experimental research of continuous concrete beams with...

Research ArticleExperimental Research of Continuous Concrete Beams withGFRP Reinforcement

Nikola Basa Mladen Ulicevic and Radomir Zejak

University of Montenegro Faculty of Civil Engineering Cetinjski put bb 81000 Podgorica Montenegro

Correspondence should be addressed to Nikola Basa nikmat-comme

Received 8 June 2018 Accepted 13 September 2018 Published 18 October 2018

Academic Editor Dongsheng Li

Copyright copy 2018 Nikola Basa et al +is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Continuous beams are often used within RC structures which are exposed to aggressive environmental impact +e use ofthe fiber-reinforced polymer (FRP) reinforcement in these objects and environments has a big significance taking intoaccount tendency of steel reinforcement to corrode +e main aim of these research studies is to estimate ability ofcontinuous beams with glass FRP (GFRP) reinforcement to redistribute internal forces as a certain way of ductility anddesirable behaviour of RC structures +is paper gives the results of experimental research of seven continuous beams overtwo spans of 1850mm length cross-section of 150 times 250mm that are imposed to concentrated forces in the middle of spansuntil failure Six beams were reinforced with different longitudinal GFRP and same transverse GFRP reinforcements andone steel-reinforced beam was adopted as a control beam +e main varied parameters represent the type of GFRP re-inforcement and ratio of longitudinal reinforcement at the midspan and at the middle support ie design moment re-distribution +e results of the research have shown that moment redistribution in continuous beams of GFRPreinforcement is possible without decreasing the load-carrying capacity compared to elastic analysis +e test results havealso been compared to current code provisions and they have shown that the American Concrete Institute (ACI) 4401R-15well predicted the failure load for continuous beams with GFRP reinforcement On the contrary current design codesunderestimate deflection of continuous beams with GFRP reinforcement especially for higher load levels Consequentlya modified model for calculation of deflection is proposed

1 Introduction

For RC structures elements reinforced with steel re-inforcement are still used nowadays As preventing of steelreinforcement to corrode in RC structures could be ex-pensive and very often without significant effects FRP in-ternal reinforcement is lately used as a replacement of steelreinforcement in RC structures especially in aggressiveenvironments Nowadays there is a significant number ofstructures such as garages bridges retaining walls reser-voirs and marine objects within which FRP reinforcementis successfully applied at RC structural elements Continuousconcrete beams are commonly used in some of thesestructures especially in bridges overpasses marine struc-tures and parking garages Additionally continuous beamswith FRP reinforcement can also find their application in

facilities with magnetic scanning equipment laboratoriesairport towers and MRI rooms in hospitals and other fa-cilities with equipment requiring electrical and magneticneutrality where the presence of steel reinforcement canhave an adverse effect on the usability of devices in thesefacilities

Due to different mechanical and deformation charac-teristics of FRP reinforcement as high tensile strength andlow modulus of elasticity the behavior of RC elements isconsiderably different compared to RC elements with steelreinforcement Concerning the fact that FRP reinforce-ment demonstrates linear elastic behavior up to failuremeaning demonstrating lack of material nonlinearitythere is a question of ability of this material in conjunctionwith concrete to realize load redistribution in staticallyindeterminate structures [1] Regarding the significant

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 6532723 16 pageshttpsdoiorg10115520186532723

contribution of the elastic redistribution in continuous RCbeams with steel reinforcement [2] it is expected thatcontinuous beams with FRP reinforcement give certainability to redistribute the internal force Redistribution ofinternal forces is expected as the result of cracks develop-ment and adopted reinforcement within them [1 3] In otherwords one of the basic characteristics of ductility is con-sidered ie variation of stiffness without loss of capacity ofthe section [4]

2 Background

So far thorough theoretical and experimental researchstudies have been carried out on simple supported beamswith FRP reinforcement in order to evaluate behaviorregarding failure modes load-carrying capacity de-flection and cracks [5ndash13] +erefore provisions of certaincodes are based on conclusions given on simple supportedbeams A great number of formulas and equations aresuggested to determine response of elements with FRPreinforcement at service load conditions especially whendeflection is concerned (Toutanji and Saafi [7] Yost et al[8] Bischoff and Gross [9] Mousavi and Esfahani [10] andJu et al [11])

Certain experimental and theoretical research studieswere also carried out on continuous beams with FRP re-inforcement [1 3 4 14ndash22] but not as much as they werecarried out on simple beams Mostofinejad [4] carried outresearch studies on two continuous beams with steel re-inforcement and eight underreinforced and overreinforcedcontinuous beams with CFRP reinforcement+ese researchstudies showed that moment redistribution in continuousbeams with FRP reinforcement is possible although in lowerdegree than in steel-reinforced beams Overreinforcedbeams with FRP reinforcement fulfill requirements of ser-viceability while underreinforced beams designed to ex-perience failure by FRP bars usually do not fulfill theseconditions Moreover overreinforced continuous beamsshow significant deformations before failure which wasdetermined as a distinctive way of ductility Grace et al [14]researched behavior and ductility of continuous beams Tcross-section reinforced by different types of longitudinaland transverse FRP reinforcements (GFRP and CFRP) Itwas indicated on different failure modes and beam ductilitywith FRP reinforcement in relation to beams with steelreinforcement It was also concluded that the use of GFRPstirrups increases shear deformations As a result of thattotal deformations increase in the midspan of continuousbeams El-Mogy et al [1] conducted the research on fourcontinuous beams of rectangular cross-section with GFRPCFRP and steel reinforcement by varying the ratio oflongitudinal reinforcement in the midspan and at the middlesupport It was concluded that continuous beams with FRPreinforcement are capable of redistributing the momentsfrommiddle support towards the midspan of 23 in relationto elastic analysis similar to the fact that they do not causeadversely effects concerning the beam characteristics nei-ther at service loads nor at failure loads Moreover it wasconcluded that the increase of reinforcement in the midspan

of continuous beams in relation to section at the middlesupport has positive effects on the increase of load capac-ity of beams decrease of deflections and postponing ofpropagation of cracks in the beamsrsquo midspan Habeeb andAshour [15] noticed signs of moment redistribution withinoverreinforced beams in the bottom zone in the midspanduring the experimental research studies on three contin-uous beams with different combinations of GFRP longitu-dinal reinforcement in the midspan and at the middlesupport As a key factor of increasing the load capacity andlimitation of deflection and propagation of cracks the in-crease of the reinforcement in the bottom zone of themidspan was noticed In the scope of same experimentalresearch studies Ashour and Habeeb [16] conducted theresearch on three continuous beams with CFRP re-inforcement designed with different configurations of re-inforcement along the beam so as to experience the failureby CFRP bars Intolerant wide cracks at the middle supportwere noticed in all beams as a result of debonding of CFRPbars from concrete It was concluded that the basic pa-rameter of increasing the load capacity of continuous beamswas the amount of CFRP reinforcement in the bottom zonein the midspan Other recent research studies on continuousbeams [3 17 18 20] also pointed out to the importance ofincreasing the reinforcement in the bottom zone of the beammidspan as a result of redistribution of moment over themiddle support

+e approach that in continuous beams reinforced withFRP reinforcement moment redistribution in critical sec-tions is not allowed could be conservative [21] +erefore itneeds additional research studies For this purpose it isnecessary to define more clearly and precisely the influenceof ratio of longitudinal reinforcement at the midspan and atthe middle support on behavior of continuous beams withFRP reinforcement+emain aim of these research studies isconsideration of behavior of continuous beams reinforcedwith GFRP reinforcement during loading until failure withdifferent configurations of reinforcement along the beam+us in these experimental research studies for the samedesign failure load for every type of GFRP reinforcementthree models with different configurations of reinforcementalong the beam were used Experimental results are dis-cussed and evaluated based on failure modes crackingdeflection moment redistribution and strains in concreteand reinforcement and compared to code predictions re-garding the load-carrying capacity and deflection Based onexperimental results a modified model for better predictionof deflection of continuous beams with GFRP reinforcementis proposed

After a literature review it is concluded that in very fewnumber of experimental research studies on continuousbeams with longitudinal FRP reinforcement FRP re-inforcement for stirrups was used [3 14 22] In the re-search studies carried out on the beams with FRPreinforcement steel reinforcement for stirrups was mainlyused In that case a problem with corrosion of reinforcedconcrete elements is still present especially in aggressiveenvironments+e problem increases when it is known thatthe effects of FRP stirrups and steel stirrups on behavior of

2 Advances in Civil Engineering

the beams are different [14] Regarding the previouslymentioned in these experimental research studies besidesthe longitudinal GFRP reinforcement it was also used forstirrups

3 Experimental Program

+e experimental program consisted of six continuousbeams of total length of 3940mm at two equal spans of1850mm length with a rectangular cross-section of150times 250mm and with longitudinal and transverse GFRPreinforcement In addition a single beam with steel re-inforcement was adopted as a control beam All beams wereexamined up to failure loaded by concentrated forces in themiddle of both spans +e beams were divided into twoseries with different GFRP longitudinal bars and all weredesigned for a similar failure load Dimensions and ge-ometry of continuous beams and load disposition are givenin Figure 1

Considering beams of Series 1 longitudinal re-inforcement of beam G1-0 was designed for the elasticbending moments along the beam while reinforcement ofbeams G1-15 and G1-25 was obtained for assumed momentredistribution at the middle support of 15 and 25 re-spectively For the beams G1-15 and G1-25 this meantsmaller amount of reinforcement at the middle support andhigher amount of reinforcement at the midspan comparedto beam G1-0 In this way for designed failure load modelswith 0 (G1-0) 15 (G1-15) and 25 (G1-25) of designedmoment redistribution from the middle support to themidspan were obtained+e reinforcement ratio of the beamG1-0 at the middle support has been chosen so as to beapproximately 3 times higher than the balanced re-inforcement ratio which corresponds to recommendationsof codes that beams with FRP reinforcement should bedesigned to experience concrete compression failure In thisway it was provided after the moment redistribution wasmade that all cross-sections in all beams of Series 1 weredesigned to have reinforcement ratio above the balancedreinforcement ratio +e control beam with steel re-inforcement (S1-15) was designed to achieve the momentredistribution of 15 from the middle support to themidspan +e beams of Series 2 were designed in the sameway as the beams of Series 1 only with different types oflongitudinal GFRP reinforcement Models with 0 (G2-0)15 (G2-15) and 25 (G2-25) of designed moment re-distribution from the middle support to the beam midspanwere also adopted

All beams were designed in accordance with ACI 4401R-15 [23] while CSA S806-12 [24] CNR-DT-203 [25] andEC2-04 [26] were used as control For shear reinforcementGFRP stirrups were adopted for beams with GFRP longi-tudinal reinforcement similar to steel stirrups for the beamS1-15 with longitudinal steel reinforcement Stirrups witha diameter of 8mm were adopted at the space of 60mm forinterior shear span and at the space of 120mm for exteriorshear span for all beams in order to prevent beams toexperience failure due to shear Details of reinforcing forexperimental models are given in Table 1

31 Materials

311 Reinforcement In these experimental research studiestwo types of GFRP reinforcement were used wrapped GFRPbars with 70 of longitudinal glass fibers (E-glass) in totalvolume impregnated in the unsaturated polyester matrix forSeries 1 (marked G1) and GFRP reinforcement with 75 oflongitudinal glass fibers (E-glass) impregnated in an epoxymatrix for Series 2 (marked G2) GFRP reinforcement withpolyester was wrapped in glass fibers while GFRP re-inforcement with epoxy resin was with rebars (Figure 2) Inall beams GFRP stirrups with polyester were usedAccording to the prospect of the manufacturer GFRP re-inforcement with the polyester matrix has a nominal tensilestrength of f 700MPa and a modulus of elasticity ofE 40000MPa while GFRP reinforcement with the epoxymatrix has a nominal tensile strength of f 1100MPa anda modulus of elasticity of E 50000MPa In order to definedesign moment redistribution more precisely and to provideidentical failure load for beams of the same series differentdiameters of GFRP and steel reinforcements were used alongthe beam For each diameter of GFRP reinforcement realcross-sectional areas of the bar similar to the equivalentdiameter on at least five samples of 200mm length weredetermined Also for each diameter of the bars five sampleswere examined to tension until failure in order to definemechanical and deformation characteristics of GFRP re-inforcement all in accordance with ACI 4403R-12 [27]Average values of the test results are given in Table 2

312 Concrete Two designed classes of concrete of 40MPaand 45MPa were used in experimental research studies forthe beams of Series 1 and Series 2 respectively in order toprovide a similar failure load for all beams For each series ofbeams concrete compressive strength after 28 days wasobtained according to the investigation of 8 cubes of 150mmedge 8 cubes of 200mm edge and 17 cylinders of150300mm dimension Average values of test results ofconcrete compressive strength on cylinders 150300mm aregiven in Table 1

32 Test Setup and Instrumentation Continuous beamsconsisted of two equal spans placed on three supports oversteel bearings End supports were designed as horizontallymovable while the middle support was designed to preventhorizontal movement Experimental models were examinedin a closed frame which consisted of a unique system ofhorizontal beams and vertical ties +e load was placed overtwo hydraulic presses capacity of 200 kN in the middle ofboth spans

Twelve electrical strain gauges were placed on longitu-dinal tension reinforcement in both bottom and upper zonesof each beam Also three strain gauges were placed oncompression reinforcement according to the scheme shownin Figure 3 Two strain gauges were placed on the com-pression zone of continuous beams in critical sections at1 cm from the bottom one (at the middle support) similar tothat at the upper edge of concrete (in the midspan) so as

Advances in Civil Engineering 3

strains could be measured in compression concrete De-13ections of continuous beams along the span were registeredby LVDT transducers 1100mm and 150mm of accuracywhich were placed at the level of the bottom edge of thebeamree LVDTtransducers were attached on every span

in the middle in the quarter and three quarters of the beamspan For each increment ie load level appearance anddevelopment of vertical and possibly shear cracks along thebeam were registered Maximal width of a few cracks wasmeasured in critical sections in the span and at the middlesupport by amicroscopic magnier (Zeiss) with 0025mm ofaccuracy Load cells were placed below the end supportscapacity of 100 kN due to measurement of end reactionse scheme of the measuring equipment of continuousbeams is given in Figures 3 and 4

33 Test Procedure e load was applied to the beams asmonotonically static growing load in increments from zeroup to the failure At the beginning of the tests load wasapplied in increments of approximately 2-3 kN and afterdevelopment of rst cracks in increments of 5 kN Whenapproximately 80 of the estimated failure load wasreached again the load was applied in increments of 2-3 kN

120

120

G1-0 G1-15 G1-25 G2-0 G2-15 G2-25

1850 1850

3940

7oslash812 P P37oslash86

3oslash14 2oslash10 3oslash10

2oslash10

1oslash10

2oslash9 2oslash9

3oslash91oslash14

1oslash14

2oslash10

2oslash12 2oslash142oslash12 2oslash12 3oslash12

1oslash12

1oslash12

1oslash10 1oslash12

4oslash12

7oslash812 1oslash12S1-15

2oslash10

1oslash10

oslash8612

oslash8612 oslash8612 oslash8612 oslash8612 oslash8612 oslash8612

2oslash12

925 925 925 925 120

120

150

250

Figure 1 Geometry and reinforcement details for tested beams (all dimensions are in mm)

Table 1 Reinforcement details and compressive strength of concrete for tested beams

Beam Day oftesting

Middle support-top reinforcement Midspan-bottom reinforcementConcrete

compressivestrength fc (MPa)

Longitudinalreinforcement

EA(kN)

Reinforcementratio (ACI) Longitudinal

reinforcementEA(kN)

Reinforcementratio (ACI)

ρf()

ρfb() ρfρfb

ρf()

ρfb() ρfρfb

S1-15 28 2Oslash10+ 1Oslash12 49526 082 126 065 2Oslash12+ 1Oslash10 54763 092 131 071 422G1-0 29 3Oslash14 20318 140 046 301 2Oslash12+ 1Oslash10 13558 100 057 175 422G1-15 30 2Oslash10+ 1Oslash14 12604 086 053 163 2Oslash12+ 1Oslash14 17415 119 046 258 422

G1-25 30 2Oslash10+ 1Oslash12 11153 074 051 144 2Oslash14+ 1Oslash12 18867 125 045 280 422

G2-0 28 4Oslash12 17654 111 033 335 2Oslash10+ 2Oslash9 10734 065 029 227 502G2-15 29 3Oslash10+ 1Oslash12 12482 079 033 237 2Oslash12+ 2Oslash9 14182 086 032 269 502

G2-25 30 3Oslash9 8033 048 029 170 3Oslash12+ 1Oslash10 15930 110 037 302 502

oslash8

oslash14 oslash12 oslash10 oslash10 oslash9oslash12

Figure 2 Samples of GFRP longitudinal and transversereinforcement


Table 2 Mechanical and deformation characteristics of GFRP reinforcement

Diameter Real area of barA (mm2) Tensile strength fu (MPa) Yield strength fy (MPa) Modulus of elasticity E (MPa) Ultimate strain εu (permil)

GFRP-1-Oslash8 399 7148 mdash 42640 168GFRP-1-Oslash10 706 7031 mdash 41300 170

GFRP-1-Oslash12 1161 8659 mdash 45832 189




Steel-Oslash10 785 6395 5096 188064 27a

Steel-Oslash12 1131 6225 4527 176835 26aaεy yield strain of steel reinforcement

1045

SG-10

SG-9

120 120

120 4625Load cell Load cell

4625 4625 4625 4625 4625 4625 4625 120

675 675 675 675250 250 250 250

SG-8SG-6

UG-6SG-6

SG-7

P P

P P

SG-14

SG-4

SG-4

UG-4

SG-1SG-2

SG-1

UG-1

SG-2

UG-2

SG-3

SG-3

UG-3

SG-15

SG-5

UG-5SG-5

SG-11SG-12

SG-13

1045

1045 1045

725

925 925

3940

200 200 725

SG - Strain gauge on reinforcementSG - Strain gauge on concreteUG - Transducers for measure the deflection

Figure 3 Experimental setup and instrumentation for tested beams (all dimensions are in mm)

Figure 4 Equipped continuous beam before testing


Speed of load exposure of each increment was approximately5 kNmin All electronic data were collected in the computerusing the data logger

4 Test Results

41Modes of Failure All beams of Series 1 and Series 2 weredesigned to experience concrete compression failure BeamS1-15 demonstrated typical ductile flexural behavior withhigh values of strains and deflections before failure At themiddle support existing cracks experienced significantwidths at failure First the tensile reinforcement yielded atthe middle support and after that tensile reinforcement inthe beam midspan +e failure of the beam G1-0 was ini-tiated by concrete compression failure in the midspan incombination with shear when one crack in the span di-agonally propagated toward the load location +is leads torupture of GFRP bars in the compressed zone by the doweleffect and one GFRP stirrup at the location of its bendingWithin the beam G1-15 concrete compression failure tookplace at themiddle support when one crack near the supportdiagonally propagated toward the support +e failure of thebeam G1-25 appeared at the same time at the middlesupport where concrete crushing was followed by the shearand at the midspan where concrete crushing was manifestedby spalling of the cover in the extension of the diagonal crackthat occurred in the exterior shear span

+e failure mode of the beams G2-0 and G2-25 wassimilar initiated by concrete compression failure in themidspan in combination with shear when one crack in theinterior shear span diagonally propagated toward the loadlocation+e failure at themidspan was followed by concretecrushing in the compression zone at the middle supportwithin both beams Also in beam G2-25 at the same timeconcrete crushing was manifested by spalling of the cover inthe midspan in the extension of the diagonal crack thatoccurred in the exterior shear span Within the beam G2-15concrete compression failure took place at the middlesupport in combination with shear with the characteristicbang All longitudinal compressed and tensioned GFRP barsand stirrups ruptured at that section by the dowel effect +efailure modes of all beams are given in Figure 5 It can beconcluded that all continuous beams with GFRP re-inforcement experienced concrete compression failurecombined with shear while beam with steel reinforcementexperienced ductile flexural tension failure

42 Crack Patterns In Table 3 failure loads are givensimilar to the first crack loads in the midspan and at themiddle support for all beams It is evident that the first crackload was significantly higher in the beam S1-15 than in thebeams with GFRP reinforcement without exception +iscould be attributed to high modulus of elasticity of steelreinforcement compared to GFRP reinforcement (38ndash45times higher) which leads to conclusion that the crackingmoment does not only depend on the concrete tensionstrength but also on the modulus of elasticity of re-inforcement Concerning all beams with GFRP

reinforcement the first cracks at the midspan and at themiddle support were vertical and they appeared almostsimultaneously at very similar loads Moreover especiallyfor the beams of Series 1 right after the appearance crackssignificantly propagated along the height and entered the lastquarter of section height which additionally affected thedecrease of stiffness of this section

Appearance of new cracks and propagation of existingcracks in the beams of Series 1 with GFRP reinforcementstabilized at load that corresponded to approximately 60 ofthe failure load +e space between cracks in average was120 to 180mm and it did not match the space betweenstirrups It is evident that in beams with GFRP re-inforcement a smaller number of cracks occurred than inthe beam S1-15 with steel reinforcement where the spacebetween cracks was from 60 to 100mm in the interior spanwhich basically matched the space between stirrups +isindicated poor bond strength between GFRP reinforcementand surrounding concrete which caused great wideness onalready developed cracks in critical sections +is phe-nomenon was also recorded by a few researchers who ex-amined beams with FRP reinforcement [16] Concerning thebeams G1-15 and G1-25 it was a visible appearance of longhorizontal cracks in the tension zone at loads near failurewhich implies due to large deflections slipping of re-inforcement from concrete in that part of the beam(Figure 5)

Concerning beams of Series 2 with GFRP reinforcementwith rebars the number of cracks was greater with lesswidths compared to the beams of Series 1 Cracks appearedin the sagging and in the hogging moment region untilfailure regarding the fact that an utmost number of themformed until the load that corresponded to approximately60 of failure load +e development of the cracks withincreasing load corresponded fully to the adopted re-inforcement in critical sections ie the higher amount ofreinforcement corresponded to a higher number of formedcracks in the section +e largest number of cracks at themiddle support formed in the beam G2-0 with an extremelywide hogging zone where cracks appeared due to the largestaxial stiffness of the reinforcement compared to the beamsG2-15 and G2-25 In the midspan the most number ofcracks with the widest sagging zone appeared in the beamG2-25 with the largest amount of reinforcement in themidspan +e development of the cracks in the beams ofSeries 2 was similar to that in the beam S1-15 and corre-sponded to the space between stirrups indicating the goodbond strength between GFRP reinforcement and sur-rounding concrete+emore pronounced diagonal cracks athigher load levels for the beams of Series 2 especially in theinterior shear span compared to the beam S1-15 indicatedan increase of the shear stresses in the beams with GFRPreinforcement which can be directly attributed to the use ofGFRP stirrups instead of steel stirrups +is was particularlypronounced in the beam G2-0 in which due to the higheraxial stiffness of reinforcement at the middle support andachieved ldquooppositerdquo redistribution of internal forces (Section45) higher shear stresses in the interior shear spanappeared compared to the beams G2-15 and G2-25 causing


a large number of shear cracks at the hogging momentregion (Figure 5)

43 Crack Width In Figures 6 and 7 developments ofmaximal 13exural crack widths depending on loads are given

for all beams in the midspan and at the middle supportrespectively It can be seen that beams of Series 1 had largermaximum 13exural crack widths than the beams of Series 2is is not only the consequence of a bit lower modulus ofelasticity of the GFRP reinforcement used in beams of Series1 but also the consequence of poor bond strength of this

S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)

Figure 5 Failure modes of tested beams (a) S1-15 (b) G1-0 (c) G1-15 (d) G1-25 (e) G2-0 (f ) G2-15 (g) G2-25

Table 3 First crack loads and failure loads

BeamLoad at rst crack Pcr (kN) Failure load Pu (kN)

PcrPu

Left midspan Right midspan Middle support Midspan Middle supportS1-15 32 32 25 1343 0238 0186G1-0 15 13 13 1156 0112 0112G1-15 11 13 13 1152 0095 0113G1-25 13 13 13 1196 0109 0109G2-0 20 20 17 1252 0160 0136G2-15 17 17 17 1249 0136 0136G2-25 17 17 15 1378 0123 0109


GFRP reinforcement with concrete Also beam S1-15 hadthe smallest crack width in relation to the beams with GFRPreinforcement because of the significantly larger modulus ofelasticity of the steel reinforcement compared to the GFRPreinforcement However at higher load levels when the steelreinforcement yielded the maximum crack widths weregreater in the beam S1-15 than in the beams with GFRPreinforcement

Within the midspan of the beams of Series 1 with GFRPreinforcement the development of the maximum crackwidth was much equalized until loads that corresponded to40 of the failure load regardless of the fact that re-inforcement in the beam G1-0 had less stiffness(EA 13558 kN) in relation to reinforcement of the beamsG1-15 (EA 17415 kN) and G1-25 (EA 18867 kN) At the

failure the smallest maximum crack width in the midspanwas in the beam G1-25 with the highest amount of re-inforcement in the midspan At the support the influence ofstiffness of reinforcement was evident meaning that lessaxial stiffness of reinforcement at the middle support gen-erated larger crack widths in the beams +erefore for themost of different load levels the largest crack width was inthe beam G1-25 (EA 11153 kN) and the smallest was in thebeam G1-0 (EA 20318 kN)

Within the beams of Series 2 the axial stiffness of theGFRP reinforcement was clearly expressed on the maxi-mum cracks width both in the midspan and at the middlesupport For initial load levels the maximum crack widthin the midspan was almost uniform for all beams of Series2 For higher load levels the beam G2-25 exhibited thesmallest maximum crack width with the largest re-inforcement axial stiffness in the midspan (EA 15930 kN)and the beam G2-0 exhibited the largest maximum crackwidth with the smallest reinforcement axial stiffness in themidspan (EA 10734 kN) At the middle support beamG2-25 exhibited the largest maximum crack width withthe smallest reinforcement axial stiffness at the support(EA 8033 kN) compared to the beams G2-0 (EA

12482 kN) and G2-15 (EA 17654 kN)

44 Deflection Response In Figure 8 the diagrams of load-average deflection for both spans are given for all beams It isdistinctive for all beams that they showed linear behavior ofload-deflection before cracking Right after the first crackappeared in the beams with GFRP reinforcement a signifi-cant decrease of section stiffness occurred which is the resultof low modulus of elasticity of GFRP reinforcement and itwas manifested by a sudden change in the rate of load-deflection curves +e beams of Series 1 recorded a higherincrease of deflection right before the appearance of crackscompared to the beams of Series 2

Within the beams of Series 1 for the same load level asexpected deflections in beams with GFRP reinforcementwere much higher than in the beam S1-15 with steel re-inforcement +is is a result of larger crack widths in thebeams with GFRP reinforcement ie lower stiffness of thesection At higher load levels the largest deflection exhibitedthe beam G1-0 with the smallest stiffness of the re-inforcement in the midspan +e beams G1-15 and G1-25practically had the same average values of deflection duringthe loading which is expected due to a small difference in thestiffness of GFRP reinforcement in the beam midspan

For the beams of Series 2 it could be seen that deflectionswere fairly uniform during loading regardless of the dif-ferent values of the axial stiffness of reinforcement in thecritical sections At higher load levels the largest deflec-tion was exhibited by beam G2-15 (EA 14182 kN) andthe smallest deflection was exhibited by beam G2-25(EA 15390 kN) Nonetheless the beam G2-0 had signifi-cantly lower stiffness in the midspan (EA 10734 kN)compared to beam G2-15 and also had a lower deflection+is is a consequence of a significant ldquooppositerdquo momentredistribution from the midspan to the middle support

0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)

Maximum crack width at midspan (mm)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 6 Load-maximum crack width relationship at the midspanfor tested beams

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6Maximum crack width at middle support (mm)

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 7 Load-maximum crack width relationship at the middlesupport for tested beams


(Section 45) ie significantly lower moment in the midspanof the beamG2-0 It can therefore be concluded that the axialstiffness of the reinforcement in the midspan is of crucialimportance not only for the deflection of the beam but alsofor the axial stiffness ratio of the tensile reinforcement at themiddle support and in the midspan

45 Moment Redistribution Measuring of reactions servedfor determining internal forces ie bending momentsalong the continuous beam based on which the process ofmoment redistribution was analyzed Moment re-distribution was obtained by comparing actual bendingmoments and those obtained by elastic analysis In Table 4bending moments at failure and bending moments obtainedby elastic analysis are given similar to the percentage ofachieved moment redistribution at failure for all beams

Development of bending moments and moment re-distribution at the middle support for all beams dependingon the applied load are given in Figures 9 and 10 re-spectively Upturns ie changes in trends are evident indiagrams of moments and moment redistribution at lowerload levels especially for the beams of Series 1 at appearanceof first cracks in the midspan and at the middle support+iscould be explained by a sudden change in stiffness of criticalsectionsmdashfrom uncracked into cracked section (significantwidth and height of the cracks) After stabilization of thecrack pattern at higher levels of loads upturns in diagramsof moment redistribution are less expressed

Within the beam G1-0 that was designed based onelastic analysis ldquooppositerdquo moment redistribution is noticedwith a highest value of 23 after appearance of first cracksAt failure this value is significantly decreased and it was05 which totally corresponded to designed valuesldquoOppositerdquo redistribution caused the ratio between axialstiffness of tensile GFRP reinforcement between the middlesupport and midspan that was numbered 15 +e beam G1-15 was designed to achieve redistribution of 15 and it hadthe relation of axial stiffness of tensile reinforcement in the

midspan and at the middle support of 138 At failuremoment redistribution at the middle support was signifi-cantly increased and it was numbered 27 Within thebeam G1-25 designed to achieve moment redistribution of25 a failure moment redistribution of 185 was achievedeven though the relation between axial stiffness of re-inforcement in critical sections was numbered 169 For themost levels during loading the beam G1-25 had momentredistribution higher than 20 (Figure 10)

Within the beam S1-15 with steel reinforcement mo-ment redistribution was expected after yielding of re-inforcement at the support Nevertheless in the diagram ofFigure 9 it could be seen that after appearance of cracksgrowth of moment at the support was higher than thegrowth of moment in the midspan+e reason for this fact isthat after yielding of reinforcement at the support yieldingof reinforcement in the midspan also appeared +en muchhigher strains at the middle support than those in themidspan probably lead to the strengthening of re-inforcement at the support which provided acceptance ofadditional moment Because of that moment redistributionwas achieved by only 3 In the diagram of Figure 10 itcould be noticed that moment redistribution in the beam S1-15 was almost always lower than that in the beamG1-15+ereason for this behaviour of the beam S1-15 compared to thebeam G1-15 was the relation between stiffness of criticalsections Moreover a much lower modulus of elasticity ofGFRP reinforcement compared to steel provides muchwider cracks in beams with GFRP reinforcement similar toa more dominant influence of reinforcement on the stiffnessof section along the continuous beam +erefore the ratiobetween stiffness of critical sections mainly depends on axialstiffness of reinforcement which provides the large ratiobetween stiffness of critical sections In this way easily couldbe seen the emphasis of elastic redistribution of internalforces in the beams with GFRP reinforcement in relation tothe beams with steel reinforcement

Within the beam G2-0 designed based on the internalforces obtained by the elastic analysis at initial load levels

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35Deflection at midspan (mm)

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 8 Load-deflection relationship at the midspan for tested beams


the increase of moment in the midspan was noticed inrelation to the moment at the middle support After theappearance of the first cracks along the beam a trend ofmoment redistribution was changed ie a significant in-crease of the hogging moment in relation to the momentobtained by the elastic analysis +is trend of moment

growth was kept to the failure of the beam +ereforeldquooppositerdquo moment redistribution happened at failure of164 which was greatly influenced by the axial stiffnessratio of reinforcement at the middle support and in themidspan which was numbered 165 Beams G2-15 and G2-25 designed to achieve moment redistribution from themiddle support into the midspan of 15 and 25 achievedhigher percentage of redistribution at failure of 185 and267 with ratio of axial stiffness of GFRP reinforcementbetween critical sections of 114 and 198 respectivelyDuring the complete process of loading beams had positivemoment redistribution which was the result of ldquoset uprdquo ofthe beams by means of adopted reinforcement ie axialstiffness of reinforcement which in the cracked section hada great contribution in the stiffness of critical sections aspreviously discussed Within the beams G2-15 and G2-25an increase in the moment redistribution at failure wasobserved probably as a result of the development of fullnonlinearity of the compressed concrete

461e Strains in Reinforcement andConcrete In Figures 11and 12 developments of the strains in tensile reinforcementand compressed concrete in the midspan and at the middlesupport against the applied load for tested beams are givenrespectively It is an evident characteristic upturn in values ofthe strains in tensile reinforcement after appearance of firstcracks in every critical section which is especially noticed inbeams of Series 1

For the beams of Series 1 at load levels after appearanceof first cracks the strains in reinforcement in the midspanand at the support were higher in beams with GFRP re-inforcement than in beam S1-15 with steel reinforcementHowever at higher load levels after yielding of steel re-inforcement strain in the beam S1-15 significantly increasedand overcame values of strains in beams with GFRP re-inforcement Comparing strains in reinforcement of thebeams with strains in GFRP reinforcement it is evident thatin the midspan strains were highest in the beam G1-0 asa result of lowest stiffness of this reinforcement while at thesupport strains were highest in the beamG1-25 especially athigher load levels

Within the beams of Series 2 quite uniform develop-ment of strains in the tensile reinforcement in the midspanregardless of the significant differences in amount ie theaxial stiffness of adopted reinforcement of beams could benoticed At higher load levels before failure strains in the

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60Moment at middle support (kNm)

Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 9 Load-moment relationship at the middle support fortested beams

0

20

40

60

80

100

120

140

ndash30 ndash20 ndash10 0 10 20 30 40Moment redistribution at middle support ()

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 10 Load-percentage of moment redistribution relationshipat the middle support for tested beams

Table 4 Moments at failure moments based on elastic analysis and achieved percentage of moment redistribution

BeamMoments at failure (kNm) Moments based on elastic

analysis (kNm) Achieved percentage of momentredistribution at failure ()

Middle support Left midspan Right midspan Middle support MidspanS1-15 451 392 399 466 388 31G1-0 403 327 339 401 334 minus05G1-15 292 388 385 400 333 269G1-25 338 382 387 415 346 185G2-0 506 312 340 434 362 minus164G2-15 353 419 383 433 361 185G2-25 350 468 457 478 398 267


midspan of the beamG2-0 were about 10 higher than thosein the beam G2-15 and in an average 5 higher compared tothe beam G2-25 At the failure strains in the beams G2-0 and G2-15 were practically identical while the largeststrains were in the beam G2-25 which reached the highestload-carrying capacity As it has been already mentionedthis could be explained by achieved moment redistributionwhich contributed that stiffness of reinforcement corre-sponded to higher bending moments Because of that lowerstrains did not correspond to higher amount of re-inforcement and vice versa Comparing the strains in thetensile reinforcement at the middle support the difference instrain values was significantly more pronounced than at themidspan +e higher strains were within the beam G2-25

and the smallest strains were within the beam G2-0 whichfully corresponded to the adopted reinforcement at themiddle support +e maximum tensile strains did not reachneither the ultimate values nor a single beam of Series 1 andSeries 2 which responded to the fact that beams weredesigned to experience concrete compression failure +elargest measured strains at the middle support were in thebeam G2-25 and amounted to 23permil which was very close tothe ultimate value of 233permil shown in Table 2

From Figures 11 and 12 it is noticed that in certaincritical sections at the midspan strain values in the com-pressed concrete of 3permil which are defined as ultimate byACI 4401R-15 [23] have been reached and exceeded bothin the beams of Series 1 and in the beams of Series 2 Forsome beams at the middle support it is also noticed thatslightly lower strain values were measured in compressedconcrete because at higher load levels higher than 70 offailure loads strains start to decrease which can beexplained by appearance of diagonal cracks near the locationof strain gauge

5 Comparison of Experimental Results withCode-Predicted Results

51 Load Capacity All beams were designed in accordancewith the ACI 4401R-15 [23] while CSA S806-12 [24] andEC2-04 [26] were used as control In designing data fromthe manufacturer for GFRP reinforcement were used so asdesigned concrete compression strength Regarding thedifference in actual and designed characteristics of materialsdifferent experimental values of failure load were obtainedCalculated failure load was obtained as load at which one ofthe critical sections reached flexural capacity ie as thelower value of load capacity in the midspan and at themiddle support In determining the calculated failure loaddesigned moment redistribution from the middle supportinto the midspan was taken into consideration In Table 5experimental failure loads are given in comparison to cal-culated failure loads in accordance with the current codesfor elements with FRP reinforcement ACI 4401R-15 [23]CSA S806-12 [24] and EC2-04 [26] for all experimentalmodels

From Table 5 it is clear that ACI 4401R-15 [23] providesa very good prediction of failure load for continuous beamswith GFRP reinforcement CSA S806-12 [24] and EC2-04[26] predict higher values of failure loads than those ob-tained by experimental tests +is happens because the ACI4401R-15 [23] suggests an ultimate strain of 30permil and theCSA S806-12 [24] and EC2-04 [26] suggest an ultimatestrain of 35permil Measured values of strains in concrete nearfailure are closer to values of 3permil which is the reason thatobtained experimental failure loads are in agreement withcalculated values in accordance with ACI 4401R-15 [23]Every beam in accordance with ACI 4401R-15 [23] reachedcalculated load capacity where for beams of Series 1 relationPexpPcal is 10ndash103 and for beams of Series 2 it is 107ndash124

Although the beams of Series 1 and Series 2 with GFRPreinforcement were designed to achieve similar failure loadssome higher values of failure loads were obtained for beams

0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)

Strain at midspan (micro strain)

Concrete Reinforcement

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 11 Load-strain relationship at the midspan for testedbeams

0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)

Strain at middle support (micro strain)

ReinforcementConcrete

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25

Figure 12 Load-strain relationship at themiddle support for testedbeams


of Series 2 +e reason for this phenomenon could be thesliding of GFRP reinforcement and surrounding concrete inthe beams of Series 1 Reducing the amount of GFRP re-inforcement at the middle support and increase in themidspan of continuous beams as a result of designedmoment redistribution did not have influence on decreaseof load capacity of continuous beams Moreover the beamsG1-25 and G2-25 with the designed moment redistributionof 25 achieved higher load capacity compared to thebeams with a designed moment redistribution of 0 and15 for 5 and 10 respectively

52 Load-Deflection Response In the background of thispaper it is stated that until now as a result of a number ofresearch studies on investigation of behavior of simplebeams with FRP reinforcement a number of expressions fordetermining deflection-load response is suggested Forcalculation of deflection of continuous beams loaded byconcentrated forces at the middle of the span the followingequation obtained by elastic analysis is used

Δ 7768

middotPL3

EcIe (1)

where stiffness EcIe is used and Ie represents the effectivemoment of inertia of the considered section Effectivemoment of inertia Ie is calculated at both critical sections asfollows

Ie 085Iem + 015Iec (2)

where Iem and Iec are the effective moment of inertia at themidspan and at the middle support respectively

ACI 4401R-15 [23] suggests an equation for de-termining effective moment of inertia based on researchstudies made by Bischoff and Gross [9] with a remark that itcould also be used with a great degree of reliability forelements with steel reinforcement and for elements with FRPreinforcement without empirical parameters

Ie Icr

1minus c middot McrMa( 11138572

middot 1minus IcrIg1113872 1113873 (3)

where c is the integration factor that influences stiffnessvariation along elements and for the beams loaded byconcentrated forces it is calculated from the followingexpression

c 3minus 2 middotMcr

Ma1113888 1113889 (4)

Calculation of deflection in accordance with CSA S806-12 [24] is based on relation to the moment-curvature alongthe span For calculation of deflection of continuous beamson two spans loaded by concentrated forces in the middle ofthe spans the following expression can be used

Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)

Habeeb and Ashour [15] investigated behavior of con-tinuous beams with GFRP reinforcement and they sug-gested modification of expression for calculation ofdeflection of continuous beams ie effective moment ofinertia that is given in ACI 4401R-06 [28]

Ie Mcr

Ma1113888 1113889

3

middot βd middot Ig + 1minusMcr

Ma1113888 1113889

3⎛⎝ ⎞⎠ middot Icr middot cG le Ig (6)

where the factor βd reduces tension stiffening for elementswith FRP reinforcement and it is given as follows

βd 15ρfρfble 10 (7)

and where cG 06 is a reduction factor and it is introducedinto calculation for the condition after the appearance ofcracks because it is concluded that modified Bransonrsquosequation underestimates deflections for higher load levels

Kara and Ashour [19] concluded based on previousresearch studies on continuous beams with FRP re-inforcement [1 15 16] that current codes underestimatedeflections of continuous beams due to appearance of widecracks above the middle support that influence a significantdecrease of effective stiffness of the section Modified stiff-ness of the section in the midspan of continuous beamsthrough effective moment of inertia is suggested

Ie Icr middotα

1minus 05 middot (1minus α) middot McrMser( 1113857 (8)

where α is the reduction factor for beams with GFRP andAFRP reinforcement given by the following expression

α 065 middot 07 + 036 middotEf

Esmiddotρfρfb

1113888 1113889le 065 (9)

Table 5 Experimental and calculated failure loads for tested beams

BeamFailure load-load-carrying capacity (kN) PexpPcal

Experiment ACI CSA EC2 ExpACI ExpCSA ExpEC2S1-15 1343 901 888 901 149 151 149G1-0 1156 1154 1263 1413 100 092 082G1-15 1152 1118 1230 1370 103 094 084G1-25 1196 1174 1286 1438 102 093 083G2-0 1252 1136 1280 1452 110 098 086G2-15 1249 1172 1317 1498 107 095 083G2-25 1378 1108 1252 1417 124 110 097


Ju et al [11] proposed a semiempirical model for de-termining the effective moment of inertia which is based onthe modification of the Bransonrsquos equation following theapproach of Toutanji and Saffi [7] A nonlinear parameter K

is introduced which reduces the effective moment of inertiaat higher load levels +e equations are proposed as follows

Ie Mcr

Ma1113888 1113889

m

middot Ig + 1minusMcr

Ma1113888 1113889

m

minusK1113888 1113889 middot Icr le Ig

m 6minus 13 middot ρfEf

Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)

Load-deflection diagrams obtained by calculationaccording to expression (1) using effective moment ofinertia according to ACI 4401R-15 [23] CSA S806-12[24] Ju et al [11] Habeeb and Ashour [15] and Kara andAshour [19] are compared to experimental results inFigure 13 for all beams Since the cracking moment Mcr iskey to the accuracy of the deflection calculation the ex-perimental values were used for all models in order toeliminate its influence on the characteristics of the curveIn accordance with ACI 4401R-15 [23] CSA S806-12[24] and Ju et al [11] for the beams of Series 1 al-ready at initial load levels deflections obtained by theexperiment are higher than calculated deflections and forthe beams of Series 2 there is a matching for experimentaland calculated diagrams only for the loads that corre-spond to 35ndash40 of the failure load For higher load levelsthe values obtained by the experiment are higher thancalculated +e suggested model for deflection calculationaccording to Habeeb and Ashour [15] shows betteragreement with experimental results At loads near fail-ure exceptions occur primarily due to additional fall ofthe deflection-load curve obtained by the experimentwhen it comes to full development of nonlinearity ofconcrete Kara and Ashourrsquos model for deflection calcu-lation [19] for continuous beams with GFRP re-inforcement overestimates deflections especially for lowerload levels for all beams

In order to overcome stated shortcomings of the pre-vious models a modified model for calculation of deflectionis proposed +e model is based on Bransonrsquos equation usedin ACI 4401R-06 [28] introducing a coefficient with a valueof 07 which reduces the effective moment of inertia after theappearance of cracks in analogy with Habeeb and Ashourrsquosmodel [15] and a nonlinear parameter K proposed by Juet al [11] which additionally reduces the effective momentof inertia at higher load levels

Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3

minusK⎛⎝ ⎞⎠ middot Icr middot 07le Ig

(11)

+e very good match of the proposed model and ex-perimental results was shown both at lower and at higher

load levels +e exception occurs in the beams G1-15 andG1-25 at loads immediately after cracking where a largeincrease in deflection happened which indicates poor bondstrength between GFRP bars and concrete in these beams Inparticular it is noted that the proposed model using thecoefficient K defined by Ju et al [11] describes good de-velopment of deflection for higher load levels close to failurewhen it comes to full development of nonlinearity of con-crete and an additional drop in the slope of the deflection-load curve Further experimental testing would be requiredto verify the proposed model

6 Conclusions

+e subject of the experimental research shown in thispaper is consideration of six continuous beams reinforcedwith GFRP reinforcement loaded by concentrated forces inthe middle of the span until failure for different ar-rangements of reinforcement along the beam Results ofexperimental research studies are compared to provisionsof current regulations and codes by means of load capacityand load-deflection response Based on these researchresults following conclusions could be made

(i) Continuous beams with GFRP reinforcement havethe ability of moment redistribution in relation tomoments obtained by linear elastic analysis afterappearance of first cracks in concrete Values ofmoment redistribution dominantly depend onstiffness of critical sections at the support and in themidspan which primarily due to wide and deepcracks come to relation of axial stiffness of GFRPreinforcement in critical sections Elastic re-distribution of internal forces is based on this

(ii) Continuous beams with GFRP reinforcement showsignificant warnings before failure in terms of largedeflections and wide and deep cracks It is speciallydefined additional curving of the deflection diagramat loads close to failure as a result of the devel-opment of full nonlinearity of the compressedconcrete

(iii) Reducing the amount of GFRP reinforcement at themiddle support and increase of amount of GFRPreinforcement in the midspan of continuous beamsas a result of designed moment redistribution inrelation to the moments obtained by elastic analysisdo not have negative influence on load capacity ofcontinuous beams and mainly influence the de-crease of deflection By increasing the designedmoment redistribution to 25 the load-carryingcapacity increases by 5 to 10 in the beams withGFRP reinforcement

(iv) Wide and deep cracks that are formed in criticalsections of continuous beams with wrapped GFRPbars with the unsaturated polyester matrix ina smaller number compared to beams reinforced bysteel reinforcement or GFRP bars with rebars andepoxy matrix point out at poor bond strength


0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)

Midspan deflection (mm)

G1-0

ExperimentACI-15CSA-12Ju-16

Habeeb and Ashour-08Kara and Ashour-12Proposed model

(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)

Figure 13 Experimental and predicted deflection for tested beams (a) G1-0 (b) G2-0 (c) G1-15 (d) G2-15 (e) G1-25 (f ) G2-25


between GFRP reinforcement and surroundingconcrete On the contrary beams with GFRP re-inforcement with rebars and epoxy matrix basedon development of the cracks of the beams indi-cate very good bond strength between GFRP re-inforcement and concrete

(v) ACI 4401R-15 [23] reasonably predicts failureload for continuous beams with GFRP re-inforcement for overreinforced sections CSAS806-12 [24] and EC2-04 [26] predict quite highervalues of failure loads than those obtained by theexperiment

(vi) Current codes ACI 4401R-15 [23] and CSA S806-12 [24] underestimate deflection of continuousbeams with GFRP reinforcement for higher loadlevels Habeeb and Ashourrsquos suggested model [15]shows better agreement to experimental results+e proposed model for calculation of deflection ofcontinuous beams with GFRP reinforcementshows very good prediction to experimental re-sults during the entire loading process

Nomenclature

P Applied load at the midpoint of each span (kN)Pu Load at failure (kN)Pcr Load at the first crack (kN)Pexp Experimental failure load (kN)Pcal Calculated failure load (kN)L Beam span (mm)Lg Uncracked length at half of the beam (mm)Ig Moment of inertia of the gross section (mm4)Icr Cracked moment of inertia (mm4)Ie Effective moment of inertia (mm4)Mcr Cracking moment (kNm)Ma Applied moment (kNm)Af Cross-sectional area of tensile GFRP reinforcement

(mm2)Ef Modulus of elasticity of GFRP reinforcement (MPa)Es Modulus of elasticity of steel reinforcement (MPa)Ec Modulus of elasticity of concrete (MPa)ff Tensile strength of GFRP reinforcement (MPa)fy Yield strength of steel reinforcement (MPa)fc Concrete compressive strength of cylinder (MPa)εfu Ultimate strain of GFRP reinforcementεy Yield strain of steel reinforcementεcu Ultimate strain of concreteρf GFRP reinforcement ratioρfb Balanced GFRP reinforcement ratiocG Proposed reduction factor used in the calculation of

the effective moment of inertia for the continuousbeam with GFRP reinforcement

α Proposed reduction factor used in the calculation ofthe effective moment of inertia for the continuousbeam with FRP reinforcement

βd Reduction factor used in the calculation of theeffective moment of inertia

Δ Deflection at the midspan of the beam (mm)

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors would like to express their gratitude to theEngineering Chamber of Montenegro for the financialsupport and China Road and Bridge Corporation Mon-tenegro Branch for the donation of GFRP reinforcement forthis research and local construction companies fromMontenegro for the donation of concrete admixtures Alsothe first author is grateful for the technical help of theLaboratory of the Faculty of Civil Engineering at the Uni-versity of Montenegro

References

[1] M El-Mogy A El-Ragaby and E El-Salakawy ldquoFlexuralbehavior of continuous FRP-reinforced concrete beamsrdquoJournal of Composites Construction vol 14 no 6 pp 669ndash680 2010

[2] R H Scott and R T Whittle ldquoMoment redistribution effectsin beamsrdquo Magazine of Concrete Research vol 57 no 1pp 9ndash20 2005

[3] M El-Mogy A El-Ragaby and E El-Salakawy ldquoEffect oftransverse reinforcement on the flexural behavior of con-tinuous concrete beams reinforced with FRPrdquo Journal ofComposites for Construction vol 15 no 5 pp 672ndash681 2011

[4] D Mostofinejad Ductility and moment redistribution incontinuous FRP reinforced concrete beams PhD thesis De-partment of Civil and Environmental Engineering CarletonUniversity Ottawa ON Canada 1997

[5] H Wang and A Belarbi ldquoDuctility characteristics of fiber-reinforced-concrete beams reinforced with FRP rebarsrdquoConstruction and Building Materials vol 25 no 5pp 2391ndash2401 2011

[6] M M Rafi A Nadjai F Ali and D Talamona ldquoAspects ofbehavior of CFRP reinforced concrete beams in bendingrdquoConstruction and Building Materials vol 22 no 3 pp 277ndash285 2008

[7] H A Toutanji and M Saafi ldquoFlexural behaviour of concretebeams reinforced with glass fiber-reinforced polymer GFRPbarsrdquoACI Structural Journal vol 97 no 5 pp 712ndash719 2000

[8] J R Yost S P Gross and D W Dinehart ldquoEffective momentof inertia for glass fiber-reinforced polymer-reinforced con-crete beamsrdquo ACI Structural Journal vol 100 no 6pp 732ndash739 2003

[9] P H Bischoff and S P Gross ldquoEquivalent moment of inertiabased on integration of curvaturerdquo Journal of Composites forConstruction vol 15 no 3 pp 263ndash273 2011

[10] S R Mousavi and M R Esfahani ldquoEffective moment ofinertia prediction of FRP-reinforced concrete beams based onexperimental resultsrdquo Journal of Composites Constructionvol 16 no 5 pp 490ndash498 2012


[11] M Ju H Oh J Lim and J Sim ldquoA modified model fordeflection calculation of reinforced concrete beam with de-formed GFRP rebarrdquo International Journal of Polymer Sci-ence vol 2016 Article ID 2485825 10 pages 2016

[12] C Barris L Torres A Turon M Baena and A Catalan ldquoAnexperimental study of the flexural behaviour of GFRP RCbeams and comparison with prediction modelsrdquo CompositeStructures vol 91 no 3 pp 286ndash295 2009

[13] C Barris L Torres J Comas and C Mias ldquoCracking anddeflections in GFRP RC beams an experimental studyrdquoComposites Part B Engineering vol 55 pp 580ndash590 2013

[14] N F Grace A K Soliman G Abdel-Sayed and K R SalehldquoBehavior and ductility of simple and continuous FRPreinforced beamsrdquo Journal of Composites for Constructionvol 2 no 4 pp 186ndash194 1998

[15] M N Habeeb and A F Ashour ldquoFlexural behavior ofcontinuous GFRP reinforced concrete beamsrdquo Journal ofComposites Construction vol 12 no 2 pp 115ndash124 2008

[16] A F Ashour and M N Habeeb ldquoContinuous concrete beamsreinforced with CFRP barsrdquo Proceedings of the Institution ofCivil Engineers-Structures and Buildings vol 161 no 6pp 349ndash357 2008

[17] B Matos J R Correia L M S Castro and P FranccedilaldquoStructural response of hyperstatic concrete beams reinforcedwith GFRP bars effect of increasing concrete confinementrdquoComposite Structures vol 94 no 3 pp 1200ndash1210 2012

[18] P Santos G Laranja P M Franca and J R Correia ldquoDuctilityand moment redistribution capacity of multi-span T-sectionconcrete beams reinforced with GFRP barsrdquo Construction andBuilding Materials vol 49 pp 949ndash961 2013

[19] I F Kara and A F Ashour ldquoFlexural performance of FRPreinforced concrete beamsrdquo Composite Structures vol 94no 5 pp 1616ndash1625 2012

[20] I F Kara and A F Ashour ldquoMoment redistribution incontinuous FRP reinforced concrete beamsrdquo Construstionand Building Materials vol 49 pp 939ndash948 2013

[21] T Lou S M R Lopes and A V Lopes ldquoNeutral axis depthand moment redistribution in FRP and steel reinforcedconcrete continuous beamsrdquo Composites Part B Engineeringvol 70 pp 44ndash52 2015

[22] K Mahmoud and E El-Salakawy ldquoShear strength of GFRP-reinforced concrete continuous beams with minimumtransverse reinforcementrdquo Journal of Composites for Con-struction vol 18 no 1 article 4013018 2014

[23] ACI Committee 440 Guide for the Design and Construction ofStructural Concrete Reinforced with Fiber-Reinforced Polymer(FRP) Bars (ACI 4401R-15) American Concrete InstituteFarmington Hills MI USA 2015

[24] CSA S806-12 Design and Construction of Buildings Compo-nents with Fiber-Reinforced Polymers Canadian StandardsAssociation (CSA) Toronto ON Canada 2012

[25] CNR-DT 2032006 Guide for the Design and Construction ofConcrete Structures Reinforced with Fiber-Reinforced PolymerBars National Research Council Rome Italy 2006

[26] EN 1992-1-1 Eurocode 2 Design of Concrete StructuresGeneral Rules and Rules for Buildings Part 1-1 CEN BrusselsBelgium 2004

[27] ACI Committee 440 Guide Test Methods for Fiber-ReinforcedPolymers (FRPs) for Reinforcing or Strengthening ConcreteStructures (ACI 4403R-12) American Concrete InstituteFarmington Hills MI USA 2012

[28] ACI Committee 440 Guide for the Design and Construction ofStructural Concrete Reinforced with FRP Bars (ACI 4401R-06)American Concrete Institute FarmingtonHills MI USA 2006


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contribution of the elastic redistribution in continuous RCbeams with steel reinforcement [2] it is expected thatcontinuous beams with FRP reinforcement give certainability to redistribute the internal force Redistribution ofinternal forces is expected as the result of cracks develop-ment and adopted reinforcement within them [1 3] In otherwords one of the basic characteristics of ductility is con-sidered ie variation of stiffness without loss of capacity ofthe section [4]

2 Background

So far thorough theoretical and experimental researchstudies have been carried out on simple supported beamswith FRP reinforcement in order to evaluate behaviorregarding failure modes load-carrying capacity de-flection and cracks [5ndash13] +erefore provisions of certaincodes are based on conclusions given on simple supportedbeams A great number of formulas and equations aresuggested to determine response of elements with FRPreinforcement at service load conditions especially whendeflection is concerned (Toutanji and Saafi [7] Yost et al[8] Bischoff and Gross [9] Mousavi and Esfahani [10] andJu et al [11])

Certain experimental and theoretical research studieswere also carried out on continuous beams with FRP re-inforcement [1 3 4 14ndash22] but not as much as they werecarried out on simple beams Mostofinejad [4] carried outresearch studies on two continuous beams with steel re-inforcement and eight underreinforced and overreinforcedcontinuous beams with CFRP reinforcement+ese researchstudies showed that moment redistribution in continuousbeams with FRP reinforcement is possible although in lowerdegree than in steel-reinforced beams Overreinforcedbeams with FRP reinforcement fulfill requirements of ser-viceability while underreinforced beams designed to ex-perience failure by FRP bars usually do not fulfill theseconditions Moreover overreinforced continuous beamsshow significant deformations before failure which wasdetermined as a distinctive way of ductility Grace et al [14]researched behavior and ductility of continuous beams Tcross-section reinforced by different types of longitudinaland transverse FRP reinforcements (GFRP and CFRP) Itwas indicated on different failure modes and beam ductilitywith FRP reinforcement in relation to beams with steelreinforcement It was also concluded that the use of GFRPstirrups increases shear deformations As a result of thattotal deformations increase in the midspan of continuousbeams El-Mogy et al [1] conducted the research on fourcontinuous beams of rectangular cross-section with GFRPCFRP and steel reinforcement by varying the ratio oflongitudinal reinforcement in the midspan and at the middlesupport It was concluded that continuous beams with FRPreinforcement are capable of redistributing the momentsfrommiddle support towards the midspan of 23 in relationto elastic analysis similar to the fact that they do not causeadversely effects concerning the beam characteristics nei-ther at service loads nor at failure loads Moreover it wasconcluded that the increase of reinforcement in the midspan

of continuous beams in relation to section at the middlesupport has positive effects on the increase of load capac-ity of beams decrease of deflections and postponing ofpropagation of cracks in the beamsrsquo midspan Habeeb andAshour [15] noticed signs of moment redistribution withinoverreinforced beams in the bottom zone in the midspanduring the experimental research studies on three contin-uous beams with different combinations of GFRP longitu-dinal reinforcement in the midspan and at the middlesupport As a key factor of increasing the load capacity andlimitation of deflection and propagation of cracks the in-crease of the reinforcement in the bottom zone of themidspan was noticed In the scope of same experimentalresearch studies Ashour and Habeeb [16] conducted theresearch on three continuous beams with CFRP re-inforcement designed with different configurations of re-inforcement along the beam so as to experience the failureby CFRP bars Intolerant wide cracks at the middle supportwere noticed in all beams as a result of debonding of CFRPbars from concrete It was concluded that the basic pa-rameter of increasing the load capacity of continuous beamswas the amount of CFRP reinforcement in the bottom zonein the midspan Other recent research studies on continuousbeams [3 17 18 20] also pointed out to the importance ofincreasing the reinforcement in the bottom zone of the beammidspan as a result of redistribution of moment over themiddle support

+e approach that in continuous beams reinforced withFRP reinforcement moment redistribution in critical sec-tions is not allowed could be conservative [21] +erefore itneeds additional research studies For this purpose it isnecessary to define more clearly and precisely the influenceof ratio of longitudinal reinforcement at the midspan and atthe middle support on behavior of continuous beams withFRP reinforcement+emain aim of these research studies isconsideration of behavior of continuous beams reinforcedwith GFRP reinforcement during loading until failure withdifferent configurations of reinforcement along the beam+us in these experimental research studies for the samedesign failure load for every type of GFRP reinforcementthree models with different configurations of reinforcementalong the beam were used Experimental results are dis-cussed and evaluated based on failure modes crackingdeflection moment redistribution and strains in concreteand reinforcement and compared to code predictions re-garding the load-carrying capacity and deflection Based onexperimental results a modified model for better predictionof deflection of continuous beams with GFRP reinforcementis proposed

After a literature review it is concluded that in very fewnumber of experimental research studies on continuousbeams with longitudinal FRP reinforcement FRP re-inforcement for stirrups was used [3 14 22] In the re-search studies carried out on the beams with FRPreinforcement steel reinforcement for stirrups was mainlyused In that case a problem with corrosion of reinforcedconcrete elements is still present especially in aggressiveenvironments+e problem increases when it is known thatthe effects of FRP stirrups and steel stirrups on behavior of







31 Materials









120

120

G1-0 G1-15 G1-25 G2-0 G2-15 G2-25

1850 1850

3940



2oslash10

1oslash10

2oslash9 2oslash9

3oslash91oslash14

1oslash14

2oslash10


1oslash12

1oslash12

1oslash10 1oslash12

4oslash12


2oslash10

1oslash10

oslash8612


2oslash12

925 925 925 925 120

120

150

250



Beam Day oftesting




EA(kN)


reinforcementEA(kN)


ρf()

ρfb() ρfρfb

ρf()

ρfb() ρfρfb





oslash8











Steel-Oslash10 785 6395 5096 188064 27a


1045

SG-10

SG-9

120 120


4625 4625 4625 4625 4625 4625 4625 120

675 675 675 675250 250 250 250

SG-8SG-6

UG-6SG-6

SG-7

P P

P P

SG-14

SG-4

SG-4

UG-4

SG-1SG-2

SG-1

UG-1

SG-2

UG-2

SG-3

SG-3

UG-3

SG-15

SG-5

UG-5SG-5

SG-11SG-12

SG-13

1045

1045 1045

725

925 925

3940

200 200 725






4 Test Results











S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)




PcrPu







12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







31 Materials









120

120

G1-0 G1-15 G1-25 G2-0 G2-15 G2-25

1850 1850

3940



2oslash10

1oslash10

2oslash9 2oslash9

3oslash91oslash14

1oslash14

2oslash10


1oslash12

1oslash12

1oslash10 1oslash12

4oslash12


2oslash10

1oslash10

oslash8612


2oslash12

925 925 925 925 120

120

150

250



Beam Day oftesting




EA(kN)


reinforcementEA(kN)


ρf()

ρfb() ρfρfb

ρf()

ρfb() ρfρfb





oslash8











Steel-Oslash10 785 6395 5096 188064 27a


1045

SG-10

SG-9

120 120


4625 4625 4625 4625 4625 4625 4625 120

675 675 675 675250 250 250 250

SG-8SG-6

UG-6SG-6

SG-7

P P

P P

SG-14

SG-4

SG-4

UG-4

SG-1SG-2

SG-1

UG-1

SG-2

UG-2

SG-3

SG-3

UG-3

SG-15

SG-5

UG-5SG-5

SG-11SG-12

SG-13

1045

1045 1045

725

925 925

3940

200 200 725






4 Test Results











S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)




PcrPu







12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





120

120

G1-0 G1-15 G1-25 G2-0 G2-15 G2-25

1850 1850

3940



2oslash10

1oslash10

2oslash9 2oslash9

3oslash91oslash14

1oslash14

2oslash10


1oslash12

1oslash12

1oslash10 1oslash12

4oslash12


2oslash10

1oslash10

oslash8612


2oslash12

925 925 925 925 120

120

150

250



Beam Day oftesting




EA(kN)


reinforcementEA(kN)


ρf()

ρfb() ρfρfb

ρf()

ρfb() ρfρfb





oslash8











Steel-Oslash10 785 6395 5096 188064 27a


1045

SG-10

SG-9

120 120


4625 4625 4625 4625 4625 4625 4625 120

675 675 675 675250 250 250 250

SG-8SG-6

UG-6SG-6

SG-7

P P

P P

SG-14

SG-4

SG-4

UG-4

SG-1SG-2

SG-1

UG-1

SG-2

UG-2

SG-3

SG-3

UG-3

SG-15

SG-5

UG-5SG-5

SG-11SG-12

SG-13

1045

1045 1045

725

925 925

3940

200 200 725






4 Test Results











S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)




PcrPu







12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Steel-Oslash10 785 6395 5096 188064 27a


1045

SG-10

SG-9

120 120


4625 4625 4625 4625 4625 4625 4625 120

675 675 675 675250 250 250 250

SG-8SG-6

UG-6SG-6

SG-7

P P

P P

SG-14

SG-4

SG-4

UG-4

SG-1SG-2

SG-1

UG-1

SG-2

UG-2

SG-3

SG-3

UG-3

SG-15

SG-5

UG-5SG-5

SG-11SG-12

SG-13

1045

1045 1045

725

925 925

3940

200 200 725






4 Test Results











S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)




PcrPu







12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



4 Test Results











S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)




PcrPu







12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





S1-15

(a)

G1-0

(b)

G1-15

(c)

G1-25

(d)

G2-0

(e)

G2-15

(f )

G2-25

(g)




PcrPu







12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






12482 kN) and G2-15 (EA 17654 kN)




0

20

40

60

80

100

120

140

0 05 1 15 2 25 3 35

Load

P (k

N)


S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25










0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25








0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







0

20

40

60

80

100

120

140


Elastic analysis

Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140


Load

P (k

N)

S1-15G1-0G1-15G1-25

G2-0G2-15G2-25














0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









0

20

40

60

80

100

120

140ndash4

000

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25


0

20

40

60

80

100

120

140

ndash400

0

ndash200

0 0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

2000

0

2200

0

2400

0

Load

P (k

N)



S1-15G1-0G1-15G1-25

G2-0G2-15G2-25





Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Δ 7768

middotPL3

EcIe (1)


Ie 085Iem + 015Iec (2)



Ie Icr





Ma1113888 1113889 (4)


Δmax PL3

48EcIcr

516minus158

1minusIcr

Ig1113888 1113889 middot

Lg

L1113888 1113889

3⎛⎝ ⎞⎠ (5)


Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889






Ie Icr middotα




Esmiddotρfρfb

1113888 1113889le 065 (9)







Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Ie Mcr

Ma1113888 1113889

m


Ma1113888 1113889

m



Es

K 111

middotMcr

Ma1113888 11138891113888 1113889

4

(10)



Ie Mcr

Ma1113888 1113889

3


Ma1113888 1113889

3


(11)



6 Conclusions







0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-0



(a)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-0



(b)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-15



(c)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G2-15



(d)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Load

P (k

N)


G1-25



(e)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Load

P (k

N)


G2-25



(f)






Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Nomenclature







Data Availability




Acknowledgments


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


experimental research of continuous concrete beams with...

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