torsionalbehaviorofhigh-strengthconcretebeamswith...

Research ArticleTorsional Behavior of High-Strength Concrete Beams withMinimum Reinforcement Ratio

Changbin Joh 1 Imjong Kwahk 2 Jungwoo Lee 2 In-Hwan Yang 3

and Byung-Suk Kim4

1Research Fellow Korea Institute of Civil Engineering and Building Technology Department of Infrastructure Safety ResearchGoyang Gyeonggi 10223 Republic of Korea2Senior Researcher Korea Institute of Civil Engineering and Building Technology Department of Infrastructure Safety ResearchGoyang Gyeonggi 10223 Republic of Korea3Professor Kunsan National University Department of Civil Engineering Kunsan Jeonbuk 54150 Republic of Korea4Senior Research Fellow Korea Institute of Civil Engineering and Building TechnologyDepartment of Infrastructure Safety Research Goyang Gyeonggi 10223 Republic of Korea

Correspondence should be addressed to Changbin Joh cjohkictrekr

Received 25 April 2018 Revised 18 September 2018 Accepted 18 October 2018 Published 17 January 2019

Academic Editor Constantin Chalioris

Copyright copy 2019 Changbin Joh 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

Although there is a growing trend to use higher strength for concrete and steel in reinforced concrete structures due to thelightness and slenderness of these members together with the simplified arrangement of their reinforcement there is still thenecessity to inspect the reduction of ductility resulting from the gain in strength Taking into account that this also concerns thedesign for torsion this study intends to investigate the regulations related to the torsional minimum reinforcement ratio in view ofthe minimum ductility requirement with focus on Eurocode 2 To that goal the relation between the torsional cracking momentand the ductile behavior is discussed for the beam reinforced with the minimum torsional reinforcement ratio to examine theeventual properness of the minimum torsional reinforcement ratio recommended by Eurocode 2 Moreover a pure torsion test isperformed on 18 beams made of 80MPa concrete reinforced by high-strength bars with rectangular section and various testvariables involving the minimum torsional reinforcement ratio the transverse-to-longitudinal reinforcement ratio and the totalreinforcement ratio As a result for the high-strength concrete beams the minimum torsional reinforcement ratio recommendedby Eurocode 2 was insufficient to prevent the sudden loss of strength after the initiation of the torsional cracking But with regardto the compatibility torsion of statically indeterminate structure the adoption of the minimum torsional reinforcement ratiorecommended by Eurocode 2 might secure enough deformability under displacement-controlled mode to allow the redistributionof the torsional moment

1 Introduction

(ere is a growing trend to use higher strength for concreteand steel in reinforced concrete structures (e near futurewill see wider application of members applying concretewith the compressive strength higher than 80MPa andreinforced by steel with the yield strength of 600MPa (isnew popularity is due to the lightness and slenderness ofthese members together with the simplified arrangement oftheir reinforcement However there is still the necessity to

inspect the reduction of ductility resulting from the gain instrength Need is thus to verify if the current design codesunder force are capable to control adequately the strength-ductility balance Particularly the regulations related to theminimum reinforcement ratio should be examined in viewof the minimum ductility requirement

(is also concerns the design for torsion In generalsimilar to the minimum reinforcement for shear and flexurethe minimum torsional reinforcement intends to provide themember with sufficient postcracking torsional resistance

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 1432697 11 pageshttpsdoiorg10115520191432697

(is means controlling the crack width and securing enoughductility to prevent sudden loss of the torsional strength aftercracking Numerous researchers however already pointedout the issues resulting from the behavioral change broughtby the increase of the strength or related to the minimumtorsional reinforcement ratio recommended by ACI 318-14Code or Eurocode 2 (EC 2) [1ndash19]

Rasmussen and Baker [3] and Lopes and Bernardo [4]compared the torsional characteristics of reinforced beamsmade of normal concrete and high-strength concrete andconcluded that the use of high-strength concrete was fa-vorable with respect to the torsional stiffness and the stress inthe reinforcement but increased the brittle tendency aftercracking Chiu et al [5] performed pure torsion tests onbeams made of normal concrete and high-strength concreteto investigate the effect of the minimum reinforcement ratioin the longitudinal and transverse directions Based upontheir experimental results these authors reported that thepostcracking strength ie the ductile failure modedepended significantly on the total reinforcement ratio inthe longitudinal and transverse directions as well as the ratioof the longitudinal to the transverse reinforcement (isdependency was more marked in the high-strength concretemembers than in those made of normal concrete Ismail [6]who performed a literature review on previous torsion testsand Yoon et al [7] who studied experimentally the effect ofhigh-strength reinforcement also reported that the use ofhigh-strength concrete favored the occurrence of the brittlebehavior beyond the torsional strength

Numerical methods were also studied Rahal and Collins[8 9] successfully applied the modified compression fieldtheory to estimate the torsional behavior of concrete beamsand Chalioris [10] combined the smeared crack model andthe softened truss model to predict the initial torsionalstiffness torsional cracking moment and strength of con-crete beams Bernardo and Lopes [11] proposed a parameterfor the plastic behavior and twist capacity of high-strengthconcrete hollow beams based on the analysis of their test

In concern with the minimum torsional reinforcementratio Koutchoukali and Belarbi [12] stated that the mini-mum torsional reinforcement of ACI 318-95 Code [13] wasinadequate for high-strength concrete beams and stressedthe necessity to provide at least 20 reserve of strength aftercracking to prevent the brittle failure Both Ali and White[14] and Kim et al [15] indicated the problems of theminimum torsional reinforcement ratio and proposed newminimum reinforcement ratios enabling to maintain thepostcracking strength

Accordingly this study intends to investigate the ap-propriateness of the current design codes for torsion withfocus on EC 2 To that goal the relation between theminimum torsional reinforcement ratio and the torsionalcracking moment is analyzed theoretically and the puretorsion test is performed on beams made of 80MPa concretereinforced by high-strength reinforcement Moreover therelation between the torsional cracking moment and theductile behavior is discussed for the beam reinforced withthe minimum torsional reinforcement ratio to examine the

eventual properness of the minimum torsional re-inforcement ratio recommended by EC 2

2 Minimum Torsional Reinforcement Ratioand Torsional Cracking Moment

Since the torsional design methods of EC 2 and ACI 318-14Code provide conceptually identical minimum torsionalreinforcement this study analyzes theoretically the relationbetween the minimum torsional reinforcement and thetorsional cracking moment (Tcr) with reference to EC 2

In EC 2 the torsional load is decomposed into shearforces applied in each face of the member and design isperformed only with respect to these shear forces (ereforeρvmin can be expressed as follows in function of the tensilestrength of concrete and the yield strength of the stirrups

ρvmin Avmin

sbw 008

fck

1113968

fyv (1)

where Avmin cross-sectional area of minimum shear re-inforcement s spacing of stirrups bw width of the crosssection fck compressive strength of concrete and fyv

yield strength of shear and torsional reinforcementBesides according to the theory of the thin-walled tube

and the space truss analogy the torsional cracking strength(Tcr) and the torsional strength (Tn) can be expressed asfollows [1 20]

Tcr 2A0tft (2)

Tn 2A0Atfyv

scot θ (3)

where t effective thickness of the tube resisting to torsionA0 internal area inside the central axis of effectivethickness ft tensile strength of concrete At cross-sectional area of closed torsional stirrup and θ angle ofcrack

In Equation (2) the tensile strength of concrete can beassumed as ft 033

fck

1113968[1 20] (e beam in torsion can

be seen to be in a biaxial state under the simultaneousoccurrence of compression and tension and accordingly theconcrete tensile strength can be lowered compared to theuniaxial tension state Following Equation (2) can be re-written as

Tcr 2A0t 033

fck

1113969

1113874 1113875 (4)

Besides if ρvmin is accepted in the usual way as theminimum reinforcement ratio enabling the member tomaintain ductility without sudden loss of the torsionalstrength after cracking Tcr Tn and the following equationis obtained by equaling Equations (3) and (4)

Tcr 2A0t 033

fck

1113969

1113874 1113875 Atfyv

s2A0( 1113857cot θ (5)

If the beam is not prestressed and is reinforced equally inthe transverse and longitudinal directions the crack angle θ

2 Advances in Civil Engineering

can be assumed to be 45deg Consequently Equation (5) can berewritten as follows

Atfyv

st 033

fck

1113969

(6)

According to EC 2 (EN 1992-1-12004 632 (1)) theeffective thickness t may be taken as the total cross-sectional area (Acp bwh h height of the section) di-vided by the outer circumference of the cross section(pcp 2(bw + h)) To make the discussion as simple andpractical as possible only rectangular members are con-sidered here Considering the aspect ratio of the crosssection hbw 1sim 10 t ranges between 025bw and 045bwAccordingly the reinforcement ratio resisting to Tcr can beobtained by the following equation

ρv Av

sbw2At

sbw (0165sim 0297)

fck

1113968

fyv (7)

(is value corresponds to about 2 to 37 times theminimum reinforcement ratio given in Equation (1) assuggested by EC 2

From Equation (7) ρvfyv can be expressed as a functionof fck (is function is plotted in Figure 1 together with thevalues recommended by EC 2 ACI 318-14 CSA-04MC2010 and KCI by applying the condition Tcr Tn[21ndash24]

It appears that the minimum reinforcement ratio ρvminmust be 2 to 37 times the value required by EC 2 to satisfythe condition Tcr Tn (is indicates that the application ofthe current ρvmin recommended by the design codes presentshigh risk of strength loss to occur after the initiation oftorsional cracking

3 Torsion Test

31 Material Characteristics (e concrete used in the fab-rication of the torsional members is a high-strength concretedeveloping 80MPa class compressive strength Table 1 ar-ranges the mix composition for 1m3 In Table 1 Sa andSPB stand respectively for sand-to-aggregate ratio andsuperplasticizer-to-binder ratio OPC BS and FA designaterespectively ordinary Portland cement blast furnace slagand fly ash

Six batches of concrete with the same mix compositionwere used to fabricate 6 series of specimens (e specimenswere subjected to air-dry curing during 24 hours followed by24 hours of high-temperature steam curing at 90degC (esame curing process was applied to the cylinders used tomeasure the compressive strength and the splitting tensilestrength (Figure 2)

(e average compressive strength of each batch isarranged in Table 2 (e average of the elastic modulusmeasured on 19 cylinders is 416GPa (e average of thesplitting tensile strength measured on 28 cylinders is37MPa

Table 3 lists the measured yield strength of the re-inforcement used in the fabrication of the specimens (esevalues were reflected in the design of the specimens

Even if it is better to use rebar-like D6 (As 3163mm2)with the smallest area as possible to adjust precisely thereinforcement ratio of the specimens there was no avail-ability of bars smaller than D10 in the market and the barslisted in Table 3 were used to fabricate the specimensMoreover the SD600 D10 bar is not available in the marketand there was difficulty to secure SD500 D19 bar nor SD600D13 and D19

32 Test Variables andDetails of Specimens Table 4 arrangesthe designation and characteristics of the 18 beam membersthat were designed and fabricated in this study (esespecimens were planned to evaluate the effect of the min-imum torsional reinforcement ratio (ρvmin) specified byEC 2 transverse-to-longitudinal reinforcement ratio(ρtfyvρlfyl) total reinforcement ratio (ρt+l) and yieldstrength of the reinforcement (fyv fyl) on the torsionalbehavior Here ρt ρl and ρt+l are the volumetric ratios

All the high-strength concrete specimens present thesame rectangular cross section of 300 times 400mm for a totallength of 3m Figure 2 shows representative cross sectionand reinforcement details (e clear concrete cover is30mm and 135deg hook is used for all stirrups

(e designation of the specimens includes 5 fieldsspecifying their characteristics (e first field RA meansrectangular section A to prepare for future tests on memberswith other cross sections(e second section (SD4 SD5 andSD6) indicates the steel grade of the adopted reinforcement(SD400 SD500 and SD600) (e third field indicates theratio of the stirrup (ρv 2At(bws)) to ρvmin of EC 2 (efourth field corresponds to the transverse-to-longitudinalreinforcement ratio (ρtfyvρlfyl) (e fifth field representsthe total reinforcement ratio (ρt+l)

(e 18 specimens are classified into 6 series of 3 spec-imens reinforced with different steel grades (SD400 SD500

000

050

100

150

200

250

0 20 40 60 80 100 120

ρ vm

inlowastf yv

fck (MPa)

EN2 MC2010 Korea highway Br design codeCSA-04ACI318-14 KCI codeTn = Tcr (Assuming bw = 3t)Tn = Tcr (Assuming bw = 4t)

bw

t

Figure 1 Minimum reinforcement ratio and torsional crackingmoment

Advances in Civil Engineering 3

and SD600) Apart from the steel grade each series gathers 3similar test variables All the specimens are reinforcedtransversally by D10 stirrups Note that the third specimenin each series uses SD500 D10 instead of the nonavailableSD600 D10 and that SD600 is used only for the longitudinalreinforcement

Figure 3 shows how the specimens were designed withrespect to minimum reinforcement ratios Series 1 and 2involve the specimens designed to approach at the mostρvmin of EC 2 by applying D10 stirrups in order to examinethe behavior of the torsional members with the minimumtorsional reinforcement Since D10 stirrups are used inSeries 1 the spacing s of the stirrups was increased from theminimum of 175mm prescribed by EC 2 to 240mm to loweras possible ρt (e design also adopted values between 02and 03 for ρtfyvρlfyl and 162 for ρt+l to exceed theminimum of 1 required by ACI 318-14 Similarly to Series1 the reinforcement of Series 2 was arranged to be as close aspossible to achieve the minimum reinforcement ratio (edifference is that ρtfyvρlfyl was increased to let ρt+l be

smaller than 1 with a value of 092 (is means that themembers of Series 2 have the smallest amount ofreinforcement

Series 3 4 and 5 all with ρt 32 times ρvmin are intended toevaluate the effect of ρt+l and ρtfyvρlfyl on the torsionalbehavior (e specimens of Series 3 were reinforced withρtfyvρlfyl of Series 1 Series 4 presents ρt similar to Series 3but with increased ρtfyvρlfyl to lower ρt+l to the level ofSeries 1 within a range of 163 to 213 Series 5 isreinforced as Series 3 but with further increase of ρtfyvρlfylcompared to Series 4 so that ρt+l approaches 1

Series 6 is intended for comparing the torsional behaviorwith that of Series 5 In Series 6 ρt is set to about 5 timesρvmin and ρtfyvρlfyl is increased to minimize ρt+l rangebetween 200 and 249 so as to lower ρl

33 TestMethod Figure 4 depicts the experimental setup forthe pure torsion test (e torsional member was loadedvertically through steel beams disposed at its extremities tomake the 1600mm long part at its center be in pure torsionEach end support was hinged by two cylindrical blocks withlubricated surfaces (Figure 4) which allows not only rotationbut also longitudinal motion Loading was applied throughdisplacement control at a speed of 10mmmin (the durationof a test in average was 60 minutes) (e rotation angle wascalculated based upon the deflections measured by twodisplacement transducers (DT) disposed along the portionof the member in pure torsion

300

35

3516

5

400

165

SD500 D16 1450 = 700mm 1450 = 700mm80 + 2406 + 80 = 1600mm3000mm

35

35115 115

Figure 2 Typical reinforcement details of the specimen (RA-SD5-15-02-162)

Table 2 Compressive strength and splitting tensile strength of high-strength concrete

Number of the batchAverage compressive strength Average splitting tensile strength

Strength (MPa) Number of cylinders Strength (MPa) Number of cylinders1 800 4 35 32 728 4 38 53 737 5 32 54 847 5 37 55 831 5 39 56 900 5 40 5

Table 3 Nominal area and yield strength of steel reinforcement

Reinforcement D10 D13 D16 D19 D22Nominal area As (mm2) 7133 1267 1986 2865 3871

Yield strength fy(MPa)

SD400 4838 4741 3946 4561 4523SD500 5380 5224 5290 NA 4994SD600 NA NA 6270 NA 6309

Table 1 Mix composition for 1m3 of high-strength concrete

WB () W (kg) Sa () SPB ()Mixture (kg)

OPC BS FA Sand (sea) Sand (crushed) Aggregate 19mm SP024 164 045 130 4200 2240 560 4033 2710 8279 9101


For Series 1 and 2 the test was conducted up to therotation that gives 50 of the peak (the maximum torsionalmoment) after the peak in order to examine the post-cracking deformability of the beams (e other series weretested up to the rotation that gives 75 of the peak after thepeak

4 Test Results and Discussion

41 Cracking Pattern Figure 5 illustrates the crackingpatterns of the 6 series of specimens In order to conductobjective comparison the cracking patterns are shown forthe specimens reinforced by SD400 reinforcement Note thatthe patterns are similar for SD500 and SD600

For Series 1 and 2 with ρt close to ρvmin of EC 2(Figures 5(a) and 5(b)) the torsional strength is seen to

decrease after the initiation of the cracks (e specimens ofboth series did not show particular difference in theircracking behavior After the first cracks almost no addi-tional cracks were developed and the initial cracks in-creased to failure Consequently as theoretically implied inSection 2 this indicates that ρvmin of EC 2 cannot preventbrittle failure after cracking regardless of the satisfaction ofρt+l ge 1

For Series 3 4 and 5 in which ρt 32 times ρvmin thepostcracking torsional strengths increased and additional crackswere developed with ductile behavior (Figures 5(c)ndash5(e)) Itappears that relatively better distribution of the cracks occurredwith larger ρt+l Series 5 in Figure 5(e) exhibited ductile behaviorowing to the relatively large value of ρt 32 times ρvmin even if ρt+l(133) was smaller than 162 of Series 1

For Series 6 with the largest ρt in Figure 5(f) ρt+l (249)was smaller than 328 of Series 3 (Figure 5(c)) but thecracks were distributed more evenly to develop the betterductile behavior at the end It should be noted that theshorter spacing of stirrups (60 or 70mm) compared to theother series increased the concrete confinement and influ-enced the torsional response [25]

42 Torsion-Displacement Behavior

421 Minimum Torsional Reinforcement Ratio (ρvmin) andDeformability Figures 6(a) and 6(b) plot the relationbetween the torsion and the rotation angle for Series 1and 2 (e specimens of both series were reinforced by 13to 15 times ρvmin of EC 2 but could not resist to thetorsional cracking moment (Tcr) after cracking (isbrittle failure mode is expected in Section 2 andKoutchoukali and Belarbi [12] and Chiu et al [5] alsoreported similar brittle behaviors in the specimens with

0

05

1

15

2

25

3

35

00 10 20 30 40 50 60

Tota

l rei

nfor

cem

ent r

atio

ρt+

l (

)

Ratio of ρv = (2AtbwS) to ρvmin

Min volumetric ratioof torsional reinforcement

(ACI)

ρvmin(EC 2)

Series 2

Series 1

Series 3

Series 4

Series 6

Series 5

Figure 3 Reinforcement ratios of specimens and minimum re-inforcement requirement

Table 4 Designation and reinforcement details of specimens

Series Designation of specimenConcrete strength

Reinforcement detailsStirrup Longitudinal

fck At fyv Spacing ρt Al fyl Number of rebars ρlMPa mm2 MPa mm mm2 MPa

1RA-SD4-13-03-162

800

D10

484

240

0293D16

3958

1324RA-SD5-15-02-162 538 0293 529 1324RA-SD6-15-02-162 538 0293 627 1324

2RA-SD4-13-05-092

728484 0289 D13 474 6 0634

RA-SD5-15-05-092 538 0289 D13 522 6 0634RA-SD6-15-04-095 538 0289 D16 627 4 0662

3RA-SD4-32-03-328

737484 100 0695

D22452

82581

RA-SD5-32-03-321 538 110 0631 499 2581RA-SD6-32-02-321 538 110 0631 630 2581

4RA-SD4-32-05-213

847484 100 0702 D19 456

61433

RA-SD5-32-07-163 538 110 0638 D16 529 0993RA-SD6-32-06-163 538 110 0638 D16 627 0993

5RA-SD4-32-11-133

831484 100 0695 D13 474 6 0634

RA-SD5-32-10-126 538 110 0631 D13 522 6 0634RA-SD6-32-08-126 538 110 0631 D16 627 4 0662

6RA-SD4-54-11-249

900484 60 1700

D16395 8 1324

RA-SD5-51-10-200 538 70 1003 529 6 0993RA-SD6-51-09-200 538 70 1003 627 6 0993


Load cell

DTs

200mm

200mm

330mm 300mm

HingesFree to rotate and move in longitudinal

direction

Testbeam

Figure 4 Setup of the torsion test

(a)

(b)

(c)

(d)

(e)

(f )

Figure 5 Cracking patterns of high-strength beams reinforced by SD400 bars (a) Series 1 RA-SD4-13-03-162 (b) Series 2 RA-SD4-13-05-092 (c) Series 3 RA-SD4-32-03-328 (d) Series 4 RA-SD4-32-05-213 (e) Series 5 RA-SD4-32-11-133 (f ) Series 6 RA-SD4-54-11-249


the reinforcement close to ρvmin It seems that ρvmin of EC2 is not sufficient to maintain the torsional strength aftercracking

Nevertheless all the specimens of Series 1 and 2exhibited meaningful deformability in the test conductedthrough displacement control Loss of the resistance to

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )

Figure 6 Torsional behavior of high-strength beams (a) Series 1 (b) Series 2 (c) Series 3 (d) Series 4 (e) Series 5 (f ) Series 6


torsion occurred instantly at the initiation of cracking butthe reinforcement took rapidly charge of the load and en-abled the specimens to recover their resistance and maintainit to 80 of Tcr until a rotation angle θ of about 002 radmUnder further loading the specimens secured torsionalresistance up to 50 of Tcr until 006 radm

It is noteworthy that the design for torsion in EC 2distinguishes the equilibrium torsion and the compatibilitytorsion according to the behavior of the structure For theequilibrium torsion where the torsional moment is requiredfor the equilibrium of the structure the reinforcement mustsecure a definite safety factor against the external loadsHowever for the compatibility torsion where the torsionalmoment results from the compatibility of deformationsbetween members meeting at a joint [20] the minimumtorsional reinforcement (Equation (1)) is employed tocontribute to the redistribution of the load generated by theincrease of the displacement [2] For reference in the ACI318-14 code the design torsion of the members for com-patibility torsion is the cracking torsion given by the code[1] which means the reinforcement of the member is alwaysgreater than the minimum torsional reinforcement requiredby the code

Considering EC 2 the results of Series 1 and 2 indicatethat the member designed for the compatibility torsion withonly ρvmin of EC 2 could develop considerable torsionaldisplacement enabling it to redistribute the load to thesurrounding members even when the member experienceddisplacement-induced cracking (is means that ρvmin ap-plied in the design for the compatibility torsion of EC 2cannot secure postcracking resistance comparable to thatprovided by theminimum reinforcement ratio applied in thedesign for shear or flexure but can reduce the possibility ofthe brittle behavior of the whole structure by redistributingthe load

Besides in view of the results of Series 1 the re-inforcement arranged with respect to the minimum tor-sional reinforcement ratio of ACI 318-14 and withadditionally ρt+l ge 1 is insufficient to prevent the loss oftorsional resistance after cracking However Series 2 withlower ρt+l showed comparatively faster strength loss (isindicates that under similar ρt ρt+l influences thedeformability

(e 18 specimens exhibited similar values for the tor-sional cracking moment Tcr since Tcr is more sensitive to thecross-sectional shape and tensile strength of concrete than tothe amount of reinforcement Table 5 arranges the values ofTcr for each specimen

422 Transverse-to-Longitudinal Reinforcement Ratio(ρtfyvρlfyl) and Total Reinforcement Ratio (ρt+l) At theexception of specimen RA-SD4-35-05-213 ρt+l of Series 1and 4 ranged between 162 and 163 (e comparison oftheir torsional behavior reveals that the specimens withlarger ρt showed relatively more ductile behavior aftercracking (Figures 6(a) and 6(d)) (is means that for similarρt+l the torsional ductility is secured with larger ρtfyvρlfyl(is tendency rejoins the conclusions of Chiu et al [5] For

information the choice of a low θ in the design results insmaller ρt but the value of ρt+l remains practically un-changed because ρl must be increased to resist the requireddesign torsional moment

In view of the results of Series 3 4 and 5 (Figures 6(c)ndash6(e))the maximum torsional moment and the ductility increasedwhen ρt+l increased for the same ρt In other words theincrease of ρl lowered the angle of the concrete strutsconstituting the space truss which improved the resistanceto the torsional strength (Tn) by letting more stirrups resistto torsion

423 High-Strength Reinforcement In view of the results ofSeries 1 to 6 it was difficult to find a specific tendency in therelation between the use of high-strength reinforcement andthe torsional behavior Yoon et al [7] pointed out that in thecase of stirrups with yield strength higher than 500MPa therisk of sudden loss of strength due to the crushing failure ofthe concrete struts is subjected to compression since thestirrups did not yield even under the maximum torsionalmoment (Tmax) However the torsion-rotation angle curvesin Figure 6 did not show the expected sudden loss of thestrength following the crushing failure of the concrete strutsbeyond Tmax Specifically stable decrease of the strengthseemed to occur During the redistribution of the torsionalload inside the member the angle by which the concretestruts transferred the compressive force appeared to reduceand the load sustained by the reinforcement increased withlarger displacement Prior to the completion of the tests thedeformation of the specimens of Series 3 and 6 with thelarger amount of high-strength reinforcement shown inFigure 7 also verified that crushing of the concrete struts didnot happen beyond Tmax

43 Comparison of Predicted and Experimental TorsionalStrengths Table 5 compares the values of the torsionalstrengths Tcr and Tn predicted by Equations (2) and (3)derived from the thin-walled tube theory and the space trussanalogy and those obtained experimentally (e predictedstrengths vary according to the value of the effectivethickness t assumed by the designer Since t also interferes inthe computation of A0 its value affects both Tcr and Tn Inthis study the value of 857mm is assumed for t based on thesuggestion of EC 2 (EN 1992-1-12004 632 (1)) (e ex-perimental values of ft and fyv in Tables 2 and 3 are appliedfor each corresponding series

(e comparison reveals that the experimental values ofTcr and Tn are conservative reaching respectively 157 and123 of the prediction on the average (e prediction ap-pears to be more accurate for Tn than Tcr Despite the as-sumption of t the better prediction provided for Tn can beattributed to the comparatively even value of the yieldstrength of the reinforcement On the contrary the loss ofaccuracy in the prediction of Tcr can be explained by thereliance on the more versatile tensile strength of concreteeven if the effect of the subjective choice of the designer isreduced to some extent because A0 decreases with larger t


(a) (b)

(c) (d)

Figure 7 Behavior of the softening zone in specimens using high-strength reinforcement (a) Series 3 RA-SD5-32-03-321 (θ 011 radmT 486 kNmiddotm) (b) Series 3 RA-SD6-32-02-321 (θ 0111 radm T 642 kNmiddotm) (c) Series 6 RA-SD5-51-10-200 (θ 013 radm T

680 kNmiddotm) (d) Series 6 RA-SD6-51-09-200 (θ 014 radm T 663 kNmiddotm)

Table 5 Comparison of predicted and experimental torsional strengths

Series Designation of specimenPrediction Test Testprediction

Tcr (kNmiddotm) Tn (kNmiddotm) Tcr (kNmiddotm) Tn (kNmiddotm) Tcr Tn

1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions

(is study evaluated the effect of the specifications rec-ommended by current design codes (focused on Eurocode 2)for torsion on the torsional characteristics of 80MPa high-strength concrete beams To that goal the torsion test wasperformed on beam specimens with rectangular cross sec-tion and various test variables involving the minimumtorsional reinforcement ratio (ρvmin) the transverse-to-longitudinal reinforcement ratio (ρtfyvρlfyl) and the to-tal reinforcement ratio (ρt+l) (e following conclusions canbe drawn

(1) For the high-strength concrete beams the adoptionof ρvmin recommended by EC 2 was insufficient toprevent the sudden loss of strength after the initi-ation of the torsional cracking

(2) For the high-strength concrete beams the applica-tion of ρvmin and ρt+l ge 1 recommended by ACI318-14 was also insufficient to prevent the suddenloss of the torsional strength after cracking

(3) With regard to the compatibility torsion of staticallyindeterminate structure (statically indeterminatetorsion) the adoption of ρvmin recommended by EC2 secured enough deformability to allow the re-distribution of the torsional moment

(4) (e ductile behavior could be secured with largerρtfyvρlfyl for the same ρt+l

(5) (e experimental results of this study did not revealthat the use of high-strength reinforcement withyield strength of 500MPa has negative effect on theductile behavior of the beam

(6) (e experimental data on the average gave conser-vative torsional cracking moment (Tcr) and torsionalstrength (Tn) reaching respectively 157 and 123of the prediction from the formulae (Equations (2)and (3)) based on the thin-walled tube theory andspace truss analogy with the effective thickness basedon EC 2

Data Availability

(e data used to support the findings of this study may beavailable from the corresponding author upon request

Additional Points

(i) (e relation between the torsional cracking moment andthe ductile behavior is discussed for the beam reinforcedwith the minimum torsional reinforcement ratio to examinethe eventual properness of the minimum torsional re-inforcement ratio recommended by Eurocode 2 (ii) (epure torsion test is performed on 18 beams made of 80MPaconcrete reinforced by high-strength bars with the rectangularsection and various test variables involving the minimumtorsional reinforcement ratio the transverse-to-longitudinalreinforcement ratio and the total reinforcement ratio(iii) For the high-strength concrete beams the minimum

torsional reinforcement ratio recommended by Eurocode 2 isinsufficient to prevent the sudden loss of strength after theinitiation of the torsional cracking (iv) But with regard to thecompatibility torsion of statically indeterminate structure theadoption of the minimum torsional reinforcement ratiorecommended by Eurocode 2 may secure enough deform-ability under the displacement-controlled mode to allow theredistribution of the torsional moment

Conflicts of Interest

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

Acknowledgments

(is research was supported by a grant (13SCIPA02) fromthe Smart Civil Infrastructure Research Program funded bytheMinistry of Land Infrastructure and Transport (MOLIT)of the Korean government and Korea Agency for In-frastructure Technology Advancement (KAIA)

References

[1] ACI Committee American Concrete Institute and In-ternational Organization for Standardization Building CodeRequirements for Structural Concrete (ACI 318-14) andCommentary (318R-14) American Concrete InstituteFarmington Hills MI USA 2014

[2] European Standards 1-1 2004 Eurocode 2 Design of ConcreteStructures-Part 1-1 General Rules and Rules for BuildingsEuropean Standards London UK 2004

[3] L J Rasmussen and G Baker ldquoTorsion in reinforced normaland high-strength concrete beams part 1 experimental testseriesrdquo Structural Journal vol 92 no 1 pp 56ndash62 1995

[4] S M R Lopes and L F A Bernardo ldquoCracking and failuremode in HSC hollow beams under torsionrdquo Construction andBuilding Materials vol 51 pp 163ndash178 2014

[5] H J Chiu I K Fang W T Young and J K Shiau ldquoBehaviorof reinforced concrete beams with minimum torsional re-inforcementrdquo Engineering Structures vol 29 no 9pp 2193ndash2205 2007

[6] M Ismail Behavior of UHPC Structural Members Subjected toPure Torsion Vol 24 Kassel University Press GmbH KasselGermany 2015

[7] S K Yoon S C Lee D H Lee and J Y Lee ldquoFailure modesof RC beams with high strength reinforcementrdquo Journal of theKorea Concrete Institute vol 26 no 2 pp 143ndash150 2014

[8] K N Rahal and M P Collins ldquoCombined torsion andbending in reinforced and prestressed concrete beamsrdquo ACIStructural Journal vol 100 no 2 pp 157ndash165 2003

[9] K N Rahal and M P Collins ldquoCompatibility torsion inspandrel beams using modified compression field theoryrdquoACI Structural Journal vol 103 no 3 p 328 2006

[10] C E Chalioris ldquoBehaviour model and experimental study forthe torsion of reinforced concrete membersrdquo WIT Trans-actions on the Built Environment vol 85 2006

[11] L F A Bernardo and S M R Lopes ldquoPlastic analysis andtwist capacity of high-strength concrete hollow beams underpure torsionrdquo Engineering Structures vol 49 pp 190ndash2012013

[12] N E Koutchoukali and A Belarbi ldquoTorsion of high-strengthreinforced concrete beams and minimum reinforcement


requirementrdquo Structural Journal vol 98 no 4 pp 462ndash4692001


[14] M A Ali and R N White ldquoToward a rational approach fordesign of minimum torsion reinforcementrdquo ACI StructuralJournal vol 96 no 1 pp 40ndash45 1999

[15] K Kim D Lee M K Park J Y Lee and H Ju ldquoMinimumtorsional reinforcement ratio of reinforced concrete membersfor safe designrdquo Journal of the Korea Concrete Institutevol 25 no 6 pp 641ndash648 2013

[16] I K Fang and J K Shiau ldquoTorsional behavior of normal-andhigh-strength concrete beamsrdquo Structural Journal vol 101no 3 pp 304ndash313 2004

[17] K N Rahal ldquoTorsional strength of normal and high strengthreinforced concrete beamsrdquo Engineering Structures vol 56pp 2206ndash2216 2013

[18] I H Yang C Joh J W Lee and B S Kim ldquoTorsional be-havior of ultra-high performance concrete squared beamsrdquoEngineering Structures vol 56 pp 372ndash383 2013

[19] M M Teixeira and L F A Bernardo ldquoDuctility of RC beamsunder torsionrdquo Engineering Structures vol 168 pp 759ndash7692018

[20] J K Wight and J G MacGregor Reinforced Concrete Me-chanics and Design 6E Pearson London UK 2012

[21] CSA ldquoDesign of concrete structuresrdquo in Standard CANCSAA233-04 Canadian Standards Association Mississauga ONCanada 2004

[22] FIBModel Code for Concrete Structures 2010 Ernest and SonBrigantine NJ USA 2013

[23] Korea Concrete Institute (KCI) Structural Concrete DesignCode Korea Concrete Institute (KCI) Seoul South Korea2012

[24] Korea Ministry of Land Infrastructure and Transport(MOLIT) Concrete Bridge Design Code (Limit State Design)KDS Issy-les-Moulineaux France 2016

[25] C E Chalioris ldquoExperimental study of the torsion of rein-forced concrete membersrdquo Structural Engineering and Me-chanics vol 23 no 6 pp 713ndash737 2006


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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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SensorsJournal of



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wwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

(is means controlling the crack width and securing enoughductility to prevent sudden loss of the torsional strength aftercracking Numerous researchers however already pointedout the issues resulting from the behavioral change broughtby the increase of the strength or related to the minimumtorsional reinforcement ratio recommended by ACI 318-14Code or Eurocode 2 (EC 2) [1ndash19]

Rasmussen and Baker [3] and Lopes and Bernardo [4]compared the torsional characteristics of reinforced beamsmade of normal concrete and high-strength concrete andconcluded that the use of high-strength concrete was fa-vorable with respect to the torsional stiffness and the stress inthe reinforcement but increased the brittle tendency aftercracking Chiu et al [5] performed pure torsion tests onbeams made of normal concrete and high-strength concreteto investigate the effect of the minimum reinforcement ratioin the longitudinal and transverse directions Based upontheir experimental results these authors reported that thepostcracking strength ie the ductile failure modedepended significantly on the total reinforcement ratio inthe longitudinal and transverse directions as well as the ratioof the longitudinal to the transverse reinforcement (isdependency was more marked in the high-strength concretemembers than in those made of normal concrete Ismail [6]who performed a literature review on previous torsion testsand Yoon et al [7] who studied experimentally the effect ofhigh-strength reinforcement also reported that the use ofhigh-strength concrete favored the occurrence of the brittlebehavior beyond the torsional strength

Numerical methods were also studied Rahal and Collins[8 9] successfully applied the modified compression fieldtheory to estimate the torsional behavior of concrete beamsand Chalioris [10] combined the smeared crack model andthe softened truss model to predict the initial torsionalstiffness torsional cracking moment and strength of con-crete beams Bernardo and Lopes [11] proposed a parameterfor the plastic behavior and twist capacity of high-strengthconcrete hollow beams based on the analysis of their test

In concern with the minimum torsional reinforcementratio Koutchoukali and Belarbi [12] stated that the mini-mum torsional reinforcement of ACI 318-95 Code [13] wasinadequate for high-strength concrete beams and stressedthe necessity to provide at least 20 reserve of strength aftercracking to prevent the brittle failure Both Ali and White[14] and Kim et al [15] indicated the problems of theminimum torsional reinforcement ratio and proposed newminimum reinforcement ratios enabling to maintain thepostcracking strength

Accordingly this study intends to investigate the ap-propriateness of the current design codes for torsion withfocus on EC 2 To that goal the relation between theminimum torsional reinforcement ratio and the torsionalcracking moment is analyzed theoretically and the puretorsion test is performed on beams made of 80MPa concretereinforced by high-strength reinforcement Moreover therelation between the torsional cracking moment and theductile behavior is discussed for the beam reinforced withthe minimum torsional reinforcement ratio to examine the

eventual properness of the minimum torsional re-inforcement ratio recommended by EC 2

2 Minimum Torsional Reinforcement Ratioand Torsional Cracking Moment

Since the torsional design methods of EC 2 and ACI 318-14Code provide conceptually identical minimum torsionalreinforcement this study analyzes theoretically the relationbetween the minimum torsional reinforcement and thetorsional cracking moment (Tcr) with reference to EC 2

In EC 2 the torsional load is decomposed into shearforces applied in each face of the member and design isperformed only with respect to these shear forces (ereforeρvmin can be expressed as follows in function of the tensilestrength of concrete and the yield strength of the stirrups

ρvmin Avmin

sbw 008

fck

1113968

fyv (1)

where Avmin cross-sectional area of minimum shear re-inforcement s spacing of stirrups bw width of the crosssection fck compressive strength of concrete and fyv

yield strength of shear and torsional reinforcementBesides according to the theory of the thin-walled tube

and the space truss analogy the torsional cracking strength(Tcr) and the torsional strength (Tn) can be expressed asfollows [1 20]

Tcr 2A0tft (2)

Tn 2A0Atfyv

scot θ (3)

where t effective thickness of the tube resisting to torsionA0 internal area inside the central axis of effectivethickness ft tensile strength of concrete At cross-sectional area of closed torsional stirrup and θ angle ofcrack

In Equation (2) the tensile strength of concrete can beassumed as ft 033

fck

1113968[1 20] (e beam in torsion can

be seen to be in a biaxial state under the simultaneousoccurrence of compression and tension and accordingly theconcrete tensile strength can be lowered compared to theuniaxial tension state Following Equation (2) can be re-written as

Tcr 2A0t 033

fck

1113969

1113874 1113875 (4)

Besides if ρvmin is accepted in the usual way as theminimum reinforcement ratio enabling the member tomaintain ductility without sudden loss of the torsionalstrength after cracking Tcr Tn and the following equationis obtained by equaling Equations (3) and (4)

Tcr 2A0t 033

fck

1113969

1113874 1113875 Atfyv

s2A0( 1113857cot θ (5)

If the beam is not prestressed and is reinforced equally inthe transverse and longitudinal directions the crack angle θ



Atfyv

st 033

fck

1113969

(6)


ρv Av

sbw2At

sbw (0165sim 0297)

fck

1113968

fyv (7)




3 Torsion Test










000

050

100

150

200

250

0 20 40 60 80 100 120

ρ vm

inlowastf yv

fck (MPa)


bw

t









300

35

3516

5

400

165

SD500 D16 1450 = 700mm 1450 = 700mm80 + 2406 + 80 = 1600mm3000mm

35

35115 115








SD400 4838 4741 3946 4561 4523SD500 5380 5224 5290 NA 4994SD600 NA NA 6270 NA 6309














0

05

1

15

2

25

3

35

00 10 20 30 40 50 60

Tota

l rei

nfor

cem

ent r

atio

ρt+

l (

)



(ACI)

ρvmin(EC 2)

Series 2

Series 1

Series 3

Series 4

Series 6

Series 5






1RA-SD4-13-03-162

800

D10

484

240

0293D16

3958

1324RA-SD5-15-02-162 538 0293 529 1324RA-SD6-15-02-162 538 0293 627 1324

2RA-SD4-13-05-092

728484 0289 D13 474 6 0634

RA-SD5-15-05-092 538 0289 D13 522 6 0634RA-SD6-15-04-095 538 0289 D16 627 4 0662

3RA-SD4-32-03-328

737484 100 0695

D22452

82581

RA-SD5-32-03-321 538 110 0631 499 2581RA-SD6-32-02-321 538 110 0631 630 2581

4RA-SD4-32-05-213

847484 100 0702 D19 456

61433

RA-SD5-32-07-163 538 110 0638 D16 529 0993RA-SD6-32-06-163 538 110 0638 D16 627 0993

5RA-SD4-32-11-133

831484 100 0695 D13 474 6 0634

RA-SD5-32-10-126 538 110 0631 D13 522 6 0634RA-SD6-32-08-126 538 110 0631 D16 627 4 0662

6RA-SD4-54-11-249

900484 60 1700

D16395 8 1324

RA-SD5-51-10-200 538 70 1003 529 6 0993RA-SD6-51-09-200 538 70 1003 627 6 0993


Load cell

DTs

200mm

200mm

330mm 300mm


direction

Testbeam


(a)

(b)

(c)

(d)

(e)

(f )





0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )















(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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



Atfyv

st 033

fck

1113969

(6)


ρv Av

sbw2At

sbw (0165sim 0297)

fck

1113968

fyv (7)




3 Torsion Test










000

050

100

150

200

250

0 20 40 60 80 100 120

ρ vm

inlowastf yv

fck (MPa)


bw

t









300

35

3516

5

400

165

SD500 D16 1450 = 700mm 1450 = 700mm80 + 2406 + 80 = 1600mm3000mm

35

35115 115








SD400 4838 4741 3946 4561 4523SD500 5380 5224 5290 NA 4994SD600 NA NA 6270 NA 6309














0

05

1

15

2

25

3

35

00 10 20 30 40 50 60

Tota

l rei

nfor

cem

ent r

atio

ρt+

l (

)



(ACI)

ρvmin(EC 2)

Series 2

Series 1

Series 3

Series 4

Series 6

Series 5






1RA-SD4-13-03-162

800

D10

484

240

0293D16

3958

1324RA-SD5-15-02-162 538 0293 529 1324RA-SD6-15-02-162 538 0293 627 1324

2RA-SD4-13-05-092

728484 0289 D13 474 6 0634

RA-SD5-15-05-092 538 0289 D13 522 6 0634RA-SD6-15-04-095 538 0289 D16 627 4 0662

3RA-SD4-32-03-328

737484 100 0695

D22452

82581

RA-SD5-32-03-321 538 110 0631 499 2581RA-SD6-32-02-321 538 110 0631 630 2581

4RA-SD4-32-05-213

847484 100 0702 D19 456

61433

RA-SD5-32-07-163 538 110 0638 D16 529 0993RA-SD6-32-06-163 538 110 0638 D16 627 0993

5RA-SD4-32-11-133

831484 100 0695 D13 474 6 0634

RA-SD5-32-10-126 538 110 0631 D13 522 6 0634RA-SD6-32-08-126 538 110 0631 D16 627 4 0662

6RA-SD4-54-11-249

900484 60 1700

D16395 8 1324

RA-SD5-51-10-200 538 70 1003 529 6 0993RA-SD6-51-09-200 538 70 1003 627 6 0993


Load cell

DTs

200mm

200mm

330mm 300mm


direction

Testbeam


(a)

(b)

(c)

(d)

(e)

(f )





0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )















(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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








300

35

3516

5

400

165

SD500 D16 1450 = 700mm 1450 = 700mm80 + 2406 + 80 = 1600mm3000mm

35

35115 115








SD400 4838 4741 3946 4561 4523SD500 5380 5224 5290 NA 4994SD600 NA NA 6270 NA 6309














0

05

1

15

2

25

3

35

00 10 20 30 40 50 60

Tota

l rei

nfor

cem

ent r

atio

ρt+

l (

)



(ACI)

ρvmin(EC 2)

Series 2

Series 1

Series 3

Series 4

Series 6

Series 5






1RA-SD4-13-03-162

800

D10

484

240

0293D16

3958

1324RA-SD5-15-02-162 538 0293 529 1324RA-SD6-15-02-162 538 0293 627 1324

2RA-SD4-13-05-092

728484 0289 D13 474 6 0634

RA-SD5-15-05-092 538 0289 D13 522 6 0634RA-SD6-15-04-095 538 0289 D16 627 4 0662

3RA-SD4-32-03-328

737484 100 0695

D22452

82581

RA-SD5-32-03-321 538 110 0631 499 2581RA-SD6-32-02-321 538 110 0631 630 2581

4RA-SD4-32-05-213

847484 100 0702 D19 456

61433

RA-SD5-32-07-163 538 110 0638 D16 529 0993RA-SD6-32-06-163 538 110 0638 D16 627 0993

5RA-SD4-32-11-133

831484 100 0695 D13 474 6 0634

RA-SD5-32-10-126 538 110 0631 D13 522 6 0634RA-SD6-32-08-126 538 110 0631 D16 627 4 0662

6RA-SD4-54-11-249

900484 60 1700

D16395 8 1324

RA-SD5-51-10-200 538 70 1003 529 6 0993RA-SD6-51-09-200 538 70 1003 627 6 0993


Load cell

DTs

200mm

200mm

330mm 300mm


direction

Testbeam


(a)

(b)

(c)

(d)

(e)

(f )





0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )















(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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

05

1

15

2

25

3

35

00 10 20 30 40 50 60

Tota

l rei

nfor

cem

ent r

atio

ρt+

l (

)



(ACI)

ρvmin(EC 2)

Series 2

Series 1

Series 3

Series 4

Series 6

Series 5






1RA-SD4-13-03-162

800

D10

484

240

0293D16

3958

1324RA-SD5-15-02-162 538 0293 529 1324RA-SD6-15-02-162 538 0293 627 1324

2RA-SD4-13-05-092

728484 0289 D13 474 6 0634

RA-SD5-15-05-092 538 0289 D13 522 6 0634RA-SD6-15-04-095 538 0289 D16 627 4 0662

3RA-SD4-32-03-328

737484 100 0695

D22452

82581

RA-SD5-32-03-321 538 110 0631 499 2581RA-SD6-32-02-321 538 110 0631 630 2581

4RA-SD4-32-05-213

847484 100 0702 D19 456

61433

RA-SD5-32-07-163 538 110 0638 D16 529 0993RA-SD6-32-06-163 538 110 0638 D16 627 0993

5RA-SD4-32-11-133

831484 100 0695 D13 474 6 0634

RA-SD5-32-10-126 538 110 0631 D13 522 6 0634RA-SD6-32-08-126 538 110 0631 D16 627 4 0662

6RA-SD4-54-11-249

900484 60 1700

D16395 8 1324

RA-SD5-51-10-200 538 70 1003 529 6 0993RA-SD6-51-09-200 538 70 1003 627 6 0993


Load cell

DTs

200mm

200mm

330mm 300mm


direction

Testbeam


(a)

(b)

(c)

(d)

(e)

(f )





0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )















(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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


Load cell

DTs

200mm

200mm

330mm 300mm


direction

Testbeam


(a)

(b)

(c)

(d)

(e)

(f )





0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )















(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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




0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-13-03-162RA-SD5-15-02-162RA-SD6-15-02-162

RA-SD4-13-03-162

RA-SD6-15-02-162

RA-SD5-15-02-162

(a)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-13-05-092RA-SD5-15-05-092RA-SD6-15-04-095

RA-SD4-13-05-092RA-SD6-15-04-095

RA-SD5-15-05-092

Tors

ion

(kN

m)

(b)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-03-328RA-SD5-32-03-321RA-SD6-32-02-321

RA-SD4-32-03-328

RA-SD6-32-03-321RA-SD5-32-03-321

(c)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-32-05-213RA-SD5-32-07-163RA-SD6-32-06-163

RA-SD4-32-05-213

RA-SD6-32-06-163RA-SD5-32-07-163

Tors

ion

(kN

m)

(d)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018

Tors

ion

(kN

m)

Rotation (radm)

RA-SD4-32-11-133RA-SD5-32-10-126RA-SD6-32-08-129

RA-SD4-32-11-133RA-SD6-32-08-129

RA-SD5-32-10-126

(e)

Tors

ion

(kN

m)

0102030405060708090

100

0 002 004 006 008 01 012 014 016 018Rotation (radm)

RA-SD4-54-11-249RA-SD5-54-10-200RA-SD6-51-10-200

RA-SD4-54-11-249

RA-SD6-51-10-200RA-SD5-54-10-200

(f )















(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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














(a) (b)

(c) (d)






1RA-SD4-13-03-162 404 388 672 556 166 143RA-SD5-15-02-162 404 472 684 579 169 123RA-SD6-15-02-162 404 520 631 600 156 115

2RA-SD4-13-05-092 439 295 613 515 140 175RA-SD5-15-05-092 439 327 656 520 150 159RA-SD6-15-04-095 439 366 676 537 154 147

3RA-SD4-32-03-328 369 896 632 868 171 097RA-SD5-32-03-321 369 946 652 880 176 093RA-SD6-32-02-321 369 1080 636 894 172 083

4RA-SD4-32-05-213 427 676 623 763 146 113RA-SD5-32-07-163 427 612 642 745 150 122RA-SD6-32-06-163 427 661 659 700 154 106

5RA-SD4-32-11-133 450 465 742 700 165 151RA-SD5-32-10-126 450 486 677 655 150 135RA-SD6-32-08-126 450 540 661 699 147 129

6RA-SD4-54-11-249 462 774 725 922 157 119RA-SD5-51-10-200 462 764 695 862 151 113RA-SD6-51-09-200 462 834 687 840 149 101

Average 157 123


5 Conclusions








Data Availability


Additional Points





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


5 Conclusions








Data Availability


Additional Points





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


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