Research Article Strength of Footing with Punching Shear ...A new method to increase the punching shear strength and ductility of the footing-to- column connection was proposed. For

Research ArticleStrength of Footing with Punching Shear Preventers

Sang-Sup Lee1 Jiho Moon2 Keum-Sung Park1 and Kyu-Woong Bae1

1 Advanced Building Research Division Korea Institute of Civil Engineering and Building Technology (KICT)Goyang-si Gyeonggi-do 411-712 Republic of Korea

2New Transportation Research Center Korea Railroad Research Institute (KRRI) Uiwang-siGyeonggi-do 437-757 Republic of Korea

Correspondence should be addressed to Jiho Moon jmoon1979gmailcom

Received 30 May 2014 Revised 23 July 2014 Accepted 21 August 2014 Published 21 October 2014

Academic Editor Brian Uy

Copyright copy 2014 Sang-Sup Lee et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The punching shear failure often governs the strength of the footing-to-column connection The punching shear failure is anundesirable failure mode since it results in a brittle failure of the footing In this study a new method to increase the strengthand ductility of the footing was proposed by inserting the punching shear preventers (PSPs) into the footing The validation andeffectiveness of PSPwere verified through a series of experimental studiesThenonlinear finite element analysis was then performedto demonstrate the failuremechanismof the footingwith PSPs in depth and to investigate the key parameters that affect the behaviorof the footing with PSPs Finally the design recommendations for the footing with PSPs were suggested

1 Introduction

The punching shear failure of the slab-to-column or thefooting-to-column connection is undesirable since it resultsin a brittle and catastrophic failure of the concrete structuresExtensive studies have been conducted for punching shearfailure of the normal flat slab in the past decades andlarge numbers of experimental databases were constructed byprevious researchers [1ndash3] Several methods to enhance thepunching shear strength of the slab-to-column connectionhave been studied Fernandez Ruiz et al [4] and Clementet al [5 6] studied the strengthening method of the slab-to-column connection by using prestressing technic Pilakoutasand Li [7] developed the shearband system which is a shearreinforcement system using steel strips with high ductility Ashearhead system was developed by Corley and Hawkins [8]Adding a steel plate to the flat slab to increase the effectivecolumn head area is another way of increasing the punchingshear strength of the slab-to-column connectionAs an exam-ple a NUUL system was developed by Subedi and Baglin [9]This NUUL system is composed of a steel plate and several Ubars The effect of fiber reinforced concrete on the punchingshear failure of the slab-to-column connection has beenstudied by McHarg et al [10] Cheng and Parra-Montesinos[11] Harajli et al [12] and Nguyen-Minh et al [13] Also

carbon fiber reinforced polymer (CFRP) sheets [14] andfunnel-shaped punching shear preventer (or UFO punchingpreventer) [15] have been proposed to strengthen the slab-to-column connection Above this some strengthening meth-ods of existing slab-to-column connections and their basicmechanism are summarized by Koppitz et al [16] Whilenumerous studied have been performed for the punchingshear failure of the slab-to-column connection the study onthe punching shear failure of footing-to-column connectionis still limited [17ndash19] As a result the punching shear designof footing is mainly based on the research results of the slab-to-column connection [19] and most design codes such asCEB-FIP [20] and ACI [21] do not distinguish between theslab and footing in the design specification [19]

This study focused on punching shear behavior of thefooting-to-column connection A new method to increasethe punching shear strength and ductility of the footing-to-column connection was proposed For the flat slab funnel-shaped punching shear preventer shown in Figure 1(a) issometimes used to increase the punching shear strengthof flat slab-to-column connection [15] Generally conven-tional design codes [20 21] define the punching shearstrength in terms of a nominal shear capacity on a controlperimeter at a certain distance from the column perimeterWhen the funnel-shaped punching shear preventer shown

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 474728 15 pageshttpdxdoiorg1011552014474728

2 The Scientific World Journal

PSPs

PSP

P

Compression strut

Cracks

(a)

P

Cracks

Funnel typed punching preventer

Control perimeter


(b)

Figure 1 Schematic view of (a) footing with PSPs and (b) flat slab with funnel typed punching shear preventer

in Figure 1(a) is used for the flat slab control perimeter canbe determined by the size of the funnel-shaped punchingshear preventer Thus increasing the size of the funnel-shaped punching shear preventer can produce higher punch-ing shear strength However funnel-shaped punching shearpreventer shown in Figure 1(a) is not suitable for large scaleconstruction such as high rise building column-to-footingor bridge pier-to-footing connection since the size of thefunnel-shaped punching shear preventer becomes very largewhich makes it hard to handle

As an alternative in this study four small punching shearpreventers (PSPs) are inserted into the footing as shown inFigure 1(b) PSP has cone shape and it is made of steel Basi-cally PSP has smooth surface However the bond strengthbetween PSP and concrete can be improved by introducingpunched holes as shown in Figure 1(b) By inserting PSPsinto the footing the following benefits can be expected (1)propagation of shear crack could be effectively prevented(2) PSP could enhance the compression strut developed bythe axial compression from the columnTherefore enhancedpunching shear strength and ductile failure of the footing-to-column connection are expected by using the PSPs

In this study the validation and effectiveness of the PSPwere verified through a series of tests and nonlinear finiteelement analysis A total number of five large scale testspecimens were constructed and tested in order to investigatethe effect of PSP on the punching shear strength and thefailure mode of the footing with PSP Then a series ofparametric studies was conducted to demonstrate the failuremechanism in depth and to study the effect of key parametersof PSP on the behavior of the footing Finally the designrecommendations for the footing with PSPs were suggested

2 Experimental Study

21 Description of Test Specimen A total of five large scaletest specimens were constructed and tested All five footingshad the same dimensions and reinforcing bar layout Figure 2

shows the dimensions of the footingThe footing had a squareshape with side length of 2400mm and depth of 500mmThe axial load was applied through the square column inthe center of the footing where the width and the height ofthe column were 350mm and 300mm respectively 40mmdiameter holes were spaced at 500mm to insert the anchorbars as shown in Figure 2

Figure 3 shows the layout of the reinforcing bars andPSPsThebottomflexural reinforcing bars consisted of SD500D25 bars spaced at 200mm where the yield stress andthe diameter of SD500 D25 bar are 530MPa and 254mmrespectively The resulting flexural reinforcement ratio wasapproximately 05 The top flexural reinforcing bars spacedat 200mm were installed with the length of 500mm at theedge of the test specimens as shown in Figure 3 to preventthe premature cracking and failure due to negative bendingmoment at the edges The SD500 D25 bars were also used forthe top reinforcing bars According toACI code [21] concretecover for concrete casted against and permanently exposedto earth is 3 in (762mm) Thus 80mm of concrete coverdepth was adopted for the top and the bottom reinforcingbars To prevent the premature failure of the column duringthe test the columnwas reinforced by using eight SD500D25longitudinal bars and SD500 D13 stirrups spaced at 50mmwhere the yield stress and the diameter of SD500 D13 bar are530MPa and 127mm respectively As shown in Figure 3 twostrain gauges (S1 and S2) were installed at the bottom flexuralreinforcing bars tomeasure the longitudinal strain of the bars

All test specimens were casted at the same time TypeI ordinary Portland cement was used with water-to-cementratio of 048 Crushed shape coarse aggregate was used wherethe maximum size was 25mm From the material test theaverage compressive strength was 252MPa PSPs were madeof steel where yield stress was 400MPa from mill sheet

The names and the test parameters for each specimenare shown in Table 1 P0 RC is the reference test specimenwhere PSPswere not installed in the footing For P5 32 P5 6P5H 32 and P7 32 specimens four PSPs were inserted into

The Scientific World Journal 3

Table 1 Description of test specimens and test results

Name PSP (119889119905times 119889119887times ℎ) (mm) 119905 (mm) 119889

119905119889119887

ℎ119905 Test parameter 119875lowast (kN) 119875

119906(kN)

P0 RC None None None None Reference model 2105 2105P5 32 500 times 100 times 200 32 5 625 Effect of PSP 2572 2572P5 6 500 times 100 times 200 6 5 333 Effect of thickness of PSP 2433 2796

P5H 32 500 times 100 times 200 (with 6holes) 32 5 625 Effect of holes in PSP 2454 2675

P7 32 700 times 200 times 250 32 35 781 Effect of size of PSP 2361 2361

300

500

(a)

200

400

350

400Electionhook

350

200

240

020

020

0

2400

Hole Φ40

4500

4500

(b)

Figure 2 Dimensions of the test specimen

PSP

h

PSP (dt times db times h) 500 times 100 times 200 or 700 times 200 times 250

6-Φ100 holes

dt

db

(a)

7200

2400

240

0

7200

20012

200

12

500

500

500500

S1 S2

(b)

Figure 3 Reinforcement and PSP layout for the test specimen


Column

times 800 times 690mm

350mm

350 times 350mm

2000mm

350mm

2000

mm

Steel block 1250

(a) (b)Figure 4 Test setup

the footing as shown in Figure 3 Two different sizes of PSPswere used for the test (500times100times200 and 700times200times250) asshown in Table 1 where 119889

119905and 119889

119887represent the diameters of

the top and bottom of PSP respectively ℎ is the height of PSPFor both PSP (500 times 100 times 200) and PSP (700 times 200 times 250)PSP was inclined with 45∘ angle PSP (500 times 100 times 200)was used for P5 32 P5 6 and P5H 32 specimens whilePSP (700 times 200 times 250) was applied to P7 32 specimen Thethickness of the PSP was 32mm except P5 6 specimen Thethickness of PSP used for P5 6 specimen was 6mm In thecase of P5H 32 specimens six punched holes were uniformlydistributed along the centerline of PSP where the diameter ofthe holes was 100mm

From Table 1 it can be known that the effect of PSP canbe investigated by comparing the results of P0 RC specimenwith other test results Also the effect of thickness size andholes of PSP can be evaluated by comparing the test resultsof P5 32 specimen with those of P5 6 P7 32 and P5H 32specimens respectively

Figure 4 shows the test setup used in this study The testspecimen was placed on the reaction block and anchor barswere inserted to center the specimen It should be noted thatthe anchor bars were not fastened Thus it allows upwardvertical movement of the test specimen at the position ofanchor bar The vertical displacement was applied by usingthe actuator shown in Figure 4 The vertical displacement ofthe footing was measured by the linear variable differentialtransducers (LVDTs) installed below the bottom of the testspecimen

22 Discussion of Test Results Figure 5 shows the relation-ships between the applied axial load and vertical displace-ment at the center of the test specimens From Figure 5 itcan be found that the difference in the stiffness between the

0 5 10 15 20 250

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)

Vertical displacement (mm)

P7 32

P5H 32

P5 6

P5 32

P0 RC

Figure 5 Applied load versus vertical displacement at the center

test specimens with and without PSPs was not significantHowever the strength and ductility of the test specimenswith PSPs were considerably improved compared to the testresult of the specimen without PSPs (P0 RC specimen) ForP0 RC specimen the ultimate strength 119875

119906 was 2105 kN and

the applied load was suddenly dropped after reaching 119875119906 On

the other hand for P5 32 P5 6 and P5H 32 specimenstwo different peaks were observed The applied loads weredecreased after reaching the first peakThen the applied loadswere continuously increased up to the second peak and aconsiderable additional deformation capacity was achievedIn this study the applied loads corresponding to the first andthe second peaks are defined as 119875lowast and 119875lowastlowast respectivelyThe ultimate strength of the footing is then obtained as the


0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)

Yield strain

Strain (times10minus6)

P0 RC S1P0 RC S2

(a)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500Yield strain

Appl

ied

load

(kN

)


P5H 32 S1

(b)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500 Yield strain

Appl

ied

load

(kN

)


P5 6 S1P5 6 S2

(c)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Yield strainAp

plie

d lo

ad (k

N)


P7 32 S1P7 32 S2

(d)

Figure 6 Applied load versus strain in the reinforcing bar (a) P0 RC (b) P5H 32 (c) P5 6 and (d) P7 32

maximum value of 119875lowast and 119875lowastlowast 119875lowast and 119875119906of each of the

specimens are shown in Table 1For P5 32 specimen 119875lowast was larger than 119875lowastlowast 119875

119906of P5 32

specimen was 2572 kN which is 22 larger than that ofP0 RC specimen In the case of P5 6 and P5H 32 specimens119875lowastlowast was larger than 119875lowast 119875

119906of P5 6 and P5H 32 specimens

were 32 and 27 larger than that of P0 RC specimenP7 32 specimen showed a single peak similarly with P0 RCspecimen 119875

119906of P7 32 specimen was 12 larger than P0 RC

specimen It is interesting that P7 32 specimen showed thesmallest increase in 119875

119906among the test specimens with PSP

even if the size of PSP is larger than the other test specimensThe larger size of PSP did not provide a better performance ofthe footing It can also be found that the thickness of PSP andholes in PSP also affect the behavior of the footing with PSPBy increasing the thickness of PSP the ultimate strength wasincreased (refer to the results of P5 32 and P5 6 specimens)Further approximately 10 increase in the ultimate strengthwas observed by introducing the punched holes in PSP (refer

to the results of P5 32 and P5H 32 specimens) since thepunched hole enhances the attachment between the steel andthe concrete

Figure 5 does not provide sufficient amount of infor-mation on the failure mode of the footing Generally thepunching failure is divided into two different types [22 23]The first one is shear failure that occurs suddenly with a smalldisplacement This type of failure is frequently observed inthe footing or slab with a large flexural reinforcement ratioThe second type of failure mode is the flexural failure Thisfailure takes place when the flexural reinforcement ratio issmall and the footing or slab is failed by the yielding of thereinforcing bar The mixed punching shear-flexural failure isalso possible Thus it is needed to evaluate the axial strainin the flexural reinforcing bar in order to classify the failuremode of the test specimens

Figures 6(a)ndash6(d) show the axial strain data of flexu-ral reinforcing bars of P0 RC P5H 32 P5 6 and P7 32specimens respectively The locations of S1 and S2 strain


Major crack

P0 RC

(a)

Major crack

PSPPSP

P5 32

(b)

Figure 7 Crack pattern in the middle plane of the test specimen (a) P0 RC and (b) P5 32

PSPPSP

Major crack

P5 6

(a)

PSP PSP

Major crack

P5H 32

(b)

Figure 8 Crack pattern in the middle plane of the test specimen (a) P5 6 and (b) P5H 32

gauges are shown in Figure 3 It should be noted that thestrain data of P5 32 specimen and S2 strain data of P5H 32specimen were corrupted during the test and these dataare not shown in Figure 6 From Figure 6(a) it can be seenthat the strain of flexural reinforcing bar of P0 RC specimendid not reach the yield strain where the yield strain of thereinforcing bar is 2650 times 10minus6 Further the strain in theflexural reinforcing bar suddenly jumped without significantincreasing of the applied load Thus it can be concluded thatthe P0 RC specimenwas failed by punching shear failureTheaxial strain of the flexural reinforcing bar of P7 32 specimenalso did not achieve the yield strain and the axial strainwas relatively small compared to those of P5H 32 and P5 6specimens as shown in Figures 6(b)ndash6(d) From Figure 5only one peak was observed for P7 32 and the applied loadwas considerably reduced after 119875

119906Thus it can be known that

punching shear failure also occurred for P7 32 specimeneven if the large size of PSP (700 times 200 times 250) was installedinto the footing

Similar to the applied load-displacement relationshipshown in Figure 5 axial strains were reduced near the firstpeak for P5H 32 and P5 6 specimens Then the axial strainis continuously increased by increasing the applied load Inparticular for the P5 6 specimen the axial strain of theflexural reinforcing bar exceeded the yield strain as shown inFigure 6(c) even though the yield plateau is not considerableThen ductility of P5 6 specimen was considerably increasedThus it can be found that PSPs could prevent the brittlepunching shear failure by redistributing the applied load

PSP PSP

Major crack

P7 32

Figure 9 Crack pattern in themiddle plane of P7 32 test specimen

to the flexural reinforcing bars P5H 32 specimen did notachieve the yield strain and punching shear failure governedthe strength of the footing Also the ductility of P5H 32specimen was smaller than P5 6 specimen

After the test the specimens were cut to documentthe crack patterns Figures 7ndash9 show the crack patterns ofeach test specimen For P0 RC specimen the cracks weredeveloped in diagonal direction from the top to the bottomof the footing as shown in Figure 7(a) This is a typical shearcrack developed by punching shear On the other hand forP5 32 P5 6 and P5H 32 specimens major cracks initiatedat the interface between the column and the top surface of thefooting were stopped approximately at the center of the exte-rior part of PSP as shown in Figures 7(b) 8(a) and 8(b) Asa result shear cracks were isolated by PSP and the resistancewas not significantly reduced In the case of P7 32 specimen


PSP 4-node shell elementxy

Rebar 2-node trusselement

Concrete 8-nodesolid element

z

FootingColumn

x

y

Reaction block

14 model

Figure 10 Typical finite element model for the test specimen

it can be seen that the distance from the interface betweenthe column and the top surface of the footing where the shearcrack initiated to the exterior part of PSP is relatively far awaycompared to P5 32 P5 6 and P5H 32 specimens Thus theshear cracks were not effectively isolated Taken as a wholethe following observations and conclusions were made fromthe experimental study

(a) Introducing PSPs into the footing the punchingshear strength and ductility of the footing can beimproved since PSPs effectively isolate the shearcrack and redistribute the applied load to the flexuralreinforcing bars

(b) By using proper PSPs brittle punching shear failurecan be prevented due to improved ductility

However the effectiveness of PSPs depends on their sizeFurther the location of the PSP may affect the behaviorof the footing Thus a series of parametric studies wasundertaken to investigate the failuremechanism in depth andto investigate the effect of size thickness and location of PSPon the punching behavior of the footing by using nonlinearfinite element analysis in the following sections

3 Finite Element Analysis

31 Description of Finite Element Analysis Model Figure 10shows the typical finite element model for the footing withPSP used in this study The general purpose structuralanalysis program ABAQUS [24] was used Quarter modelwas used for efficient modeling by taking advantage of thesymmetry properties The concrete footing was modeledusing 8-node solid elements and PSP was modeled using4-node shell elements The 2-node truss element was usedto model the reinforcing bars PSP and the reinforcing barwere embedded into the concrete by using EMBEDEDoptionin ABAQUS [24] Thus it was assumed that PSP and thereinforcing bar are perfectly bonded to the concrete Fromthe test separation of interface between the PSP and theconcrete was observed andmore accurate interfacemodelingmay be needed to improve the finite element analysis modelfor the footing with PSPs However analysis results with fullinteraction interface between the PSP and the concrete show

reasonable prediction of load-displacement relationship andcrack patterns Thus to guarantee convergence of analysisthe perfectly bonded interface between the PSP and theconcrete was used in this study

Figure 11 represents the loading and the boundary condi-tions for the finite element models Since the quarter modelwas used in this study displacements in 119909 and 119910 directionwere restrained for the left side and the bottom sectionrespectively as shown in Figure 11 To simulate the boundarycondition of the reaction block displacements in 119911 directionof the right and top edges were constrained as shown inFigure 11 (only for 625mm which is the half width of thereaction block Refer to test setup shown in Figure 4) Inaddition displacements in 119909 and 119910 direction in the locationof anchor bar installed in the right and top edges wererestrained respectively It is noted that the diameter of theanchor bar is 40mm Finally the displacement loading in 119911direction was applied to simulate the load acting through thecolumn

Figures 12(a) and 12(b) show the uniaxial stress-strainrelationship used for the concrete and the reinforcing barin this study respectively Uniaxial compressive and tensilebehavior of the plain concrete wasmodeled using expressionsproposed by Saenz [25] and Hsu and Mo [26] respectivelywhere Youngrsquos modulus of the concrete 119864

119888 was estimated

as 4700radic119891119888(MPa) according to ACI design code [21] It

is also assumed that the stress-strain relationship of theconcrete in compression is linear up to a stress of 051198911015840

119888and

the maximum compressive strength 1198911015840119888 is achieved when

compressive strain is 0003 Tensile stress-strain relationshipis linear up to stress at cracking of concrete 119891

119888119903 and the

softening relationship is given by the following equation [14]

119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)

The tensile stress of the concrete 119891119888119903 usually varies from

5 to 10 of 1198911015840119888 In this study a series of parametric studies

was performed to evaluate the proper value of 119891119888119903 and

119891119888119903

was assumed to be 75 of 1198911015840119888based on the results of

the parametric study To simulate the inelastic behavior ofthe concrete under a general 3D stress state the concretedamaged plasticity model incorporated in ABAQUS [24] was


Symmetric section about x-axisDisplacement load

Displacement in z direction was restrainedx

yx

z

Reaction block

FootingColumn

x

y

Location of the holes (displacement in x or y direction was restrained)

Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩

⟨Elevation view⟩

Figure 11 Loading and boundary condition of the finite element model

fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)

Embedded reinforcing bar

Bare reinforcing bar

Smea

red

rein

forc

ing

bar s

tressfr

Smeared reinforcing bar strain 120576r

120576998400r

Er

fyr

f998400yr

E998400pr

(b)

Figure 12 Material models (a) concrete and (b) reinforcing bar

adopted This model follows the nonassociated flow ruleThus plastic flow is governed by a flow potential functionThe flow potential in concrete damaged plasticity model isa function of dilation angle 120595 [27] The dilation angle ofthe concrete varies depending on the concrete properties Inthis study 120595 of 31∘ was adopted for the analysis based on theresults of Lee and Fenves [27]

The average stress-strain relationship of a reinforcing barembedded in concrete is different from that of a bare reinforc-ing bar [26]Theprimary difference is the lower effective yieldstress of the reinforcing bar 119891

119910119903 as shown in Figure 12(b)

In this study the average stress-strain relationship of anembedded reinforcing bar proposed by Hsu andMo [26] wasadopted The average stress-strain relationship of embeddedreinforcing bar proposed by Hus and Mo [26] is given by

119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)

In (2a) and (2b) 119864119903is Youngrsquos modulus of the reinforcing

bar where 119864119903is assumed as 200000MPa 119891

119903and 120576119903are the

stress and strain in the reinforcing bar respectively 1198911015840119910119903

isthe reduced yield stress of embedded reinforcing bars ForPSPs Youngrsquos modulus of the steel 119864

119904 was approximated as

200000MPa and the yield stress was 400MPa

32 Verification of the Analysis Model and Failure Mechanismof Footing with PSP All test specimens were modeled byusing the methods described in the previous section exceptP5H 32 specimen P5H 32 specimen was not simulatedsince the PSPs are assumed to be perfectly bonded to theconcrete in the analysis and the effect of punched holeson the PSP cannot be properly modeled in the analysisFigures 13(a)ndash13(d) show the comparison of the results


0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P0 RC (FEM)P0 RC (test)

(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 6 (FEM)P5 6 (test)

(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)

Figure 13 Comparison with test results (a) P0 RC (b) P5 32 (c) P5 6 and (d) P7 32

obtained from the analysis with those from tests for P0 RCP5 32 P5 6 and P7 32 specimens respectively It canbe seen that the analysis results agreed well with overallload-displacement relationships obtained from the test Theultimate strengths of the analysis models were 21037 kN26155 kN 28538 kN and 24562 kN for P0 RC P5 32P5 6 and P7 32 specimens respectively The maximumdifference between the analysis results and the tests wasapproximately 4 for P7 32 specimenThe analysis providedgoodprediction for the ultimate strength of the test specimen

From the analysis results crack patterns were evaluatedat the middle plane shown in Figure 14 Figures 15(a)ndash15(d)represent the distribution of the maximum principle plastictensile strain in the middle plane of the analysis models forP0 RC P5 32 P5 6 and P7 32 specimens respectively Inthe concrete damaged plasticity model it is assumed thatcrack initiates where the tensile equivalent plastic strain isgreater than zero and themaximumprincipal plastic strain ispositiveThe direction of the vector normal to the crack plane

is assumed to be parallel to the direction of the maximumprincipal plastic strain [24] Thus the crack pattern can beevaluated by using the distribution of themaximumprincipleplastic tensile strain shown in Figure 15 From Figure 15it can be seen that the major diagonal shear crack wasdeveloped and propagated to the bottom of the footing forP0 RC analysis model as shown in Figure 15(a) This crackpattern was similar to the one obtained from the test (refer toFigure 7(a))

On the other hand for P5 32 and P5 6 analysis modelsthe diagonal shear cracks were effectively isolated by the PSPas shown in Figures 15(b) and 15(c) Then the flexural cracksbelow the PSPs were expended As a result the applied loadredistributed to the flexural reinforcing bars The diagonalshear crack of P5 6 analysis model was smaller than that ofP5 32 analysis model It resulted in greater ultimate strengthof P5 6 analysis model than P5 32 model In the case ofP7 32 analysis model similar to the test results shown inFigure 9 the shear cracks were not effectively isolated and


Table 2 Models for parametric study


119905119889119887ℎ119905 119889

1(mm) 119889

2(mm) Study parameter

P RC None None None None None None Reference modelPB 350 times 50 times 150 3 7 50 0 0 Reference model and effect of PSPPS 1 450 times 150 times 150 3 3 50 0 0 Effect of size of PSPPS 2 650 times 350 times 150 3 19 50 0 0 Effect of size of PSPPT 1 350 times 50 times 150 15 7 100 0 0 Effect of thickness of PSPPT 2 350 times 50 times 150 6 7 25 0 0 Effect of thickness of PSPPL 1 350 times 50 times 150 3 7 50 150 0 Effect of location of PSPPL 2 350 times 50 times 150 3 7 50 100 100 Effect of location of PSP

Reaction block

FootingColumn

x

y

Crackobservation plane

(middle plane)

z

Figure 14 Location of crack observation plane for test specimens

the relatively large diagonal shear crack was developed asshown in Figure 15(d) As a result the increase in the ultimatestrength and ductility was limited For all analyzed footingswith PSPs no significant cracks outside PSPs were observed

Taken as a whole it can be known that as long as PSPcan effectively isolate the diagonal shear cracks the ultimatestrength and ductility of the footing can be improved Thecrack isolating ability of PSP depends on the size thicknessand location of PSP Thus a series of parametric studies wasperformed to find the optimum size thickness and locationof PSP Details on the parametric study are presented in thefollowing section

4 Parametric Study

41 Description of Models for Parametric Study Figure 16shows the dimensions of the models for parametric studyThe concrete footing had a square shape with side lengthof 2000mm The depth of the footing was 400mm Thebottom flexural reinforcing bar consisted of SD500 D29 barsspaced at 150mm which results in reinforcement ratio of 1The nominal diameter of the SD500 D29 is 286mm Theyield stress of SD500 D29 was assumed to be 530MPa Thecover depth of the concrete 119888

1 was 50mm The compressive

strength of the concrete was taken as 25MPa The compres-sion was applied through 300 times 300mm square area FourPSPs were installed into the footing as shown in Figure 16

The yield stress of the PSP was assumed to be 400MPa Thequarter model was used for the analysis and the four bottomedges of the footing were assumed to be simply supported

Table 2 shows the descriptions of the models for theparametric study P RC is the reference model for the con-ventional footing without PSPs PB is the base model for thefooting with PSPs where the top and the bottom diameter ofthe PSP (119889

119905and 119889

119887) were 350mm and 50mm respectively

Thus the PSP is inclined at a 45∘ angle In this study the angleof the slope of the PSPwas limited to 45∘ for all test specimensand analysis models The height of the PSP was 150mm andthe concrete cover depth for PSP 119888

2 was the same as that for

the reinforcing bar (1198881= 50mm) Thus the summation of

the concrete cover depth for PSP and the height of PSP is thesame as half of the total depth of the footing

The effect of the size thickness and location of PSP wasinvestigated comparing the result of PB analysis model withthose of PS PT and PL analysis model series respectivelyFor PS 1 and PS 2 analysis models the size of the PSPs was450 times 150 times 150 and 650 times 350 times 150 respectively whilethe thickness of PSP was the same at 3mm For PT 1 andPT 2 analysis models the thickness of PSP was 15 and 6mmrespectively where the size of PSP was the same as that ofPB model In the case of PL 1 and PL 2 analysis models thelocation of PSP was varied by relocating the center of thePSP 119889

1and 119889

2shown in Figure 16 are the horizontal and the

vertical distance from the original center of PSP to the newcenter location of the PSP The values of 119889

1and 119889

2for PL 1

and PL 2 analysis models are shown in Table 2

42 Results of Parametric Study and Design Recommenda-tion Figures 17 and 18 show the applied load-vertical dis-placement relationships and crack patterns of the analysismodels respectively From Figure 17(a) it can be seen thatthe strength and ductility of the footing with PSPs wereconsiderably increased by comparing with the analysis resultof P RC model PB model showed approximately 12 largerstrength than P RC model

It is noted that the deformation capacity of PS 2 modeldecreased comparing with PB and PS 1 models as shown inFigure 17(a) This is due to the large size of the PSP whichmakes it unsuitable to prevent the diagonal shear crack Fromthe crack patters of PB and PS 2 analysis models shownin Figures 18(a) and 18(b) it can be seen that considerablediagonal shear crack was developed for PS 2 analysis model


x

z

PE max principal(avg 75)

+5003e minus 02+4586e minus 02+4169e minus 02+3752e minus 02+3335e minus 02+2918e minus 02+2501e minus 02+2084e minus 02+1668e minus 02+1251e minus 02+8338e minus 03+4169e minus 03

PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC


PE max principalSNEG (fraction = minus10)

x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32

+8826e minus 02+8091e minus 02+7355e minus 02+6620e minus 02+5884e minus 02+5149e minus 02+4413e minus 02+3678e minus 02+2942e minus 02+2207e minus 02+1471e minus 02+7355e minus 03+0000e + 00


x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32

Figure 15 Crack patterns of the test specimens (a) P0 RC (b) P5 32 (c) P5 6 and (d) P7 32

while the major crack in PB analysis model was developed bythe flexure

In the parametric study the height of the PSP was fixedThus the size of PSP varies depending on the ratio betweenthe top and the bottom diameter of PSP 119889

119905119889119887 Smaller value

of 119889119905119889119887results in larger size of the PSP As a result 119889

119905119889119887

should be large enough to effectively isolate the diagonalshear crack and to increase the strength and ductility ofthe footing Based on the results of tests and parametric

study the shear crack was effectively prevented for P5 32P5 6 P5H 32 PB and PT 2 test specimens or analysismodels For these models 119889

119905119889119887varied from 5 to 7 and these

values are recommendedThe effect of the thickness of PSP on the behavior of the

footing can be evaluated from Figure 17(b) The thickness ofPSP was normalized by the height of PSP as ℎ119905 Smallerℎ119905 represents a larger thickness of PSP For PB PT 1 andPT 2 analysis models ℎ119905 were 50 100 and 25 respectively


PSP

Four edges are simply supported

Quarter model was used

Center of PSP

Crack observation plane (middle plane)

2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm

⟨PB analysis model⟩

Figure 16 Dimensions of model for parametric study

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)

Figure 17 Results of parametric study (load-displacement relationship) (a) effect of the size of PSP (b) effect of thickness of the PSP and(c) effect of the location of PSP



x

z

+3654e minus 02

+3045e minus 02+2741e minus 02+2436e minus 02+2132e minus 02+1827e minus 02

+1218e minus 02+9135e minus 03+6090e minus 03+3045e minus 030000e + 00

PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z

+4297e minus 02+4688e minus 02

+3907e minus 02+3516e minus 02+3125e minus 02+2735e minus 02+2344e minus 02+1953e minus 02+1563e minus 02+1172e minus 02+7813e minus 03+3907e minus 03+0000e + 00

PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z


+4185e minus 02+3836e minus 02+3487e minus 02+3139e minus 02+2790e minus 02+2441e minus 02+2092eminus 02+1744e minus 02+1395e minus 02+1046e minus 02+6975e minus 03+3487e minus 03+0000e + 00

PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1

Figure 18 Cracking patterns of analysis models (a) PB (b) PS 2 (c) PT 1 and (d) PL 1

When the thickness of PSP was small such as PT 1 analysismodel (ℎ119905 = 100) the significant diagonal shear crack wasobserved as shown in Figure 18(c) and the increase in thestrength and ductility was limited as shown in Figure 17(b)For PB and PT 2 analysis models where ℎ119905 is smaller than50 the analysis results were almost identical to each other asshown in Figure 17(b) Based on the test and analysis resultsthe PSP shows a good performance when ℎ119905 is smaller than625 and this value is recommended for the design purpose

Figure 17(c) represents the effect of the location of PSP onthe behavior of the footing For both PL 1 and PL 2 analysismodels the applied load-vertical displacement relationshipswere similar compared to that of the footing without PSP

(P RC) as shown in Figure 17(c) In particular for PL 1analysis model the behavior is almost identical to that ofP RC analysis model The crack pattern of PL 1 analysismodel is presented in Figure 18(d) It can be seen that PSP islocated outside the compression strut and the diagonal shearcrack governs the behavior of the footing In the case of PL 2analysis model the location of PSP was in the zone of thecompressive strut However PSP was placed just above thebottom flexural reinforcing bars and the distance from thePSP to the interface between the column and the top surfaceof the footing is relatively far away compared to other analysismodels Thus it can be concluded that PSP should be placedin the zone of the compressive strut and as close to the top


Table 3 Comparison with ACI design code

(a) The foundation without PSP

Name 119875119906test or FEM119875119906ACI Remark

Po RC 103 TestP RC 092 FEMAverage 098

(b) The foundation with PSP that meets the design recommendationproposed in this study


P5 32 126 TestP5 6 119 TestP5H 32 120 TestPB 103 FEMPT 2 103 FEMAverage 114 mdash

surface of the footing as possible to take the benefits of thePSP

Finally the following initial design recommendations forthe footing with PSPs were suggested

(a) 1198882+ ℎ should not exceed or be similar to the half

of the depth of the footing where 1198882and ℎ are the

concrete cover depth for PSP and height of the PSPrespectively

(b) 119889119905119889119887should be ranged from 5 to 7 ℎ119905 should be

smaller than 625 But when ℎ119905 = 25 there is noincrease in the strength and deformation capacityfrom the analysis results

(c) To take the benefit of PSP PSP should be placed at thezone of the compressive strut

43 Comparison with ACI Design Code According to ACI[21] the punching shear strength of the slab or the footingsubjected to a square column can be determined as

033radic11989110158401198881205821198870119889 (inMPa) (4)

where 1198870is the control perimeter and it is 05119889 from the loaded

area 119889 is the effective depth of the slab or the footing 120582 in(4) is a modification factor to take into account the effectof lightweight concrete For the normal weight concrete 120582 isequal to 1

The ultimate strength of the test specimens and analysisresults that meet the proposed initial design recommenda-tions were compared with (4) in this sectionThe comparisonresults are shown in Table 3 From Table 3 it can be foundthat (4) agrees well with the punching shear strength ofthe footing without PSP The average discrepancy was 2For the footings with PSPs that meet the proposed designrecommendations ACI design code [21] underestimates theultimate strength of the footing by 14 The strength of thefooting with PSPs was approximately 16 higher than that ofthe footing without PSPs

5 Conclusions and Further Study

This study presents a new method to improve the strengthand ductility of the footing by inserting the PSPs into thefooting The validation and effectiveness of the proposedmethod were verified by a series of tests and nonlinear finiteelement analysis From the test results it can be found thatthe strength and ductility of the footing were considerablyincreased by using the PSPs since the diagonal shear crackscan be effectively isolated by PSPs Then the applied loadredistributed to the flexural reinforcing bars

The nonlinear finite element analysis model was con-structed and successfully verified by comparing with the testresults Then a series of parametric studies was conducted toinvestigate the effect of the size thickness and location of PSPon the behavior of the footing with PSPs From the results ofparametric study it can be found that PSPs should be placedin the zone of the compressive strut to take the benefit ofPSP Further the analysis results show that increase in the sizeand thickness of the PSP does not always guarantee a betterstrength and ductility of the footing with PSPs Based on theresults of the test and the parametric study initial designrecommendations for the footing with PSPs were proposed

Finally the strengths obtained from the test and para-metric study that meet the proposed design recommenda-tions were compared with ACI design equation ACI designequation underestimates the strength of the footing withPSPs by approximately 14 To examine the efficiency of theproposed footing with PSPs a comparison to a footing withconventional punching shear reinforcements is necessaryAlso more systematic comparison with current design codesand development of mechanical model for the footing withPSPs that explain the enhancement of the punching shearperformance is needed in the future study

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by a Grant from InternalResearch Project (2014-0059) funded by the Korea Instituteof Civil Engineering and Building Technology Also thisresearch was supported by a Grant (13AUDP-C068788-01)from Housing Environment Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] A A Elshafey E Rizk H Marzouk and M R Haddara ldquoPre-diction of punching shear strength of two-way slabsrdquo Engineer-ing Structures vol 33 no 5 pp 1742ndash1753 2011

[2] K-K Choi M M Reda Taha and A G Sherif ldquoSimplifiedpunching shear design method for slab-column connectionsusing fuzzy learningrdquoACI Structural Journal vol 104 no 4 pp438ndash447 2007


[3] D DTheodorakopoulos and R N Swamy ldquoUltimate punchingshear strength analysis of slab-column connectionsrdquo Cementand Concrete Composites vol 24 no 6 pp 509ndash521 2002

[4] M Fernandez Ruiz YMirzaei andAMuttoni ldquoPost-punchingbehavior of flat slabsrdquo ACI Structural Journal vol 110 no 5 pp801ndash811 2013

[5] T Clement A P Ramos M F Ruiz and A Muttoni ldquoDesignfor punching of prestressed concrete slabsrdquo Structural Concretevol 14 no 2 pp 157ndash167 2013

[6] T Clement A Pinho Ramos M Fernandez Ruiz and AMuttoni ldquoInfluence of prestressing on the punching strength ofpost-tensioned slabsrdquo Engineering Structures vol 72 pp 56ndash692014

[7] K Pilakoutas and X Li ldquoAlternative shear reinforcement forreinforced concrete flat slabsrdquo Journal of Structural Engineeringvol 129 no 9 pp 1164ndash1172 2003

[8] W G Corley andNM Hawkins ldquoShearhead reinforcement forslabsrdquoACI Journal Proceedings vol 65 no 10 pp 811ndash824 1968

[9] N K Subedi and P S Baglin ldquoDesign of slab-column junctionsin flat slabsrdquo Proceedings of the Institution of Civil EngineersStructures and Buildings vol 156 no 3 pp 319ndash331 2003

[10] P J McHarg W D Cook D Mitchell and Y S Yoon ldquoBenefitsof concentrated slab reinforcement and steel fibers on perfor-mance of slab-column connectionsrdquoACI Structural Journal vol97 no 2 pp 225ndash234 2000

[11] M-Y Cheng and G J Parra-Montesinos ldquoEvaluation of steelfiber reinforcement for punching shear resistance in slab-column connections Part IMonotonically increased loadrdquoACIStructural Journal vol 107 no 1 pp 101ndash109 2010

[12] MHHarajli DMaalouf andH Khatib ldquoEffect of fibers on thepunching shear strength of slab-column connectionsrdquo Cementand Concrete Composites vol 17 no 2 pp 161ndash170 1995

[13] L Nguyen-Minh M Rovnak T Tran-Ngoc and T Le-PhuocldquoPunching shear resistance of post-tensioned steel fiber rein-forced concrete flat platesrdquo Engineering Structures vol 45 pp324ndash337 2012

[14] M R Esfahani M R Kianoush and A R Moradi ldquoPunchingshear strength of interior slab-column connections strength-ened with carbon fiber reinforced polymer sheetsrdquo EngineeringStructures vol 31 no 7 pp 1535ndash1542 2009

[15] C Alander ldquoAdvanced systems for rational slab reinforcementrdquoin Proceedings of the Conference ldquoHeading for concrete solutionsldquoThe European Ready Mixed concrete Association ERMCOHelsinki Finland 2004

[16] R Koppitz A Kenel and T Keller ldquoPunching shear of RC flatslabsmdashreview of analyticalmodels for new and strengthening ofexisting slabsrdquo Engineering Structures vol 52 pp 123ndash130 2013

[17] M Hallgren S Kinnunen and B Nylander ldquoPunching sheartests on column FootingsrdquoNordic Concrete Research vol 21 no3 pp 1ndash22 1998

[18] J Hegger A G Sherif and M Ricker ldquoExperimental investi-gations on punching behavior of reinforced concrete footingsrdquoACI Structural Journal vol 103 no 4 pp 604ndash613 2006

[19] J Hegger M Ricker and A G Sherif ldquoPunching strength ofreinforced concrete footingsrdquo ACI Structural Journal vol 106no 5 pp 706ndash716 2009

[20] CEB-FIP Model Code ldquoBulletin DrsquoInformation no 203ndash305rdquoLausanne Switzerland 1990

[21] American Concrete Institute Building Code Requirements forStructural Concrete ACI 318-11 American Concrete InstituteFarmington Hills Mich USA 2011

[22] HMarzouk andAHussein ldquoExperimental investigation on thebehavior of high-strength concrete slabsrdquo ACI Structural Jour-nal vol 88 no 6 pp 701ndash713 1991

[23] S Guandalini O L Burdet and A Muttoni ldquoPunching tests ofslabs with low reinforcement ratiosrdquoACI Structural Journal vol106 no 1 pp 87ndash95 2009

[24] ABAQUS ABAQUS Analysis Userrsquos Manual Version 69-2Dassault Systemes Simulia Providence RI USA 2009

[25] L P Saenz ldquoDiscussion of ldquoequation for the stress-strain curveof concreterdquo by P Desayi and S Krishnanrdquo American ConcreteInstitute Journal vol 61 pp 1229ndash1235 1964

[26] T T C Hsu and Y-L MoUnifiedTheory of Concrete StructuresJohn Wiley amp Sons New York NY USA 2nd edition 2010

[27] J Lee andG L Fenves ldquoPlastic-damagemodel for cyclic loadingof concrete structuresrdquo Journal of Engineering Mechanics vol124 no 8 pp 892ndash900 1998

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



PSPs

PSP

P

Compression strut

Cracks

(a)

P

Cracks


Control perimeter


(b)

Figure 1 Schematic view of (a) footing with PSPs and (b) flat slab with funnel typed punching shear preventer

in Figure 1(a) is used for the flat slab control perimeter canbe determined by the size of the funnel-shaped punchingshear preventer Thus increasing the size of the funnel-shaped punching shear preventer can produce higher punch-ing shear strength However funnel-shaped punching shearpreventer shown in Figure 1(a) is not suitable for large scaleconstruction such as high rise building column-to-footingor bridge pier-to-footing connection since the size of thefunnel-shaped punching shear preventer becomes very largewhich makes it hard to handle

As an alternative in this study four small punching shearpreventers (PSPs) are inserted into the footing as shown inFigure 1(b) PSP has cone shape and it is made of steel Basi-cally PSP has smooth surface However the bond strengthbetween PSP and concrete can be improved by introducingpunched holes as shown in Figure 1(b) By inserting PSPsinto the footing the following benefits can be expected (1)propagation of shear crack could be effectively prevented(2) PSP could enhance the compression strut developed bythe axial compression from the columnTherefore enhancedpunching shear strength and ductile failure of the footing-to-column connection are expected by using the PSPs

In this study the validation and effectiveness of the PSPwere verified through a series of tests and nonlinear finiteelement analysis A total number of five large scale testspecimens were constructed and tested in order to investigatethe effect of PSP on the punching shear strength and thefailure mode of the footing with PSP Then a series ofparametric studies was conducted to demonstrate the failuremechanism in depth and to study the effect of key parametersof PSP on the behavior of the footing Finally the designrecommendations for the footing with PSPs were suggested

2 Experimental Study

21 Description of Test Specimen A total of five large scaletest specimens were constructed and tested All five footingshad the same dimensions and reinforcing bar layout Figure 2

shows the dimensions of the footingThe footing had a squareshape with side length of 2400mm and depth of 500mmThe axial load was applied through the square column inthe center of the footing where the width and the height ofthe column were 350mm and 300mm respectively 40mmdiameter holes were spaced at 500mm to insert the anchorbars as shown in Figure 2

Figure 3 shows the layout of the reinforcing bars andPSPsThebottomflexural reinforcing bars consisted of SD500D25 bars spaced at 200mm where the yield stress andthe diameter of SD500 D25 bar are 530MPa and 254mmrespectively The resulting flexural reinforcement ratio wasapproximately 05 The top flexural reinforcing bars spacedat 200mm were installed with the length of 500mm at theedge of the test specimens as shown in Figure 3 to preventthe premature cracking and failure due to negative bendingmoment at the edges The SD500 D25 bars were also used forthe top reinforcing bars According toACI code [21] concretecover for concrete casted against and permanently exposedto earth is 3 in (762mm) Thus 80mm of concrete coverdepth was adopted for the top and the bottom reinforcingbars To prevent the premature failure of the column duringthe test the columnwas reinforced by using eight SD500D25longitudinal bars and SD500 D13 stirrups spaced at 50mmwhere the yield stress and the diameter of SD500 D13 bar are530MPa and 127mm respectively As shown in Figure 3 twostrain gauges (S1 and S2) were installed at the bottom flexuralreinforcing bars tomeasure the longitudinal strain of the bars

All test specimens were casted at the same time TypeI ordinary Portland cement was used with water-to-cementratio of 048 Crushed shape coarse aggregate was used wherethe maximum size was 25mm From the material test theaverage compressive strength was 252MPa PSPs were madeof steel where yield stress was 400MPa from mill sheet

The names and the test parameters for each specimenare shown in Table 1 P0 RC is the reference test specimenwhere PSPswere not installed in the footing For P5 32 P5 6P5H 32 and P7 32 specimens four PSPs were inserted into




119905119889119887


119906(kN)




300

500

(a)

200

400

350

400Electionhook

350

200

240

020

020

0

2400

Hole Φ40

4500

4500

(b)


PSP

h


6-Φ100 holes

dt

db

(a)

7200

2400

240

0

7200

20012

200

12

500

500

500500

S1 S2

(b)



Column


350mm

350 times 350mm

2000mm

350mm

2000

mm

Steel block 1250



119905and 119889






0 5 10 15 20 250

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32

P5H 32

P5 6

P5 32

P0 RC



119906 was 2105 kN and




0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)

Yield strain


P0 RC S1P0 RC S2

(a)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500Yield strain

Appl

ied

load

(kN

)


P5H 32 S1

(b)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500 Yield strain

Appl

ied

load

(kN

)


P5 6 S1P5 6 S2

(c)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Yield strainAp

plie

d lo

ad (k

N)


P7 32 S1P7 32 S2

(d)




119906of P5 32












Major crack

P0 RC

(a)

Major crack

PSPPSP

P5 32

(b)


PSPPSP

Major crack

P5 6

(a)

PSP PSP

Major crack

P5H 32

(b)






PSP PSP

Major crack

P7 32








z

FootingColumn

x

y

Reaction block

14 model














119888and



119888119903 and the


119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)




119891119888119903






yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119905119889119887


119906(kN)




300

500

(a)

200

400

350

400Electionhook

350

200

240

020

020

0

2400

Hole Φ40

4500

4500

(b)


PSP

h


6-Φ100 holes

dt

db

(a)

7200

2400

240

0

7200

20012

200

12

500

500

500500

S1 S2

(b)



Column


350mm

350 times 350mm

2000mm

350mm

2000

mm

Steel block 1250



119905and 119889






0 5 10 15 20 250

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32

P5H 32

P5 6

P5 32

P0 RC



119906 was 2105 kN and




0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)

Yield strain


P0 RC S1P0 RC S2

(a)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500Yield strain

Appl

ied

load

(kN

)


P5H 32 S1

(b)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500 Yield strain

Appl

ied

load

(kN

)


P5 6 S1P5 6 S2

(c)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Yield strainAp

plie

d lo

ad (k

N)


P7 32 S1P7 32 S2

(d)




119906of P5 32












Major crack

P0 RC

(a)

Major crack

PSPPSP

P5 32

(b)


PSPPSP

Major crack

P5 6

(a)

PSP PSP

Major crack

P5H 32

(b)






PSP PSP

Major crack

P7 32








z

FootingColumn

x

y

Reaction block

14 model














119888and



119888119903 and the


119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)




119891119888119903






yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Column


350mm

350 times 350mm

2000mm

350mm

2000

mm

Steel block 1250



119905and 119889






0 5 10 15 20 250

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32

P5H 32

P5 6

P5 32

P0 RC



119906 was 2105 kN and




0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)

Yield strain


P0 RC S1P0 RC S2

(a)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500Yield strain

Appl

ied

load

(kN

)


P5H 32 S1

(b)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500 Yield strain

Appl

ied

load

(kN

)


P5 6 S1P5 6 S2

(c)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Yield strainAp

plie

d lo

ad (k

N)


P7 32 S1P7 32 S2

(d)




119906of P5 32












Major crack

P0 RC

(a)

Major crack

PSPPSP

P5 32

(b)


PSPPSP

Major crack

P5 6

(a)

PSP PSP

Major crack

P5H 32

(b)






PSP PSP

Major crack

P7 32








z

FootingColumn

x

y

Reaction block

14 model














119888and



119888119903 and the


119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)




119891119888119903






yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)

Yield strain


P0 RC S1P0 RC S2

(a)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500Yield strain

Appl

ied

load

(kN

)


P5H 32 S1

(b)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500 Yield strain

Appl

ied

load

(kN

)


P5 6 S1P5 6 S2

(c)

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

Yield strainAp

plie

d lo

ad (k

N)


P7 32 S1P7 32 S2

(d)




119906of P5 32












Major crack

P0 RC

(a)

Major crack

PSPPSP

P5 32

(b)


PSPPSP

Major crack

P5 6

(a)

PSP PSP

Major crack

P5H 32

(b)






PSP PSP

Major crack

P7 32








z

FootingColumn

x

y

Reaction block

14 model














119888and



119888119903 and the


119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)




119891119888119903






yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Major crack

P0 RC

(a)

Major crack

PSPPSP

P5 32

(b)


PSPPSP

Major crack

P5 6

(a)

PSP PSP

Major crack

P5H 32

(b)






PSP PSP

Major crack

P7 32








z

FootingColumn

x

y

Reaction block

14 model














119888and



119888119903 and the


119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)




119891119888119903






yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













z

FootingColumn

x

y

Reaction block

14 model














119888and



119888119903 and the


119891119888= 119891119888119903(120576119888119903

120576119888

)

04

when 120576119888le 120576119888119903 (1)




119891119888119903






yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












yx

z

Reaction block

FootingColumn

x

y


Sym

met

ric se

ctio

n ab

outy

-axi

s

1000mm

500

mm

625

mm

40mm20mm

(175 times 175mm)

14 model

⟨Plane view⟩



fc

f998400c

05f998400c

120576cr

fcr

120576998400c 120576c

Ec

(a)



Smea

red

rein

forc

ing

bar s

tressfr


120576998400r

Er

fyr

f998400yr

E998400pr

(b)






119891119903= 119864119903120576119903

when 119891119903le 1198911015840

119910119903 (2a)

119891119903= (091 minus 2119861) 119891

119910119903+ (002 + 025119861) 119864

119903120576119903

when 119891119903gt 1198911015840

119910119903

(2b)

where

119891119910119903= (093 minus 2119861) 119891

119910119903 119861 =

1

120588(119891119888119903

119891119910119903

)

15

(3)



119903and 120576119903are the







0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(a)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P5 32 (FEM)P5 32 (test)

(b)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)



(c)

0 3 6 9 12 15 18 210

500

1000

1500

2000

2500

3000

3500

Appl

ied

load

(kN

)


P7 32 (FEM)P7 32 (test)

(d)









119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119905119889119887ℎ119905 119889

1(mm) 119889



Reaction block

FootingColumn

x

y


(middle plane)

z




4 Parametric Study






119905and 119889







1and 119889



1and 119889

2for PL 1





x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

z



PE max principal

lowast Direction

lowast Magnitude

+0000e + 00

(a) P0 RC



x

z


PSP

PSP

lowast Direction

lowast Magnitude

+0000e + 00

(avg 75)

(b) P5 32



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(c) P5 6



x

z


PSP

PSP

lowast Direction

lowast Magnitude

(avg 75)

(d) P7 32




119905119889119887 Smaller value


119905119889119887







PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PSP



Center of PSP


2000mm400

mm

c2

c1 = 50mm

45∘d2

d1

300mm



0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PS 2PS 1

P RC

(a)

0 4 8 12 16 200

400

800

1200

1600

PB

Appl

ied

load

(kN

)


PT 1

PT 2

P RC

(b)

0 4 8 12 16 200

400

800

1200

1600PB

Appl

ied

load

(kN

)


PL 2

PL 1

P RC

(c)




x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











x

z

+3654e minus 02



PSP

PSP


lowast Direction

lowast Magnitude

+3350e minus 02

+1523e minus 02

(avg 75)

(a) PB


x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(b) PS 2

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(c) PT 1

x

z



PSP

PSP


lowast Direction

lowast Magnitude

(avg 75)

(d) PL 1






















033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























033radic11989110158401198881205821198870119889 (inMPa) (4)










Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Strength of Footing with Punching Shear ...A new method to increase the punching shear strength and ductility of the footing-to- column connection was proposed. For