StudyonStressingStateandFailureCriterionofConcrete-Filled ... · 2020. 7. 20. · columns and...

Research ArticleStudy on Stressing State and Failure Criterion of Concrete-FilledStainless Steel and Steel Tubular Column

Baisong Yang12 Wei Wang3 Lingxian Yang12 Guorui Sun12 and Sijin Liu 4

1Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education Harbin Institute of TechnologyHarbin 150090 China2Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry andInformation Technology Harbin Institute of Technology Harbin 150090 China3Academy of Combat Support Rocket Force University of Engineering Xirsquoan 710025 China4China Railway 14th Bureau Group Co Ltd Jinan China

Correspondence should be addressed to Sijin Liu ahlsj126com

Received 26 March 2020 Accepted 16 June 2020 Published 20 July 2020

Academic Editor Jiang Jin

Copyright copy 2020 Baisong Yang et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper the mechanical characteristics of concrete-filled stainless steel and steel tubular (CFSSAST) columns under axial andeccentric loads are analyzed by using the theory of structural stressing state Firstly the sum of generalized strain energy density(GSED) values of the short column at every load value (Fj) is normalized as Ejnorm to describe the structural stressing state (enaccording to MannndashKendall (M-K) criterion and the natural law from quantitative change to qualitative change the transition ofstressing state is distinguished which leads to the update of failure load (en the corresponding finite element models areestablished and the accuracy of the models is verified by the experimental data and the stress contour maps are analyzed bysimulation data Finally the simulation data are used to perform parameter analysis (is study explores a new method to revealthe invisible working characteristics of structures and provides a new reference for the study of similar structures

1 Introduction

(e structure concrete-filled stainless steel and steel tubular(CFSSAST) column is a new combined structure developedon the basis of the traditional concrete filled double-skinsteel tubular (CFDSST) columns (is kind of compositestructure not only inherits the advantages of high bearingcapacity good toughness good fire resistance high bendingrigidity and light weight but also has good corrosion re-sistance and durability due to the use of stainless steel And itcan be widely applied in structures such as cross-sea bridgestructures and offshore platforms that require high resis-tance to corrosion

As a kind of special concrete filled double-skin steeltubular the mechanical properties of CFSSAST compo-nents are very similar to those of ordinary CFDSST col-umns (erefore the research on ordinary CFDSSTcolumns could provide significant and valuable references

Tao conducted a series of experiments on concrete-filleddouble skin steel tubular stub columns (fourteen) andbeam-columns (twelve) providing practical checkingmethod for the bearing capacities of the composite col-umns [1] Zhao and Wei derived the unified calculationformula of bearing capacity of CFDSST componentssubjected to axial compressive loading based on the TwinShear Unified Strength (eory [2] Zhang et al carried outthe experiment on the short CFDSST columns with dif-ferent eccentricity (e results indicated that with theincrease of eccentricity the ultimate bearing capacity ofshort column obviously decreased and its lateral defor-mation capacity weakened while the eccentricity has littleeffect on the ductility of short column [3] Ren et alconducted a finite element (FE) analysis of the compressivebehavior of circular inclined concrete-filled steel tubularstub columns and verified the FE method by experimentaldata (e result showed that the FE method is available for

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8868438 18 pageshttpsdoiorg10115520208868438

predicting the bearing capacities of the circular inclinedspecimens [4] Li et al established a general finite elementanalysis model of CFDSST columns under preloading andproposed corresponding formulas for calculating the ultimatebearing capacity of CFDSSTcolumns with preloading on steeltubes [5] Subsequently many researchers had studied theaxial compression performance of CFDSST columns [6ndash8]Hassanein and Kharoob summarized previously developedformulas for predicting the compressive strength of theCFDSST columns and used the ABAQUSstandard softwareto perform numerical nonlinear simulations (roughcomparing tested results with simulated results a new designformula is suggested [9] Liang established a new mathe-matical model which could compute the axial load-deflectionperformance of high-strength circular CFDSST slender col-umns subjected to eccentric loading (e model accuratelypredicted the residual concrete strength and strain in thepostyield regime [10]

In recent years many scholars had conducted exper-imental research on concrete-filled stainless steel and steeltubular (CFSSAST) columns For instances Han et alconducted a series of performance tests on CFSSASTcolumns and proposed a simplified model for predictingthe strength of the column section [11] Chang et alcarried out a range of compression tests on CFSSASTcolumns (e results indicated that the column strengthincreased with the increasing of the diameter ratio wallthickness ratio yield strength ratio and concrete strength[12] Cao took the shear span ratio of CFSSASTcolumns asthe main variable parameter and carried out bending tests(e results showed that the CFSSAST specimens exhibitedoutstanding ductile damage performance under bendingload and the flexural capacity was inversely proportionalto the shear span ratio [13] Zhou and Xu conducted cyclicload test on double-layer stainless steel tube concrete beamcolumn (e results showed that the axial compressiveload level and thickness of outer tubes have a primaryinfluence on the behavior of the test specimens [14] Wenconducted an experimental study on the mechanical be-havior of CFSSAST columns (e experiment results in-dicated that for long columns under eccentric loadingconditions the stiffness and bearing capacity decreasedobviously with the increase of the hollow ratio slendernessratio and load eccentricity [15] Zhang et al carried outthe experimental research on the shear resistance per-formance of concrete-filled double stainless-steel tubularcolumns and proposed empirical equation for calculatingthe shear bearing capacity of specimens [16] Some otherresearchers tested the impact resistance of CFSSASTcolumns [17 18] (e experimental results showed that theglobal deformation and local deformation of specimensdeveloped with the increase of the impact force the impacttime and impact height

Although these research results greatly promoted theapplication of CFSSAST columns in engineering projectsthere are still some problems of CFSSAST columns to beresolved summarized as follows (1) Up to now the failureload of CFSSAST columns is determined on the semiem-pirical and semitheoretical basis with considerable

inaccuracy and the failure mechanism of the columns is notinvolved (2) At present most of the researches tend to focuson the mechanical properties of CFSSAST columns underaxial loads while the researches of specimens under ec-centric loads are inadequate

In order to address these two issues the authors deeplystudy the mechanical properties of CFSSASTcolumns underaxial and eccentric loads based on the theory of structuralstressing states (e measured strain data of CFSSASTcolumns are modeled as generalized strain energy density(GSED) to describe the structural stressing state modes(en M-K method is applied to GSED sum-load curve todistinguish the mutation feature of the curve and reveal thefailure mechanism of CFSSAST columns in the process ofloading so as to update the definition of the existing columnfailure load

2 Methods for Modelling and AnalyzingStructural Stressing State

21 Structural Stressing State Concept and GSED Curve(e authors define the stressing state of a structure as thestructural working behavior characterized by the distributionpattern of strain energy density values displacements strainsand stresses of measuring points [19 20] Generally the strainenergy density Ei of the i-th point can be calculated by

Ei 1113946 σ1dε1 + σ2dε2 + σ3dε3 (1)

where σ1 σ2 σ3 and ε1 ε2 ε3 are three principal stresses andstrains respectively Ei is the i-th strain energy densityHowever due to the directionality of stress and strain thisnumerical model is not convenient for further processingand analysis(erefore the generalized strain energy density(GSED) is used as the parameter to characterize the stressingstate at a certain point (us equation (1) is simplified as

Eij 12

Eε2ij (2)

where Eij is the GSED value of the i-th measured pointunder the j-th load E is the elastic modulus of the materialεij is the strain value of the i-th point under the j-th load Inorder to better compare and analyze the change charac-teristics of GSED sum curve of different components orstructures it can be normalized as

Ejnorm 1113936

Ni1 Eij

Emax (3)

where Ejnorm is the sum of the normalized GSED values ofall the measured points to the j-th loadN is the number of allmeasuring points Emax is the maximum of the strain energyvalues over the loading process (us the Ejnorm minus Fj curveof the structure can be plotted to investigate differentstructural stressing states and corresponding characteristics

22 M-K Criterion (e MannndashKendall (M-K) method isapplied to distinguish the stressing state mutation of thestructure through the Ejnorm minus Fj curve because it does not

2 Advances in Civil Engineering

need the sample to obey some distributions or be interferedby some outliers For this study it is assumed that the se-quence of Eprime(i) (the load step i 1 2 n) is statisticallyindependent (en a new stochastic variable bm at the m-thload step is defined as

bm 1113944

m

i

hi(2lemle n) hi +1 Eprime(i)gtEprime(j)(1le jle i)

0 otherwise

⎧⎨

⎩

(4)

where hi is the cumulative number of the samples ldquo+1rdquomeans adding one more to the existing value if the inequalityon the right side is satisfied for the jth comparison(e meanvalue D (bm) and variance Var (bm) of bm are calculated by

D bm( 1113857 m(m minus 1)

4 2lemle n (5)

Var bm( 1113857 m(m minus 1)(2m + 5)

72 2lemle n (6)

Under the assumption that the Eprime(i) sequence isstatistically independent a new statistic NFm is defined by

NFm

0 m 1

bm minus D bm( 1113857Var bm( 1113857

1113969 2lemle n

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)

(us the NFm minus F curve can be formed by all the NFkdata and the NBk minus F curve can be formed by the inverseEprime(i) sequence Consequently two NFk and NBk curvescan intersect at the mutation point of the Ejnorm minus Fj curvewhich is taken as a criterion to distinguish structuralstressing state mutation

3 Experiment and Simulation of Concrete-Filled Stainless Steel and SteelTubular Column

31 Brief Introduction of Experiment Wen et al conductedexperimental studies on the mechanical properties of theCFSSAST columns under axial and eccentric pressure [15](e outer tube is stainless steel and the inner tube is Q235carbon steel as shown in Figure 1

In the axial compression test the hollow ratio χ(χ Di(D0 minus 2t0) is the main variable parameter and sixshort columns are made for experimental research (esizes of specimen and material strength are shown inTable 1 in which only one end of specimens of class a hasan end plate and both end of class b has an end plate wherefy0 is the yield strength of stainless steel fyi is the yieldstrength of carbon steel and fcu is the compressivestrength of concrete

Eighteen CFSSAST columns were made for the researchof the eccentric compression test with the hollow ratio χ(χ Di(D0 minus 2t0)) slenderness ratio (λ Li) and eccen-tricity ratio (er) as the main parameters Table 2 shows thespecific size andmaterial strength of the specimens and bothends of each specimen have an end plate

32 LoadingDevice ofExperiment 500tYAW-5000 pressuretester is used for axial compression and eccentric com-pression test as shown in Figure 2 Four displacementmeters are used to measure the axial displacement (Δ) ofthe specimens in the axial compression test and thelongitudinal strain gauges and the transverse strain gaugesare pasted in the middle of four longitudinal sections Inthe eccentric compression test the two ends of thespecimen are respectively loaded by the knife edge hingeDue to the difference of the section size load eccentricityand other parameters of the specimens a loading platewith groove is added between the end of the specimen andthe knife edge hinge so as to evenly act the load on thespecimen In the eccentric compression test five dis-placement meters are used to measure the axial dis-placement the lateral deflection at the height of 14 12and 34 column and the longitudinal and transversestrain gauges are pasted in the middle of four longitudinalsections

33 FEA Model of CFSSAST Column Figure 3 shows theFEA model of CFSSAST columns built by Software ABA-QUS (e concrete of CFSSAST short column and end platewere simulated by the solid element C3D8R and the innerand outer steel tubes were simulated by the shell unit S4R(is paper adopted Rasmussenrsquos stainless steel constitutiverelationship model [21] and Hanrsquos carbon steel constitutiverelationship model [22](e constitutive relation of stainlesssteel is as follows

ε

σE0

+ 0002σσ02

1113888 1113889

n

σ le σ02

σ minus σ02

E02+ εu

σ minus σ02

σu minus σ021113888 1113889

m

+ ε02 σ02 lt σ

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

where E0 is the initial modulus of elasticity of stainless steelE02 is the tangent modulus corresponding to the stress-strain curve when the residual strain is 02 σ02 is thecorresponding stress when the residual strain is 02 σu isthe ultimate stress of stainless steel εu is the ultimate strainof stainless steel

(e concrete adopted Guo tensile concrete constitutiverelationship model [23] and Han compression concreteconstitutive relationship models [22] (e constitutive re-lation of concrete in tensile zone is as follows

σσ0

12εεp

minus 02ε06

εp

εεp

le 1

εεp1113872 1113873

03σ2p εεp1113872 1113873 minus 11113872 111387317

+ εεp

εεp

gt 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

where σp is the peak tensile stress of concrete andσp 026 times (125fc

prime)23 εp is the strain corresponding to thepeak tensile stress and εp 431 σp

Advances in Civil Engineering 3

4 StressingStateCharacteristicsofCFSSTShortColumns under Axial Compression

41 Characteristics of Ejnorm minus Fj Curve For the Z-48-bshort column exampled here the sum of GSED at each load(Fj) can be normalized as Ejnorm according to equations(1)ndash(3) and then the Ejnorm minus Fj curve can be plottedFurthermore the loads P (325 kN) and U (609 kN) are twocharacteristic points distinguished by the M-K criterion

which are elastoplastic critical load and failure load re-spectively as shown in Figure 4 Two mutation points dividethe curve into three stages (1) before load P the curve isalmost a horizontal straight line indicating that the concretecould be in linear-elastic working state without cracks (2)after load P the curve increases nonlinearly signifying thatthe short column enters the elastic-plastic stressing statestage until load U At this time the concrete exposed at theends of the specimen begins to produce small and slowly

Table 1 Size and strength of axial compression specimens

Specimen number D0 times t0 (mmtimesmm) Di times t (mmtimesmm) L (mm) χ fy0 (MPa) fyi (MPa) fcu (MPa)Z-48-a 114times 2 48times16 342 044 2787 235 48Z-48-b 114times 2 48times16 342 044 2787 235 48Z-76-a 114times 2 76times16 342 069 2787 235 48Z-76-b 114times 2 76times16 342 069 2787 235 48Z-89-a 114times 2 89times16 342 081 2787 235 48Z-89-b 114times 2 89times16 342 081 2787 235 48

Table 2 Size and strength of eccentric compression specimens

Specimen number D0 times t0 (mmtimesmm) Di times ti (mmtimesmm) L (mm) fy0 (MPa) fyi (MPa) fcu (MPa)P800-50-4-a 114times 2 50times12 800 2787 235 58P800-50-4-b 114times 2 50times12 800 2787 235 58P800-76-14-a 114times 2 76times16 800 2787 235 58P800-76-14-b 114times 2 76times16 800 2787 235 58P800-89-45-a 114times 2 89times16 800 2787 235 58P800-89-45-b 114times 2 89times16 800 2787 235 58P1300-50-4-a 114times 2 50times12 1300 2787 235 58P1300-50-4-b 114times 2 50times12 1300 2787 235 58P1300-76-14-a 114times 2 76times16 1300 2787 235 58P1300-76-14-b 114times 2 76times16 1300 2787 235 58P1300-89-45-a 114times 2 89times16 1300 2787 235 58P1300-89-45-b 114times 2 89times16 1300 2787 235 58P1800-50-4-a 114times 2 50times12 1800 2787 235 58P1800-50-4-b 114times 2 50times12 1800 2787 235 58P1800-76-14-a 114times 2 76times16 1800 2787 235 58P1800-76-14-b 114times 2 76times16 1800 2787 235 58P1800-89-45-a 114times 2 89times16 1800 2787 235 58P1800-89-45-b 114times 2 89times16 1800 2787 235 58

t0ti

Di

D0

Concrete

Stainless steel

Carbon steel

Figure 1 Section diagram of CFSSAST column


expanding cracks (3) after load U the curve rises sharplyimplying that the short column enters the failure state inwhich the concrete produces more cracks and the crackinglevel increases rapidly (erefore load U is defined as thefailure load of the short column which conforms to thenatural law of quantitative change to qualitative changeAccording to the natural law it can be considered that theelastic working state and elastic-plastic working state of theshort column before the failure load are a process of con-tinuous ldquoquantitative changerdquo When a certain critical value

(ie failure load) is reached there will be a qualitativechange in the stressing state of the short column and it canno longer bear the load stably

To verify the general applicability of the failure load to alltest short columns the mutation of Ejnorm minus Fj curves ofother short columns are also distinguished by M-K criterion(e failure loads of short columns Z-48-a Z-48-b Z-76-aZ-76-b Z-89-a and Z-89-b are 613 kN 609 kN 535 kN540 kN 462 kN and 468 kN respectively Obviously eachcurve has a mutation point from the stable stressing state tofailure state that is failure load By comparing the failureloads of short columns of class a and b it can be seen that theimpact of end plates on the failure load is very small(erefore the failure load is deterministic which reflects thegeneral and common failure behavior of structural stressingstate and will be applied in the following analysis

42 Verification of Simulated Data In order to verify theaccuracy of the simulated data the ultimate loads and failureloads of the experimental columns and the models are

Displacementmeter

Displacement meter

342

N

Specimen

Displacementmeter

Displacementmeter Strain

gauge

114

(a)

Tester

Displacementmeter

Straingauge

Loadingplate

Knifeedgehinge

N

N

(b)

Figure 2 (e loading device of (a) CFSSAST column under axial compression and (b) CFSSAST column under eccentric compression

(a) (b)

Figure 3 FEA model of short column (a) under axial compressionand (b) under eccentric compression


compared as shown in Table 3 (e maximal absolute valueof the error of simulated ultimate load and simulated failureload is 83 and 36 respectively so the simulated data areaccurate enough for further analysis

It can be seen from Figure 5 that the simulation data are inagreement with the experiment data At the same time thedisplacement corresponding to the ultimate load in thesimulation is smaller than that in the experiment which maybe the fact that the contact between the backing plate and thespecimen as well as the loading device and the backing plate isnot close As for the comparison of other short columns notlisted here the results are also similar to those shown(erefore the simulated data are reliable and can be used forfurther analysis

43 Stress Contour Maps Analysis of Axial CompressionModel (emodel Z-76 is taken as an example to analyze thestress change of the CFSSAST column during the loadingprocess (e stress contour maps corresponding to the fourcharacteristic loads are selected for analysis and the se-quence is (1) point A elastoplastic critical load (2) point Bfailure load (3) point C ultimate load (4) point Dunloading load as shown in Figure 6

Figure 7 shows the longitudinal stress contour maps ofthe stainless steel tube It can be seen that at point A thelongitudinal stress at the end and the stress in the middle areminus206MPa and minus180MPa respectively (e stress at the endis 114 times that in the middle and the stainless steel doesnot reach yield strength At point B the end stress isminus284MPa the stress in the middle is minus249MPa and theratio is still 114 When the load reaches ultimate load theend stress and stress in the middle are minus301MPa andminus256MPa respectively and the ratio is 11 At point D thedeformation of the stainless steel tube is obvious (e endstress and the stress in the middle are almost the same Afterthe failure load the transverse deformation of the middlepart increases significantly and finally the middle partldquobulgesrdquo outwards

Figure 8 shows the longitudinal stress contour maps ofthe core concrete and the end effect also exists at the initialstage of loading At point A the end stress and the stress in

the middle of the outer side (the side close to the stainlesssteel tube) are minus40MPa and minus34MPa respectively and theratio of is 118(e stresses of the inner side (the side close tothe carbon steel tube) are minus27MPa and minus34MPa respec-tively with a ratio of 079 For the end of the core concretethe stress gradually decreases from the outer side to the innerside For the midsection of the column the stress at eachpoint is almost the same When the load reaches failure loadthe ratio of outer side and inner side is 122 and 072 re-spectively After the failure load the transverse deformationof the middle section of concrete increases rapidly

As shown in Figure 9 due to the transverse supportingeffect of concrete on carbon steel tube the stressing state ofcarbon steel tube is different from that of stainless steel tubeAt point A the stress at the end and the stress in middle ofsteel tube is minus187MPa and minus241MPa respectively and themiddle part of carbon steel tube has reached the yieldstrength As the load continues the end stress graduallyincreases but it does not reach yield strength Overall it canbe inferred that the carbon steel tube provides a lateralbracing force for the concrete instead of directly bearing thevertical load

44 Orthogonal Parameter Analysis of Axial CompressionModel In this paper L16 (45) orthogonal table is selected forparameter analysis where 16 represents the number ofmodels to be established 4 means setting 4 levels for eachparameter 5 means that there are five parameters (especific parameter settings of all 16 short column models areshown in Table 4 and the range of ultimate load (Ru) and therange of failure load (Rf ) are shown in Table 5 where Nu isthe ultimate load of short column andNf is the failure load ofshort column

According to Table 5 the range relation of each pa-rameter is as follows stainless steel strengthgt nominal steelratiogt concrete strengthgt carbon steel strengthgt hollowratio (e results show that the strength of stainless steel andnominal steel ratio are the most important factors affectingthe failure load and ultimate load of the short columnsfollowed by the strength of concrete while the strength ofcarbon steel and the hollow ratio are the least

U

P

P = 325 kN

U = 609 kN

02468

10

Stat

istic

s

200 400 6000Fj (kN)

00

02

04

06

08

10

100 200 300 400 500 600 7000Fj (kN)

450 500 550 600 650 700400Fj (kN)

0

2

4

6

8

Stat

istic

sE jn

orm

Figure 4 Ejnorm minus Fj curve of Z-48-b


45 Single Variable Parameter Analysis In this paper fiveparameters (concrete strength stainless steel yield strengthcarbon steel strength hollow ratio and nominal steel ratio)are analyzed quantitatively by using the finite element modelAt the same time in order to compare the influence of

different factors on the bearing capacity of short columns thispaper attempts to construct the parameter K as shown in

K C1

C2 (10)

where C1 |U1 minus U2|min(U1 U2) C2 |X1 minus X2|min(X1 X2) X1 and X2 are the parameter levels re-spectively and U1 and U2 are the limit load and failureload corresponding to the two parameter levelsrespectively

46 Influence of Concrete Strength It can be seen fromFigure 10 that with the increase of concrete strength theultimate load and failure load of the short column modelincrease When the concrete strength increases from 40MPato 80MPa increased by 100 (C2 is 1) the correspondingultimate loads are 52362 kN 55929 kN 60733 kN65318 kN and 70321 kN which are increased by 343 (C1is 0343) and the value of K is 03430 (e correspondingfailure loads are 48815 kN 53517 kN 54490 kN 61050 kNand 65258 kN which are increased by 3368 (C1 is 03368)and K is 03368 In addition with the concrete strengthincreases the falling section after the ultimate load is moreobvious which shows that the ductility of the CFSSASTcolumns decreases with the increase of concrete strength

578 kN618 kN

567 kN

Z-76-aZ-76-bModel Z-76

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)

Figure 5 (a) Fj minus D curve of Model Z-76 (b) Ejnorm minus Fj curve of Model Z-76

Table 3 Comparison of experimental data and simulated data

Specimennumber

Failure load ofexperiment (kN)

Simulated ultimateload (kN)

Error()


Simulated failureload (kN) Error ()

Z-48-a 698 670 40 613 610 minus06Z-48-b 660 670 15 609 610 01Z-48-a 618 567 83 535 521 minus28Z-76-b 578 567 19 540 521 minus36Z-89-a 493 494 02 462 459 minus07Z-89-b 520 494 50 468 459 minus20

D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)

Figure 6 Fj minus D (displacement) curve of model z-76


(a) (b) (c) (d)

ndash1709e + 02ndash1839e + 02ndash1968e + 02ndash2098e + 02ndash2228e + 02ndash2357e + 02ndash2487e + 02ndash2617e + 02ndash2746e + 02ndash2876e + 02ndash3006e + 02ndash3135e + 02ndash3265e + 02

Figure 7 (e longitudinal stress contour maps of the stainless steel tube (a) Point A (b) Point B (c) Point C (d) Point D


(a) (b) (c) (d)

Figure 8 (e longitudinal stress contour maps of the core concrete (a) Point A (b) Point B (c) Point C (d) Point D

(a) (b) (c) (d)


Figure 9 (e longitudinal stress contour maps of the carbon steel tube (a) Point A (b) Point B (c) Point C (d) Point D


461 Effect of Yield Strength of Stainless Steel As shown inFigure 11 the strength of stainless steel increases from275MPa to 496MPa increased by 834 the corre-sponding ultimate load increases by 3971 and Kis 04762 (e failure load increases by 4048 and Kis 04854 It can be seen from Figure 11 that the ductilityof short columns is less affected by stainless steelstrength

462 Effect of Nominal Steel Ratio (e steel ratio increasesfrom 00435 to 00898 (the nominal steel ratio is achieved bychanging the thickness of stainless steel tube) which in-creases by 10644 and the corresponding limit load in-creases by 2567 and K value is 02421 (e failure loadincreases by 2745 and K value is 02590 At the same timeFigure 12(a) shows that with the increase of nominal steelratio the falling stage of Fj minus D (displacement) curve becomes

Table 4 Model parameter level settings

Specimen number Di (mm) t0 (mm) fcu (MPa) fyo (MPa) fyi (MPa) Nu (kN) Nf (kN)1 40 12 40 275 235 514 4812 40 16 50 335 300 600 5183 40 20 60 412 345 911 8214 40 24 70 496 400 1163 10435 50 24 40 335 345 804 7616 50 20 50 275 400 738 6517 50 16 60 496 235 929 7938 50 12 70 412 300 790 7099 60 16 40 412 400 740 66610 60 12 50 496 345 754 67311 60 24 60 275 300 779 68112 60 20 335 235 235 837 76313 70 20 40 496 300 908 81114 70 24 50 412 235 801 70515 70 12 60 335 400 670 57116 70 16 70 275 345 700 601

Table 5 (e calculation results of range

Di t0 fcu fyo fyiRu 46 205 149 256 59Rf 57 189 142 226 47

C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)

Figure 10 (a) Fj minus D curves of different concrete strength (b) Ejnorm minus Fj curves of different concrete strength


more and more gentle indicating that the increase of nominalsteel ratio can improve the ductility of short columns

47 Equationof theCFSSASTColumnsunderAxialCompressionAt present there are few researches on the equation ofbearing capacity of the CFSSASTcolumns and the equationof failure load is not involved (is paper attempts to fit theequation of ultimate load and failure load on the basis ofparameter analysis and relevant research

471 Equation of Ultimate Load Huang Hong put forwardthe equations of the bearing capacity of the CFDSTcolumns(Nu) through a lot of parameter analyses [1] (e equation iscomposed of two parts the compound bearing capacity ofthe outer steel tube and the concrete (Nosc u) and thebearing capacity of the inner steel tube (Niu) (e inter-action between the steel tube and the concrete is consideredin Nosc u and the equation is shown as follows

Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi

fscy C1χ2fyo + C2(114 + 102ξ)fck

C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)

where fscy is the compound strength of outer steel tube andconcreteAsco is the sumof cross sectional area of outer steel tubeand concrete fyi fyo and fck are the yield strength of inner steeltube yield strength of outer steel tube and compressive strengthof concrete respectively Asi Aso and Ac are the cross sectionalareas of inner steel tube outer steel tube and concrete re-spectively a and an are the steel ratio and nominal steel ratiorespectively χ is the slenderness ratio ξ is constraint effectcoefficient ξ antimes (fyofck) Equation (11) is applicable to thecalculation of the ultimate bearing capacity of the CFDSTcolumns However the outer steel tube of the CFSSASTcolumnin this paper is made of stainless steel so it is assumed to fit theequation of the ultimate bearing capacity (Nuz) on the basis ofequation (11) Because the inner steel tube of CFSSASTcolumnis still the carbon steel the equation of Niu is still the same Andthe equation only needs to improve Noscu (that is to fit somecalculating coefficients of fscy ) After analysis the equation is asfollows

Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi

fscy C1χ2fyo + C2 301ξ3 minus 631ξ2 + 578ξ + 0311113872 1113873fck

C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa

Yield strength of stainless steel412MPa

496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)

Figure 11 (a) Fj minus D curves of different yield strength of stainless steel (b) Ejnorm minus Fj curves of different yield strength of stainless steel


According to the newly fitted equations the ultimateloads of 137 different short columns (including 6 test shortcolumns and 131 simulated short columns) are calculatedamong which 97 (accounting for 708) short columns haveerrors within 3 with an average error of 089 and astandard deviation of 345 (e accuracy of the equation isenough for analysis

472 Equation of Failure Load (e equation for calcu-lating the failure load is still in the form of ultimate load(Nf ) that is the equation is composed of two parts Onepart is the compound failure load (Noscf) of the outer steeltube and concrete (taking into account the constraint effectof steel tube on concrete) and the other part is the failureload of the inner steel tube (Nif) (e fitting equation is asfollows

Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi

fscyf C1χ2fyo + C2 197ξ3 minus 416ξ2 + 433ξ + 0451113872 1113873fck

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)

(e failure loads of 137 different specimens are calcu-lated by the equation Among them the 89 specimens haveerrors within 3 accounting for 650 the average error is007 and the standard deviation is 305(ese data provethe accuracy of the equation

5 StressingStateCharacteristicsofCFSSTShortColumns under Eccentric Compression

51 Characteristics of Ejnorm minus Fj Curve Take the modelP1300-76-14 (eccentric compression column) as an

example the Ejnorm minus Fj curve can be plotted with theexperimental data as shown in Figure 13 Similar to shortcolumns under axial compression two characteristic loadsof P and U are obtained by M-K criterion (e columnsunder eccentric compression are divided into three stagesduring loading process elastic working state (before load P)elastic-plastic working state (between load P and load U)and failure state (after load U)

52 Verification of Simulated Data To verify the rationalityof the FE model the errors of the simulated ultimate loadsare obtained by comparing the simulated results with theexperimental results as shown in Table 6 (e errors of themodel are all within 10 and the average error is minus108 Ina word the accuracy of the model meets the requirementsfor further analysis

53 Transverse Strain Analysis of Different Sections Inorder to further explain the mutations of the stressing stateof the eccentric compression columns several crosssections are selected for analysis (ey are section A (inthe middle of column) section D (at the end) andsections B and C (B and C are sections of trisection ofsections A and D) where section B is closer to section AIt can be seen from Figure 14 that before load P thecurve of each section changes linearly and the straindifferences of different sections are very small From loadP onwards the curves tend to increase in a nonlinear wayand begin to diverge that is the growth rate of section Dstarts to be smaller than that of the other three sectionsAfter load U the curve of each section increases rapidlyand the growth rate of section A is larger than that ofother sections

Nominal steel ratio0043500586

0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)

Figure 12 (a) Fj minus D curves of different nominal steel ratio (b) Ejnorm minus Fj curves of different nominal steel ratio


54 Stress Contour Maps Analysis of Eccentric CompressionModel Similar to the axial compression column modelP1300-76-14 is selected for analyzing the stress change ofeccentric compression column during the whole loading

process (e stress contour maps corresponding to fourrepresentative loads are selected for analysis (e four loadsare (1) point A elastoplastic critical load (2) point B failureload (3) point C ultimate load and (4) point D load

P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)

Figure 13 Ejnorm minus Fj curve of P1300-76-14


Specimen number Mean value of experimental ultimate load (kN) Mean value of simulated ultimate load (kN) Error ()P800-50-4 653 66993 259P800-76-14 436 40641 minus679P800-89-45 200 21883 942P1300-50-4 556 55434 minus030P1300-76-14 380 35898 minus553P1300-89-45 201 19398 minus349P1800-50-4 492 48719 minus098P1800-76-14 300 30507 169P1800-89-45 181 16949 minus636

P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)

Figure 14 (a) Transverse strainminus Fj curves of different sections (b) Slope of transverse strainminus Fj curves of different sections


corresponding to 30 reduction of bearing capacity re-spectively (Figure 15)

Figure 16 shows the longitudinal stress contour mapsof the stainless steel tube at four points (e side where theeccentric load is located is defined as the inner side whilethe opposite side is defined as the outer side At point Athe longitudinal stress of the inner side of the middlesection is minus145MPa and the outer side of the middlesection is minus17MPa which do not reach the yield strengthof stainless steel At point C the stress of inner sidegradually decreases from the middle to both ends and themaximum stress (in the middle section) and the minimumstress (at the end section) are minus283MPa and minus227MParespectively (the stainless steel tube reaches yieldstrength) (e stress of outer side is tensile stress and thestress distribution is similar to that of the inner side Atthe same time the maximum stress (in the middle section)and the minimum stress (at the end section) are 185Mpaand 4MPa respectively In the falling stage of load thestructural deformation is more and more large and thestress on both sides tends to concentrate on the middlesection

(e stress of concrete at four points is different fromthat of stainless steel tube as shown in Figure 17 Whenthe load reaches elastoplastic critical load the compres-sive stress of the middle section is the largest and theinner side and the outer side are minus29MPa and minus7MParespectively At point B the stresses of inner side andouter side of the middle section are minus50MPa andminus06MPa respectively and the tensile stress is about toappear on the outer side When the load reaches the ul-timate load the stress in most middle areas of the innerside is minus62MPa and the stress at both ends is minus48MPa(e maximum tensile stress of the outer side is 37MPaAs the load continues the deformation of the structurebecomes larger and the compressive stress of inner sidetends to concentrate on the middle section and themaximum tensile stress of outer side gradually approachesthe end section

55 Single Variable Parameter Analysis According to theprinciple of single variable the influences of 7 factors onthe bearing capacity of eccentrically loaded columns areanalyzed including nominal steel ratio slenderness ra-tio hollow ratio concrete strength stainless steelstrength carbon steel strength and load eccentricity Inorder to ensure the reliability of simulated results thelevel of each parameter should be maintained at theexperimental level

551 Influence of Nominal Steel Ratio Figures 18(a) and18(b) are the Fj(load) minus MPD (middle point deflection ofthe columns) curves and Ejnorm minus Fj characteristic curvesof eccentrically compressed columns respectively (epoints marked on the deflection curves are the ultimateloads and the points marked on the characteristic curvesare the failure loads (these points are also used for the

following parameter analysis) (e nominal steel ratioincreases from 00435 to 00898 increased by 1064 andthe corresponding ultimate loads are 27998 kN30968 kN 34013 kN and 36569 kN respectively in-creased by 3061 and the value of K is 02877 (ecorresponding failure loads are 26708 kN 29176 kN31339 kN and 34093 kN increased by 2765 and K is02599 Figure 18(a) shows that although the ultimate loadof eccentric compression column increases the deflectionin the column corresponding to the ultimate load keeps thesame and the trend of the falling stage after the ultimateload also remains the same indicating that the change ofnominal steel ratio has few effects on the ductility of theeccentric compression column

552 Influence of the Slenderness Ratio As shown inFigure 19 the ultimate load and failure load of the eccentriccompression column will decrease obviously with the rise ofslenderness ratio (e slenderness ratio increases by 1500(from 2597 to 6492) and the corresponding ultimate loaddecreases by 6540 and K is 04360 (e correspondingfailure load reduces by 7586 and K is 05057 (e de-flection of the column corresponding to the ultimate loadalso improves with the slenderness ratio increasing and thedecline stage after the ultimate load tends to be gentle whichshows that in a certain range the ductility of the eccentriccompression column increases with the rise of slendernessratio

553 Influence of Hollow Ratio (e hollow ratio increasesby 1996 (from 0273 to 0818) and the correspondingultimate load decreases by 2856 and the K is 01431 (ecorresponding failure load reduces by 2725 and K is01365 With the increase of hollow ratio the decrease ofultimate load becomes more obvious and the deflection ofthe column corresponding to ultimate load is smaller (edifference of ultimate load with hollow ratio of 0273 and

D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)

Figure 15 Fj minus D (displace) curves of the model P1300-76-14


0455 is within 5 and the curves almost coincide It maybe the fact that when the hollow ratio is small to a certaincritical value it is equivalent to the solid stainless steeltubular concrete column so the curves of the two columnsof different hollow ratio are almost the same Meanwhilethe falling stages of several curves are nearly parallelwhich shows that the change of hollow ratio has few effectson the ductility of eccentric compression columns(Figure 20)

(e analysis of other parameters is the same as aboveand the comprehensive comparison of the R (range) andK ofeach parameter shows that the load eccentricity and slen-derness ratio have the most significant impact on the bearing

capacity of eccentrically compressed columns followed bythe stainless steel strength nominal steel ratio and concretestrength while the hollow ratio and carbon steel strengthhave the least impact on the bearing capacity

6 Equation of the CFSSAST Columns underEccentric Compression

61 Equation for Predicting Ultimate Load Based on theexperiment and a large number of simulation parameteranalyses Tao et al [1] found that the CFDSTcolumns undereccentric compression meet the following equations

(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01

Figure 17 (e longitudinal stress contour maps of the concrete (a) Point A (b) Point B (c) Point C (d) Point D



0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)

Figure 18 (a) Fj minusMiddle point deflection of the columns curves under different nominal steel ratio (b) Ejnorm minus Fj curves under differentnominal steel ratio

Slenderness ratio25973895

51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)

Figure 19 (a) Fj minusMiddle point deflection of the columns curves under different slenderness ratio (b) Ejnorm minus Fj curves under differentslenderness ratio


1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0

a 1 minus 2φ2 times η0

b 1 minus ζ0φ3 times η20

c 2 times ζ0 minus 1( 1113857

η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)

NE π2 middot Escm middotAsc

λ2

Escm EsIso + EcIc + EsIsi

Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)

η0 (05 minus 0245 middot ξ) minus18χ2 + 02χ + 1( 1113857 ξ le 04

01 + 014 middot ξminus 0841113872 1113873 minus18χ2 + 02χ + 1( 1113857 ξ gt 04

⎧⎨

⎩

(16)

where ξ is constraint effect coefficient χ is the slendernessratioNu is the axial bearing capacity of the columnMu is theflexural capacity of the column Es and Ec are the moduluselasticity of steel tube and concrete respectively Iso Isi and Icare the section moments of inertia of outer inner steel tubesand concrete respectively φ is the stability coefficient ofaxial compression According to the above equation theultimate bearing capacity of the column under eccentriccompression can be calculated which is recorded as N1 (eonly difference between the CFSSAST column in this paperand the CFDST column is that the outer steel tube changesfrom carbon steel to stainless steel so it is assumed that therelationship betweenN1 and the ultimate bearing capacity ofCFSSAST column under eccentric compression (Nup) is

Nup βN1 (17)

where β is fitting coefficient Since eccentricity and slen-derness ratio are the key factors affecting the ultimatebearing capacity the function β f (e λ) is constructedBased on numerous researches β is calculated as follows

β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)

where λ is the slenderness ratio and e is the eccentricity ofload According to the newly fitted equations the ultimate

Hollow ratio02730455

06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)

Figure 20 (a) Fj minusMiddle point deflection of the columns curves under different hollow ratio (b) Ejnorm minus Fj curves under different hollowratio


loads of 171 specimens (17 experimental specimens and 154simulated specimens) are calculated Among them 129specimens have errors within 5 accounting for 754 theaverage error is 014 and the standard deviation is 45

62 Equation for Predicting Failure Load (e equation offailure load is still in the form of ultimate load that is thefailure load is deduced by using ultimate load (roughparameter analysis the equation of failure load is as follows

Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)

where λ is the slenderness ratio and e is the eccentricity ofload (e failure loads of 171 specimens (17 experimentalspecimens and 154 simulated specimens) are calculated byequation (17) Among them 144 specimens have errorswithin 5 accounting for 842 the average error is 030and the standard deviation is 42 (e accuracy of theequations is enough for analysis

7 Conclusion

(is study reveals the stressing state characteristics of theCFSSAST columns under eccentric compression and axialcompression Based on the experimental data the Ejnorm minus

Fj curve is drawn and then the failure load is determined byMann-Kendall (M-K) criterion to distinguish the stressingstate transition following the law from quantitative changeto qualitative change (e qualitative mutation of thecomponentrsquos stressing state significantly manifests thestarting point in the process of the componentrsquos failure sothe definition of the existing failure load is updated (estress distribution of short columns under different loadsand the influence of different parameters on the ultimateload and failure load of short columns are analyzed by usingsimulated data On the basis of parameter analysis andrelated research the failure load and ultimate load equationsof CFSSASTcolumns are fitted (ose provide references forthe improvement of relevant design codes

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

Authorsrsquo Contributions

Sijin Liu Wei Wang and Baisong Yang conceived the studyand were responsible for the design and development of the

data analysis Wei Wang and Sijin Liu were responsible fordata collection analysis and interpretation Lingxian Yangand Guorui Sun helped perform the analysis with con-structive discussions Baisong Yang wrote the original draftof the article Baisong Yang and Wei Wang equally con-tributed to this manuscript as co first author

Acknowledgments

(e authors would like to express their gratitude toXiaofei Wen for carrying out the excellent experiment ofCFSSAST columns and giving the complete experimentaldata (e authors would also like to thank the members ofthe HIT 504 office for their selfless help and usefulsuggestions

References

[1] Z Tao L H Han and H Huang ldquoMechanical behavior ofconcrete filled double skin steel tubular columns with circularcular sectionsrdquo China Civil Engineering Journal vol 37no 10 pp 41ndash51 2004

[2] J H Zhao and J Wei ldquoAnalysis of ultimate bearing ofconcrete filled double skin steel tubular columnsrdquo Science-paper Online vol 2 no 9 pp 688ndash692 2007

[3] L Zhang X G Wang and Y C Han ldquoExperiment analysis ofconcrete filled circular steel tubular columns under eccentricloadrdquo Journal of Railway Science and Engineering vol 7 no 5pp 50ndash53 2010

[4] Q X Ren Y B Lv L G Jia and D Q Liu ldquoPreliminaryanalysis on inclined concrete-filled steel tubular stub columnswith circular section under axial compressionrdquo AppliedMechanics and Materials vol 88-89 pp 46ndash49 2011

[5] W Li L-H Han and X-L Zhao ldquoAxial strength of concrete-filled double skin steel tubular (CFDST) columns with preloadon steel tubesrdquo Min-Walled Structures vol 56 pp 9ndash202012

[6] K Uenaka H Kitoh and K Sonoda ldquoConcrete filled doubleskin circular stub columns under compressionrdquo Min-WalledStructures vol 48 no 1 pp 19ndash24 2010

[7] Y Z Wang and B S Li ldquoAxial behavior of concrete-filleddouble skin steel tubular stub columns filled with demolishedconcrete lumprdquo Advanced Materials Research vol 898pp 407ndash410 2014

[8] M Pagoulatou T Sheehan X H Dai and D Lam ldquoFiniteelement analysis on the capacity of circular concrete-filleddouble-skin steel tubular (CFDST) stub columnsrdquo Engi-neering Structures vol 72 no 1 pp 102ndash112 2014

[9] M F Hassanein and O F Kharoob ldquoCompressive strength ofcircular concrete-filled double skin tubular short columnsrdquoMin-Walled Structures vol 77 pp 165ndash173 2014

[10] Q Q Liang ldquoNumerical simulation of high strength circulardouble-skin concrete-filled steel tubular slender columnsrdquoEngineering Structures vol 168 pp 205ndash217 2018

[11] L H Han Q X Ren and W Li ldquoTests on stub stainless steel-concrete-carbon steel double-skin tubular (DST) columnsrdquoJournal of Constructional Steel Research vol 63 no 3pp 473ndash452 2011

[12] X Chang Z Liang Ru W Zhou and Y-B Zhang ldquoStudy onconcrete-filled stainless steel-carbon steel tubular (CFSCT)stub columns under compressionrdquo Min-Walled Structuresvol 63 pp 125ndash133 2013


[13] M Cao Flexural Behavior of Stainless Steel-Concrete-SteelConcrete Filled Double Skin Steel Tube MS thesis TaiyuanUniversity of Technology Taiyuan China 2015

[14] F Zhou and W Xu ldquoCyclic loading tests on concrete-filleddouble-skin (SHS outer and CHS inner) stainless steel tubularbeam-columnsrdquo Engineering Structures vol 127 pp 304ndash3182015

[15] X F Wen Experimental and Meoretical Analysis of Me-chanical Behavior of Concrete-Filled the Gap between StainlessSteel and Steel Tubular Columns MS thesis Taiyuan Uni-versity of Technology Taiyuan China 2017

[16] J G Zhang F F Liu and T J Zhao ldquoExperimental researchon the shear resistance performance of concrete-filled doublestainless-steel tubular columnsrdquo Journal of Harbin Engi-neering University vol 40 no 7 pp 1311ndash1318 2019

[17] S Jiang and R Wang ldquoExperiment study and finite elementanalysis of concrete filled stainless and steel double skin tubesmember under lateral impactrdquo Industrial Constructionvol 46 no 11 pp 161ndash167 2016

[18] H Zhao R Wang C C Hou and D Lam ldquoPerformance ofcircular CFDST members with external stainless steel tubeunder transverse impact loadingrdquo Min-Walled Structuresvol 145 2019

[19] G C Zhou M Y Rafiq G Bugmann and D J EasterbrookldquoCellular automata model for predicting the failure pattern oflaterally loadedmasonry wall panelsrdquo Journal of Computing inCivil Engineering vol 20 no 6 pp 400ndash409 2006

[20] G Zhou D Pan X Xu and Y M Rafiq ldquoInnovative ANNtechnique for predicting failurecracking load of masonry wallpanel under lateral loadrdquo Journal of Computing in CivilEngineering vol 24 no 4 pp 377ndash387 2010

[21] F ChenNonlinear StaticWind Stability Analysis of Long SpanConcrete Filled Steel Tubular Arch Bridge PhD (esisChangrsquoan University Xian China 2003

[22] L H Han Concrete Filled Steel Tubular StructuresMeory andPractice Science Press Beijing China 2004

[23] Z H Guo Strength and Constitutive Relation of ConcretePrinciple and Application China Construction amp IndustryPress Beijing China 2004


predicting the bearing capacities of the circular inclinedspecimens [4] Li et al established a general finite elementanalysis model of CFDSST columns under preloading andproposed corresponding formulas for calculating the ultimatebearing capacity of CFDSSTcolumns with preloading on steeltubes [5] Subsequently many researchers had studied theaxial compression performance of CFDSST columns [6ndash8]Hassanein and Kharoob summarized previously developedformulas for predicting the compressive strength of theCFDSST columns and used the ABAQUSstandard softwareto perform numerical nonlinear simulations (roughcomparing tested results with simulated results a new designformula is suggested [9] Liang established a new mathe-matical model which could compute the axial load-deflectionperformance of high-strength circular CFDSST slender col-umns subjected to eccentric loading (e model accuratelypredicted the residual concrete strength and strain in thepostyield regime [10]

In recent years many scholars had conducted exper-imental research on concrete-filled stainless steel and steeltubular (CFSSAST) columns For instances Han et alconducted a series of performance tests on CFSSASTcolumns and proposed a simplified model for predictingthe strength of the column section [11] Chang et alcarried out a range of compression tests on CFSSASTcolumns (e results indicated that the column strengthincreased with the increasing of the diameter ratio wallthickness ratio yield strength ratio and concrete strength[12] Cao took the shear span ratio of CFSSASTcolumns asthe main variable parameter and carried out bending tests(e results showed that the CFSSAST specimens exhibitedoutstanding ductile damage performance under bendingload and the flexural capacity was inversely proportionalto the shear span ratio [13] Zhou and Xu conducted cyclicload test on double-layer stainless steel tube concrete beamcolumn (e results showed that the axial compressiveload level and thickness of outer tubes have a primaryinfluence on the behavior of the test specimens [14] Wenconducted an experimental study on the mechanical be-havior of CFSSAST columns (e experiment results in-dicated that for long columns under eccentric loadingconditions the stiffness and bearing capacity decreasedobviously with the increase of the hollow ratio slendernessratio and load eccentricity [15] Zhang et al carried outthe experimental research on the shear resistance per-formance of concrete-filled double stainless-steel tubularcolumns and proposed empirical equation for calculatingthe shear bearing capacity of specimens [16] Some otherresearchers tested the impact resistance of CFSSASTcolumns [17 18] (e experimental results showed that theglobal deformation and local deformation of specimensdeveloped with the increase of the impact force the impacttime and impact height

Although these research results greatly promoted theapplication of CFSSAST columns in engineering projectsthere are still some problems of CFSSAST columns to beresolved summarized as follows (1) Up to now the failureload of CFSSAST columns is determined on the semiem-pirical and semitheoretical basis with considerable

inaccuracy and the failure mechanism of the columns is notinvolved (2) At present most of the researches tend to focuson the mechanical properties of CFSSAST columns underaxial loads while the researches of specimens under ec-centric loads are inadequate

In order to address these two issues the authors deeplystudy the mechanical properties of CFSSASTcolumns underaxial and eccentric loads based on the theory of structuralstressing states (e measured strain data of CFSSASTcolumns are modeled as generalized strain energy density(GSED) to describe the structural stressing state modes(en M-K method is applied to GSED sum-load curve todistinguish the mutation feature of the curve and reveal thefailure mechanism of CFSSAST columns in the process ofloading so as to update the definition of the existing columnfailure load

2 Methods for Modelling and AnalyzingStructural Stressing State

21 Structural Stressing State Concept and GSED Curve(e authors define the stressing state of a structure as thestructural working behavior characterized by the distributionpattern of strain energy density values displacements strainsand stresses of measuring points [19 20] Generally the strainenergy density Ei of the i-th point can be calculated by

Ei 1113946 σ1dε1 + σ2dε2 + σ3dε3 (1)

where σ1 σ2 σ3 and ε1 ε2 ε3 are three principal stresses andstrains respectively Ei is the i-th strain energy densityHowever due to the directionality of stress and strain thisnumerical model is not convenient for further processingand analysis(erefore the generalized strain energy density(GSED) is used as the parameter to characterize the stressingstate at a certain point (us equation (1) is simplified as

Eij 12

Eε2ij (2)

where Eij is the GSED value of the i-th measured pointunder the j-th load E is the elastic modulus of the materialεij is the strain value of the i-th point under the j-th load Inorder to better compare and analyze the change charac-teristics of GSED sum curve of different components orstructures it can be normalized as

Ejnorm 1113936

Ni1 Eij

Emax (3)

where Ejnorm is the sum of the normalized GSED values ofall the measured points to the j-th loadN is the number of allmeasuring points Emax is the maximum of the strain energyvalues over the loading process (us the Ejnorm minus Fj curveof the structure can be plotted to investigate differentstructural stressing states and corresponding characteristics

22 M-K Criterion (e MannndashKendall (M-K) method isapplied to distinguish the stressing state mutation of thestructure through the Ejnorm minus Fj curve because it does not



bm 1113944

m

i


0 otherwise

⎧⎨

⎩

(4)


D bm( 1113857 m(m minus 1)

4 2lemle n (5)

Var bm( 1113857 m(m minus 1)(2m + 5)

72 2lemle n (6)


NFm

0 m 1


1113969 2lemle n

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)








ε

σE0

+ 0002σσ02

1113888 1113889

n

σ le σ02

σ minus σ02

E02+ εu

σ minus σ02

σu minus σ021113888 1113889

m

+ ε02 σ02 lt σ

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)



σσ0

12εεp

minus 02ε06

εp

εεp

le 1

εεp1113872 1113873

03σ2p εεp1113872 1113873 minus 11113872 111387317

+ εεp

εεp

gt 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)











t0ti

Di

D0

Concrete

Stainless steel

Carbon steel







Displacementmeter

Displacement meter

342

N

Specimen

Displacementmeter


gauge

114

(a)

Tester

Displacementmeter

Straingauge

Loadingplate

Knifeedgehinge

N

N

(b)


(a) (b)












U

P

P = 325 kN

U = 609 kN

02468

10

Stat

istic

s

200 400 6000Fj (kN)

00

02

04

06

08

10

100 200 300 400 500 600 7000Fj (kN)

450 500 550 600 650 700400Fj (kN)

0

2

4

6

8

Stat

istic

sE jn

orm





K C1

C2 (10)



578 kN618 kN

567 kN


0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)



Specimennumber



Error()




D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)



(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References



























bm 1113944

m

i


0 otherwise

⎧⎨

⎩

(4)


D bm( 1113857 m(m minus 1)

4 2lemle n (5)

Var bm( 1113857 m(m minus 1)(2m + 5)

72 2lemle n (6)


NFm

0 m 1


1113969 2lemle n

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)








ε

σE0

+ 0002σσ02

1113888 1113889

n

σ le σ02

σ minus σ02

E02+ εu

σ minus σ02

σu minus σ021113888 1113889

m

+ ε02 σ02 lt σ

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)



σσ0

12εεp

minus 02ε06

εp

εεp

le 1

εεp1113872 1113873

03σ2p εεp1113872 1113873 minus 11113872 111387317

+ εεp

εεp

gt 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)











t0ti

Di

D0

Concrete

Stainless steel

Carbon steel







Displacementmeter

Displacement meter

342

N

Specimen

Displacementmeter


gauge

114

(a)

Tester

Displacementmeter

Straingauge

Loadingplate

Knifeedgehinge

N

N

(b)


(a) (b)












U

P

P = 325 kN

U = 609 kN

02468

10

Stat

istic

s

200 400 6000Fj (kN)

00

02

04

06

08

10

100 200 300 400 500 600 7000Fj (kN)

450 500 550 600 650 700400Fj (kN)

0

2

4

6

8

Stat

istic

sE jn

orm





K C1

C2 (10)



578 kN618 kN

567 kN


0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)



Specimennumber



Error()




D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)



(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References

































t0ti

Di

D0

Concrete

Stainless steel

Carbon steel







Displacementmeter

Displacement meter

342

N

Specimen

Displacementmeter


gauge

114

(a)

Tester

Displacementmeter

Straingauge

Loadingplate

Knifeedgehinge

N

N

(b)


(a) (b)












U

P

P = 325 kN

U = 609 kN

02468

10

Stat

istic

s

200 400 6000Fj (kN)

00

02

04

06

08

10

100 200 300 400 500 600 7000Fj (kN)

450 500 550 600 650 700400Fj (kN)

0

2

4

6

8

Stat

istic

sE jn

orm





K C1

C2 (10)



578 kN618 kN

567 kN


0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)



Specimennumber



Error()




D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)



(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References






























Displacementmeter

Displacement meter

342

N

Specimen

Displacementmeter


gauge

114

(a)

Tester

Displacementmeter

Straingauge

Loadingplate

Knifeedgehinge

N

N

(b)


(a) (b)












U

P

P = 325 kN

U = 609 kN

02468

10

Stat

istic

s

200 400 6000Fj (kN)

00

02

04

06

08

10

100 200 300 400 500 600 7000Fj (kN)

450 500 550 600 650 700400Fj (kN)

0

2

4

6

8

Stat

istic

sE jn

orm





K C1

C2 (10)



578 kN618 kN

567 kN


0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)



Specimennumber



Error()




D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)



(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References



































U

P

P = 325 kN

U = 609 kN

02468

10

Stat

istic

s

200 400 6000Fj (kN)

00

02

04

06

08

10

100 200 300 400 500 600 7000Fj (kN)

450 500 550 600 650 700400Fj (kN)

0

2

4

6

8

Stat

istic

sE jn

orm





K C1

C2 (10)



578 kN618 kN

567 kN


0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)



Specimennumber



Error()




D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)



(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References




























K C1

C2 (10)



578 kN618 kN

567 kN


0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 50D (mm)

(a)

540 kN

521 kN

535 kN


00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)



Specimennumber



Error()




D

CB

Model Z-76

A

0

100

200

300

400

500

600

F j (k

N)

1 2 3 4 5 6 70D (mm)



(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References


























(a) (b) (c) (d)




(a) (b) (c) (d)


(a) (b) (c) (d)










C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References
































C40

C50

C60

C70

C80

0

100

200

300

400

500

600

700

F j (k

N)

2 4 6 80D (mm)

(a)

C40

C50

C60

C70

C80

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 600 7000Fj (kN)

(b)






Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References





























Nu Noscu + Niu

Noscu fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


Nuz Noscz + Niu

Noscz fscyAsco

Niu fyiAsi


C1 α

(1 + α)

C2 1 + αn( 1113857

(1 + α)

Asco Aso + Ac

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

275MPa

335MPa


496MPa

0

200

400

600

800

F j (k

N)

2 4 6 80D (mm)

(a)

275MPa

335MPa


496MPa

200 400 600 8000Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References




























Nf Noscf + Nif

Noscf fscyfAsco

Nif 093Asifyi


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)








0074100898

0

100

200

300

400

500

600F j

(kN

)

2 4 6 80D (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

100 200 300 400 500 6000Fj (kN)

(b)





P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References




























P

U

P = 192 kN

U = 323 kN

0

2

4

6

Stat

istic

s

300 350250Fj (kN)50 100 150 200 250 300 350 4000

Fj (kN)

00

02

04

06

08

10

E jn

orm

0

2

4

6

8

10

Stat

istic

s

100 200 300 4000Fj (kN)




P = 192 kN

U = 323 kN

AC

BD

00

05

10

15

20

25

Tran

sver

se st

rain

(times10

ndash3)

50 100 150 200 250 300 3500Fj (kN)

(a)

323 kN

P = 192 kN

AC

BD

00

02

04

06

08

10

Slop

e of t

rans

vers

e str

ain

(times10

ndash4)

50 100 150 200 250 300 3500Fj (kN)

(b)











D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References


































D

C

B

P1300-76-14

A

0

50

100

150

200

250

300

350

400

F j (k

N)

5 10 15 20 25 30 350D (mm)








(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References































(a) (b) (c) (d)

+3880e + 02

+3276e + 02

+2672e + 02

+2068e + 02

+1463e + 02

+8592e + 01

+2550e + 01

ndash3492e + 01

ndash9533e + 01

ndash1558e + 02

ndash2162e + 02

ndash2766e + 02

ndash3370e + 02


(a) (b) (c) (d)

+3650e + 00

ndash2404e + 00

ndash8458e + 01

ndash1451e + 01

ndash2057e + 01

ndash2662e + 01

ndash3267e + 01

ndash3873e + 01

ndash4478e + 01

ndash5084e + 01

ndash5689e + 01

ndash6295e + 01

ndash6900e + 01




0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References



























0074100898

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 20 250MPD (mm)

(a)


0074100898

00

02

04

06

08

10

E jn

orm

50 100 150 200 250 300 3500Fj (kN)

(b)



51936492

0

100

200

300

400

F j (k

N)

10 20 30 400MPD (mm)

(a)


51936492

00

02

04

06

08

10

E jn

orm

100 200 300 4000Fj (kN)

(b)



1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References


























1φ

N

Nu

+a

d

M

Mu

1N

Nu

ge 2φ3η0

minusb NNu

1113874 11138752

minus cN

Nu

1113888 1113889 +1d

M

Mu

1113888 1113889 1N

Nu

lt 2φ3η0




η0

d 1 minus 04 timesN

NE

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)


λ2


Iso + Ic + Isi

ζ0 018 minus 02χ2( 1113857ξminus 115+ 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)



⎧⎨

⎩

(16)


Nup βN1 (17)


β Ae2 + Be + C

A 00250λ minus 0525

B minus0024λ + 0281

C minus00002λ + 1304

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)



06360818

0

50

100

150

200

250

300

350F j

(kN

)

5 10 15 200MPD (mm)

(a)


06360818

50 100 150 200 250 300 3500Fj (kN)

00

02

04

06

08

10

E jn

orm

(b)





Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References




























Nfp δN1

δ De2 + Ee + F

D 00260λ minus 0600

E minus00260λ + 0388

F minus00002λ + 1210

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)


7 Conclusion



Data Availability







Acknowledgments


References


























StudyonStressingStateandFailureCriterionofConcrete-Filled ... · 2020. 7. 20. · columns and...

Documents

Transcript of StudyonStressingStateandFailureCriterionofConcrete-Filled ... · 2020. 7. 20. · columns and...