is clearlyvisible in the diagrams in Figure 9, where the specimensin Figure 9e failed through anchorage of the vertical grids,while in Figure 9f, the C-shaped reinforcement rupturedin the bend. The load deflection curve alone does notreveal which type of failure occurred.

3.3 | Influence of arch action and shearslenderness

The results of the reference tests without shear reinforce-ment are compared in Figure 9 to a previous test seriesfrom Reference 45 by their shear stress τ = Vu/(b�d) andshear slenderness ratio a/d excluding self-weight. Thenormalized form compensates variations in effectivedepth. All specimens were saw-cut after testing, and thereal effective depth of each yarn was measured. The valued represents the geometrical centroid of all yarns. Speci-mens from Reference 45, which failed in flexure werealso included in the Figure 9a, as the shear resistance atflexural failure represents at least a lower boundary forthe actual resistance. The following observations resultfrom a first comparison:

• Despite the same longitudinal reinforcement ratio andsimilar concrete strength, members with larger effec-tive depth fail at smaller shear stress. This well-knownsize effect is present for both series.

• The influence of shear slenderness on shear resistanceis clearly recognizable. The decline between a/d = 4and 5 almost vanishes for a/d = 5 and 6. The testswere performed deliberately at large shear slendernessto minimize the influence of arching action. The physi-cal explanation for the influence of shear slendernesson shear resistance is well known from steel-reinforcedconcrete: The larger moment due to larger a leads tolarger strain in the longitudinal reinforcement andthus to larger flexural-shear crack openings. The largerthe crack opening, the smaller the micro-interlock ofthe crack surfaces. However, the reduction effectdeclines when a certain threshold of crack opening issurpassed. Furthermore, the plane of strain (in the

0

10

20

30

40

50

60

70

0 5 10 15 20

sh

ea

rfo

rceV

[kN

]

def n at midlectio -span w [mm]

2I-116-V1

2I-116-V2

2I-116-V3

2C-116-V1

2C-116-V2

2C-116-V3

(a)

a/d≈ 4

l ≈ 0.37 (planar)%

nm,w = 0. ‰95l ≈ 0.39 (C-shape)%

0

10

20

30

40

50

60

70

0 5 10 15 20

sh

ea

rfo

rceV

[kN

]

def n at midlectio -span w [mm]

4I-116-V1

4I-116-V2

4I-116-V3

4C-116-V1

4C-116-V2

4C-116-V3

(b)

a/d≈ 4.1

l ≈ 0.40 (planar)%

nm,w = . ‰1 90l ≈ 0.47 (C-shape)%

connecting longitudinalcracks at level of C-legs

FIGURE 8 Shear force–deflection behavior of specimens with

145 mm height and different shear reinforcement types and

reinforcement ratios

BIELAK AND HEGGER 11

idealized Euler-Bernoulli beam) has to rotate furtherat higher moment levels, which reduces the depth ofthe uncracked compression zone and its contributionto shear resistance.

• Specimens with identical configuration exhibit surpris-ingly large scatter at ultimate load. This is especiallythe case for the 2016 series with d = 120 mm. After theshear crack progressed through the compression zone,the three-axial stress state below the load introductionconfines the concrete and allows for redistribution ofload toward a tied arch. The white boxes/circles repre-sent the total failure load, while the actual failure loadhas been corrected to the lower level where the initialshear crack progression into the compression zoneoccurred. The present series (2019) features smallerscatter.

The effect of arching action is also present in theshear-reinforced members. Two specimens withthe smallest shear slenderness λ = 3, one with planar andone with C-shaped shear reinforcement, failed at signifi-cantly larger ultimate loads than their identicallyreinforced companion tests with λ = 4 (Figure 10). Adrop or plateau can be identified at the same load levelwhere the specimens with λ = 4 failed. The DIC analysisreveals that the dowel and bond cracks were fully con-nected and reached almost to the support in the respec-tive load stages (Figure 10a,c). The last inclined cracks inthe vicinity of the support formed at this stage, diagonaltension cracks opened, and the shear crack visibly prog-ressed toward the compression zone (Figure 10b,d). Con-sequently, the increase of 20% and 27% after the plateaucan be attributed to tied arch action. The direct compari-son of 2I-230-V1b and -V2b reveals that the activation ofthis mechanism is not guaranteed: In 2I-230-V1b(Figure 10e), the progression of the shear crack to thecompression zone directly led to failure. Up to this point,

both specimens show nearly identical load-deflectionbehavior. This tied arch action was observed for none ofthe specimens with a/d ≥ 4, and it will therefore not beconsidered in the following evaluations, which focus onbeam shear action rather than strut-and-tie action.

The comparison of all shear-reinforced tests inFigure 11 reveals only a slight reduction of shear resis-tance for increasing shear slenderness for both types ofshear reinforcement. The small scatter per configurationand the similar behavior regarding the influence of a/dfor both reinforcement types apparent.

3.4 | Absolute and relative shearstrength

The observation that an increase of shear reinforcementratio leads to an increase in shear resistance might betrivial but is not granted. Depending on the shear trans-fer mechanism of the shear reinforcement, a prematurefailure might occur. All results and their respective ref-erence tests are compared in Figure 12. Self-weight isnot included. The dashed lines are linear trendsobtained with the least-squares method. The increase ofshear resistance through shear reinforcement is evident:Doubling the shear reinforcement approximatelydoubles its total contribution to shear resistance. Onlymembers with 80 mm effective depth and two C-shapedgrids slightly deviate from this rule. A part of theincrease of resistance can be attributed to the additionallongitudinal yarns in the tension zone provided by theshear reinforcement. This is more relevant for thesmaller height, where the relative increase in reinforce-ment ratio is larger.

The larger the effective depth, the higher the totalincrease. However, in normalized form (τ = Vu,exp/(b�d)),all trend lines become nearly parallel, and the shear

FIGURE 9 Influence of

shear slenderness on ultimate

shear stress: (a) 2016 series

from45 and (b) present series

(from 2019) with higher

longitudinal reinforcement ratio

(Reproduced from Bielak36)

12 BIELAK AND HEGGER

stress per configuration varies in a narrow band for theshear-reinforced members (Figure 13). A size effect isonly noticeable for the reference tests. The slightly largerultimate resistance of the planar members with fourlayers of shear reinforcement is compensated by asmaller effective depth for the C-shaped elements. Inother words, the contribution of total resistance per verti-cal yarn crossing the shear crack is similar irrespective tothe type of anchorage. With regard to the different failure

mechanisms of the C-shaped reinforcement, this is mostremarkable. Yet both types of reinforcement had thesame cross-section, spacing, and material and led to simi-lar crack patterns and mostly similar load-deflectionbehavior.

It could be a coincidence that the smaller ultimateresistance of the C-shaped profiles, and their smallermodulus of elasticity is compensated by their betteranchorage. Note that the possible contribution of shear

2I-230-V2b= 62.0 kNV

2C-230-V1b= 62.5 kNV

)c()a(

)d()b(= 63.0 kNV = 60.7 kNV

opening ofcrack

new (last)crack

new (last)crack

progressionin compressionzone

significantopening

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0�1 [%]

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35

2I-160-V1

2I-160-V2

2I-230-V1a

2I-230-V2a

2I-230-V1b

2I-230-V2b

(e)

(a)(b)

arch action+ kN12.2(+ %)20

� = 3.1

� = 4.1� = 4.1

w [mm]

shear

forc

eV

[kN

]

deflection at load introduction

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35

2C-160-V1

2C-160-V2

2C-160-V3

2C-230-V1a

2C-230-V1b

(f)

(c)

(d)

arch action+17.1 kN(+ %)27

deflection at load introduction

� = 3.1

� = 4.2

� = 4.2

w [mm]shear

forc

eV

[kN

]

FIGURE 10 Influence of

arch action for shear-reinforced

specimens of height 200 mm

with λ ≈ 3 and comparison to

similar specimens with larger

shear slenderness λ ≈ 4

(Reproduced from Bielak36)

0

15

30

45

60

75

3 4 5 6

sh

ea

r fo

rceV

u[k

N]

shear slenderness a/d [-]

2 I - mm= 80d 2 I - mm= 120d

4 I - mm= 80d 4 I - mm= 120d

2 I - mm= 17d 3

planar grid

(a)

0

15

45

60

75

3 4 5 6

shear slenderness a/d [-]

2 C - mm= 80d 2 C - mm= 120d

4 C - mm= 80d 4 C - mm= 120d

2 C - mm= 17d 3

30

C-shaped preformed grid

sh

ea

r fo

rceV

u[k

N]

(b)

FIGURE 11 Influence of

shear slenderness on shear

resistance of shear-reinforced

single span slab segments:

(a) with planar shear

reinforcement (Adapted from

Bielak et al.32) and (b) with C-

shaped reinforcement

(Reproduced from Bielak36)

BIELAK AND HEGGER 13

reinforcement at a given shear crack opening depends ontwo factors: The elastic stiffness of the free yarn as wellas the stiffness of the anchorage that manifests in theamount of slip required to transfer load into the yarn.The vertical yarns of the planar grid feature larger ulti-mate strength, a larger modulus of elasticity, and astraighter shape, but they cannot be fully activated due topremature bond failure. Although they reach up to0–5 mm to the concrete surfaces, they are not fullyanchored in the concrete cover. In contrast, the C-shapedprofiles exhibit a stiffer anchorage response due to the90� leg with 50 mm leg length.

A different explanation to the similar behavior is thatthe same amount of vertical shear reinforcement inde-pendent of its anchorage with a similar modulus of elas-ticity has the same effect on shear crack width control.

This would lead to a constant activation of aggregateinterlock along the shear crack and a sustained contribu-tion of dowel action. The fan-shaped diagonal crack pat-tern in Figure 10 is an indicator of the ability of the zonebelow each diagonal crack to still transfer vertical loads,as new cracks are able to form. In this regard, the distrib-uted nature of the textile grids in planar or in C-shape isbeneficial, as they constantly bridge the shear crack. Tobetter exploit the reinforcement in smaller members, thespacing of vertical yarns has to be reduced so that moreyarns cross and sew the shear crack. In essence, the gridspacing has to be adapted to the member size.

4 | CONCLUSIONS

In this paper, the results from an experimental investiga-tion of the one-way shear capacity of slab segments with-out and with shear reinforcement were presented. Thefollowing conclusions can be drawn:

• The analysis of cracking and failure mechanisms fordifferent reinforcement configurations revealed thatthin slab segments with FRP textile reinforcement aresubject to similar shear failure mechanisms as steel-reinforced concrete and FRP rebar-reinforced concrete.

• FRP textile reinforcement behaves similar to FRP rebarreinforcement under one-way shear load. The distinc-tion between the two often found in literature is artifi-cial, as the transition between thin and regular-sizedslabs is actually smooth.

FIGURE 12 Relationship of shear resistance and

reinforcement ratio for different reinforcement types and member

heights: (a) planar reinforcement and (b) C-shaped reinforcement

(Reproduced from Bielak36)

FIGURE 13 Comparison of relative shear strength (shear

stress) for different reinforcement configurations and member

heights

14 BIELAK AND HEGGER

• For members without shear reinforcement, the sizeeffect and the shear slenderness could be identified asmajor influencing parameters that need to be consid-ered for prediction of shear resistance.

• For some specimens with shear slenderness betweenfour and five, an additional arching action increasedultimate shear resistance after initial shear failure.Whether this increase occurs or not depends on thecritical shear crack path and the extent of local con-finement of the concrete at load application. Due to itsarbitrary nature, it should not be accounted for indesign.

• The primary failure mechanism of all elements withplanar reinforcement was anchorage failure of verticalreinforcement. Subsequently, the specimens failed inshear compression. The C-shaped preformed elementswere ruptured only for the largest height of 200 mm.In the other tests, a combination of anchorage andshear compression failure was observed. Hence, theanchorage behavior has to be considered in shearmodels for thin slabs to account for this failure mode.

• The size effect loses absolute relevance for the shear-reinforced members, as the loss of relative shearstrength is compensated by a better anchorage of verti-cal reinforcement elements for higher specimens.

• Slab segments in three-point loading with a heightbetween 100 mm and 200 mm equipped with planar orC-shaped FRP textile shear reinforcement carry higherultimate loads than the reference tests without shearreinforcement. Both types of shear reinforcement aresuitable for enhancing shear resistance of thin slabs,and the results are surprisingly similar despite the dif-ferent anchorage type.

This paper focused on the one-way shear behavior ofsingle span members with concentrated loads. It is knownfrom steel-reinforced concrete that the shear resistance ofcontinuous systems differs. Consequently, an adapted testsetup for investigation of such members will be presentedin a subsequent paper. A shear model capable of an accu-rate prediction of thin slabs without and with shear rein-forcement will also be proposed in upcoming articles.Furthermore, the effect of distributed loading on the shearresistance as well as cyclic or sustained loading has to beinvestigated in future research.

ACKNOWLEDGMENTSThis research was funded by German Federal Ministry ofEducation and Research (BMBF), grant number03ZZ0380. This funding is gratefully acknowledged.

NOTATIONa distance of load axis to support (general)

a1, a2 distance of load axis to left/right supportanm,w area of shear reinforcement per unit lengthb specimen widthd effective depthh specimen heightfnm,l tensile strength of longitudinal reinforcementfnm,w strength of the shear reinforcement

(straight part)fc,cyl compressive strength of concrete (cylinder d/

h = 150/300)fc,cu compressive strength of concrete (cube a = 150)fc,pr compressive strength of concrete (prism halve

160 � 40 � 40)fc,fl flexural tensile strength of concrete

(prism 160 � 40 � 40)fail. failure (S: shear, i.e., diagonal tension/shear com-

pression; A: anchorage failure of vertical rein-forcement; RV: rupture of vertical reinforcement)

Ec modulus of elasticity of concreteEnm,l modulus of elasticity of longitudinal

reinforcementEnm,w modulus of elasticity of nonmetallic shear

reinforcementL span lengthLtot total specimen lengthM/(V�d)

ratio of maximum moment to shear force in dis-tance d to load introduction including self-weight

TW type of shear reinforcement (I: planar grid; C:preformed C-shaped grid)

V shear forceVu ultimate shear force without self-weightVu,exp ultimate shear force including self-weight in

distance d to load introductionλ shear slendernessρl geometrical longitudinal reinforcement ratioρnm,w geometric shear reinforcement ratio (anm,w/b)τ shear stress

AUTHORS' CONTRIBUTIONJan Bielak: Conceptualization (equal), formal analysis,investigation, methodology, visualization, writing—original draft preparation; Josef Hegger: conceptualiza-tion (equal), funding acquisition, project administration,supervision, resources, writing—review and editing.

DATA AVAILABILITY STATEMENTThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.

ORCIDJan Bielak https://orcid.org/0000-0002-3219-655XJosef Hegger https://orcid.org/0000-0003-3066-5006

BIELAK AND HEGGER 15

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AUTHOR BIOGRAPHIES

Jan Bielak, RWTH AachenUniversity, Institute of StructuralConcrete, Mies-VAN-DER-Rohe-Str.1, 52074, Aachen, Germany.

Josef Hegger, RWTH AachenUniversity, Institute of StructuralConcrete, Mies-VAN-DER-Rohe-Str. 1,52074, Aachen, Germany.

How to cite this article: Bielak J, Hegger J.Enhancing shear capacity of thin slabs with CFRPshear reinforcement: Experimental study.Structural Concrete. 2021;1–17. https://doi.org/10.1002/suco.202100325

BIELAK AND HEGGER 17