Experimental and numerical investigation into the behaviour of face-to-face built-up cold-formed steel channel sections under compression

Thin-Walled Structures 134 (2019) 291–309

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Full length article

Experimental and numerical investigation into the behaviour of face-to-face built-up cold-formed steel channel sections under compression

T

Krishanu Roy , Chia Mohammadjani, James B.P. Lim ⁎

Department of Civil and Environmental Engineering, The University of Auckland, New Zealand

ARTICLE INFO

ABSTRACT

Keywords: Face-to-face channels Cold-formed steel Buckling Fastener spacing Finite element modelling Built-up columns Axial strength

Face-to-face built-up cold-formed steel channel sections are becoming increasingly popular for column members in cold-formed steel structures; its applications include cold-formed steel trusses, space frames and portal frames. In such an arrangement, the independent buckling of the members is resisted by intermediate fasteners. In the literature, no research is available for such face-to-face built-up cold-formed steel columns. The issue is addressed herein. This paper presents the results of 36 experimental tests, conducted on face-toface built-up cold-formed steel channel-sections covering a wide range of slenderness from stub to slender columns. A nonlinear finite element model is then described that shows good agreement with the experimental results. The finite element model includes material non-linearity, initial imperfections and modelling of intermediate fasteners. Both finite element and experimental results are compared against the design strengths calculated in accordance with the American Iron and Steel Institute (AISI), Australian and New Zealand Standards (AS/NZS) and Eurocode (EN 1993-1-3). The verified finite element model is used for the purposes of a parametric study comprising 90 models. The effect of fastener spacing on the axial strength was investigated. From the results of experiments and finite element investigations, it is shown that the design in accordance with the AISI & AS/NZS and Eurocode (EN 1993-1-3) is generally conservative by around 15%, however, AISI & AS/NZS and Eurocode (EN 1993-1-3) can be un-conservative by 8% on average for face-to-face built-up columns failed through local buckling.

1. Introduction Structural engineering applications of cold-formed steel is increasing steadily and the use of face-to-face built-up cold-formed steel channel sections are becoming popular as compression members. This paper presents the results of 36 new experimental tests and 90 finite element analyses on face-to-face built-up cold-formed steel (CFS) channel sections under compression. Fig. 1 shows the general arrangement and cross-sectional details of the face-to-face built-up section investigated in this paper. As can be seen from Fig. 1, face-toface channels are connected with the help of intermediate fasteners along the length. Intermediate fasteners are not used symmetrically on both sides of the built-up channels (see Fig. 1). Such face-to-face builtup columns are used in New Zealand and other pacific countries in space frames and columns in portal frames, because of its increased lateral stability and higher strengths. Besides, these built-up columns are easy to be connected. Current design guidelines i.e. The American Iron and Steel Institute (AISI) [1] and Australian and New Zealand Standards (AS/

⁎

NZS) [2] recommends the use of modified slenderness approach to consider the longitudinal spacing of fasteners in face-to-face built-up CFS channel sections. This modified slenderness approach has been adapted from the design guidelines of hot-rolled steel and the accuracy of this approach has to be checked for the face-to-face built-up CFS channel sections. Significant research is available in the literature for back-to-back built-up CFS channel sections under axial compression [3–6]. Ting et al. [3] investigated the effect of screw-spacing on the axial strength of back-to-back built-up CFS channel sections (see Fig. 2), which was followed by Roy et al. [5,6], to investigate the beneficial effect of gap on the axial strength of back-to-back gapped built-up CFS channels (see Fig. 3). On the other hand, Crisan et al. [7], developed numerical models of back-to-back built-up CFS columns with battens/stiches Rondal and Niazi [8], conducted full scale experiments to determine axial capacity of back-to-back gapped built-up CFS columns, connected with spacers and stiches. To extend the CFS built-up column research, Roy at el. [4] investigated the effect of thickness on the axial strength of back-to-back built-up CFS channels. Recently, Roy.et al.

Correspondence to: The University of Auckland, Building 906, Level 4, Room 413, Newmarket campus, Auckland 1023, New Zealand. E-mail address: [email protected] (K. Roy).

https://doi.org/10.1016/j.tws.2018.09.045 Received 24 April 2018; Received in revised form 11 August 2018; Accepted 26 September 2018 0263-8231/ © 2018 Elsevier Ltd. All rights reserved.

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Notation A’ Ae B’ C1’ C2’ CFS COV E Fe Fn

Yield stress of the cold-formed steel; Fy (KL / r )ms Modified slenderness; (KL / r )o Overall Slenderness; FEA Finite element analysis; L Total length of the face-to-face built-up section; LVDT Linear variable displacement transducers; PAISI& AS/NZS Axial strength from AISI & AS/NZS; PEC3 Axial strength from Eurocode (EN 1993-1-3); PEXP Axial strength from experiments; PFEA Axial strength from the finite element analysis; S Longitudinal spacing of fasteners; t Nominal thickness of the channel section; λc Non-dimensional slenderness ratio as per AISI & AS/NZS;

Total length of the web; Effective area of the section; Total length of the flange; Total width of the shorter lip; Total width of the longer lip; Cold-formed steel; Coefficient of variation; Young's modulus of elasticity; Least of the elastic flexural, torsional, and flexural torsional buckling stress; Nominal buckling stress as per AISI & AS/NZS;

[9], also investigated the effect of screw spacing on the axial strength of back-to-back built-up CFS un-lipped channel sections and showed that AISI&AS/NZS can be un-conservative for stub and short columns. In recent time, the use of stainless steel in structural applications is increasing and the stainless steel built-up channels as column members are becoming popular. Cold-formed stainless steel back-to-back built-up un-lipped channels were investigated under axial compression by the authors [10]. In terms of carbon steel, Georgieva et al. [11] considered built-up columns composed of zed-sections which were connected toe-to-toe (see Fig. 4a). A new approach for the design of double-Z CFS members, based on the direct strength method, was proposed by Georgieva et al. [11]. On the other hand, Zhang and Young [12] considered back-toback built-up channel-sections, with an opening (see Fig. 4b). It was shown that the direct strength method can be used for column design of cold-formed steel I-shaped open sections with edge and web stiffeners [12]. Dabaon et al. [13] investigated CFS built-up battened columns, while Stone and LaBoube [14] considered back-to-back channel sections, which were flange stiffened and track sections. It was found that the current design guidelines by AISI & AS/NZS and European code were un-conservative for the built-up CFS battened columns failed mainly by local buckling. However, the specifications were conservative for the built-up columns failed mainly by elastic flexural buckling [13]. Whittle and Ramseyer [15] and Piyawat et al. [16] investigated back-to-back welded channel sections under compression. Whittle and Ramseyer [15] recommended the use modified slenderness approach to calculate the axial capacity of built-up members. Other works include that of Fratamico et al. [17] and Anbarasu et al. [18] who investigated the axial strength of sheathed and bare built-up CFS columns and cold-formed steel web stiffened builtup batten columns respectively. A simple design formula was developed by Anbarasu et al. [18] to determine the axial capacity of CFS web stiffened built-up batten columns, under axial compression. Liao at al. [19] investigated multi-limbs built-up CFS stub columns under compression and concluded that the screw spacing has a little impact on the ultimate axial compressive capacity and the buckling capacity of the multi-limbs built-up CFS stub columns. On the other hand, Lu et al. [20] conducted an experimental investigation and developed a novel direct strength method for design of cold-formed built-up Isection columns. Reyes and Guzmánc [21] considered face-to-face channels, but these were welded. Reyes and Guzmánc [21] found that the modified slenderness ratio could be used in place of actual slenderness ratio for material 1.5 and 2.0 mm thick while calculating the ultimate load capacity of built-up box sections if the seam weld spacing is less than or equal to 600 mm. A series of column tests on cold-formed steel built-up closed

sections with intermediate stiffeners was presented by Young and Chen [22]. The appropriateness of the direct strength method on CFS built-up closed sections with intermediate web stiffeners was assessed by Young and Chen [22]. It was shown that the direct strength method using single section to obtain the elastic buckling stresses are generally conservative and reliable [22]. Li et al. [23] investigated the axial strength of CFS built-up box and I section under axial compression. Li et al. [23] also proposed a designed method for determining the ultimate load carrying capacity of CFS built-up box and I sections under compression. However, all these sections were different from the built-up section investigated in this paper. No research has been done to investigate the axial strength of face-to-face built-up CFS channels and specially investigated the effect of fastener spacing. This issue is addressed herein. The nominal cross-sectional geometry of the face-to-face built-up section (BF180) investigated herein, is shown in Fig. 1. In total, 36 experimental tests were conducted and reported. Four different lengths in combination with different fastener spacing's were considered for experimental tests. The material properties were determined using the tensile coupon test, also the initial imperfections were measured using a laser scanner. The effect of slenderness, fastener spacing, load-axial shortening, load-lateral displacement, load-axial strain behaviour and failure modes for different lengths of face-to-face built-up columns has been investigated in this paper. A non-linear finite element model is also described, which includes material non-linearity and geometric imperfections. A parametric study was conducted, comprising 90 models, using the verified finite element model. Very good agreement was obtained between the experiment and FEA, which proved the capability of the FE model to replicate experimental results and predict ultimate buckling loads. Using the experimental and FEA results, it is shown that design in accordance with the AISI & AS/NZS [1,2] and Eurocode [24] can be conservative by as much as 15%. However, AISI & AS/NZS and Eurocode [24] can be un-conservative by 8% on average for face-to-face built-up CFS columns failed through local buckling. 2. Current design guidelines 2.1. AISI & AS/NZ Standard Axial strengths determined from the experimental tests and finite element analyses were compared against the design strengths calculated in accordance with the American Iron and Steel Institute specification and the Australia/New Zealand standard for face-to-face built-up CFS channel sections. AISI & AS/NZS uses the Effective width area (EWA) method, while calculating the axial strength of face-to-face built-

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Fig. 2. Back-to-back built-up CFS channel columns investigated by Ting et al. [3].

Fig. 3. Back-to-back gapped built-up CFS channel-sections investigated by Roy et al. [5].

up columns. Axial strength of compression members are calculated in accordance with AISI & AS/NZS standard, are as follows: (1)

PAISI & AS / NZS = A e Fn

where, “ Ae ” is the effective area of the section and “Fn ” is the nominal buckling stress as per AISI & AS/NZS. The critical buckling stress (Fn ) was determined as below:

For

c

For

c

1.5, Fn = (0.658

> 1.5, Fn =

0.877 2

c

2

c

) Fy

Fy

(2)

(3)

where, “Fy ”is the yield stress and “λc” is the non-dimensional slenderness ratio as per AISI & AS/NZS. The critical non-dimensional slenderness (λc) was calculated using Eq. (4): c

=

Fy Fe

(4)

where, “Fe ”is the least of the elastic flexural, torsional, and flexural torsional buckling stress yield stress as per AISI & AS/NZS. Modified slenderness ratio (see equation-5), was used in all calculations, while determining the axial strength of face-to-face built-up CFS channel sections.

Fig. 1. Details of the face-to-face built-up CFS channel sections considered in this paper. (a) General arrangement (3D model) All dimensions are in mm (b) Cross sectional details (BF180).

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KL r

KL r

= ms

2

+

o

s ryc

2

; For which

s ryc

0.5

KL r

o

¯=

(5)

where, “(KL / r )ms ”is the modified slenderness, “(KL / r )o ” is the overall slenderness, “s” is the longitudinal spacing of fasteners, “K” is the effective length factor, “L” is total length of the built-up column, “r” is the radius of gyration and “ryc” is the minimum radius of gyration.

1

¯2

but

= 0.5[1+ ( ¯ 0.2) + ¯ 2]

1.0

1

E Fy

(9) (10)

As indicated by the name, BF180 is built-up column from C180 channel-sections (see Fig. 1). The measured column dimensions are shown in Table 1. All test specimens were made from a base-metal thickness of 1.15 mm, without the thickness of zinc coat. Thirty six face-to-face built-up columns were tested in total, subdivided into four different column heights: 300 mm, 500 mm, 1000 mm, and 1500 mm. Pin-ended boundary conditions were applied for all built-up columns tested herein. Test specimens have been sub-divided into stub, short, intermediate and slender columns in Table 1. In the experimental test programme, the following longitudinal spacing of fastener spacing's (S) were considered:

Fy is the yield stress is the reduction factor for the relevant buckling mode 2

A e /A g

3.1. Test sections

where Ae is the effective area of the section.

+

Lcr i

3. Experimental study

(6)

1

=

i is the radius of gyration for the particular axis, dependent on cross sectional properties. is the imperfection factor and Ncr is the elastic critical force, calculated based on cross sectional properties.

Design strength of axially loaded compression members calculated using the EC3 Code (PEC3) depends on the effective area of the section. Eurocode [24] does not include the provision for face-to-face columns to buckle independently. Table 5.2 of the EC3 (BS EN1993-1-1) [24] was used in order to classify the cross-sections. According to EC3 (BSEN1993-1-3) [24], the axial strength (PEC3) is calculated as follows:

=

Ncr

where Lcr is in plane bucking length,

2.2. Eurocode (EN 1993-1-3)

PEC 3 = Ae Fy

=

Ae Fy

(7) (8)

• Column height of 300 mm; fastener spacing of 50 mm, 100 mm and 200 mm • Column height of 500 mm; fastener spacing of 100 mm, 200 mm and 400 mm • Column height of 1000 mm; fastener spacing of 225 mm, 450 mm and 900 mm • Column height of 1500 mm; fastener spacing of 350 mm, 700 mm and 1400 mm

The spacing of the fasteners were designed to cover spacing within and beyond the spacing requirement of clause C4.5 of the AISI Specification. In order to understand the effects of varying screw spacing with varying column length, the mentioned values of fastener spacing's were considered. The different columns lengths considered in the experimental investigation was mainly to cover a wide range to slenderness and to investigate the effect of fastener spacing on axial strength of different column length. In Fig. 5, fastener spacing's with two screws for face-to-face built-up columns of different lengths, are shown. 3.2. Section labels The test specimens were labelled such that the type of section, longitudinal spacing between fasteners, and nominal length of section and specimen number were indicated by the label. As shown in Fig. 6, the label “BF180-S50-L300-1” is explained as follows:

• “BF180” indicates face-to-face built-up channels with 180 mm web depth. • “S50” indicates the longitudinal spacing between the fasteners as 50 mm. • “L300” indicates nominal length of the specimen as 300 mm. • “1” indicates the specimen number as 1.

Fig. 4. Built-up CFS columns investigated by past researchers. (a) Built-up double Z members investigated by Georgieva, Schueremans and Pyl (2012) (b) Back-to-back built-up CFS channel sections with an opening by Young & Zhang (2012).

294

295

Slender BF180-S350-L1500-1 BF180-S350-L1500-2 BF180-S350-L1500-3 BF180-S700-L1500-1 BF180-S700-L1500-2 BF180-S700-L1500-3 BF180-S1400-L15001 BF180-S1400-L15002 BF180-S1400-L15003 Mean COV

Stub BF180-S50-L300-1 BF180-S50-L300-2 BF180-S50-L300-3 BF180-S100-L300-1 BF180-S100-L300-2 BF180-S100-L300-3 BF180-S200-L300-1 BF180-S200-L300-2 BF180-S200-L300-3 Mean COV Short BF180-S100-L500-1 BF180-S100-L500-2 BF180-S100-L500-3 BF180-S200-L500-1 BF180-S200-L500-2 BF180-S200-L500-3 BF180-S400-L500-1 BF180-S400-L500-2 BF180-S400-L500-3 Mean COV Intermediate BF180-S225-L1000-1 BF180-S225-L1000-2 BF180-S225-L1000-3 BF180-S450-L1000-1 BF180-S450-L1000-2 BF180-S450-L1000-3 BF180-S900-L1000-1 BF180-S900-L1000-2 BF180-S900-L1000-3 Mean COV

Specimen

36.1

35.5

180.4

182.6

36.4 33.8 35.7 34.5 34.7 34.5 35.6 35.2 35.1

178.5 181.4 182.4 179.5 180.3 178.7 177.6 182.4 182.8

35.3 35.2 35.3 35.7 35.6 34.7 34.8

35.0 34.6 33.7 33.6 34.5 36.2 35.8 34.6 35.4

181.4 180.6 181.9 182.7 178.6 179.3 183.6 181.9 180.2

178.7 180.4 181.7 179.5 180.4 182.3 181.3

34.8 35.2 34.7 34.8 36.4 35.2 36.3 34.7 35.8

B’ (mm)

A’ (mm)

180.4 181.6 179.3 180.4 180.9 179.4 178.5 180.7 181.7

Flange

Web

27.9

28.0

28.7 28.6 28.3 28.7 28.5 27.4 27.9

28.9 28.6 27.3 26.9 27.8 28.0 28.8 28.6 27.2

28.2 28.6 27.8 27.6 27.4 28.5 28.3 28.1 28.7

27.5 27.9 28.6 28.1 28.6 27.5 27.4 27.8 28.2

C1’ (mm)

Shorter lip

48.2

49.2

47.9 47.6 47.2 48.8 48.3 48.0 48.7

48.5 48.2 49.6 48.7 48.2 48.1 47.8 47.6 48.7

47.9 48.5 48.7 48.6 48.7 48.2 47.7 49.5 49.8

49.2 48.7 48.9 49.2 49.0 49.5 49.3 48.7 48.4

C2’ (mm)

Longer lip

1532.2

1514.3

1524.6 1520.7 1506.4 1536.8 1542.4 1479.8 1499.4

1002.4 1016.4 1014.8 1029.8 990.4 984.7 1026.8 1003.7 996.8

524.2 504.6 512.4 536.7 510.4 516.8 542.7 530.5 502.7

301.4 294.7 302.5 299.8 298.4 291.4 302.5 299.1 300.6

L (mm)

Length

Table 1 Axial strength of face-to-face built-up CFS (BF180) channel-sections.

1.15

1.17

1.14 1.17 1.14 1.14 1.15 1.16 1.16

1.14 1.14 1.15 1.16 1.17 1.14 1.16 1.15 1.14

1.15 1.16 1.14 1.15 1.14 1.15 1.14 1.16 1.15

1.15 1.16 1.14 1.14 1.14 1.15 1.15 1.16 1.17

t (mm)

Thickness

674.5

689.8

670.1 688.4 671.2 670.1 672.5 682.4 680.7

666.4 669.5 672.5 680.2 688.4 671.5 679.8 676.4 670.2

678.4 680.2 672.3 679.7 670.8 679.8 674.2 681.8 677.8

677.4 681.6 672.4 670.2 672.4 677.4 676.4 681.5 691.5

Ae (mm2)

Effective area

1902.6

1895.7

475.9 472.4 479.8 950.7 950.8 951.8 1900.7

226.4 224.8 225.1 450.4 450.8 452.4 901.4 902.8 899.7

100.7 100.1 99.8 197.8 201.6 199.7 400.4 397.8 402.4

51.0 50.6 50.4 99.8 98.6 101.2 200.4 200.8 199.3

S (mm)

Spacing

192.4

190.4

165.5 168.9 162.4 180.6 177.4 172.4 187.5

106.8 108.6 107.5 119.9 117.5 116.8 130.5 127.4 125.8

49.7 46.9 48.5 57.9 54.7 55.2 62.8 61.8 60.5

10.9 9.2 11.1 13.6 13.6 13.0 17.7 16.9 17.1

Modified slenderness (KL/r)m -

17.1

17.8

27.5 26.1 28.4 21.4 20.1 22.8 19.2

58.7 55.6 57.2 45.7 48.9 50.7 40.3 41.5 42.4

116.4 118.7 117.2 111.4 109.7 110.7 105.4 106.7 107.4

142.1 144.5 145.3 138.4 137.4 135.7 133.4 132.4 134.5

PEXP (kN)

Experimental results

14.9

15.7

24.3 22.9 24.9 18.6 17.5 20.0 16.8

51.9 48.8 49.7 39.1 41.4 43.3 34.7 35.5 36.6

105.8 106.9 104.6 98.6 97.9 99.7 92.5 94.4 95.9

154.5 164.2 157.9 148.8 146.2 142.8 145.0 147.1 147.8

PAISI & (kN) AS/NZS

1.14 0.02

1.15

1.13

1.13 1.14 1.14 1.15 1.15 1.14 1.14

1.13 1.14 1.15 1.17 1.18 1.17 1.16 1.17 1.16 1.16 0.02

1.10 1.11 1.12 1.13 1.12 1.11 1.14 1.13 1.12 1.12 0.01

0.95 0.94 0.95 0.94 0.98 0.92 1.03 1.00 0.95 0.92 0.02

PEXP/ PAISI -

AISI & AS/NZS design strengths

23.9

15.2

23.9 22.5 24.5 18.3 17.0 19.2 16.7

50.6 47.5 50.2 38.7 42.2 42.6 33.6 35.2 35.6

103.6 106.6 106.3 99.2 96.7 95.8 92.1 91.5 94.7

144.7 145.7 144.9 139.5 142.8 141.1 140.1 141.8 138.4

PEC3 (kN)

1.17 0.01

1.15

1.17

1.15 1.16 1.16 1.17 1.18 1.19 1.15

1.16 1.17 1.14 1.18 1.16 1.19 1.20 1.18 1.19 1.17 0.02

1.12 1.11 1.10 1.12 1.13 1.16 1.14 1.17 1.13 1.13 0.02

0.98 0.99 1.00 0.99 0.96 0.96 0.95 0.93 0.97 0.97 0.02

PEXP/ PEC3 -

EC3 design strengths

17.8

18.7

28.6 26.9 29.3 21.6 20.5 23.5 20.0

62.2 58.4 59.5 48.0 50.9 53.7 41.9 43.6 44.9

122.2 125.8 125.4 118.1 115.2 115.1 112.8 112.0 113.8

146.4 151.7 151.1 145.3 145.6 143.8 140.1 141.7 142.6

PFEA (kN)

0.97 0.02

0.96

0.95

0.96 0.97 0.97 0.99 0.98 0.97 0.96

0.94 0.95 0.96 0.95 0.96 0.94 0.96 0.95 0.94 0.95 0.01

0.95 0.94 0.93 0.94 0.95 0.96 0.93 0.95 0.94 0.95 0.01

0.97 0.95 0.96 0.95 0.94 0.94 0.95 0.93 0.94 0.95 0.01

PEXP/ PFEA -

FEA results

K. Roy et al.

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Fig. 5. Fastener spacing with two screws for face-to-face built-up columns with 0.25 < S/L < 0.50 (i) Front facing (ii) Back facing (a) Stub column (i) Front facing (ii) Back facing (b) Short column (i) Front facing (ii) Back facing (c) Intermediate column (i) Front facing (ii) Back facing (d) Slender column.

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3.3. Material testing Tensile coupon tests were conducted to determine the material properties of the test specimens. The tensile coupons were cut from the centre of the face-to-face channels tested herein, in accordance with British Standard for Testing and Materials [25]. Five coupons were obtained from both longitudinal and transverse directions of the face-to-face channels. The coupons were tested in an Instron 4469 (see Fig. 7(a)) tensile testing machine which has a capacity of 50 kN. A calibrated extensometer of 50 mm gauge length was used to determine the tensile strain of the coupons. The tensile coupons are shown in Fig. 7(b). Initial and full stress–strain curves of the steel, used in this research, are shown in Fig. 7(c) and Fig. 7(d) respectively. As can be seen from Table 2, the average Young's modulus and yield strength were 205 GPa and 568 MPa respectively. 3.4. Testing-rig and loading procedure A schematic drawing of the test setup is shown in Fig. 8. Photographs of the experimental setup is also shown in Fig. 9(a) and 9(b) for stub and slender column tests respectively. The external load cell was placed at the top of the built-up column. Seven LVDTs were used for each tests, other than stub and short column tests, where only 3 LVDTs were used. For intermediate and slender columns, 6 LDVTs (3 each on tension and compression side) were used in the lateral directions and one LVDT was used to measure axial deflection. LVDT positions are shown in Fig. 8. LVDT-1 was used to determine the axial shortening of the built-up column. LVDT-2 and LVDT-4 were used to determine the lateral displacements at one-fourth height, on one side of the built-up column from bottom and top respectively. Similarly, LVDT-5 and LVDT-7 were used to measure the lateral displacements on other face of the built-up column at one-fourth height from top and bottom base plates respectively. On the other hand, LVDT-3 and LVDT-6 were used to measure the lateral displacements at midheight of the built-up columns from both faces. To measure the axial strain in the face-to-face built-up columns, strain gauges installed in the built-up columns. For each test, six longitudinal strain gauges were installed (3 on each side of the built-up columns) (see Fig. 8). Two strain gauges (SG-1, SG-3) were installed in the quarter length of the column from the top and bottom and one strain gauge was installed in the middle (SG-2) of the built-up column for each test. SG-1 and SG-3 were used to measure the axial strain at quarter length of the column from the top and bottom end of the built-up column while SG-2 recorded axial strain values at mid-height of the built-up column. A Universal Testing Machine (UTM) AVERY-E59715, of 500 kN capacity, was used to apply axial load to the face-to-face built-up columns. The displacement control method was used to

Fig. 7. Details of the tensile coupon tests. (a) Instron machine (b) Tensile test coupon specimens (c) Initial stress–strain curve of cold-formed steel used in this research (d) Full stress–strain curve of cold-formed steel used in this research.

apply the axial load to the columns. The benefit of using the displacement control is that, it can predict the post-buckling behaviour of the built-up columns. Displacement rate was kept as 0.02 mm/s for all test specimens. LVDT and strain gauge readings were recorded with each increment of loading.

Fig. 6. Specimen labelling.

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Table 2 Material properties obtained from tensile coupon tests. Section

Nominal thickness

Base metal thickness

Gauge Length

Yield stress

Gauge width

Ultimate stress

Young's modulus

Longitudinal Transverse Average

t (mm) 1.16 1.15 –

T (mm) 1.15 1.15 –

L0 (mm) 50 50 –

σ0.2 (MPa) 572 564 568

b (mm) 12.5 12.5 –

σu (MPA) 692 676 684

E GPA 204 206 205

3.5. Initial imperfections measurement

3.6. Experimental results

Fig. 10 shows the details of the laser scanner assembly used to measure the initial imperfections present in the built-up columns. As can be seen in Fig. 10, it is comprised of a 5500 × 2500 × 1500 mm steel frame which supports a travelling platform mounted on precision rails in the longitudinal (5500 mm) direction. The platform supports a stepper motor (see Fig. 10(a)), which allows displacement controlled motion using a rack and pinion system. The platform is designed to have a precision shaft in the transverse (2500 mm) direction which guides a moveable laser scanner (see Fig. 10(b)). The laser scanner cannot capture local and global imperfections on multiple scans across specimen length, it can only read the return cross-sectional distortions from the nominal shape cross-sectional geometries. Therefore, cross sectional distortions were measured for all specimens using the laser scanner. The laser scanner records reading at every 0.0001 mm along each of the mid-web, mid-flange, mid-lip of the face-to-face built-up columns. In Figs. 10(c) and 10(d), laser scanning of BF180-S350-L15001 and BF180-S50-L300-1 is shown. A typical initial imperfection profile, plotted against length is shown in Fig. 10(e) for BF180-S350-L1500-1. The maximum initial imperfections of the face-to-face built-up channels are shown in Table 3. These values were used as the maximum global imperfection, in the finite element modelling descried in Section 4.5. Similar procedure was used to measure the initial imperfections of coldformed steel channels by Ye at al. [26], where they have measured local, distortional and overall imperfections of channel sections using a laser scanner.

All columns were expected to buckle in global, minor-axis flexure potentially with local buckling interaction or only though local buckling. Distortional buckling is not expected for built-up box columns. From general test observations, this hypothesis holds. Table 1 shows the built-up column dimensions and experimental failure loads (PEXP). As shown in Table 1, all stub columns failed through local buckling. Most of the short columns, failed through either local or a combination of local and global buckling. In general, stiffness and capacity decreases with increase in column length, as shown in Table 1. For intermediate and slender columns, global buckling failure was observed. Therefore, built-up columns, having lengths more than 1000 mm or modified slenderness higher than 60, failed through global buckling. Axial capacity of most of the face-to-face built-up intermediate and slender columns were significantly reduced. On the other hand, for BF180, the design strengths are also calculated as per AISI & AS/NZS and Eurocode: EN 1993-1-3 (see Table 1). While calculating the axial strength of stub columns, the effect of local buckling was included. The modified slenderness of the face-to-face built-up columns are shown in Table 1. It is also shown that the AISI & AS/NZ standards and Eurocode: EN 1993-1-3 are un-conservative for stub columns and conservative by around 15% for both 1000 and 1500 mm high columns. The mean values of PEXP / PAISI & AS/NZS is 0.92 for stub columns, with a COV of 0.02. Similarly, the mean values of PEXP / PAISI & AS/NZS are 1.12, 1.16 and 1.14 respectively for 500 mm, 1000 mm and 1500 mm columns with a COVs of 0.01, 0.02 and 0.02 respectively. Similarly, the mean values of axial strengths determined from experiments and design strengths calculated in accordance with Eurocode: EN 1993-1-3 are shown in Table 1 for stub, short, intermediate and slender columns. Different buckling modes were observed for 300 mm, 500 mm, 1000 mm and 1500 mm columns. Nine stub columns were tested (see Table 1). Load-axial shortening behaviour for stub, short, intermediate and slender columns are plotted in Figs. 11–14 respectively. It was noticed that the load-axial shortening behaviour was linear up to a load of 68.4 kN, which is approximately 52% of the ultimate failure load for BF180-S50-L300-1. After that, nonlinear behaviour was noticed until the failure load is reached, which is 142.1 kN. Similar observations were made for other fastener spacing of face-to-face builtup stub columns. Load-lateral displacements are also plotted for BFS350-L1500-1 at the middle and quarter-length of the column (see Fig. 15). Six strain gauges, three each on tension and compression sides, were used to determine the axial strain at mid-length and quarter-length from both ends of the built-up columns. Load -axial strain relationship for BF-S350-L1500-1 is plotted in Fig. 16. Both at mid-length and quarter-length of the built-up columns, strain values are recorded and plotted in Fig. 16. Maximum compressive micro-strains observed at failure load, are 1177.4 and 969.1 at the middle and quarter-length respectively for BF-S350-L1500-1. The effect of the fastener spacing on axial strength, were investigated and shown in both Table 1 and Fig. 17. As can As can be

Fig. 8. Drawing of loading test-rig.

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Fig. 9. Photograph of loading test-rig. (a) Stub column test (b) Slender column test.

seen from Fig. 17(a), when the spacing was increased from 50 mm to 100 mm, axial strength was reduced by 2.6% on average for stub columns. Further, doubling the fastener spacing i.e. from 100 mm to 200 mm, a reduction of 2.6% on axial strength was observed for stub columns. In Fig. 17(b), the average strength of short column was decreased by 4.3%, when the spacing was increased from 100 to 200 mm. A reduction of 5.4% was observed when the spacing was changed from 200 mm to 400 mm for face-to-face built-up short columns. For intermediate columns, as shown in Fig. 17(c), the average decrease in the axial strength is by around 22.1% when doubling the fastener spacing from 225 mm to 450 mm for BF180 columns. However, when the fastener spacing was changed from 450 mm to 900 mm, the axial strength was reduced by 11.2%. On the other hand, for BF180 slender columns, increasing the fastener spacing from 350 mm to 700 mm, reduces the axial strength by 22.2%. However, the axial strength of the face-to-face built-up columns are reduced by 10.3% when the fastener spacing is increased from 700 to 1400 mm (see Fig. 17(d)). BF180-S50-L300-1 test specimen with five fasteners spaced at

50 mm, failed through local buckling. Face-to-face channels remain integral at failure, showing some plastic deformation near the bottom or top end of the stub columns as shown in Fig. 22(a). For, most of the short columns of 500 mm length, local buckling was observed. For intermediate and slender columns, global buckling was noticeable. When the ultimate load was reached, localized deformation was noticeable near the compression side of the columns. The deformed shapes for stub, short and intermediate columns of face-to-face built-up channels are shown in Fig. 22. 4. Numerical study 4.1. General ABAQUS [27] was used to develop a nonlinear elasto-plastic finite element model for the face-to-face built-up CFS channel sections. The modelling techniques described by Ying et al. [28–31] are applied. Centre line dimensions of the cross sectional geometry was used in the finite element model. Fasteners were also modelled between the two-

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Fig. 10. Details of imperfection measurements (c) BF180-S350-L1500-1 (d) BF180-S50-L300-1 (e) Typical imperfection profile (BF180-S350-L1500-1).

channel sections, forming the built-up section. Modelling techniques are discussed in detail as below. The full geometries of the face-to-face built-up columns were modelled for all test specimens. It is very important to model the intermediate fasteners, accurately for the built-up columns. In the FE model, only the fastener head was modelled, which was connected to the lips of face-to-face channels using the MPC beam connector element, available in ABAQUS [27].

from the tensile coupon tests and included in the finite element models. Tensile coupon tests shows, the average values of yield strength, ultimate stress and young's modulus of elasticity were 568 MPa, 684 MPa and 205 GPa respectively. These values were used in the finite element modelling. A true material curve is generated from the engineering material curve as per given in the ABAQUS manual [27], following the equations below: true

4.2. Modelling of geometry and material properties The full geometry of the face-to-face built-up columns was modelled using the classical metal plasticity model available in ABAQUS [27]. In order to define the isotropic yielding and plastic hardening of the faceto-face built-up columns, the von Mises yield surface was used in the classical metal plasticity model. The material properties were taken

=

true (pl)

(11)

(1 + )

= ln 1 +

true

E

(12)

where E is the Young's modulus, σ true is the true stress, σ u is the tensile ultimate strength, and are the engineering stress and strain respectively in ABAQUS [27].

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Table 3 Maximum initial imperfections present in face-to-face built-up CFS (BF180) channel sections. Specimen

Maximum initial imperfections (mm)

Stub BF180-S50-L300-1 BF180-S50-L300-2 BF180-S50-L300-3 BF180-S100-L300-1 BF180-S100-L300-2 BF180-S100-L300-3 BF180-S200-L300-1 BF180-S200-L300-2 BF180-S200-L300-3 Short BF180-S100-L500-1 BF180-S100-L500-2 BF180-S100-L500-3 BF180-S200-L500-1 BF180-S200-L500-2 BF180-S200-L500-3 BF180-S400-L500-1 BF180-S400-L500-2 BF180-S400-L500-3 Intermediate BF180-S225-L1000-1 BF180-S225-L1000-2 BF180-S225-L1000-3 BF180-S450-L1000-1 BF180-S450-L1000-2 BF180-S450-L1000-3 BF180-S900-L1000-1 BF180-S900-L1000-2 BF180-S900-L1000-3 Slender BF180-S350-L1500-1 BF180-S350-L1500-2 BF180-S350-L1500-3 BF180-S700-L1500-1 BF180-S700-L1500-2 BF180-S700-L1500-3 BF180-S1400-L1500-1 BF180-S1400-L1500-2 BF180-S1400-L1500-3

0.14 0.16 0.15 0.18 0.12 0.13 0.14 0.17 0.21 0.11 0.17 0.15 0.21 0.13 0.18 0.09 0.10 0.13 0.12 0.16 0.18 0.21 0.18 0.17 0.21 0.18 0.22 0.23 0.21 0.20 0.18 0.19 0.21 0.22 0.19 0.17

Fig. 12. Load versus axial-shortening relationship for short (500 mm length) columns.

Fig. 11. Load versus axial-shortening relationship for stub (300 mm length) columns.

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Fig. 16. Load versus axial-strain relationship for BF-S350-L1500-1.

Fig. 13. Load versus axial-shortening relationship for intermediate (1000 mm length) columns.

4.3. FE meshing The face-to-face channel sections were modelled using the S4R shell elements available in ABAQUS [27]. The S4R elements are linear 4noded quadrilateral thick shell elements which has six degrees of freedom per node. Rigid quadrilateral shell elements (R3D4) were used to model the upper and lower end plates. In order to model the screw head, three-dimensional eight-noded continuum elements were used with a mesh size of 2 mm by 2 mm. Based on the mesh sensitivity analysis, an element size of 5 mm by 5 mm was used for the face-to-face channels and both the base plates. The aspect ratio of the elements was close to one. A typical finite element mesh is shown in Fig. 18 for BF180-S350-L1500-1. 4.4. Applied boundary conditions and loading procedure The face-to-face built-up CFS channels considered in this study, were pin-ended columns. In order to simulate the upper and lower pin-end supports, the displacements and rotations (boundary conditions) were assigned to the upper and lower end plates through reference points. A typical finite element model for BF180-S350L1500-1, is shown in Fig. 19. The boundary conditions were assigned to both reference points. All three translations were constrained against at the top layer nodes of the screw heads. Constraint conditions between the lips of face-to-face channels and the screw head must be modelled adequately. For this purpose, master-slave contact pair option was used between the channels. Also, between the screw head and top channel, master-slave contact pair was modelled. MPC beam connector element available in ABAQUS library was used to model the stiffness of the intermediate fasteners. MPC was connected to an area in the mesh. In order to validate the test results accurately, the connector elements between the lip of channels and screw head, were assigned a stress of 62.10 MPa. The connector element stress was calculated based on the screw diameter, channel thickness and a safety factor of 3. Both the bearing stress and shear stress were considered while calculating the connector element stress. The maximum of the bearing and shear stress was considered as the connector element stress. The load was applied in increments using the modified RIKS method available in the ABAQUS library, through the reference point of the top base plate (see Fig. 20).

Fig. 14. Load versus axial-shortening relationship for slender (1500 mm length) columns.

Fig. 15. Load versus lateral displacements relationship for BF-S350-L1500-1.

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Fig. 17. Effect of screw spacing on axial strength of face-to-face built-up coldformed steel channel sections. (a) Stub columns (Length = 300 mm) (b) Short columns (Length = 500 mm) (c) Intermediate columns (Length = 1000 mm) (d) Slender columns (Length = 1500 mm). Fig. 18. Typical finite element mesh (BF180-S350-L1500-1).

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Fig. 19. Finite element model of face-to-face built-up CFS channel Sections (BF180-S350-L1500-1).

finite element results were close in terms of load carrying capacity and failure modes of face-to-face built-up channels. Fig. 22 shows the deflected shapes of stub, short and intermediate columns obtained from the FE analysis, which has good agreement with experimental failure modes. Load-axial shortening behaviour, from both the FEA and experiments, is plotted in Figs. 11–14, for stub, short, intermediate and slender columns respectively. As can be seen, FEA strengths are close to experimental strengths, in fact, FEA results are a little conservative for all columns, when compared to experimental results. This may be because of the friction between the base plates and the edge of face-toface built-up column. In experiments, the localized slip was observed between the head of the fasteners and built-up channels. Therefore, a little difference of initial stiffness is observed between the tests and FEA results (see Figs. 11–14). Also, load verses lateral displacement is plotted in Fig. 15 for BF-S350-L1500-1, which showed good comparison between FEA and test result, at both mid and quarter length of the column. Load-axial strain relationship from both the finite element analysis and experiments is shown in Fig. 16, for BF-S350-L1500-1. As shown, good agreement is obtained between the FEA and experimentally measured strain values at the middle and quarter-length of the built-up columns.

4.5. Modelling of initial imperfections Local and overall buckling behaviour of face-to-face CFS built-up channels is dependent on many factors such as: the ratio of length to thickness (L/t), flange width -thickness ratio (B/t), lip-thickness (C/t) etc. Initial imperfections are caused in CFS channels as a result of transportation and fabrication processes. Therefore, both local and overall buckling modes are superimposed for accurate FE analysis. Eigenvalue analyses of the face-to-face built-up columns were performed with very small to large profile thickness to determine the contours for the local and overall imperfections. The lowest buckling mode (Eigen mode 1) in ABAQUS [27], is used as the shape of local and overall buckling mode. This technique is used to model the initial local and overall geometric imperfections of the built-up columns investigated in this study since it has been adopted successfully in previous studies detailed in [13,32–34]. The imperfections used in the modelling of face-to-face built-up channels, were scaled to the values given in the experimental program (see Table 3). In addition, local imperfections of magnitude 0.5% of the section thickness were incorporated as recommended by Ellobody and Young [32]. In Fig. 21, local and overall buckling modes obtained for BF180-S350-L1500-1, are shown.

5. Parametric study

4.6. Analysis procedure

A parametric study, comprising 90 finite element models was conducted in order to understand the effect of fastener spacing on the axial strength of face-to-face built-up CFS columns. A wide range of slenderness, covering stub to slender columns was considered. The same cross-section as used in the experimental and numerical investigations i.e. BF180 was considered in the parametric study. Column lengths from 300 mm to 2000 mm was considered as shown in Table 4. As can be seen, three different number of fasteners were considered in the parametric study: 3, 5 and 10. Fig. 23(a), shows the variation of axial strength against the length for BF180. Axial strength verses the modified slenderness is plotted in Fig. 23(b). In Figs. 23(a) and 23(b), also plotted the experimental data points and the design strengths as per AISI & AS/NZS. Comparison of FEA strength and design strengths according to AISI & AS/NZS are shown in Fig. 24. Single C-channels did not buckle independently, rather the built-up box column buckle as a whole. Weak-axis buckling of the built-up

Two different methods of analysis were used to model the face-toface built-up channels, elastic buckling and nonlinear static RIKS method. Elastic buckling analyses were used to obtain the eigenvectors for the geometric imperfections. Nonlinear static RIKS analysis was used to apply the axial load on the face-to-face built-up CFS channels. The RIKS method can predict the post-buckling behaviour of the builtup columns. RIKS method is best suited to problems where there is unstable buckling or collapse - it uses an arc-length method to determine the response of the loaded structure, where there are significant changes in the structure's stiffness. Therefore general RIKS was preferred over the general static as the analysis method. 4.7. Validation of the finite element model The comparison of axial strength from tests and the FE analysis are shown in Table 1 for BF180. When compared against the test results,

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Fig. 20. Boundary condition and loading procedure in the finite element model (BF180-S350-L1500-1).

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The effect of fastener spacing was also investigated from the parametric study. For stub and short columns, increasing the number of fasteners from 3 to 10, has very less effect (less than 5%) of axial strength of face-to-face built-up channel sections. However, for intermediate and slender columns, fastener spacing had significant effect of the axial strength of such columns. For intermediate columns, the axial strength was reduced by approximately 15–20%, when the fastener spacing was doubled. Also, for slender columns, when the fastener spacing was doubled, axial strength was reduced by 20% on average. 6. Conclusions A detailed experimental test program on the axial strength of faceto-face built-up CFS channel-sections is presented in this paper. A total of 36 experiments are reported. Material properties and initial imperfections were measured for all test specimens. The failure modes, axial capacity, load-axial shortening, load-lateral displacement and load-axial strain relationships are discussed. CFS built-up stub and short columns failed through local buckling. However, intermediate and slender columns failed through either global buckling or a combination of local and global buckling. Effect of the fastener spacing on the axial strength of face-to-face built-up CFS channel sections is investigated. It was found that the fastener spacing has a negligible effect on column strength of stub and short columns. However, for intermediate columns, the axial strength was reduced by approximately 15–20%, when the fastener spacing was doubled. Also, for slender columns, when the fastener spacing was doubled, axial strength was reduced by 20% on average. A nonlinear finite element model is then presented, which includes non-linear material properties and geometric imperfections. FE model includes the modelling of intermediate fasteners. Finite element results are validated against the experimental results, which showed good agreement. Both the test and finite element results are compared against the current design guidance by the AISI & AS/NZS and Eurocode EN 1993-1-3. The validated finite element models were used to perform a parametric study, comprising 90 finite element models, to investigate the effect of fastener spacing on the axial strength of face-to-face built-up CFS channels. The axial strength of the built-up columns, determined from the finite element analysis was compared against the design strengths calculated in accordance with the current AISI & AS/NZS and Eurocode: EN 1993-1-3. Both FEA and test results were over-conservative by around 15% for all face-to-face built-up columns failed through flexural buckling, however, the design standards were unconservative by 8% on average for all built-up columns failed through local buckling.

Fig. 21. Initial imperfection contours (BF180-S350-L1500-1) (a) Local buckling (b) Overall buckling.

sections became more pronounced with increased column length. Local–global buckling controlled in most cases for intermediate columns, and single-mode global buckling was observed in case of slender columns. In these longer built-up columns, global buckling was more pronounced and less local interaction was observed before peak loads were reached. In shorter columns, local buckling reduced the global capacity. As can be seen from Figs. 23(a) and 23(b), both the AISI & AS/ NZ standards were conservative by around 15% for all columns failed through flexural buckling or a combination of local and flexural buckling. It is also shown that the face-to-face built-up columns having modified slenderness less than 30, failed through local buckling and built-up columns exceeding modified slenderness value of 65, failed through flexural buckling. Between, 30 and 65, face-to-face built-up columns, failed through a combination of local and flexural buckling.

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Fig. 22. Deformed shapes at failure face-to-face built-up cold-formed steel channel sections. (i) Experimental (ii) FEA (1) BF180-S50-L300-1 (fastener spacing 50 mm) (i) Experimental (ii) FEA (2) BF180-S100-L300-1 (fastener spacing 100 mm) (i) Experimental (ii) FEA (3) BF180-S200-L300-1 (fastener spacing 200 mm) (a) Stub columns (i) Experimental (ii) FEA (b) Short column, BF180-S100-L500-1 (fastener spacing 100 mm) (i) Experimental (ii) FEA (1) BF180-S225-L1000-1 (fastener spacing 225 mm) (i) Experimental (ii) FEA (2) BF180-S450-L1000-1 (fastener spacing 450 mm) (c) Intermediate columns.

307

BF75-L300 BF75-L400 BF75-L500 BF75-L600 BF75-L700 BF75-L800 BF75-L900 BF75-L1000 BF75-L1100 BF75-L1200 BF75-L1300 BF75-L1400 BF75-L1500 BF75-L1600 BF75-L1700 BF75-L1800 BF75-L1900 BF75-L2000

Specimen

Flange

B’ mm

35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0

Web

A’ mm

180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0

28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0

C1’ mm

Shorter Lip

49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0

C2’ mm

Shorter Lip

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

L mm

Length

75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

3 screws mm 50.0 66.7 83.3 100.0 116.7 133.33 150.0 166.7 183.3 200.0 216.7 233.3 250.0 266.7 283.3 300.0 316.7 333.3

5 screws mm

Spacing(s) For

141.7 127.8 111.9 95.2 78.6 63.3 51.9 43.4 36.3 30.5 26.0 22.4 19.5 17.2 15.2 13.6 12.2 11.0

Local Local Local Local Local Local + Flexural Local + Flexural Local + Flexural Flexural Local + Flexural Local + Flexural Flexural Flexural Flexural Flexural Flexural Flexural Flexural

27.3 36.4 45.5 54.6 63.6 72.7 81.8 90.9 100.0 109.1 118.2 127.3 136.4 145.5 154.6 163.6 172.7 181.8

for

148.5 137.1 123.8 109.3 94.3 79.6 65.8 55.1 46.9 40.3 34.3 29.6 25.8 22.7 20.1 17.9 16.1 14.5

5 screws kN

& AS/NZ

3 screws kN

PAISI

10 screws mm

Failure Mode(s)

Table 4 Finite element and AISI & AS/NZS strength with varying length of the section for 3, 5 and 10 screws.

153.8 142.9 130.2 116.0 101.1 86.4 72.1 60.4 51.5 44.4 38.1 32.8 28.6 25.1 22.3 19.9 17.8 16.1

10 screws kN 135.4 130.0 117.0 101.2 83.8 68.1 56.1 46.3 39.2 32.3 27.9 25.0 21.2 19.0 17.5 15.4 14.2 12.3

3 screws kN

PFEA for

143.7 136.5 127.9 112.3 99.8 85.1 70.1 57.8 49.7 42.6 37.2 32.8 27.8 24.1 21.8 19.8 17.5 15.8

5 screws kN 149.8 142.0 134.3 120.1 106.2 90.4 77.1 64.2 55.2 46.8 40.8 35.4 30.7 27.1 24.1 21.4 19.5 18.1

10 screws kN

/

PAISI

0.96 1.02 1.05 1.06 1.07 1.08 1.08 1.07 1.08 1.06 1.07 1.12 1.09 1.10 1.15 1.13 1.16 1.12

3 screws

PFEA

0.97 1.00 1.03 1.03 1.06 1.07 1.07 1.05 1.06 1.06 1.08 1.11 1.08 1.06 1.08 1.11 1.09 1.09

5 screws

& AS/NZ

0.97 0.99 1.03 1.04 1.05 1.05 1.07 1.06 1.07 1.05 1.07 1.08 1.07 1.08 1.08 1.08 1.10 1.12

10 screws

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Fig. 23. Effect of varying number of screws and slenderness for BF180 (a) Variation of strength against length (b)Variation of strength against modified slenderness.

Fig. 24. Comparison of FEA strength and design strength in accordance with AISI & AS/NZ Standards.

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[29]

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