鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) AN EVALUATION METHOD FOR ULTIMATE COMPRESSIVE STRENGTH OF STAINLESS STEEL PLATES BASED ON STRESS-STRAIN DIAGRAM * ** Yasuhiro MIYAZAKI* Satoshi NARA** ABSTRACT This paper proposes a method for predicting precisely ultimate strength and displacement of stainless steel plates under uniaxial compression. Based on stress-strain diagrams of stainless steels obtained by coupon tests, the method consists of two classified parts. At the first part, the ultimate strength is estimated by plate slenderness and proposed constants of each stainless steel in the region of elastic buckling. In the region of apparent difference of the stress-strain diagrams between stainless steel and mild steel, the ultimate strength is calculated by predicted ultimate displacement and stress-strain diagrams. The proposed method is independent of proof stress which is 0.1% or 0.2%, because of a proposed conversion factor. Key words: Stainless Steel, Ultimate Strength, Strain Hardening, Ductility, Plate Slenderness 1 [1], [2] [3], [4] [1] [5] JIS * 940-8532 888 ** 2 565-0871 2-1 [6] Gardner [7] Mahmud [8] [1] Mahmud [8] 67
Steel Construction Engineering Vol.20 No.79 (September 2013) [9], [10] [11] [9], [10] 2 SUS304, SUS316, SUS304N2 SUS410L SUS329J3L JIS E 1 % Grade C Si Mn P S Ni Cr Mo N SUS304 0.08 1.00 2.00 0.045 0.030 8.00 10.50 18.00 20.00 SUS304N2 0.08 1.00 2.50 0.045 0.030 7.50 10.50 18.00 20.00 0.15 0.30 SUS316 0.08 1.00 2.00 0.045 0.030 10.00 14.00 16.00 18.00 2.00 3.00 SUS410L 0.03 1.00 1.00 0.040 0.030 11.00 13.50 SUS329J3L 0.03 1.00 2.00 0.040 0.030 4.50 6.50 21.00 24.00 2.50 3.50 0.08 0.20 2 Young s 0.1% proof 0.2% proof ultimate tensile yield Grade modulus stress stress stress elongation ratio E(GPa) 0.1 (MPa) 0.2 (MPa) u (MPa) (% ) 0.2 / u SUS304 157 236 261 697 70.2 0.374 SUS304N2 173 360 402 723 66.5 0.557 SUS316 174 230 254 561 75.9 0.452 SUS410L 204 346 362 487 38.6 0.744 SUS329J3L 202 485 533 749 47.9 0.712 1 (1) 3 Ramberg-Osgood [9] if 0 < P E ε = E + ε A if P < 0.2 (1) E + ε B + ε C if 0.2 ε P (= 0.01 ) 0.2 0.2% ε A ε B, ε C (2) (3), (4) ε A = 0.002 n n P n 0.2 n P ε B = 0.002nn 1 0.2 0.2 n + ε 0.2 0.2 n P E 0.2 (2) (3) 68
鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) 3 3 Ramberg-Osgood 0.01% proof material parameter Grade stress n m ε 0.2 E 0.2 ε 10 10 0.01 (MPa) (MPa) (MPa) SUS304 143 2.88 1.67 0.00350 29700 0.100 481 SUS304N2 253 3.93 1.79 0.00415 34400 0.100 680 SUS316 162 6.97 1.74 0.00349 16500 0.0823 457 SUS410L 306 15.2 1.25 0.00382 11400 0.101 523 SUS329J3L 346 7.01 2.52 0.00469 30900 0.0597 729 ε C = ε 10 ε 0.2 m 10 0.2 0.2 E 0.2 10 0.2 (4) m,n ε 0.2 0.2% E 0.2 0.2% ε 10 (10% ) 10 (ε 10 ) (1) (4) (1) (1) (4) 3 3.1!! (5) F (0.1% 0.1 0.2% 0.2 ) (=0.3) k (k=4.0)!! b t α(=a /b) 1.0 [11] w 0 (6) λ p = b t F E w 0 = w 0,a cos πx a 12(1 ν 2 ) π 2 k cos πy b (6) a (6) w 0,a b /150 2 3 bc bt [12]!!" =!!.!!!" = 0.3!!.! (7) 69
Steel Construction Engineering Vol.20 No.79 (September 2013) rt rc 3.2 (5) ( k=0.425) α(=a/b) 3.0 (8) y πx w 0 = w 0,a cos b a (8) (8) w 0,a b /100 [11] [12]!!" =!!.!!!" = 0.4!!.! (9) 4 Lagrange von Mises 4 [11] SUS316 P 0.2% P0.2 0.2% 0.2 4 8 [11] 1.5 1% 5 SUS304 (a) 4 SUS316 (b) 5 SUS304 70
鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) 4 (10) Boundary condition Type Material strength λp,cr b p Simply supported Austenitic F = 0.2 0.494 0.719 F = 0.1 0.544 0.720 Ferritic F = 0.2 0.457 0.662 F = 0.1 0.506 0.712 Duplex F = 0.2 0.557 0.763 F = 0.1 0.584 0.731 All F = 0.2 0.482 0.690 F = 0.1 0.529 0.705 Outstanding Austenitic F = 0.2 0.565 0.466 F = 0.1 0.606 0.417 Ferritic F = 0.2 0.606 0.396 F = 0.1 0.613 0.353 Duplex F = 0.2 0.572 0.430 F = 0.1 0.647 0.403 All F = 0.2 0.583 0.436 F = 0.1 0.618 0.397 6 0.3 5 4.1 u F!! (10) [13]!!!! =!!!,!"!!!!!!!,!"!!! (10a, b)!!!!,!" <!!! u γ b!!,!" [13] 0.7 b p [13] 0.86 (10) 7 (10) ( ) (10) (10)!!,!" b p γ b 1.0 (10b)!!,!" b p (10b) F 0.2% F 0.1% (10b) u F (10) (10) ( u / F ) pre ( u / F ) mea 71
Steel Construction Engineering Vol.20 No.79 (September 2013) (10b) 5% (10a) -5% 4.2 (10) (10b) (10b)!!,!" b p (10b) F 0.2% F 0.1% (10) u F (10) (10) ( u / F ) pre ( u / F ) mea 5% (10a) 5% 5 5.1 (10) ( ) β 72
鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) Gardner [14] (11) ε u ( β 1.5 ) εu 6.44 = ε β 0 2.85 0.27β (11) ε 0 0.2% β (12) b 0.2 4 = t E k β (12) (11) [8] [11] (11) [11] [8] (11) (11) (13) C ε u = 1 C (13) 2 ε F λp ε F C 1 C 2 (13) (13) C 1 C 2 (13) (13) (13) 5.2 4 (10) Gardner [14] (13) (1) u 5 (13) Boundary condition Type Material strength C 1 C 2 Simply supported Austenitic F = 0.2 0.565 2.64 F = 0.1 0.510 2.69 Ferritic F = 0.2 0.270 3.06 F = 0.1 0.283 3.02 Duplex F = 0.2 0.688 2.45 F = 0.1 0.626 2.50 All F = 0.2 0.471 2.73 F = 0.1 0.442 2.76 Outstanding Austenitic F = 0.2 0.886 2.49 F = 0.1 0.803 2.55 Ferritic F = 0.2 0.209 3.41 F = 0.1 0.418 2.78 Duplex F = 0.2 0.793 2.58 F = 0.1 0.754 2.61 All F = 0.2 0.549 2.80 F = 0.1 0.589 2.74 73
Steel Construction Engineering Vol.20 No.79 (September 2013) 10% 29% 10% 4% (13) (14) C u ( χ λ p ) = exp (14) χ (14) (13) 5% 6 (14) χ Boundary condition Type Material strength χ Simply supported Austenitic F = 0.2-0.125 F = 0.1-0.176 Ferritic F = 0.2-0.0576 F = 0.1-0.0808 Duplex F = 0.2-0.0484 F = 0.1-0.0588 All F = 0.2-0.0731 F = 0.1-0.113 Outstanding Austenitic F = 0.2-0.0535 F = 0.1-0.0409 Ferritic F = 0.2 0.343 F = 0.1 0.289 Duplex F = 0.2 0.0192 F = 0.1-0.00132 All F = 0.2 0.0902 F = 0.1 0.0762 74
鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) 5% 16% (14) (14) 5% 7% (14) (15)! # 1 ( G a! p +G b ) D! = u " (15) $ # 1 G c G a G b G c u (15) 75
Steel Construction Engineering Vol.20 No.79 (September 2013) (15) (14) (15) (14) (15) (14) [15] ε u,sm ε y ε u ε F (b) (d) [15] (a) ( F < u ) (b) ( F u ) (c) ( F < u ) (d) ( F u ) 76
鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) i)!! 0.2 I (13)!! =0.2 ε u (1) (14) (15) u ii) 0.2 <!! <!!,!" II (!!,!" u = F ( )) (13) ε u (1) (14) (15) u iii)!!,!"!! III (10) u SUS304 F 0.1% 0.2% (16) γ = (16) u u 0.1 0.2 γ (17) 0.2 γ = (17) 0.1 (16) (17) 0.1% 0.2% (16)!! 0.2!! 0.2!! (16) 10% 0.2% SUS304 u [15] G, SUS (14)!! 0.2 19 77
Steel Construction Engineering Vol.20 No.79 (September 2013)!! 0.2!! 1.73 2.01 6 (a) (b) ( SUS304) (1) (10) (2) (13) (3) (13) (14) 5% +16% -7% (4) (13) (15) (5)0.1% 0.2% (16) (6) 1.73 2.01 78
鋼構造論文集第 20 巻第 79 号 (2013 年 9 月 ) [1]EN1993-1-4. Eurocode 3: Design of steel structures Ð Part1.4 General rules Ð Supplementary rules for stainless steel, CEN, 1996. [2]ASCE: Specification for the Design of Cold-Formed Stainless Steel Structural Members, American Society of Civil Engineers, New York, ANSI/ASCE 8-02, 2002. [3]Euro Inox: Pedestrian Bridge in Stainless Steel, Euro Inox, Vol.7, 1 st edition, 2004. [4] JSSC, No.73, pp.14-15, 2009. [5] 1995. [6],,,, :,, 55A, pp.68-79, 2009. [7]L. Gardner, D. A. Nethercot: Numerical modeling of stainless steel structural components Ð a consistent approach, Journal of Structural Engineering, Vol. 130, pp.1586-1601, 2004. [8]Mahmud Ashraf, Leroy Gardner, David A. Nethercot: Structural stainless steel design: Resistance based on deformation capacity, Journal of Structural Engineering, Vol.134, pp.402-411, 2008. [9] SUS410L - 15 pp.633-638, 2007. [10] Vol.55A, pp.80-91, 2009. [11] 17 pp.367-374, 2009. [12] No.265, pp.25-35, 1977. [13] 2007. [14]L. Gardner, D. A. Nethercot: Structural stainless steel design: a new approach, The Structural Engineer, Vol.82, No. 21, pp. 21-28, 2004. [15] Vol.56A, pp.122-134, 2010. (2012 年 12 月 13 日原稿受理 ) 79