國內冷軋型鋼構造設計規範及解說之研擬

Transcription

1 MOIS 89014

2 (Cold-Formed Steel Structures) (88) - ( ) 1

3 ABSTRACT Recently, the cold-formed steel has been considerably adopted in the construction of steel structures such as buildings, bridges, transmission towers, and highway products due to the demand of market. Even the thickness of cold-formed steel is quite thin as compared to the structure-used steel, the cold-formed steel structure can still take sufficient load-carrying capacity. Therefore, the development of cold-formed steel structure plays a very important role in the recent and future construction field. Due to the environmental concern and lack of construction materials such as lumber, sand, and gravel, standardized single-story metal buildings have been widely used in industrial, commercial, and residential applications in U.S. and European. It can be observed that the utilization of cold-formed steel in the construction area is getting popular in Taiwan. Therefore, fully understanding the domestic conditions about the manufacture and application of cold-formed steel is the first thing to do. Meanwhile, it is necessary to establish the native specification for the design of cold-formed steel member in the near future. Due to the advantages such as lightness, high strength and stiffness, and easy to fabrication and erection, the cold-formed steel has been widely used as the construction material. Most advanced countries like U.S., Japan, Australia, and U.K. have studied the cold-formed steel for decades. However, the cold-formed steel is not included in the domestic specification or code relative to the steel construction in Taiwan, the development of cold-formed steel design specification is the way to go. The main objective of this project is to draft the design specification and commentary for cold-formed steel. In order to promote the native specification for the design of thin-walled structures (cold-formed steel members), the suggested foreign documents and related materials will be based on the previous research - "The Investigation of Design Specification for Cold-Formed Steel Structure".

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5 91 (Cold-Formed Steel) (Yu 000 SDI 1987) (carbon or low alloy steel sheet, strip, plate or flat bar) (cold roll forming, press brake or bending brake operation) in (0.378mm) 0.5 in (6.35mm)

6 -Specification for the Design of Cold-Formed Steel Structural Members (AISI 1999) -Recommendations for the Design and Fabrication of Light Weight steel structures(aij 1985) (1) () (3) (4) (National Association of Home Builders-NAHB) (U.S Department of Housing and Urban Department-HUD) (American Iron and Steel Institute-AISI) - Prescriptive Method for Residential Cold-Formed Steel Framing (AISI 1997) 5

7 ( ) (88) - ( ) steel home ( ) 6

8 RC 7

9 (American Iron and Steel Institute - AISI) (Specification for the Design of Cold-Formed Steel Structural Members) (American Institute of Steel Construction - AISC) (Design Specification for Structural Steel Buildings) (1) () (3) (4) (5) (Commentary) AISI (Allowable Stress Design - ASD) (Plastic Design - PD) ( Limit State Design or Load Resistant Factor Design) 8

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11 (Specification for the Design of Cold-Formed Steel Structural Members) 1. Word 97. Times New Roman 1 3. : :16 4. : :14 10

12 5. : :1 6. : :1 :0.8cm : :1 :1.cm : C (4.1-1) 15. [1.] [ ] [4.1] [4.] 4.5. Winter, G., Commentary on the 1968 Edition of Light Gage Cold-formed Steel Design Manual, American Iron and Institute, cm

13 % ( 000) ( 0 %) (1997) 13 % - Recommendations for the Design and Fabrication of Light Weight steel structures (British Standards Institute) British Standard: Structural Use of Steelwork in Building. Part 5. Code of Practice for 1

14 Design of Cold-formed Sections (The Steel Construction Institute) (Cold-Formed Steel Design Manual) (88) - ( ) 13

15 (National Association of Home Builders - NAHB) (U.S Department of Housing and Urban Department - HUD) - Prescriptive Method for Residential Cold-Formed Steel Framing (000) 14

16 194 George Winter 15

17 1. American Iron and Steel Institute, 1999, Specification for the Design of Cold-Formed Steel Structural Members with Commentary, 1996 Edition, Supplement No.1, July, American Iron and Steel Institute, 1997, Prescriptive Method for Residential Cold-Formed Steel Framing, Second Edition. 3. Architectural Institute of Japan. 1985, Recommendations for the Design and Fabrication of Light Weight Steel Structures. 4. Baehre, R., 1983, Cold-Formed Steel Structural Elements, Development in Design and Application, Instability and Plastic Collapse of Steel Structures, Ed. L.J. Morris, Granada. 5. British Standards Institution, 1987, British Standards: Structural Use of Steelwork in Building. Part 5. Code of Practice for Design of Cold-Formed Sections, BS Steel Construction Institute, 1993, Building Design using Cold-Formed Steel Sections : Worked Examples to BS 5950 : Part 5 : SDI, Steel Deck Institute, 1987, Design Manual for Composite Decks, Form Decks and Roof Decks, Canton, Ohio. 8. Yu, W.W., 000, Cold-Formed Steel Design, New York: John Wiley. 9.,

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24 mm [1.1] [1.] 1. (hot-rolling) (uneven cooling). 3. (cold-rolling) (anneal) (cold-reducing stress) 4. (element) 5. (sharp-yielding type) (gradual- yielding type) (corner fillet) (Specification for the Design of Cold-Formed Steel Structural Members) [1.3] [ ]

25 1.3 (LRFD) φr n R u (1.3-1) R u = R n = φ = φr n = (Limit State) (post-buckling) [ ] LRFD (1) () LRFD r i Q i φr n (C-1.3-1) R u φr n R n φ ( ) φ<1.0 Q i r i LRFD (1) () (a) Q R ( C-1.3-1) R<Q 1 -

26 Q R Q m R m Q R Q m R m Q R C Q R βσ ln(r/q) ln(r/q) m ln(r/q) C-1.3- C-1.3- l n (R/Q) ln(r/q) 0 R m Q m R Q * ln(r/q)= ln(r/q) m ln(r/q) 0 1-3

27 R ln( m ) Qm β = (C-1.3-) VR + VQ V R = R /R m V Q = Q /Q m S e F y / = L S S/8D+L C S e = =5/3 F y = L s = S= D L R m [1.8] R m = R n (P m M m F m ) (C-1.3-4) R n R n = S e F y (C-1.3-5) P m = ( / ) M m =( / ) F m =( / ) R V = V + V + V (C-1.3-6) R P M F [ ] P m =1.11 V p =0.09 M m =1.10 V M =0.10 F m =1.0 V F =0.05 R m =1. R n V R =0.14 Q m = (L S S/8)(D m +L m ) 1-4

28 (C-1.3-7) ( DmVD ) + ( LmVL ) VQ = (C-1.3-8) Dm + Lm D m L m V D V L D m =1.5D V D =0.1 L m =L V L =0.5[1.11] (C-1.3-7) (C-1.3-8) LS S 1.05D Qm = ( + 1) L (C-1.3-9) 8 L (1.05D / L) VD + VL VQ = (C ) (1.05D / L + 1) Q m V Q (D/L) LRFD (D/L)=1/5 Q m =1.1L V Q =0.1 (C-1.3-3) (C-1.3-5) D/L=1/5 =5/3 R n =L(L S S/8) (C-1.3-) R m =1. R n Rm 1..0 L( LS S /8) = =.0 Qm 1.1L( LS S /8) β = (0.14) ln(.0) + (0.1) =.79 =.79 [1.1] (b) LRFD AISI [1.8] [ ] [ ] [1.18] 0 LRFD 0=3.0 0=4.5 0=.5 D/L=1/5 =

29 .79 0=.5 0=3.5 AISI [1-3] 1.4 (E) 050 / (G)790 / (µ) /ºC 1-6

30 .1 [.1]. ( ) (1) 1.4D + L () 1.D + 1.6L + 0.5(L r S R r ) (3) 1.D + 1.6(L r S R r ) + (0.5L 0.8W) (4) 1.D + 1.3W+ 0.5L + 0.5(L r S R r ) (5) 1.D + E + 0.5L + 0.S (6) 0.9D (1.3W E) D = E = L = L r = S = R r = W = kg/m (100 psf) (3) (4) (5) (L) (3) L r [.1..3] ( ) ASCE

31 1. 1.4D. 1.D+1.6L+0.5(L S R r ) 3. 1.D+1.6(L r S R r )+(0.5L 0.8W) 4. 1.D+1.3W+0.5L+0.5(L r S R r ) 5. 1.D+1.0E+(0.5L 0.S) D-1.3W +1.0E. (a) (1) (1.4D+L) (b) 1.4 ASCE 1.6 (c) (d) 1.0 (Composite Construction) 1. D s +1.6 C W +1.4C D s = C W = C = φ ( 1.D+1.6L 0=.5 0=3.5 ) φr n = c(1.d+1.6l) = (1.D/L+1.6)cL (C-.-1) c = D/L=1/5 (C-.-1) (C-1.3-9) R n = 1.84(cL/φ) (C-.-) Q m = (1.05D/L+1)cL = 1.1cL (C-.-3) R m /Q m = (1.51/φ)(R m /R n ) (C-.-4) φ C-1.3- C C-.-4 [.4] φ = 1.51( P M F ) exp( β V + V ) (C-.-5) m m m 0 R Q -

32 0 φ 1.D+1.6L = (1.D/L+1.6)/[φ(D/L+1)] (C-.-6) D/L.3 F( ) H( ) P( ) T( ) 1.3F 1.6H 1.P 1.T. [.1] - 3

33 CNS608 (CNS) CNS 3. CNS 6183 CNS 9704 CNS

34 CNS CNS 8499 CNS 978 ASTM AWS (1) () (3) ( CNS ASTM ) 1. CNS 473 ASTM A36. ( ) CNS 947 ASTM A36 A83D A57 A ( ) CNS 469 ASTM A4 Type I 4. CNS 460 SPA-H ASTM A588 A709 Gr.50W 5. CNS 1381 (AISI) [3.1] 1. A36. A4 A A83 4. A59 5. A ( ) A57 7. A A A A A A79 [3.] CNS 6183( ) SSC 400 CNS 6183 Z L C (steel deck CNS 9704) (steel panel for roof CNS 818) (steel panel for wall CNS 8184) (steel panel for floor CNS 8186) (steel roof deck CNS 8339) CNS

35 CNS 46( ) CNS 978( ) CNS 473( ) CNS 460( ) CNS 818 CNS 8184 CNS 8186 CNS 144( ) CNS 10804( ) CNS 1005( ) CNS 8339 CNS 460( ) CNS 144( ) CNS 10804( ) CNS 9998( ) CNS 965( ) CNS 1005( ) CNS ( ) CNS 6183 SSC 400 [3.1] (1) MPa (5 80 ksi) () MPa (4 100 ksi) (3) 1.13 (4) (elongation) 10 percent (1) MPa () MPa (3) 1.08 (4) ( )F y C (a) sharp yielding type (b) gradual - yielding type (b) - (yield point) offset method strain under load method C-3.3-(a) offset method 0.% offset strain under load method ( C-3.3-(b)) 0.5% (E) 3-3

36 E / E=050 / C (a) (b) 3-4

37 C (F y ) (F ya F ya F ya F ya = C F yc +(1-C)F yf (3.4-1) C = F yf = F yc = = B c F yv /(R/t) m (3.4-) 3-5

38 B c = 3.69(F uv /F yv )-0.819(F uv /F yv ) (3.4-3) m = 0.19(F uv / F yv ) (3.4-4) R = F yv = F yu =. C [3.3] C (Strain Hardening) (Strain Aging) [3.4] C-3.4- C-3.4- A - B C - D - C D (cold-work effect) 3-6

39 (F u /F y ratio) 5. (inside-radius-to-thickness ratio, R/t) 6. [3.1] F y D C A A B C C ASTM [3.5] (1) 1.08 ()5.08cm(in) cm(8in) 7 AISI 3-7

40 % (coating) 3-8

41 4.1 C C (w/t) (1) a

42 b. I s I a D/w 0.8 ( 4.5. ) 90 () 500 (3) I s I a D/w 0.8 ( 4.5. ) 60 w t. - (c f ) (4.-1) 0.061tdE 100 c f w 4 f = (4.-1) f d av d = f av = ( ) t = w f = U 1/ 3. w f w f ( ) L/w f L/w f L L L w f I U 1/ I w f

43 ( ) c f (4.-1) w f [4.1] ( ) ( C-4.-1) [4.] 4..1 I C (h/t) (1) 60 () 300 h t ( ) h/t ( ) ( ) ( ) 4-3

44 4.. [ ] (b) λ b = w (4.3-1) λ > b = ρw (4.3-) w = C-4.3- ρ = (1-0./λ)/λ 1.0 (4.3-3) λ = w f λ = (4.3-4) k t E (4.3-4) t E k 4.0 f (1) a I f = F y f (M y ) b II f (M n ) c. 6.. f (M c /S f ) () f F n. (b d ) λ b d = w (4.3-5) λ > b d = ρw (4.3-6) w = ρ = (1) I f d f (4.3-3) (4.3-4) ρ f d 4-4

45 () II ρ λ ρ = 1 (4.3-7) 0.673<λ<λ c ρ = ( /λ)/λ (4.3-8) λ λ c ρ = ( F / f 0. / λ ) / λ (4.3-9) + y d λ c = ( w / t) Fy / E (4.3-10) λ f d f (4.3-4) ρ 1.0 (w/t) C4.3-1 kπ E f cr = (C-4.3-1) 1 µ t ( 1 )( w / ) E = k = t = w = µ = 0.3 C

46 C-4.3- (C-4.3-1) [4.10] (1) () ( C-4.3-3) C C f max F y 193 Th. v. Karman [4.11] 4.3 (1) () 4-6

47 (3) (w) (f max (b) Th. v. Karman [4.11] Winter 1946 E t E b = 1.9t (C-4.3-) f max w f max f cr /f max b w f = cr cr f max f max f (C-4.3-3) (C-4.3-) [4.] E t E b = 1.9t (C-4.3-4) f max w f max (C-4.3-4) f cr /f max b f 1 0. = cr cr f max f max f (C-4.3-5) b = ρw (C-4.3-6) ρ = ( 1 0. / max / f cr ) / f max f / f cr = (1-0. / λ) / λ 1 (C-4.3-7) λ = f / f cr = f [1(1 µ )( w / t) ] /( kπ E) max max = 1.05 / k )( w / t) f / E (C-4.3-8) ( max I f d b d I Weng Pekoz [4.1] ( ) 4-7

48 I II (b) 0.50 d h /w 0 w/t w 3d h λ b = w d (4.3-11) h d w 1 λ w λ > b = λ (4.3-1) b w - d h w = d h = λ = (4.3-4). h (4.3-1) (b d ) ( I) 4.3. Ortiz-Colberg Pekoz [4.13] Yu [4.10] b 1 b ( C ) b 1 = b e / (3 - ψ) (4.3-13) ψ b = b e / (4.3-14) b 1 +b ψ > b = b e b 1 (4.3-15) b e = f 1 f k k = 4+(1-ψ) 3 +(1-ψ) (4.3-16) ψ = f / f 1 (4.3-17) f 1 f = C

49 f 1 (+) f (-) (+) f 1 f f 1 f. f d1 f d f 1 f f d1 f d (C-4.3-1) (h/t) (k) 3.9 ( C-4.3-1) Pekoz [4.14] Cohen Pekoz [4.15] C

50 C (b) k 0.43 (w) C (b d ) I k 0.43 f d f f d (w/t) 4-10

51 (C-4.3-1) (k) 0.43 ( C ) C (b) k 0.43 f 3 f f 3 C (b d ) I k 0.43 f d3 f f d3 Pekoz [4.14] Winter ( C-4.3-4) k=0.43 f 4.5 A s = A s A se = ( 4-11

52 ) b 0 = C C 1, C = C-4.5- d, D = C-4.5- d s = d s 4.5. d se = d s = I a = I s = k = S = 1.8 E / f (4.5-1) C-4.5- I s = (d 3 t sin θ)/1 (4.5-) A se = d se t (4.5-3) U I C

53 C ( ) Pekoz [4.14] C b 0 / t S I a = 0 ( ) 4-13

54 b = w (4.5-4) A s = A se (4.5-5) S < b 0 / t < 3S I a /t 4 = [50(b 0 /t)/s]-50 (4.5-6) b A s k = 3(I s /I a ) 1/ +1 4 (4.5-7) A s = A se (I s /I a ) A se (4.5-8) b 0 / t 3S I a /t 4 = [18(b 0 /t)/s]-85 (4.5-9) b A s k = 3(I s /I a ) 1/ (4.5-10) A s = A se (I s /I a ) A se (4.5-11). (b d ) (4.5.1) f d f Bulson [4.16] Pekoz [ ] ( ) (b) (A s ) I s /I a I s I a I a w / t S / 3 I a = 0 ( ) b = w (4.5-1) d s = d se (4.5-13) A s = A se (4.5-14) S / 3 < w / t < S I a {[( w / t) / S] k / 4} 3 4 / t 399 u = (4.5-15) n = 1/ C = I s / I a 1 (4.5-16) C 1 = C (4.5-17) b = k = C n (K a - K u ) + K u (4.5-18) 4-14

55 k u = 0.43 (1) D/w θ 40 (θ C-4.5- ) k a = (D/w) 4.0 (4.5-19) d s = C d se (4.5-0) () w / t S k a = 4.0 A s = C A se (4.5-1) I a /t 4 = [115(w/t)/S]+5 (4.5-) C 1 C b k d s A s (S/3<w/t<S ) n = 1/3. (b d ) (4.5.) f d f Desmond Pekoz Winter [4.18] Pekoz Cohen [4.14] (4.5-3) 4 I / t 3.66 ( w / t) (0.136E) / F 18.4 (4.5-3) min = y w/t = ( ) I s = (b<w) (b<w) 4-15

56 b = w ( ) (b 0 ) (t s ) t s (4.5-4) t 3 s = 1I sf / b0 (4.5-4) I sf = ( ) ( ) 4. w/t > 60 (b e ) b e b w = (4.5-5) t t t w/t = b = b e = b e ( ) (A st ) (A ef ) (1) 60<w/t<90 A ef = αa st (4.5-6) α = (3-b e /w) 1/30(1-b e /w)(w/t) (4.5-7) () w/t 90 A ef = (b e /w)a st (4.5-8) A ef A st (I s ) (4.5-3) ( ) 4-16

57 ( ) (b 0 ) (t s ) w/t ( ) 60 C C

58 (P n ) (4.6-1) (4.6-) P n = F wy A c (4.6-1) P n = 7. (4.6-) ( A e A b ) φ c = 0.85 A c = 18t +A s A c = 10t +A s F wy = (F y or F ys ) A b = b 1 t+a s A b = b t+a s A s = b 1 = 5t[0.004(L st /t)+0.7] 5t b = 1t[0.0044(L st /t)+0.83] 1t L st = t = (w/t s ) 1.8(E/F ys ) 1/ 0.37(E/F ys ) 1/ F ys t s (4.6-1) (4.6-) ( ) (A b A c (b 1 b ) Nguyen Yu[4.19] Hsiao Yu Galambos[4.0] 61 (LRFD) (φ c ) (V n ) a/h [60/(h/t)] 3.0 (I s ) 4 3 h a h 5ht 0.7 I s min = (4.6-3) a h

59 A st 1 C = v a h ( a / h) ( a / h) ( a / h) YDht (4.6-4) 1.53Ekv Cv = C v 0.8 (4.6-5) F ( h / t) y C v 1.11 h / t Ek v = C v > 0.8 (4.6-6) F y 5.34 k v = a/h 1.0 (4.6-7) ( a / h) 4.00 k v = a/h > 1.0 (4.6-7) ( a / h) a = D = 1.0 D = 1.8 D =.4 Y = ( )/( ) t h = 4.. (4.6-3) (4.6-4) Nguyen Yu[4.19] 4-19

60 5.1 (LRFD) ( ) ( ) 5. (T n ) T n = A n F y (5.-1) φ t = 0.95 A n = F y = 3.4 T n = ( ) (LRFD) (φ t 1.3 (β 0 ).5 R m R n R m = A n (F y ) m (C-3.-1) R n = A n F y (C-3.-) R m /R n = (F y ) m /F y (C-3.-3) A n Rang Galambos Yu[4.1] (F y ) m 1.10F y V M = 0.10 V F = 0.05 V P = 0 (V R coefficient of variation) 5-1

61 V R = VM + VF + VP = 0.11 V Q = (β).4 β 0 =.5 5 -

62 6.1 (a) (b) (c) (d) (a) (b) (c) 6.~6.6 (d) 6. M n ~ 6..4 ( 6..1 ) (Lateral-Torsional Buckling 6.. ) C Z ( 6..3 ) C Z ( 6..4 ) 6..1 [ ] [ ] φ b = 0.95 φ b = [ ] Mn M n = S e F y (6.-1) F y = S e = ( F y ) 6-1

63 . [ ] (1) () F y (3) λ 1 (4) 0.35F y ht (5) 30 M n (a)1.5s e F y [ ] (b) C y e y e y = = F y E E = C y = (1) C y C y = 3 w t C y = 3- λ 1 λ λ w t λ 1 w λ < λ t C y = 1 w t λ λ 1 = (6.-) F y E 1. 8 λ = (6.-3) F y E () C y C y = 1 (3) C y C y = 1 M n (a) (b) (c) [ ] M n M y 6 -

64 M y ( ) C-6.-1 C-6.-1(a) C-6.-1(b) (c) C-6.-1 (a) (b) (c) C-6.-1) M y = S e F y (C-6.-1) F y = 6-3

65 S e = ( F y ) S e (1) λ w/t f=f y () F y (closed-form solution) (successive approximation) LRFD φ M b n φb / 1/ [6.1 6.]. [ ] [ ] (partial plastification) 1980 AISI M n 1.5M y M y M n /M y M n cu [6.3] AISI C y y C y (C-6.-) w/t C-6.- cu M n (C-6..1-) (C ) σ da = 0 σ yda = M n (C-6.-) (C-6.-3) σ M n 1996 AISI Part I[6.6] [6.7] 6-4

66 C-6.- C y 6.. M c M n = Sc (6.-4) S φ b = 0.9 f S f = S c = M c /S f M c = 1. M e.78 M y M c = M y (6.-5)..78 M y > M e > 0.56 M y 10 10M y M c M y 1 (6.-6) 9 36M e 3. M e 0.56 M y M c = M e (6.-7) M y = = S f F y (6.-8) M e = (1) () (1) 6-5

67 M e = C r A σ σ (6.-9) b o ey t a. x x b. 0.5 M e c. M e () M e s ex [ j Cs j r ( t ex )] + 0 σ σ CTF = C Aσ (6.-10) C s = +1 C s = -1 σex = π ( K L r ) x E x x (6.-11) σey = π ( K L r ) y E y y (6.-1) σt = GJ Aro π EC w + ( K ) tlt (6.-13) A = C b = M max.5m max 1.5M max + 3M + 4M A B + 3M C (6.-14) M A M B M C 3/4 C b 1 1 C b C b 1 E CTF M1 ( ) = (6.-15) M M 1 M ( M 1 ) M 1 M C TF 1 r 0 polar radius of gyration M 6-6

68 x y + 0 r + r x (6.-16) r x r y radius of gyration K x K y K t x y L x L y L t x y x 0 x J St.Venant C w 3 j 1 x I y x da + xy da 0 A A (6.-17) I Z C U 6..3 () (x ) I Z (1) M e π ECbdI yc I M e = (6.-18) L π ECbdI yc Z M e = (6.-19) L d = L = I yc = ( ) ( ) (1) 6.. I (C-6.-4) M cr π L π EC GJ 1 + GJL = w EI y (C-6.-4) E G I y y C w (Warping constant of torsion) J St. Venant L [ ] 6-7

69 π E I y JI y L σ ( ) + cr = ( 1 ) (C-6.-5) L I X + µ I πd x d C-6.-5 I [6.9] π Ed 4GJL σ cr = I yc I yt I y (C-6.-6) L Sxc π I yed S xc I yc I yt I yc = I yt = I y / (C-6.-5) (C-6.-6) (C-6.-6) I y = 4GJL π I y Ed C-6.-6) π EdI yc σ cr = (C-6.-7) L S xc C b σ cr Cbπ E σ cr = (C-6.-8) L Sxc di yc C b (bending coefficient) 1 M 1 M 1 C b = (C-6.-9) M M M 1 M C AISI Kirby and Nethercot [6.10] C M max C b (C-6.-10).5M max + 3M A + 4M B + 3M C M max = M A = 1/4 M B = M C = 3/4 6-8

70 C ( ) LRFD C-6.-3 (C-6.-9) (C-6.-10) C-6.-3 C b (C-6.-8) I (C-6.-11) (6.-18) Cbπ EdI yc ( M cr ) = (C-6.-11) e L (C-6.-8) σ pr (C-6.-1) [6.7] ( L S / di ) Fy xc yc ( σ = cr ) I Fy 1 (C-6.-1) 9 36 cbπ E I 6-9

71 10 10 M y ( M cr ) I = M y (1 ) M y (C-6.-13) 9 36 ( M ) cr e C-6.-4 C-6.-4 AISI (C-6.-8 ) (C-6.-11) (C-6.-11) (C-6.-13) 1996 (6.-9) (6.-10) [ ] ( Z ) AISI I 1986 AISI ( M ) cr M y M y 1 ( M ) (C-6.-14) 4 cr e I 1996 AISI 1980 AISI I Z ( ) 0.56M y 0.56 M y (10/9) M y ( 0) Johnson Parabola (10/9) [6.13] M y M y Johnson 6-10

72 Parabola Sc M n = M c (C-6.-15) S f M c = S c = M c S f S f = (S c /S f ) φ b =0.9 LRFD β I Z C-6.-5 U U C-6.-6 C

73 C-6.-6 U U AISI 6..3 C Z M n : M n = R S e F y (6.-0) φ = 0.9 R = 0.4 C = 0.5 Z = 0.6 C = 0.7 Z S e F y 6..1 R (11.5 ) ( ) 1.5d (33 ) 8. 0% mm (0.019 in) 5.4 mm (1in) 305mm (1 in) mm (6in) 1. #

74 mm( 3/16in ) 1.7mm(0.5in) 13. stand off mm (1in) [ ] R M=0.08wL La Boube [6.16] [6.1 6.] LRFD φb (C-6.-0) = 0. 9 β W-0.9D W D C Z M n 6.. M n = R S e F y (6.-1) φ = 0.9 R = S e F y 6..1 ( ) 1996 AISI R 6-13

75 6.3 V n 1. h t Ek v F y V = 0. F ht (6.3-1) n 6 y φ v = Ekv F y < h t Ekv F y V n = 0.64t k F E (6.3-) v y φ v = h t > Ek v F y V n φ v = π Ekvt 3 = = 0.905Ekvt h 1(1 µ ) h V n = t = h = k v (6.3-3) = (1) k v = 5.34 () ( ) a. a / h 1.0 k v 5.34 = (6.3-4) ( a h) b. a / h > 1.0 k v 4.0 = (6.3-5) ( a h) a = = 6-14

76 h/t h/t V = A τ = A F 3 0. F ht (C-6.3-1) n w y w y 6 A w = ht y τ y F 3 y h/t V n kvπ EAw = Awτ cr = (C-6.3-) 1(1 µ )( h / t) τ cr = k v = E = µ = h = t = µ = 0.3 V n V n 3 = 0.905Ek t h (C-6.3-3) v h/t V n = 0.64t k F E (C-6.3-4) v y LRFD M u V u M φbm u nxo Vu + φvv n 1.3 (6.4-1) M u V u φ V φ V b n M v n φ M 0 V φ V > M u > u v n ( ).5 ( ) 0. 7 u b nxo V u 6-15

77 M u Vu φbm nxo φvvn φ b = φ v = 6.3 (6.4-) M n = M nxo = 6..1 x V n = Bleich[6.0] f f b cr τ + τ cr = 1.0 (C-6.4-1) f b = f cr = τ = τ cr = diagonal tension field action [6.1] 4.5 f 0.6 f b b max + τ τ max = 1.3 (C-6.4-) C (C-6.4-) 6-16

78 C τ/τ max f b /f bmax 6.5 P n φ w = 0.75 I φ w = 0.8 Z (two-nested Z sections) (6.5-4) φ w = 0.85 h / t R / t 6 R / t 7 N / t 10 N / h 3.5 Z (6.5-1)

79 1. h / t 150. R / t mm (0.06in.) mm (3/16 in.) P n P n I P n ( ) I (3) (6.5-1) (6.5-) (6.5-3) >1.5h () (4) (6.5-4) (6.5-4) (6.5-5) (3) (6.5-6) (6.5-6) (6.5-7) 1.5h (5) (4) (6.5-8) (6.5-8) (6.5-9) C I ( C ). 1.5h h h h [ ( h θ )] [ 0.01( N )] t kc C C C t [ ( h θ )] [ 0.01( N )] t kc C C C > 60 t t 1 + t * (6.5-1) 1 + t * (6.5-) N [ ( N ) ] [ ( N )] t t 6-18

80 t F C y N t [ ( h θ )] [ 0.007( N )] t kc C C C > 60 t t (6.5-3) 1+ (6.5-4) t N [ ( N ) ] [ ( N )] t F C + m y 5 ( ) t N t [ ( h θ )] [ 0.01( N )] t kc C C C ( m) N t FyC8 5 t [ ( h θ 771. )] [ ( N )] t kc C C C ( m) N t FyC7 5 t t (6.5-5) 1 + t * (6.5-6) t (6.5-7) 1 + (6.5-8) t t (6.5-9) P n = N C 1 = 1.-0.k (6.5-10) C = R/t 1.0 (6.5-11) C 3 = k (6.5-1) C 4 = R/t 1.0 ( 0.5) (6.5-13) C 5 = k 0.6 (6.5-14) h t C 6 = h 150 t (6.5-15) = 1. h > 150 t (6.5-16) C 7 = 1 h/t (6.5-17) k h t 1 = k h/t > 66.5 (6.5-18) h t 1 C 8 = k h/t (6.5-19) C 9 = 6.9 ( N mm) C θ = ( θ ) 90 h/t (6.5-0) F y = MPa h = (mm) 6-19

81 k = 894Fy/E (6.5-1) m = t / 1.91 (mm) (6.5-) t = (mm) N = (mm) N R = θ = (45 θ < 90 ) C I C [6.7] ( ) AISI [6.-6.4] I (1) () (3) (4) C-6.5- (a) (b) 6-0

82 1.5 C-6.5- (a) (b) (c) (d) ( Z ) I ( ) C (6.5.1) (6.5.) (6.5.3) (6.5-4) (6.5-5) (6.5-6) (6.5-7) (6.5-8) (6.5-9) [ ] C C-6.5-3(b) C-6.5-3(a) P n ( AISI ) 6-1

83 C

84 C

85 (6.5-1) (6.5-) (h/t) (N/t) (R/t) (t) (F y ) (θ) LRFD φ=0.75 φ=0.8 I (safety index) Z [ ] 7% 55% 30% (AISI 1996) Z [6.8] (6.5-4) Pu 1.07( φ P w n M ) + ( φ M b u nx0 ) 1.4 (6.6-1) (6.6-1) 54mm (10in.). Pu M u 0.8( ) + ( ) 1.3 φ P φ M w n b nxo (6.6-) h/t.33/ Fy E λ φ w P n (6.6-) (6.6-) φ b = ( 6..1 ) φ w = ( 6.5 ) P u = P n = 6.5 M u = P u M nxo = 6..1 w = t = 6-4

86 λ = ( ) 3. Z (two-nested Z sections) M u Pu φ M P no n φ = 0.9 M u = (6.6-3) M no = Z 6..1 P u = P n = Z (6.6-3) 1. h / t 150. N / t F y 483 Mpa (70 ksi) 4. R / t mm (0.5 in.) A mm (0.5 in.) A (6.6-1) (6.6-) (C-6.6-1) (C-6.6-) 551 φ w =0.75 φ w =0.8 I Z (6.6-3) [6.8]

87 C C-6.6- I 6-6

88 φ c P n φ c =0.85 P n =A e F n (7.-1) A e = F n A e F n λ c 1.5 n ( λ F y c F = ) (7.-) λ c >1.5 F n = F λc y (7.-3) Fy λ c = (7.-4) F e F e = M ux M uy 8.3 KL/r 00 KL/r 300 (1) () ( - ) (3) 7-1

89 1. P y =A g F y (C-7.-1) A g = F y =. (1) Euler ( P cr ) e π EI = (C-7.-) ( KL) (P cr ) e E I K L ( F cr ) e ( Pcr ) e π E = = (C-7.-3) A ( KL / r) g r KL/r () (C-7.-3) (F cr ) e (F pr ) 1996 AISI ( F cr ) I Fy = Fy (1 ) (C-7.-4) 4( F ) cr e F pr =F y / (C-7.-4) (F cr ) e F y / λ c (C-7.-4) c λ ( F cr ) I = (1 ) Fy (C-7.-5) 4 Fy λ c = = ( F ) cr e KL rπ F y E (C-7.-6) (C-7.-6) λ c (3) (w/t) P n =A g F cr (C-7.-7) 7 -

90 P n = A g = F cr = (4) (w/t) (C-7.-7) (F cr ) (A e ) [7.1 7.] P n =A e F cr (C-7.-8) F cr A e F cr 1996 AISI [7.1] AISC LRFD [7.3] λ c 1.5 F ( c = λ ) F (C-7.-9) n y λ c >1.5 F n = F λc y (C-7.-10) F n λ = F / F F e c y (C-7.-3) P n = A e F n (C-7.-11) (5) K K KL ( C-7.-1) K=1 K=1 K 1 C-7.-1 K [7.4] K=1.0 [7.5] K 0.75 e 7-3

91 C-7.- ( ) K 1.0 C-7.-3 K [7.6] [ ] K [7.4] C-7.-1 C

92 C-7.-1 K C-7.-3 K 3. Torsional Buckling I Z 7-5

93 [7.6] 1 π EC w σ t = GJ + (C-7.-1) Aro ( K ) t Lt A r o G J St Venant E C W K t K t C σ t F n λ c 4. - Torsional-Flexural Buckling - T I - C C

94 - [ ] P n 1 = ( Px + Pz ) ( Px + Pz ) 4βPx Pz β (C-7.-13) - F e Fe 1 = ( σ + ) ( + ) ex σ t σ ex σ t 4βσ exσ t β (C-7.-14) X σ ex = π E /( K xlx / rx ) X Euler t ( (C-7.-1)) β = 1 ( χ o / ro ) - ex Y - (C-7.-10) - ( w/t ) w/t - A e F e F e π E = (7.3-1) ( KL / r) E= K= L= R= - F e (7.3-1) (7.3-) Fe 1 = ( σ + ) ( + ) ex σ t σ ex σ t 4βσ exσ t β (7.3-) F e σ σ t ex F e = (7.3-3) σ t + σ ex 7-7

95 ex π E σ = (7.3-4) ( K L r ) x x / x σ t = 1 Ar o GJ π EC + ( K L ) t w t 6.. (7.3-5) ( X / ) o r β = (7.3-6) 1 o X F e (7.3-1) F e = σ t (7.-1) - - Y (X ) (C-7.-1) - (C-7.-14) F e σ tσ ex σ + σ = (C-7.3-1) t ex [7.11] 1 P n 1 1 = + (C-7.3-) P P x z 1 F e 1 σ ex 1 + σ = (C-7.3-3) t 7.4 F e - C w [ ] 7-8

96 T u M ux M uy M b ux φ M nxt M + φ M b uy nyt Tu + φ T t n 1.0 (8.-1) M b ux φ M nx M + φ M b uy ny Tu φ T t n 1.0 (8.-) T u = M ux M uy = T n = ( ) M nx M ny = ( ) M nxt M nyt = S ft F y S ft = φ b = ( 6..1 ) 0.90( 6.. φ t = 0.95 ) (8.-1) (8.-) P u M ux M uy 8-1

97 C b mx φ M M nx ux α x CmyM uy + φ M α b ny y Pu + φ P c n 1.0 (8.3-1) M b ux φ M nx M + φ M b uy ny Pu + φ P c no 1.0 (8.3-) P u / φ c P n 0.15 M b ux φ M nx M + φ M b uy ny Pu + φ P c n 1.0 (8.3-3) P u α x = 1 (8.3-4) PEx P u α x = 1 (8.3-5) PEy P P Ex Ey π EI x = (8.3-6) ( K L ) x x π EI y = (8.3-7) ( K L ) y y P u = M ux M uy = M uy P u L/1000 P u P n = ( ) P no = ( F n =F y ) M nx M ny = ( ) φ b = ( 6..1 ) 0.90( 6.. ) φ c = 0.85 I x = x I y = y L x = x L y = y K x = x 8 -

98 K y = y C mx C my = 1. (joint translation) C m = C m = (M 1 /M ) M 1 M M 1 /M M 1 /M 3. C m (a) C m = 0.85 (b) C m = 1.0 [8.1 8.] AISC LRFD [8.3] [8.4] AISC 8-3

99 9.1 (D/t) 0.441E/F y (imperfection) - Plantema [9.1] Plantema F ult /F y (E/F y )(t/d) t D F ult AISI D/t 0.11 E/F y 0.11 E/F y < D/t < E/F y (D/t) 0.441E/F y D/t 9. (M n ) D/t E/F y (9.-1) M n = 1.5 F y S f E/F y D/t E/F y 9-1

100 M n E / Fy = FyS f D t (9.-) / E/F y D/t E/F y M n = [0.38E/(D/t)] S f (9.-3) φ b = 0.95 S f = 1.9 ( ) Sherman[9.] (shape factor) ( ) (P n ) P n = F n A e (9.3-1) φ b = 0.95 F n λ c 1.5 n λ c > 1.5 λ ( ) F y F c = (9.3-) F n = F λc y (9.3-3) Fy λ c = (9.3-4) F e F e = ( 7.3 ) A e = [1-(1-R )(1-A 0 /A)]A (9.3-5) R = (F y /F e ) 0.5 (9.3-6) 9 -

101 A 0 = A DF y te A D/t (E/F y ) (9.3-7) ( ) /( ) A = (F e ) (A e ) (9.3-5)

102 10.1 (1)C I ()C Z (3) I I C ( ) (S max ) 1. Lrcy S = max r (10.-1) I L = r I = I r cy = C. S max L gts = (10.-) 6 mq L = T s = ( ) g = m = C (1) C w f m = (10.-3) w + d / 3 f () C 10-1

103 w f dt m = w 4I x f 4D d + D d 3d (10.-4) w f = C w f d = C D = I x = C q = ( -LRFD ) q q (s) T s = P s m / g (10.-5) P s (S max ) (1) () T s g I C 1. I (10.-1) (S max ) C I C S max /r cy I (L/r I ) 1/ [ ] I (10.-1) C r I. I (10.-) [10.] C C Q (Qm) (T s (T s g) 10 -

104 Qm=T s g (C-10.-1) T s =Qm/g (C-10.-) C-10.- q ( ) s Q = qs/ (S max ) Q (C-10.-) q C C C-10.- C L/3 L/6 (10.-)

105 ( ) t(E/f c ) 0.5 t f c t(E/F y ) 0.5 ( w/t < 0.50(E/F y ) 0.5 ) 1.33t(E/F y ) 0.5 ( w/t 0.50(E/F y ) 0.5 ) mm (0.5 in) C (W) 1.67f c C f c, [ ] σ = cr π E ( KL / r) σ cr = 1.67f c K = 0.6 L = s r = t/(1) 0.5 K ( ) [ ] C

106 ( ) Winter [10.3] Haussler [10.4] Haussler Pabers [10.5] Lutz Fisher [10.6] Salmon Johnson [10.7] Yura [10.8] SSRC [10.9] C Z C Z (1) () C Z C Z / C C 0.05W W ( ) 0.05W/. Z 4 0 Z 10-5

107 (1) P L b = 0.5 sinθ W n p d t () 1/3 P L b = 0.5 sinθ W n p d t (3) P L b = sinθ W n p d t (4) P L b L = Ctr sinθ W n p d t (10.3-1) (10.3-) (10.3-3) (10.3-4) C tr = 0.63 C tr = 0.87 C tr = 0.81 (5) 1/3 P L b L = Cth sinθ W n p d t (10.3-5) C th = 0.57 C th = 0.48 (6) P L b L = Cms sinθ W n p d t (10.3-6) C ms = 1.05 C ms = 0.90 b = d = t = L = 10-6

108 θ = Z ( ) n p = W = P L ( ) 0 ( ) n p 0 W Z Murray Elhouar [10.10] (10.3-1) (10.3-6) Murray Elhouar 1/ ( ) (P L P L 1. P L =1.5 K ( 0.5a ). P L =1.0 K ( 0.3a ) 1.4 K (1-x/a) ( 0.3a 1.0a ) C Z x = a = C K = m/d (10.3-7) m = d = Z K =I xy / I x (10.3-8) I xy = I x = 10-7

109 C I C C C C C-10.- I I C (1) ( ) () C C C C C [10.1] C 10-8

110 C (Qm) P = Qm/d C Winter Lansing McCalley[10.11] C C (P L ) C C C E/F y 10-9

111 F n (A e ) A e (1) 610mm () 0.5 d 63.5mm (3) 114mm (4) (d/t) 0 (5) 54mm (A e ) F y 345 Mpa d 15 mm t 1.91 mm L 4.88 mm 305 mm 610 ( ) ( I x /I y ) I C Z 10-10

112 ( ) Green Winter Cuykendall [10.1] ( ) C Z Yu [10.] Simaan [10.13] Simaan Pekoz [10.14] Simaan [10.13] Simaan Pekoz [10.14] Davis Yu [10.15] M nxo M nyo φ b = 0.95 φ b = 0.90 M nxo M nyo P n = A e F n (10.4-1) φ c = 0.85 A e = F n F n = 1. F n 10-11

113 KL. F n F e σ CR σ CR (1) C σ CR = σ ey + Q (10.4-) a [ ex tq ex tq 4βσ exσ tq ] 1 + β (10.4-3) σ CR = ( σ σ ) ( σ + σ ) () Z σ CR = σ t + Q (10.4-4) t σ CR = 1 {( σ ) [( ) 4( )]} ex + σ ey + Q a σ ex + σ ey + Q a σ exσ ey + σ ex Q a σ exy (3) I ( ) (10.4-5) σ CR = σ ey + Q (10.4-6) a σ CR = σ ex (10.4-7) π E σ ex = ( ) L / r x π σ exy = AL EI xy π E σ ey = ( ) L / r y (10.4-8) (10.4-9) ( ) σ t = 1 Ar 0 GJ π EC + L w ( ) σ tq = Q = σ + Q (10.4-1) t t Q o (-s/s ) ( ) s = (mm) 15mm s 305mm s =305mm 10-1

114 Q o = Q a = Q / A ( ) A = L = t ( Qd ) ( 4Ar ) Q = ( ) / o d = I xy = 3. F n γ = (π/l)[c 1 +(E 1 d/)] ( ) C 1 E 1 C 1 E 1 (1) C C 1 = (F n C o )/( σ ey -F n + Q ) ( ) a Fn [( σ ex Fn )( ro Eo xodo ) Fn xo( Do xoe E 1 = ( σ F ) r ( σ F ) ( F x ) ex n o tq n n o o )] ( ) ()Z Fn [ Co( σ ex Fn ) Doσ exy ] C 1 = ( σ F + Q )( σ F ) σ ey n a ex n exy ( ) E 1 = (F n E o ) / ( σ tq -F n ) (10.4-0) (3) I C 1 = (F n C o )/( σ ey -F n + Q ) (10.4-1) E 1 = 0 a x o = x ( ) C o E o D o C o = L/350 ( ) (10.4-) D o = L/700 ( ) (10.4-3) E o = L/(d 10,000) rad (10.4-4) F n >0.5F y σ ex σ ey σ exy σ tq E G E 10-13

115 G E G E = 4EF n (F y -F n )/F y G = G/(E /E) (10.4-6) (10.4-5) Q o γ ( ) Q o γ kn / mm 15.9mm ( ) ( ) S-1 1.7mm Q o γ C ( C-10.4-) Simaan[10.13] Simaan Pekoz[10.14] 10.4 ( ) Pekoz [10.17] Miller Pekoz [ ] 10-14

116 C C P n = (8.3-1) (8.3-) (8.3-3) M nx M ny M nxo M nyo 10-15

117 11.1 [11.1] 1. ( ) ). (1) ( ) () mm mm (AWS) AWS D1.3 AWS D AWS C1.1 AWS C

118 11..1 V L T F F F F F H H H H H V V V V OH OH OH OH F F F F H H V V OH OH (F= H= V= OH= ) ( ) ( ) Pekoz McGuire [11.] [11.3] Pekoz McGuire[11.] (American Welding Society) ( ) [11.4] AWS C C mm (0.15 in) mm (0.18 in) ( 11.-3) 3.81 mm P n 1. P n = L t e F y (11.-1) φ = (11.-) (11.-3) 11 -

119 P n = L t e 0.6F xx (11.-) φ = 0.80 P n = L t e F y / 3 (11.-3) φ = 0.90 P n = F xx = F y = L = t e = mm 1.7 mm.03 mm 9.53 mm d e 9.5mm C

120 C-11.- ( ) ( ) P n πd e 1. P n = 0.75Fxx 4 φ =0.60. (d a /t) E / F ) ( u (11.-4) P n =.0 t d a F u (11.-5) φ = E / F ) < (d a /t) <1.397 E / F ) ( u ( u E / F P n = u t d a F u (11.-6) d a / t φ =0.50 (d a /t) E / F ) ( u P n =1.40 t d a F u (11.-7) φ =0.50 P n = 11-4

121 d = d a = d a =(d-t) d a =(d- t) ( ) d e = =0.7d-1.5t 0.55d (11.-8) t = ( ) F xx = F u = C C e min Pu e min = φf t F u /F sy 1.08 φ = 0.70 F u /F sy 1.08 u φ = 0.60 (11.-9) P u = t = F sy = C C d 1.0 [11.] (1) () (3) (4) C ( C ) mm 11-5

122 C C C

123 C C P n πd 1. P n = e Fxx 4 φ =0.60. F u /E < (11.-10) Pn = [ (F u /E)]td a F u 1.46td a F u (11.-11) F u /E Pn = 0.70 td a F u (11.-1) φ = 0.60 e min d 11-7

124 F xx 414 Mpa F u 565 Mpa F xx F u % % - [ ] (1) () [ ] % [ ] C C ( C ) [11.7] 70% ( C-11.-9) 11-8

125 1. ( ). ( ) ( ) P n πd P n = e Ld 4 + e 0.75F xx (11.-1) P n =.5 t F u (0.5L+0.96d a ) (11.-13) φ =0.60 P n = D = L = ( L 3d ) d a = d a =(d-t) d a =(d-t). d e = = 0.7d-1.5t F u F xx ( C ) [11.4] C

126 C P n 1. L/t < 5 P n = 0.01L 1 - tlfu (11.-14) t φ = 0.60 L/t 5 P n =0.75tLF u (11.-15) φ = P n =tlf u (11.-16) φ =0.60 t C C t 1 t t 3.81mm P n =0.75t w LF xx (11.-17) φ =0.60 P n = L = t w = = 0.707w w 11-10

127 w 1 w = ( C C-11.-1) L w 1 t 1 F u F xx [11.] L w 1 w w 1 ( C ) C C L C T [11.] 3.81mm 11-11

128 3.81mm C V. 3. P n 1. ( C ) P n =0.833tLF u (11.-18) φ =0.55. ( C ~ C d) (1) t t w <t h L P n =0.75tLF u (11.-19) φ =0.55 () t w t h L P n =1.50tLF u (11.-0) φ =0.55 t P n =0.75t w LF xx (11.-1) φ =0.60 P n = h = L = 11-1

129 t w = 90 ( C a C b) = 5/16R V =1/R( R>1.7mm 3/8R = 90 = 0.707w w ( C c C d) = R = w 1 w = ( C c C d) F u F xx ( C ) a b 90 AWS D1.1-96[11.8] c d 90 W 1 ( c) ( d) C

130 C C V C a (W 1 =R) 11-14

131 C b (W 1 =R) C c (W 1 >R) C d (W 1 <R) 11-15

132 C P n P n = 11.. φ = (mm) (mm) (kn) (kn) mm Recommended Practice for Resistance Welding Coated Low-Carbon Steel AWS C (.1- ) 3. mm Recommended Practice for Resistance Welding Coated Low-Carbon Steel AWS C1.1-66( 1.3- ).7 N/m AWS C AWS C

133 AWS C AWS C1.1-66[ ] CNS 6183 SSC41 CNS 115 CNS mm 4.76 mm ASTM A194/A194M ASTM A307 (Type A) ASTM A35 ASTM A35M ASTM A354 (Grade BD) ASTM A449 ASTM A490 ASTM A490M ASTM A563 ASTM A563M ASTM A436 ASTM A436M ASTM F844 ASTM F959 ASTM F959M 11-17

134 ( ) d < d h d d d h (d+0.8)by(d+6.4) (d+0.8)by(.5d) (d+0.6)by(d+6.4) (d+1.6)by(.5d) d d mm 4.76 mm [11.11] ( 4.76 mm). A35 A mm A449 A354 Grade BD 1.7 mm

135 mm ( ) [ ] 1.7 mm mm (P n ) P n = tef u (11.3-1) F u /F sy 1.08 φ = 0.70 F u /F sy <1.08 φ = 0.60 P n = F u = F sy = e = t = (3d) 1.5 (1.5d) e - d h / e d h

136 (d) (d) e min (F u ) F u /F sy P e = (C ) Fu t e = P = t = (C ) Winter [ ] Yu [ ] P n 1. P n = ( r+3rd/s)F u A n F u A n (11.3-) φ = 0.65 φ = P n = (1.0-r+.5rd/s)F u A n F u A n (11.3-3) φ = 0.65 P n = F y A n (11.3-4) φ = 0.95 A n = r = r 0. r 0.0 s = ( ) s d = t = F u = F y = 11-0

137 mm (P n ) (F u ) r d/s 3. [11.19] 4. ( ) (P n ) F u /F sy (P n ) φ φ P n d F u t t (mm) F u /F sy φ P n 0.61 t<4.76 t F u dt < F u dt F udt t (mm) F u /F sy φ P n 0.61 t< F u dt F u dt t

138 F u /F sy (Winter[ ] Yu[ ] Chong Matlock[11.19]) P n P n = A b F (11.3-5) A b = F F nv F nt φ F F nt φ

139 F φ nt F φ nv (MPa) (MPa) A307 Grade A mm d<1.7 mm A307 Grade A d 1.7 mm A A A354 Grade BD 6.4 mm d<1.7 mm A354 Grade BD 6.4 mm d<1.7 mm A mm d<1.7 mm A mm d<1.7 mm A mm d<1.7 mm A mm d<1.7 mm

140 F nt (MPa) φ A f v f v 61 A354 Grade BD f v f v 696 A f v f v 558 A f v f v 776 A307 Grade A 6.4 mm d<1.7 mm d 1.7 mm 34-5f v f v mm (1/ in.) A307 A449 A mm 10% 6.35 mm (1/4 in.) 9.63 mm (3/8 in.) (tensile-stress area / gross-area) mm(1/ in) 5.4 mm(1 in.) % LRFD ( ) (pull-out failure) ( ) C Z 11.4 d = ( C ) φ = 0.5 P ns = P nt = P not = P nov = t 1 = t = F u1 = F u = 11-4

141 mm(0.08 in.) 6.35 mm(0.5 in.) [11.0] [ ] [11.3] C C C d mm (in.) (0.060) (0.073).18 (0.086) 3.51 (0.099) 4.84 (0.11) (0.15) (0.138) (0.151) (0.164) (0.190) (0.16) 1/ (0.50) 11-5

142 C (3d) (3d) 1.5 (1.5d) (P ns ) t /t P ns P ns = 4.(t 3 d) 1/ F u (11.4-1) P ns =.7 t 1 df u1 (11.4-) P ns =.7 t df u (11.4-3) t /t 1.5 P ns P ns =.7 t 1 df u1 (11.4-4) P ns =.7 t df u (11.4-5) 1.0 < t /t 1 <.5 P ns C

143 P ns Eq Eq C t ( C ) ( C ) N/A t 1.7 t 1 df u1 t.7 t df u C (t 3 d) 1/ F u t 1.7 t 1 df u1 t.7 t df u C P ns φ

144 ( ) d w 7.94 mm 1.7 (1) (pull-out failure) () (pull-over failure) (3) 1.7 mm (P not ) P not =0.85 t c d F u (11.4-6) t c t [11.1] Pekoz [11.3] (P nov ) P nov =1.5t 1 d w F u1 (11.4-7) d w 1.7 mm [11.] Pekoz [11.3] (P nt ) 1.5 P not P nov φ (V n ) V n = 0.6 F u A wn (11.5-1) φ =

145 A wn = (d wc n d h ) t d wc = n = d h = F u = t = Birkernoe Gilmor [11.4] C [11.11] [11.11] P C P p = 0.85f c A 1 (11.6-1) P p = 0.85f c A 1 A / A (11.6-) 1 φ c =

146 f c = A 1 = A = A / A ( ) ( ) /

147 CNS- 8.ASTM-The material standard of the American Society for Testing and Materials. 9.AWS Code-The Structural Welding Code of American Welding Society ( ) (Shop drawing) (Approve) (Detail Dimension)

148 CNS AWS JIS

149 (1) () (3). (1) () CNS ASTM (3) (White Rust) 1-3

150 (studs) (top and bottom track) (anchors) 10 ( ) (axially loaded studs) 5. (lintels) 6. (horizontal strap bracing) (joist bridging) (metal deck or plywood). (end clips) 3. (joist) (wall studs) (lintels)

151 CNS147. ASTM (studs) (gage) (depth and width) (spacing) (joists) (gage) (depth and width) (spacing)

152

153 1-7

154 13.1 UBC-97 AISC-97 UBC D + 0.5L + 1.6W (13.-1) 1.D + 1.6L + 1.6W (13.-) 1.D + 0.5L + 1.6W (13.-3) 1.D + 0.5L + E (13.-4) 0.9D E 5L + 1.6W (13.-5) 0.9D - 1.6W + 1.6W (13.-5) D= L= W= E= y y 1.0 UBC-97 AISC-97 ( ) (l/r) (Ω 0 ) 4. (braced bay)

155 P DL +0.5P LL +Ω 0 P E (13.4-1). 0.9P DL -Ω 0 P EE (13.4-) P DL P LL P E Ω R 1.6~ C.5 Fu 1.6~ y Fu 1.764~.38 UBC-97 Ω 0.~.8 C/Fu<=1 Ω

156 American Iron and Steel Institute, Cold-Formed Steel Design Manual 1996 Edition. 1.4 Yu, W. W., V. A. Liu, and W. M. Mckinney, Structural Behavior and Design of Thick, Cold Formed Steel Members, Proceeding of the Second Specialty Conference on Cold Formed Steel Structure, University of Missouri Rolla, Rolla, MO, October Yu, W. W., V. A. Liu, and W. M. Mckinney, Structural Behavior of thick Cold Formed steel Menders, Journal of the Structural Division, ASCE, Vo1. 100, No. ST1, January Pekoz, T. B, Development of a Unified Approach to the Design of Cold Formed Steel Members, Report SG-86-4, American Iron and Steel Institute, Yu, W. W., Cold Formed Steel Design, nd Edition, Wiley-Interscience, New York, NY, Ravindra, M.. K. and T. V. Galambos, Load and Resistance Factor Design for steel, Journal of the Structural Division ASCE, Vo1. 104, No. ST9, September Hsiao, L. E., W. W Yu and T. V. Galambos, Load and Resistance Factor Design of Cold Formed Steel Calibration of the AISI Design Provisions, Ninth Progress Report, civil Engineering Study 88-, University of Missouri-Rolla, Rolla, MO, February Hsiao, L. E., W. W. Yu and T. V. Galambos; AISI LRFD Method for Cold Formed Steel Structural Members, Journal of Structural Engineering, ASCE, Vo1. 116, No., February Ellingwood, B., T. V. Galambos, J. G. MacGregor, and C. A. Cornell, Development of a Probability Based Load Criterion for American National Standard A58:Building Code Requirements for Minimum Design Loads in Buildings and Other Structures, U. S. Department of Commerce, National Bureau of Standards, NBS Special Publication, June Galambos, T. V., B. Ellingwood, J. G. MacGregor, and C. A. Cornell, Probability Based Load Criteria: Assessment of Current Design Practices, Journal of the Structural Division, ASCE, Vo1. 108, No. ST5, May 198. R - 1

157 1.13 Rang, T. N., T. V. Galambos, and W. W. Yu, Load and Resistance Factor Design of Cold Formed Steel: Study of Design Formats and Safety Index Combined with Calibration of the AISI Formulas for Cold Work and Effective Design Width, First Progress Report, Civil Engineering Study 79-1, University of Missouri-Rolla, Rolla, MO, January Rang, T. N., T. V. Galambos, and W. W. Yu, Load and Resistance Factor Design of Cold Formed Steel: Statistical Analysis of Mechanical Properties and Thickness of Material Combined with Calibration of the AISI Design Provisions on Unstiffened Compression Elements and Connections, Second Progress Report, Civil Engineering Study 79-, University of Missouri-Rolla, Rolla, MO, January Rang, T. N., T. V. Galambos, and W. W. Yu, Load and Resistance Factor Design of Cold Formed Steel: Calibration of the Design Provisions on Connections and Axially Loaded Compression Members, Third Progress Report, Civil Engineering Study 79-3, University of Missouri-Rolla, Rolla, MO, January Rang, T. N., T. V. Galambos, and W. W. Yu, Load and Resistance Factor Design of Cold Formed Steel: Calibration of the Design Provisions on Laterally Unbraced Beams and Beam-Columns, Fourth Progress Report, Civil Engineering Study 79-4, University of Missouri-Rolla, Rolla, MO, January Supomsilaphachai, B., T. V. Galambos, and W. W. Yu, Load and Resistance Factor Design of Cold Formed Steel: Calibration of the Design Provisions on Beam Webs, Fifth Progress Report, Civil Engineering Study 79-5, University of Missouri-Rolla, Rolla, MO, September Ellingwood, B., J. G. MacGregor, T. V. Galambos, and C. A. Cornell, Probability Based Load Criteria: Load Factors and Load Combinations, Journal of the Structural Division, ASCE, Vo1. 108, No. ST5, May American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE Standard 7-95, Ellingwood, B., T. V. Galambos, J. G. MacGregor, and C. A. Cornell, Development of a Probability Based Load Criterion for American National Standard A58:Building Code Requirements for Minimum Design Loads in Buildings and Other Structures, U. S. Department of Commerce, National Bureau of Standards, NBS Special Publication, June Ellingwood, B., J. G. MacGregor, T. V. Galambos, and C. A. Cornell, R -

158 Probability Based Load Criteria: Load Factors and Load Combinations, Journal of the Structural Division, ASCE, Vo1. 108, No. ST5, May Hsiao, L. E., W. W. Yu and T. V. Galambos, Load and Resistance Factor Design of Cold-Formed Steel: Comparative Study of Design Methods for Cold-Formed Steel, Eleventh Progress Report, Civil Engineering Study 88-4, University of Missouri-Rolla, Rolla, MO, February American Iron and Steel Institute, Cold-Formed Steel Design Manual, 1996 Edition Karren, K. W. and G. Winter, Effects of Cold-Work on Light Gage Steel Members, Journal of the Structural Division, ASCE, Vo1. 93, No. ST1, February Chajes, A., S. J. Britvec, and G. Winter, Effects of Cold-Straining on Structural Steels, Journal of Structure Division, ASCE, Vol. 89, No. ST, February American Society for Testing and Materials, Standard Methods and Definitions for Mechanical Testing of Steel Products, ASTM 370, Winter, G., Performance of Thin Steel Compression Flanges, Preliminary Publication, 3 rd Congress of the International Association of Bridge and Structural Engineering, Liege, Belgium. 4. Winter, G., Commentary on the 1968 Edition of the Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, New York, NY, LaBoube, R. A. and W. W. Yu, Structural Behavior of Beam Webs Subjected Primarily to Shear Stress, Final Report, Civil Engineering Study 78-, University of Missouri-Rolla, Rolla, MO, June LaBoube, R. A. and W. W. Yu, Structural Behavior of Beam Webs Subjected to a Combination of Bending and Shear, Final Report, Civil Engineering Study 78-3, University of Missouri-Rolla, Rolla, MO, June LaBoube, R. A. and W. W. Yu, Bending Strength of Webs of Cold-Formed Steel Beams, Journal of the Structural Division, ASCE, Vol. 108, No. ST7, July Hetrakul, N. and W. W. Yu, Structural Behavior of Beam Webs Subjected to Web Crippling and a Combination of Web Crippling and Bending, Final Report, Civil Engineering Study 78-4, University of Missouri-Rolla, Rolla, MO, R - 3

159 June Hetrakul, N. and W. W. Yu, Cold-Formed Steel I-Beams Subjected to Combined Bending and Web Crippling, Thin-Walled Structures Recent Technical Advances and Trends in Design, Research and Construction, Rhodes, J. and A. C. Walker (Eds), Granada Publishing Limited, London, Nguyen, P. and W. W. Yu, Structural Behavior of Transversely Reinforced Beams Webs, Final Report, Civil Engineering Study 78-5, University of Missouri-Rolla, Rolla, MO, July Nguyen, P. and W. W. Yu, Structural Behavior of Longitudinally Reinforced Beams Webs, Final Report, Civil Engineering Study 78-6, University of Missouri-Rolla, Rolla, MO, July Yu, W. W., Cold-Formed Steel Design, nd Edition, Wiley-Interscience, New York, NY, Bleich, F., Buckling strength of Metal Structures, McGraw-Hill Book Co., New York, NY, Weng, C. C. and T. B. Pekoz, Subultimate Behavior of Uniformly Compressed Stiffened Plate Elements, Research Report, Cornell University, Ithaca, NY, Ortiz-Colberg, R. and T. B. Pekoz, Load Carrying Capacity of Perforated Cold-Formed Steel Columns, Research Report No. 81-1, Cornell University, Ithaca, NY, Pekoz, T. B., Development of a Unified Approach to the Design of Cold-Formed Steel Members, Report SG-86-4, American Iron and Steel Institute, Cohen, J. M. and T. B. Pekoz, Local Buckling Behavior of Plate Elements, Research Report, Cornell University, Ithaca, NY, Bulson, P. S., The Stability of Flat Plates, American Elsevier Publishing Company, New York, NY, Pekoz, T. B., Development of a Unified Approach to the Design of Cold-Formed Steel Members, Proceedings of the Eighth International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, November Desmond, T. P., T. B. Pekoz, and G. Winter, Edge Stiffeners for Thin-Walled Members, Journal of Structural Division, ASCE, Vol. 107, No. ST, Feb Nguyen, P. and W. W. Yu, Structural Behavior of Transversely Reinforced Beam Webs, Final Report, Civil Engineering Study 78-5, University of Missouri-Rolla, Rolla, MO, July Hsiao, L. E., W. W. Yu, and T. V. Galambos, Loads and Resistance Factor R - 4

160 Design of Cold-Formed Steel: Calibration of the AISI Design Provisions, Ninth Progress Report, Civil Engineering Study 88-, University of Missouri-Rolla, Rolla, MO, Feb American Iron and Steel Institute, LRFD Cold-Formed Steel Design Manual, Washington, D. C., Hsiao, L. E., W. W. Yu, and T. V. Galambos, Load and Resistance Factor Design of Cold-Formed Steel: Calibration of the AISI Design Provisions, Ninth Progress Report, Civil Engineering Study 88- University of Missouri-Rolla, Rolla, MO, February Reck, H. P., T. Pekoz, and G. Winter, Inelastic Strength of Cold-Formed Steel Beams, Journal of Structural Division, ASCE, Vol. 101, No. ST11, November Yener, M. and T. B. Pekoz, Partial Stress Redistribution in Cold-Formed Steel, Journal of Structural Engineering, ASCE, Vol. 111, No. 6, June Yener, M. and T. B. Pekoz, Partial Moment Redistribution in Cold-Formed Steel, Journal of Structural Engineering, ASCE, Vol. 111, No. 6, June American Iron and Steel Institute, Cold-Formed Steel Design Manual, Washington, D. C., Yu, W. W., Cold-Formed Steel Design, nd edition, Wiley-Interscience, NY, Winter, G., Discussion of Strength of Beams as Determined by Lateral Buckling, by Karl de Vries, Transactions, ASCE, Vol. 11, Winter, G., Lateral Stability of Unsymmetrical I-beams and Trusses, Transactions, ASCE, Vol. 198, Kirby, P. A. and D. A. Nethercot, Design for Structural Stability, John Wiley and Sons, Inc., NY, Pekoz, T. B. and G. Winter, Torsional-Flexural Buckling of Thin-Walled Sections Under Eccentric Load, Journal of Structural Division, ASCE, Vol. 95, No. ST5, May Pekoz, T. B. and N. Celebi, Torsional-Flexural Buckling of Thin-Walled Sections Under Eccentric Load, Engineering Research Bulletin 69-1, Cornell University, Galambos, T. V., Inelastic Buckling of Beams, Journal of Structural Division, ASCE, Vol. 89, No. ST5, October Pekoz, T. B. and P. Soroushian, Behavior of C- and Z- Purlins Under Uplift, Report, No. 81-, Cornell University, R - 5