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Strength enhancements induced during cold forming of stainless steel sections
Journal of Constructional Steel Research 64 (2008) 1310–1316
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Strength enhancements induced during cold forming of stainless steel sections Rachel B. Cruise a,∗ , Leroy Gardner b a
Department of Architecture and Civil Engineering, University of Bath, UK
b
Department of Civil and Environmental Engineering, Imperial College London, UK
article
info
Article history: Received 14 November 2007 Accepted 30 April 2008 Keywords: Stainless steel Cold-formed sections Strain hardening Residual stresses Strength enhancement
a b s t r a c t The material properties of stainless steel are sensitive to plastic deformation which causes an increase in yield strength by a process termed cold working. The different strain paths experienced around cold-formed cross sections during manufacture create unique material strength distributions for sections from different forming routes and also influence residual stress patterns. The research program presented herein has examined experimentally the material and residual stress distributions found in two types of cold-formed sections–cold-rolled box sections and press-braked angles. Predictive tools to harness the observed strength enhancements have been proposed and incorporated into models. Subsequent comparisons have shown that these strength enhancements, in particular those observed for cold-rolled box sections, should be employed in structural design to avoid considerable underestimation of member resistance. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Achieving material efficiency in structural stainless steel design is an important step towards encouraging wider use and thus enabling its aesthetics and low maintenance requirements to be further utilised to create elegant and durable structures. Due to the characteristics of its material stress–strain curve, stainless steel is very sensitive to cold working. Material strength in stainless steel cross sections, commonly taken as the 0.2% proof stress, is dependant on the amount of plastic deformation and heat treatment experienced during production (and service). Strength enhancements induced during the forming routes of cold-formed sections, which are the most common type of stainless steel cross section, offer higher material strength than that currently assumed in design. At present, structural stainless steel design is based on the minimum material properties specified in material standards. As part of a recent research program carried out at Imperial College London to investigate the link between the production route and structural behaviour of stainless steel members, a series of experiments were performed. A total of 15 cold-formed stainless steel (grade 1.4301) members – 8 press-braked angles and 7 cold-rolled box sections – were first measured for their geometric imperfections, as reported in Cruise and Gardner [1], and then sectioned into a series of strips and analysed. The strains released during this sectioning process were recorded using strain gauges and used to calculate residual stresses, as detailed in Cruise and
∗
Corresponding author. Tel.: +44 01125 386748; fax: +44 01225 386691. E-mail address: [email protected] (R.B. Cruise).
0143-974X/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2008.04.014
Gardner [2]. The strips were then tested in tension in accordance with EN 10002-1 [3] and from the resulting stress–strain data the 0.2% proof stresses and ultimate stresses were identified. The complete set of material and residual stress data is published in [4]. The test results presented herein and collated from other studies highlights considerable cold work-induced strength increases in the corners of press-braked stainless steel sections and in the flat faces and corners of cold-rolled box sections. However, due to physical restraints in the size of the tensile coupons, the resolution to which the material properties could be determined was limited. In order to map the material strength to a higher resolution, Vickers microhardness tests were performed. This provided, in particular, more detailed information on the extent of the strength enhancements associated with corner forming. The material strength data obtained from the tensile coupon tests and inferred from the hardness tests were used to develop expressions to predict the strength enhancements in the faces of the cold-rolled box sections, and to re-evaluate previously proposed expressions to determine strength enhancements in the corners of press-braked and cold-rolled sections. The implications of the proposed predictive models on structural stainless steel design have been assessed. 2. Production routes Cold-formed stainless steel sections are formed from sheet material in two principal ways. The simplest forming process is press braking where individual folds are created in the sheet material between a tool and die. This production process is controlled manually and is used to manufacture small quantities
R.B. Cruise, L. Gardner / Journal of Constructional Steel Research 64 (2008) 1310–1316
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List of symbols b d HVav t ri Ri
Section face width Section face width Average Vickers Hardness value along coupon width Section thickness Section corner radius Tube radius prior to crushing σ 0.2av,exp Weighted average of the 0.2% proof stresses obtained experimentally for the central 50% of the faces of cold-rolled box sections or the 80% of the section face furthest from the corner for pressbraked sections σ00 .2av,exp Weighted average of the 0.2% proof stresses predicted from Hardness values for the central 50% of the faces of cold-rolled box sections or the 80% of the section face furthest from the corner for pressbraked sections σ0.2,exp Experimentally determined 0.2% proof stress σ00 .2,exp Predicted 0.2% proof stress from Hardness values σ00 .2,f Predicted 0.2% proof stress for the central 50% of the faces of cold-rolled box sections σ0.2,mill 0.2% proof stress given in inspection document or mill certificate σ0.2,min Minimum specified 0.2% proof stress given in EN 10088 (2005) σultav,exp Weighted average of the ultimate stress obtained experimentally for the central 50% of the faces of cold-rolled box sections or the 80% of the section face furthest from the corner for press-braked sections σult,f Ultimate stress from the centre of the faces of coldrolled box sections 0 σult Predicted ultimate stress for the central 50% of the ,f faces of cold-rolled box σult,mill Ultimate stress given in inspection document or mill certificate σ0.2,c 0.2% proof stress of the corners of cold-formed sections σ0.2,cr ,c 0.2% proof stress of the corners of cold-rolled box sections σ00 .2,cr ,c Predicted 0.2% proof stress of the corners of coldrolled box sections σ00 .2,pb,c Predicted 0.2% proof stress of the corners of pressbraked sections
of sections. Angle sections, such as those considered in this study, are formed with one press braking operation as shown in Fig. 1, although more complex sections can be produced with multiple folds. Cold rolling is a more automated process whereby sheet material is uncoiled from a roll and flattened before being fed through a series of forming rollers that gradually deform the sheet into a desired section shape. This automated process has been developed especially to produce large quantities of nominally similar sections. Box sections, including those examined in this study, are commonly produced by first forming a circular tube which is welded closed and subsequently crushed into a box section through a Turks head die. An illustration of a circular tube being crushed into a box section is shown in Fig. 2. In compliance with EN 10204 [5] the material strength of the sheet formed in either of these cold forming processes is quality assured by performing tensile coupon tests. This material data, including the 0.2% proof stress σ0.2,mill and the ultimate stress σult,mill is made available with the cold-formed sections in a type
Fig. 1. Press braking of an angle.
Fig. 2. Cold rolling of a box section.
2.2 inspection document or mill certificate. However, the recently introduced stainless steel design code (EN 1993-1-4 [6]) employs the minimum material strengths σ0.2,min specified in the material standard EN 10088-2 [7]. 3. Material strength distributions The 0.2% proof stress data σ0.2,exp from the tensile coupon tests performed in the current experimental program were combined with data from other research programs [8–14]. The experimental data from the current experimental program is plotted in Figs. 3 and 4 showing the material strength distribution from eight press-braked angles and seven cold-rolled boxes, respectively. The different cold-formed sections are identified in Figs. 3 and 4 firstly by the production route: PB for press-braked and CR for cold-rolled sections followed by the two cross section dimensions and the thickness, t and finally the internal corner radii, ri , if specified. Figs. 5 and 6 show the same 0.2% proof stress σ0.2,exp data normalised by values taken from the corresponding inspection documents σ0.2,mill and plotted against the position in the section face normalised by the face width b or d. It can be seen in Fig. 5 that the material strength of the flat face of press-braked sections is close to that of the unformed sheet material, demonstrating that during section forming the faces of press-braked sections do not experience significant plastic deformation. However, strength increases above the strength of the unformed sheet material are observed in the corner regions where large plastic deformations are known to occur during forming. In Fig. 6 for cold-rolled sections, similar to press-braked sections, strength increases in the corner regions can be observed. However, strength increases are also seen in the flat faces of the sections indicating that the flat faces in cold-rolled box sections must also experience plastic deformation. This may be largely attributed to the initial formation of the circular tube followed by crushing into the box faces.
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Fig. 3. 0.2% proof stress for section faces of press-braked angles.
Fig. 4. 0.2% proof stress for section faces of cold-rolled boxes.
Fig. 5. 0.2% proof stress normalised by inspection document value for section faces of press-braked angles.
Fig. 6. 0.2% proof stress normalised by inspection document value for section faces of cold-rolled boxes.
4. Strength increases in section faces
the cold-rolled boxes σ0.2,exp normalised by the weighted average of the 0.2% proof stress values from the central 50% of each respective section face σ0.2av,exp . From the data, the 80% of the section face furthest from the corner for press-braked sections, and the central 50% of cold-rolled sections have been identified as being uninfluenced by corner forming. Whilst no strength enhancements are observed in the regions of the press-braked sections uninfluenced by corner forming, this is not the case for the box sections.
To identify the regions of the flat faces of the cold-formed sections where the material strength has not been influenced by corner forming, the normalised material test data have been examined. Fig. 7 shows the 0.2% proof stress σ0.2,exp for pressbraked angles normalised by the weighted average of the 0.2% proof stress values from the face of the section (i.e. omitting the corner data) σ0.2av,exp and Fig. 8 shows the 0.2% proof stresses for
R.B. Cruise, L. Gardner / Journal of Constructional Steel Research 64 (2008) 1310–1316
Fig. 7. 0.2% proof stress normalised by average face data for press-braked angles.
Fig. 8. 0.2% proof stress normalised by average central 50% face data for cold-rolled boxes.
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Fig. 10. Increase in cold working parameter with section face forming strain.
As a measure of the level of cold work that has occurred during the forming of the section faces, the parameter (σult,mill /σ0.2,mill )/ (σultav,exp /σ0.2av,exp ) has been utilised. The larger the value of this parameter, the greater the level of cold work that the section has undergone. Plotting this parameter against the simplified strain parameter (Eq. (1)) yields a second linear relationship (see Fig. 10) with a coefficient of determination R2 of 0.64. The two relationships given in Figs. 9 and 10 can be combined and used to predict the 0.2% proof stress of the central 50% of cold-rolled box sections σ00 .2,f , resulting in Eq. (2). This expression includes the 0.2% proof stress given in inspection documents σ0.2,mill and geometrical parameters equivalent to an Ri /t ratio. From the relationship 0 described in Fig. 9, the corresponding ultimate stress σult ,f can also be predicted using Eq. (3).
σ00 .2,f =
0.85σ0.2,mill
−0.19 +
σult,f = σult,mill 0.19 0
(2)
1 12.42 2(bπ+t d) +0.83
σ00 .2,f
σ0.2,mill
+ 0.85 .
(3)
5. Strength increases in corners
Fig. 9. Relationship between ultimate stress and 0.2% proof stress normalised by inspection document value.
Based on the central 50% of the cold-rolled box faces, the two ratios σ0.2av,exp /σ0.2,mill and σultav,exp /σult,mill indicate the increase in 0.2% proof stress and ultimate stress, respectively, due to the face forming process only. A linear relationship between these two parameters is described by the experimental data in Fig. 9, with a coefficient of determination R2 of 0.71, where a small increase of the ultimate stress relates to a more significant increase in the 0.2% proof stress. Cold working thereby brings the 0.2% proof stress closer to the ultimate stress. The strain experienced by the section face during the forming of a box from a circular tube can be described in terms of the radius of the circular tube formed Ri and the thickness of the section material t. Ri can be written in terms of the section geometry (Fig. 2). Assuming pure bending during forming and by removing the insignificant ri terms, a simplified strain expression given by Eq. (1) can be obtained.
εf =
πt . 2(b + d)
(1)
The strength increases in the corner regions of cold-formed sections due to plastic deformation was first observed in carbon steel sections. Karren [15] proposed a power model to predict these strength increases based on the strain experienced in the sheet material during corner forming and the yield strength of the sheet material formed. The strain induced during corner forming is closely related to the ratio of the internal radius of the corner and the thickness of the material ri /t. Karren’s expression was modified by van den Berg and van der Merwe [16] and more recently by Ashraf et al. [17] for stainless steel sections. Two further methods to predict corner strength (0.2% proof stress and ultimate tensile stress) in stainless steel sections were also proposed by Ashraf et al. [17] based on all available test data. The first method employs the 0.2% proof stress σ0.2,mill of the unformed sheet material in a simple power model and is given by Eq. (4), whilst the second utilises both the 0.2% proof stress σ0.2,mill and the ultimate stress σult,mill of the unformed material. Both equations yielded an accurate prediction of test data, with the simple power model showing a slightly higher scatter with a coefficient of variation of 0.06 compared to 0.04. A third, linear equation, independent of the ri /t ratio, was proposed to predict the ultimate strength of the corners based on the 0.2% proof stress of the corner material σ0.2,c , and the 0.2% proof stress σ0.2,mill and the ultimate stress σult,mill from the mill certificate.
σ0.2,c =
1.881σ0.2,mill ri 0.194 t
.
(4)
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Gardner and Nethercot [9] studied data from cold-rolled box sections and noted an approximately linear relationship between the 0.2% proof strength σ0.2,cr ,c of the formed corners and the ultimate strength σult,f of the flat faces. The resulting expression is given in Eq. (5). The coefficient of proportionality was modified by Ashraf et al. [17] to fit all published data.
σ0.2,cr ,c = 0.85σult,f .
(5)
To determine appropriate models to predict the enhanced corner strength in press-braked and cold-rolled sections, denoted as σ00 .2,pb,c and σ00 .2,cr ,c , respectively, both Eqs. (4) and (5) were modified by refitting the models to include data from the current test program and all currently published data. Eq. (4) was refitted to both press-braked and cold-rolled data whilst Eq. (5) was refitted to cold-rolled data only. It was decided that, of the models proposed by Ashraf et al. [17], the simple power model, despite its slightly higher scatter of predictions, relied upon less detailed information about the unformed sheet material and was therefore easier to implement. Cold-rolled corner data included in the study was reported in [9–13]. Press-braked data was sourced from [8, 16,18]. The modified expressions are given by Eqs. (6) and (7). For Eq. (7), the value for the ultimate stress of the flat section regions was obtained from Eqs. (2) and (3).
σ00 .2,pb,c =
1.673σ0.2,mill ri 0.126 t
0 σ00 .2,cr ,c = 0.83σult ,f .
Fig. 11. Correlation between 0.2% proof stress σ0.2,exp and average hardness value H vav .
(6) (7)
It is proposed that the modified simple power model be used to predict the 0.2% proof stress of the press-braked corners since this is a function of the ri /t ratio, which tends to be more variable for press-braked sections and may often be directly specified. Cold-rolled corner data has been employed in addition to pressbraked data to devise equation (6) due to limited availability of press-braked sections with low ri /t ratios. For cold-rolled sections, prediction of the 0.2% proof stress of the corner region utilising Eq. (7) and the predicted 0.2% proof stress σ00 .2,f of the flat face is more accurate than using Eq. (6). Eq. (7) does not feature the ri /t ratio that represents the strain involved in corner forming, but the expression is generally reliable since this ratio does not vary significantly in cold-rolled sections. Eq. (7) is therefore proposed to predict the corner strength of cold-rolled box sections.
Fig. 12. Normalised predicted 0.2% proof stress in press-braked angle faces.
6. Extent of corner strength enhancements In addition to knowledge of the magnitude of the corner strength enhancements, the degree to which the enhanced strength extends beyond the curved corner regions is also important. Vickers microhardness tests were carried out on 9 coldformed stainless steel sections in order to establish a relationship between hardness values and 0.2% proof stress, and therefore to predict the variation of material strength in the corners regions of the sections. Hardness tests could be carried out to a finer resolution than tensile coupon tests. The complete set of hardness values has been presented by Cruise [4]. By correlating the 0.2% proof stress σ0.2,exp from the tensile tests of each strip with the corresponding average hardness measurements, a proportional relationship between hardness HVav and 0.2% proof stress σ0.2,exp from the tensile coupons, as described by Tabor [19], can be defined — see Fig. 11. On the basis of the relationship shown in Fig. 11, predicted values of 0.2% proof stress σ00 .2,exp were obtained from the hardness values. In Fig. 12, the predicted 0.2% proof stress σ00 .2,exp for the press-braked angles has been normalised by the average predicted 0.2% proof stress for the flat region of the section σ00 .2av,exp and plotted against the normalised section position. For the cold-rolled
Fig. 13. Normalised predicted 0.2% proof stress in cold-rolled box section faces.
boxes, the predicted 0.2% proof stress σ00 .2,exp has been normalised by the average 0.2% proof stress of the central 50% of each section face σ00 .2av,exp and also plotted against a normalised section position in Fig. 13. For both the press-braked and cold-rolled sections the regions that are uninfluenced by corner forming, which were previously defined in Figs. 7 and 8 have been confirmed by the hardness data. In order to determine a distance beyond the corner radii that exhibits strength enhancements due to corner forming, the data for both press-braked and cold-rolled sections has been plotted against the section position normalised by the section thickness in Figs. 14 and 15. The origin of these two graphs indicates the junction between the corner radii and the sections’ flat faces. It can be seen for the press-braked sections that the material strength reaches its maximum value at the centre of the formed corner (Fig. 12) and that there are no notable strength increases beyond the corner radius (Fig. 14). In contrast, the material strength in the cold-rolled box sections peaks at the junction of the corner
R.B. Cruise, L. Gardner / Journal of Constructional Steel Research 64 (2008) 1310–1316
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Fig. 16. Proposed 0.2% proof stress distributions for press-braked sections and cold-rolled boxes.
Fig. 14. Normalised predicted 0.2% proof stress for press-braked angles at a section position/t.
Fig. 15. Normalised predicted 0.2% proof stress for cold-rolled boxes at a section position/t.
radius to the flat face, depreciates slightly towards the centre of the corner and drops gradually moving into the flat face of the section. The material strength of the flat face is reached approximately 4t away from the corner to flat face junction. It is therefore proposed that Eq. (6) should be used to predict strength enhancements confined within the corner radius for press-braked sections and that Eq. (7) is used to predict a uniform strength enhancement for a region including the corner radius but which extends 2t beyond it (representing an assumed linear decrease in strength of a distance of 4t by a sharp drop from the corner strength to the flat strength at 2t). 7. Significance of harnessing strength enhancements Based on the tensile coupon data and the extent of the corner strength enhancements identified through Vickers microhardness tests, 0.2% proof stress distributions are proposed for stainless steel press-braked sections and cold-rolled boxes as illustrated in Fig. 16. The proposed distribution for a press-braked section takes the 0.2% proof stress given in the inspection document for the material strength of the flat faces and uses Eq. (6) to determine the corner strength enhancements, which are confined to the corner radius of the section. For cold-rolled box sections, the proposed distribution uses Eq. (2) to determine the material strength in the flat faces and Eq. (7) to determine the material strength in a region extending 2t beyond the corner radius. The proposed strength enhancements offer increased material efficiency if employed in structural design. The proposed models were adopted in combination with the current stainless steel structural design code (EN 1993-1-4 [6]) to predict cross section and member resistances in compression and bending. Effective section properties were calculated for Class 4 sections. In addition,
an alternative option was considered assuming that no mill certificate data were available during design where the proposed models were employed by replacing the inspection document data in Eq. (6) for the press-braked sections and Eqs. (2) and (7) for the cold-rolled sections with the minimum specified 0.2% proof stress σ0.2,min . The results were then compared to those obtained by assuming a uniform distribution of the minimum specified 0.2% proof stresses σ0.2,min from EN 10088-2 [7] and published test results. The test data available comprised stub column test data for press-braked angles, channels and lipped channel sections [20] together with stub column, long column and beam test data for cold-rolled box sections [9,12,13,21,22]. The results of these comparisons for the two types of cold-formed section are given in Table 1. In all cases the proposed 0.2% proof stress distributions brought the average predicted member resistance closer to the test values. The average increase in resistance demonstrates large improvements in efficiency. The values shown in brackets correspond to the option where the minimum specified material data σ0.2,min is taken as an alternative to the inspection document data σ0.2,mill in the proposed Eqs. (2), (6) and (7). In this case, average increases in resistance are lower but, particularly in the case of cold-rolled box sections, are still significant. 8. The influence of residual stresses Plastic deformation experienced during section forming causes cold working of the material, but it also induces residual stress patterns in the cold-formed cross sections. The general influence of residual stresses on structural members is to cause premature yielding, leading to loss of stiffness and a reduction in load-carrying capacity and therefore the significance of these effects should be considered in predicting structural behaviour. Two components of longitudinal residual stress can be identified from the strains released during sectioning: membrane (associated with axial strain) and bending stresses (associated with strains varying through the material thickness). Based on the strain data measured during sectioning, the two types of cold-formed sections generally show low membrane residual stresses (10%–40% of the corresponding 0.2% proof stress values obtained from tensile coupon tests), but larger bending residual stresses, particularly in the cold-rolled sections (15%–60% of the corresponding 0.2% proof stress values obtained from tensile coupon tests). These bending residual stresses are based on assuming a rectangular stress block distribution through the thickness, as detailed in [2]. The bending residual stresses are principally associated with plastic deformation. Fig. 17 shows the correlation between the 0.2% proof stress of the examined cold-rolled sections and the corresponding bending residual stresses. Since the bending residual stresses are re-introduced into the strips during the tensile coupon tests (due to straightening), the material data used herein to predict strength increases will include any effects caused by the bending residual stresses. Membrane stresses are not accounted
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Table 1 Increases in efficiency offered by proposed material models Resistance
Stub column Column Bending
Press-braked sections [20]:
Cold-rolled box sections [9,12,13,21,22]:
Average predicted/test values
Coefficient of variation
Average increases in resistance
Average predicted/test values
Coefficient of variation
Average increases in resistance
0.87 (0.70) – –
0.07 (0.10) – –
1.4 × (1.1 ×) – –
0.90 (0.70) 1.02 (0.91) 0.79 (0.65)
0.13 (0.11) 0.16 (0.19) 0.19 (0.14)
2.1 × (1.6 ×) 1.5 × (1.3 ×) 1.9 × (1.5 ×)
References
Fig. 17. Bending residual stresses versus material strength for cold-rolled box sections.
for in the stress–strain data obtained from the tensile coupon tests and are generally thought to have a more significant influence on structural behaviour. As such, they are commonly included in finite element simulations. A number of studies [23,24] have however found that the influence of membrane residual stresses on the structural behaviour of cold-formed stainless steel sections is generally small. 9. Conclusions Based on an experimental program comprising tensile coupon tests and hardness tests, a method for predicting the distribution of 0.2% proof stress around press-braked and cold-rolled stainless steel sections has been proposed. Due to cold working during forming, strength increases beyond the material strength of the sheet material are observed in the corner regions of both section types and in the flat faces of the cold-rolled box sections. New models have been proposed to predict the strength enhancements in the faces of the cold-rolled box sections, and existing models have been modified to predict the corner strength enhancements. The region over which these corner strength enhancements exist has been defined. The models have been assessed in combination with current structural design guidance to demonstrate the increases in design efficiency. The magnitude and distribution of residual stresses in cold-formed stainless steel sections has been quantified, but are not thought to significantly affect structural behaviour. The achieved enhancements in efficiency are significant and highlight the importance and benefit of harnessing the strength increases that arise during forming of cold-formed stainless steel members.
[1] Cruise RB, Gardner L. Measurement and prediction of geometrical imperfections in stainless steel members. Structural Engineering and Mechanics 2006; 24(1):63–89. [2] Cruise RB, Gardner L. Residual stress analysis of structural stainless steel sections. Journal of Constructional Steel Research 2008;64(3):352–66. [3] EN 10002-1. Metallic materials — Tensile testing, Part 1: Method of test at ambient temperature. European Standard, CEN. 1990. [4] Cruise RB. The influence of production routes on the behaviour of stainless steel structural members. Ph.D. thesis. UK: Department of Civil and Environmental Engineering, Imperial College London; 2007. [5] EN 10204. Metallic products — Types of inspection documents. European Standard, CEN. 2004. [6] EN 1993-1-4. Eurocode 3: Design of steel structures — Part 1.4: General rules. Supplementary rules for stainless steels. European standard, CEN. 2006. [7] EN 10088-2. Stainless steels — Part 2: Technical delivery conditions for sheet/plate and strip of corrosion resisting steel for general purposes. European Standard, CEN. 2005. [8] Coetzee JS, van den Berg GJ, van der Merwe P. The effect of work hardening and residual stresses due to cold-work of forming on the strength of coldformed stainless steel lipped channels. In: Proc. of the 10th int. specialty conf. on cold-formed steel structures, 1990, p. 143–62. [9] Gardner L, Nethercot DA. Experiments on stainless steel hollow sections — Part 1: Material and cross-sectional behaviour. Journal of Constructional Steel Research 2004;60(9):1291–318. [10] Gardner L, Talja A, Baddoo NR. Structural design of high-strength austenitic stainless steel. Thin-walled structures 2006;44(5):517–28. [11] Hyttinen V. Design of cold-formed stainless steel SHS beam-columns. Report 41. Finland: Laboratory of Structural Engineering, University of Oulu; 1994. [12] Talja A, Salmi P. Design of stainless steel RHS beams, columns and beamcolumns. Research note: 1619. Finland: VTT Building Technology; 1995. [13] Rasmussen KJR, Hancock GJ. Design of cold-formed stainless steel tubular members, I: Columns. Journal of Structural Engineering, ASCE 1993;119(8): 2349–67. [14] Uppfeldt B, Ala-Outinen T, Veljkovic M. A design model for stainless steel box columns in fire. Journal of Constructional Steel Research 2008;64(11): 1294–301. [15] Karren KW. Corner properties of cold-formed steel shapes. Journal of the Structural Division, ASCE 1967;93(ST1):401–32. [16] Van den Berg GJ, van der Merwe P. Prediction of corner mechanical properties for stainless steels due to cold forming. In: Proc. of the 11th int. speciality conf. on cold-formed steel structures. 1992. p. 571–86. [17] Ashraf M, Gardner L, Nethercot DA. Strength of the corner regions of stainless steel cross sections. Journal of Constructional Steel Research 2005;61(1): 37–52. [18] Lecce M, Rasmussen KJR. Experimental investigation of distortional buckling of cold-formed stainless steel sections. In: Proc. of the 17th int. specialty conf. on cold-formed steel structures. 2004. [19] Tabor D. The hardness of metals. UK: Oxford University Press; 1951. [20] Kuwamura H. Local buckling of thin-walled stainless steel members. Steel Structures 2003;3:191–201. [21] Gardner L, Nethercot DA. Experiments on stainless steel hollow sections — Part 2: Member behaviour of columns and beams. Journal of Constructional Steel Research 2004;6(9):1319–32. [22] Rasmussen KJR, Hancock GJ. Design of cold-formed stainless steel tubular members, II: Beams. Journal of Structural Engineering, ASCE 1993;119(8): 2368–86. [23] Gardner L, Nethercot DA. Numerical modelling of stainless steel structural components — a consistent approach. Journal of Structural Engineering, ASCE 2004;130(10):1586–601. [24] Ellobody E, Young B. Structural performance of cold-formed high strength stainless steel columns. Journal of Constructional Steel Research 2005;61(12): 1631–49.
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Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Strength enhancements induced during cold forming of stainless steel sections Rachel B. Cruise a,∗ , Leroy Gardner b a
Department of Architecture and Civil Engineering, University of Bath, UK
b
Department of Civil and Environmental Engineering, Imperial College London, UK
article
info
Article history: Received 14 November 2007 Accepted 30 April 2008 Keywords: Stainless steel Cold-formed sections Strain hardening Residual stresses Strength enhancement
a b s t r a c t The material properties of stainless steel are sensitive to plastic deformation which causes an increase in yield strength by a process termed cold working. The different strain paths experienced around cold-formed cross sections during manufacture create unique material strength distributions for sections from different forming routes and also influence residual stress patterns. The research program presented herein has examined experimentally the material and residual stress distributions found in two types of cold-formed sections–cold-rolled box sections and press-braked angles. Predictive tools to harness the observed strength enhancements have been proposed and incorporated into models. Subsequent comparisons have shown that these strength enhancements, in particular those observed for cold-rolled box sections, should be employed in structural design to avoid considerable underestimation of member resistance. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Achieving material efficiency in structural stainless steel design is an important step towards encouraging wider use and thus enabling its aesthetics and low maintenance requirements to be further utilised to create elegant and durable structures. Due to the characteristics of its material stress–strain curve, stainless steel is very sensitive to cold working. Material strength in stainless steel cross sections, commonly taken as the 0.2% proof stress, is dependant on the amount of plastic deformation and heat treatment experienced during production (and service). Strength enhancements induced during the forming routes of cold-formed sections, which are the most common type of stainless steel cross section, offer higher material strength than that currently assumed in design. At present, structural stainless steel design is based on the minimum material properties specified in material standards. As part of a recent research program carried out at Imperial College London to investigate the link between the production route and structural behaviour of stainless steel members, a series of experiments were performed. A total of 15 cold-formed stainless steel (grade 1.4301) members – 8 press-braked angles and 7 cold-rolled box sections – were first measured for their geometric imperfections, as reported in Cruise and Gardner [1], and then sectioned into a series of strips and analysed. The strains released during this sectioning process were recorded using strain gauges and used to calculate residual stresses, as detailed in Cruise and
∗
Corresponding author. Tel.: +44 01125 386748; fax: +44 01225 386691. E-mail address: [email protected] (R.B. Cruise).
0143-974X/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2008.04.014
Gardner [2]. The strips were then tested in tension in accordance with EN 10002-1 [3] and from the resulting stress–strain data the 0.2% proof stresses and ultimate stresses were identified. The complete set of material and residual stress data is published in [4]. The test results presented herein and collated from other studies highlights considerable cold work-induced strength increases in the corners of press-braked stainless steel sections and in the flat faces and corners of cold-rolled box sections. However, due to physical restraints in the size of the tensile coupons, the resolution to which the material properties could be determined was limited. In order to map the material strength to a higher resolution, Vickers microhardness tests were performed. This provided, in particular, more detailed information on the extent of the strength enhancements associated with corner forming. The material strength data obtained from the tensile coupon tests and inferred from the hardness tests were used to develop expressions to predict the strength enhancements in the faces of the cold-rolled box sections, and to re-evaluate previously proposed expressions to determine strength enhancements in the corners of press-braked and cold-rolled sections. The implications of the proposed predictive models on structural stainless steel design have been assessed. 2. Production routes Cold-formed stainless steel sections are formed from sheet material in two principal ways. The simplest forming process is press braking where individual folds are created in the sheet material between a tool and die. This production process is controlled manually and is used to manufacture small quantities
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List of symbols b d HVav t ri Ri
Section face width Section face width Average Vickers Hardness value along coupon width Section thickness Section corner radius Tube radius prior to crushing σ 0.2av,exp Weighted average of the 0.2% proof stresses obtained experimentally for the central 50% of the faces of cold-rolled box sections or the 80% of the section face furthest from the corner for pressbraked sections σ00 .2av,exp Weighted average of the 0.2% proof stresses predicted from Hardness values for the central 50% of the faces of cold-rolled box sections or the 80% of the section face furthest from the corner for pressbraked sections σ0.2,exp Experimentally determined 0.2% proof stress σ00 .2,exp Predicted 0.2% proof stress from Hardness values σ00 .2,f Predicted 0.2% proof stress for the central 50% of the faces of cold-rolled box sections σ0.2,mill 0.2% proof stress given in inspection document or mill certificate σ0.2,min Minimum specified 0.2% proof stress given in EN 10088 (2005) σultav,exp Weighted average of the ultimate stress obtained experimentally for the central 50% of the faces of cold-rolled box sections or the 80% of the section face furthest from the corner for press-braked sections σult,f Ultimate stress from the centre of the faces of coldrolled box sections 0 σult Predicted ultimate stress for the central 50% of the ,f faces of cold-rolled box σult,mill Ultimate stress given in inspection document or mill certificate σ0.2,c 0.2% proof stress of the corners of cold-formed sections σ0.2,cr ,c 0.2% proof stress of the corners of cold-rolled box sections σ00 .2,cr ,c Predicted 0.2% proof stress of the corners of coldrolled box sections σ00 .2,pb,c Predicted 0.2% proof stress of the corners of pressbraked sections
of sections. Angle sections, such as those considered in this study, are formed with one press braking operation as shown in Fig. 1, although more complex sections can be produced with multiple folds. Cold rolling is a more automated process whereby sheet material is uncoiled from a roll and flattened before being fed through a series of forming rollers that gradually deform the sheet into a desired section shape. This automated process has been developed especially to produce large quantities of nominally similar sections. Box sections, including those examined in this study, are commonly produced by first forming a circular tube which is welded closed and subsequently crushed into a box section through a Turks head die. An illustration of a circular tube being crushed into a box section is shown in Fig. 2. In compliance with EN 10204 [5] the material strength of the sheet formed in either of these cold forming processes is quality assured by performing tensile coupon tests. This material data, including the 0.2% proof stress σ0.2,mill and the ultimate stress σult,mill is made available with the cold-formed sections in a type
Fig. 1. Press braking of an angle.
Fig. 2. Cold rolling of a box section.
2.2 inspection document or mill certificate. However, the recently introduced stainless steel design code (EN 1993-1-4 [6]) employs the minimum material strengths σ0.2,min specified in the material standard EN 10088-2 [7]. 3. Material strength distributions The 0.2% proof stress data σ0.2,exp from the tensile coupon tests performed in the current experimental program were combined with data from other research programs [8–14]. The experimental data from the current experimental program is plotted in Figs. 3 and 4 showing the material strength distribution from eight press-braked angles and seven cold-rolled boxes, respectively. The different cold-formed sections are identified in Figs. 3 and 4 firstly by the production route: PB for press-braked and CR for cold-rolled sections followed by the two cross section dimensions and the thickness, t and finally the internal corner radii, ri , if specified. Figs. 5 and 6 show the same 0.2% proof stress σ0.2,exp data normalised by values taken from the corresponding inspection documents σ0.2,mill and plotted against the position in the section face normalised by the face width b or d. It can be seen in Fig. 5 that the material strength of the flat face of press-braked sections is close to that of the unformed sheet material, demonstrating that during section forming the faces of press-braked sections do not experience significant plastic deformation. However, strength increases above the strength of the unformed sheet material are observed in the corner regions where large plastic deformations are known to occur during forming. In Fig. 6 for cold-rolled sections, similar to press-braked sections, strength increases in the corner regions can be observed. However, strength increases are also seen in the flat faces of the sections indicating that the flat faces in cold-rolled box sections must also experience plastic deformation. This may be largely attributed to the initial formation of the circular tube followed by crushing into the box faces.
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Fig. 3. 0.2% proof stress for section faces of press-braked angles.
Fig. 4. 0.2% proof stress for section faces of cold-rolled boxes.
Fig. 5. 0.2% proof stress normalised by inspection document value for section faces of press-braked angles.
Fig. 6. 0.2% proof stress normalised by inspection document value for section faces of cold-rolled boxes.
4. Strength increases in section faces
the cold-rolled boxes σ0.2,exp normalised by the weighted average of the 0.2% proof stress values from the central 50% of each respective section face σ0.2av,exp . From the data, the 80% of the section face furthest from the corner for press-braked sections, and the central 50% of cold-rolled sections have been identified as being uninfluenced by corner forming. Whilst no strength enhancements are observed in the regions of the press-braked sections uninfluenced by corner forming, this is not the case for the box sections.
To identify the regions of the flat faces of the cold-formed sections where the material strength has not been influenced by corner forming, the normalised material test data have been examined. Fig. 7 shows the 0.2% proof stress σ0.2,exp for pressbraked angles normalised by the weighted average of the 0.2% proof stress values from the face of the section (i.e. omitting the corner data) σ0.2av,exp and Fig. 8 shows the 0.2% proof stresses for
R.B. Cruise, L. Gardner / Journal of Constructional Steel Research 64 (2008) 1310–1316
Fig. 7. 0.2% proof stress normalised by average face data for press-braked angles.
Fig. 8. 0.2% proof stress normalised by average central 50% face data for cold-rolled boxes.
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Fig. 10. Increase in cold working parameter with section face forming strain.
As a measure of the level of cold work that has occurred during the forming of the section faces, the parameter (σult,mill /σ0.2,mill )/ (σultav,exp /σ0.2av,exp ) has been utilised. The larger the value of this parameter, the greater the level of cold work that the section has undergone. Plotting this parameter against the simplified strain parameter (Eq. (1)) yields a second linear relationship (see Fig. 10) with a coefficient of determination R2 of 0.64. The two relationships given in Figs. 9 and 10 can be combined and used to predict the 0.2% proof stress of the central 50% of cold-rolled box sections σ00 .2,f , resulting in Eq. (2). This expression includes the 0.2% proof stress given in inspection documents σ0.2,mill and geometrical parameters equivalent to an Ri /t ratio. From the relationship 0 described in Fig. 9, the corresponding ultimate stress σult ,f can also be predicted using Eq. (3).
σ00 .2,f =
0.85σ0.2,mill
−0.19 +
σult,f = σult,mill 0.19 0
(2)
1 12.42 2(bπ+t d) +0.83
σ00 .2,f
σ0.2,mill
+ 0.85 .
(3)
5. Strength increases in corners
Fig. 9. Relationship between ultimate stress and 0.2% proof stress normalised by inspection document value.
Based on the central 50% of the cold-rolled box faces, the two ratios σ0.2av,exp /σ0.2,mill and σultav,exp /σult,mill indicate the increase in 0.2% proof stress and ultimate stress, respectively, due to the face forming process only. A linear relationship between these two parameters is described by the experimental data in Fig. 9, with a coefficient of determination R2 of 0.71, where a small increase of the ultimate stress relates to a more significant increase in the 0.2% proof stress. Cold working thereby brings the 0.2% proof stress closer to the ultimate stress. The strain experienced by the section face during the forming of a box from a circular tube can be described in terms of the radius of the circular tube formed Ri and the thickness of the section material t. Ri can be written in terms of the section geometry (Fig. 2). Assuming pure bending during forming and by removing the insignificant ri terms, a simplified strain expression given by Eq. (1) can be obtained.
εf =
πt . 2(b + d)
(1)
The strength increases in the corner regions of cold-formed sections due to plastic deformation was first observed in carbon steel sections. Karren [15] proposed a power model to predict these strength increases based on the strain experienced in the sheet material during corner forming and the yield strength of the sheet material formed. The strain induced during corner forming is closely related to the ratio of the internal radius of the corner and the thickness of the material ri /t. Karren’s expression was modified by van den Berg and van der Merwe [16] and more recently by Ashraf et al. [17] for stainless steel sections. Two further methods to predict corner strength (0.2% proof stress and ultimate tensile stress) in stainless steel sections were also proposed by Ashraf et al. [17] based on all available test data. The first method employs the 0.2% proof stress σ0.2,mill of the unformed sheet material in a simple power model and is given by Eq. (4), whilst the second utilises both the 0.2% proof stress σ0.2,mill and the ultimate stress σult,mill of the unformed material. Both equations yielded an accurate prediction of test data, with the simple power model showing a slightly higher scatter with a coefficient of variation of 0.06 compared to 0.04. A third, linear equation, independent of the ri /t ratio, was proposed to predict the ultimate strength of the corners based on the 0.2% proof stress of the corner material σ0.2,c , and the 0.2% proof stress σ0.2,mill and the ultimate stress σult,mill from the mill certificate.
σ0.2,c =
1.881σ0.2,mill ri 0.194 t
.
(4)
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Gardner and Nethercot [9] studied data from cold-rolled box sections and noted an approximately linear relationship between the 0.2% proof strength σ0.2,cr ,c of the formed corners and the ultimate strength σult,f of the flat faces. The resulting expression is given in Eq. (5). The coefficient of proportionality was modified by Ashraf et al. [17] to fit all published data.
σ0.2,cr ,c = 0.85σult,f .
(5)
To determine appropriate models to predict the enhanced corner strength in press-braked and cold-rolled sections, denoted as σ00 .2,pb,c and σ00 .2,cr ,c , respectively, both Eqs. (4) and (5) were modified by refitting the models to include data from the current test program and all currently published data. Eq. (4) was refitted to both press-braked and cold-rolled data whilst Eq. (5) was refitted to cold-rolled data only. It was decided that, of the models proposed by Ashraf et al. [17], the simple power model, despite its slightly higher scatter of predictions, relied upon less detailed information about the unformed sheet material and was therefore easier to implement. Cold-rolled corner data included in the study was reported in [9–13]. Press-braked data was sourced from [8, 16,18]. The modified expressions are given by Eqs. (6) and (7). For Eq. (7), the value for the ultimate stress of the flat section regions was obtained from Eqs. (2) and (3).
σ00 .2,pb,c =
1.673σ0.2,mill ri 0.126 t
0 σ00 .2,cr ,c = 0.83σult ,f .
Fig. 11. Correlation between 0.2% proof stress σ0.2,exp and average hardness value H vav .
(6) (7)
It is proposed that the modified simple power model be used to predict the 0.2% proof stress of the press-braked corners since this is a function of the ri /t ratio, which tends to be more variable for press-braked sections and may often be directly specified. Cold-rolled corner data has been employed in addition to pressbraked data to devise equation (6) due to limited availability of press-braked sections with low ri /t ratios. For cold-rolled sections, prediction of the 0.2% proof stress of the corner region utilising Eq. (7) and the predicted 0.2% proof stress σ00 .2,f of the flat face is more accurate than using Eq. (6). Eq. (7) does not feature the ri /t ratio that represents the strain involved in corner forming, but the expression is generally reliable since this ratio does not vary significantly in cold-rolled sections. Eq. (7) is therefore proposed to predict the corner strength of cold-rolled box sections.
Fig. 12. Normalised predicted 0.2% proof stress in press-braked angle faces.
6. Extent of corner strength enhancements In addition to knowledge of the magnitude of the corner strength enhancements, the degree to which the enhanced strength extends beyond the curved corner regions is also important. Vickers microhardness tests were carried out on 9 coldformed stainless steel sections in order to establish a relationship between hardness values and 0.2% proof stress, and therefore to predict the variation of material strength in the corners regions of the sections. Hardness tests could be carried out to a finer resolution than tensile coupon tests. The complete set of hardness values has been presented by Cruise [4]. By correlating the 0.2% proof stress σ0.2,exp from the tensile tests of each strip with the corresponding average hardness measurements, a proportional relationship between hardness HVav and 0.2% proof stress σ0.2,exp from the tensile coupons, as described by Tabor [19], can be defined — see Fig. 11. On the basis of the relationship shown in Fig. 11, predicted values of 0.2% proof stress σ00 .2,exp were obtained from the hardness values. In Fig. 12, the predicted 0.2% proof stress σ00 .2,exp for the press-braked angles has been normalised by the average predicted 0.2% proof stress for the flat region of the section σ00 .2av,exp and plotted against the normalised section position. For the cold-rolled
Fig. 13. Normalised predicted 0.2% proof stress in cold-rolled box section faces.
boxes, the predicted 0.2% proof stress σ00 .2,exp has been normalised by the average 0.2% proof stress of the central 50% of each section face σ00 .2av,exp and also plotted against a normalised section position in Fig. 13. For both the press-braked and cold-rolled sections the regions that are uninfluenced by corner forming, which were previously defined in Figs. 7 and 8 have been confirmed by the hardness data. In order to determine a distance beyond the corner radii that exhibits strength enhancements due to corner forming, the data for both press-braked and cold-rolled sections has been plotted against the section position normalised by the section thickness in Figs. 14 and 15. The origin of these two graphs indicates the junction between the corner radii and the sections’ flat faces. It can be seen for the press-braked sections that the material strength reaches its maximum value at the centre of the formed corner (Fig. 12) and that there are no notable strength increases beyond the corner radius (Fig. 14). In contrast, the material strength in the cold-rolled box sections peaks at the junction of the corner
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Fig. 16. Proposed 0.2% proof stress distributions for press-braked sections and cold-rolled boxes.
Fig. 14. Normalised predicted 0.2% proof stress for press-braked angles at a section position/t.
Fig. 15. Normalised predicted 0.2% proof stress for cold-rolled boxes at a section position/t.
radius to the flat face, depreciates slightly towards the centre of the corner and drops gradually moving into the flat face of the section. The material strength of the flat face is reached approximately 4t away from the corner to flat face junction. It is therefore proposed that Eq. (6) should be used to predict strength enhancements confined within the corner radius for press-braked sections and that Eq. (7) is used to predict a uniform strength enhancement for a region including the corner radius but which extends 2t beyond it (representing an assumed linear decrease in strength of a distance of 4t by a sharp drop from the corner strength to the flat strength at 2t). 7. Significance of harnessing strength enhancements Based on the tensile coupon data and the extent of the corner strength enhancements identified through Vickers microhardness tests, 0.2% proof stress distributions are proposed for stainless steel press-braked sections and cold-rolled boxes as illustrated in Fig. 16. The proposed distribution for a press-braked section takes the 0.2% proof stress given in the inspection document for the material strength of the flat faces and uses Eq. (6) to determine the corner strength enhancements, which are confined to the corner radius of the section. For cold-rolled box sections, the proposed distribution uses Eq. (2) to determine the material strength in the flat faces and Eq. (7) to determine the material strength in a region extending 2t beyond the corner radius. The proposed strength enhancements offer increased material efficiency if employed in structural design. The proposed models were adopted in combination with the current stainless steel structural design code (EN 1993-1-4 [6]) to predict cross section and member resistances in compression and bending. Effective section properties were calculated for Class 4 sections. In addition,
an alternative option was considered assuming that no mill certificate data were available during design where the proposed models were employed by replacing the inspection document data in Eq. (6) for the press-braked sections and Eqs. (2) and (7) for the cold-rolled sections with the minimum specified 0.2% proof stress σ0.2,min . The results were then compared to those obtained by assuming a uniform distribution of the minimum specified 0.2% proof stresses σ0.2,min from EN 10088-2 [7] and published test results. The test data available comprised stub column test data for press-braked angles, channels and lipped channel sections [20] together with stub column, long column and beam test data for cold-rolled box sections [9,12,13,21,22]. The results of these comparisons for the two types of cold-formed section are given in Table 1. In all cases the proposed 0.2% proof stress distributions brought the average predicted member resistance closer to the test values. The average increase in resistance demonstrates large improvements in efficiency. The values shown in brackets correspond to the option where the minimum specified material data σ0.2,min is taken as an alternative to the inspection document data σ0.2,mill in the proposed Eqs. (2), (6) and (7). In this case, average increases in resistance are lower but, particularly in the case of cold-rolled box sections, are still significant. 8. The influence of residual stresses Plastic deformation experienced during section forming causes cold working of the material, but it also induces residual stress patterns in the cold-formed cross sections. The general influence of residual stresses on structural members is to cause premature yielding, leading to loss of stiffness and a reduction in load-carrying capacity and therefore the significance of these effects should be considered in predicting structural behaviour. Two components of longitudinal residual stress can be identified from the strains released during sectioning: membrane (associated with axial strain) and bending stresses (associated with strains varying through the material thickness). Based on the strain data measured during sectioning, the two types of cold-formed sections generally show low membrane residual stresses (10%–40% of the corresponding 0.2% proof stress values obtained from tensile coupon tests), but larger bending residual stresses, particularly in the cold-rolled sections (15%–60% of the corresponding 0.2% proof stress values obtained from tensile coupon tests). These bending residual stresses are based on assuming a rectangular stress block distribution through the thickness, as detailed in [2]. The bending residual stresses are principally associated with plastic deformation. Fig. 17 shows the correlation between the 0.2% proof stress of the examined cold-rolled sections and the corresponding bending residual stresses. Since the bending residual stresses are re-introduced into the strips during the tensile coupon tests (due to straightening), the material data used herein to predict strength increases will include any effects caused by the bending residual stresses. Membrane stresses are not accounted
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Table 1 Increases in efficiency offered by proposed material models Resistance
Stub column Column Bending
Press-braked sections [20]:
Cold-rolled box sections [9,12,13,21,22]:
Average predicted/test values
Coefficient of variation
Average increases in resistance
Average predicted/test values
Coefficient of variation
Average increases in resistance
0.87 (0.70) – –
0.07 (0.10) – –
1.4 × (1.1 ×) – –
0.90 (0.70) 1.02 (0.91) 0.79 (0.65)
0.13 (0.11) 0.16 (0.19) 0.19 (0.14)
2.1 × (1.6 ×) 1.5 × (1.3 ×) 1.9 × (1.5 ×)
References
Fig. 17. Bending residual stresses versus material strength for cold-rolled box sections.
for in the stress–strain data obtained from the tensile coupon tests and are generally thought to have a more significant influence on structural behaviour. As such, they are commonly included in finite element simulations. A number of studies [23,24] have however found that the influence of membrane residual stresses on the structural behaviour of cold-formed stainless steel sections is generally small. 9. Conclusions Based on an experimental program comprising tensile coupon tests and hardness tests, a method for predicting the distribution of 0.2% proof stress around press-braked and cold-rolled stainless steel sections has been proposed. Due to cold working during forming, strength increases beyond the material strength of the sheet material are observed in the corner regions of both section types and in the flat faces of the cold-rolled box sections. New models have been proposed to predict the strength enhancements in the faces of the cold-rolled box sections, and existing models have been modified to predict the corner strength enhancements. The region over which these corner strength enhancements exist has been defined. The models have been assessed in combination with current structural design guidance to demonstrate the increases in design efficiency. The magnitude and distribution of residual stresses in cold-formed stainless steel sections has been quantified, but are not thought to significantly affect structural behaviour. The achieved enhancements in efficiency are significant and highlight the importance and benefit of harnessing the strength increases that arise during forming of cold-formed stainless steel members.
[1] Cruise RB, Gardner L. Measurement and prediction of geometrical imperfections in stainless steel members. Structural Engineering and Mechanics 2006; 24(1):63–89. [2] Cruise RB, Gardner L. Residual stress analysis of structural stainless steel sections. Journal of Constructional Steel Research 2008;64(3):352–66. [3] EN 10002-1. Metallic materials — Tensile testing, Part 1: Method of test at ambient temperature. European Standard, CEN. 1990. [4] Cruise RB. The influence of production routes on the behaviour of stainless steel structural members. Ph.D. thesis. UK: Department of Civil and Environmental Engineering, Imperial College London; 2007. [5] EN 10204. Metallic products — Types of inspection documents. European Standard, CEN. 2004. [6] EN 1993-1-4. Eurocode 3: Design of steel structures — Part 1.4: General rules. Supplementary rules for stainless steels. European standard, CEN. 2006. [7] EN 10088-2. Stainless steels — Part 2: Technical delivery conditions for sheet/plate and strip of corrosion resisting steel for general purposes. European Standard, CEN. 2005. [8] Coetzee JS, van den Berg GJ, van der Merwe P. The effect of work hardening and residual stresses due to cold-work of forming on the strength of coldformed stainless steel lipped channels. In: Proc. of the 10th int. specialty conf. on cold-formed steel structures, 1990, p. 143–62. [9] Gardner L, Nethercot DA. Experiments on stainless steel hollow sections — Part 1: Material and cross-sectional behaviour. Journal of Constructional Steel Research 2004;60(9):1291–318. [10] Gardner L, Talja A, Baddoo NR. Structural design of high-strength austenitic stainless steel. Thin-walled structures 2006;44(5):517–28. [11] Hyttinen V. Design of cold-formed stainless steel SHS beam-columns. Report 41. Finland: Laboratory of Structural Engineering, University of Oulu; 1994. [12] Talja A, Salmi P. Design of stainless steel RHS beams, columns and beamcolumns. Research note: 1619. Finland: VTT Building Technology; 1995. [13] Rasmussen KJR, Hancock GJ. Design of cold-formed stainless steel tubular members, I: Columns. Journal of Structural Engineering, ASCE 1993;119(8): 2349–67. [14] Uppfeldt B, Ala-Outinen T, Veljkovic M. A design model for stainless steel box columns in fire. Journal of Constructional Steel Research 2008;64(11): 1294–301. [15] Karren KW. Corner properties of cold-formed steel shapes. Journal of the Structural Division, ASCE 1967;93(ST1):401–32. [16] Van den Berg GJ, van der Merwe P. Prediction of corner mechanical properties for stainless steels due to cold forming. In: Proc. of the 11th int. speciality conf. on cold-formed steel structures. 1992. p. 571–86. [17] Ashraf M, Gardner L, Nethercot DA. Strength of the corner regions of stainless steel cross sections. Journal of Constructional Steel Research 2005;61(1): 37–52. [18] Lecce M, Rasmussen KJR. Experimental investigation of distortional buckling of cold-formed stainless steel sections. In: Proc. of the 17th int. specialty conf. on cold-formed steel structures. 2004. [19] Tabor D. The hardness of metals. UK: Oxford University Press; 1951. [20] Kuwamura H. Local buckling of thin-walled stainless steel members. Steel Structures 2003;3:191–201. [21] Gardner L, Nethercot DA. Experiments on stainless steel hollow sections — Part 2: Member behaviour of columns and beams. Journal of Constructional Steel Research 2004;6(9):1319–32. [22] Rasmussen KJR, Hancock GJ. Design of cold-formed stainless steel tubular members, II: Beams. Journal of Structural Engineering, ASCE 1993;119(8): 2368–86. [23] Gardner L, Nethercot DA. Numerical modelling of stainless steel structural components — a consistent approach. Journal of Structural Engineering, ASCE 2004;130(10):1586–601. [24] Ellobody E, Young B. Structural performance of cold-formed high strength stainless steel columns. Journal of Constructional Steel Research 2005;61(12): 1631–49.