Concrete-filled VHS-to-steel fabricated section stub columns subjected to axial compression

Journal of Constructional Steel Research 95 (2014) 141–161

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Journal of Constructional Steel Research

Concrete-filled VHS-to-steel fabricated section stub columns subjected to axial compression Fidelis R. Mashiri a,⁎, Brian Uy b, Zhong Tao c, Zhi-Bin Wang d,e a

School of Computing Engineering and Mathematics, University of Western Sydney, Penrith, NSW 2751, Australia The School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia Institute for Infrastructure Engineering, University of Western Sydney, Penrith, NSW 2751, Australia d College of Civil Engineering, Fuzhou University, Fuzhou, Fujian Province, 350108, China e Department of Civil Engineering, Tsinghua University, Beijing 100084, China b c

a r t i c l e

i n f o

Article history: Received 2 December 2012 Accepted 23 November 2013 Available online 5 January 2014 Keywords: Columns Concrete filled sections Compressive strength Codes of practice Strength index Very high strength steel

a b s t r a c t The use of very high strength materials is currently being researched as a way to reduce material use and improve sustainability. In this investigation a total of 32 specimens were fabricated using very high strength (VHS) steel tubes and plates to form stub columns. The VHS-plate fabricated stub columns were tested under axial compression. The specimens comprised 20 fabricated square sections and 12 fabricated triangular sections. The VHS steel tubes used have a nominal yield stress of 1350 MPa and a nominal ultimate tensile strength of 1500 MPa. Mild steel plates and high strength steel plates were used to connect the VHS tubes at the vertices thereby forming square and triangular cross sections. Normal strength concrete with a standard concrete strength grade of 32 MPa was used as concrete in-fill. Finite element models are developed to simulate the behaviour of the VHS-plate stub columns. The finite element models predicted the load–deformation behaviour of the fabricated columns well with the peak strength and post-peak behaviour similar to the experimental results. A parametric study was also carried out to determine the effect of concrete strength, facet plate yield strength and facet plate width to wall thickness ratio. The parametric study shows that there is benefit in concrete confinement through the use of higher strength steel facet plates. This paper also proposes a method for determining the axial compression capacity of fabricated VHS-plate stub columns. The predicted peak strength from the proposed design method is in good agreement with the test results. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction Very high strength steel tubes can be manufactured with nominal tensile yield stresses in the order of 1350 MPa. The very high strength steel (VHS) tubes are quenched and tempered and have a nominal tensile yield stress that is more than 3 times that of common steel grades which typically have a nominal tensile yield stress of 350 MPa [1]. At present, VHS tubes have typically found their application in the automotive and mechanical industries where they are used as side door impact bars [2]. The obvious benefits of very high strength steel sections in the construction industry is that they may be able to be deployed in columns for multi-storey buildings through the fabrication of columns of various cross sections consisting of tubes welded to facet plates as shown in Fig. 1a and 1b. This use of the fabricated sections has the advantage of eliminating the need of column formwork when these fabricated sections are concrete filled. Previous research by Zhao et al. [3] investigated the strength of empty stub columns of fabricated VHS tube to mild steel plate similar to those reported in this current investigation. The research by Zhao ⁎ Corresponding author. Tel.: +61 2 47360355. E-mail address: [email protected] (F.R. Mashiri). 0143-974X/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jcsr.2013.11.022

et al. [3] extended research carried out by Aoki and Ji [4]. Aoki and Ji [4] investigated the buckling strength of fabricated sections of triangular cross sections using normal strength steel. This paper proposes a method for determining the axial compression capacity of concrete-filled fabricated VHS-plate stub columns. Both the square and triangular fabricated VHS-plate stub columns are investigated. The fabricated stub columns use both mild steel and high strength steel as facet plates. Normal strength concrete with a standard concrete strength grade of 32 MPa was used as concrete in-fill. Although normal strength concrete has been used in the current study, the use of high strength concrete and high strength steel will also be investigated in future, as part of this research programme. The method for determining the axial compression capacity uses the principle of superposition to take into account the contribution of steel and concrete in the composite stub columns. The effective areas of the steel plates and the VHS tubes used in the columns are also considered to ensure that local buckling effects under compression are taken into account. Finite element (FE) models are developed to simulate the behaviour of the VHS-plate stub columns. The three-dimensional (3D) finite element models are developed using ABAQUS software. The design and FE models also consider the material behaviour of the heat-affected zone (HAZ).

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B

d

d d

B

d

T VHS tube

T VHS tube

Facet Plate

t

Facet Plate

Concrete In-fill t

Strain gauge

Fig. 1. Fabricated VHS-plate square and triangular hollow sections.

S3H were used for validating the finite element model of the empty fabricated sections.

A good comparison in load–deformation behaviour is obtained between the FE model and the test results. A parametric study was used to determine the influence of parameters such as concrete strength, yield strength of the facet plates and the facet plate width (B) to wall thickness (t) ratio. The proposed design method also gives a good prediction of the peak strength in both the concrete-filled square and triangular VHS-plate stub columns.

2.1.2. Material properties The material properties of the steel used for the different fabricated VHS-plate square hollow section test series are shown in Table 1. The nominal yield stress and nominal ultimate tensile strength of the VHS tube, fynt and funt respectively as well as the nominal yield stress and nominal ultimate tensile strength of the facet plates, fynp and funp respectively are given in Table 1. For all the specimens, VHS tubes with a nominal yield stress and nominal ultimate tensile strength of 1350 MPa and 1500 MPa respectively were used. Mild steel and high strength steel facet plates were used in the specimens. The mild steel facet plates had a nominal yield stress and nominal ultimate tensile strength of 250 MPa and 350 MPa, respectively. The high strength steel plates had a nominal yield stress and nominal ultimate tensile strength of 400 MPa and 520 MPa, respectively. The corresponding measured yield stress and ultimate tensile strength of the VHS tube, fyt and fut respectively as well as the measured yield stress and nominal ultimate tensile strength of the facet plates, fyp and fup respectively are also given in Table 1. The yield stress and ultimate tensile strength of the VHS tubes and facet plates were determined using the procedure

2. Test programme 2.1. Fabricated VHS-plate square hollow sections 2.1.1. General Twenty fabricated VHS-plate square hollow sections were manufactured and tested under compression in this investigation. A fabricated square hollow section is shown in Fig. 1a. Eighteen of the fabricated square section stub columns were concrete-filled using grade 32 MPa concrete prior to compression testing. Two of the fabricated square section stub columns were tested as hollow section stub columns. The properties of the test series of the fabricated square hollow sections tested in this investigation are shown in Table 1. All the tests series except for test series S1H and S3H were concrete filled. Test series S1H and Table 1 Fabricated VHS-plate square hollow section test series. Test series

Number of specimens tested

V1NP1 V1NP2 V1NP3

Very high strength (VHS) steel tube

Plate

d (mm)

t (mm)

d/t

Material properties

B (mm)

T (mm)

B T

Material properties

2 2 2

38.1 38.1 38.1

1.6 1.6 1.6

23.8 23.8 23.8

90 120 150

3 3 3

30 40 50

V1HP1 V1HP2 V1HP3

2 2 2

38.1 38.1 38.1

1.6 1.6 1.6

23.8 23.8 23.8

Nominal values: fynt = 1350 MPa funt = 1500 MPa Measured values: fyt = 1392 MPa fut = 1515 MPa

90 120 150

3 3 3

30 40 50

S1H S3H S2Con S4Con S5Con S6Con S7Con S8Con

1 1 1 1 1 1 1 1

38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1

1.8 1.6 1.8 1.6 1.6 1.8 1.6 1.8

21.17 23.81 21.17 23.81 23.81 21.17 23.81 21.17

90 90 90 90 120 120 150 150

3 3 3 3 3 3 3 3

30 30 30 30 40 40 50 50

Nominal values: fynp = 250 MPa funp = 350 MPa Measured values: fyp = 268.9 MPa fup = 357.6 MPa Nominal values: fynp = 400 MPa funp = 520 MPa Measured values: fyp = 439.3 MPa fup = 851 MPa Nominal values: fynp = 250 MPa funp = 350 MPa Measured values: fyp = 271 MPa fup = 356 MPa

Nominal values: fynt = 1350 MPa funt = 1500 MPa Measured values: fyt-1.6 = 1369 MPa* fut-1.6 = 1522 MPa* fyt-1.8 = 1330 MPa* fut-1.8 = 1522 MPa*

Concrete Material properties fc′ = 32 MPa fcm = 33 MPa

Height of specimen (H) (mm) 300 400 500

300 400 500

Empty fc′ = 32 MPa fcm = 35 MPa

300 300 300 300 400 400 500 500

NOTE: *fyt-1.6 = measured yield stress in the 1.6 mm thick VHS tubes; *fyt-1.8 = measured yield stress in the 1.8 mm thick VHS tubes; *fut-1.6 = measured ultimate tensile strength in the 1.6 mm thick VHS tubes; *fyt-1.8 = measured ultimate tensile strength in the 1.8 mm thick VHS tubes.

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Table 2 Fabricated VHS-plate triangular hollow section test series. Test series

Number of specimens tested

Very high strength (VHS) steel tube

Plate

d (mm)

t (mm)

d/t

Material properties

B (mm)

T (mm)

B T

Material properties

Material properties

T-V1NP1 T-V1NP2 T-V1NP3

2 2 2

38.1 38.1 38.1

1.6 1.6 1.6

23.8 23.8 23.8

Nominal values: fynt = 1350 MPa funt = 1500 MPa Measured values: fyt = 1392 MPa fut = 1515 MPa

90 120 150

3 3 3

30 40 50

fc′ = 32 MPa fcm = 38 MPa

T-V1HP1 T-V1HP2 T-V1HP3

2 2 2

38.1 38.1 38.1

1.6 1.6 1.6

23.8 23.8 23.8

90 120 150

3 3 3

30 40 50

Nominal values: fynp = 250 MPa funp = 350 MPa Measured values: fyp = 274.5 MPa fup = 359 MPa Nominal values: fynp = 400 MPa funp = 520 MPa Measured values: fyp = 477 MPa fup = 915 MPa

specified in Australian Standard AS1391 [5]. The measured yield stresses and ultimate tensile strengths for both the VHS tubes and facet plates used for the fabrication of square hollow section stub columns are greater than the corresponding nominal values shown in Table 1. The material properties of the concrete used for the different fabricated VHS-plate square hollow sections test series are also shown in Table 1. Concrete-filling of the specimens was done using concrete with a standard concrete strength grade, fc′ of 32 MPa. It can be seen in Table 1 that the mean concrete compressive strength, fcm from the concrete cylinder tests is greater than the standard concrete strength grade. Concrete strength was measured at 28 days on cured 100 mm diameter and 200 mm high concrete cylinders according to Australian Standard AS1012.9 [6]. The concrete infill in these specimens is in the area bounded by the facet plates and the VHS tubes at the vertices of the fabricated square hollow sections. There is no concrete inside the VHS tubes at the vertices of the fabricated VHS-plate square hollow section because of the small size of these tubes which have a diameter of 38.1 mm. 2.1.3. Fabrication process The 20 fabricated VHS-plate square hollow sections were manufactured through welding of the facet plates onto the VHS tubes at the vertices to create the section shown in Fig. 1a. The facet plates were joined to the VHS tubes using both external and internal welds. The external welds were performed using the pulsed metal arc welding (MIG) process, whilst the internal welds were done using the gas tungsten arc welding (GTAW) method. The welding was done using the AWS

(a) Test setup

Concrete

Height of specimen (H) (mm) 300 400 500

300 400 500

A5.2ER110S-G solid wire. Macro-cross examination tests were carried out and showed a satisfactory level of penetration and no occurrence of cold-laps, root gaps or porosity. 2.2. Fabricated VHS-plate triangular hollow sections 2.2.1. General Twelve fabricated VHS-plate triangular hollow sections were also manufactured and tested under compression in this investigation. A fabricated triangular hollow section is shown in Fig. 1b. The properties of the test series of the fabricated triangular hollow sections tested in this investigation are shown in Table 2. The fabricated triangular hollow sections shown in Fig. 1b were also concrete filled using grade 32 MPa concrete prior to compression testing. 2.2.2. Material properties Very high strength steel (VHS) tubes were also used in the fabrication of all the VHS-plate triangular hollow section stub columns as shown in Table 2, where the measured yield stress and ultimate tensile strength of the VHS tubes are given. The VHS tubes had a nominal yield strength of 1350 MPa and a nominal ultimate tensile strength of 1500 MPa. Six of the VHS-plate triangular hollow section stub columns, series T-V1NP, were fabricated using mild steel plates with a nominal yield stress and a nominal ultimate tensile strength of 250 MPa and 350 MPa respectively, see Table 2. Tensile coupon tests carried out for the mild steel facet plates show that the measured yield stress and ultimate tensile

(b) Failure mode (Square section) (c) Failure mode (Triangular section)

Fig. 2. Setup and failure modes of test specimens.

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(a) B=90 mm, t=3 mm, B/t=30

(b) B=120 mm, t=3 mm, B/t=40 2500

Axial load N (kN)

Axial load N (kN)

2000

1500 V1NP2(A)

1000

V1NP2(B) V1HP1(A)

500

2000 1500 V1NP2(A)

1000

V1HP1(B)

V1NP2(B) V1HP2(A)

500

V1HP2(B)

0

0

10000

20000

30000

0

40000

0

Axial strain (με)

10000

20000

30000

40000

Axial strain (με)

(c) B=120 mm, t=3 mm, B/t=50

Axial load N (kN)

3000 2400 1800 V1NP3(A)

1200

V1NP3(B)

600

V1HP3(A) V1HP3(B)

0

0

10000

20000

30000

40000

Axial strain (με) Fig. 3. Comparison between fabricated square columns with mild steel plates and high strength steel plates.

strength were greater than the nominal values. Another 6 VHS-plate triangular hollow section stub columns, series T-V1HP, were fabricated using high strength steel plates with a nominal yield stress and a nominal ultimate tensile strength of 400 MPa and 520 MPa, respectively. Tensile coupon tests for the high strength steel facet plates shown in Table 2 also reveal that the measured yield stress and ultimate tensile strength were greater than the nominal values. The fabricated VHS-plate triangular hollow section stub columns were also concrete filled using concrete with a strength grade of 32 MPa. Concrete cylinder tests carried out at 28 days show that the mean concrete compressive strength, fcm is greater than the standard concrete strength grade. 2.2.3. Fabrication process The 12 fabricated VHS-plate triangular hollow section stub columns were also manufactured by joining the VHS tubes and facet plates using external and internal welds. All the welds were carried using the gas metal arc welding method and AWS A5.2ER110S-G solid wire. There was no evidence of defects on the macro-cross examination tests. 2.3. Test setup The stub columns fabricated using VHS tubes and plates were tested on an Instron 8506 Testing Machine with a capacity of 3000 kN. A specimen under load is shown in Fig. 2a. The test setup was used to determine the compression behaviour of the fabricated VHS-plate square and triangular hollow section concrete-filled stub columns. Casting plaster was used at the top surfaces of the stub columns to ensure that the surface was level prior to load application. The specimens were tested using displacement control with a cross-head speed of

0.01 mm/min. This rate was increased to 0.02 mm/min after the peak load was reached. Strain gauges were placed at mid-height on two facet plates for both the square and triangular section stub columns. Two strain gauges were also placed at mid-height on two VHS tubes at the vertices of the specimens. Each of the strain gauges had two elements to measure strain parallel and perpendicular to the longitudinal axis of the stub columns. The locations of the gauges are shown in Fig. 1a and b. Linear potentiometers were attached to one of the facet plates and to one of the VHS tubes to determine the axial shortening of the stub columns. The strain and axial shortening measurements enabled load deformation characteristics of the stub columns to be determined.

3. Test results and discussion Typical failed specimens are shown in Fig. 2b for a concrete-filled fabricated VHS-plate square hollow section, and in Fig. 2c for a concretefilled fabricated VHS-plate triangular hollow section. Fig. 2b and c show that there is outward buckling of the facet plates in both the fabricated square and triangular section stub columns. This is because the concrete in-fill prevents inward buckling of the facet plates in the concrete-filled specimens. Buckling of the facet plates is followed by buckling of the tubes at the vertices of the fabricated section. Since the VHS tubes at the vertices are empty, inward as well as outward buckling of the tubes can be observed as shown in Fig. 2b and c. Buckling of the VHS tubes occurs in the vicinity of the buckles in the facet plates. At higher deformation, buckles in the shape of an elephant foot can also be formed at the interface of the VHS tubes and the stub column end plates.

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Both inward and outward buckling of the facet plates as well as elephant foot buckling of the VHS tubes was observed for the empty fabricated square hollow section stub columns as shown in Fig. 8. Typical axial load versus axial strain curves for concrete-filled fabricated VHS-plate square hollow section stub columns are shown in Fig. 3. It can be seen that greater load carrying capacity was achieved as the higher strength steel plates were used. However, it is worth noting that for specimens with higher strength steel plates, there was a reduction in ductility of the specimens. The axial load versus axial shortening curves for concrete-filled fabricated VHS-plate triangular hollow section stub columns are shown in Fig. 4. Once again, greater load carrying capacity was achieved as the higher strength steel plates were used. A similar observation relating to ductility can also be made, with the specimens with higher strength steel plates exhibiting reduced ductility compared with those consisting of mild steel plates. Based on the experimental results, a FE model was developed and calibrated and gives a good representation of the experimental results for determining the strength and load–deformation characteristics of both the fabricated triangular and square hollow section stub columns. The FE model is presented in the next sections.

using 4-node shell elements with reduced integration (S4R). The concrete core was modelled using 8-node brick elements (C3D8R), with three translation degrees of freedom at each node [7]. The FE models for typical square and triangular fabricated section columns are illustrated in Fig. 5. In the normal direction, a surface-based interaction model with contact pressure was adopted whereas in the tangential direction a Coulomb friction model for the surface between the steel tube and core concrete was used. A friction coefficient was set as 0.6 based on the studies of Han et al. [7]. The ends of these specimens were fixed against three displacement degrees of freedom except for the vertical displacement at the top of the specimens. Loading was applied in a displacement control mode at the top end to simulate the axial loading condition.

4. Finite element model and verification

4.2.2. Property of HAZ area of VHS tube Tests and theoretical work have been carried out by several researchers to understand the behaviour of VHS tubes [9,10]. Jiao and Zhao [9] found that the ultimate strength in the HAZ was about 50% of the parent yield strength fyt. Therefore, the yield stress of the HAZ area (ƒyHAZ) was taken as approximately equal to 0.5ƒyt as suggested by

4.1. General The software ABAQUS 6.10 was used to simulate the compressive behaviour of composite stub columns. The steel tube was simulated by

(a) B=90 mm, t=3 mm, B/t=30

4.2. Empty steel stub columns 4.2.1. Steel model An elastic-perfectly plastic model was employed to simulate the steel tube of concrete-filled VHS-plate square and triangular steel tubular columns as proposed by Liu [8]. This model was used to simulate the VHS tubes and steel plates of the stub columns.

(b) B=120 mm, t=3 mm, B/t=40 1600 1400

1000

1200

Axial Load (kN)

1200

800 T-V1HP1 B

600

T-V1HP1 A

400

T-V1NP1 B

200 0

1000

T-V1NP1 A

0

5

10

15

800 T-V1HP2 B

600

T-V1HP2 A

400

T-V1NP2 B

200

T-V1NP2 A

0

0

Axial Shortening (mm)

5

10

Axial Shortening (mm)

(c) B=120 mm, t=3 mm, B/t=50 1800 1600 1400

Axial Load (kN)

Axial Load (kN)

1400

1200 1000 T-V1HP3 B

800

T-V1HP3 A

600

T-V1NP3 B

400

T-V1NP3 A

200 0

0

5

10

15

Axial Shortening (mm) Fig. 4. Comparison between fabricated triangular columns with mild steel plates and high strength steel plates.

15

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(a) General view

(b) FE mesh

Fig. 5. Typical finite element solid models of CFST columns.

Ling et al. [10]. The HAZ regions are equal to the thickness of the plate, T, plus twice weld leg length, s, on each side of the plate as recommended by Ling et al. [10]. 4.2.3. Initial imperfections The imperfections of the empty steel columns are defined as the first buckling eigenmode obtained from a previous eigenvalue buckling prediction. Fig. 6 presents the typical shape of these longitudinal imperfections. The amplitude of imperfections was taken as 0.01B according to the Chinese Standard GB50018-2002 [11]. In this investigation imperfections were measured and reported by Mashiri et al. [12]. Mashiri et al. [12] showed that the magnitude of the geometric imperfections in facet plates depends on the plate element slenderness, which is consistent with previous research by Zhao et al. [3]. 4.2.4. Model verification using empty fabricated square hollow sections A FE model incorporating initial imperfections, the behaviour of the HAZ material and an elastic-perfectly plastic model for steel was developed to predict the behaviour of empty fabricated VHS-plate square hollow section stub columns. This model was adopted for verification purposes. The test results and simulated results together with specimen details are presented in Table 3. Nc1 is the FE predicted load carrying

capacity without HAZ area and imperfections. Nc2 is the FE predicted load carrying capacity with HAZ area but without imperfections. Nc3 is the FE predicted load carrying capacity with HAZ area and imperfections. Ne is the peak load from the tests. The axial load (N)–axial strain (ε) curves determined experimentally are shown in Fig. 7. From Table 3 and Fig. 7, it can be found that the mean values of Nc1/Ne, Nc2/ Ne and Nc3/Ne are 1.223, 1.099 and 1.034, respectively. Therefore, it is necessary to consider the effect of the HAZ area and imperfections in the FE model for the pure empty steel column with VHS tubes. It can be concluded that the steel model described above can be used to conduct further analysis for concrete-filled fabricated VHS-plate stub columns. In Fig. 7, it can also be seen that the axial strain at the peak load is close to 7000 με which would typically exceed the crushing strain of normal strength concrete. In Fig. 8, the failure mode of the FE model is compared with the observed failure in the tests. A close agreement is observed in Fig. 8 which illustrates the failure modes where the steel plate and VHS tubes can buckle outwardly or inwardly. However, the difference is the buckling position. For the test specimen, the position is near the top of the column due to the imperfection of top surface and the fact that no end plate or stiffeners were used to prevent local failure at the ends of the fabricated section. The predicted buckling position is near the midsection of the column. 4.3. Concrete-filled fabricated VHS-plate stub columns 4.3.1. Steel model and property of HAZ area of VHS tube The steel model and the property of HAZ area of the VHS tube described in Sections 4.2.1 and 4.2.2 were used in the concrete-filled fabricated VHS-plate stub column model. 4.3.2. Concrete Two concrete models were adopted for simulating the behaviour of concrete in the steel tube. One of the concrete models was proposed by Han et al. [7] and the other by Tomii and Sakino [13]. In Han et al. [7], in order to obtain the proper concrete model, a rectangular section is equivalent to the square section with the same confining factor. For a triangular section, the concrete model adopted was such that the triangular section is equivalent to the square section with the same confining factor. However, further research is required to understand concrete models for the triangular section concrete-filled columns.

Fig. 6. Local imperfections of empty steel stub columns.

(1) Han et al.'s model An equivalent concrete model was developed by Han et al. [7] on the basis of a large database of tests on concrete-filled steel

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Table 3 Predicted and actual capacity of empty fabricated square stub columns. Specimen

D (mm)

t (mm)

fyt (MPa)

B (mm)

T (mm)

fyp (MPa)

Ne (kN)

Nc1 (kN)

Nc2 (kN)

Nc3 (kN)

Nc1/Ne

Nc2/Ne

Nc3/Ne

S1H S3H

38.1 38.1

1.8 1.6

1330 1369

90 90

3 3

271 271

1170 1100

1437 1339.1

1290.4 1204.2

1218.8 1128.5 Mean

1.23 1.22 1.223

1.10 1.09 1.099

1.04 1.03 1.034

where λ ¼ E −ðEfc0 =ε Þ;

tubular stub columns. Han et al.'s stress–strain model is described by the following expression:

y¼

8 <

c

2

ðx≤1Þ 2x−x x ðx N1Þ : β0 ðx−1Þη þ x

c

cc

qffiffiffiffiffi Ec ¼ 3320 f 0c þ 6900 ðMPaÞ; 8 0 > 0:002 f c ≤28 > < 0 f −28 0 εcc ¼ 0:002 þ c 28bf c ≤82 : > 54000 > : 0 0:003 f c N82

ð1Þ

where x = ε/ε0; y = σ/σ0; 0 σ 0 ¼f c



  0:2 −6 0 −6 N=mm ; ε0 ¼εc þ 800ξ  10 ; ε c ¼ 1300 þ 12:5f c  10 2

(

2 ðcircularÞ ; 1:6 þ 1:5=x ðsquareÞ 8 ½0:25þðξ−0:5Þ7    −5 0 0:5 > > fc  0:5≥ 0:12 ðcircularÞ < 2:36  10  0 0:1 β0 ¼ fc > > pffiffiffiffiffiffiffiffiffiffiffi ðsquareÞ : 1:2 1 þ ξ η¼

in the above formula, fc′ is the cylinder strength of the concrete in N/mm2, and ξ is the confinement factor. (2) Tomii and Sakino's model In Tomii and Sakino's model [13], the stress–strain model is defined as: 8 > > > > > <

f 0c λðε=εcc Þ λ−1 þ ðε=εcc Þλ 0 σ¼ fc  0 > 0 0 > > β f þ 100 ð 0:015−ε Þ f c −β f c > c > : 0 βfc

1:5−

B 48t

0:5

ω¼

   ω0 2πx 2πy 1− cos 1− cos 4 B B

ð4Þ

ð2Þ

ð3Þ

4.3.4. Simulated results and discussion In Fig. 11, the failure modes of FE models are compared with the failure modes from the tests. A close agreement is observed in Fig. 11 where the steel plate and VHS tubes only buckled outwardly. However, the difference is in the buckling position, as was observed for empty steel columns. The failure modes for the composite square section

(a)

(b) 1500

1500

Axial load N (kN)

> > > > > :

B ≤24 t B 24b ≤48 t B N48 t

1

Axial load N (kN)

β¼

8 > > > > > <

4.3.3. Initial imperfections The imperfections of steel plates in concrete-filled fabricated VHSplate stub columns are different to those of empty steel columns. As proposed by Tao et al. [14], the following form of imperfection was used in steel plates of concrete-filled VHS-to-steel fabricated section stub columns.

where x and y are the lateral and axial coordinates, respectively, from one end of the tube; B and ωo are the width and the magnitude of local imperfections of the steel plate, respectively. ωo was taken as 0.01B as recommended by Tao et al. [14]. The local imperfection shape is presented in Fig. 10.

ε ≤ε cc εcc bε ≤0:005 0:005bε ≤0:015 ε N0:015

Fig. 9 compares the axial stress (σ) versus axial strain (ε) curves used in the FE model based on the different concrete models. The axial stress after peak decreases as the B/t ratio increases. The curve of Tomii and Sakino's model generally predicts higher stresses compared with the curve of Han et al.'s model, as shown in Fig. 9c.

1000

S1H

500

Idealised model FE with HAZ area

1000

S3H

500

Idealised model FE with HAZ area

FE with HAZ area and imperfections

0

0

10000

20000

Axial strain (με)

30000

40000

FE with HAZ area and imperfections

0

0

10000

20000

Axial strain (με)

Fig. 7. Load versus axial strain curves for empty fabricated square hollow section stub columns.

30000

40000

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(a) Observed

(b) Predicted

Fig. 10. Local imperfections of steel plate of composite columns.

Fig. 8. Comparison of observed and predicted failure modes.

stub columns without end plates are shown in Fig. 11a. The failure modes for the composite square section stub columns with end plates are shown in Fig. 11b. The failure modes for the triangular section columns with end plates are shown in Fig. 11c. This paper compares the accuracy of the different concrete models used in the FE analysis. In Fig. 12 and Table 4, the FE predicted results are compared with the test results for square fabricated sections with end plates. For the load carrying capacity, Tomii and Sakino's model performs well and superior to Han et al.'s model. The mean values of Nc3/Ne and Nc4/Ne are 0.92 and 1.028 respectively, where Nc3, Nc4 and Ne represent the predicted load carrying capacity by Han et al.'s model; the predicted load carrying capacity by Tomii and Sakino's model; and test results, respectively. However, after the peak load, Han et al.'s model

(a) Han et al.’s Model

more closely predict the test results than Tomii and Sakino's model, as shown in Fig. 12. Han et al.'s model was used to simulate six square composite columns without end steel plates. The predicted results were shown in Fig. 13 and Table 5. The mean of Nc3/Ne was 1.066. The predicted load carrying capacity is higher than the test results different to those specimens in Fig. 12 with end plates, when Han et al.'s model is used. The reason was due to the fact that the specimens without the steel end plates experience failure at the column ends. It is difficult to ensure that the load is applied evenly across the cross-section and simultaneously to the steel and concrete in composite columns without steel end plates or some other form of method to restrain end failure. Han et al.'s model was also used to simulate the twelve triangular section composite columns with end plates listed in Table 6. The predicted curves versus test result load–deformation curves are shown in Fig. 14. The mean value of Nc3/Ne is 0.943, showing that Han et al.'s model underestimates the peak strength when end plates are used. This is similar to the result for square section composite columns with end plates where Han et al.'s model underestimates the peak strength.

(b) Tomii and Sakino’s model

40

40 V1HP1(B/t=30)

Axial stress σ (MPa)

V1HP2(B/t=40)

30

V1HP3(B/t=50)

20 10 0

0

10000

20000

V1HP2(B/t=40)

30 20 10 0

30000

V1HP3(B/t=50)

0

10000

Axial strain (με)

40 Han et al.’s Model

30

Tomii and Sakino’s model

20 10 0

0

20000

Axial strain (με)

(c) V1HP3 (B/t=50) Axial stress σ (MPa)

Axial stress σ (MPa)

V1HP1(B/t=30)

10000

20000

30000

40000

Axial strain (με) Fig. 9. Comparison of axial stress (σc)–axial strain (ε) curves of different concrete models.

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F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(a) Square column without end plates

149

(b) Square column with end plates

(c) Triangular column with end plates

Fig. 11. Comparison of observed and predicted failure modes.

Therefore Han et al.'s model provides a conservative estimate of the strength of both the square and triangular section composite columns. The effect of initial imperfections was analysed as shown in Fig. 15 by considering the square composite column with the largest B/t ratio using high strength facet plates. The load carrying capacity predicted by Han et al.'s model and Tomii and Sakino's model decreased by 2.16% and 0.12%, respectively. Therefore, the effect of initial imperfections is relatively small for this form of construction. This is because for the largest B/t ratio of 50 used in this investigation, the steel ratio [αs = Asp / (Asp + Ac)] is only 7.8%. Asp and Ac are the areas of steel plates and concrete respectively. The steel ratio shows that the load provided by steel plates is relatively small for the whole of the composite column. The effect of the HAZ area was analysed as shown in Fig. 16. The load carrying capacity calculated by Han et al.'s model and Tomii and Sakino's model decreased by 1.8% and 4.79%, respectively. This is because the axial peak strain of the composite column, which is 7000 με as presented in Fig. 3, is larger than the axial peak stain of concrete suggested by Han et al.'s model but is closer to the axial peak strain of concrete recommended by Tomii and Sakino's model, as shown in Fig. 9c. Therefore, the effect of the HAZ area predicted by Han et al.'s model is slighter than that predicted by Tomii and Sakino's model. Fig. 17 shows the axial load (N)–axial strain (ε) curves for predicted results from different concrete models. The axial loads carried by the steel plates, VHS tubes and core concrete are also presented in Fig. 17 as a function of strain ε. For Han et al.'s model, the concrete shows a marked strain-softening behaviour because of its axial stress (σ)–axial strain (ε) curve shape shown in Fig. 9c. For Tomii and Sakino's model,

the strength decline of concrete is not obvious. Thus, the axial strain at peak load predicted by Tomii and Sakino's model is higher than that predicted by Han et al.'s model. As shown in Fig. 17, the peak strain of VHS tubes curves is near 6500 με and there is no obvious strength decline in the curves. For the results predicted by Tomii and Sakino's model, the distance between the peak strain of concrete and the peak strain of VHS tubes is smaller than the counterpart values predicted by Han et al.'s model. Thus, the load carrying capacity predicted by Tomii and Sakino's model is higher than that predicted by Han et al.'s model. In Fig. 17, it should be noted that the strength of the steel plates begins to decrease at an axial strain of 6500 με for local buckling. 5. Parametric study A parametric study was carried out to determine the effects of concrete strength, facet plate yield strength and facet plate width (B) to thickness (t) ratio. The influence of the different shaped section columns on confinement was also studied. The base model used in the parametric study had the following parameters: fc′ = 60 MPa, fy = 300 MPa, fyt = 1400 MPa, d = 38 mm, t = 1.5 mm, B = 150 mm, T = 3 mm. The axial load (N)–axial strain (ε) curves resulting from the parametric study are shown in Fig. 18. With increasing concrete strength, the ultimate strength of composite columns is significantly enhanced, but the ductility of the composite columns is clearly reduced. Fig. 18a and b shows the axial load–strain curves for the base model as well as load–deformation curves for models with concrete strengths of 30 MPa, 40 MPa and 100 MPa for both the triangular and square fabricated section stub columns.

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F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(b) B=90 mm, fyp=493.3 MPa

2000

2000

1600

1600

Axial load N (kN)

Axial load N (kN)

(a) B=90 mm, fyp=268.9 MPa

1200 V1NP1(A)

800

V1NP1(B) Han et al.’s Model

400

1200 V1HP1(A)

800

Han et al.’s Model

400

Tomii and Sakino’s model

0 0

10000

20000

30000

V1HP1(B)

0

40000

Tomii and Sakino’s model

0

10000

Axial strain (µ )

2500

2000

2000

1500 V1NP2(A) V1NP2(B) Han et al.’s Model

500

1500 V1HP2(A) V1HP2(B)

1000

Han et al.’s Model Tomii and Sakino’s model

500

Tomii and Sakino’s model

0

0 0

10000

20000

30000

40000

0

10000

Axial strain (µ )

2400

2500

Axial load N (kN)

Axial load N (kN)

3000

1800 V1NP3(A) V1NP3(B) Han et al.’s Model

0

10000

20000

40000

2000 1500

30000

V1HP3(A)

1000

V1HP3(B) Han et al.’s Model

500

Tomii and Sakino’s model

0

30000

(f) B=150 mm, fyp=493.3 MPa

3000

600

20000

Axial strain (µ )

(e) B=150 mm, fyp=268.9 MPa

1200

30000

(d) B=120 mm, fyp=493.3 MPa

2500

Axial load N (kN)

Axial load N (kN)

(c) B=120 mm, fyp=268.9 MPa

1000

20000

Axial strain (µ )

0

40000

Tomii and Sakino’s model

0

10000

Axial strain (µ )

20000

30000

40000

Axial strain (µ )

Fig. 12. Load versus axial strain curves for square composite stub columns with end plates. Table 4 Predicted and actual capacity of concrete-filled fabricated square stub columns with end plates. Specimen

D (mm)

t (mm)

fyt (MPa)

B (mm)

T (mm)

fyp (MPa)

Ne (kN)

Nc3 (kN)

Nc3/Ne

Nc4 (kN)

Nc4/Ne

V1N1P(A) V1N1P(B) V1N2P(A) V1N2P(A) V1N3P(A) V1N3P(A) V1H1P(A) V1H1P(A) V1H2P(A) V1H2P(A) V1H3P(A) V1H3P(A)

38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

1392 1392 1392 1392 1392 1392 1392 1392 1392 1392 1392 1392

90 90 120 120 150 150 90 90 120 120 150 150

3 3 3 3 3 3 3 3 3 3 3 3

268.9 268.9 268.9 268.9 268.9 268.9 439.3 439.3 439.3 439.3 439.3 439.3

1609.9 1630.3 1937.2 1963.1 2340.9 2401.4 1896.1 1829.6 2238.1 2245.1 2661.5 2668.9

1528.8 1528.8 1764.8 1764.8 2168.7 2168.7 1735.4 1735.4 2019.2 2019.2 2458.5 2458.5 Mean

0.95 0.938 0.911 0.899 0.926 0.903 0.915 0.949 0.902 0.899 0.924 0.921 0.920

1713.6 1713.6 2038.7 2038.7 2460.2 2460.2 1906.5 1906.5 2254.1 2254.1 2732.9 2732.9

1.064 1.051 1.052 1.039 1.051 1.024 1.005 1.042 1.007 1.004 1.027 1.024 1.028

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(b) B=90 mm, fyp=271 MPa, t=1.6mm

2000

2000

1600

1600

Axial load N (kN)

Axial load N (kN)

(a) B=90 mm, fyp=271 MPa, t=1.8mm

1200 800

S2Con Han et al.’s Model

400

1200 800

S4Con Han et al.’s Model

400

0

0 0

10000

20000

30000

0

40000

10000

Axial strain (µ )

1600

1600

Axial load N (kN)

Axial load N (kN)

2000

1200 S6Con Han et al.’s Model

400

30000

40000

(d) B=120 mm, fyp=271 MPa, t=1.6mm

2000

800

20000

Axial strain (µ )

(c) B=120 mm, fyp=271 MPa, t=1.8mm

1200 800

S5Con Han et al.’s Model

400

0

0 0

10000

20000

30000

40000

0

10000

Axial strain (µ )

20000

30000

40000

Axial strain (µ )

(e) B=150 mm, fyp=271 MPa, t=1.8mm

(f) B=150 mm, fyp=271 MPa, t=1.6mm

2400

2400

Axial load N (kN)

Axial load N (kN)

151

1800

1200

S8Con Han et al.’s Model

600

1800

1200 S7Con Han et al.’s Model

600

0

0 0

10000

20000

30000

40000

0

10000

Axial strain (µ )

20000

30000

40000

Axial strain (µ )

Fig. 13. Load versus axial strain curves for square composite stub columns without end plates.

Fig. 18c and d shows the load–deformation curves for the triangular and square fabricated section stub columns made up of facet plates with different yield strength values. The parametric study to determine the influence of the yield strength of the facet plates covered plates with yield strength of 250 MPa, 300 MPa, 400 MPa, 500 MPa, 600 MPa and 700 MPa for both the triangular and square fabricated section stub columns. It shows that as the yield strength of steel facet plate (fy) increases, the ultimate strength of the composite column is significantly improved. Fig. 18e and f shows the load–deformation curves for the triangular and square fabricated section stub columns made up of facet plates with

Table 5 Predicted and actual capacity of concrete-filled fabricated square stub columns without end plates. B T fyp Ne Specimen D t fyt (mm) (mm) (MPa) (mm) (mm) (MPa) (kN)

Nc3 (kN)

Nc3/Ne

S2Con S4Con S5Con S6Con S7Con S8Con

1585.8 1493.2 1746.8 1839.8 2161.3 2233.7 Mean

1.005 1.011 1.084 1.051 1.136 1.109 1.066

38.1 38.1 38.1 38.1 38.1 38.1

1.8 1.6 1.8 1.6 1.8 1.6

1330 1369 1330 1369 1330 1369

90 90 120 120 150 150

3 3 3 3 3 3

271 271 271 271 271 271

1578 1477 1612 1751 1902 2014

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F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

Table 6 Predicted and actual capacity of concrete-filled fabricated triangular stub columns with end plates. Specimen

D (mm)

t (mm)

fyt (MPa)

B (mm)

T (mm)

fyp (MPa)

Ne (kN)

Nc3 (kN)

Nc3/Ne

T-V1HP1-A T-V1HP1-B T-V1HP2-A T-V1HP2-B T-V1HP3-A T-V1HP3-B T-V1NP1-A T-V1NP1-B T-V1NP2-A T-V1NP2-B T-V1NP3-A T-V1NP3-B

38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9

90 90 120 120 150 150 90 90 120 120 150 150

2.93 2.93 2.93 2.93 2.93 2.93 2.85 2.85 2.85 2.85 2.85 2.85

477.1 477.1 477.1 477.1 477.1 477.1 274.5 274.5 274.5 274.5 274.5 274.5

1277.5 1273.7 1462.7 1488.4 1659.5 1674.4 1067.1 1080.8 1272.8 1210.7 1444.2 1516.6

1202.7 1202.7 1379.1 1379.1 1684.7 1684.7 1017.3 1017.3 1120.5 1120.5 1359 1359 Mean

0.941 0.944 0.943 0.927 1.015 1.006 0.953 0.941 0.880 0.925 0.941 0.896 0.943

(b) B=90 mm, fyp=274.5 MPa

1500

1500

1200

1200

Axial load N (kN)

Axial load N (kN)

(a) B=90 mm, fyp=477.1 MPa

900 T-V1HP1-A

600

T-V1HP1-B Han et al.’s Model

300 0

0

10000

20000

30000

40000

900 T-V1NP1-A

600

Han et al.’s Model

300 0

50000

T-V1NP1-B

0

Axial strain (µ )

Axial load N (kN)

Axial load N (kN)

60000

1500

1200

800

T-V1HP2-A T-V1HP2-B

400

Han et al.’s Model

0

10000

20000

30000

1200 900

T-V1NP2-B Han et al.’s Model

300 0

40000

T-V1NP2-A

600

0

Axial strain (µ )

15000

30000

45000

60000

Axial strain (µ )

(e) B=150 mm, fyp=477.1 MPa

(f) B=150 mm, fyp=274.5 MPa

2000

1600

1600

Axial load N (kN)

Axial load N (kN)

45000

(d) B=120 mm, fyp=274.5 MPa

1600

1200 T-V1HP3-A

800

T-V1HP3-B Han et al.’s Model

400 0

30000

Axial strain (µ )

(c) B=120 mm, fyp=477.1 MPa

0

15000

0

10000

20000

1200

800

T-V1NP3-A T-V1NP3-B

400

Han et al.’s Model

30000

Axial strain (µ )

40000

0

0

15000

30000

Axial strain (µ )

Fig. 14. Load versus axial strain curves for triangular composite stub columns with end plates.

45000

60000

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(b) Tomii and Sakino’s model

3000

3000

2500

2500

Axial load N (kN)

Axial load N (kN)

(a) Han et al.’s Model

2000 1500 V1HP3(A)

1000

V1HP3(B) FE without imperfections

500

153

2000 1500 V1HP3(A)

1000

V1HP3(B) FE without imperfections

500

FE with imperfections

FE with imperfections

0

0 0

10000

20000

30000

0

40000

10000

Axial strain (µ )

20000

30000

40000

Axial strain (µ )

Fig. 15. Effect of initial imperfections on column V1HP3 (B/t = 50).

various B/T ratios. For both the triangular and square fabricated section stub columns, load–deformation curves with B/T values of 15, 20, 25, 30, 35, 40, 50, 60 and 80 were determined. As can be seen, the ultimate strength of the composite column increases as the width-thickness ratio (B/T) decreases. The predicted concrete ultimate strength indexes (SI = Nc/(Acfc′)) are presented in Fig. 19. Nc is the FE predicted ultimate strength of core concrete. Ac and fc′ are the area and cylinder strength of core concrete, respectively. The parameters B, T and fy are the width, the thickness and the yielding strength of the steel plate respectively. From Fig. 19, it can be observed that the influence of the concrete strength (fc′) and width-to-thickness ratio (B/T) on the concrete ultimate strength is less than 10%. The influence of concrete strength (fc′) is shown in Fig. 19a and b for the triangular and square fabricated section stub columns respectively. The influence of width-thickness ratio (B/T) is shown in Fig. 19e and f for the triangular and square fabricated section stub columns respectively. For typical examples with different concrete strength and width-to-thickness ratio, the confinement of steel plates on core concrete can be minimal. However, with the increase of yield strength of the facet plate, fy, the values of the strength index, SI are improved. SI of composite columns with triangular section are higher than that of composite columns with square section. The confinement of the steel tube on the core concrete in midsection of the base models is shown in Fig. 20. It can be seen that the confinement is concentrated only on the corner regions. For the corner regions, the confinement of the concrete core in the triangular section is

6. Design of concrete-filled fabricated VHS-plate stub columns 6.1. General The proposed method for determining the section capacity of the concrete-filled fabricated VHS-plate stub columns is based on the principle of superposition to account for the strength contribution due to the concrete and steel respectively. The proposed design method takes into account local buckling of the VHS tube and the plate as well as the observed material behaviour of the heat affected zone. The ultimate compressive strength is given by: 0

Nu ¼ f c Ac þ f yp Aep þ f yt Aet

(b) Tomii and Sakino.’s model

3000

3000

2500

2500

2000 1500 V1HP3(A)

1000

V1HP3(B) FE without HAZ area

500

2000 1500 V1HP3(A)

1000

V1HP3(B) FE without HAZ area

500

FE with HAZ area

FE with HAZ area

0

0

10000

ð5Þ

where fc′ is the compressive strength of the concrete, Ac is the area of the concrete, fyp is the mean yield strength of the steel plate, fyt is the mean yield strength of the VHS steel tube, Aep is the effective area of the steel plate and Aet is the effective area of the VHS steel tube. The effective areas of the steel plate and VHS steel tube take into account the effects

Axial load N (kN)

Axial load N (kN)

(a) Han et al.’s Model

clearly higher than that in the square section. Fig. 21 shows the longitudinal concrete stress distribution at the mid section of base model columns, reflecting higher confinement in the concrete core in fabricated triangular section stub columns compared to that in the fabricated square section stub columns. In general, the confinement effect is not significant in both types of columns.

20000

30000

40000

0

0

10000

Axial strain (µ ) Fig. 16. Effect of the HAZ area on column V1HP3 (B/t = 50).

20000

30000

Axial strain (µ )

40000

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F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(a) Han et al.’s Model 3000 V1HP3(A)

Axial load N (kN)

2500

V1HP3(B) 2000

Han et al.’s Model

1500

concrete steel plate

1000

VHS tube

500 0 0

10000

20000

30000

Axial strain (µ )

(b) Tomii and Sakino’s model 3000 V1HP3(A)

Axial load N (kN)

2500

V1HP3(B) 2000 Tomii and Sakino’s Model concrete

1500 1000

steel plate 500 VHS tube 0 0

10000

20000

30000

Axial strain (µ ) Fig. 17. Load versus axial strain curves of different parts of V1HP3 (B/t = 50).

of local buckling. According to the previous analysis, the effect of concrete confinement on strength increase is not considered in Eq. (5). 6.1.1. Effective diameter of VHS steel tube The effective diameter (de) of the empty VHS steel tube can be determined using the Australian Standard for Steel Structures AS 4100-1998 (Incorporating Amendment 1-2012), Clause 6.2.4 [15]. The effective diameter, de, can be evaluated using Eq. (6). sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8   > λey > > d < 0 λe de ¼ The lesser of   ≤d0 > 3 λey 2 > > : d0 λe

ð6Þ

where d0 is the diameter of the VHS tube, λe is the element slenderness for circular hollow sections (do/t × fyt/250), λey is the yield slenderness limit recommended by AS 4100 [15]. 6.1.2. Effective plate width The effective width of the steel plates in the fabricated sections can be determined based on modified models that take into account residual stresses and initial imperfection as proposed by Bradford [16] and Bradford et al. [17].

The effective width (be) is given by [18]: be ¼α b

sffiffiffiffiffiffiffi σ ol σy

ð7Þ

where b is the width of the steel plate, α is the parameter which takes into account residual stresses and initial imperfections, σ0l is the local buckling stress and σy is the yield stress. When σ0l N σy then σ0l = σy. The parameter which takes into account residual stresses and initial imperfections, α, for plates that are heavily welded and supported on two longitudinal edges is 0.65. For plates that are lightly welded and supported on two longitudinal edges, α is 0.74. Based on the results from this investigation a value of α = 0.65 was adopted as it resulted in conservative estimates of ultimate compressive strength in both the square and the triangular VHS-plate fabricated section stub columns. This is desirable for safe design of structural systems. The value of α of 0.65 reflects that the plates are heavily welded. This is because the tubes and plates used in this investigation are thin-walled, having thicknesses less that 4 mm. The local buckling stress (σ0l) [19]:

σ 0l ¼

k π2 E  2 s 2 : 12 1‐v ðb=t Þ

ð8Þ

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(a) Effect of fc (Triangular section)

1500 1000 500

0

f'c=40 MPa

f'c=30 MPa

10000

20000

f'c=80 MPa

3000 2000

0

fy=400 MPa

fy=250 MPa

fy=300 MPa

Axial load N (kN)

1000 500

10000

f'c=40 MPa

f'c=30 MPa

0

10000

20000

30000

fy=700 MPa

20000

fy=400 MPa

2000

fy=300 MPa

fy=250 MPa 1000

30000

(e) Effect of B/T ratio (Triangular section)

fy=600 MPa fy=500 MPa

3000

0 0

f'c=60 MPa

(d) Effect of fy (Square section)

1500

0

4000

4000

fy=500 MPa

2000

f'c=100 MPa

30000

fy=700 MPa fy=600 MPa

2500

5000

1000

(c) Effect of fy (Triangular section)

Axial load N (kN)

Axial load N (kN)

f'c=60 MPa Axial load N (kN)

Axial load N (kN)

f'c=80 MPa

2000

0

(b) Effect of fc (Square section)

f'c=100 MPa

2500

155

0

10000

20000

30000

(f) Effect of B/T ratio (Square section)

3000

5000

2500

B/T= 15

2000

B/T= 20 B/T= 25

1500 1000

B/T= 80

500 0

B/T= 35 B/T= 50 B/T= 40 B/T= 60

Axial load N (kN)

Axial load N (kN)

B/T= 30 4000 3000 2000

10000

20000

B/T= 80

1000 0

0

B/T= 30

B/T= 15 B/T= 20 B/T= 25

30000

0

10000

B/T= 35 B/T= 50 B/T= 40 B/T= 60 20000

30000

Fig. 18. Parametric analysis to determine the influence of fc′, fy, and B/T for triangular and square fabricated section stub columns using load versus axial strain curves.

For steel structures, the Young's Modulus, Es = 200,000 MPa and the Poisson's ratio, ν = 0.30. Uy and Bradford [20] showed that the buckling coefficient, k = 10.31 for local buckling of plates in composite structures. 6.1.3. VHS tube heat affected zone The effect of the welding process on the yield stress of VHS tube was considered in the determination of the section capacity. High strength steels are prone to strength reduction in the heat affected zone (HAZ). The reduction in strength is due to the thermal cycle as influenced by the state of the weld metal and the parent metal. The thermal cycle can cause microstructural changes at the interface of the weld metal

and parent metal to form the heat affected zone [21]. Previous research on VHS tubes showed that welded VHS tubes have an ultimate tensile strength about half that of the unwelded VHS tubes due to heataffected zone softening [1,9,10]. The heat-affected zone area (AHAZ) was calculated using Eq. (9) as proposed by Ling et al. [10]. The yield stress of VHS tubes in this area was taken to be 0.5 fyt where fyt is the mean yield stress of the VHS tube.

arcsin AHAZ ¼

  T þ 4s h i d 2 2 : d −ðd−2t Þ 4

ð9Þ

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F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

(a) Effect of fc (Triangular section) SI=1.1

1.2 1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0 20

40

60

80

SI=1.1

1.2

SI

SI

(b) Effect of fc (Square section)

0 20

100

40

f'c (MPa)

(c) Effect of fy (Triangular section) 1.25

1.2

1

1

SI

SI 0.5

SI=1.1

0.6 0.4

0.25

0.2 300

400

500

600

0 200

700

300

400

fy (MPa)

0.8

0.8

SI

1

0.6

0.6

0.4

0.4

0.2

0.2 50

700

SI=1.1

1.2

1

30

600

(f) Effect of B/T ratio (Square section)

SI=1.1

1.2

500

fy (MPa)

(e) Effect of B/T ratio (Triangular section)

SI

100

0.8

0.75

0 10

80

(d) Effect of fy (Square section)

SI=1.2

0 200

60

f'c (MPa)

70

90

0 10

B/T

30

50

70

90

B/T Fig. 19. Concrete ultimate strength analysis.

where d is the tube diameter, t is the tube thickness, T is the plate thickness and s is the weld leg length. 6.2. Design of concrete filled fabricated VHS-plate square section stub columns with end plates The estimated ultimate compressive strength (Nu) in pure compression for concrete-filled fabricated VHS-Plate square section stub columns with end plates is shown in Table 7. When the measured mechanical properties are used in the estimation of ultimate compressive strength, Table 7 shows that the mean ratio of the estimated ultimate compressive strength (Nu) to the experimental peak axial load (Ne) is 0.866. In practice nominal material properties are used for determining the capacities of structural members. Table 7 shows that when

nominal material properties are used to determine the ultimate compressive strength (Nun), a more conservative estimate of design load is obtained. The mean ratio of the ultimate compressive strength based on nominal material properties to the experimental peak axial load, Nun/Ne is 0.838. 6.3. Design of concrete filled fabricated VHS-plate square section stub columns without end plates Table 8 shows a comparison between the ultimate compressive strength (Nu) and the experimental peak axial load (Ne) for concretefilled fabricated square stub columns with no end plates. The mean ratio of Nu/Ne is 1.078. On the other hand, when nominal mechanical properties are used to determine the ultimate compressive strength

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

157

(a) Triangular section B

293.8

293.8

C D

A

90.7

90.7

A B

C

D

(b) Square section B A

C D

161.9

161.9 24.9

A

B

24.9 C

D

Fig. 20. Confinement analysis in mid-sections of base model columns.

(Nun), the mean ratio of Nun/Ne is 1.023. This shows that the proposed design model overestimates the capacities of the composite square fabricated stub columns with no end plates. This is consistent with the observations made through the FE predicted capacities for these stub columns. This observation reflects buckling failure at the ends of the columns where no end plates or stiffeners are used. This failure is evident in Fig. 8. 6.4. Design of concrete filled fabricated VHS-plate triangular sections with end plates The estimated ultimate compressive strength (Nu) in pure compression for concrete-filled fabricated VHS-Plate triangular section stub columns with end plates is shown in Table 9. When the measured mechanical properties are used in the estimation of ultimate compressive strength, Table 9 shows that the mean ratio of the estimated ultimate compressive strength to the experimental peak axial load (Ne) is 0.988. Design engineers however adopt nominal material properties in the estimation of design capacities for structural systems. Table 9 shows that when nominal material properties are used to determine the ultimate compressive strength (Nun), a more conservative estimate of design load is obtained. The mean ratio of Nun /N e is of 0.950. The use of nominal mechanical properties therefore yields a conservative estimate of the ultimate compressive strength for concrete-filled fabricated VHS-plate triangular section stub columns with end plates. 6.5. Comparison of compression capacities from parametric study and proposed design model To further calibrate the proposed design model, it was used to predict the compression capacities determined for the parametric study used to determine the influence of concrete strength, yield strength of the facet plates and the facet plate width to thickness ratio.

Table 10 shows the parameters that were used to study the influence of concrete strength (fc′) on fabricated square section stub columns and the compression capacities (Nc3) that were predicted using finite element models. The ultimate compression strength estimated using the proposed design model (Nu) is also shown in Table 10. Table 11 shows a comparison of the compression capacities (Nc3) from the finite element models used in the study of the influence of facet plate yield strength (fy) to those predicted by the proposed design model (Nu) for the fabricated square section stub columns. Table 12 similarly shows a comparison of the compression capacities (Nc3) from the finite element models used in the study of the influence of facet plate width to thickness ratio (B/T) to those predicted by the proposed design model (Nu) for the fabricated square section stub columns. The mean ratios of Nu/ Nc3 in Tables 10, 11 and 12 are all close to 1.0 and show that the compression capacities estimated using the proposed design model can be used to reasonably predict the compression capacity of fabricated square section stub columns. The proposed design model was also used to predict the compression capacities of the fabricated triangular section stub columns used in the parametric study. Tables 13, 14 and 15 show a comparison of the compression capacities from the finite element models (Nc3) and those from the proposed design model (Nu), for the studies considering the influences of concrete strength (fc′), facet plate yield strength (fy) and facet plate width to thickness ratio (B/T) respectively. The comparison of the compression capacities in Tables 13, 14 and 15 shows that the proposed design model can be used to reasonably predict the compression capacities of fabricated triangular section stub columns in the parametric study as indicated by the mean ratios of Nu/Nc3 which are close 1.0.

7. Conclusions A total of 32 stub columns were fabricated using very high strength steel (VHS) tubes and facet plates. The facet plates were made from mild

158

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(a) Triangular section 1.29f'c 1.25f'c 1.17f'c

Eight of the square section stub columns were tested with no end plates. Two of the square stub columns with no end plates were tested as empty hollow section stub columns. These two empty hollow section stub columns were used to develop an FE model for verification purposes. Six of the square section stub columns without end plates were concrete-filled. Twelve of the square section stub columns were concrete filled and tested with end plates. Twelve triangular section stub columns were also concrete filled and tested with end plates. The FE models developed consider an elastic perfectly plastic model for both the VHS tube and facet plates; concrete confinement; the material properties of the HAZ and the initial imperfections of the facet plates. The proposed design model for the concrete-filled stub columns considers local buckling in both the VHS tubes and the facet plates as well as the properties of the HAZ in the VHS tube. A parametric study was carried out to determine the influence of concrete strength, facet plate yield strength and the width-tothickness ratio of the facet plates. The following conclusions can be made from the parametric study:

1.21f'c 1.13f'c

1.09f'c

0.89f'c

1.05f'c 0.93f'c

f'c

0.93f'c 0.97f'c

0.97f'c

f'c

1.05f'c

1. An increase in concrete strength results in an increase in capacity of the fabricated triangular and square section stub columns. An increase in concrete strength however results in a reduction in ductility of the stub columns. 2. The use of facet plates with higher yield strength in the manufacture of the VHS-plate stub columns results in an increased capacity of the columns. There is a beneficial improvement in the use of higher steel facet plates as reflected by the strength index (SI) versus yield strength (fy) graphs. The use of higher yield strength facet plates results in an improvement in concrete confinement thereby improving the strength index in both the fabricated triangular and square section stub columns. Better concrete confinement is however obtained in the triangular section stub columns. 3. For stub columns with a given set of parameters, increasing the facet plate width to thickness ratio (B/T) results in a reduction in the compression capacity of the fabricated stub columns. However, a plot of strength index (SI) versus B/T in both the fabricated triangular and square section stub columns shows that there is no clear reduction in strength index (SI) as B/T increases for B/T values between 25 and 80. This shows that the composite action of the steel facet plate and core concrete is not significantly affected by B/T as in traditional concrete filled square hollow section stub columns. This might be due to the strengthening effect of the VHS tubes at the vertices.

(b) Square section 1.03f'c 0.36f'c

f'c 0.97f'c

0.67f'c

f'c

0.97f'c 0.93f'c

1.07f'c

1.03f'c 1.03f'c f'c

1.07f'c

1.03f'c

0.97f'c

f'c

1.07f'c

The following conclusions were made for the fabricated VHS-plate square stub columns with no end plates:

Fig. 21. Longitudinal concrete stress distribution in mid-sections of columns.

steel plates as well as high strength steel plates. Twenty of these stub columns were of square cross-section, and 12 of the stub columns were of triangular cross section. All the specimens were tested under pure axial compression.

1. For the empty fabricated square stub columns, a good agreement was obtained between the peak axial compressive load predicted by the FE model to the experimental peak axial load.

Table 7 Design and actual capacity of concrete-filled fabricated square stub columns with end plates. Specimen

V1N1P(A) V1N1P(B) V1N2P(A) V1N2P(A) V1N3P(A) V1N3P(A) V1H1P(A) V1H1P(A) V1H2P(A) V1H2P(A) V1H3P(A) V1H3P(A)

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Ne

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

1392 1392 1392 1392 1392 1392 1392 1392 1392 1392 1392 1392

90 90 120 120 150 150 90 90 120 120 150 150

3 3 3 3 3 3 3 3 3 3 3 3

268.9 268.9 268.9 268.9 268.9 268.9 439.3 439.3 439.3 439.3 439.3 439.3

33 33 33 33 33 33 33 33 33 33 33 33

14567 14567 22973 22973 33179 33179 14567 14567 22973 22973 33179 33179

702.0 702.0 936.0 936.0 1170.0 1170.0 702.0 702.0 936.0 936.0 1170.0 1170.0

570.3 570.3 570.3 570.3 570.3 570.3 570.3 570.3 570.3 570.3 570.3 570.3

94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5

1609.9 1630.3 1937.2 1963.1 2340.9 2401.4 1896.1 1829.6 2238.1 2245.1 2661.5 2668.9

1397.5 1397.5 1737.8 1737.8 2137.5 2137.5 1517.1 1517.1 1897.3 1897.3 2336.9 2336.9 Mean

Nu/Ne

Nun

Nun/Ne

(kN) 0.868 0.857 0.897 0.885 0.913 0.890 0.800 0.829 0.848 0.845 0.878 0.876 0.866

1360.3 1360.3 1687.7 1687.7 2072.8 2072.8 1465.6 1465.6 1828.1 1828.1 2248.3 2248.3

0.845 0.834 0.871 0.860 0.885 0.863 0.773 0.801 0.817 0.814 0.845 0.842 0.838

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

159

Table 8 Design and actual capacity of concrete-filled fabricated square stub columns without end plates. Specimen

S2Con S4Con S5Con S6Con S7Con S8Con

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Ne

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

38.1 38.1 38.1 38.1 38.1 38.1

1.8 1.6 1.8 1.6 1.8 1.6

1330 1369 1330 1369 1330 1369

90 90 120 120 150 150

3 3 3 3 3 3

271 271 271 271 271 271

35 35 35 35 35 35

14567 14567 22973 22973 33179 33179

702.0 702.0 936.0 936.0 1170.0 1170.0

694.7 575.3 694.7 575.3 694.7 575.3

105.8 94.5 105.8 94.5 105.8 94.5

1578 1477 1612 1751 1902 2014

1553.7 1423.0 1911.3 1780.6 2332.0 2201.2 Mean

Aep

Aet

Ne

Nu

Nu/Ne

Nun

Nun/Ne

(kN) 0.985 0.963 1.186 1.017 1.226 1.093 1.078

1486.98 1360.25 1814.47 1687.74 2199.56 2072.83

0.942 0.921 1.126 0.964 1.156 1.029 1.023

Nu/Ne

Nun

Nun/Ne

0.914 0.917 0.986 0.969 1.054 1.045 0.961 0.949 0.984 1.034 1.047 0.997 0.988

1106.8 1106.8 1362.5 1362.5 1652.3 1652.3 1001.5 1001.5 1222.1 1222.1 1476.8 1476.8

Table 9 Design and actual capacity of concrete-filled fabricated triangular stub columns with end plates. Specimen

T-V1HP1-A T-V1HP1-B T-V1HP2-A T-V1HP2-B T-V1HP3-A T-V1HP3-B T-V1NP1-A T-V1NP1-B T-V1NP2-A T-V1NP2-B T-V1NP3-A T-V1NP3-B

d

t

B

fyt

T

fyp

fc

Ac 2

2

AHAZ 2

2

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm )

(mm )

(mm )

(mm )

(kN)

(kN)

38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1 38.1

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9 1391.9

90 90 120 120 150 150 90 90 120 120 150 150

3 3 3 3 3 3 3 3 3 3 3 3

477.1 477.1 477.1 477.1 477.1 477.1 274.5 274.5 274.5 274.5 274.5 274.5

38 38 38 38 38 38 38 38 38 38 38 38

7555.07 7555.07 11819.3 11819.3 16983.5 16983.5 7555.07 7555.07 11819.3 11819.3 16983.5 16983.5

702.0 702.0 936.0 936.0 1170.0 1170.0 702.0 702.0 936.0 936.0 1170.0 1170.0

427.7 427.7 427.7 427.7 427.7 427.7 427.7 427.7 427.7 427.7 427.7 427.7

70.9 70.9 70.9 70.9 70.9 70.9 70.9 70.9 70.9 70.9 70.9 70.9

1277.5 1273.7 1462.7 1488.4 1659.5 1674.4 1067.1 1080.8 1272.8 1210.7 1444.2 1516.6

1168.0 1168.0 1441.7 1441.7 1749.6 1749.6 1025.8 1025.8 1252.1 1252.1 1512.5 1512.5 Mean

2. For the concrete-filled fabricated square stub columns with no end plates, the FE model incorporating Han et al.'s model of concrete confinement was found to slightly overestimate the peak axial compressive load. This was considered to be due to the failure at the column ends in the experimental investigation when no end plates are used. 3. When applied to concrete-filled fabricated square stub columns with no end plates, the proposed design model for composite stub

(kN) 0.866 0.869 0.931 0.915 0.996 0.987 0.939 0.927 0.960 1.009 1.023 0.974 0.950

columns was also found to overestimate the peak axial compressive load. The following conclusions were made for the fabricated VHS-plate square stub columns with end plates: 1. For the concrete-filled fabricated square stub columns with end plates, the FE model incorporating Han et al.'s model of concrete confinement was found to slightly underestimate the peak axial compressive load.

Table 10 Comparison of design and finite element predicted capacities: influence of fc′ for concrete-filled fabricated square section stub columns with end plates. Model

SM-Fc30 SM-Fc40 SM-Fc60 SM-Fc80 SM-Fc100

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Nc3

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

38 38 38 38 38

1.5 1.5 1.5 1.5 1.5

1400 1400 1400 1400 1400

150 150 150 150 150

3 3 3 3 3

300 300 300 300 300

30 40 60 80 100

33147.9 33147.9 33147.9 33147.9 33147.9

1170.0 1170.0 1170.0 1170.0 1170.0

516.3 516.3 516.3 516.3 516.3

88.9 88.9 88.9 88.9 88.9

2056 2417 3056 3778 4500

2006.0 2337.5 3000.5 3663.4 4326.4 Mean

0.976 0.967 0.982 0.970 0.961 0.971

Nu/Nc3

Nu/Nc3

Table 11 Comparison of design and finite element predicted capacities: influence of fy for concrete-filled fabricated square section stub columns with end plates. Model

SM-Fy250 SM-Fy300 SM-Fy400 SM-Fy500 SM-Fy600 SM-Fy700

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Nc3

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

38 38 38 38 38 38

1.5 1.5 1.5 1.5 1.5 1.5

1400 1400 1400 1400 1400 1400

150 150 150 150 150 150

3 3 3 3 3 3

250 300 400 500 600 700

60 60 60 60 60 60

33147.9 33147.9 33147.9 33147.9 33147.9 33147.9

1170.0 1170.0 1170.0 1170.0 1170.0 1170.0

516.3 516.3 516.3 516.3 516.3 516.3

88.9 88.9 88.9 88.9 88.9 88.9

2956 3067 3289 3467 3622 3778

2942.0 3000.5 3117.5 3234.5 3351.5 3468.5 Mean

0.995 0.978 0.948 0.933 0.925 0.918 0.950

160

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

Table 12 Comparison of design and finite element predicted capacities: influence of B/T for concrete-filled fabricated square section stub columns with end plates. Model

SM-BT15 SM-BT20 SM-BT25 SM-BT30 SM-BT35 SM-BT40 SM-BT50 SM-BT60 SM-BT80

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Nc3

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

Nu/Nc3

38 38 38 38 38 38 38 38 38

1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

1400 1400 1400 1400 1400 1400 1400 1400 1400

150 150 150 150 150 150 150 150 150

10 7.5 6 5 4.287 3.75 3 2.5 1.875

300 300 300 300 300 300 300 300 300

60 60 60 60 60 60 60 60 60

30738.8 31588.2 32103.6 32449.7 32697.7 32885.1 33147.9 33323.6 33544

3900.0 2925.0 2340.0 1950.0 1671.9 1462.5 1170.0 975.0 720.4

516.3 516.3 516.3 516.3 516.3 516.3 516.3 516.3 516.3

135.2 118.0 108.1 101.6 97.0 93.6 88.9 85.7 81.9

4444 3972 3694 3500 3361 3250 3056 2972 2861

3642.5 3413.0 3275.4 3183.7 3118.3 3069.2 3000.5 2954.7 2894.3 Mean

0.820 0.859 0.887 0.910 0.928 0.944 0.982 0.994 1.012 0.891

Nu/Nc3

Table 13 Comparison of design and finite element predicted capacities: influence of fc′ for concrete-filled fabricated triangular section stub columns with end plates. Model

TM-Fc30 TM-Fc40 TM-Fc60 TM-Fc80 TM-Fc100

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Nc3

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

38 38 38 38 38

1.5 1.5 1.5 1.5 1.5

1400 1400 1400 1400 1400

150 150 150 150 150

3 3 3 3 3

300 300 300 300 300

30 40 60 80 100

16967.6 16967.6 16967.6 16967.6 16967.6

1170.0 1170.0 1170.0 1170.0 1170.0

387.2 387.2 387.2 387.2 387.2

66.6 66.6 66.6 66.6 66.6

1238 1399 1720 2030 2362

1355.5 1525.2 1864.5 2203.9 2543.2 Mean

2. The proposed design model for composite columns provides a conservative estimate of the peak axial compressive load. This provides a safe estimate of the ultimate compressive strength of concrete filled fabricated square stub columns.

nominal material properties are used. This provides a safe estimate of the ultimate compressive strength of concrete filled fabricated square stub columns. The use of measured material properties in the model produces capacities very close to the peak axial compressive load.

The following conclusions were made for the fabricated VHS-plate triangular stub columns with end plates: 1. For the concrete-filled fabricated triangular stub columns with end plates, the FE model incorporating Han et al.'s model of concrete confinement was found to slightly underestimate the peak axial compressive load. 2. The proposed design model for composite columns provides a conservative estimate of the peak axial compressive load when the

1.095 1.090 1.084 1.086 1.077 1.086

Acknowledgements This project was sponsored by the University of Western Sydney Research Grant Scheme (RGS) and an ARC Discovery Project Grant DP120101944. The authors wish to thank the technical support of Mr Robert Marshall, Mr Murray Bolden and Mr Mitch Quirk.

Table 14 Comparison of design and finite element predicted capacities: influence of fy for concrete-filled fabricated triangular section stub columns with end plates. Model

TM-Fy250 TM-Fy300 TM-Fy400 TM-Fy500 TM-Fy600 TM-Fy700

d

t

fyt

B

T

fyp

fc

Ac

Aep

Aet

AHAZ

Nc3

Nu

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm2)

(mm2)

(mm2)

(mm2)

(kN)

(kN)

38 38 38 38 38 38

1.5 1.5 1.5 1.5 1.5 1.5

1400 1400 1400 1400 1400 1400

150 150 150 150 150 150

3 3 3 3 3 3

250 300 400 500 600 700

60 60 60 60 60 60

16967.6 16967.6 16967.6 16967.6 16967.6 16967.6

1170.0 1170.0 1170.0 1170.0 1170.0 1170.0

387.2 387.2 387.2 387.2 387.2 387.2

66.6 66.6 66.6 66.6 66.6 66.6

1630 1713 1878 2017 2127 2279

1806.0 1864.5 1981.5 2098.5 2215.5 2332.5 Mean

1.108 1.088 1.055 1.040 1.042 1.023 1.060

Nu

Nu/Nc3

Nu/Nc3

Table 15 Comparison of design and finite element predicted capacities: influence of B/T for concrete-filled fabricated triangular section stub columns with end plates. Model

TM-BT15 TM-BT20 TM-BT25 TM-BT30 TM-BT35 TM-BT40 TM-BT50 TM-BT60 TM-BT80

d

t

fyt

B

T

fyp

fc

Ac

Aep 2

Aet 2

AHAZ 2

Nc3 2

(mm)

(mm)

(MPa)

(mm)

(mm)

(MPa)

(MPa)

(mm )

(mm )

(mm )

(mm )

(kN)

(kN)

38 38 38 38 38 38 38 38 38

1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

1400 1400 1400 1400 1400 1400 1400 1400 1400

150 150 150 150 150 150 150 150 150

10 7.5 6 5 4.287 3.75 3 2.5 1.875

300 300 300 300 300 300 300 300 300

60 60 60 60 60 60 60 60 60

16650.1 16763.1 16831.1 16876.5 16909 16933.4 16967.6 16990.5 17019

3900.0 2925.0 2340.0 1950.0 1671.9 1462.5 1170.0 975.0 720.4

387.2 387.2 387.2 387.2 387.2 387.2 387.2 387.2 387.2

101.4 88.5 81.1 76.2 72.8 70.2 66.6 64.3 61.4

2740 2384 2150 2014 1918 1836 1712 1644 1520

2640.1 2363.4 2197.2 2086.4 2007.3 1947.7 1864.5 1809.0 1736.4 Mean

0.964 0.991 1.022 1.036 1.047 1.061 1.089 1.100 1.142 1.020

F.R. Mashiri et al. / Journal of Constructional Steel Research 95 (2014) 141–161

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