19
Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 1 Experimental Study on Bearing Capacity of Stainless Steel Lipped C Section Stub Columns FAN Shenggang 1 LIU Fang 2 ZHENG Baofeng 3 SHU Ganping 4 1 Associate Professor, School of Civil Engineering, Key Lab of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, NO.2 Sipailou Nanjing, China. 2 Engineer, International Century Design of Architecture Co.,LTD , NO.11 TaiHu Middle. ChangZhou, China 3 PhD Candidate, School of Civil Engineering, Southeast University, Nanjing, China 4 Professor, School of Civil Engineering, Key Lab of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, NO.2 Sipailou Nanjing, China. This paper researches the failure mechanism and ultimate bearing capacity of stainless steel stub columns of lipped C section under axial and eccentric compression. A series tests were performed on stainless steel material S30408, including 16 mechanical property tests, 10 axially loaded stub column tests and 28 eccentrically loaded stub column tests. Standard tensile tests in the flat and corner regions were conducted to investigate anisotropy, hardening index and stress- strain behaviour of stainless steel. Axially and eccentrically loaded stub columns tests investigate the load-displacement curve, ultimate bearing capacity and section strain variation law of stub columns. The loaded tests results of stub columns imply that the difference between test values and code computational values shows diminishing trend as slenderness coefficient increases. Keyword Stainless steel; Lipped C section; Stub column; Cold working; Ultimate bearing capacity 1 Introduction The emergence of stainless steel material is one of the greatest innovations in metal material field in the early 20 th century. Compared with traditional metal materials, stainless steel is a new type of green environmental, recoverable and sustainable material, which contains more complex alloy composition, such as nickel (Ni), chromium (Cr) and molybdenum (Mo). Stainless steel is widely used and gains much attention from all walks of life due to the attractiveness of its mechanical properties, appearance, corrosion resistance and chemical compatibility. In addition, booming production growth of stainless steel together with its great varieties and improvement in processing paves way for the new trend of its application in building structure in recent years, taking into consideration the design idea of whole life cycle and market requirement. Therefore, stainless steel shows extensive application prospects and is favored by many architects and structure engineers. The studies of stainless steel have gone through three stages, dating back to the 1960s. The first stage: 1966~2000, studies mainly focused on material properties and involved few component calculations. The second stage: 2000~2008, during this peak period, large numbers of achievements were obtained on material properties, component calculations, connection calculations and integrality performances of structure. The third stage: after 2008, as more attention is paid to fire resistance of stainless steel, studies have been carried out to investigate its material properties at high temperature, fire resistance of components and fire-resistant design methods. The earlier work on nonlinearity of metal material was conducted by Ramberg and Osgood [1]. They put forward the classic material model, Ramberg-Osgood equation(R-O equation), in which harden exponent was introduced to divide the stress-strain curve of nonlinear material into two segments. Hill [2] modified R-O equation by using σ 0.2 , proposing the basic expression to describe the nonlinear stress-strain relationship of metal material. Uniaxial and biaxial tensile tests of stainless steel plate were carried out by Olsson [3] to correct R-O equation again. Rasmussen [4] summed up the results of tensile tests of stainless steel material and made a correction in the expression of the second segment of R-O type curve. Gardner et al. [5-7] performed tensile and compression tests of cold-formed stainless steel and perfected the expression of its stress-strain behaviour. They also carried out corner mechanical property tests for roll-formed steel and established the formula of nominal yield strength of corner regions and ultimate strength of flat regions. Plenty of experimental work was conducted by Coetzee et al. [8, 9] on corner mechanical property of cold-formed stainless steel members of lipped C section. Two major parameters which influenced the strength of cold-formed stainless steel were determined: the ratio of corner radius to material thickness (r i /t) and the ratio of ultimate tensile strength to yield strength of the flat regions (σ u f ). Cruise [10] analyzed experimental results to access the formula which could predict corner mechanical properties of cold-formed and roll-formed steel. A total of 15 stainless steel members – 11 I sections and 4 box sections – were measured for their axial compression capacity, as reported in Johnson et al. [11], and then tangent modulus method was proposed for stability bearing capacity calculation. Rasmussen [12] performed axial compression tests for stainless steel stub columns and long columns.

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Page 1: Experimental Study on Bearing Capacity of Stainless … · Experimental Study on Bearing Capacity of ... beams of rectangular and square section. Three failure ... stub columns and

Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 1

Experimental Study on Bearing Capacity of Stainless Steel Lipped C Section Stub Columns

FAN Shenggang1 LIU Fang2 ZHENG Baofeng3 SHU Ganping4

1Associate Professor, School of Civil Engineering, Key Lab of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, NO.2 Sipailou Nanjing, China.

2 Engineer, International Century Design of Architecture Co.,LTD , NO.11 TaiHu Middle. ChangZhou, China 3PhD Candidate, School of Civil Engineering, Southeast University, Nanjing, China

4Professor, School of Civil Engineering, Key Lab of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, NO.2 Sipailou Nanjing, China.

This paper researches the failure mechanism and ultimate bearing capacity of stainless steel stub columns of lipped C section under axial and eccentric compression. A series tests were performed on stainless steel material S30408, including 16 mechanical property tests, 10 axially loaded stub column tests and 28 eccentrically loaded stub column tests. Standard tensile tests in the flat and corner regions were conducted to investigate anisotropy, hardening index and stress-strain behaviour of stainless steel. Axially and eccentrically loaded stub columns tests investigate the load-displacement curve, ultimate bearing capacity and section strain variation law of stub columns. The loaded tests results of stub columns imply that the difference between test values and code computational values shows diminishing trend as slenderness coefficient increases.

Keyword Stainless steel; Lipped C section; Stub column; Cold working; Ultimate bearing capacity

1 Introduction The emergence of stainless steel material is one of the greatest innovations in metal material field in the early 20th century. Compared with traditional metal materials, stainless steel is a new type of green environmental, recoverable and sustainable material, which contains more complex alloy composition, such as nickel (Ni), chromium (Cr) and molybdenum (Mo). Stainless steel is widely used and gains much attention from all walks of life due to the attractiveness of its mechanical properties, appearance, corrosion resistance and chemical compatibility. In addition, booming production growth of stainless steel together with its great varieties and improvement in processing paves way for the new trend of its application in building structure in recent years, taking into consideration the design idea of whole life cycle and market requirement. Therefore, stainless steel shows extensive application prospects and is favored by many architects and structure engineers.

The studies of stainless steel have gone through three stages, dating back to the 1960s. The first stage: 1966~2000, studies mainly focused on material properties and involved few component calculations. The second stage: 2000~2008, during this peak period, large numbers of achievements were obtained on material properties, component calculations, connection calculations and integrality performances of structure. The third stage: after 2008, as more attention is paid to fire resistance of stainless steel, studies have been carried out to investigate its material properties at high temperature, fire resistance of components and fire-resistant design methods.

The earlier work on nonlinearity of metal material was conducted by Ramberg and Osgood [1]. They put forward the classic material model, Ramberg-Osgood equation(R-O equation), in which harden exponent was introduced to divide the stress-strain curve of nonlinear material into two segments. Hill [2] modified R-O equation by using σ0.2, proposing the basic expression to describe the nonlinear stress-strain relationship of metal material. Uniaxial and biaxial tensile tests of stainless steel plate were carried out by Olsson [3] to correct R-O equation again. Rasmussen [4] summed up the results of tensile tests of stainless steel material and made a correction in the expression of the second segment of R-O type curve. Gardner et al. [5-7] performed tensile and compression tests of cold-formed stainless steel and perfected the expression of its stress-strain behaviour. They also carried out corner mechanical property tests for roll-formed steel and established the formula of nominal yield strength of corner regions and ultimate strength of flat regions. Plenty of experimental work was conducted by Coetzee et al. [8, 9] on corner mechanical property of cold-formed stainless steel members of lipped C section. Two major parameters which influenced the strength of cold-formed stainless steel were determined: the ratio of corner radius to material thickness (ri/t) and the ratio of ultimate tensile strength to yield strength of the flat regions (σu/σf). Cruise [10] analyzed experimental results to access the formula which could predict corner mechanical properties of cold-formed and roll-formed steel.

A total of 15 stainless steel members – 11 I sections and 4 box sections – were measured for their axial compression capacity, as reported in Johnson et al. [11], and then tangent modulus method was proposed for stability bearing capacity calculation. Rasmussen [12] performed axial compression tests for stainless steel stub columns and long columns.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 2

Mechanical properties were accessed on the basis of stub column tests, and the simplified calculation method for stability bearing capacity of axially loaded compression columns as well as the corresponding curves was fitted based on long column test results. Young et al. [13-15] conducted experimental studied on 9 stainless steel axially loaded columns with fixed ends. Comparison results of test results with design results implied that the design result was reliable. Gardner et al. [16, 17] carried out tests to study bearing capacity of 37 stub columns and 22 long columns with articulated ends. A new method to calculate bearing capacity of axially compressed columns was proposed through parametric analysis. Besides, load-displacement curve was obtained through tests on 9 cold-formed SHS and RHS stainless steel beams with two simple supported ends. Rasmussen et al. put forward new design criteria and formula of cold formed stainless steel beams based on American Specification and validated the formula by tests. Zhou and Young et al. [18, 19] performed theoretical and experimental studies on stainless steel beams of rectangular and square section. Three failure modes of beams were proposed: bending failure, buckling failure in the web and coupling failure of bending and buckling. In addition, formula of buckling strength in the web under concentrated load was given as well as the coupling effect of bending moment and concentrated load. Experimental studies were conducted by Shu GanPing and Zheng BaoFeng et al. [20] on 60 stainless steel columns and 40 stainless steel beams. Calculation methods for bearing capacity of stainless steel columns and beams were proposed.

Above all, existing studies are mainly about mechanical properties of closed section stainless steel members. Few studies have been carried out to investigate bearing capacity of open section members, especially for stainless steel members of lipped C section. Therefore, this paper performs 16 mechanical property tests for stainless steel specimens, 10 axially loaded stub column tests and 28 eccentrically loaded stub column tests. Mechanical property tests investigate strong nonlinear stress-strain behaviour, anisotropy and cold hardening property of stainless steel material, giving mechanical property values. Stub column tests reveal the failure phenomenon, process and mechanism of stub columns subjected to axial and eccentric load, providing strain variation curves, σ ε- curves and ultimate bearing capacity values of specimens under different load. The ultimate bearing capacity values of stub columns are compared with those in three design codes, American Specification (ASCE), European Code (EC3) and Chinese Code of Cold-formed Thin-wall Steel Structures. Based on the comparison, design strengths are obviously less than test strengths and the difference presents diminishing trend as the slenderness coefficient increases. Research findings provide reference for future investigation into bearing capacity of lipped C section stainless steel stub columns and theoretical support for design of stainless steel structures.

2 Mechanical property tests The stress-strain relationship of stainless steel is characterized with its strong nonlinearity, significant hardening property, low proportional limit and high elongation. Besides, the material is anisotropic and highly influenced by cold-formed effect. In order to study the anisotropic and cold-work hardening properties of stainless steel, two kinds of mechanical property tests are carried out on the basis of existing experimental studies. Flat specimen tests (both longitudinal and transverse) are intended to investigate anisotropy of the material and corner specimen tests are performed to reveal the influence of cold working (cold bending) on material properties.

The flat specimens were cut from stainless steel plates, the dimensions detailed in Fig. 1. The corner specimens were taken from the corners regions of lipped C section steel, the cutting locations and dimensions detailed in Fig. 2 (a) and (b). Moreover, to facilitate axial tensile load on corner regions, two corner parts cut from symmetric positions were merged to form a corner specimen. A steel bar was set in the middle to ensure the firmness of the specimen, as shown in Fig. 2 (c).

40205040 20

40

3.2

R=30

12.5

170

Fig. 1 Dimensions of tensile specimen in the flat regions

CT-a-I-1 CT-a-O-1

CT-a-I-2 CT-a-O-2t t

4010 90 40 10170

Corner region

barSteel

Steel bar

Corner region

Corner region (a) Cutting locations (b) Specimen dimensions (c) Specimen detail

Fig. 2 Tensile specimen in the corner regions

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 3

2.1 Flat specimen tests In order to effectively control the smoothness and cutting speed of specimens, a laser cutting machine was employed to cut all the specimens once from 2mm and 3mm parent material. After cutting out the specimens, cutting edges were polished and then dimension of each specimen was measured. The processed flat specimens are shown in Fig. 3 (a), grouping and dimensions detailed in Table 1.

Table 1 Grouping and dimensions of tensile specimens in the flat regions

Group number

Specimen code

Material thickness

/mm

Measured dimensions/mm Group

number Specimen

code Material

thickness/mm

Measured dimensions/mm

Thickness Width Thickness Width

1 S-a-1 2.0 1.76 12.48

3 L-a-1 2.0 1.76 12.37

S-a-2 2.0 1.76 12.47 L-a-2 2.0 1.76 12.39 S-a-3 2.0 1.76 12.46 L-a-3 2.0 1.78 12.41

2 S-b-1 3.0 2.76 12.48

4 L-b-1 3.0 2.80 12.54

S-b-2 3.0 2.74 12.51 L-b-2 3.0 2.82 12.37 S-b-3 3.0 2.76 12.50 L-b-3 3.0 2.80 12.53

Specimen code: S represents longitudinal tensile specimen; L represents transverse tensile specimen; a stands for specimen from 2mm parent material; b stands for specimen from 3mm parent material.

A 10T capacity electronic universal testing machine was employed for standard tensile tests, which applied tensile load to the specimens with the deformation rate of 0.5mm/min. And the strain was recorded by strain acquisition instruments, thus, the stress-strain curve was obtained. The failure phenomena of longitudinally loaded and transversely loaded tensile specimens are shown in Fig. 3 (b) and Fig. 3 (c). The failure phenomena show that stainless steel material extended significantly after tensile failure with a high elongation rate which nearly reaches or exceeds 50%, besides, the fracture surface was trimness and the necking range was small.

(a) After processing (b) After longitudinal tensile failure (c) After transversal tensile failure

Fig. 3 Flat specimens in different states

The test results of various parameters of stainless steel mechanical property are shown in Table 2, n and n f as two hardening indexes in R-O model also shown in the table, in which n is hardening index ( [ ]0.2 0.01ln(20) ln( / )n σ σ= ); n f is hardening index fitted by least-square method with DataFit software.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 4

Table 2 Mechanical property test results of stainless steel in the flat regions

Group number

Specimen code

0E

/2N mm

0.01σ

/ 2N mm 0.2σ

/ 2N mm n fn

1.0σ

/2N mm

t0.2ε 0.2n t1.0ε uσ

/2N mm

1

S-a-1 183785 141.38 268.11 4.68 7.67 313.87 0.00346 2.71 0.01171 674.83 S-a-2 190025 134.75 262.00 4.51 7.00 308.20 0.00338 1.96 0.01162 658.67 S-a-3 185795 140.04 262.70 4.76 7.30 307.72 0.00341 1.97 0.01166 681.95 Average 186535 138.72 264.27 4.65 7.32 309.93 0.00342 2.21 0.01166 671.82

2

S-b-1 161486 154.11 321.46 4.07 5.16 388.37 0.00399 2.57 0.01240 643.85 S-b-2 188018 130.40 322.41 3.31 4.50 390.28 0.00371 2.50 0.01208 659.79 S-b-3 164311 153.07 320.23 4.06 5.35 386.21 0.00394 2.44 0.01235 631.63 Average 171272 145.86 321.37 3.79 5.00 388.29 0.00388 2.50 0.01228 645.09

3

L-a-1 195065 155.22 262.57 5.70 8.48 306.08 0.00335 2.00 0.01157 678.94 L-a-2 191892 158.20 263.82 5.86 8.58 305.26 0.00337 2.13 0.01159 695.19 L-a-3 189868 147.94 258.79 5.36 7.30 303.07 0.00336 1.99 0.01160 652.10 Average 192275 153.79 261.73 5.63 8.12 304.80 0.00336 2.04 0.01159 675.41

4

L-b-1 175595 192.38 338.01 5.32 6.12 399.12 0.00392 2.53 0.01227 687.71 L-b-2 190848 163.62 337.17 4.14 5.60 399.29 0.00377 2.42 0.01209 670.93 L-b-3 196104 164.16 341.30 4.09 5.44 403.08 0.00374 2.52 0.01206 686.07 Average 187516 173.39 338.82 4.47 5.72 400.50 0.00381 2.49 0.01214 681.57

Where, E0 is material initial elastic modulus; σ0.01 is the stress corresponding to 0.01% residual deformation; σ0.2is the stress corresponding to 0.01% residual deformation; σ1.0 is the stress corresponding to 1.0% residual deformation;ε t0.2 represents the strain corresponding to σ0.2; ε t1.0 represents the strain corresponding to σ1.0; σu is ultimate stress.

The obtained σ-ε curves are shown in Fig. 4 (a) and Fig. 4 (b), only including curves of specimen S-a-1, S-b-1, L-a-1 and L-b-1. Each specimen has three σ-ε curves acquired through the following methods: (1) to fit the curve according to test data; (2) to draw the curve based on classic R-O equation; (3) to fit the σ-ε curve after replacing index n with n f in classic R-O equation. Comparing the curves shown in Fig. 4 (a) and Fig. 4 (b), it can be seen that the second method generates the lowest σ-ε curve and the curve obtained through the third method fits the test results best. Consequently, it is suggested that the third method should be adopted to fit σ-ε curves in accurate calculation and analysis of stainless steel material. Fig. 4 (c) shows the comparison results of σ-ε curves obtained through longitudinal tensile tests and transverse tensile tests.

0.0000.0020.0040.0060.0080.0100.0120.0140

50100150200250300350400

ε

σN

/mm

2 S-a-1(Test) S-a-1(Method2) S-a-1(Method3) S-b-1(Test) S-b-1(Method2) S-b-1(Method3)

0.0000.0020.0040.0060.0080.0100.0120.0140

50100150200250300350400

σN/

mm

2

ε

L-a-1(Test) L-a-1(Method2) L-a-1(Method3) L-b-1(Test) L-b-1(Method2) L-b-1(Method3)

0.0000.0020.0040.0060.0080.0100.0120.0140

50100150200250300350400

σN/

mm

2

ε

S-a S-b L-a L-b

(a) Longitudinal tensile tests (b) Transversal tensile tests (c) Comparison of tests results

Fig. 4 σ-ε curves of flat specimen tests

According to the data in Table 2, the elastic modulus of stainless steel material is about 2.0×105 N/mm2. It is also shown that the elastic modulus obtained through transverse tensile tests slightly exceeds that obtained through longitudinal tensile tests but with small difference. Conclusions can be drawn based on Table 2 and Fig. 4 (c): (1) for tensile specimens from 2mm parent material, little difference exists between material properties acquired from longitudinal tensile tests and transverse tests and the corresponding σ-ε curves are close to each other; for tensile specimens from 3mm parent material, the values of elastic modulus and strength acquired from transverse tensile tests are both larger than those from longitudinal tensile tests together with the former σ-ε curve higher than the latter; (2) the nominal yield stresses of 3mm specimens apparently exceed those of 2mm specimens; the nominal yield stresses range from 200 to 400 N/mm2, and the ultimate tensile strengths range from 630 to700 N/mm2; (3) for tensile specimens taken from 2mm parent material, the values of hardening index n obtained through transverse tensile tests are obviously smaller than those through longitudinal tensile tests, however, for 3mm tensile specimens, the values of transversely loaded specimens barely differ from whose of longitudinally loaded ones. Therefore it is known that the thickness of stainless steel has certain influence on the hardening index n of both transversely and longitudinally loaded specimens.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 5

2.2 Corner specimen tests For stainless steel members of lipped C section, the material properties at the corners are significantly affected by cold working. Therefore, corner specimens were also tested to access accurate mechanical properties. Corner specimens were extracted from stub column members of C140×40×15×2.0 (3.0) as shown in Fig. 2 (a) and the cutting position was set at the start of the arc. It was difficult to measure the section area of the corner regions as well as to guarantee the smoothness of specimens. Consequently, wire cutting machine was employed for specimen processing. To access accurate section area of each specimen, a 40mm×40mm standard block was cut from the surface of a stub column and then weighed, based on which the accurate density of stainless steel was available. Next the section area of each specimen could be calculated. The processed corner specimens are shown in Fig. 5 (a) and grouping as well as geometric dimensions are detailed in Table 3.

Table 3 Grouping and dimensions of tensile specimens in the corner regions

Group number

Specimen code Material type/mm Mass/g Length/mm Section area/ 2mm Density/

3kg mm 1 C-a-O-1 C160×60×15×2.0 25.59 170 18.91

0.00796 C-a-O-1 C160×60×15×2.0 25.35 170 18.74

2 C-a-I-1 C160×60×15×2.0 25.14 170 18.58 C-a-I-1 C160×60×15×2.0 25.41 170 18.78

3 C-b-O-1 C160×60×15×3.0 49.15 170 36.58

0.00790 C-b-O-1 C160×60×15×3.0 50.35 170 37.47

4 C-b-I-1 C160×60×15×3.0 48.61 170 36.18 C-b-I-1 C160×60×15×3.0 49.21 170 6.63

Specimen code: C represents corner tensile specimen; I represents the corner region as the intersection of flange and web; O represents the corner region as the intersection of flange and lip; a stands for specimen from 2mm lipped C section; b stands for specimen from 3mm lipped C section.

The testing machine, loading rate and measuring method of corner specimen tests are the same as those in flat specimen tests. Fig.5 (b) shows the specimens on the testing machine. A corner specimen consisted of two symmetric parts cut from the corner regions. As the two section areas might not accurately coincide, moreover, tiny eccentricity was inevitable in process of setup, tensile failure appeared in one part firstly and the other failure followed closely. The fracture surface was vertical to the axis of the specimen and obvious necking effect was observed. The test specimens elongated by over 20%, lower than that of flat specimens. Fig. 7 (c) shows the failure phenomena of specimens.

(a) After processing (b) On test setup (c) After tensile failure

Fig. 5 Corner specimens in different states

Test results of various corner mechanical properties of stainless steel material are summarized in Table 4.

Table 4 Mechanical property test results of stainless steel in the corner regions

Group number

Specimen code

0E /2N mm

0.01σ /2N mm

0.2σ /2N mm

n 1.0σ /2N mm t0.2ε 0.2n t1.0ε uσ /

2N mm 1 C-a-O-1 210437 196.68 424.34 4.62 520.65 0.00402 3.09 0.01247 796.98 2 C-a-I-1 206555 212.54 432.19 4.76 528.62 0.00409 3.15 0.01256 807.52 Average 208496 204.61 428.26 4.69 524.64 0.00405 3.12 0.01252 802.25 3 C-b-O-1 197547 235.99 510.79 4.36 627.30 0.00459 3.38 0.01318 ——— 4 C-b-I-1 200421 240.13 512.12 4.38 629.68 0.00456 3.50 0.01315 818.21 Average 198984 238.06 511.45 4.37 628.49 0.00457 3.44 0.01316 818.21 Where, the notation is the same as that in table 2.

It can be seen, from comparison of results in Table 2 and Table 4, the cold-forming process leads to a significant strength enhancement of the material properties at the corners. For instance, the average nominal yield strength σ0.2 of 2mm material increases by 62.8% and that of 3mm material increases by 54.93%. Nevertheless, other mechanical property parameters barely changed.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 6

The σ-ε curves obtained from corner specimen tests are shown in Fig. 6. The three σ-ε curves of each specimen correspond to the same methods as used in flat specimen tests. Fig.6 presents that the σ-ε curves obtained by the second and third method are in good agreement with those fitted by test results.

0.0000.0020.0040.0060.0080.0100.0120.0140

100200300400500600700

σN/

mm

2

ε

C-a-O-1(Test) C-a-O-1(Method2) C-a-O-1(Method3) C-b-O-1(Test) C-b-O-1(Method2) C-b-O-1(Method3)

0.0000.0020.0040.0060.0080.0100.0120.0140

100200300400500600700

σN/

mm

2

ε

C-a-I-1(Test)C-a-I-1(Method2) C-a-I-1(Method3) C-b-I-1(Test) C-b-I-1(Method2) C-b-I-1(Method3)

(a) Intersection of flange and lip (b) Intersection of flange and web

Fig. 6 σ-ε curves of corner specimen tests

3 Stub column tests Stub column tests were performed to investigate the bearing capacity of stainless steel columns with low slenderness ratio. Based on European Code (EC3) [21], the length of stub column specimens should be limited from triple the maximum section width to 20 times of the minimum gyration radius in order that section properties could be revealed but overall instability not happen. Stub column specimens used in this test meet the requirement above.

3.1 Processing of test specimens Cold-formed stainless steel members of lipped C section are selected, section sizes including C80×40×15×2.0, , C120×40×15×2.0, C140×60×15×2.0, C160×60×15×2.0, C80×40×15×3.0, C100×40×15×3.0, C120×40×15×3.0, C140×60×15×3.0 and C160×60×15×3.0. Specimens went through cutting, fold bending, polishing to be eventually shaped up, as shown in Fig.7 (a). Tests on both axially compressed and eccentrically compressed columns were carried out. Two parallel plates were welded to the top and seat of a stub column in case the specimen would twist about its weak axis subjected to eccentric load, as shown in Fig.7 (b).

(a) Processed specimens (b) Welded specimens

b

Rr

t

t

a

h

A-2A-1

A-3

A-4A-5

Fig. 7 Stainless steel stub column specimens Fig.8 Section Dimensions Fig.9 measuring point of initial imperfection

Stub column specimens included 10 axially loaded columns and 28 eccentrically loaded columns, grouping and geometric parameters detailed in Table 5. Code A specimens were axially loaded, while Code B, C, D are eccentrically loaded with the strong axis as the eccentric direction. Under eccentric load three states of stress distribution in the web could be realized: (1) both ends subjected to compressive load with one end bearing half the load of the other; (2) one end in compression and the other free of load; (3) one end in compression and the other in tension with the tensile area taking up 1/8 of total web height. Geometric parameters of stub columns were measured by vernier caliper and radius gauge. As it was difficult to measure the dimensions after fold bending, the actual masses of stub column specimens (M) were weighed beforehand so as to validate the accuracy of measurements. A 40mm×40mm standard block was cut from a stub column member and then weighed so as to access the accurate density of stainless steel material, leading to the theoretical mass of a stub column specimen (Mt). According to the data in Table 5, the error between actual mass and theoretical mass is small with the maximum value of 1.26%, which ensured that geometric parameters of specimen were measured accurately.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 7

Table 5 Dimensions of lipped C section stub column specimens

Specimen code Section code h

/mm b

/mm a

/mm t

/mm L

/mm M /kg

r /mm

A / 2mm

tM /kg

tM MM−

T-1-A C80×40×15×2(Tr.) 79.44 39.86 15.35 1.76 239.6 0.564 6.75 296.11 0.5647 0.00121 T-1-B C80×40×15×2(Tr.) 80.23 39.93 15.58 1.76 239.5 0.566 6.75 298.56 0.5691 0.00547 T-1-C C80×40×15×2(Tr.) 79.41 39.92 15.21 1.76 239.8 0.563 6.75 295.78 0.5645 0.00267 T-1-D C80×40×15×2(Tr.) 79.72 39.94 15.35 1.76 239.5 0.564 6.75 296.89 0.5659 0.00341 T-2-A C100×40×15×2(Lo.) 100.08 40.19 14.92 1.76 299.6 0.784 6.75 332.09 0.7919 0.01004 T-2-B C100×40×15×2(Lo.) 100.26 40.12 15.00 1.76 299.9 0.786 6.75 332.44 0.7935 0.00954 T-2-C C100×40×15×2(Lo.) 100.28 40.10 14.97 1.76 299.5 0.786 6.75 332.30 0.7921 0.00775 T-3-A C120×40×15×2(Lo.) 120.80 40.27 14.67 1.76 359.5 1.047 6.75 367.96 1.0528 0.00556 T-3-B C120×40×15×2(Lo.) 120.82 40.27 14.64 1.76 360.0 1.046 6.75 367.89 1.0541 0.00772 T-3-C C120×40×15×2(Lo.) 120.97 40.26 14.82 1.76 360.2 1.046 6.75 368.74 1.0571 0.01062 T-3-D C120×40×15×2(Lo.) 120.98 40.15 14.57 1.76 359.5 1.045 6.75 367.50 1.0515 0.00621 T-4-A C140×60×15×2(Lo.) 140.33 60.11 14.95 1.76 419.5 1.581 6.75 473.16 1.5798 -0.00077 T-4-B C140×60×15×2(Lo.) 140.60 60.19 14.97 1.76 419.8 1.581 6.75 473.98 1.5836 0.00166 T-4-C C140×60×15×2(Lo.) 140.42 60.18 14.82 1.76 419.5 1.579 6.75 473.10 1.5796 0.00036 T-4-D C140×60×15×2(Lo.) 140.19 60.20 15.00 1.76 419.6 1.581 6.75 473.41 1.5810 -0.00001 T-5-A C160×60×15×2(Lo.) 160.73 60.06 14.77 1.76 479.5 1.934 6.75 508.25 1.9396 0.00291 T-5-B C160×60×15×2(Lo.) 159.90 60.09 15.00 1.76 479.2 1.933 6.75 507.70 1.9363 0.00172 T-5-C C160×60×15×2(Tr.) 160.29 60.03 14.88 1.76 479.1 1.929 6.75 507.73 1.9361 0.00365 T-5-D C160×60×15×2(Lo.) 160.58 60.03 14.98 1.76 479.2 1.931 6.75 508.62 1.9398 0.00457 T-6-A C80×40×15×3(Lo.) 80.47 40.12 15.82 2.80 240.1 0.874 6.75 464.39 0.8812 0.00828 T-6-B C80×40×15×3(Lo.) 80.23 40.11 15.75 2.80 240.0 0.869 6.75 463.23 0.8787 0.01112 T-6-C C80×40×15×3(Lo.) 80.64 40.16 15.75 2.80 240.0 0.873 6.75 464.67 0.8814 0.00963 T-6-D C80×40×15×3(Lo.) 80.09 40.13 15.77 2.80 240.3 0.874 6.75 463.10 0.8795 0.00632 T-7-A C100×40×15×3(Lo.) 100.93 40.21 15.83 2.80 299.9 1.225 6.75 522.28 1.2379 0.01057 T-7-B C100×40×15×3(Tr.) 99.40 39.87 15.96 2.80 299.9 1.225 6.75 516.74 1.2248 -0.00015 T-7-C C100×40×15×3(Lo.) 101.19 40.22 15.55 2.80 300.0 1.221 6.75 521.46 1.2364 0.01262 T-8-A C120×40×15×3(Lo.) 120.10 40.04 15.95 2.80 360.0 1.631 6.75 575.64 1.6379 0.00420 T-8-B C120×40×15×3(Lo.) 120.04 39.93 15.75 2.80 360.1 1.631 6.75 573.70 1.6328 0.00109 T-8-C C120×40×15×3(Lo.) 119.66 40.05 15.92 2.80 360.0 1.627 6.75 574.26 1.6339 0.00426 T-8-D C120×40×15×3(Lo.) 119.67 40.10 15.84 2.80 359.5 1.630 6.75 574.11 1.6312 0.00074 T-9-A C140×60×15×3(Tr.) 139.98 59.97 16.09 2.80 419.8 2.467 6.75 743.66 2.4674 0.00016 T-9-B C140×60×15×3(Tr.) 139.98 60.01 15.82 2.80 419.9 2.463 6.75 742.37 2.4637 0.00027 T-9-C C140×60×15×3(Tr.) 139.95 59.97 15.81 2.80 420.0 2.463 6.75 742.08 2.4633 0.00013 T-9-D C140×60×15×3(Tr.) 139.89 60.11 16.23 2.80 419.9 2.467 6.75 744.98 2.4723 0.00217 T-10-A C160×60×15×3(Tr.) 159.28 59.85 16.12 2.80 479.1 3.017 6.75 797.19 3.0186 0.00053 T-10-B C160×60×15×3(Tr.) 159.47 59.96 15.92 2.80 479.2 3.022 6.75 797.22 3.0193 -0.00088 T-10-C C160×60×15×3(Tr.) 159.67 60.01 15.91 2.80 479.8 3.027 6.75 798.08 3.0264 -0.00020 T-10-D C160×60×15×3(Tr.) 158.93 59.92 15.90 2.80 479.1 3.023 6.75 795.41 3.0119 -0.00369 Note: (1) Tr. is short for transversal; Lo. is short for longitudinal. (2) One of C100×40×15×2.0 specimens as well as C100×40×15×3.0 specimen is spared for mechanical material tests; (3) h is height of lipped C section; b is flange width; a is lip width; t is thickness in

rolling direction (Fig. 8). For example, C160×60×3.0 (transverse) means that the nominal value of section height is 160mm, the nominal value of flange width is 60mm, that of lip width is 15mm and the thickness is 3mm.

3.2 Initial imperfection measurements Before the test, initial imperfections of specimens were measured using milling machine for later accurate analysis and calculation of axial and eccentric compressive bearing capacity of stub columns. For each cross-section, initial imperfections were measured along five lines: three on the web (shown as point A-2, A-3, A-4 in Fig.9) and one on each flange (point A-1, A-2 in Fig. 9), as detailed in Fig. 9. 15 mm intervals were set between two measuring lines.

According to initial imperfection measurement results of square tubular columns in Ref. [5], the segment close to cutting end of stub column would expand outward because of residual bending stress. So it is recommended that the imperfection measurements within 3/4 of total length in the middle of the column be taken as actual initial imperfections. When measuring initial imperfection of stainless steel lipped C section stub columns, deformations near the cutting end were found to exceed those in other areas a lot due to residual stress. Consequently, deformation values at two measuring points near the cutting end (within 30mm to the end) were eliminated, taking for reference the method above. Initial

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 8

imperfection curves of stainless steel stub column specimens are shown in Fig. 10 and Table 6 details the maximum measured imperfections.

In Fig. 10 maximum initial imperfections of stub column specimens occurred in the middle of the web, namely point A-3, except for C140×60×15×3.0 specimens whose maximum imperfections were on the flange. This should be attributed to specimens crashing into each other during transport.

30 60 90 120 150 180 210 240-0.02-0.010.000.010.020.030.040.05

Defe

ctive

Valu

e /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(a) C80×40×15×2

30 60 90 120 150 180 210 240-0.01

0.00

0.01

0.02

0.03

0.04

Defe

ctive

Valu

e /m

mDisplacement /mm

A-1 A-2 A-3 A-4 A-5

(b) C80×40×15×3

30 60 90 1201501802102402703000.000.010.020.030.040.050.06

Defe

ctive

Valu

e /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(c) C100×40×15×2

30 60 90 120 150 180 210 240 270 300-0.010.000.010.020.030.040.050.060.070.080.09

Defe

ctiv

e Val

ue /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(d) C100×40×15×3

30 60 90 1201501802102402703003303600.000.020.040.060.080.100.120.140.160.180.20

Defe

ctive

Valu

e /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(e) C120×40×15×2

30 60 90 120150180210240270300330360-0.10-0.050.000.050.100.150.200.25

Defec

tive V

alue /

mm

Displacement /mm

A-1A-2A-3A-4A-5

(f) C120×40×15×3

60 120 180 240 300 360 4200.00

0.05

0.10

0.15

0.20

0.25

Defec

tive V

alue /

mm

Displacement /mm

A-1A-2A-3A-4A-5

(g) C140×60×15×2

60 120 180 240 300 360 4200.00

0.05

0.10

0.15

0.20

Defe

ctive

Valu

e /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(h) C140×60×15×3

60 120 180 240 300 360 420 4800.00

0.05

0.10

0.15

0.20

0.25

0.30

Defe

ctive

Valu

e /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(i) C160×60×15×2

60 120 180 240 300 360 420 4800.00

0.05

0.10

0.15

0.20

0.25

Defe

ctive

Valu

e /m

m

Displacement /mm

A-1A-2A-3A-4A-5

(j) C160×60×15×3

Fig.10 Imperfection curves of stub column specimens

(Where, positive value represents convex imperfection and negative value represents concave imperfection.)

Table 6 Maximum values of initial imperfection of stub column specimens

Specimen code Member code Imperfection

position

Measured value /mm

Specimen code Member code Imperfection position

Measured value /mm

T-1-A(B/C/D) C80×40×15×2 web 0.0430 T-6-A(B/C/D) C80×40×15×3 web 0.0325

flange 0.0147 flange 0.0090

T-2-A(B/C) C100×40×15×2 web 0.0563 T-7-A(B/C) C100×40×15×3 web 0.0805 flange 0.0329 flange 0.0280

T-3-A(B/C/D) C120×40×15×2 web 0.1740 T-8-A(B/C/D) C120×40×15×3 web 0.2122

flange 0.0616 flange 0.0800 T-4-

A(B/C/D) C140×60×15×2 web 0.2340 T-9-A(B/C/D) C140×60×15×3 web 0.1809 flange 0.1474 flange 0.1974

T-5-A(B/C/D) C160×60×15×2 web 0.2919 T-10-A(B/C/D) C160×60×15×3 web 0.2490

flange 0.1530 flange 0.1984

3.3 Bearing capacity tests of stub columns

(1) Test setups Stub column tests adopted test setups including a 30T capacity electronic universal testing machine, TDS dynamic strain gauges, displacement meters, etc. Fig. 11 (a) shows the test setup of axially loaded columns and the ends of the specimen were connected directly to the loading discs. The test setup of stub columns under eccentric compressive load is shown in Fig. 11 (b). Loading discs were replaced by two steel end plates which were rather stiff and could be recycled, as detailed in Fig. 12 (a) and Fig. 12 (b). Besides, slots were made on the plates so that load eccentricity could be adjusted, as shown

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 9

in Fig. 12 (c). Eighteen strain gauges were attached around the cross section at the mid-length of stub column in order to measure the strain variation in the cross section of stub columns under different stress states and the layout of strain gauges is shown in Fig. 13. After setting up the stub column specimen, four displacement gauges were placed at the four corners of the specimen to measure its axial compression and end rotation. A TDS dynamic strain gauge was employed to collect the strains and the readings of displacement gauges corresponding to different load levels.

Steel bar

Base plate

Pier

End plate

Steel bar

Steel brick

Pier

Loading plateEnd plate

End plate

(a) Axially compressed (b) Eccentrically compressed

Fig. 11 Test setups for specimens under two stress states

M16 bolt

M8 bolt Loading plate

End plate

ConnectorSlotted plate

Base plate

Stiffener

Steel brick

350

7531 30

120 3025 1203025

14 25 75 23302225

4535

4535

160

bolt holeM16

Steel brickEnd plate

(a) Detail drawing (b) Photograph (c) Slot dimensions

Fig. 12 End plates details

10 10

10

Strain gauge

Fig. 13 Strain gauges

(2) Loading mechanisms At the initial stage of loading, force control was used to apply 10% of the estimated bearing capacity for each level. The static load was obtained by maintaining the applied stress for 2 min. After the load reached 60% of the estimated bearing capacity, displacement control was adopted instead with a constant speed of 0.5mm/min. The applied strain was maintained for 2 min before reading. The test terminated if the load declined to 80% of the ultimate strength.

(3) Failure process and phenomena For stub columns with high width-thickness ratios (such as C120×40×15×2.0, C140×60×15×2.0 and C160×60×15×2.0), the failure process and phenomena are as follows: Firstly under small load, buckling failure occurred first in the web near the loading end and then grew to the other end of the specimen, but neither concave nor convex buckling was observed in the flange and its lip which barely deformed. As the load climbed, local buckling in the web came to be distinct and the deformation in the flange and its lip developed rapidly. Then when the load approached the ultimate value, concave or convex buckling in the flange became rather apparent. Eventually after the load reached the ultimate value and started descending, buckling in the end web gradually disappeared. However, large rotation of the middle cross section occurred in the flange and its lip about the intersection line of flange and web leading to a plastic hinge and failure of the specimen. The failure process and phenomenon of test specimen (T-3-C) under various load levels are shown in Fig. 14. For stub columns with low width-thickness ratios, deformation was hardly observed in the specimen under small load and then when the load grew to the ultimate value, the flange rotated around the intersection line of flange and web first together with concave or convex buckling in the middle web. Finally when the ultimate load was reached, both the flange and the web of the specimen deformed significantly.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 10

(a) P=38.91KN (b) P=50.97KN (c) P=53.51KN (d) P=52.72KN

(e) P=51.60KN (f) P=48.26KN (g) Failure (front) (h) Failure (back)

Fig. 14 Failure process and phenomena of stub column specimen T-3-C

Fig. 15 (a) and Fig. 15 (b) respectively present the ultimate failure phenomena of a group of axially and eccentrically loaded stub columns. It can be seen that, for specimens with the same cross section dimensions and height, eccentrically loaded columns developed more buckling waves than axially loaded ones. In addition, because eccentrically loaded stub columns had lower ultimate bearing capacity than axially loaded columns, the former deformation was obviously less than the latter.

(a) Axially compressed (b) Eccentrically compressed

Fig. 15 Failure phenomena of compressed stainless steel stub columns

The test values of failure loads and the buckling modes of stainless steel stub columns are shown in Table 7. There are two buckling modes of stub columns (including axially loaded and eccentrically loaded): (1) convex in the web near the middle cross section and concave in the flange, as shown in Fig. 16 (a); (2) concave in the web near the middle cross section and convex in the flange, as shown in Fig. 16 (b). 23 specimens developed the first buckling mode with the rest 15 in the second mode.

(a) Mode 1 (b) Mode 2

Fig. 16 Buckling modes of stainless steel stub columns

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 11

(4) Analysis of test results The test values of failure loads and the buckling modes of stainless steel stub columns are shown in Table 7, in which the theoretical and actual eccentricity value of each specimen is also given. Certain deviations existed between theoretical eccentricity values and actual values, as a result at the beginning the stress distribution across the cross section of stub column was determined based on the strain in the flange under the first few levels of load. Assuming that under ultimate load the maximum compressive stress in the web reached the yielding strength, the actual eccentricity of each specimen could be calculated by / /N A Ney I f+ = .

Table 7 Ultimate loads and failure modes of stub columns

Specimen code

Eccentricity/mm Buckling

mode

Test strength

testF /kN

Specimen code

Eccentricity /mm Buckling

mode

Test strength

testF /kN

Theoretical Actual Theoretical Actual

T-1-A 0.00 2.50 Mode 2 82.70 T-6-A 0.00 1.48 Mode 2 182.55 T-1-B 8.90 9.70 Mode 1 76.98 T-6-B 8.90 10.98 Mode 1 151.68 T-1-C 26.70 23.00 Mode 1 63.99 T-6-C 26.70 26.51 Mode 1 113.71 T-1-D 35.60 33.55 Mode 1 50.80 T-6-D 35.60 34.36 Mode 1 107.65 T-2-A 0.00 2.16 Mode 2 75.60 T-7-A 0.00 2.29 Mode 2 190.72 T-2-B 10.73 9.60 Mode 1 79.17 T-7-B 10.73 11.45 Mode 2 175.01 T-2-C 32.20 31.20 Mode 1 61.12 T-7-C 32.20 33.00 Mode 2 130.45 T-3-A 0.00 2.85 Mode 2 76.55 T-8-A 0.00 0.50 Mode 2 188.33 T-3-B 12.45 14.51 Mode 1 69.76 T-8-B 12.45 13.91 Mode 2 173.52 T-3-C 37.34 39.34 Mode 1 53.35 T-8-C 37.34 37.96 Mode 1 127.17 T-3-D 49.78 48.46 Mode 2 46.48 T-8-D 49.78 47.80 Mode 2 115.9 T-4-A 0.00 2.34 Mode 1 89.78 T-9-A 0.00 -1.27 Mode 1 223.95 T-4-B 15.34 15.99 Mode 2 78.42 T-9-B 15.34 18.08 Mode 1 196.35 T-4-C 46.03 46.46 Mode 2 58.42 T-9-C 46.03 47.96 Mode 1 154.25 T-4-D 61.37 58.72 Mode 1 54.06 T-9-D 61.37 56.70 Mode 1 130.28 T-5-A 0.00 4.30 Mode 1 86.77 T-10-A 0.00 1.75 Mode 1 220.29 T-5-B 17.04 17.20 Mode 1 77.23 T-10-B 17.04 16.76 Mode 2 192.84 T-5-C 51.11 48.82 Mode 1 61.91 T-10-C 51.11 50.08 Mode 2 152.50 T-5-D 68.15 65.32 Mode 1 51.41 T-10-D 68.15 70.10 Mode 1 130.23

The load-displacement curves, obtained from tests, of axially loaded and eccentrically loaded stub columns are shown in Fig. 17. It can be seen that at the initial stage, the displacement of each specimen appears linear growth with load. Then as the load climbs, the increase rate of displacement accelerates, leading to nonlinear load-displacement relationship. But after the load reaches the ultimate value, the displacement increases rapidly, which put them in almost linear relationship again. The load-rotation curves of eccentrically loaded stub columns are shown in Fig. 18. Figure 17 and Figure 18 indicate that the load-rotation curves follow similar rules with those of load-displacement curves. Namely, before the load reaches the ultimate bearing capacity, the rotation increment is small but increases rapidly after the ultimate bearing capacity is reached.

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 12

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

102030405060708090

Load

/kN

Displacement /mm

T-1-AT-1-BT-1-CT-1-D

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

20406080

100120140160180200

Load

/kN

Displacement /mm

T-6-AT-6-BT-6-CT-6-D

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

1020304050607080

Load

/kN

Displacement /mm

T-2-AT-2-BT-2-C

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

20406080

100120140160180200

Load

/kN

Displacement /mm

T-7-AT-7-BT-7-C

(a) C80×40×15×2 (b) C80×40×15×3 (c) C100×40×15×2 (d) C100×40×15×3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

1020304050607080

Load

/kN

Displacement /mm

T-3-AT-3-BT-3-CT-3-D

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

20406080

100120140160180200

Load

/kN

Displacement /mm

T-8-AT-8-BT-8-CT-8-D

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

20406080

100

Load

/kN

Displacement /mm

T-4-AT-4-BT-4-CT-4-D

(e) C120×40×15×2 (f) C120×40×15×3 (g) C140×60×15×2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

50100150200250

Load

/kN

Displacement /mm

T-9-AT-9-BT-9-CT-9-F

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

20406080

100

Load

/kN

Displacement /mm

T-5-AT-5-BT-5-CT-5-D

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

50100150200250

Load

/kN

Displacement /mm

T-10-AT-10-BT-10-CT-10-D

(h) C140×60×15×3 (i) C160×60×15×2 (j) C160×60×15×3

Fig. 17 Load-displacement curves of stub column specimens

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Paper Presented by Dr. Shenggang Fan - [email protected] © S.G. Fan, F. Liu, B.F. Zheng, G.P. Shu, Southeast University, Nanjing 13

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.510203040506070

Load

/kN

Rotation /degree

T-1-CT-5-D

0 1 2 3 4 5 60

20406080

100120140160

Load

/kN

Rotation /degree

T-6-BT-6-CT-6-D

0.00.20.40.60.81.01.21.41.61.80

1020304050607080

Load

/kN

Rotation /degree

T-2-B

0.0 0.5 1.0 1.5 2.0 2.5 3.00

20406080

100120140160180

Load

/kN

Rotation /degree

T-7-BT-7-C

(a) C80×40×15×2 (b) C80×40×15×3 (c) C100×40×15×2 (d) C100×40×15×3

0.00.20.40.60.81.01.21.41.61.82.00

10203040506070

Load

/kN

Rotation /degree

T-3-BT-3-CT-3-D

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

20406080

100120140160180

Load

/kN

Rotation /degree

T-8-BT-8-CT-8-D

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80

1020304050607080

Load

/kN

Rotation /degree

T-4-BT-4-CT-4-D

(e) C120×40×15×2 (f) C120×40×15×3 (g) C140×60×15×2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80

20406080

100120140160180200

Load

/kN

Rotation /degree

T-9-BT-9-CT-9-D

0.00 0.25 0.50 0.75 1.00 1.25 1.500

1020304050607080

Load

/kN

Rotation /degree

T-5-BT-5-CT-5-D

0.00.20.40.60.81.01.21.41.61.80

20406080

100120140160180200

Load

/kN

Rotation /degree

T-10-BT-10-CT-10-D

(h) C140×60×15×3 (i) C160×60×15×2 (j) C160×60×15×3

Fig. 18 Load-rotation curves of stub column specimens

In order to study the strain variation law in the cross section of stub columns under various eccentric compressive loads, a number of strain gauges were attached around the middle cross section of stub column. The strain gauge number and layout are shown in Fig. 19. Each number corresponds to two strain gauges, which were set on both inner and outer surfaces. The average value was regarded as the strain at this position. For lack of space, this paper only presents two representative groups (T-3-A~D and T-5-A~D) of strain distributions across the middle cross section of the specimen in Fig. 20. It can be seen from Figure 20 (a) and 20 (e) that for axially loaded stub columns at the initial stage of loading, the strain distribution is nearly a horizontal line. Then as the load climbs, the strain distribution appears low in the middle and high at both sides. Besides, Fig. 20 (b), (c), (d) together with Fig. 20 (f), (g), (h) show that for eccentrically loaded stub columns, the strain in the edge increases with load much faster than that in the middle. And with further increase of the load, the stress on the cross section gradually concentrates towards the corner regions. Consequently, the strain variation law in the middle cross section of stainless steel stub column basically conforms to large deflection theory of slab.

The strain variation law indicates that buckling failure occurs simultaneously in the web and the flange and the strain distribution of the flange becomes non-uniform soon after that appears in the web. Comparing the buckling modes of stub column specimens in Table 7 as well as the strain variation curves of cross section in Fig. 20, it can be seen that for specimens with the buckling mode of concave in the flange, the maximum strain occurs in the lip, as shown in Fig. 20 (b), (c), (e), (f), (g) and (h); for specimens with the buckling mode of convex in the flange, the maximum strain occurs in the flange, as shown in Fig.20 (a) and (d).

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0

123

4

5

6

7

8

11109

12

Fig. 19 Number and layout of strain gauges

0 2 4 6 8 10 12-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

ε

Number of Section Position

9.91kN20.19kN30.08kN39.29kN58.43kN67.09kN73.57kN76.55kN

0 2 4 6 8 10 12

-0.0050-0.0045-0.0040-0.0035-0.0030-0.0025-0.0020-0.0015-0.0010-0.00050.0000

εNumber of Section Position

10.11kN20.35kN29.99kN39.50kN49.52kN59.09kN65.44kN68.65kN69.76kN

(a) T-3-A (Eccentricity e=0) (b) T-3-B (Eccentricity e=14.51mm)

0 2 4 6 8 10 12-0.007-0.006-0.005-0.004-0.003-0.002-0.0010.0000.001

ε

Number of Section Position

10.08kN20.15kN29.70kN38.91kN45.86kN50.97kN53.17kN53.35kN

0 2 4 6 8 10 12

-0.0040-0.0035-0.0030-0.0025-0.0020-0.0015-0.0010-0.00050.00000.00050.0010

ε

Number of Section Position

10.08kN20.12kN29.57kN38.75kN44.71kN46.48kN

(c) T-3-C (Eccentricity e=39.34mm) (d) T-3-D (Eccentricity e=48.46mm)

0 2 4 6 8 10 12-0.0050-0.0045-0.0040-0.0035-0.0030-0.0025-0.0020-0.0015-0.0010-0.00050.00000.0005

ε

Number of Section Position

10.24kN20.51kN30.21kN39.75kN49.33kN67.78kN78.09kN89.73kN86.44kN86.77kN

0 2 4 6 8 10 12

-0.0050-0.0045-0.0040-0.0035-0.0030-0.0025-0.0020-0.0015-0.0010-0.00050.0000

ε

Number of Section Position

10.09kN19.86kN34.52kN44.02kN53.97kN62.90kN71.64kN75.97kN77.23kN

(e) T-5-A (Eccentricity e=0) (f) T-5-B (Eccentricity e=17.2mm)

0 2 4 6 8 10 12-0.006-0.005-0.004-0.003-0.002-0.0010.0000.001

ε

Number of Section Position

10.04kN19.78kN29.59kN39.37kN51.24kN57.62kN60.52kN61.62kN61.91kN

0 2 4 6 8 10 12

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

0.001

ε

Number of Section Position

10.18kN19.78kN29.28kN38.30kN43.81kN47.85kN50.21kN51.33kN51.41kN

(g) T-5-C(Eccentricity e=48.82mm) (h) T-5-D(Eccentricity e=65.32mm)

Fig. 20 Strain distribution across the middle section of stub column specimens

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4 Comparisons of test strengths with design strengths of stub columns In stub column tests, specimens were divided into four groups (A, B, C and D) according to load eccentricity, as detailed in Table 5. The bearing capacities of specimens in four groups could be obtained respectively based on calculation methods elaborated in three design codes, American Specification (ASCE), European Code (EC3) and Chinese Code. Considering the differences among design codes, relevant assumptions were made: (1) measured values were adopted as geometric dimensions of stub column; (2) test results of flat specimen tests were used as mechanical property values of stainless steel, regardless of strength enhancements of the corner regions induced during cold forming; (3) the eccentricity values of stub column specimens were obtained from measurements; (4) due to small lip width, the stress state of the lip under vertical load was simplified as uniform compression; (5) resistance partial coefficient was not considered in calculation, namely taken as 1.0.

The test strengths and design strengths of stainless steel stub columns in four groups (A, B, C and D) are detailed in Table 8~10, in which F test is the test result; FASCE is the calculation result according to American Specification; FEC3 is the calculation result according to European Code; FCN is the calculation result according to Chinese Code.

Table 8 Comparisons of test strengths (Group A) and design strengths of stub columns

Specimen code Section code

Slenderness coefficient

λ

Eccentricity /mm Bearing capacity/kN Error (%)

Theoretical Actual testF ACSEF EC3F CHF ASCE 3EC CH

T-1-A C80×40×15×2.0(Tr.) 0.664 0.00 2.50 82.7 71.11 66.80 69.71 -14.02 -19.23 -15.70 T-2-A C100×40×15×2.0(Lo.) 0.909 0.00 2.16 75.6 75.33 70.26 74.39 -0.35 -7.06 -1.61 T-3-A C120×40×15×2.0(Lo.) 1.142 0.00 2.85 76.55 74.78 70.84 76.71 -2.32 -7.46 0.21 T-4-A C140×60×15×2.0(Lo.) 1.362 0.00 2.34 89.78 83.82 84.29 88.16 -6.64 -6.11 -1.80 T-5-A C160×60×15×2.0(Lo.) 1.591 0.00 4.30 86.77 81.73 82.01 86.94 -5.81 -5.48 0.19 T-6-A C80×40×15×3.0(Lo) 0.473 0.00 1.48 182.55 151.72 145.30 144.16 -16.89 -20.41 -21.03 T-7-A C100×40×15×3.0(Lo.) 0.640 0.00 2.29 190.72 166.52 153.35 159.95 -12.69 -19.59 -16.13 T-8-A C120×40×15×3.0(Lo.) 0.796 0.00 0.50 188.33 178.72 163.39 183.85 -5.10 -13.24 -2.38 T-9-A C140×60×15×3.0(Tr.) 0.940 0.00 -1.27 223.95 224.49 213.85 225.48 0.24 -4.51 0.68

T-10-A C160×60×15×3.0(Tr.) 1.094 0.00 1.75 220.29 216.24 205.34 220.17 -1.84 -6.78 -0.05 Average error -18.41 -23.61 -16.90

Table 9 Comparisons of test strengths (Group B) and design strengths of stub columns

Specimen code Section code

Slenderness coefficient

λ

Eccentricity /mm Bearing capacity/kN Error (%)

Theoretical Actual testF ACSEF EC3F CHF ASCE 3EC CH

T-1-B C80×40×15×2.0(Tr.) 0.587 8.90 9.70 76.98 57.81 52.88 54.07 -24.91 -31.30 -29.76 T-2-B C100×40×15×2.0(Lo) 0.795 10.73 9.60 79.17 63.45 57.57 61.24 -19.85 -27.28 -22.65 T-3-B C120×40×15×2.0(Lo) 0.997 12.45 14.51 69.76 59.48 54.98 61.56 -14.74 -21.19 -11.76 T-4-B C140×60×15×2.0(Lo) 1.191 15.34 15.99 78.42 68.37 66.36 72.16 -12.81 -15.37 -7.98 T-5-B C160×60×15×2.0(Lo) 1.381 17.04 17.20 77.23 68.96 66.74 73.67 -10.71 -13.58 -4.61 T-6-B C80×40×15×3.0(Lo) 0.411 8.90 10.98 151.68 109.68 103.89 104.94 -27.69 -31.51 -30.81 T-7-B C100×40×15×3.0(Tr.) 0.537 10.73 11.45 175.01 134.13 126.27 126.92 -23.36 -27.85 -27.48 T-8-B C120×40×15×3.0(Lo) 0.694 12.45 13.91 173.52 136.66 121.90 132.69 -21.25 -29.75 -23.53 T-9-B C140×60×15×3.0(Tr.) 0.820 15.34 18.08 196.35 162.84 153.32 168.38 -17.07 -21.91 -14.25

T-10-B C160×60×15×3.0(Tr.) 0.956 17.04 16.76 192.84 170.23 161.41 200.19 -11.72 -16.30 3.81 Average error -18.41 -23.61 -16.90

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Table 10 Comparisons of test strengths (Group C) and design strengths of stub columns

Specimen code Section code

Slenderness coefficient

λ

Eccentricity /mm Bearing capacity/kN Error (%)

Theoretical Actual testF ACSEF EC3F CHF ASCE 3EC CH

T-1-C C80×40×15×2.0(Tr.) 0.254 26.70 23.00 63.99 41.10 38.95 37.21 -35.78 -39.13 -41.86 T-2-C C100×40×15×2.0(Lo) 0.226 32.20 31.20 61.12 44.23 38.99 41.54 -27.64 -36.21 -32.04 T-3-C C120×40×15×2.0(Lo) 0.203 37.34 39.34 53.35 42.71 38.30 44.18 -19.95 -28.21 -17.20 T-4-C C140×60×15×2.0(Lo) 0.159 46.03 46.46 58.42 45.24 46.25 50.72 -22.56 -20.84 -13.19 T-5-C C160×60×15×2.0(Lo) 0.148 51.11 48.82 61.91 46.85 47.53 52.56 -24.32 -23.23 -15.10 T-6-C C80×40×15×3.0(Lo) 0.316 26.70 26.51 113.71 76.19 72.44 71.67 -33.00 -36.29 -36.97 T-7-C C100×40×15×3.0(Tr.) 0.282 32.20 33.00 130.45 84.01 80.37 79.98 -35.60 -38.39 -38.69 T-8-C C120×40×15×3.0(Lo) 0.256 37.34 37.96 127.17 92.35 85.72 87.91 -27.38 -32.59 -30.87 T-9-C C140×60×15×3.0(Tr.) 0.198 46.03 47.96 154.25 116.26 109.14 118.91 -24.63 -29.25 -22.91

T-10-C C160×60×15×3.0(Tr.) 0.184 51.11 50.08 152.5 118.75 113.25 141.01 -22.13 -25.74 -7.53 Average error -27.30 -30.99 -25.64

Table 11 Comparisons of test strengths (Group C) and design strengths of stub columns

Specimen code Section code

Slenderness coefficient

λ

Eccentricity /mm Bearing capacity/kN Error (%)

Theoretical Actual testF ACSEF EC3F CHF ASCE 3EC CH

T-1-D C80×40×15×2.0Tr.) 0.253 35.60 33.55 50.8 33.89 32.04 31.38 -33.29 -36.94 -38.23 T-3-D C120×40×15×2.0(Lo) 0.204 49.78 48.46 46.48 41.64 34.48 38.77 -10.42 -25.82 -16.60 T-4-D C140×60×15×2.0(Lo) 0.158 61.37 58.72 54.06 41.18 41.08 44.37 -23.82 -24.01 -17.93 T-5-D C160×60×15×2.0(Lo) 0.147 68.15 65.32 51.41 40.37 40.92 45.66 -21.48 -20.41 -11.18 T-6-D C80×40×15×3.0(Lo) 0.317 35.60 34.36 107.65 65.58 62.29 61.29 -39.08 -42.14 -43.07 T-8-D C120×40×15×3.0(Lo) 0.256 49.78 47.80 115.9 81.15 76.73 76.71 -29.98 -33.79 -33.81 T-9-D C140×60×15×3.0(Tr.) 0.197 61.37 56.70 130.28 106.35 101.22 107.56 -18.37 -22.31 -17.44

T-10-D C160×60×15×3.0(Tr.) 0.185 68.15 70.10 130.23 105.77 95.65 110.04 -18.78 -26.55 -15.51 Average error -24.40 -29.00 -24.22

Fig.21 depicts the distributions of error in design strengths of stub columns in four groups according to the slenderness coefficient λ of the web.

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0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

-0.24

-0.20

-0.16

-0.12

-0.08

-0.04

0.00

0.04

ASCE EC3 GB

Error

Flexibility Coefficient of Web λ

0.2 0.4 0.6 0.8 1.0 1.2 1.4

-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.050.00

ASCE EC3 GB

Erro

r

Flexibility Coefficient of Web λ

(a) Group A (b) Group B

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.050.00

ASCE EC3 GB

Erro

r

Flexibility Coefficient of Web λ

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.050.00

ASCE EC3 GB

Error

Flexibility Coefficient of Web λ

(c) Group C (d) Group D

Fig.21 Relation of the error in stub column design strengths with the slenderness coefficient λ of the web

On the basis of Table 8~11 and Fig.21 conclusions are drawn as follows:

(1) Bearing capacities of stainless steel stub column specimens calculated according to three design codes are obviously less than test results. This can be attributed to the following reasons: a) Nominal yield strength σ0.2 is regarded as the maximum stress of the section when calculating design strengths leading to certain limitation of the results. However in response to strong strain-hardening effect of stainless steel material, the section stress commonly exceeds σ0.2 when ultimate bearing capacity is reached. b) Strength enhancement of the corner regions induced during cold forming is ignored in the three design methods, but material cold workability may boost the bearing capacity significantly.

(2) When λ = 0.4~0.8, the error between calculation results and test results narrows with the increase of λ, however when λ > 0.8, the error basically remains unaltered. The reasons are as follows: a) when the specimen with a small value of λ reaches ultimate bearing capacity, the section stress often surpasses nominal yield strength σ0.2 under the influence of hardening property of stainless steel, but in design methods the stress is assumed equal to nominal yield strength σ0.2. b) As λ rises, the hardening property of stainless steel weakens; therefore, material nonlinearity becomes the major influencing factor leading to lower test strengths than design strengths. c) In response to gradual decline of λ, the width-thickness ratio of cross section lowers and the corner regions account for larger percentage of the total section. Consequently, process property of the corner regions may have more significant impact on material strength; however the design methods ignore the influence.

(3) For eccentrically loaded stub columns, the errors between calculation results and test results are enlarged as the eccentricity of specimen widens.

(4) The largest error occurs in the design strengths of European Code (EC3), then American Specification (ASCE), at last Chinese Code. This can be attributed to: a) with same value of λ, design strengths of European Code (EC3) are the smallest as a result of minimum calculated effective widths; b) the plate assembly effect is considered in Chinese Code by using restraint coefficients, but not in American Specification or European Code, leading to least error of Chinese Code.

5 Conclusions This paper carries out experimental studies into tensile specimen tests of stainless steel material and stub column tests of lipped C sections. Conclusions can be drawn as follows:

(1) For stainless steel material with different thickness, the values of elastic modulus and strength acquired from transverse tensile tests are both larger than those from longitudinal tensile tests together with the former σ-ε curve higher than the latter. Consequently, stainless steel material is anisotropic and material thickness has certain influence on the

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hardening index n. Besides, R-O model proposed by Gardner (2004) can fit mechanical properties of stainless steel with relative accuracy, but the hardening index needs modification.

(2) Nominal yield strength of stainless steel material enhances significantly during cold forming, especially for the corner regions. Test results indicate that test value of corner nominal yield strength exceeds that of the flat regions by about 60%.

(3) The maximum initial imperfections of stainless steel stub column specimens occur in the middle of the web.

(4) There are two buckling modes of stainless steel stub column specimens: a) convex in the web near the middle cross section and concave in the flange; b) concave in the web near the middle cross section and convex in the flange.

(5) With the increase of load the load-displacement and load-rotation curves of stub columns appear firstly linear growth, then nonlinear behavior, and at last downward sloping lines.

(6) The strain variation law indicates that buckling failure occurs simultaneously in the web and the flange. For specimens with the buckling mode of concave in the flange, the maximum strain occurs in the lip; for specimens with the buckling mode of convex in the flange, the maximum strain occurs in the flange.

(7) For axially loaded stub columns at the initial stage of loading, the strain distribution is nearly a horizontal line; as the load climbs, the distribution appears low in the middle and high at both sides. For eccentrically loaded stub columns, the strain in the edge increases with load much faster than that in the middle, and the stress gradually concentrates towards the corner regions. Consequently, the strain variation law in the middle cross section of stainless steel stub column basically conforms to large deflection theory of slab.

(8) It can been seen, from comparison of test strengths with design strengths of stainless steel stub columns, that design strengths are obviously less than test strengths, and the error between them shows diminishing trend as λ increases. When λ = 0.4~0.8, the error diminishes with the increase of λ, however when λ > 0.8, the error basically remains unaltered.

Acknowledgements The research was supported by a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and Jiangsu Provincial Forward-Looking Cooperation Foundation of Industry, Education and Research (No. BY2012200 and No. BY2009151). The authors are grateful to the financial support.

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