13 258 final libre

1441ACI Structural Journal/November-December 2014

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Code provisions for one-way shear assume a linear relation between

the shear capacity of a reinforced concrete member and its width.

For wide members subjected to a concentrated load, an effective

width in shear should be introduced. To study the effective width

and the inluence of the member width on shear capacity, a series of experiments was carried out on continuous one-way elements of

different widths. The size of the loading plate, the moment distri-

bution at the support, and the shear span-depth ratio were varied

and studied as a function of the member width. The effective width

can be determined by using a 45-degree load-spreading method

from the far side of the loading plate to the face of the support.

This proposed effective width is easy to implement, yet gives good

results in combination with code provisions.

Keywords: effective width of slab; punching shear; shear; slab; structural

load test.

INTRODUCTION

The code provisions (ACI Committee 318 2011; CEN

2005) for shear assume a linear relation between the shear

capacity and the member width. The expressions for the

beam shear capacity are semi-empirical equations resulting

from databases of shear tests (Reineck et al. 2013) on mostly

small, heavily-reinforced, simply-supported beams in a

four-point bending test as developed by Regan (1987) for

the expressions in NEN-EN 1992-1-1:2005 and by Morrow

and Viest (1957) for ACI 318-11. Recent research on wide

members subjected to line loads (Sherwood et al. 2006)

showed that the code provisions for beam shear are appli-

cable to these cases. For loads that are smaller than the full

member width, it is necessary to introduce an effective width

in shear (Chauvel et al. 2007). A loading case in which it

is necessary to deine such an effective width is the case of a solid slab bridge subjected to design truck loads (from

NEN-EN 1991-2:2003). For this case, the wheel load or axle

load should be distributed over a certain effective width to

determine the contribution of this load to the shear stress at

the support (Steenbergen et al. 2011). Very little information

on the shear distribution in bridges is available (Zokaie 1992).

The effective width is theoretically determined from the

stress distribution over the width of the element (Goldbeck

and Smith 1916; Goldbeck 1917) and is deined so that the resisting action due to the maximum stress distributed over

the effective width equals the resisting action due to the vari-

able stresses over the entire width (Fig. 1). In Dutch prac-

tice, a 45-degree horizontal load-spreading method from the

center of the load is used to determine the effective width

at the face of the support (Fig. 2(a)), and in French prac-

tice (Chauvel et al. 2007), the load spreading is taken from

the farthest side of the load (Fig. 2(b)). In German prac-

tice, a conservative formula is used to deine the effective width (Grasser and Thielen 1991). The Model Code 2010

(ib 2012) guidelines for the determination of the effective

Title No. 111-S123

Inluence of Width on Shear Capacity of Reinforced

Concrete Membersby Eva O. L. Lantsoght, Cor van der Veen, Ane de Boer, and Joost C. Walraven

ACI Structural Journal, V. 111, No. 6, November-December 2014.MS No. S-2013-258, doi:10.14359/51687107, received February 19, 2014, and

reviewed under Institute publication policies. Copyright 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors closure, if any, will be published ten months from this journals date if the discussion is received within four months of the papers print publication.

Fig. 1Principle of effective width beff: area under curve

v(x) of shear stresses over width b equals area of maximum

shear stress vmax over beff.

Fig. 2(a) Load spreading under 45 degrees and resulting

effective width as used in Dutch practice; and (b) load

spreading and resulting effective width as used in French

practice (Chauvel et al. 2007).

1442 ACI Structural Journal/November-December 2014

width are given as indicated in Fig. 3. For simply supported

elements, the angle of horizontal load spreading is taken as

60 degrees, and for clamped elements, 45 degrees, as based

on the Swiss Code (SIA 162 1968). In the Model Code

approach, the shear stress is checked at a distance x = dl from

the support, provided that dl av /2.In the literature, additional methods for calculating the

effective shear width for well-deined cases are suggested, none of which are suitable for extrapolation towards a more

general use (Diaz de Cossio et al. 1962; Graf 1933; Regan

and Rezai-Jorabi 1988; Taylor et al. 2003). When slabs are

not supported by a line support but instead by a number of

discrete bearings, a similar problem arises (Lubell et al.

2008; Ross et al. 2012). Experiments studying this problem

did not result in generally applicable expressions for the case

of members not loaded over their full width. For deck slabs

in steel-concrete bridges, Zheng et al. (2010) developed an

expression, but it is not suitable for solid-slab bridges.

If the concept of an effective width can be applied to wide

concrete members loaded in shear, then the shear capacity

should cease to increase as the member width is increased

after reaching a threshold valuethe effective width. As

long as the element width is smaller than the effective width,

increasing widths lead to increasing shear capacities. When

the element width is larger than the effective width, only the

effective width at the support can carry the shear load, and

further increasing of the element width will not result in an

increase in the shear carrying capacity. Previous research

(Regan and Rezai-Jorabi 1988) showed increasing shear

capacities for slabs with a concentrated load placed at such a

location that a/dl = 5.42 for increasing widths (0.4 to 1.2 m

[1.3 to 3.9 ft]) up to a certain value (1 m [3.3 ft]), after which

the shear capacity remained constant. In other experiments

(Reien and Hegger 2013), however, a threshold value was

not observed for a load placed at a/dl = 4.17 as the width

increased (0.5 to 3.5 m [1.6 to 11.5 ft]).

RESEARCH SIGNIFICANCE

The inluence of the member width on the one-way shear capacity of reinforced concrete wide beams subjected to

concentrated loads is studied in a comprehensive series of

experiments. Based on these experiments, recommendations

are given for the effective width, which previously was only

based on local practice and rules of thumb. The conducted

experiments are important as they explore the transition

zone from one-way shear to a mixed mode of one-way and

two-way shear, and the proposed effective width can be used

for solid slab bridges subjected to truck loads.

CODE PROVISIONS

According to NEN-EN 1992-1-1:2005 (CEN 2005)

Section 6.2.2 (1), the shear resistance for a structural member

without stirrups is calculated as follows (SI units: fck in MPa;

1 MPa = 145 psi; k1 = 0.15):

VRd,c = [CRd,ck(100lfck)1/3 + k1cp]bwdl (vmin + k1cp) bwdl (1)

kdl

= + 1200

2 0. (2)

The values of CRd,c and vmin are nationally determined param-

eters. The default values are CRd,c = 0.18/c with c=1.5 in general and

v k fmin ck= 0 0353 2 1 2

./ / (3)

NEN-EN 1992-1-1:2005 Section 6.2.6(6) accounts for

the beneicial inluence of direct load transfer through a compression strut for loads close to the support. For

beams, the contribution of a load, applied within a distance

0.5dl av 2dl from the edge of a support, to the shear force VEd may be multiplied by = av/2dl.

The ACI 318-11 Section 11.2.2.1 formula (11-5) for

normalweight concrete ( = 1, with notations altered to be uniform with the previously used notations), describes the

shear resistance as

V fV d

Mb d f b dc ck l

l

w l ck w l= +

0 16 17 0 29. .

ACI

ACI

(4)

ACI 318-08 recommends the use of nonlinear analysis or

strut-and-tie models for members with concentrated loads

within a distance twice the member depth from the support.

EXPERIMENTAL INVESTIGATION

Specimens

The experimental program consisted of three reinforced

concrete elements (BS series) sized 5.0 x 0.5 x 0.3 m (16.4 ft x

1.6 ft x 11.8 in.); three elements (BM series) sized 5.0 x 1.0 x

0.3 m (16.4 ft x 3.3 ft x 11.8 in.); three elements (BL series)

sized 5.0 x 1.5 x 0.3 m (16.4 ft x 4.9 ft x 11.8 in.); and three

elements (BX series) sized 5.0 x 2.0 x 0.3 m (16.4 ft x 6.6 ft

x 11.8 in.). The results of slabs S8 and S9, sized 5.0 x 2.5 x

0.3 m (16.4 ft x 8.2 ft x 11.8 in.), from a previous series of

experiments (Lantsoght et al. 2013) were used to complete

the series of specimens with increasing widths. The depth of

0.3 m (11.8 in.) is a 1:2 scale representation of typical Dutch

solid slab bridges. An overview of the properties of these

specimens is given in Table 1.

All specimens were reinforced with deformed steel bars

with a yield strength of 500 MPa (72.5 ksi). The deformed

bars with a diameter of 20 mm (0.79 in.) had fym = 542 MPa

(78.6 ksi) and fum = 658 MPa (95.4 ksi), and the bars with a

diameter of 10 mm (0.39 in.) had fym = 537 MPa (77.9 ksi)

Fig. 3Location and length of the control section beff for

determination of shear resistance of wide members with

point loads located close to support line; simple edge

support (ib 2012).


and fum = 628 MPa (91.1 ksi). A concrete cover of 25 mm

(0.98 in.) over the reinforcement was applied. The effec-

tive depth to the longitudinal reinforcement dl was 265 mm

(10.4 in.) and depth to the transverse reinforcement dt was

250 mm (9.8 in.). The reinforcement layout of the BS spec-

imens is shown in Fig. 4. For wider elements, the number

of bars was increased to maintain the same reinforcement

percentage of l = 0.948%. For comparison to the previously tested slab specimens of 2.5 m (8.2 ft.), the percentage of

transverse lexural reinforcement is kept at t = 0.258%.High-strength concrete of Class C53/65 from NEN-EN

1992-1-1:2005 Section 3.1.2 (3) Table 3.1 (CEN 2005) was

used with a target cylinder strength fc,cyl of 61 MPa (8847 psi),

which corresponds to the compressive strengths found when

testing cores taken from existing solid slab bridges. Glacial

river aggregates with a maximum aggregate size of 16 mm

(0.63 in.) were used.

Test setup

A top view of the test setup for the reinforced concrete

elements is given in Fig. 5(a) and a section elevation is

given in Fig. 5(b). A photograph is given in Fig. 5(c). The

line supports (sup 1 and sup 2 in Fig. 5) consist of a

steel beam (HEM 300) 300 mm (11.8 in.) wide, a layer of

plywood, and a layer of felt 100 mm (3.9 in.) wide (Prochaz-

kova and Lantsoght 2011), so that the support width

bsup = 100 mm (3.9 in.). Experiments are carried out close

to the simple support (sup 1, SS in Fig. 5(a)) and close to

the continuous support (sup 2, CS in Fig. 5(a)), where the

rotation is partially restrained by vertical prestressing bars,

ixed to the strong loor of the laboratory. An initial force of 5 kN (1.1 kip) per prestressing bar was used for the BS

and BM specimens, 10 kN (2.2 kip) for the BL specimens,

12 kN (2.7 kip) for BX, and 15 kN (3.4 kip) for the S series.

Load cells were used to measure the force in the prestressing

bars during the experiment. For the specimens 0.5 m (1.6 ft)

wide, only one prestressing bar was used, and for the spec-

imens 1.0 m (3.3 ft) wide, two prestressing bars were used.

All wider elements were tested with three prestressing bars,

as shown in Fig. 5(a).

The concentrated load is applied in a displacement-

controlled way through a hydraulic jack (Fig. 5(b)) onto a

steel loading plate either 200 x 200 mm (7.9 x 7.9 in.) or

300 x 300 mm (11.8 x 11.8 in.). The 200 x 200 mm (7.9 x

7.9 in.) loading plate is a 1:2 scale representation of the 400 x

400 mm (15.8 x 15.8 in.) contact surface for each wheel of

the axle load used in the live load model (Load Model 1) of

NEN-EN 1991-2:2002 (CEN 2003). Laser distance inders are used to measure the deformations, as shown in Fig. 5(c).

A full description of the materials and instrumentation and

the experimental observations are given in the full test report

(Lantsoght 2011).

EXPERIMENTAL RESULTS AND DISCUSSION

Test results

On every specimen, one experiment was carried out at

the simple support (SS in Fig. 5) and one at the continuous

support (CS in Fig. 5). The results are reported in Table 2. As

shown in Fig. 6, the following failure modes are observed:

Failure as a beam in shear with a noticeable shear crack

at the side (B, Fig. 6(a));

Table 1Properties of specimens BS1 through BX3, plus S8 and S9 for comparison

Specimen no. b, m fc,meas, MPa fct,meas, MPa l, % t, % a, mm a/d zload, mm Age, daysBS1 0.5 81.5 6.1 0.948 0.258 600 2.26 300 55

BM1 1.0 81.5 6.1 0.948 0.258 600 2.26 300 62

BL1 1.5 81.5 6.1 0.948 0.258 600 2.26 300 189

BS2 0.5 88.6 5.9 0.948 0.258 400 1.51 200 188

BM2 1.0 88.6 5.9 0.948 0.258 400 1.51 200 188

BL2 1.5 94.8 5.9 0.948 0.258 400 1.51 200 180

BS3 0.5 91.0 6.2 0.948 0.258 600 2.26 300 182

BM3 1.0 91.0 6.2 0.948 0.258 600 2.26 300 182

BL3 1.5 81.4 6.2 0.948 0.258 600 2.26 300 171

BX1 2.0 81.4 6.0 0.948 0.258 600 2.26 300 47

BX2 2.0 70.4 5.8 0.948 0.258 400 1.51 200 39

BX3 2.0 78.8 6.0 0.948 0.258 600 2.26 200 40

S8 2.5 77.0 6.0 0.996 0.258 600 2.26 300 48

S9 2.5 81.7 5.8 0.996 0.258 400 1.51 200 77

Notes: 1 m = 3.3 ft; 1 MPa = 145 psi; 1 mm = 0.04 in.

Fig. 4Reinforcement layout for test specimens: (a) top

view of BS1; and (b) cross-section of BS1. (Note: measure-

ments in mm; 1 mm = 0.04 in.)


Failure as a wide beam in shear with cracks at an angle

of the span direction, resulting in inclined cracks on the

bottom (WB, Fig. 6(b)); or

Development of a partial punching surface on the

bottom face (P, Fig. 6(c)).

Shear span-depth ratio

To study the relation between the member width and the

inluence of the shear span-depth ratio (a/dl), the results of BS3, BM3, BL3, BX3, and the previously tested specimen

S3 (Lantsoght et al. 2013) with the concentrated load at

a = 600 mm (23.6 in.) are compared to the results of BS2,

BM2, BL2, BX2, and S5 with the concentrated load at a =

400 mm (15.7 in.). Loading close to the support is studied,

as initial assessment of the existing solid slab bridges indi-

cated that the largest shear stresses at the support are found

when the design truck is placed at a distance dl from the

support. For the B series of experiments, the size of the

loading plate is 200 x 200 mm (7.9 x 7.9 in.), while for S3

and S5, a 300 x 300 mm (11.8 x 11.8 in.) plate was used. The

B-series specimens are made from high-strength concrete,

while S3 and S5 were made from normal-strength concrete.

The experimental observations are summarized in Table 3,

showing the measured average ratio of the shear capacity

for a = 400 mm (15.7 in.), Vexp,400, to the shear capacity for

a = 600 mm (23.6 in.), Vexp,600. The results in Table 3 show

a clear increase in shear capacity with decreasing distance

to the support, as known from the literature (Kani 1964)

and observed in the previous experiments on one-way slabs

subjected to concentrated loads (Lantsoght et al. 2011).

Moreover, the results in Table 3 show an inluence of the overall member width b on the quantity of the increase of the

shear capacity with a decrease in the shear span-depth ratio.

For members with a small width (0.5 m [1.6 ft]), the increase

in the shear capacity, when the load is placed closer to the

support, is larger than for wider members (b 1.5 m [4.9 ft]).The lower increase in capacity for a decrease in a/dl as

observed for wider members can be explained when studying

the compressive struts in wide members under concentrated

loads. In wide members, a fan of struts (Fig. 7) can develop,

Fig. 5Test setup: (a) top view; (b) elevation; and (c) photo-

graph showing laser distance inders on measurement frame, line support, load and prestressing bars, BL1T2 at failure.

Fig. 6Observed failure modes: (a) B: shear crack at the

side face (BS1T2); (b) WB crack pattern: inclined cracks on

the bottom face (BL3T1); and (c) P: partial punching at the

bottom face (S9T1).


while for beams, a single strut develops over the distance a

(shown as a/dl = 1 in Fig. 7). In wide members, the resulting

a/dl will depend on the fan of struts and their resulting load

path, which is on average longer than the direct straight strut.

This larger average a/dl can explain the smaller inluence of the shear span-depth ratio in wider members, as was previ-

ously shown in preliminary research on slabs subjected to

concentrated loads (Lantsoght et al. 2013).

Size of loading plate

To study the relation of the overall member width to the

inluence of the size of a square loading plate (representing a tire contact area) on the shear capacity of wide beams, the

results of BS1 and BS3 can be compared, as well as BM1 and

BM3, BL1 and BL3, and BX1 and BX3. These results can be

compared to the inluence of the size of the loading plate on

the shear capacity of slabs S1 and S2 of 2.5 m (8.2 ft.) wide

(Lantsoght et al. 2010). It should be noted that all specimens

from the B-series are made of high-strength concrete, while

slabs S1 and S2 were made of normal-strength concrete.

The results are shown in Table 4, displaying the measured

average increase in shear capacity for an increase in size of

the loading plate. The results of the specimens with widths

ranging from 1 to 2.5 m (3.3 to 8.3 ft) in Table 4 show an

increasing inluence of the loading plate size on the shear capacity as the overall width of the specimen increases. The

inluence of the size of the loading plate and its relation to the member width can be explained based on the transverse

load-distribution capacity in wide members. From this point

of view, it is clear that a larger loading plate provides a larger

base from which the compressive struts can fan out.

Table 2Experimental results for tested specimens

Test a, m Support type* Pexp, kN Failure mode Fpres, kN Vexp, kN Vadd, kN Vconc, kN

BS1T1 0.60 SS 290 B 37 242 0 242

BS1T2 0.60 CS 623 B 212 562 43 519

BS2T1 0.40 SS 633 B 100 552 11 563

BS2T2 0.40 CS 976 B 267 919 52 868

BS3T1 0.60 SS 356 B 57 293 3 297

BS3T2 0.60 CS 449 B 107 399 25 374

BM1T1 0.60 CS 923 WB + B 160 811 41 769

BM1T2 0.60 SS 720 WB + B 127 591 9 600

BM2T1 0.40 SS 1212 WB + B 167 1062 15 1077

BM2T2 0.40 CS 1458 WB + B 262 1354 58 1296

BM3T1 0.60 SS 735 WB + B 110 607 6 613

BM3T2 0.60 CS 895 WB + B 183 791 45 746

BL1T1 0.60 SS 1034 WB + B 215 844 17 862

BL1T2 0.60 CS 1252 WB + B 320 1119 75 1043

BL2T1 0.40 SS 1494 WB + B 212 1311 17 1328

BL2T2 0.40 CS 1708 WB + B 277 1586 68 1518

BL3T1 0.60 SS 1114 WB + B 242 907 22 928

BL3T2 0.60 CS 1153 WB + B 312 1035 74 961

BX1T1 0.60 SS 1331 WB + P 325 1080 30 1109

BX1T2 0.60 CS 1596 WB + B + P 335 1415 85 1330

BX2T1 0.40 SS 1429 WB + B + P 217 1259 11 1270

BX2T2 0.40 CS 1434 WB + P 167 1332 57 1275

BX3T1 0.60 SS 1141 WB + P 245 935 16 951

BX3T2 0.60 CS 1193 WB + B 210 1059 64 994

S8T1 0.60 SS 1481 WB + B 233 1226 8 1234

S8T2 0.60 CS 1356 WB + B 278 1213 83 1130

S9T1 0.4 SS 1523 WB + P 175 1355 2 1354

S9T4 0.4 CS 1842 WB + P 255 1717 79 1637

*SS indicates simple support and CS is continuous support.

B is beam shear failure; WB is wide beam shear failure; and P is punching shear failure.

Notes: 1 m = 3.3 ft; 1 kN = 0.225 kip.


Moment distribution at support

All specimens are tested at the simple and continuous

support, as shown in Fig. 4. As the force in the vertical

prestressing bars close to the continuous support (CS in

Fig. 4) is only applied at the beginning of every test, the

moment over the continuous support is on average only

about 26% of the moment in a fully clamped support for

the specimens from the S series and 31% for the B series.

The inluence of the moment distribution at the support on the shear capacity is studied in Table 5. The rows in Table 5

show the results with regard to the inluence of the moment distribution for the different widths that were tested, compli-

mented with the results of specimens S1 to S10 (Lantsoght

et al. 2013) that were 2.5 m (8.2 ft) wide. The columns

in Table 5 show the average (AVG) increase of the shear

capacity when an experiment at the continuous support,

Vexp,CS, is compared to an identical experiment at the simple

support, Vexp,SS, as well as the associated standard deviation

(STD) and coeficient of variation (COV), showing that the shear capacity at the continuous support is larger than at the

simple support. The inluence of the moment distribution at the support decreases with an increase in the element width.

For wider members, the transverse moment starts to inlu-ence the shear behavior and should be taken into account.

The inluence of the moment distribution at the support for complex loading situations was tested on girders in the

Stevin II Laboratory (Yang 2012).

EFFECTIVE WIDTH

Measured threshold effective width

To deine the threshold effective width for the shear capacity, the results of S8 and S9 (2.5 m [8.2 ft]) (Lant-

soght et al. 2012) were compared to the results of the current

series of specimens (BS1 of 0.5 m [1.6 ft] to BX3 of 2 m

[6.6 ft]), all of which were made with high-strength concrete

(Table 1). The results are displayed by showing the shear

capacity as a function of the member width in Fig. 8. The

boundary line between beams and slabs at 5h from

NEN-EN 1992-1-1:2005 (CEN 2005) is also given. Addi-

tionally, the trendlines through datapoints at widths smaller

than the threshold value are shown together with the lines of

averaged constant shear capacities for wide members (above

the threshold width) in Fig. 8. The intersection of these lines

determines the measured threshold for the considered series.

These results show that the concept of using an effective

width for wide members is indeed valid as the shear capacity

does not increase linearly for larger widths. The results for

Table 3Inluence of decrease in shear span

from 600 to 400 mm (23.6 to 15.7 in.) on observed

increase of shear capacity

Specimens b, m

AVG

Vexp,400/Vexp,600 STD COV, %

BS2, BS3 0.5 2.09 0.297 14.2

BM2, BM3 1.0 1.73 0.027 1.6

BL2, BL3 1.5 1.49 0.061 4.1

BX2, BX3 2.0 1.30 0.063 4.8

S3 to S5 2.5 1.38 0.026 1.9

Note: 1 m = 3.3 ft.

Fig. 7Larger average a/dl ratio for wide elements as

compared to elements of small width.

Table 4Measured increase in ultimate shear

capacity Vexp for an increase in size of loading

plate from 200 x 200 mm (7.9 x 7.9 in.) to 300 x

300mm (11.8 x 11.8 in.), with a/dl = 2.26

Specimens b, m Average increase Vexp, %

BS1 to BS3 0.5 11.5

BM1 to BM3 1.0 0.1

BL1 to BL3 1.5 0.6

BX1 to BX3 2.0 24.6

S1, S2 2.5 40.6

Note: 1 m = 3.3 ft.

Table 5Comparison between ultimate shear

capacity at simple (Vexp,SS) and continuous

support (Vexp,CS)

Experiments b, m AVG Vexp,CS/Vexp,SS STD COV, %

BS 0.5 1.783 0.492 28%

BM 1.0 1.329 0.069 5%

BL 1.5 1.225 0.093 8%

BX 2.0 1.167 0.130 11%

S1 S10 2.5 1.112 0.133 12%

Note: 1 m = 3.3 ft.

Fig. 8Inluence of overall width on shear capacity. Test results for BS, BM, BL, BX, S8 and S9 are shown. (Notes:

1 mm = 0.04 in.; 1 kN = 0.225 kip.)


the estimated threshold effective width based on the experi-

mental results are given in Table 6 and are compared to the

calculated widths based on the load spreading methods from

Fig. 2 and 3.

Inluence of tested parameters on effective width

The results of the threshold effective width from Table 6

show a difference between loading at the simple (SS) and

continuous (CS) support. Consistently, lower effective

widths are found at the continuous support as compared to

the simple support due to the transverse moment. The results

from Table 6 also show a different effective width depending

on the size of the loading plate. The size of the loading plate

is taken into account in the French load-spreading method as

well as in the ib Model Code load-spreading method. More-over, the results from Table 6 show that the effective width

becomes smaller as the load is placed closer to the support,

which corresponds to the idea of horizontal load spreading

from the load towards the support at a certain angle. The

comparison between the threshold width and the effective

widths based on the load-spreading methods in Table 6

shows that the threshold width corresponds best to the effec-

tive width based on the French load-spreading method.

COMPARISON BETWEEN EXPERIMENTAL

RESULTS AND CODE PREDICTIONS

The experimental shear capacities of the experiments

from the B-series are compared to the shear provisions from

ACI 318-11 and NEN-EN 1992-1-1:2005, using both beff1

and beff2. The mean values of the measured material proper-

ties are used and all partial safety factors are taken equal to 1.

The properties of the concrete are determined on cube spec-

imens in the laboratory. The cylinder compressive strength

fc,cyl is assumed as 0.82 fc,meas (van der Veen and Gijsbers

2011). To compare the shear provisions from NEN-EN

1992-1-1:2005 to the experimental results, CRd,c,test = 0.15

(Regan 1987) is used for mean values. The measured shear

forces Vexp and moments Mexp at failure are used to determine

the ratio VACIdl/MACI from ACI 318-11, here expressed as

Vexpdl/Mexp. The comparison between the experimental

results and the code methods is shown in Fig. 9. The two

load-spreading methods from Fig. 2 are studied in combina-

tion with the shear provisions from NEN-EN 1992-1-1:2005

(Fig. 9(a)) and ACI 318-11 (Fig. 9(b)).

The results in Fig. 9 show that NEN-EN 1992-1-1:2005

leads to conservative results for all experiments, and that

ACI 318-11 on average more closely predicts the shear

capacity. The code methods, however, are aimed at the

inclined cracking load of slender beams (Joint ACI-ASCE

Committee 426 1973; Regan 1987). In the current experi-

ments, direct load transfer can lead shear capacities beyond

the inclined cracking load.

It can be seen in Fig. 9 that using beff2 (Fig. 2(b)) in combi-

nation with ACI 318-11 and NEN-EN 1992-1-1:2005 gives

a better estimate of the capacity than beff1, as seen when the

results of the ratio between the experimental and predicted

shear capacities are plotted as a function of the specimen

width, Fig. 10. When using beff1, the ratio between experi-

mental and predicted value increases for an increasing spec-

imen width, while this ratio remains more constant when

beff2 is used.

The statistical properties of the comparison between the

experiments and the code predictions are given in Table 7.

Overall better results are obtained when beff2 is used instead

of beff1 (Fig. 9). The combination of beff2 and NEN-EN 1992-

1-1:2005 results in the smallest coeficient of variation,

Table 6Effective width as calculated from

experimental results, compared to effective width

based on different load-spreading methods

No. Series bmeas, m beff1, m beff2, m bMC, m

1300 x 300 mm

SS, a/dl = 2.262.0 1.1 1.7 1.0

2300 x 300 mm

CS, a/dl = 2.261.8 1.1 1.7 1.0

3200 x 200 mm

SS, a/dl = 1.511.3 0.7 1.1 0.6

4200 x 200 mm

CS, a/dl = 1.510.9 0.7 1.1 0.6

5200 x 200 mm

SS, a/dl = 2.261.5 1.1 1.5 1.0

6200 x 200 mm

CS, a/dl = 2.261.3 1.1 1.5 1.0

Notes: 1 m = 3.3 ft; 1 mm = 0.04 in.

Fig. 9Comparison between experimental results and expected values according to ACI 318-11 and NEN-EN 1992-1-1:2005.

(Note: 1 kN = 0.225 kip.)


while the combination of ACI 318-11 and beff2 results in the

closest predictions of the experimental results. The inlu-ence of the specimen width can be seen on the BS, BM,

BL, and BX rows of Table 7. The average of the ratio

between the experimental and predicted result increases

with the width when beff1 is used, and remains more constant

when beff2 is used, as also observed in Fig. 10. Comparing the

last two rows shows that the code methods underestimate the

increased capacity at the continuous support. In ACI 318-11,

the inluence of the moment distribution at the support is taken into account by the factor VACIdl/MACI. Applying this

factor, however, still leads to a larger average ratio of Vexp/VACI

for tests carried out close to the continuous support than

close to the simple support. Studying the results of Vexp,EC/VR,c

shows that separating the results of the experiments at the

continuous support from the results of the experiments at

the simple support leads to a signiicant improvement of the coeficient of variation. Therefore, it is recommended to take into account the inluence of the moment distribution at the support in NEN-EN 1992-1-1:2005 and to revise the expres-

sion from ACI 318-11 in terms of VACIdl/MACI.

SUMMARY AND CONCLUSIONS

Load-spreading methods are used in practice to deter-

mine a threshold for the relationship between the member

width and the shear capacity. Previous series of experi-

mental research were inconclusive about the existence of a

threshold width and the determination of the effective width.

Therefore, a series of 12 specimens of 5.0 m length x 0.3 m

depth (16.4 ft x 11.8 in.) of variable widths was tested. A

total of 24 experiments were carried out. These results were

analyzed together with the results of slabs that were tested

in earlier research.

The experiments show that, as the member width increases,

the inluence of the size of the loading plate increases and the inluence of the shear span-depth ratio decreases. Both results can be explained by understanding that a three-

dimensional load-carrying mechanism is activated in wider

specimens. This mechanism differs considerably from the

two-dimensional load-carrying mechanism in members of

small width. The inluence of the moment distribution at the support becomes smaller as the member width increases.

The results of the experiments to deine the shear capacity on members with an increasing width are used to deine experimentally the threshold width. This experimental

threshold width most closely resembles the effective width

based on the French load-spreading method: horizontal

load spreading from the far side of the loading plate under

a 45-degree angle towards the face of the support. It is

also found that the effective width from the French load-

spreading method leads to the best predictions of the exper-

iments when combined with the studied code provisions. A

45-degree load-spreading method was previously adopted in

practice based on engineering judgment, but it is now shown

to be valid through rigorous experimentation.

AUTHOR BIOSEva O. L. Lantsoght is an Assistant Professor at Universidad San Fran-cisco de Quito, Quito, Ecuador, and a Researcher at Delft University of Technology, Delft, the Netherlands. She received her engineering degree from Vrije Universiteit Brussel, Brussels, Belgium; her MS from the Georgia Institute of Technology, Atlanta, GA; and her PhD from Delft University of Technology.

Cor van der Veen is an Associate Professor at Delft University of Tech-nology, where he received his MSc and PhD. His research interests include high-strength steel iber concrete, concrete bridges, and computational mechanics.

Ane de Boer is a Senior Advisor at Rijkswaterstaat, the Ministry of Infra-structure and the Environment, Utrecht, the Netherlands. He received his MSc and PhD from Delft University of Technology. His research interests include remaining lifetime, existing structures, computational mechanics, trafic loads and composites.Joost C. Walraven is an Emeritus Professor at Delft University of Tech-nology. He received his MSc and PhD from Delft University of Technology.

Fig. 10Ratio between experimental results and calcu-

lated values according to ACI 318-11 and NEN-EN 1992-1-

1:2005 as function of specimen width. (Note: 1 m = 3.3 ft.)

Table 7Statistical properties obtained from comparing experimental results to predicted shear

capacities as prescribed by NEN-EN 1992-1-1:2005 and ACI 318-11

Test data

Vexp/VACI,beff1 Vexp/VACI,beff2 Vexp,EC/VR,c,beff1 Vexp,EC/VR,c,beff2

AVG STD COV AVG STD COV AVG STD COV AVG STD COV

BS 1.52 0.75 0.49 1.52 0.75 0.49 2.12 0.74 0.35 2.12 0.74 0.35

BM 1.60 0.84 0.52 1.33 0.43 0.32 2.15 0.56 0.26 1.88 0.27 0.15

BL 1.96 0.88 0.45 1.34 0.49 0.37 2.68 0.55 0.21 1.86 0.29 0.16

BX 2.15 0.82 0.38 1.42 0.48 0.34 2.90 0.39 0.14 1.94 0.22 0.11

SS 1.57 0.76 0.48 1.21 0.42 0.35 2.10 0.54 0.26 1.64 0.17 0.11

CS 2.04 0.83 0.40 1.60 0.56 0.35 2.83 0.51 0.18 2.26 0.36 0.16

all 1.81 0.81 0.45 1.40 0.52 0.37 2.46 0.64 0.26 1.95 0.42 0.22


ACKNOWLEDGMENTSThe authors wish to express their gratitude and sincere appreciation to the

Dutch Ministry of Infrastructure and the Environment (Rijkswaterstaat) for inancing this research work and to InfraQuest for coordinating the coopera-tion between Delft University of Technology, Rijkswaterstaat, and research institute TNO.

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