New Approach to Improve the Distortional Strength of ... - Springer Link

KSCE Journal of Civil Engineering (2013) 17(7):1720-1727 Copyright ⓒ2013 Korean Society of Civil Engineers DOI 10.1007/s12205-013-0271-7

Structural Engineering

pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205

New Approach to Improve the Distortional Strength of Intermediate Length Web Stiffened Thin Walled Open Columns M. Anbarasu*, D. Amali**, and S. Sukumar*** Received May 31, 2012/Accepted February 1, 2013

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Abstract This paper describes a method which can be adopted to improve the distortional strength of web stiffened thin walled Cold formed Steel columns under axial compression by adding simple spacers. Two types of sections were considered. Totally, eight columns were experimented with hinged-hinged end condition, four columns from each type. The section properties and length of the columns are predicted by performing elastic buckling analysis using CUFSM software. Finite Element Models were developed by using ANSYS and validated on the basis of the test results and very good agreement was achieved. This was followed by an extensive parametric study of the influence of spacers by varying the depth and number of spacers. Experimental and numerical strength of two types of open sections were compared with the predicted resistance by AS/NZ specifications for effective width and direct strength method. Details of this investigation and the results are presented in this paper. Keywords: axial compression member, thin walled member, distortional buckling, spacer ··································································································································································································································

1. Introduction A cold formed profile is naturally an open profile. In compression, cold formed open cross-section can exhibit three modes of instabilities: Local, distortional and flexural or flexural-torsional buckling. Local modes and global modes (i.e., flexural and flexuraltorsional buckling) are largely covered in the main design codes by means of effective widths for the plate elements and by column design equations for global buckling. Interaction of local and global modes is also considered in these codes. Interaction mode between local and overall buckling is called distortional buckling. Distortional buckling plays an important role in the use of open cold formed steel columns. The occurrence of the distortional buckling depends on the sectional geometry and the length of the member. Distortional buckling occurs at intermediate length between the lengths where local and overall buckling occurs. In the past, researchers have investigated the various buckling modes of commonly used cold-formed steel sections. A brief review of literature on the ultimate strength and buckling modes of cold-formed steel columns are presented here. Takahashi (1978) was the first to publish a paper describing distortion of thin walled open section. The design equations taking account of distortional buckling are based on the works of Hancock, Davies and co-workers (1996) (see, for example, Lau and Hancock (1987) and Davies and Jiang (1996)). The use of

Generalized Beam Theory (GBT) pioneered by Schardt (1989) and improved by Davies et al. has led to a better understanding of complex distortional buckling mode. Hancock (1985) presented a detailed study of a range of buckling modes (Local, distortional, and flexural-torsional) in a lipped channel sections. Lau and Hancock (1990) provided design curves for sections where the distortional buckling stress and yield stress were approximately equal. Kwon and Hancock (1992) studied simple lipped channels and lipped channels with intermediate stiffener under fixed boundary conditions. They chose section geometry and yield strength of steel to ensure that a substantial post-buckling strength reserve occurs in a distortional mode for the test section. Distortional buckling strength of few innovative and complex geometrical sections have been studied by Narayanan and Mahendran (2003). For intermediate length pallet rack columns, the distortional strength was studied by providing spacers to connect the flanges of upright sections by Talikoti and Bajoria (2005). The partly closed thin walled steel columns were studied by Veljkovic and Johanson (2008). Kwon et al. (1990) studied the buckling interaction of the channel columns. Anil Kumar and Kalyanaraman (2010) studied the evaluation of direct strength method for CFS Compression members without stiffeners. Though many studies have been performed on buckling of thinwalled columns, no studies have been made on effect of spacers on

*Assistant Professor, Dept. of Civil Engineering, Government College of Engineering, Salem 636011, India (Corresponding Author, E-mail: gceanbu@ gmail.com) **Assistant Professor, Dept. of Civil Engineering, Government College of Engineering, Salem 636011, India (E-mail: [email protected]) *** Professor, Dept. of Civil Engineering, Government College of Engineering, Salem 636011, India (E-mail: [email protected]) − 1720 −

New Approach to Improve the Distortional Strength of Intermediate Length Web Stiffened Thin Walled Open Columns

the behavior and strength of intermediate length cold formed steel open columns. This paper describes the details of such a study. The objective of the paper is to propose a new approach to improve the strength of the intermediate length pin-ended open columns by adding the simple spacers externally. Spacers are the transverse elements of CFS sheet used to connect the lips of the open sections using self-driving screw. For this work, two types of sections are considered Type-I section with lip projecting inwards (channel) and Type-II section with lip projecting outwards (hat). An accurate finite element model simulating the behavior of these two types of sections is developed. The results obtained from the finite element analysis are verified against the tests conducted on these two types of sections. Totally eight columns are tested (4 Nos of Type-I and 4 Nos of Type-II). Parametric study is performed to investigate the effect of spacers on the behavior and strength of these sections by varying the depth and interval of spacers. The results obtained from the numerical analysis and experimental study for the full open sections are compared with design strength calculated using the Australian/New Zealand standard AS/NZ4600 (2005) (EWMClause 3.4 and DSM-Clause 7) and Indian standard IS 801 (1975) for cold-formed steel structures.

Fig. 2. (a) Type-I (Channel) Columns, (b) Type-II (Hat) Columns Table 1. Specimen Details

2. Testing Program The dimensions of the cross section are keeping the plate slenderness ratio within limits to eliminate local buckling as per IS 801 (1975). The length of 1000 mm was chosen for both the type of sections. The intermediate length were chosen to investigate the distortional buckling by performing elastic buckling analysis using CUFSM software. Fig. 1 shows the typical buckling plot of Type-II specimen obtained from CUFSM software. The dimensions and the section configuration for Type-I and Type-II Columns are shown in Fig. 2(a) and Fig. 2(b), respectively. Eight cold-formed steel columns, four Nos of channel columns and four Nos of hat columns with and without spacers were tested to failure. The details of the specimen and their labelling are given in Table 1. The representation of the labelling is the first term ‘T1’ denotes the type of column, second term ‘C’ the cross section type, third term ‘S0’ the number of spacers and the last term ‘d-50’ the depth of the spacer. The primary experimental parameters are column cross section and presence of spacers. The column compression tests are

Fig. 1. Typical Buckling Plot for Type-II (Hat) Section Columns Vol. 17, No. 7 / November 2013

performed with the 400 kN capacity loading frame. The specimens are mounted between the platens and its verticality is checked. At either ends between the platens and the end plates of the specimen rubber gasket were placed to facilitate the hinge condition at either supports. Dial gauges were placed at mid height on web and flange to measure lateral displacement and one at the lower end to measure the axial deformation. The details of test arrangement are shown in Fig. 3. The lateral and axial displacements of the column were recorded after every increment of 2000 N load. The critical load at which the deflection increased without increase of load is also recorded. The tensile coupon tests were carried out in accordance with IS 1608-2005 (Part-1). The properties obtained from coupon test are listed below: Poisson’s Ratio (m) = 0.3 Tangent Modulus (Et) = 20.12 Gpa = 450 Mpa Ultimate Stress (fu) = 350 Mpa Yield Stress (σy) Young’s Modulus (E) = 201 GPa % of elongation = 27%

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M. Anbarasu, D. Amali, and S. Sukumar

Fig. 6. Load vs Axial Deformation Curve for Type-I Columns

Fig. 3. Experimental Setup

Fig. 7. Load vs Axial Deformation Curve for Type-II Columns

Fig. 4. Stress-Strain Curve of the Sheet

The stress strain curve of a tensile test on a coupon made from parent sheet is shown in Fig. 4. 2.1 Test Results The deformed shape of Type-I and Type-II columns are shown in Fig. 5(a) and Fig. 5(b), respectively. On observation it clearly

Fig. 5. (a) Deformed Shape of Type-I Columns, (b) Deformed Shape of Type-II Columns

indicates that the predominant mode of failure of the fully opened section in case of both types of columns is distortional buckling. Also the failure mode change from distortional buckling to local buckling is inferred due to the provision of spacers. The Load Vs axial deformation curves for both the columns in Fig. 6 and Fig. 7.

3. Finite Element Model The numerical simulations were performed with ANSYS program. Shell 181 four noded finite linear strain element were used for meshing of the model. The element has six degrees of freedom per each node. This element accounts for finite strain and is suitable for large strain analysis. The influence of round corners with internal radius r ≤ 5t was neglected and the cross section was assumed to consists plane element with sharp corners. The strain hardening of the corners due to cold forming is neglected. Two types of analysis were carried out. The first is eigen value analysis to determine the buckling modes and load, where the second is non-linear analysis. The elastic modulus (E) was taken as 201000 N/mm2. Convergence study is performed to obtain an optimal element size used for the study. The yield stress of the material (σy) considered 350 N/mm2. In order to account for the

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KSCE Journal of Civil Engineering


Elasto-plastic behaviour, a bilinear stress-strain curve is adopted, having a tangent modulus (Et) of 20120 N/mm2. The pin-end conditions of the columns were modeled with the loaded end prevented from both rotation about the y-axis, and translations in both x and z directions. On the other hand, the unloaded end is prevented from translation in the three directions x, y, and z and from rotation along the y-axis. A rigid surface was modeled in the loaded end. The load was applies in increment through the master node which is modeled at the centroid of the section. The material and geometric nonlinearity is included in the finite element model. In the nonlinear analysis, initial geometric imperfections are modeled by providing initial out-of-plane deflections to the model. The local and distortional buckling mode shapes are extracted from linear buckling analysis and scaled to percentage of thickness is used to create a geometric imperfection for the non-linear analysis. The maximum value of distortional imperfection was taken equal to the plate thickness as recommended by Schafer and Pekoz (1998). Local buckling imperfection was taken as 0.25 times the thickness. Since kwon and Hancock (1992) found that the overall imperfections had little effect on the buckling of the columns of intermediate length since these columns generally buckled in a local, distortional, or mixed mode of local and distortional buckling. Therefore this study does not include any overall imperfections in finite element modelling. The residual stresses were not included in the non-linear analysis since their effect on the ultimate load is considered to be negligible as recommended by Schafer and Pekoz (1998).

Fig. 8. Correlation of FEA with Test Results

Fig. 9. Comparison of Results

4. Verification of the Finite Element Model In the verification of the finite element model, a total of 8 coldformed steel columns are analyzed. A comparison between the Table 2. Comparison of the Test Strengths (PEXP) with Numerical Strength (PFEA) Sl. no 1 2 3 4

Sl. no 5 6 7 8

Experimental Results (kN) PEXP T1-C-S0 125.00 T1-C-S1-d50 136.00 T1-C-S2-d50 168.50 T1-C-S3-d50 173.12 Specimen

Numerical Results (kN) PFEA 128.90 139.90 172.00 180.80 Mean = Standard deviation =

Numerical Results (kN) PFEA 140.540 175.502 160.141 176.906 Mean = Standard deviation

Experimental Results (kN) PEXP T2-H-S0 136.00 T2-H-S1-d50 171.25 T2-H-S2-d50 157.14 T2-H-S3-d50 162.29 Specimen

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PEXP/PFEA 0.97 0.97 0.98 0.96 0.97 0.01

PEXP/PFEA 0.97 0.98 0.98 0.92 0.96 0.03

experimental results and the results obtained from the finite element analysis is carried out. The main objective of this comparison is to verify and check the accuracy of the finite element model. The comparison of ultimate loads (PEXP and PFEA) for T1-C and T2-H series are shown in Table 2. It can be seen that good agreement has been achieved between the experimental and numerical results of all the columns. The mean values of PEXP/PFEA ratio are 0.97 and 0.96 with the corresponding standard deviation of 0.01 and 0.03 for T1-C and T2-H series respectively. Fig. 8 shows the deformed shape of the T1-C-S0 and T2-H-S1-d50 column observed experimentally and confirmed by the FE analysis. It can be seen that the finite element model closely predicted the failure mode observed in the test. Load versus axial shortening curves predicted by FEA are compared with the experimental curves as shown in Fig. 9 for specimen T1-C-S0. It is shown that the load versus axial shortening curve predicted by FEA follow closely the experimental results. Similar results are obtained for all the specimens.

5. Parametric Study It is shown that the FEM closely predicted the column strengths and the behavior of the tested specimens. Hence the parametric − 1723 −


In case of Type-I column, the width of the spacer is 235 mm. Hence four group of sections are formulated based on the ‘d/S’ ratio. They are 0.085, 0.128, 0.170,0.213 & 0.255. Since the number of spacers varies in each group from 1 to 3, the ‘l/L’ ratio varies from 0.50, 0.33 and 0.25. Similarly, in case of Type-II column, the width of the spacer is 265 mm. Hence four group of sections are formulated based on the ‘d/S’ ratio. They are 0.075, 0.113, 0.151, 0.189 and 0.226. The variation of ‘l/L’ is similar to Type-I columns. The Slenderness ratio of both Type-I and Type-II column is 32.5. The Numerical analysis is carried out for all the specimens and the results are shown in Figs. 11-15 and 16 for both Type-I columns and Type-II columns. Fig. 10. Geometry of the Columns

6. Numerical Results

study was carried out using the verified finite element model to study the effect of spacers on the strength and behaviour of intermediate length columns. There are several parameters that have direct influence on the response/behaviour of the column. The descriptions of the parameters that are illustrated in Fig. 10 are as follows: The term ‘λs’ which is defined as the spacer plate slenderness ratio and is given by: σ d λs = --- × -----y E t

(1)

The Numerical analysis is carried out for all the specimens and the results are graphically represented in the following sub sections. Appendix-I and Appendix-II shows the numerical result details of the parametric study for Type-I and Type-II columns, respectively. Figures 12 and 13 demonstrates the relationship between the normalized ratio of the centre to centre length between spacers to the overall length of the Column (l/L), and the normalized ratio of the ultimate stress to the yield stress of the column (σu/σy) for different values of (d/S). Obviously, the centre to centre length

− The overall column length (L), which is represented in the form of an integrated slenderness ratio (λ) of the Column. − The term l/L which is defined as the ratio of the center to center distance (l) between spacers to-the overall length (L) of the Column. − The term d/S which is defined as the ratio of the depth of the spacer plate-to-the width of the spacer plate. A total of 30 Nos. of specimens (i.e., 15 of Type-I Column and 15 Nos. of Type-II columns) were analyzed numerically with the help of the developed model. The combination of the no. of spacers and the depth of the spacers are shown schematically in Fig. 11. Fig. 12. σu/σy vs l/L for T1-C Series

Fig. 11. Schematic Representation of Parametric Study

Fig. 13. σu/σy vs l/L for T2-H Series − 1724 −



Fig. 17. σu/σy vs λs/λ for T2-H Series

Fig. 14. σu/σy vs d/S for T1-C Series

Table 3. Theoretical Analysis Results Specimen ID T1-C-S0 T2-H-S0

Ultimate Load in kN Experiment AS/NZ -DSM AS/NZ-EWM IS Method 125 117.22 111.74 182.87 136 124.24 117.05 185.99

ratio on the column strength for a slenderness ratio of 32.50. Apparently, for Type-I columns as shown in Fig. 16 the column strength uniformly increases with the increase in plate slenderness ratio. Similar pattern is found for Type-II columns also, but nonuniformly. Fig. 15. σu/σy vs d/S for T2-H Series

7. Theoretical Analysis

Fig. 16. σu/σy vs λs/λ for T1-C Series

between spacers has a significant effect on the strength of columns. As the centre to centre length between spacers increases, the corresponding ultimate load decreases. Increasing the number of spacers from 1 to 3 improved the ultimate strength of the columns for both the type of sections. Figures 14 and 15 demonstrate the influence of changing the depth of the spacer plate on the column strength for a slenderness ratio of 32.50. Apparently, for Type-I columns as shown in Fig. 14 the column strength uniformly increases with the increase in depth of the spacer plate. Similar pattern is found for Type-II columns also, but non-uniformly. Figures 16 and 17 demonstrate the influence of plate slenderness Vol. 17, No. 7 / November 2013

The unfactored design column strengths were calculated for fully opened section using the Indian standards (IS 801, 1975), Australian/New Zealand Standards (EWM-Clause 3.4 and DSMClause 7). The comparison of the unfactored design strengths predicted using the Australian/New Zealand (4600-2005), Direct strength method (AS/NZ 4600 (2005) (DSM-Clause 7)) and Indian Standard method (IS 801, 1975) are shown in Table 3. The design strength predicted by the AS/NZ 4600 (2005) (EWM-Clause 3.4 and DSM-Clause 7) standard are conservative for both the series T1-C & T2-H. Since the predominant mode of failure of intermediate length columns is distortional, the mode of failure inferred from EWM and DSM of AS/NZ specifications was distortional buckling. Whereas in IS method, the mode of failure inferred was flexuraltorsional as there is no check for distortional buckling. Hence the IS method shows an elevated result than the other two specifications. So, it is mandatory that the IS code has to be revised incorporating the distortional buckling check.

8. Discussions It is observed that relationship between spacer plate slenderness ratio (λs), ratio of length (l/L) and ratio of depth to width of spacer plate (d/S) on the ultimate strength of columns under axial

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load varies non-linearly. From the parametric study, it is ascertained that interaction between parameters like spacer plate slenderness ratio (λs), ratio of length (l/L) and ratio of depth to width of spacer plate (d/S) influence the strength of the columns. The effect of yield stress (σy) and Young’s modulus of elasticity (E) of the material are taken care in the calculation of spacer plate slenderness ratio. With the addition of spacers in both the type of sections, the failure mode shifted from distortional mode to interference of local and distortional mode, since the spacers help in enhancing the torsional rigidity of the section, their by enhancing the load carrying capacity.

9. Conclusions Numerical investigations of pin ended web stiffened cold formed steel columns using finite element analysis have been presented. The finite element model including geometric and material nonlinearities has been developed and verified against experimental results. The finite element analysis predictions were generally in good agreement with the experimental ultimate loads of two types of columns. An extensive parametric study of varying the depth and number of spacers has been performed using the developed finite element model. For open sections, the results obtained based on the AS/NZDSM and AS/NZ-EWM codal provisions are conservative. The mode of failure predicted by IS codal provision is Flexural torsional and the design strength is unconservative. Because the code does not provide check for distortional buckling. This means that a further improvement of IS 801 (1975) by calibrating the resistance formulae to the experimental data is required. The effect of spacers on the ultimate strength under axial compression is found. The effect of spacer plate slenderness ratio to slenderness ratio of the column (λs/λ), clear distance between the spacer plates-to-the overall length of the column (l/L), spacer plate depth-to-the width of the spacer plate (d/S) on ultimate strength is determined using non-linear finite element analysis. The provisions of spacers increase the ultimate strength for both types of sections. The ultimate strength increases with increase in depth and number of spacers. This investigation has shown that the use of spacers at proper width and intervals do help increasing not only load carrying capacity but also vary mode of failure due to enhancement in the torsional rigidity of the sections. This investigation has also shown that further research is needed in this area to add the effect of spacers in the design

codal provisions for intermediate length columns.

References Anil Kumar, M. V. and Kalyanaraman, V. (2010). “Evaluation of direct strength method for CFS compression members without stiffeners.” Journal of Structural Engineering, Vol. 136, No. 7, pp. 879-885. AS/NZ 4600 (2005). Cold-formed steel structures, Australian/New Zealand Standard. Davies, J. M. and Jiang, C. (1996). “Design of thin-walled columns for distortional buckling.” Proceedings of the 2nd International Conference on Coupled Instabilities in Metal Structures, Liege, Belgium, Imperial College Press, pp. 141-8. Hancock, G. J. (1985). “Distortional buckling of steel storage rack column.” Journal of Structural Engineering ASCE, Vol. 111, pp. 2770-2783. IS 801 (1975). Design of cold formed steel structures. Kwon, Y. B. and Hancock, G. J. (1992). “Tests of cold formed channel with local and distortional buckling.” Journal of Structural Engineering, ASCE, Vol. 117, No. 2, pp. 1786-1803. Lau, S. C. W. and Hancock, G. J. (1987). “Distortional buckling formulas for channel column.” Journal of Structural Engineering, ASCE, Vol. 113, No. 5, pp. 1063-78. Lau, S. C. W. and Hancock, G. J. (1990). “Inelastic buckling of channel columns in the distortional model.” Thin Walled Structures, Vol. 29, No. 1, pp. 59-84. Leach P., Davis J. M. (1996). “An experimental verification on the generalized beam theory applied to interactive buckling problems.” Thin Walled Structures, Vol. 25, No. 1, pp. 61-79. Milan Veljkovic, and Bernt Johansson. (2008), “Thin-walled steel columns with partially closed cross-section: Tests and computer simulations.” Journal of Constructional Steel Research, Vol. 64, Nos. 7-8, pp. 816-821. Narayanan, S. and Mahendran, M. (2003). “Ultimate Capacity of Innovative Cold-formed Steel Columns.” Journal of Constructional Steel Research, Vol. 59, No. 4, pp. 489-508. Schafer, B. W. and Pekoz, T. (1998). “Computational modelling of coldformed steel: Characterizing geometric imperfections and residual stresses.” Journal of Construct Steel Research, Vol. 47, No. 3, pp. 193-210. Schardt, R. (1989). Verallgemeinerate technische biegothoorie, Berlin: Springer. Takahashi, K. and Mizuno, M. (1978). “Distortion of thin-walled open section member.” Bulletin of the Japan Society of Mechanical Engineers, Vol. 21, No. 160, pp. 1448-58. Talikoti, R. S. and Bajoria, K. M. (2005). “New approach to improving distortional strength of intermediate length thin-walled open section columns.” Electronic Journal of Structural Engineering, Vol. 5, pp. 69-79.

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Appendix

Table 4. Numerical Analysis Results of Type-I Columns Specimen ID T1-C-S1-d20 T1-C-S2-d20 T1-C-S3-d20 T1-C-S1-d30 T1-C-S2-d30 T1-C-S3-d30 T1-C-S1-d40 T1-C-S2-d40 T1-C-S3-d40 T1-C-S1-d50 T1-C-S2-d50 T1-C-S3-d50 T1-C-S1-d60 T1-C-S2-d60 T1-C-S3-d60

No. of spacers 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Depth of spacers in mm 20

30

40

50

60

Interval of spacers in mm 500 333 250 500 333 250 500 333 250 500 333 250 500 333 250

l/L 0.500 0.333 0.250 0.500 0.333 0.250 0.500 0.333 0.250 0.500 0.333 0.250 0.500 0.333 0.250

d/S 0.0851

0.128

0.170

0.213

0.255

Slenderness ratio of spacer (λs) 0.523 1.046 1.569 0.784 1.568 2.353 1.045 2.091 3.137 1.307 2.615 3.922 1.569 3.137 4.706

σu/σy 0.4946 0.5072 0.5199 0.5036 0.5199 0.5289 0.5052 0.5325 0.6648 0.5350 0.6570 0.6910 0.5940 0.6740 0.7210

Table 5. Numerical Analysis Results of Type-II Columns Specimen ID T2-H-S1-d20 T2-H-S2-d20 T2-H-S3-d20 T2-H-S1-d30 T2-H-S2-d30 T2-H-S3-d30 T2-H-S1-d40 T2-H-S2-d40 T2-H-S3-d40 T2-H-S1-d50 T2-H-S2-d50 T2-H-S3-d50 T2-H-S1-d60 T2-H-S2-d60 T2-H-S3-d60

No. of spacers 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Vol. 17, No. 7 / November 2013

Depth of spacers in mm 20

30

40

50

60

Interval of spacers in mm 500 333 250 500 333 250 500 333 250 500 333 250 500 333 250

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l/L 0.500 0.333 0.250 0.500 0.333 0.250 0.500 0.333 0.250 0.500 0.333 0.250 0.500 0.333 0.250

d/S 0.075

0.113

0.151

0.189

0.226

Slenderness ratio of spacer (λs) 0.523 1.046 1.569 0.784 1.569 2.353 1.046 2.092 3.137 1.307 2.615 3.922 1.569 3.137 4.706

σu/σy 0..5370 0.5371 0.5375 0.5371 0.5372 0.5386 0.6517 0.5893 0.6384 0.6708 0.6121 0.6762 0.6120 0.6270 0.6760