Alexandria Engineering Journal (2016) 55, 2665–2678

HO ST E D BY

Alexandria University

Alexandria Engineering Journal

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ORIGINAL ARTICLE

Structural design of isolated column footings

* Corresponding author.

Peer review under responsibility of Faculty of Engineering, Alexandria University.

http://dx.doi.org/10.1016/j.aej.2016.06.0161110-0168 � 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Fathi Abdrabbo, Zaki I. Mahmoud *, Mariana Ebrahim

Structural Eng. Dept., Faculty of Eng., Alexandria Univ., Egypt

Received 21 November 2015; revised 31 May 2016; accepted 9 June 2016Available online 9 August 2016

KEYWORDS

Footing;

Codes;

Punching shear;

Shear span;

Correlation;

Contact stress

Abstract Superstructure loads are transmitted to the underlying soil strata through a suitably

designed foundation. Therefore, the foundation of a structure is considered the most crucial struc-

tural element in a building. The foundation may be classified into two main categories, shallow and

deep foundations. Shallow foundation comprises isolated column footings, combined footings and

reinforced concrete mat. The design of isolated column footing is accomplished through the appli-

cation of geotechnical and structural analysis concepts. So that, the input research into isolated col-

umn footings comes from two different disciplines, geotechnical and structural. This may be one of

the main causes that attributed to the limited research input to the subject. Therefore, the structural

design of isolated column footings is based on empirical rules and the calculations of bending

moments (BM) and shearing forces (SF) induced in a footing are based on the rules of beam theory,

which is questionable. On the other hand, punching theory was developed on relatively thin floor

slab, even though the theory is implemented for the calculation of punching shear in relatively thick

footings. Also experimental research on isolated column footings is scarce, due to the difficulties

involved in the setup of the laboratory models and the cost of experiments. The work presented

in this article deals with the correlation between failure loads predicted by different code provisions,

ECP203-11, ACI318-08, BS 8110.1-1997 and EC2-2004, of isolated column footings, and the cor-

responding measured values.

The study showed that shear span to depth ratio of a footing and distributions of contact stress at

footing–soil interface are key factors in the structural design of the footing. ECP203-11, ACI318-08,

and EC2-2004 code provisions, underestimate the structural failure loads of isolated column foot-

ings, while BS 8110.1-1997 overpredicts the failure loads of isolated column footings, if punching

provisions at perimeter of column are pulled out from the code.� 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria

University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/

licenses/by-nc-nd/4.0/).

1. Literature review

It was established that the failure mechanism of floor slab andfoundation plate depends on the shear slenderness ratio (a/d)

[1,2]. The most important parameters that influence punchingshear are the effective or total footing depth, the flexural rein-forcement ratio, and compressive strength of concrete [1]. The

angle of shear cracks of foundation plate is between 50 and 60

Nomenclature

L length of footing

B width of footingd depth of footingc width/length of column stuba shear span, distance from edge of column to edge

of footingf0c cylinder compressive strength of concretefcu cube compressive strength of concrete

q reinforcement ratioV experimental failure load

cs material coefficient of steel

cc material coefficient of concretePp predicted failure load due to punching shearA contact area of footingAo punching contact area of footing at the level of

flexural steel enclosed by line at distance d fromthe edge of the column

Sc one way shear capacity of footing

Ps predicted failure load based on one way shearPupc punching shear capacity of footing

2666 F. Abdrabbo et al.

(1 vertical to 1.19–1.73 horizontal) which is significantly higherthan the angle for slender slabs, which varies between 30 and

40 (1 vertical to 0.57–0.83) [2].The difficulties associated with laboratory modeling and

testing of isolated column footings, lead to that the experimen-

tal research input to the subject is quite scarce [3]. It is worthnoting that, the majority of technical regulations do not distin-guish between punching through floor slabs and punching

through foundation slabs. A comparative analysis [4] indicatedthat foundation slab failure mechanism is different when com-pared to slender slabs. Theoretical explanation of the platepunching phenomenon, based on the critical shear crack for

the reinforced concrete slab without and with transverse rein-forcement was emphasized [5,6]. The theory is referred as crit-ical shear crack theory (CSCT). The theory was recognized by

new fib model code 2010, Draft Bulletins 55 and 56. The differ-ence between the punching mechanism of foundation platesand floor slabs has generally been neglected in technical regu-

lations [7]. This can be attributed to that experimental researchrelated to foundations has so far been quite scarce, because ofthe complicated arrangement of such experiments. Further-more, there is noticeable difference in the calculations of

punching loads given by different codes [7]. Experimentalstudy on 17-column footing revealed that the shear span/depthof footing, which is called shear slenderness ratio, significantly

affects the bearing capacity to punching-shear [7].The punching failure through a footing is brittle, and the

use of shear reinforcement increases the punching capacity sig-

nificantly, and increases the ductility and the possibility ofredistribution of forces [8,14].

A review of the theoretical and experimental research work

including Codes/Regulations for punching calculation of col-umn footings leads to that cracks pattern because punchingdepends upon a/d ratio, in which cracks are inclined in caseof column footings with greater a/d ratio, than in case of col-

umn footings with a smaller a/d ratio [9]. In Switzerland, theshear reinforcement in footing is calculated on the basis ofthe theory of plasticity, according to SIA 262, and the contribu-

tion of concrete to punching capacity is neglected, which leadsto conservative calculation results for shear reinforcement [9].

2. Objectives of the research

The main objective of the presented work was to correlatebetween the predicted structural failure loads of isolated

column footings, through the implementation of code

provisions, and the measured failure loads documented inthe literature. A trial was given to adjust some code provisions

during the correlation process to obtain a better correlationresults. ECP 203-11, ACI 318-08, BS 8110.1-1997 and EC2-2004 code provisions are considered for the prediction of fail-

ure loads. The structural design of isolated column footing,most often is controlled by punching shear induced in the foot-ing. So that, the most attention is given to code provisions

dealing with punching shear. No attention was paid to thebehavior of footings included shear reinforcement due to thevery limited experimental work on such footings.

3. Procedure of the study

The work presented was accomplished through the followingsteps:

1. The ECP 203-2011, ACI 318-08, BS 8110.1-1997 andEC2-2004 provisions related to the structural design of

isolated column footings were used through spread sheetsfor the calculation of ultimate failure loads.

2. The available previous work documented in literature was

reviewed, for experimental work on isolated columnfootings.

3. The laboratory work completed with enough data on class

of concrete, footing dimensions, failure load, reinforcementand grade of steel was tabulated, as data base.

4. The predicted loads using code provisions were obtainedusing experimental data. One way and punching shear

according to ECP 203-11, ACI 318-08, BS 8110.1-1997provisions were implemented in the prediction. Punchingshear only of EC2-2004 provision is considered in the study.

4. One way and punching shear code provisions

Code provisions consider two types of shear in the design ofreinforced concrete isolated column footings subjected to axialloads, One-way shear and punching shear. The Egyptian code

provisions ECP 203-2011 defined the critical section of one-way shear and punching shear at distance d/2 from the edgeof the column as shown in Fig. 1. ACI (318-08) provisions con-

sidered critical section for one-way shear at distance d from theedge of the column and punching shear at distance d/2. BS(8110-1997) provisions considered the control section of one-way shear at distance d from the edge of the column, and to

Figure 1 ECP code – critical section.

Structural design of isolated column footings 2667

calculate punching shear at distances 0.5d, d, and 1.5d from theedge of the column, and at the perimeter of the column. Euro

code (2-2004) stated that the control section of punching shearis at distance 2.0d from the edge of column and the lowestvalue of resistance at different sections controls the design.

5. Data base

Nineteen experimental test results on reinforced concrete foot-

ings were collected from the available literature, to carry outcomparison between predicated and experimental failureloads. The data of the tested footing models such as; amount

of reinforcement, dimensions of footings, and failure loadswere tabulated. Table 1 presents the dimensions of the testedfootings L, B and d. The length L equals to the width B.The side dimension of the footing varies between 850 mm

and 1800 mm, while the depth (d) varies between 100 mm to470 mm. The dimensions of column stubs (c) are varying from175 mm to 200 mm. Th ratio of shear span to footing thickness

Table 1 Details of test specimens.

Test L= B

(mm)

d

(mm)

C

(mm)

a/d f0c(MPa)

q(%)

V test

(kN)

DF6 1200 395 200 1.27 19 0.87 2836

DF7 1400 395 200 1.52 20.9 0.87 2569

DF8 1200 250 200 2.00 22.5 0.88 1203

DF10 1200 250 200 2.00 38.1 0.91 1638

DF11 1200 395 200 1.27 21.4 0.87 2813

DF12 1400 395 200 1.52 21.2 0.88 2208

DF13 1800 395 200 2.03 21.1 0.87 1839

DF14 1400 295 200 2.00 21.2 0.88 1478

DF15 1400 470 200 1.28 21.7 0.85 2750

DF19 1200 395 200 1.27 21.8 0.87 2790

DF20 1200 395 200 1.27 35.7 0.87 3037

DF21 1400 395 200 1.52 36.3 0.87 2860

DF22 1800 395 200 2.03 36.4 0.87 2405

TI 850 175 175 1.92 30.7 0.40 906

TII 850 125 175 2.70 30.7 0.40 1050

TIX 850 100 175 3.37 17 0.40 430

TX 850 150 175 2.25 17 0.40 656

TXI 850 125 175 2.70 15.4 0.40 451

TXII 850 125 175 2.70 8 0.40 440

a/d varies between 1.28 and 3.37. The concrete compressive

strength, f 0c , varies from 8.0 MPa to 38.10 MPa, and steel rein-

forcement ratio from 0.4% to 0.91%. The measured failureload (v) varies from 430 kN to 3037 kN. The yield strength

of steel reinforcement is 552 MPa, and the tensile strength634 MPa. Tests TI to TXII after Bonic and Folic [9], whiletests DF6 to DF22 after Heggar et al. [7].

It is worth noting that in Table 1, tests denoted DF6 toDF10 were carried out while the footings are supported onsand. Tests marked TI to TXII were carried out on supporting

sand gravel; 25% by weight sand content, maximum nominalsize of gravel 50 mm. In tests coded DF11 to DF22 the soilwas simulated by small hydraulic jacks transferred its load

via steel beams to two polytetrafluoroethylene (PTFE) coatedsliding bearings. Therefore scale effects may influence the testresults of tests denoted TI to TXII. It is interesting to note thatthe ratio of maximum nominal size of gravel to footing width

in tests TI to TXII is 1/170 which is unrealistic ratio comparedby practical applications. While, in footings DF6 to DF10where the footings are supported on sand, the maximum sand

size to footing width varies from 1/600 to 1/700 assuming max-imum nominal size of sand size is 2 mm. It is documented thatthe tested specimens failed when the induced punching shear

stress in specimens attained the punching shear strength pro-vided by concrete section.

6. Procedure of comparison

The comparison between predicted and measured failure loadswas conducted taking into consideration that the cube strength

of concrete was assessed by dividing cylinder concrete strength

f 0c by 0.80, to implement Egyptian and British code provisions.

The material coefficients cs and cc of steel reinforcement andconcrete were taken equal to unity, in the prediction of failureload.

The total failure load Pp was predicted as,

Pp ¼ Pupc 1� A0

A

� ��ð1Þ

Therefore, the parameter bp is expressed as,

bp ¼ Pp=V ð2ÞAssuming the contact stress at footing–soil interface is uni-

formly distributed, and by considering one way shear at theedge of the column, failure load of the footing is calculated as,

Ps ¼ 2Sc

BðB� cÞA ð3Þ

And for one way shear at distance d/2 from the edge of thecolumn,

Ps ¼ 2Sc

BðB� cþ dÞA ð4Þ

The parameter bs is expressed as,

bs ¼ Ps=V ð5Þ

6.1. ECP (203-2011) provisions [10]

Fig. 2 and Table 2 present comparison between the measuredand the predicted failure loads Pus obtained from one-way

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.5 1 1.5 2 2.5 3 3.5

pred

icte

dlo

ad,k

N*1

03

Measured failure load kN*103

Figure 2 Comparison between predicted and measured failure

loads (ECP 203-11) one way shear.

Table 2 Predicted and measured failure loads, (ECP 203-11),

one way shear and punching shear.

Test Measured

load (kN)

Predicted

failure load Ps

(kN)

bs Predicted

failure load Pp

(kN)

bp

DF6 2836 1466.2 0.52 1919.7 0.68

DF7 2569 1573.0 0.61 1853.1 0.72

DF8 1203 814.6 0.68 877.5 0.73

DF10 1638 1060.0 0.65 1141.9 0.70

DF11 2813 1556.0 0.55 2037.4 0.72

DF12 2208 1584.3 0.72 1866.4 0.85

DF13 1839 1839.2 1.00 1712.8 0.93

DF14 1478 1052.5 0.71 1085.9 0.73

DF15 2750 2103.1 0.76 2688.9 0.98

DF19 2790 1570.5 0.56 2056.3 0.74

DF20 3037 2009.8 0.66 2631.4 0.87

DF21 2860 2073.1 0.72 2442.2 0.85

DF22 2405 2292.5 0.95 2249.7 0.94

TI 906 501.2 0.55 577.5 0.64

TII 1050 325.5 0.31 335.4 0.32

TIX 430 185.4 0.43 179.0 0.42

TX 656 304.5 0.46 332.7 0.51

TXI 451 230.8 0.51 237.8 0.53

TXII 440 166.2 0.38 171.2 0.39

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

re-a

djus

ted

load

,kN

*103

Measured failure load kN*103

Figure 3 Comparison between re-adjusted and measured failure

loads (ECP 203-11) one way shear.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

pred

icte

d lo

ad, K

N*1

03

Measured failure load KN*103

Figure 4 Comparison between predicted and measured failure

loads (ECP 203-11) punching shear.

2668 F. Abdrabbo et al.

shear at code defined critical section. The predicted failureloads were drawn against measured failure loads. Table 2 pre-

sents the ratio bs of the predicted to the measured failure loads.The ratio bs varies from 0.52 to 1.0 for tests DF6 to DF22 withan average value of 0.70. Footings TI to TXII revealed bs valuevaries from 0.31 to 0.55 with an average value of 0.44.

The bs –values of tests TI to TXII are less than the valuesobtained from tests DF6 to DF22, This may be explained bythe concentration of contact stress, at footing – soil interface,

beneath column stub. It is obvious from Fig. 2 that the codeprovision underestimates the failure load obtained from one-way shear at code defined critical section, by an average ratio

of 0.62.The following is a proposal to adjust ECP 203-11 provi-

sions for one way shear to predict values nearly equal to the

measured failure load. The multiple factor in the equationgiven by code provisions for the calculations of shear capacitywas calculated for each test by equating the predicted load tothe measured failure load. By omitting four test results DF13,

DF22, TII and TXII, an average value of the multiple factorbecomes 0.27 instead of 0.16.

Therefore the proposed adjusted equation for the calcula-

tion of shear capacity is proposed:

qc ¼ 0:27

ffiffiffiffiffifcucc

sð6Þ

The failure loads (Ps) were recalculated again using Eq. (6)

and compared with the measured values, Fig. 3. The figureindicates better correlation between the measured and calcu-lated failure loads. The average value of bs of all tests is1.03, while the average value of bs of test series DF6 to

DF22 is 1.1 after omitting the results of two tests and the aver-age value of test series T1 to TXII is 0.83, after omitting theresults of two tests.

Employing ECP code punching shear provisions, the failureloads were calculated and compared with the measured failureloads and the ratio bp was drawn, Fig. 4.

Table 2 indicates that the values of bp obtained from testsDF6 to DF22 vary from 0.68 to 0.98, with an average of0.80; Tests TI to TXII revealed an average value of 0.47, while

values of b ranged from 0.32 to 0.64. The difference in the out-put results of bp values, between series of tests DF6 to DF22and the other series TI to TXII is due to the concentrationof stresses acting on footing models TI to TXII under column

stub. Fig. 4 and Table 2, indicate that the code provision for

y = 1.2023x - 240.14

1.52.02.53.03.54.04.5

uste

d lo

ad, k

N*1

03

Structural design of isolated column footings 2669

punching shear underestimates the failure load by an averagevalue of 0.7. If test results of series TI to TXII are omitted,the average value of bp becomes 0.80.

The code provisions were adjusted by the same procedureoutline in one-way shear. Table 3 indicates unexpected smallvalues of bp corresponding to tests TII, TIX and TXII. The test

results of these specimens were omitted and the mean values ofmultiple factors in the equations given by code provisions forcalculating the shear capacity were assessed. The achieved mul-

tiple factors and the proposed equations are

qc ¼ 0:43

ffiffiffiffiffifcucc

sð7Þ

qc ¼ 0:43 0:5þ qcbc

� � ffiffiffiffiffifcucc

sð8Þ

qc ¼ 1:09 0:2þ / d

2ððac þ dÞ þ ðbcþdÞÞ� � ffiffiffiffiffi

fcucc

sð9Þ

The proposed equations for punching shear calculations

were employed in the prediction of failure loads and comparedwith the measured values. Fig. 5 shows a better correlationbetween predicted and measured failure loads; even though

scatter in results is noted. It is worth noting that the averagebp value of tests DF6 to DF22 is 1.09, while the mean valueof all test results is 1.03.

It is worth noting that the minimum predicted failure loads

of the tested specimens, in accordance with ECP 203-11 codeprovisions are controlled by the loads obtained from one-way shear at code-defined critical section, at distance d/2 from

the edge of the column.

6.2. ACI (318-08) provisions [11]

The predicted failure loads of the tested footings were obtainedbased on one-way shear at code-defined critical section, at

Table 3 Predicted and measured failure loads, (ACI 318-08),

one way shear and punching shear.

Test Measured

load (kN)

Predicted

failure load Ps

(kN)

bs Predicted

failure load Pp

(kN)

bp

DF6 2836 4014.2 1.42 1793.1 0.63

DF7 2569 2935.1 1.14 1730.9 0.67

DF8 1203 1161.2 0.97 819.7 0.68

DF10 1638 1511.0 0.92 1066.6 0.65

DF11 2813 4260.2 1.51 1903.0 0.68

DF12 2208 2956.1 1.34 1743.3 0.79

DF13 1839 2467.6 1.34 1599.9 0.87

DF14 1478 1483.9 1.00 1014.3 0.69

DF15 2750 5611.6 2.04 2511.5 0.91

DF19 2790 4299.8 1.54 1920.7 0.69

DF20 3037 5502.4 1.81 2457.9 0.81

DF21 2860 3868.1 1.35 2281.2 0.80

DF22 2405 3241.1 1.35 2101.3 0.87

TI 906 732.8 0.81 539.4 0.60

TII 1050 400.3 0.38 313.3 0.30

TIX 430 213.2 0.50 167.2 0.39

TX 656 405.1 0.62 310.8 0.47

TXI 451 283.8 0.63 222.1 0.49

TXII 440 204.4 0.46 159.9 0.36

distance d from the edge of the column and compared withthe measured failure loads. The achieved results are presentedin Table 3 and Fig. 6.

Comparison between the predicted and the measured fail-ure loads indicates that the bs values, vary from 0.92 to 2.04for tests coded DF6 to DF22 with an average value of 1.36

and from 0.38 to 0.81 for tests TI to TXII with an averagevalue of 0.57. The achieved results revealed that the distribu-tion of contact stress at footing-soil interface has a great influ-

ence on the shear strength induced in the footing. Table 3indicates that the distribution of contact stress at footing-soilinterface is a major factor in the calculations of one-way shearinduced in the footing.

The failure loads of the tested footings were predicted inaccordance with the punching shear provisions stated in ACI318-08 code. Table 3 presents the predicted failure loads, the

measured failure loads and the ratio bp. The correlationbetween experimental and the predicted failure loads wasdrawn; Fig. 7, for the sake of comparison. The table indicates

that the value of bp for tests DF6 to DF22 varies from 0.63 to0.91, with an average value of 0.75, Tests TI to TXII revealedvalues of bp vary from 0.30 to 0.60 with an average value of

0.44. The difference in the output results between series of testDF6 to DF22 and the other series TI to TXII is due to the con-centration of stresses acting on the footing model underneathcolumn stub. Generally all test results revealed that code pro-

visions for punching shear underestimate the measured failure

0.00.51.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

re-a

dj

Measured failure load kN*103

Figure 5 Comparison between re-adjusted and measured failure

loads (ECP 203-11) punching shear.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

pred

icte

d lo

ad, k

N*1

03

Measured failure load kN*103

Figure 6 Comparison between predicted and measured failure

loads (ACI 318-08) one way shear.

y = 1.2022x - 240.13

0.0

1.0

2.0

3.0

4.0

5.0

0.0 1.0 2.0 3.0 4.0 5.0

re-a

djus

ted

load

, kN

*103

measured failure load kN*103

Figure 8 Comparison between re-adjusted and measured failure

loads (ACI 318-08) punching shear.

Table 4 Predicted and measured failure loads, (BS 8110.1-

1997), one way shear at distance d and at the edge of the

column.

Test Measured

load (kN)

Predicted

failure load

Ps (kN) at

distance d

bs Predicted failure

load Ps (kN) at

the edge of the

column

bs

2670 F. Abdrabbo et al.

loads by 0.65. It is interesting to note that the Egyptian codeprovision for the calculation of failure loads based on punch-ing shear underestimated the failure load by a factor of 0.70.

While the Egyptian code provision for the calculation ofone-way shear at distance d/2 from the edge of the columnunderestimate the measured failure load by a factor of 0.62.

The adjustment of code provisions were carried out foreach test specimen and the multiple factor in the equation giv-ing the smallest value of shear strength was obtained. The fac-

tors in the other two equations were adjusted by the sameratio.

Three tests which revealed peculiar multiple values, TestsTII, TIX, TXII, were omitted and the mean values of multiple

factors were calculated. The adjustments revealed the follow-ing three equations;

Vc ¼ 0:25 1þ 2acbc

� �k

ffiffiffiffif 0c

qbod ð10Þ

Vc ¼ 0:12asdbo

þ 2

� �k

ffiffiffiffif 0c

qbod ð11Þ

Vc ¼ 0:48kffiffiffiffif 0c

qbod ð12Þ

The three proposed equations for the calculation of punch-ing shear were implemented in the calculation of failure loads

and compared with the measured values, Fig. 8. The figureindicates a better correction. The bp value varies between0.69 and 1.34 with an average value of 1.13.

It is worth noting that the minimum predicted failure loadsin accordance with ACI 318-08 code provisions is controlledby punching shear at code-defined critical section, at distance

0.5d from the edge of the column. The code provisions under-estimated the failure load by an average value of 0.75 for testseries DF6 to DF22 and by an average value of 0.44 for series

TI to TXI, and by 0.65 for all the tested specimens. The ulti-mate loads of isolated column footings are controlled by shearat distance 0.5d from the edge of the column in accordancewith ECP 203-11 and ACI 318-08 code provisions. But ECP

203-11 code provisions consider one-way shear, contrary toACI 318-08 code provisions which considered punching shear.Both ACI 318-08 code and ECP 203-11 code provisions under-

estimate the failure load of isolated column footings by anunderestimation ratio of 0.65 and 0.62 respectively.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

pred

icte

d lo

ad, k

N*1

03

Measured failure load kN*103

Figure 7 Comparison between predicted and measured failure

loads (ACI 318-08) punching shear.

6.3. (BS8110-1997) provisions [12]

The failure loads of the tested specimens were predicted by theimplementation of code provisions related to one-way shear at

distance d from the edge of the column. Table 4 presents thepredicted and the measured failure loads, bs values are alsopresented in the same table. Fig. 9 presents the correlation

between predicted and measured failure loads.Test series DF6 to DF22 revealed that the bs values varied

from 0.94 to 1.98 with an average value of 1.33, while test ser-

ies TI to TXII indicated bs values varied from 0.36 to 0.71 withan average value of 0.56. If all test results are considered theaverage values of bs becomes 1.09. Again the effect of stressdistribution at footing–soil interface on the predicted value

of the failure load is obvious. Code provisions overestimatethe failure load of test series DF6 to DF22 by an average ratio

DF6 2836 4028.8 1.42 4435.2 1.56

DF7 2569 2899.4 1.13 5276.2 2.05

DF8 1203 1275.2 1.06 3054.7 2.54

DF10 1638 1537.0 0.94 3600.0 2.20

DF11 2813 4191.8 1.49 4707.0 1.67

DF12 2208 2924.3 1.32 5313.9 2.41

DF13 1839 2433.7 1.32 6572.6 3.57

DF14 1478 1579.0 1.07 3968.6 2.69

DF15 2750 5449.0 1.98 6397.0 2.33

DF19 2790 4217.7 1.51 4750.8 1.70

DF20 3037 4971.4 1.64 5688.0 1.87

DF21 2860 3485.2 1.22 6451.7 2.26

DF22 2405 2918.8 1.21 7998.8 3.33

TI 906 642.4 0.71 1856.5 2.05

TII 1050 381.7 0.36 1326.1 1.26

TIX 430 237.2 0.55 789.5 1.84

TX 656 407.3 0.62 1184.2 1.81

TXI 451 303.5 0.67 940.2 2.08

TXII 440 184.5 0.42 541.6 1.23

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

pred

icte

d lo

ad, k

N*1

03

Measured failure load kN*103

Figure 9 Comparison between predicted and measured failure

loads (BS 8110.1-1997) one way shear at distance d.

Table 5 Predicted and measured failure loads, (BS 8110.1-

1997), punching shear at distance 0.5d from the edge of the

column and at distance d from the edge of the column.

Test Measured

load (kN)

Predicted

failure load Pp

(kN) at

distance 0.5d

bp Predicted

failure load Pp

(kN) at

distance d

bp

DF6 2836 2781.3 0.98 5463.7 1.93

DF7 2569 2642.5 1.03 3603.0 1.40

DF8 1203 1391.1 1.16 1409.4 1.17

DF10 1638 1676.7 1.02 1698.8 1.04

DF11 2813 2893.8 1.03 5684.7 2.02

DF12 2208 2665.2 1.21 3634.0 1.65

DF13 1839 2438.5 1.33 2590.7 1.41

DF14 1478 1668.1 1.13 1708.8 1.16

DF15 2750 3769.0 1.37 7336.9 2.67

DF19 2790 2911.7 1.04 5719.9 2.05

DF20 3037 3432.0 1.13 6742.1 2.22

DF21 2860 3176.4 1.11 4330.9 1.51

DF22 2405 2924.6 1.22 3107.2 1.29

TI 906 730.7 0.81 735.8 0.81

TII 1050 461.6 0.44 381.7 0.36

TIX 430 287.4 0.67 217.9 0.51

TX 656 482.8 0.74 438.0 0.67

TXI 451 367.0 0.81 303.5 0.67

TXII 440 223.6 0.51 169.4 0.39

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

pred

icte

d lo

ad k

N*1

03

Measured failure load kN*103

Figure 11 Comparison between predicted and measured failure

loads (BS 8110.1-1997) punching shear at distance 0.5d from the

edge of the column.

Structural design of isolated column footings 2671

of 1.33, while code provisions underestimate the failure load of

test series TI to TXII by an average ratio of 0.55, even thoughthe same provisions are implemented.

The failure loads were predicted using code provisions of

one way shear at the edge of the column. The achieved pre-dicted loads along with the measured failure loads are pre-sented in Table 4. Fig. 10 presents correlation between

predicted failure loads and the measured value.Test series DF6 to DF22 revealed that bs values varied from

1.56 to 3.57 with an average value of 2.32, while test series TI

to TXII indicated that bs values varied from 1.23 to 2.08 withan average value of 1.71. From all test results, the code provi-sions produce failure loads with an average value of 2.13 timesthe average value of the measured failure load. One can notice

that the bs values obtained from series DF6 to DF22 are rela-tively close to bs values obtained from series TI to TXII com-pared by values obtained from shear calculations at distance d

from the face of column.By comparing Figs. 9 and 10, one can notice that the diver-

gence between measured and predicted failure loads increases

as the control section of one way shear becomes closer to theedge of the column.

The predicted failure loads of the tested specimens were

obtained implementing punching shear provisions at distance0.5d from the edge of the column. The bp values are presentedin Table 5. The correlation between the measured and the pre-dicted failure loads is presented in Fig. 11. Table 5 indicates

0

2

4

6

8

0 1 2 3 4 5 6 7 8

pred

icte

d lo

ad k

N*1

03

Measured failure load kN*103

Figure 10 Comparison between predicted and measured failure

loads (BS 8110.1-1997) one way shear at the edge of the column.

that the values of bp obtained from test results DF6 to DF22is varying from 0.98 to 1.37, with an average value of 1.13.Tests TI to TXII revealed an average value of 0.66, while the

values of bp ranged from 0.44 to 0.81. The test results revealedthat the predicted failure loads based on punching shear at dis-tance 0.5d from the edge of the column of tests TI to TXII are

less than the measured values while, the predicted failure loadsof tests DF6 to DF22 are higher than the measured values. Thedifference in output results in bp values between test group

DF6 to DF22 and the other series TI to TXII is due to the con-centration of stresses acting on footing under column stub. Iftest results of footings DF6 to DF22 are only considered one

may conclude that, the BS 8110.1-1997 code provision forpunching shear at 0.5d from the edge of the column overesti-mate the failure load by an average value of 1.13. While ACI318-08 and ECP 203-11 code provisions underestimate the

2672 F. Abdrabbo et al.

failure load of the same footings by an average value of 0.75and 0.80 respectively.

The adjustment of code provisions was carried out, for each

test specimen, by assessing the multiple factor in the code shearequation in order to equalize the predicted and the measuredfailure loads. Four peculiar test results TII, TXI, TX and TXII

were omitted from the calculation of the mean of the multiplefactor in shear equation. Therefore the proposed equation forcalculating punching shear capacity of isolated column footing

is,

vc ¼ 0:74f100As=ðBdÞg1=3ð400=dÞ1=4=cm ð13ÞFig. 12 indicates a better correlation between the measured

and the calculated failure loads, implementing the proposed

equation, the bp value varies from 0.75 to 1.28 with an averagevalue of 1.02.

The predicted failure loads of the tested footing models

were calculated by implementing code provisions of the punch-ing shear at distance d from the edge of the column and theratio bp of the predicted to measured loads were presented inTable 5. The collected experimental and the predicted failure

loads were drawn, Fig. 13, for the sake of comparison.Table 5 indicates that the value of bp for tests DF6 to DF22

varies from 1.04 to 2.67, with an average value of 1.65. Tests

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

re- a

djus

ted

load

, kN

*103

Mesured failure load kN*103

Figure 12 Comparison between re-adjusted and measured fail-

ure loads (BS 8110.1-1997) punching shear at distance 0.5d from

the edge of the column.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

pred

icte

d lo

ad k

N*1

03

Measured failure load kN*103

Figure 13 Comparison between predicted and measured failure

loads (BS 8110.1-1997) punching shear at distance d from the edge

of the column.

TI to TXII revealed an average value of 0.57, while the valuesof bp ranged from 0.36 to 0.81.

The difference in output results in bp values between series

of tests DF6 to DF22 and the other series TI to TXII is due tothe concentration of contact stresses acting on footing undercolumn stub. Generally, test results revealed that the code pro-

visions for punching shear at distance d from the edge of thecolumn overestimate the failure load by an average ratio equalto 1.65, if the results of tests series TI to TXII are omitted. If

all test results are considered the over predicted ratio is 1.30.The code provisions were adjusted to achieve the equality

of the measured and the predicted failure loads. The multiplefactor in the code equation was adapted to achieve that

requirement. The factor for each test was calculated. Testresults TII to TXII were omitted and the mean value of themultiple factors was obtained as 0.55, therefore the equation

may be written as;

vc ¼ 0:55f100As=ðBdÞg1=3ð400=dÞ1=4=cm ð14ÞThe above equation was implemented in the calculation of

the predicted failure loads of test series DF6 to TI and com-

pared with the measured values, Fig. 14. A better agreementwas achieved. The value of bp varies from 0.56 to 1.85 withan average value of 1.10.

The failure loads of the tested footings were predicted inaccordance with punching shear provisions stated in BS8110.1-1997 code at distance 1.5d from the edge of the column,

Table 6. The values of the measured failure loads, the pre-dicted loads and the ratio bp are presented. The collectedexperimental failure loads and the predicted failure loads were

drawn, Fig. 15, for the sake of comparison.The table indicates that the value of bp for tests DF6 to

DF22 varies from 2.06 to 3.6, with an average value of 2.45.Tests TI to TXII revealed values of bp varies from 0.38 to

1.39 with an average value of 0.72. The difference in the outputresults between series of test DF6 to DF22 and the other seriesTI to TXII is due to the concentration of contact stresses act-

ing on the footings underneath column stub. Generally, testresults revealed that code provisions for punching shear at dis-tance 1.5d overestimated the measured failure load, by an aver-

age ratio equal to 1.71.The failure loads were predicted by the implementation of

code provisions of punching shear at the perimeter of the col-

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

re-a

djus

ted

load

, kN

*103

Measured failure load kN*103

Figure 14 Comparison between re-adjusted and measured fail-

ure loads (BS 8110.1-1997) punching shear at distance d from the

edge of the column.

Table 6 Predicted and measured failure loads, (BS 8110.1-

1997), punching shear at distance 1.5d from the edge of the

column and at the perimeter of the column.

Test Measured

load (kN)

Predicted

failure load

Pp (kN) at

distance 1.5d

bp Predicted failure

load Pp (kN) at

perimeter of the

column

bp

DF6 2836 NA 1267.2 0.45

DF7 2569 7882.3 3.07 1319.0 0.51

DF8 1203 2253.8 1.87 872.8 0.73

DF10 1638 2716.5 1.66 1028.6 0.63

DF11 2813 NA 1344.8 0.48

DF12 2208 7950.0 3.60 1328.5 0.60

DF13 1839 4131.2 2.25 1314.5 0.71

DF14 1478 2670.2 1.81 992.2 0.67

DF15 2750 NA 1599.3 0.58

DF19 2790 NA 1357.4 0.49

DF20 3037 NA 1625.1 0.54

DF21 2860 9474.8 3.31 1612.9 0.56

DF22 2405 4954.7 2.06 1599.8 0.67

TI 906 1257.1 1.39 633.9 0.70

TII 1050 424.8 0.40 452.8 0.43

TIX 430 215.4 0.50 269.6 0.63

TX 656 575.2 0.88 404.4 0.62

TXI 451 337.8 0.75 321.1 0.71

TXII 440 167.6 0.38 184.9 0.42

0.0

1.5

3.0

4.5

6.0

7.5

9.0

0.0 1.5 3.0 4.5 6.0 7.5 9.0

pred

icte

dloa

d, k

N*1

0^3

Measured failure load kN*103

Figure 15 Comparison between predicted and measured failure

loads (BS 8110.1-1997) punching shear provisions, at distance 1.5d

from the edge of the column.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

pred

icte

d lo

ad, k

N*1

03

Measured failure load kN*103

Figure 16 Comparison between predicted and measured failure

loads (BS 8110.1-1997) punching shear at the perimeter of the

column.

Table 7 Average over/underestimation ratio corresponding to

punching shear section, BS8110-1997.

Test group Average over/underestimation ratio (b) due to

punching shear provisions at

Edge of the column 0.5d d 1.5d

DF6 to DF22 0.58 1.13 1.65 2.45

TI to TXII 0.58 0.66 0.57 0.72

Structural design of isolated column footings 2673

umn. The achieved results are presented in Table 6 along withthe measured failure loads. The ratio bp, of the predicted to

measured failure loads are presented in the same table. Thevalues of bp for test series DF6 to DF22 varies from 0.45 to0.73, with an average value of 0.58, while test series TI to TXIIrevealed values of bp varies from 0.41 to 0.71, with an average

value 0.58. Fig. 16 presents correlation between measured andpredicted failure loads. The figure indicates an average under-estimation ratio of 0.59.

Obviously, the shape of contact stress distribution at foot-ing–soil interface has no appreciable effects on punching load,when punching is considered around the perimeter of the

column.

Table 7 presents the average over/underestimation ratio(bp) of the tested footing models denoted DF6 to DF22 with

contact stress exhibit nearly uniform distribution at footing–soil interface and for footings coded TI to TXII which exhibitcontact stress with stress concentration beneath column stub.The table revealed that the ratio of the predicted to measured

failure loads depends upon the contact stress distribution atcolumn footing soil interface, and on the location of punchingsurface.

Practically the footing fails by shear at a certain criticalplane of failure, where the imposed shear stress is equal tothe shear strength of concrete. But, in theory, the failure plane

is unknown, so a trial was given to predict the load at pre-sumed different failure planes, and the failure load was consid-ered the minimum predicted value. Therefore, for each testspecimen, the predicted failure loads were obtained assuming

that punching shear takes place at distance 0.5d, d, 1.5d fromthe edge of the column and around column perimeter. Practi-cally punching around column perimeter sound unrealistic so

that the predicted failure loads corresponding to punchingshear around column perimeter were pulled out from compar-ison. From Tables 4–6, the minimum predicted failure loads of

specimens coded DF6, DF7, DF11, DF12, DF13, DF15andDF19 to DF21 were obtained from punching shear provisionsat distance 0.5d from the edge of the column; while the mini-

mum predicted loads of test specimens DF8, DF10, DF14,DF22, TI and TX were obtained from one-way shear provisionat distance d from the edge of the column.

The minimum predicted load of test specimens TIX and

TXII were obtained from code provision of punching shearat distance 1.5d from the edge of the column. The minimumpredicted loads of test specimens TII and TXI were obtained

Table 8 Predicted and measured failure loads, (EC2-2004),

punching shear at distance d/2 and at distance d.

Test Measured

load (kN)

Predicted

failure load Pp

(kN) at

distance 0.5d

bp Predicted

failure load Pp

(kN) at

distance d

bp

DF6 2836 3913.2 1.38 7687.4 2.71

DF7 2569 3718.0 1.45 5069.3 1.97

DF8 1203 1932.2 1.61 1957.7 1.63

DF10 1638 2329.0 1.42 2359.6 1.44

DF11 2813 4071.5 1.45 7998.3 2.84

DF12 2208 3749.9 1.70 5112.9 2.32

DF13 1839 3431.0 1.87 3645.1 1.98

DF14 1478 2324.4 1.57 2381.1 1.61

DF15 2750 5135.5 1.87 9997.0 3.64

DF19 2790 4096.7 1.47 8047.9 2.88

DF20 3037 4828.8 1.59 9486.0 3.12

DF21 2860 4469.2 1.56 6093.6 2.13

DF22 2405 4114.9 1.71 4371.7 1.82

TI 906 980.1 1.08 986.9 1.09

TII 1050 569.2 0.54 470.6 0.45

TIX 430 335.2 0.78 254.1 0.59

TX 656 623.1 0.95 565.3 0.86

TXI 451 452.6 1.00 374.2 0.83

TXII 440 363.6 0.83 300.6 0.68

2674 F. Abdrabbo et al.

from code provision for punching shear at distance d from theedge of the column. It was observed from the table that oneway shear provision at the edge of the column produce unreal-

istic high predicted load. Also one way shear provisions at dis-tance d from the edge of the column reflect predicted loadsnearly equal to those obtained from punching shear provisions

at distance d/2 from the edge of the column, tests specimenDF8, DF10, DF13. Therefore, 50% of the tested Specimensrevealed minimum predicted failure loads based on punching

shear at distance 0.5d from the edge of the column; theshear-span/depth ratio of the specimens is less than 2.0;33.3% of the tested specimen revealed minimum predicted fail-ure loads based on one-way shear at distance d, the shear–

span/depth ratio of the footing is equal to or bigger than2.0, 11.2% of the tested specimens revealed minimum pre-dicted failure load based on punching shear at distance 1.5d

from the edge of the column, the shear span/depth of the foot-ing ratio is 2.70. 5.5% of the tested specimens revealed mini-mum predicted failure load based on punching shear at

distance d from the edge of the column, where a/b is biggerthan 2.7. Therefore the location of the critical shear sectionis related to shear span/depth ratio. Thus, one can conclude

that as the value of shear span/depth ratio increases, the loca-tion of critical section of shear failure goes further away fromthe column edge. Punching shear at distance 0.50d from theedge of the column is anticipated in footing having shear span

to depth ratio less than 2.0. One way shear at distance d fromthe face of the column may occur in footings having shearspan/depth ratio bigger than 2.0 and less than 2.70. Footing

having shear span/depth ratio higher than 2.70 exhibit punch-ing shear either at distance d or 1.5d from the edge of thecolumn.

Fig. 17 presents the predicted minimum failure loads ofeach footing and the corresponding measured failure loads.The figure indicates an average underestimation ratio of 93%.

If, Two test results out of nineteen test results, which repre-sent 10% of the tested specimen, are omitted due to the verylow b-values, the ratios of the predicted to measured loadsbecome equal to 1.0. However if test series TI to TXII are

omitted, the average b value becomes 1.11. So that it can beconsidered that the BS 8110.1–1997 code provisions of shearmay predict failure loads agree with the measured failure loads

within a precision of 10% (90% to 110%), irrespective of theshape of contact stress at footing –soil interface.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

pred

icte

dloa

d, k

N*1

03

Measured failure load kN*103

Figure 17 Comparison between minimum predicted and

measured failure loads (BS 8110.1-1997).

6.4. (EC2-2004) provisions [13]

Comparison between measured and predicted failure loadsbased on code provisions of punching shear at code–definedsections at distance 0.5d, d, 1.5d, 2d from the edge of the col-

umn and at column perimeter was conducted.The predicted failure loads of the tested specimens were cal-

culated based on punching shear provisions at distance 0.5dfrom the edge of the column. The ratios bp of the predicted

to the measured failure loads are presented in Table 8.Fig. 18 presents correlating between measured and predictedfailure loads.

Table 8 indicates that bp values varying from 1.38 to 1.87for test specimens DF6 to DF22, and from 0.54 to 1.08 fortests TI to TXII. The average values of b of series DF6 to

DF22 is 1.59, and the average value of series TI to TXII is0.86. If all test results are considered, the average values of b

0.0

1.0

2.0

3.0

4.0

5.0

0.0 1.0 2.0 3.0 4.0 5.0

pred

icte

d lo

ad, k

N*1

03

Measured failure load kN*103

Figure 18 Comparison between predicted and measured failure

loads (EC2-2004), punching shear at distance d/2.

Structural design of isolated column footings 2675

becomes 1.36. But there is doubt about the achieved results oftest series TI to TXII, due to unrealistic simulation of the sup-porting soil. If these test results are omitted, the average value

of Bp becomes 1.5. On the other hand, BS 8110.1-1997, ACI318-08 and ECP 203-2011 revealed values of 1.13, 0.75 and0.8 respectively, for the same test series.

The code provisions may need to be adjusted. However oneshould realize that test specimens failed by punching shear, butthe location of failure plane is not defined. This may affect the

procedure of justification of code provisions.The adjustment was carried out for each test specimen by

adjusting the multiple factor in code punching shear equation,to fulfill the requirement that the predicted failure load

becomes equal to measured failure load. Four tests resultsTII, TIX, TX, TXII were omitted from the calculation of themean value of the multiple factor in shear equation, hence

the mean value was obtained as; 0.12 instead of 0.18 of inthe code. The proposed equation was implemented in the pre-diction of failure loads of the tested specimens.

Fig. 19 indicates a better correlation between the measuredand the predicted failure loads; the mean value of b is 1.02.

The predicted failure loads were assessed from punching

shear provisions at code-defined section at distance d fromthe edge of the column and the ratio bp was presented inTable 8. The collected experimental failure loads and thecorresponding predicted failure loads were drawn, Fig. 20,

for the sake of comparison.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

re-a

djus

ted

load

, kN

*103

mesured failure load kN*103

Figure 19 Comparison between re-adjusted and measured fail-

ure loads (EC2-2004), punching shear at distance d/2.

0.0

1.5

3.0

4.5

6.0

7.5

9.0

0.0 1.5 3.0 4.5 6.0 7.5 9.0

pred

icte

dloa

d, k

N*1

03

Measured failure load kN*103

Figure 20 Comparison between predicted and measured failure

loads (EC2-2004), punching shear at distance d.

Table 8 indicates that the value of bp for tests DF6 to DF22varies from 1.44 to 3.64, with an average value of 2.32. TestsTI to TXII revealed an average value of 0.75, while the values

of bp ranged from 0.45 to 1.09.The difference in output results in b values between series of

tests DF6 to DF22 and the other series TI to TXII is due to the

concentration of contact stresses acting on footing under col-umn stub. Generally test results revealed that the code provi-sions for punching shear at distance d from the edge of the

column are not realistic for most of footing models in the casestudy.

The code provisions were adjusted to insure the equality ofthe predicted failure load and the measured value. The multi-

ply factor in punching shear equation was adapted to achievethis requirement. Five tests out of nineteen test results, whichrepresent 26% of tests, were omitted. These tests are TII,

TIX, TX, TXII, because of the resulted low values of the mul-tiple factor. The mean value of the multiple factor of all testsexcept the omitted tests is 0.09.

The failure loads were re-predicted using the above multiplefactor in the equation of punching shear and compared withthe measured failure loads, Fig. 21. A better agreement was

achieved; the mean value of b is 1.11. It is interesting to notethat the five omitted test results are in series TII to TXII.

The failure loads of the tested specimens were predicted inaccordance with punching shear provisions stated in EC2 code

provisions at distance 1.5d from the edge of the column.Table 9 presents the predicted failure loads, the measured fail-ure loads and the ratio bp. The collected experimental failure

loads and the predicted failure loads were drawn; Fig. 22,for the sake of comparison.

The table indicates that the value of bp for tests DF6 to

DF22 varies from 2.3 to 4.66, with an average value of 3.44,while tests TI to TXII revealed values of bp varies from 0.50to 1.86 with an average value of 0.90. The difference in the out-

put results between group of test DF6 to DF22 and the othergroup TI to TXII is due to the concentration of contact stres-ses acting on footing model underneath column stub.

Generally test results revealed that the code provisions for

punching shear at distance 1.5d overestimate the measured fail-ure load, and the average overestimation ratio is 2.38.

The failure loads of the tested footing were predicted in

accordance with punching shear provisions stated in EC2-2004 code at distance 2d from the edge of the column. Table 9

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

re-a

djus

ted

load

, kN

*103

measured failure load kN*103

Figure 21 Comparison between re-adjusted and measured fail-

ure loads (EC2-2004), punching shear at distance d.

Table 9 Predicted and measured failure loads (EC2-2004)

punching shear at distances 1.5d and 2d.

Test Measured

load (kN)

Predicted

failure load Pp

(kN) at

distance 1.5d

bp Predicted

failure load Pp

(kN) at

distanced 2d

bp

DF6 2836 NA NA NA

DF7 2569 11090.2 4.32 NA NA

DF8 1203 3130.5 2.60 NA NA

DF10 1638 3773.3 2.30 NA NA

DF11 2813 NA NA NA

DF12 2208 11185.6 5.07 NA NA

DF13 1839 5812.6 3.16 10342.9 5.62

DF14 1478 3720.7 2.52 4996.9 3.38

DF15 2750 NA NA NA

DF19 2790 NA NA NA

DF20 3037 NA NA NA

DF21 2860 13330.9 4.66 NA NA

DF22 2405 6971.2 2.90 12404.6 5.16

TI 906 1686.2 1.86 NA NA

TII 1050 523.9 0.50 758.8 0.72

TIX 430 251.2 0.58 289.2 0.67

TX 656 742.4 1.13 1880.1 2.87

TXI 451 416.5 0.92 603.4 1.34

TXII 440 334.6 0.76 484.7 1.10

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

pred

icte

d lo

ad,1

.5dk

N*1

03

Measured failure load kN*103

Figure 22 Comparison between predicted and measured failure

loads (EC2-2004), punching shear at distance 1.5d.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

pred

icte

d lo

ad,P

ss k

N*1

03

Measured failure load kN*103

Figure 23 Comparison between predicted and measured failure

loads (EC2-2004) punching shear at distance 2d.

Table 10 Average over/underestimation ratio corresponding

to punching shear section, (EC2-2004).

Test group Over/under prediction ratio (b) due to punching

shear at

Edge of the column 0.5d d 1.5d 2d

DF6 to DF 0.91 1.59 2.32 3.44

TI to TXI 0.8 0.85 0.75 0.90 2.70

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

pred

icte

dloa

d, k

N*1

03

Measured failure load kN*103

Figure 24 Comparison between predicted and measured failure

loads (EC2-2004) punching shear at the perimeter of the column.

2676 F. Abdrabbo et al.

presents the predicted failure load, the measured failure loadsand the ratio bp. The collected experimental failure loads and

the predicted values were drawn; Fig. 23.Table 9 indicates that the EC2-2004 code provisions of

punching shear at distance 2d from the edge of the column

are not applicable (NA) for most of the footing models in testseries DF6 to DF22. So that it is not easy to achieve a firmconclusion from the study. Even though 42% of the tested

specimens on which the code provisions are implemented,revealed that the code provisions for punching shear at dis-tance 2d overestimate the ultimate loads of the footings. Theaverage overestimation ratio bp is 2.6.

Table 10 presents the predicted failure loads based onpunching shear provisions at the perimeter of the columns.The measured failure loads and the ratio bp. The value of bpfor tests DF6 to DF22 varies from 0.6 to 1.24, with an averagevalue of 0.91, tests TI to TXII revealed values of bp varies from

0.48 to 1.14 with mean value of 0.8. All test results revealed amean value of 0.88. Tests results revealed that the code provi-

sions for punching shear at the perimeter of the column areunderestimating the measured failure loads. The collected fail-ure loads and the corresponding predicted values were drawn;

Fig. 24, for the sake of comparison. BS (8110) code provisionsunder estimate the failure load based on calculations of punch-ing shear at the perimeter of the column by a factor of 0.88.

The predicted minimum failure loads for each test specimenout of the implementation of punching shear at columnperimeter, at distances d/2, d and 1.5d in accordance withEC2 provisions were considered. The minimum predicted fail-

ure load of specimens coded DF6 to DF22, TX and TXII wasobtained from punching shear provisions at the columnperimeter. The minimum predicted failure loads of test

specimen TIX were obtained from punching shear provisionat distance 1.5d from the edge of the column. The minimum

Table 11 Predicted and measured failure loads (EC2-2004)

punching shear at the perimeter of the column.

Test Measured

load (kN)

Predicted failure

load Pp (kN) at

perimeter of column

bp

DF6 2836 1711.9 0.60

DF7 2569 1853.5 0.72

DF8 1203 1263.6 1.05

DF10 1638 1993.0 1.22

DF11 2813 1908.1 0.68

DF12 2208 1877.7 0.85

DF13 1839 1854.3 1.01

DF14 1478 1402.3 0.95

DF15 2750 2281.9 0.83

DF19 2790 1940.3 0.70

DF20 3037 2984.0 0.98

DF21 2860 3002.9 1.05

DF22 2405 2985.1 1.24

TI 906 1033.4 1.14

TII 1050 738.1 0.70

TIX 430 347.5 0.81

TX 656 521.2 0.79

TXI 451 396.9 0.88

TXII 440 212.3 0.48

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

pred

icte

d lo

ad, k

N*1

03

Measured failure load kN*103

Figure 25 Comparison between minimum predicted ultimate

loads and measured failure loads (EC2-2004), punching shear at

the perimeter of the column.

Structural design of isolated column footings 2677

predicted failure loads of test specimen TII and TXI wereobtained from code provisions for punching shear at distanced from the edge of the column. The minimum predicted failure

load of test specimen TI was obtained from punching shearprovision at distance 0.5d from the edge of the column.

Table 11 indicates that punching shear at column perimeter

of the tested specimen, prevails predicted failure loads close tothe measured values and the divergence between predicted andmeasured failure loads increases as the code defined critical

section goes further from the edge of the column.Theoretical calculations in accordance with code provisions

indicated that the minimum predicted failure loads of 79% ofthe tested specimens were achieved in accordance with code

provisions of punching shear at the perimeter of the column,5.2% of the tested specimen indicates that the minimum pre-dicted failure load was achieved by code provisions of punch-

ing shear at distance 0.5d, while 10.4% of the tested specimenrevealed minimum predicted failure loads in accordance withcode provisions of punching shear at distance d, 5.2% of the

tested specimens indicated a minimum predicted failure loadby code provisions of punching at distance 1.5d. Observationsof the effect of a/d ratio on the location of punching shear werecarried out.

These observations indicated that punching shear in foot-ings may occur at column perimeter or at distance 0.5d as longas the shear span/depth ratio is less than 2.25. Punching shear

at distance d may occur when a/d ratio is bigger than 2.25 andless than or equal to 2.7. For greater ratio of a/d punchingshear at distance 1.5d is anticipated.

The predicted minimum failure load of each footing wasassessed out of calculations failure load assuming punchingtakes place at perimeter of column, at 0.5d, 1.5d, and 2d from

the edge of the column. Fig. 25 presents correlation betweenmeasured and minimum predicted failure loads. The figureindicates an average underestimation ratio of 0.85, comparedto 0.93 obtained by the implementation of BS (8110-1997).

7. Conclusions

The main target of the work presented is to explore the preci-sion of code provisions related to the structural design of iso-

lated column footings, and to illustrate their relations from testresults. To achieve this target, comparisons between predictedfailure loads of column footings based on code provisions and

the laboratory measured failure loads were conducted. Thestudy revealed the following main conclusions.

The predicted failure loads of isolated column footings sub-

jected to uniformly distributed contact stress in accordancewith ACI318-08 code provisions are controlled by punchingshear at code-defined critical section, contrary to ECP (203-2011) code provisions which the predicted failure loads are

controlled by one-way shear at code defined critical section.The critical section provided by the two codes is at distance0.5d from the edge of the column. But ACI 318-08 code provi-

sions considered punching shear while ECP 203-11 code provi-sions considered one-way shear.

Both ACI 318-08 and ECP 203-11 provisions underestimate

the failure loads of isolated column footings subjected to uni-formly distributed contact stress. The underestimation ratio is0.75 and 0.70 respectively. If the supporting material of the

footing is producing bell shaped contact stress distribution atfooting-soil interface with maximum value beneath columnstub, the underestimation ratio becomes 0.44 in both codeprovisions.

It is not advisable to consider punching shear at the perime-ter of the column in accordance with BS 8110.1-1997. If sectionof shear failure is considered away from the edge of the col-

umn, at 0.5d, d and 1.5d for punching shear and at d forone-way shear, the minimum predicting failure loads of foot-ings subjected to uniformly distributed contact stress in accor-

dance with BS 8110-1997 shall equal 1.13 times the measuredfailure loads. The ratio is 0.56 in case of footings supportedon geomaterial producing belled shape contact stressdistribution.

Regarding BS 8110-1997 provisions, punching shear at dis-tance 0.5d from the edge of the column is anticipated in footinghaving shear span/depth ratio less than 2.0. One way shear at

distance d from the edge of the column is anticipated in footinghaving shear span to depth ratio bigger than 2 and less than2.70. Footings having shear span/depth ratio bigger than

2678 F. Abdrabbo et al.

2.70 may exhibit punching shear either at distance d or 1.5dfrom the edge of the column.

EC2-2004 provisions underestimate the ultimate load of

isolated column footings; the average underestimation is 0.91in case of footings supported on geometrical producing uni-formly distributed contact stress and 0.8 for footings on geo-

metrical producing belled shape contact stress.In accordance with (EC2-2004) provisions, punching shear

in footings at column perimeter or at distance 0.5d from the

edge of the column may occur, if shear span/depth ratio offootings is less than 2.25. For shear span/depth ratio biggerthan 2.25 and less than or equal to 2.70, punching shear isanticipated to be at distance d from the edge of the column.

For bigger ratio of shear span/depth ratio, punching shearmay be occurred at distance 1.5d.

Shear span to depth ratio of footing and distribution of

contact stress at footing soil interface are key factors, amongothers, in the structural design of isolated column footings,even though these two factors are not addressed in various

code provisions.

References

[1] M.A. Staller, Analysis studies and numerical analysis of

punching shear failure in reinforced concrete slabs, INF.

Workshop on punching shear capacity of R.C slabs,

Stockholm, 2000, p. 8.

[2] M. Hallgren, M. Bjerke, Nonlinear finite element analyses of

punching shear failure of column footings, Cement Concr.

Compos. 24 (2002) 491–496.

[3] J. Hegger, A.G. Sherif, M. Ricker, Experimental investigations

on punching behavior of reinforced concrete footings, ACI

Struct. J. (July–August) (2006) 604–613.

[4] Fib model code 2010, first complete draft, Published by the

International Federation for Structural Concrete, Switzerland,

2001.

[5] A. Muttoni, Punching shear strength of reinforced concrete

slabs without transverse reinforcement, ACI Struct. J. 105 (4)

(2008) 440–450.

[6] A. Muttoni, Application of the critical shear crack theory to

punching of R/C slabs with transverse reinforcement, ACI

Struct. J. 106 (4) (2008) 485–494.

[7] J. Hegger, M. Ricker, G. Sherif, Punching strength of reinforced

concrete footings, ACI Struct. J. (2009) 706–716.

[8] L. Tassinari, Punching of concrete slabs with shear

reinforcement, EPFL ENAC IIC, IBETON2010, <http://

ibeton.epfl.ch/resherche/arrmpoinconnement/default_e.asp>

(pristupljeno januara 2013).

[9] Z. Bonic, R. Folic, Punching of column footings, comparison of

experimental and calculation results, Gradevinar 65 (10) (2013)

887–899.

[10] Egyptian code of practice for design and construction of

reinforced concrete structures, code no. ECP 203-2011,

HBNRC, Cairo.

[11] ACI Committee 318, Building Code Requirement for Structural

Concrete (ACI 318M-08) and Commentary (318R-08),

American Concrete Institute, Farmington Hills, MI, 2008.

[12] BS 8110-1:1997, Code of practice for design and construction.

[13] European Committee for Standardization (CEN), Euro code 2:

Design of Concrete Structures – Part 1.1: General Rules and

Rules for Buildings, Brussels, Belgium, 2004.

[14] Hamed S. Askar, Repair of RC plat plates failing in punching

shear by vertical studs, Alex. Eng. J. (2015) 541–550.