Punching Strength of Reinforced Concrete...

706 ACI Structural Journal/September-October 2009

ACI Structural Journal, V. 106, No. 5, September-October 2009.MS No. S-2008-305 received September 15, 2008, and reviewed under Institute

publication policies. Copyright © 2009, 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 in the July-August 2010 ACI Structural Journal if the discussion is received by March 1, 2010.

TECHNICAL PAPERACI STRUCTURAL JOURNAL

A total of 17 reinforced concrete footings were tested to investigatethe punching shear behavior of footings. The test parametersinvestigated are the shear span-depth ratio (a/d), concretestrength, and punching shear reinforcement. The (a/d) rangedbetween 1.25 and 2.0, whereas the concrete strength rangedbetween 20 and 40 MPa (2.9 and 5.8 ksi). To study the effect ofsoil-structure interaction, five footings were realistically supportedon sand. The remaining specimens were supported on a columnstub and a uniform surface load was applied. The present experimentalinvestigations indicated that the angle of the failure shear crack issteeper in punching tests on compact footings than observed intests on more slender slabs. Furthermore, the (a/d) significantlyaffects the punching shear capacity. Based on the test results, the ACIand Eurocode 2 provisions are critically reviewed and improvementsare proposed.

Keywords: footings; punching shear; reinforced concrete; shear span-depth ratio; soil pressure redistribution; soil-structure interaction.

INTRODUCTIONThe problem of punching of reinforced concrete slabs has

been dealt with extensively in literature.1,2 Tests on reinforcedconcrete footings, however, are still limited.3-6 Furthermore,most of the available tests have unrealistic test setups. As aconsequence, the design of reinforced concrete footings ismainly based on test results of slabs and most design codesdo not distinguish between slabs and footings in the designrules. Hence, there is a need for a systematic experimentalinvestigation on reinforced concrete footings. Therefore,punching tests on 17 quadratic reinforced concrete footingswere performed. The aim of this investigation is to study themain parameters assumed to affect the punching shearstrength of footings such as shear span-depth ratio (a/d),concrete compression strength, shear reinforcement, andsoil-structure interaction.

RESEARCH SIGNIFICANCEThe punching shear capacities of footings predicted by

various codes vary significantly. By testing 17 footings, themain parameters affecting the punching strength aresystematically investigated. The parameters studied area/d, concrete compressive strength, punching shearreinforcement, and the soil-structure interaction. The provisionsof ACI 318-087 and Eurocode 28 are evaluated by comparingwith the experimental results.

DESIGN CODESIn general, design codes do not differentiate between the

punching shear strength of flat plates and footings. Thecodes allow a part of the soil reaction to be subtracted fromthe punching load. The amount to be deducted, however,differs from one code to the other.

ACI 318-08The critical section is at d/2 from the column face (Fig. 1 (a)).

The design is based on

vu < φvn (1)

where φ is a strength reduction factor (0.75 for shear); vu isthe applied factored shear stress, using load factors 1.2 and1.6 for dead and live loads; and vn is the nominal shear resistance.The applied shear stress due to factored concentric shear forceVu is calculated as

vu = Vu/(b0d) (2)

where b0 is the perimeter of the critical section, and d is thedistance from the extreme compression fiber to the centroid

Title no. 106-S66

Punching Strength of Reinforced Concrete Footingsby Josef Hegger, Marcus Ricker, and Alaa G. Sherif

Fig. 1—Critical perimeters according to: (a) ACI 318-08;and (b) Eurocode 2.

707ACI Structural Journal/September-October 2009

of tension reinforcement (effective depth). The shearresistance of the concrete vc is the smallest value obtainedfrom Eq. (3), (4), and (5)

vc = 0.17 MPa = psi (3)

vc = 0.083 MPa = psi (4)

vc = 0.33λ MPa = 4λ psi (5)

where αs is a parameter taken as 40 for interior, 30 for edge,and 20 for corner columns; βc is the ratio of long to short sideof concentrated load or reaction area; λ is a factor accountingfor the concrete density; and b0 is the perimeter of the criticalsection in Fig. 1(a). For slabs without shear reinforcement,the nominal shear resistance vn in Eq. (1) is vc. The isolatedfooting may be assumed to be rigid, resulting in a uniformsoil pressure for concentric loading. The shear force canbe reduced by the effective soil pressure within thecontrol perimeter.

If vu > φvc, shear reinforcement has to be used. Two criticalsections are to be checked: d/2 from the column face and d/2from the outer shear reinforcement (Fig. 1(a)). The punchingshear resistance inside the shear-reinforced zone is calculated as

vn = vcs + vs ≤ vmax (6)

where vcs is the shear stress resisted by the concrete insidethe shear-reinforced zone, vs is the shear stress resisted bythe shear reinforcement, and vmax is the maximum allowedshear stress.

Acknowledging the superior anchorage performance ofshear studs, ACI 318-08 distinguishes between shear studsand stirrups as shear reinforcement. The nominal shearstrength provided by concrete vcs inside the shear-reinforcedzone is calculated as

vcs = 0.17λ MPa = 2λ psi for stirrups (7)

vcs = 0.25λ MPa = 3λ psi for studs (8)

The nominal shear strength provided by shear reinforcementvs is calculated as

1 2βc

-----+⎝ ⎠⎛ ⎞ λ fc′ 2 4

βc

-----+⎝ ⎠⎛ ⎞ λ fc′

αsd

b0

--------- 2+⎝ ⎠⎛ ⎞ λ fc′

αsd

b0

--------- 2+⎝ ⎠⎛ ⎞ λ fc′

fc′ fc′

fc′ fc′

fc′ fc′

(9)

where Av is the area of shear reinforcement in one row aroundthe column, s is the spacing of the shear reinforcement, and fytis the yield strength of the shear reinforcement not to exceed413 MPa (60,000 psi). The maximum allowed shear stressvmax is determined as

vmax = 0.5 MPa = 6 psi for stirrups (10)

vmax = 0.67 MPa = 8 psi for studs (s 0.5d) (11)

Outside the shear-reinforced zone, the shear stress resistanceof the concrete is limited to the one-way shear strength value of

vc = 0.17λ MPa = 2λ psi (12)

Eurocode 2For concentric loading, the maximum shear stress vEd is

calculated as

(13)

where VEd, red is the net applied shear force, u is the controlperimeter considered, and d is the effective depth. Forconcentric loading, VEd, red is calculated as

VEd,red = VEd – ΔVEd (14)

where VEd is the column load and ΔVEd is the net upwardforce within the control perimeter considered, that is, upwarduniform pressure from soil minus self-weight of footing.

The punching resistance should be verified at controlperimeters within 2.0d from the periphery of the column(Fig. 1(b)). The lowest value of resistance at the differentsections controls the design. The punching shear stress resistanceof the concrete is calculated as

(15)

where CRd,c = 0.18/γc is an empirical factor derived from aregression analysis, with γc being the material resistance factor forconcrete (1.5); d is the effective depth; k = 1 + ≤ 2.0 isthe size factor of the effective depth (with d in mm); ρ is theflexural reinforcement ratio; fck is the characteristic cylindercompressive concrete strength; acrit is the distance from thecolumn face to the control perimeter considered; andvmin = 0.035 · k3/2· fck

1/2 is the minimum shear capacityof the concrete, including the material resistance factor forconcrete γc = 1.5.

If vEd > vRd,c , shear reinforcement will be required. Thedesign of the shear reinforcement is based on the followingexpression

vsAv fyt

b0s------------=

fc′ fc′

fc′ fc′ ≤

fc′ fc′

vEdVEd red,

ud-----------------=

vRd c, CRd c, k 100ρ fck⋅( )1 3⁄ 2dacrit

---------- vmin2d

acrit

----------≥=

200 d⁄

ACI member Josef Hegger is a Professor at the Institute of Structural Concrete,Rheinisch-Westfälische Technische Hochschule Aachen (RWTH) University, Aachen,Germany. He received his PhD from the Braunschweig University of Technology,Braunschweig, Germany, in 1985. His research interests include bond behavior, shearcapacity, high-performance concrete, textile-reinforced concrete, and composite structures.

Marcus Ricker is a Research Engineer at the Institute of Structural Concrete, RWTH.He received his Diploma degree in structural engineering from the DarmstadtUniversity of Technology, Darmstadt, Germany, in 1998. His research interestsinclude the punching behavior of footings and flat plates.

ACI member Alaa G. Sherif is a Professor in the Civil Engineering Department,Helwan University, Mataria-Cairo, Egypt. He received his BSc from Cairo University,Giza, Egypt, in 1987, and his MSc and PhD from the University of Calgary, Calgary,AB, Canada, in 1991 and 1996, respectively. He is a member of Joint ACI-ASCE Committee352, Joints and Connections in Monolithic Concrete Structures. His research interestsinclude the design and serviceability of reinforced concrete structures.


(16)

where Asw is the area of the shear reinforcement in one rowaround the column; sr is the radial spacing of perimeters ofshear reinforcement; u is the control perimeter within 2.0dfrom the column face (Fig. 1(b)); fywd,ef is the effectivedesign strength of the punching shear reinforcement,according to fywd,ef = 250 + 0.25d (with d in mm) ≤ fywd (MPa);and α is the angle between the shear reinforcement and theplane of the slab.

The maximum punching shear resistance (at the columnface) is limited to a maximum of

(with fck in MPa) (17)

where fcd = αcc fck/γc is the design concrete compressivestrength with αcc = 1.0 being a coefficient taking account forlong-term effects. The control perimeter at which shearreinforcement is not required (Fig. 1(b)) is determined by

(18)

The outermost perimeter of shear reinforcement should beplaced at a distance not greater than 1.5d within uout (Fig. 1(b)).The shear reinforcement should be provided in at least tworows and the spacing of the perimeters should not exceed0.75d. The distance between the column face and the firstrow of shear reinforcement should not exceed s0 = 0.5d(Fig. 1(b)).

EXPERIMENTAL PROGRAMThe experimental program included 17 footings. The

dimensions of the test specimens were chosen to model 1/2to 1/3 scale of a common footing. The specimens weredivided in two series. The first series included five footings(DF6 to DF10) that were realistically supported on sand.These footings were to supplement previous tests.6 Thesecond test series included 12 footings (DF11 to DF22) thatwere supported on a column stub and a uniform load wasapplied to the footing. The test parameters included the a/dratio, the concrete compressive strength, the shear reinforcement,and the soil-structure interaction.

Material propertiesFor the footings of Series I, the concrete was mixed at the

laboratory; for Series II, commercial ready mixed concretewas used. The maximum coarse aggregate size was 16 mm(0.63 in.) in all footings. Ordinary CEM III A 32.5 N portlandcement and a water-cement ratio (w/c) of 0.50 were used,resulting in a slump of approximately 480 mm (18.9 in.).The concrete mixtures were designed to produce a 28-daytarget strength of fc′ = 20 and 40 MPa (2.9 and 5.8 ksi).German steel BSt 500 (A), with the measured yield stressfsy = 552 MPa (80.1 ksi), tensile strength fsu = 634 MPa(92.0 ksi), and a Young’s modulus of 200,000 MPa (29,000 ksi),was used for all reinforcement. Table 1 summarizes theproperties of the materials used.

Test specimensThe dimensions of the footings were 1200, 1400, and 1800 mm

(47.2, 55.1, and 70.9 in.) in square with the thickness of thefootings varying between 300 and 530 mm (11.8 and 20.9 in.).The effective depth d varied between 250 and 470 mm (9.8 and18.5 in.), resulting in a/d of approximately 1.25, 1.5, and 2.0. The

vRd cs, 0.75vRd c, 1.5 dsr

----Asw fywd ef,1

ud------ αsin+=

vRd max, 0.5 0.6 1fck

250---------–⎝ ⎠

⎛ ⎞ fcd⋅ ⋅ ⋅=

uoutVEd

vRd c, d⋅-------------------=

Table 1—Details of test specimens

Testd,

mm (in.)c,

mm (in.)b,

mm (in.) a/dfc′,

MPa (ksi)Ec ,

MPa (ksi)ρ,%

Av,

cm2 (in.2)s,

mm (in.)Vservice ,

kN (kips)Vtest ,

kN (kips)Vflex ,

kN (kips)

DF6 395 (15.6) 200 (7.9) 1200 (47.2) 1.27 19.0 (2.8) 23,450 (3401) 0.87 — — 1008 (227) 2836 (638) 7146 (1607)

DF7 395 (15.6) 200 (7.9) 1400 (55.1) 1.52 20.9 (3.0) 25,067 (3636) 0.87 — — 980 (220) 2569 (578) 6544 (1471)

DF8 250 (9.8) 200 (7.9) 1200 (47.2) 2.00 22.5 (3.3) 24,850 (3604) 0.88 — — 540 (121) 1203 (270) 3028 (681)

DF9 250 (9.8) 200 (7.9) 1200 (47.2) 2.00 20.8 (3.0) 24,700 (3582) 0.89 28.4 (4.4) 90 (3.5)* 1008 (227) 2784 (626) 3069 (690)

DF10 250 (9.8) 200 (7.9) 1200 (47.2) 2.00 38.1 (5.5) 29,500 (4278) 0.91 — — 864 (194) 1638 (368) 3179 (715)

DF11 395 (15.6) 200 (7.9) 1200 (47.2) 1.27 21.4 (3.1) 22,000 (3191) 0.87 — — 1200 (270) 2813 (632) 6845 (1539)

DF12 395 (15.6) 200 (7.9) 1400 (55.1) 1.52 21.2 (3.1) 23,700 (3437) 0.88 — — 900 (202) 2208 (496) 6732 (1513)

DF13 395 (15.6) 200 (7.9) 1800 (70.9) 2.03 21.1 (3.1) 20,100 (2915) 0.87 — — 800 (180) 1839 (413) 6004 (1350)

DF14 295 (11.6) 200 (7.9) 1400 (55.1) 2.00 21.2 (3.1) 23,700 (3437) 0.88 — — 600 (135) 1478 (332) 3766 (847)

DF15 470 (18.5) 200 (7.9) 1400 (55.1) 1.28 21.7 (3.2) 22,500 (3263) 0.85 — — 1700 (382) 2750 (618) 8996 (2022)

DF16 395 (15.6) 200 (7.9) 1200 (47.2) 1.27 20.0 (2.9) 20,900 (3031) 0.87 45.2 (7.0) 190* (7.5) 1800 (405) 3680 (827) 7114 (1599)

DF17 395 (15.6) 200 (7.9) 1400 (55.1) 1.52 20.8 (3.0) 22,000 (3191) 0.87 45.2 (7.0) 190* (7.5) 1600 (360) 3619 (814) 6570 (1477)

DF18 395 (15.6) 200 (7.9) 1800 (70.9) 2.03 21.7 (3.2) 22,500 (3263) 0.87 45.2 (7.0) 190* (7.5) 1500 (337) 3361 (756) 6026 (1355)

DF19† 395 (15.6) 200 (7.9) 1200 (47.2) 1.27 21.8 (3.2) 21,900 (3176) 0.87 — — 1600 (360) 2790 (627) 7132 (1603)

DF20 395 (15.6) 200 (7.9) 1200 (47.2) 1.27 35.7 (5.2) 27,400 (3974) 0.87 — — 1600 (360) 3037 (683) 7455 (1676)

DF21 395 (15.6) 200 (7.9) 1400 (55.1) 1.52 36.3 (5.3) 26,800 (3887) 0.87 — — 1200 (270) 2860 (643) 6914 (1554)

DF22 395 (15.6) 200 (7.9) 1800 (70.9) 2.03 36.4 (5.3) 26,200 (3800) 0.87 — — 1000 (225) 2405 (541) 6338 (1425)*Spacing between column face and first row of shear reinforcement was s0 = 75 mm (3.0 in.) for Specimen DF7 and s0 = 120 mm (4.7 in.) for DF16, DF17, and DF18.†Specimen included seven circular ties, which confine compression zone near column face (refer to text).Note: d is effective depth; c is column dimensions; b is footing dimension; a is footing dimension measured from face of column; fc′ is cylinder concrete compression strength;Ec is Young’s Modulus of concrete; ρ is flexural reinforcement ratio; Av is area of one leg of stirrups along a peripheral line; s is spacing between two peripheral lines of stirrups;

Vservice is estimated service load; Vtest is ultimate failure load; and Vflex is shear force that produces flexural failure according to yield-line theory.9 Footings with shear reinforcementincluded layer of top reinforcement of ρ′ = 0.49% (DF9) and ρ′ = 0.31% (DF16, DF17, and DF18).

ACI Structural Journal/September-October 2009 709

dimensions and reinforcement details of a typical test specimenare shown in Fig. 2. The flexural reinforcement ratio variedbetween 0.85 and 0.91%. The 200 x 200 mm (7.8 x 7.8 in.)square column stubs were cast monolithically at the centerof the slabs using high-strength concrete and were reinforcedwith 10 mm (0.4 in.) steel plates to prevent a premature failure.Full details of the footings are given in Table 1. Footings DF9and DF16 to DF18 included heavy shear reinforcement andwere designed to examine the maximum punching capacity.The shear reinforcement consisted of vertical stirrups with adiameter of 10 mm (0.4 in.) and a yield strength fyw of 520 MPa(75.4 ksi) in Specimen DF9 and 12 mm (0.5 in.) and fyw of560 MPa (81.2 ksi) in Specimens DF16 to DF18. The spacingsof the stirrups are given in Table 1. As an example, the layout ofthe shear reinforcement for DF9 is shown in Fig. 2. SpecimenDF19 included seven circular ties with a diameter of 400 mm(15.7 in.), which were horizontally arranged underneath thecolumn stub to confine the compression zone near the columnface. The bar diameter was 12 mm (0.5 in.) and the spacing was40 mm (1.6 in.). The circular ties did not increase thepunching shear strength compared to a similar footingwithout confinement (DF11). Therefore, the test results arenot discussed further in this paper.

Test setup and measurementsSeries I (DF6 to DF10)—The specimens of Series I were

tested supported on sand (Fig. 3(a)). The dimension of thesand box was 3250 x 3250 x 3200 mm (128 x 128 x 126 in.).The remaining depth of the sand bed underneath the footingsvaried between 2200 and 2500 mm (87 and 98 in.), beingapproximately twice the width of the footings. To achievehomogeneous sand beds of reproducible packing, controlledpouring and tamping techniques were used to deposit sandlayers of 55 mm (2.2 in.) thickness into the sand box. Theload was applied by six hydraulic jacks (maximum capacity3540 kN [796 kips]) placed between a steel frame and the

column stub. The jacks were linked to a common manifoldand applied the same load independent of the displacement.The soil pressure distribution was measured by 21 electricstress sensors with electric/hydraulic pressure gauges. Inaddition, thin-film pressure sensors were used to measure thesoil pressure distribution. The main advantage of the sensorsused is that this system allows a two-dimensional measurementof the soil pressure distribution whereas the soil pressuregauges can only measure the soil pressure at definite points(Fig. 4(a)).

Series II (DF11 to DF22)—The specimens of test Series IIwere loaded by a uniform surface load using the test setupshown in Fig. 3(b). The footings were tested upside down.The load was applied by eight hydraulic jacks (maximumcapacity 4720 kN [1061 kips]). Each jack transferred its loadvia steel beams to two polytetrafluoroethylene (PTFE)-coatedsliding bearings of dimensions 140 x 140 mm (5.5 x 5.5 in.).Thus, the load was applied by a total of 16 bearings simulatinga uniform loading case. The reaction frame consisted of twoparallel steel beams, which were supported by four tie rodsanchored to the strong floor of the laboratory.

For both test series during testing, the vertical displacement atthe corners of the column stub and the slab corners weremeasured using linear variable differential transformer(LVDT) gauges. The flexural steel strains were monitored at14 locations as shown in Fig. 4(b) as well as at some of thestirrups. At one measuring point, two strain gauges wereattached to opposite side faces of the reinforcement bars toobtain the strains at the center of gravity of the bars. Theconcrete strains were also recorded at 14 locations on thecompression faces.

Fig. 2—Layout of flexural and shear reinforcement for testSpecimen DF9.

Fig. 3—Test setups.

Fig. 4—Arrangement of soil pressure gauges and steelstrain gauges.


Testing procedureThe load was applied in increments of 108 to 196 kN

(24.3 to 43.8 kips) for Series I and in increments of 100 to200 kN (22.5 to 45.0 kips) in Series II. For Series I, theincrements were chosen to increase the soil pressure by75 and 100 kN/m2 (10.9 and 14.5 psi), respectively.After the service load Vservice was reached (Table 1), theload was cycled 10 times between the service load and halfof the service load. After this, the load was incrementallyincreased until 80% of the calculated failure load wasreached. Then the footings were continuously loaded untilfailure took place.

EXPERIMENTAL RESULTSCracking and failure characteristic

All tests failed in punching of the footing. The failureloads are listed in Table 1. The comparison with the flexuralcapacities of the footings Vflex according to Gesund9 revealsthat the flexural capacities were not reached and confirm thefact that failure occurred due to punching (Table 1). After thetest, the specimens were sawn into two halves. In all slabs,the failure surface consisted of a wide shear crack, whichformed the surface of a truncated cone (Fig. 5). For the specimenswithout shear reinforcement, the observed inclinations of thefailure shear crack were approximately 45 degrees for thecompact footings DF11, DF20, and DF6 (a/d = 1.25) andless than 35 degrees for the more slender footings DF13 andDF22 (a/d = 2.0). For the footings without shear reinforcement,the inclination of the failure crack seems to be mainly influencedby a/d. Neither the concrete strength nor the support situation hada significant effect in this aspect. For the shear-reinforcedspecimens, an outer shear crack with an inclination ofapproximately 45 degrees, crossing the shear reinforcement, aswell as a much steeper inner crack with an inclination ofapproximately 50 to 60 degrees were observed. Strainmeasurements confirmed that the shear reinforcement wasactivated. Hence, it can be concluded that the outer, moregently inclined shear crack developed first. The failure mostlikely took place when the second, inner shear crackoccurred. In contrast to the footings without shear reinforcement,the influence of a/d on the inclination of the shear cracks seemsto be negligible.

Load-deflection characteristicThe deflections at the center of the slab for several footings

are shown in Fig. 6. For all series, the gradient of the curvesdecreases with increasing a/d; this can be attributed to theincreasing bending deformations. In contrast, the deformationsof the more compact footings are mainly induced by shear. Forthe tested specimens, the shear deformations are somewhatsmaller than the deformations due to bending irrespective ofthe boundary conditions, the concrete compressive strength,or the existence of shear reinforcement (Fig. 6). If the loaddeflection curves of the specimens DF11 to DF13 and DF20to DF22 are compared, it is obvious that the gradient of thedeflection curves increases for higher concrete grades due tothe increased stiffness (Fig. 6(b) and (d)). The specimen withshear reinforcement showed a more ductile behavior than thespecimen without shear reinforcement (Fig. 6(b) and (c)).

Steel strainsMeasurements were made to determine the steel strain

distribution for all slabs. Typical test results of thesemeasurements are shown in Fig. 7. In general, the measurementsshowed some scatter. For the specimen without shearreinforcement, the bars did not reach yield at failure. Forthe footings DF16 and DF17 with shear reinforcement, onlythe tension reinforcement in the vicinity of the columnyielded before punching took place (Fig. 7(c)). Thus, theflexural capacity had not been reached when the footingsfailed in punching.

Soil pressure distributionFor all tested footings of Series I, the soil pressure distribution

was measured. Figure 8 shows the soil pressure distribution ofthe footings DF6 and DF9 close to failure. Although themeasurements showed plenty of scatter, a concentration ofsoil pressure underneath the column stub was morepronounced for DF9 (a/d = 2.0).

DISCUSSION OF EXPERIMENTAL RESULTSFor the following discussion of the experimental results,

the critical shear section specified by ACI 318-08 is used.The failure load Vtest is multiplied by the factor (1 – A0/A),where the parameters A0 and A are the area within the shear

Fig. 5—Saw-cuts of different test specimens.


critical section and the area of the footing, respectively(Fig. 1(a)). The term (1 – A0/A) accounts for the soil reactionwithin the critical section to be subtracted from the punchingforce assuming a uniform soil pressure distribution.

Effect of a /dIn Tests DF11 to DF13, the only parameter varied was a/d.

Therefore, the tests may be used to study the effect of a/d on thepunching behavior. As shown in Fig. 9(a), the tests indicatethat the shear strength decreases with increasing a/d. TheACI 318-08 does not reflect this trend as it does not accountfor the effect of a/d.

Fig. 7—Typical steel-strain distributions at failure.

Fig. 6—Load-deflection curves.


Effect of concrete compressive strengthFor the investigation of the influence of the concrete

strength, two test series are available. The footings of thefirst series (DF11 to DF13) had a concrete compressivestrength of approximately 20 MPa (2.9 ksi) and the testspecimens of the second series (DF20 to DF22) had a targetstrength of 40 MPa (5.8 ksi). In Fig. 9(b), the failure loadsare plotted as a function of the concrete compressive strengthfc′. Although the test data are limited, it can be concludedthat for slender footings (a/d = 1.5 and 2.0), the concretestrength seems to significantly affect the punching behavior.For the less slender footings DF11 and DF20 (a/d = 1.25),the effect of the concrete strength is not significant. This isremarkable because it was expected that the behavior of themore compact footings could be described by a strut-and-tiemodel. In such a case, the failure load of the compact footingsDF11 and DF20 should be controlled by the bearing capacity ofthe compression strut if enough flexural reinforcement isprovided. Therefore, for compact footings, it was expectedthat the punching shear strength increases linearly with theconcrete compressive strength. Two test results, however,are not sufficient to draw definite conclusions and more testresults are needed on this aspect.

Effect of shear reinforcementTo investigate the influence of shear reinforcement on the

punching behavior, two series are available. In the firstseries, three specimens with closed stirrups as shearreinforcement were tested (DF16 to DF18). The secondseries included footings DF11 to DF13 that are identical tothe first series except they did not contain shear reinforcement.In Fig. 10(a), the ratio Vtest/Vc,test is plotted as a function ofa/d. Vtest is the failure load of the footing containing shearreinforcement, while Vc,test is the failure load of the corre-

sponding similar footing without shear reinforcement.Figure 10(a) shows that shear reinforcement substantiallyincreases the punching capacity of footings. The effectivenessof the shear reinforcement, however, depends on a/d. Theeffectiveness of shear reinforcement decreases withdecreasing a/d. For example, the shear strength of footingDF18 (a/d = 2.0) was increased approximately 80% by thestirrups. In contrast, the shear reinforcement increased theshear strength of the more compact footing DF16 (a/d = 1.25)by only approximately 33%. In Fig. 10(b), the ratio vs,test /vs,ACIis compared. The shear stress vs,test is calculated by(Vtest – 0.5Vc,test)/(b0d). Thus, the theoretical capacity of theshear reinforcement according to ACI 318-08 has not beenreached or the concrete contribution is overestimated.

Effect of soil-structure interactionTwo test series are available to investigate the influence of

the soil-structure interaction. Series DF6 to DF8 weresupported on sand, whereas the companion specimens ofSeries DF11 to DF13 were uniformly loaded. In general, thefootings supported on sand had a higher punching shearresistance than those uniformly loaded (Fig. 11). This maybe attributed to the soil pressure concentration underneaththe footing (Fig. 8). This concentration increases the part ofthe soil pressure that reduces the applied shear stress alongthe critical perimeter. The test Specimen DF8 supported onsand showed significantly higher shear strength than theuniformly loaded Specimen DF13 (Fig. 11). To fit into thesand box, the dimensions of Specimen DF8 had to be reducedcompared to Specimen DF13. To ensure the same a/d, the slabthickness also had to be reduced from 450 to 300 mm (17.7 to11.8 in.) for Specimens DF13 and DF8, respectively. Therefore,

Fig. 8—Soil pressure distribution close to failure.Fig. 9—Effect of: (a) a/d; and (b) concrete compressive strengthon punching shear strength of footings.


the high shear strength of the footing DF8 may be partlyattributed to the size effect. The present tests are notsufficient to evaluate the size effect quantitatively. It may beconcluded that for design purpose, the soil-structure interactionis not a major factor.6

COMPARISON OF PREDICTIONS AND EXPERIMENTAL RESULTS

For the comparison between the present tests and thecodes, all material and strength reduction factors in the codeequations are taken as unity. The comparison is mainly basedon the ratio of the failure load Vtest and the calculatedpunching shear resistance Vcode. The ratio Vtest /Vcode isplotted against the effective depth d and a/d.

Comparison with ACI 318-08The ACI 318-08 code provisions are compared with the

test results in Fig. 12. The ACI Code does not account for thesize effect on the punching shear strength. Therefore, theprovisions tend to be less conservative for larger effectivedepths. This tendency can be observed for the specimenssupported on sand as well as for the uniformly loaded footings(Fig. 12(a)). The ratio Vtest /VACI has a mean of 1.33 and acoefficient of variation of 0.13. The ACI predictions as afunction of a/d are shown in Fig. 12(b). Although the codedoes not account for a/d, the analysis of all tested footingsseem to be trend free for the concrete strengths tested. The

Fig. 10—(a) Contribution of shear reinforcement on shearstrength of footings; and (b) comparison between theoreticalcontribution of shear reinforcement to punching shearstrength according to ACI 318-08 and steel contributiondetermined by testing.

Fig. 11—Effect of soil-structure interaction on punchingshear strength of footings.

Fig. 12—Comparision between punching tests and punchingshear resistance according to ACI 318-08.


ratio Vtest /VACI is significantly higher for the specimenssupported on sand (Fig. 12(c)). This is due to the fact that forthe calculations, a uniform soil pressure distribution underneaththe footings was assumed. The soil pressure inside the criticalperimeter b0 at a distance of 0.5d from the column face wassubtracted from the applied shear force. In the tests, aconcentration of the soil pressure inside the critical perimeterwas measured. This led to a reduction of the applied shearforce and, therefore, increased the punching shear strength.Furthermore, the diameter of the punching cone differs fromthe diameter of the assumed critical perimeter to some extent(Fig. 5). The ratio Vtest /VACI for the specimens with shear

reinforcement is plotted as a function of a/d in Fig. 12(d).Except for Specimen DF9, which was supported on sand, theratio Vtest /VACI is independent of a/d.

Comparison with Eurocode 2Eurocode 2 provides two equations to determine the

punching shear strength of slabs without shear reinforcementVRd,c (Eq. (15)) and VRd,max (Eq. (17)). The smaller valuecontrols the design. The equation for VRd,max was originallyadapted from the Model Code 90.10 For slabs, Eurocode 2 aswell as Model Code 90 uses a critical perimeter at a distanceof 2.0d from the periphery of the applied load. The use of acontrol perimeter relatively far away from the column faceleads to a good correlation with slab tests with a practicalratio of column perimeter u0 to effective slab depth d (largerthan 4). The large control perimeter also offers the opportunityto use the same shear strength as for one-way shear. The largeperimeter, however, leads to the fact that the shear stressalong the periphery of very small loaded areas becomesgoverning.11 Therefore, Model Code 90 and Eurocode 2demand that the shear stress at the periphery of the applied loadshould not exceed the web-crushing limit for beams withvertical stirrups.

Unfortunately, VRu,max = γcVRd,max (with γc = 1.5 beingthe material resistance factor for concrete and VRd,maxaccording to Eq. (17)) controls the design of the present tests(except DF10) due to the small ratios u0/d, which arecharacteristic for column footings. Because the equationof VRu,max is only a function of the concrete compressivestrength, VRu,max does not reflect the influence of the effectivedepth d or a/d correctly, as shown in Fig. 13(a) and (b). Inaddition, the equation significantly overestimates thepunching shear capacity for higher concrete grades, asshown in Fig. 13(b). This is attributed to the fact that theequation accounts for a linear effect of the concrete compressivestrength on the punching capacity, which is in contrast to testresults.12,13 It is also obvious from the statistical evaluation,which leads to a mean value of 1.12 and a coefficient ofvariation of 0.23 indicating high scatter, that the equationfor VRu,max is not able to predict the punching shear strengthof footings without shear reinforcement satisfactorily. Theequation of VRu,max is also not applicable for the maximumpunching strength of footings with shear reinforcement(Fig. 13(d)). Due to the small ratios u0/d of 2.0 and 3.2, theequation calculates very conservative punching shear resistancesfor the shear-reinforced footings and does not count for anyshear reinforcement.

In Fig. 14, the resistance is calculated according to Eq. (15)and (16), while VRu,max is neglected. The aim of this comparisonis to investigate the performance of these equations. For thefootings without shear reinforcement, VRu,c = γcVRd,c (withVRd,c according to Eq. (15)) correctly reflects the influence of theeffective depth d, the concrete strength, and a/d, and results in lessscatter (Fig. 14(a), (b), and (c)). This is also confirmed by thereduced coefficient of variation of 0.10. The mean value ofonly 0.77, however, clearly indicates that for footings withoutshear reinforcement, Eq. (15) would result in an unconservativedesign. Application of Eq. (16) leads to safety factors below 0.5because the footings failed in maximum punching shear due to thehigh shear reinforcement ratio (Fig. 14(d)).

Eurocode 2 provides parameters that are optional fornational choice. In Eq. (15), the empirical factor CRd,c can begiven by the National annex. To ensure the required safety

Fig. 13—Comparision between punching tests and punchingshear resistance according to Eurocode 2.

715ACI Structural Journal/September-October 2009

level for footings, it is proposed here to reduce CRd,c to avalue of 0.12/γc.

To overcome the problem that Eq. (17) for VRd,max calculatesvery conservative punching shear resistances for the shear-reinforced footings, a new equation for the calculation ofVRd,max at the periphery of the loaded area is herein proposed

(19)

with vRd,c being the punching shear capacity of a slab withoutshear reinforcement, which is calculated as vRd,c = 0.18/γck(100ρfck)1/3. The notations are chosen in accordance withEurocode 2. Certainly, the applied shear force can only bereduced by the effective soil pressure within the columnperimeter u0. In Fig. 15, the proposed equations arecompared to the test results. The proposal correctly reflectsthe influence of the effective depth d and a/d. In addition, thescatter is reduced and the safety level is increased.VRd max, 16 d u0⁄ vRd c, u0d=

Fig. 14—Comparision between punching tests and punchingshear resistance of footings according to Eurocode 2 neglectingthe influence of Vmax.

Fig. 15—Comparision between punching tests and punchingshear resistance according to the modification proposed toEurocode 2.


CONCLUSIONSBased on the results of the experimental investigation on

footings supported on sand, as well as on footings loadeduniformly, the following conclusions can be drawn:

1. For the footings without shear reinforcement, theinclination of the failure shear crack seems to be mainlyinfluenced by a/d and not by the concrete strength. Theobserved inclinations of the failure crack were approximately45 degrees for the compact footings (a/d = 1.25) and less than35 degrees for the more slender footings (a/d = 2.0).

2. The punching shear resistance is strongly influenced bya/d. The shear strength decreases with increasing a/d.

3. Although the test data are limited, it can be concludedthat for slender footings (a/d = 1.5 and 2.0), the concretestrength seems to significantly affect the punching behavior.This effect seems to decline for more compact footings(a/d = 1.25).

4. Shear reinforcement can substantially increase thepunching capacity of footings, but is less effective withdecreasing a/d.

5. In general, the footings supported on sand showed ahigher punching shear resistance than those uniformlyloaded. This may be attributed to the soil pressure concentrationunderneath the footing. The assumption of uniformly distributedsoil pressure beneath the footings according to the buildingcodes, however, ensures a safe design.

6. ACI 318-08 does not account for the size effect on thepunching shear strength. Therefore, the provisions tend to beless conservative for larger effective depths. This tendencycan be observed for the specimens supported on sand as wellas for the uniformly loaded footings.

7. According to Eurocode 2, the shear strength of footingsof practical dimensions, as the one tested, is governed by themaximum allowed web crushing limit VRd,max at the columnface. Because VRd,max is only a function of the concretecompressive strength, this leads to the fact that it is notpossible to increase the punching resistance of footings byusing shear reinforcement. Modifications are proposed toovercome this deficiency.

ACKNOWLEDGMENTSThe authors wish to express their sincere gratitude to the Deutsche

Forschungsgemeinschaft (DFG, German Research Foundation) for thefinancing. The tests of Series I were conducted in cooperation with the Instituteof Geotechnical Engineering, RWTH Aachen University. The effectivecooperation is appreciated. This paper was written during a research visitof A. G. Sherif at the RWTH Aachen University financed by the Alexandervon Humboldt Foundation. The support of the Alexander von HumboldtFoundation is deeply appreciated.

REFERENCES1. Regan, P. E., and Braestrup, M. W., “Punching Shear in Reinforced

Concrete,” CEB-Bulletin d’Information No. 168, Lausanne, Switzerland,1985, 232 pp.

2. Polak, M. A., ed., Punching Shear in Reinforced Concrete Slabs, SP-232,American Concrete Institute, Farmington Hills, MI, 2005, 302 pp.

3. Richart, F. E., “Reinforced Concrete Wall and Column Footings,”ACI JOURNAL, Proceedings V. 45, (Part 1) No. 2, Oct. 1948, pp. 97-127, (Part2) No. 3, Nov. 1948, pp. 237-260.

4. Dieterle, H., and Rostásy, F., “Tragverhalten quadratischerEinzelfundamente aus Stahlbeton,” Deutscher Ausschuss für Stahlbeton,V. 387, Berlin, Germany, 1987, 134 pp.

5. Hallgren, M.; Kinnunen, S.; and Nylander, B., “Punching Shear Testson Column Footings,” Nordic Concrete Research, V. 21, No. 3, 1998, pp. 1-22.

6. Hegger, J.; Sherif, A. G.; and Ricker, M., “Experimental Investigationson Punching Behavior of Reinforced Concrete Footings,” ACI StructuralJournal, V. 103, No. 4, July-Aug. 2006, pp. 604-613.

7. ACI Committee 318, “Building Code Requirements for StructuralConcrete (ACI 318-08) and Commentary,” American Concrete Institute,Farmington Hills, MI, 2008, 465 pp.

8. European Committee for Standardization (CEN), “Eurocode 2: Designof Concrete Structures—Part 1.1: General Rules and Rules for Buildings,”Brussels, Belgium, 2004, 225 pp.

9. Gesund, H., “Flexural Limit Analysis of Concentrically LoadedColumn Footings,” ACI JOURNAL, Proceedings V. 80, No. 3, May-June 1983,pp. 223-228.

10. Committee Euro-International du Béton, “CEB-FIP Model Code1990: Design Code,” London: Thomas Telford, 1993, 437 pp.

11. Regan, P. E., “Punching of Slabs under Highly Concentrated Loads,”Structures and Buildings, V. 157, No. 2, 2004, pp. 165-171.

12. Elstner, R. C., and Hognestad, E., “Shearing Strength of ReinforcedConcrete Slabs,” ACI JOURNAL, Proceedings V. 53, No. 7, July 1956, pp. 29-58.

13. Moe, J., “Shearing Strength of Reinforced Concrete Slabs and Footingsunder Concentrated Loads,” Bulletin D47, Portland Cement Association,Skokie, IL, 1961, 135 pp.

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