MOIS 89014
(Cold-Formed Steel Structures) (88) - ( ) 1
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".
4 4 5 6 8 10 1 1. 13 15.. 16 ( ) 3
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) 0.0149 in (0.378mm) 0.5 in (6.35mm) 1850 1946 4
-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
( ) (88) - ( ) steel home ( ) 6
RC 7
(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
1.. 3. 4. 1.. 3. 4. 9
(Specification for the Design of Cold-Formed Steel Structural Members) 1. Word 97. Times New Roman 1 3. : :16 4. : :14 10
5. : :1 6. : :1 :0.8cm 7. 8. : :1 :1.cm 9. 10. 11. - 1. 4.1 4.1.1 13. : 1-1 - -3 C- 14. -1 - -3 (4.1-1) 15. [1.] [4.5 4.36] [4.1] [4.] 4.5. Winter, G., Commentary on the 1968 Edition of Light Gage Cold-formed Steel Design Manual, American Iron and Institute, 1970. 16..54 cm 3.17 17. 11
199 500 1998 1 10 % ( 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
Design of Cold-formed Sections (The Steel Construction Institute) (Cold-Formed Steel Design Manual) (88) - ( ) 13
(National Association of Home Builders - NAHB) (U.S Department of Housing and Urban Department - HUD) - Prescriptive Method for Residential Cold-Formed Steel Framing 1993 11 1995 (000) 14
194 George Winter 15
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, 1999.. 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 5950. 6. Steel Construction Institute, 1993, Building Design using Cold-Formed Steel Sections : Worked Examples to BS 5950 : Part 5 : 1987. 7. 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., 1995 10. 1998 11. 16
( ) 17
1.1 1-1 1. 1-1 1.3 1-3 1.4 1-6.1-1. -1.3-3 3.1 3-1 3.1.1. 3-1 3.1.. 3-1 3.1.3. 3-1 3. 3-1 3.3 3-3 3.4 3-5 3.5 3-7 3.6 3-8 4.1 4-1 4. 4-1 4..1. 4-1 4... 4-3 4.3 4-4 4.3.1. 4-4 4.3.. 4-8 4.3.3. 4-8 4.4 4-10 4.4.1. 4-10 4.4.. 4-11 1
4.5 4-11 4.5.1. 4-13 4.5.. 4-14 4.5.3. 4-15 4.6 4-17 4.6.1. 4-17 4.6.. 4-17 5.1 5-1 5. 5-1 6.1 6-1 6. 6-1 6..1. 6-1 6... 6-5 6..3. 6-1 6..4. 6-13 6.3 6-14 6.4-6-15 6.5 6-17 6.6-6-4 7.1. 7-1 7.. 7-1 7.3-7-7 7.4. 7-8 8.1. 8-1 8.. 8-1 8.3. 8-9.1. 9-1 9.. 9-1
9.3 9-9.4 9-3 10.1.. 10-1 10... 10-1 10..1 I 10-1 10.. 10-4 10.3.. 10-5 10.3.1... 10-5 10.3. C Z... 10-5 10.3..1. 10-5 10.3...... 10-7 10.4.. 10-10 10.5.. 10-10 10.5.1 10-11 10.5. 10-11 10.5.3 10-15 11.1.. 11-1 11... 11-1 11..1 11-11.. 11-3 11...1. 11-4 11.... 11-7 11..3 11-8 11..4 11-10 11..5 11-1 11..6..... 11-16 11..7... 11-17 11.3.. 11-17 11.3.1. 11-19 11.3.. 11-0 11.3.3. 11-1 11.3.4. 11-11.4 11-4 11.4.1 11-6 3
11.4.. 11-6 11.4.3. 11-6 11.4.3.1.. 11-6 11.4.3... 11-7 11.4.4. 11-8 11.4.4.1.. 11-8 11.4.4... 11-8 11.4.4.3.. 11-8 11.5. 11-8 11.6. 11-9 11.6.1.. 11-9 11.6... 11-30 11.6.3.. 11-30 1.1.. 1-1 1.1.1 1-1 1... 1-1 1.3.. 1-1 1.3.1 1-1.3. 1-1.3.3 1-1.3.4 1-1.3.5 1-3 1.3.5.1. 1-3 1.3.5.. 1-3 1.3.6 1-4 1.3.7 1-4 1.4.. 1-4 1.4.1 1-4 1.4. 1-4 1.5.. 1-5 1.5.1 1-5 1.5.1.1. 1-5 1.5.1.. 1-5 13.1.. 13-1 4
13... 13-1 13.3.. 13-1 13.4.. 13-5
1.1 5.4 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) 6. 7. (corner fillet) (Specification for the Design of Cold-Formed Steel Structural Members) [1.3] [1.4 1.5] 1. 1-1
1.3 (LRFD) φr n R u (1.3-1) R u = R n = φ = φr n = (Limit State) (post-buckling) [1.6 1.7] 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 -
Q R Q m R m Q R Q m R m Q R C-1.3-1 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
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-1.3-3 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 [1.9 1.10] 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
(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-1.3-10) (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] [1.13-1.17] [1.11 1.1 1.18] [1.18] 0 LRFD 0=3.0 0=4.5 0=.5 D/L=1/5 =.79 1-5
.79 0=.5 0=3.5 AISI [1-3] 1.4 (E) 050 / (G)790 / (µ) 0.3 0.00001/ºC 1-6
.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 = 1. 485 kg/m (100 psf) (3) (4) (5) (L) 1.0. 0.9 3. (3) L r 1.4 1.6 [.1..3] ( ) ASCE7-95 - 1
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) 6. 0.9D-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-1.3-4 C-.-4 [.4] φ = 1.51( P M F ) exp( β V + V ) (C-.-5) m m m 0 R Q -
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
3.1 3.1.1 3. 3.1. 3. CNS608 (CNS) 3.1.3 CNS 3. CNS 6183 CNS 9704 CNS 144 3-1
CNS 10804 CNS 8499 CNS 978 ASTM AWS (1) () (3) ( CNS ASTM ) 1. CNS 473 ASTM A36. ( ) CNS 947 ASTM A36 A83D A57 A709 3. ( ) 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 A588 3. A83 4. A59 5. A570 6. ( ) A57 7. A606 8. A607 9. A611 10. A653 11. A715 1. A79 [3.] CNS 6183( 84 16 ) 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 9704 3 -
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 11984 ( ) CNS 6183 SSC 400 [3.1] (1) 17 55 MPa (5 80 ksi) () 90 690 MPa (4 100 ksi) (3) 1.13 (4) (elongation) 10 percent (1) 00 500 MPa () 300 500 MPa (3) 1.08 (4) 8 3.3 ( )F y 3.1 3.4 C-3.3-1 - (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
E 000 100 / E=050 / C-3.3-1 - (a) (b) 3-4
C-3.3- - 3.4 5 6..1 7 8 9 10.5 (F y ) (F ya F ya 1. 4. 1.0 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
B c = 3.69(F uv /F yv )-0.819(F uv /F yv ) -1.79 (3.4-3) m = 0.19(F uv / F yv )-0.068 (3.4-4) R = F yv = F yu =. C-3.4-1 [3.3] C-3.4-1 (Strain Hardening) (Strain Aging) [3.4] C-3.4- C-3.4- A - B C - D - C D (cold-work effect) 3-6
1.. 3. 4. (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-3.4-3.5 ASTM [3.5] (1) 1.08 ()5.08cm(in) 10 0.3cm(8in) 7 AISI 3-7
3.6 95 % (coating) 3-8
4.1 C-4.1-1 C-4.1-1 4. 4..1 1. - (w/t) (1) a. 60 4-1
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 ( ) 4..1 4..1 L/w f L/w f 30 1.00 14 0.8 5 0.96 1 0.78 0 0.91 10 0.73 18 0.89 8 0.67 16 0.86 6 0.55 L L L w f I U 1/ I w f 30 50 4 -
60 500 ( ) c f (4.-1) w f [4.1] ( ) ( C-4.-1) [4.] 4..1 I C-4.-1 4.. (h/t) 1. 00. 4.6.1 (1) 60 () 300 h t ( ) h/t ( ) ( ) ( ) 4-3
4.. [4.3-4.9] 4.3 4.3.1 1. (b) λ 0.673 b = w (4.3-1) λ > 0.673 b = ρw (4.3-) w = C-4.3- ρ = (1-0./λ)/λ 1.0 (4.3-3) λ = w f λ = 1. 05 (4.3-4) k t E (4.3-4) t E k 4.0 f (1) a. 6..1 I f = F y f (M y ) b. 6..1 II f (M n ) c. 6.. f (M c /S f ) () f 7. 10.5. F n. (b d ) λ 0.673 b d = w (4.3-5) λ > 0.673 b d = ρw (4.3-6) w = ρ = (1) I f d f (4.3-3) (4.3-4) ρ f d 4-4
() II ρ λ 0.673 ρ = 1 (4.3-7) 0.673<λ<λ c ρ = (1.358-0.461/λ)/λ (4.3-8) λ λ c ρ = ( 0.41 0.59 F / f 0. / λ ) / λ (4.3-9) + y d λ c = 0.56 + 0.38( 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-4.3-1 4-5
C-4.3- (C-4.3-1) [4.10] (1) () ( C-4.3-3) C-4.3-3 C-4.3-3 f max F y 193 Th. v. Karman [4.11] 4.3 (1) () 4-6
(3) (w) (f max (b) Th. v. Karman [4.11] Winter 1946 E t E b = 1.9t 1 0.475 (C-4.3-) f max w f max f cr /f max b w f 1 0.5 = cr cr f max f max f (C-4.3-3) 1946 1968 (C-4.3-) [4.] E t E b = 1.9t 1 0.415 (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] (4.3-7 4.3-10) 4-7
I II 4.3. 1. (b) 0.50 d h /w 0 w/t 70 0.50 w 3d h λ 0.673 b = w d (4.3-11) h 0. 0.8d w 1 λ w λ > 0.673 b = λ (4.3-1) b w - d h w = d h = λ = (4.3-4). h (4.3-1) (b d ) 4.3.1 ( I) 4.3. Ortiz-Colberg Pekoz [4.13] Yu [4.10] 4.3.3 1. b 1 b ( C-4.3-4 ) b 1 = b e / (3 - ψ) (4.3-13) ψ -0.36 b = b e / (4.3-14) b 1 +b ψ > -0.36 b = b e b 1 (4.3-15) b e = 4.3.1 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-4.3-4 4-8
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-4.3-4 4-9
C-4.3-1 4.4 4.4.1 1. (b) 4.3.1 k 0.43 (w) C-4.4-1. (b d ) 4.3.1 I k 0.43 f d f f d (w/t) 4-10
(C-4.3-1) (k) 0.43 ( C-4.3-1 ) C-4.4-1 4.4. 1. (b) 4.3.1 k 0.43 f 3 f f 3 C-4.5-. (b d ) 4.3.1 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
) b 0 = C-4.5-1 C 1, C = C-4.5- d, D = C-4.5- d s = d s 4.5. d se = d s = 4.4.1 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-4.5-1 4-1
C-4.5-1 ( ) Pekoz [4.14] C-4.5-4.5.1 1. b 0 / t S I a = 0 ( ) 4-13
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 4.3.1 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 4.3.1 k = 3(I s /I a ) 1/3 +1 4 (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 [4.14 4.17] ( ) (b) (A s ) I s /I a I s I a I a 4.5. 1. 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 = 4.3.1 k = C n (K a - K u ) + K u (4.5-18) 4-14
k u = 0.43 (1) D/w 0.8 140 θ 40 (θ C-4.5- ) k a = 5.5 5 (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 (4.5-3) 4 I / t 3.66 ( w / t) (0.136E) / F 18.4 (4.5-3) min = y w/t = ( ) I s = 1. 4.3.1 (b<w). 4.3.1 (b<w) 4-15
3. 4.3.1 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 = 0.10 60 (4.5-5) t t t w/t = b = 4.3.1 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
( ) (b 0 ) (t s ) w/t ( ) 60 C-4.5-3 C-4.5-3 4.6 4.6.1 4-17
(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 )0.85 4.6. 6.3 (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 50 4-18
A st 1 C = v a h ( a / h) ( a / h) + 1 + ( 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 = 4.00 + a/h 1.0 (4.6-7) ( a / h) 4.00 k v = 5.34 + 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
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 = 11.3. 11.3. ( ) (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
V R = VM + VF + VP = 0.11 V Q = 0.1 0.95 (β).4 β 0 =.5 5 -
6.1 (a) (b) (c) (d) (a) (b) (c) 6.~6.6 (d) 6. M n 6..1 6.. ~ 6..4 ( 6..1 ) (Lateral-Torsional Buckling 6.. ) C Z ( 6..3 ) C Z ( 6..4 ) 6..1 [ ] [ ] φ b = 0.95 φ b = 0.9 1. [ ] Mn M n = S e F y (6.-1) F y = S e = ( F y ) 6-1
. [ ] (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 1. 11 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) 6.6 1. [ ] M n M y 6 -
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
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 / 1/5.53 4.05 [6.1 6.]. [ ] 1970 1980 [6.3-6.5] (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-6..1-3) 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
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
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) 0.6 0.4 M M 1 M ( M 1 ) M 1 M C TF 1 r 0 polar radius of gyration M 6-6
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 6.8] 6-7
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 + 1 + 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 = 1.75 + 1.05 + 0.3.3 (C-6.-9) M M M 1 M C-6.-9 1996 AISI Kirby and Nethercot [6.10] C-6.-10 1.5M 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
C-6.-10 ( ) 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 ) 10 10 Fy xc yc ( σ = cr ) I Fy 1 (C-6.-1) 9 36 cbπ E I 6-9
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) 1968 1986 (C-6.-11) (C-6.-13) 1996 (6.-9) (6.-10) [6.11 6.1] ( 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
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.4 3.8 I Z C-6.-5 U U C-6.-6 C-6.-5 6-11
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 1. 9. (11.5 ). 3. 60 170 4..8 4.5 5. 16 43 6. ( ) 1.5d 7. 10 (33 ) 8. 0% 9. 10. 0.48mm (0.019 in) 5.4 mm (1in) 305mm (1 in) 11. 0 15 mm (6in) 1. #1 4.76 6-1
mm( 3/16in ) 1.7mm(0.5in) 13. stand off 14. 30.5mm (1in) [6.14-6.19] R M=0.08wL La Boube [6.16] [6.1 6.] LRFD φb 1.5 1.6 (C-6.-0) = 0. 9 β 1.5 1.17W-0.9D W D 0.9 6..4 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
6.3 V n 1. h t 0. 96 Ek v F y V = 0. F ht (6.3-1) n 6 y φ v = 1.0. 0.96 Ekv F y < h t 1. 415 Ekv F y V n = 0.64t k F E (6.3-) v y φ v = 0.9 3. h t > 1. 415 Ek v F y V n φ v = 0.9 3 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 = 4.0 + (6.3-4) ( a h) b. a / h > 1.0 k v 4.0 = 5.34 + (6.3-5) ( a h) a = = 6-14
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 6.4 - 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
M u Vu 0.6 + 1.3 φbm nxo φvvn φ b = 6...1 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-6.4-1 (C-6.4-) 6-16
C-6.4-1 τ/τ max f b /f bmax 6.5 P n 6.5-1 φ w = 0.75 I φ w = 0.8 Z (two-nested Z sections) (6.5-4) φ w = 0.85 h / t 00 6.5-1 R / t 6 R / t 7 N / t 10 N / h 3.5 Z (6.5-1) 1.3 6-17
1. h / t 150. R / t 4 3. 1.5mm (0.06in.) 4. 4.76mm (3/16 in.) P n P n I 6.5-1 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) 6.5-1 1. C I ( C ). 1.5h 3. 1.5h 4. 1.5h 5. 1.5h 6.5-1 [ ( h θ 331 0. )] [ 0.01( N )] t kc C C C 61 3 4 9 t [ ( h θ 17 0. )] [ 0.01( N )] t kc C C C 8 3 4 9 > 60 t t 1 + t * (6.5-1) 1 + t * (6.5-) N [ 1 + 0.01 ( N ) ] [ 0.71 + 0.015( N )] t t 6-18
t F C y 6 10.0 + 1. 5 N t [ ( h θ 538 0. )] [ 0.007( N )] t kc C C C 74 1 9 > 60 t t (6.5-3) 1+ (6.5-4) t N [ 1+ 0.007 ( N ) ] [ 0.75 + 0.011( N )] t F C + m y 5 (0.88 0.1 ) 15.0 + 3. 5 t N t [ ( h θ 44 0. )] [ 0.01( N )] t kc C C C 57 3 4 9 ( 0.64 + 0.31m) 10.0 + 1. N t FyC8 5 t [ ( h θ 771. )] [ 0.0013( N )] t kc C C C 6 1 9 ( 0.8 + 0.15m) 15.0 + 3. 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 = 1.06-0.06 R/t 1.0 (6.5-11) C 3 = 1.33-0.33k (6.5-1) C 4 = 1.15-0.15 R/t 1.0 ( 0.5) (6.5-13) C 5 = 1.49-0.53k 0.6 (6.5-14) h t C 6 = 1+ 750 h 150 t (6.5-15) = 1. h > 150 t (6.5-16) C 7 = 1 h/t 66. 5 (6.5-17) k h t 1 = 1.1 665 k h/t > 66.5 (6.5-18) h t 1 C 8 = 0.98 865 k h/t 66. 5 (6.5-19) C 9 = 6.9 ( N mm) C θ = 0.7 + 0.3 ( θ ) 90 h/t 66. 5 (6.5-0) F y = MPa h = (mm) 6-19
k = 894Fy/E (6.5-1) m = t / 1.91 (mm) (6.5-) t = (mm) N = (mm) N R = θ = (45 θ < 90 ) C-6.5-1 I C-6.5-1 [6.7] 7 1.. 3. 4. ( ) 5. 6. 7. AISI [6.-6.4] I (1) () (3) (4) C-6.5- (a) (b) 6-0
1.5 C-6.5- (a) (b) (c) (d) ( Z ) I ( ) C-6.5-3 (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) [6.4 6.5] C-6.5-4 C-6.5-3(b) C-6.5-3(a) P n ( AISI ) 6-1
C-6.5-3 6.5-1 6 -
C-6.5-4 6-3
(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).4 3.8 Z [6.6 6.7] 7% 55% 30% (AISI 1996) Z [6.8] (6.5-4) 6.6-1. 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 0.673 6.5 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
λ = ( 4.3.1 ) 3. Z (two-nested Z sections) M u Pu + 1.68φ 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 140 3. F y 483 Mpa (70 ksi) 4. R / t 5.5 1. 1.7 mm (0.5 in.) A307. 1.7 mm (0.5 in.) A307 3. 4. 1.3 (6.6-1) (6.6-) (C-6.6-1) (C-6.6-) 551 φ w =0.75 φ w =0.8 I.5 3.3 Z (6.6-3) [6.8] 14 6-5
C-6.6-1 C-6.6- I 6-6
7.1 7. φ c P n φ c =0.85 P n =A e F n (7.-1) A e = F n A e 4.. 0.015 F n λ c 1.5 n ( 0.658 λ F y c F = ) (7.-) λ c >1.5 F n 0.877 = F λc y (7.-3) Fy λ c = (7.-4) F e F e = - 7.3 7.4 - M ux M uy 8.3 KL/r 00 KL/r 300 (1) () ( - ) (3) 7-1
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 -
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 ( 0.658 c = λ ) F (C-7.-9) n y λ c >1.5 F n 0.877 = 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
C-7.- ( ) K 1.0 C-7.-3 K [7.6] [7.3 7.7] K [7.4] C-7.-1 C-7.- 7-4
C-7.-1 K C-7.-3 K 3. Torsional Buckling I Z 7-5
[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-7.-10 σ t F n λ c 4. - Torsional-Flexural Buckling - T I - C-7.-4 - C-7.-4 - - 7-6
- [7.8 7.9 7.10] 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 7.3 - - 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
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 [7.1 7.10] 7-8
8.1 8. -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 = 0.90 0.95( 6..1 ) 0.90( 6.. φ t = 0.95 ) (8.-1) (8.-) 8.3 - P u M ux M uy 8-1
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 = 0.90 0.95( 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 -
K y = y C mx C my = 1. (joint translation) C m = 0.85. C m = 0.6-0.4(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
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 < 0.441 E/F y (D/t) 0.441E/F y D/t 9. (M n ) D/t 0.070 E/F y (9.-1) M n = 1.5 F y S f 0.070 E/F y D/t 0.319 E/F y 9-1
M n E / Fy = 0.970 + 0.00 FyS f D t (9.-) / 0.319 E/F y D/t 0.441 E/F y M n = [0.38E/(D/t)] S f (9.-3) φ b = 0.95 S f = 1.9 (9.-1 9.-3) Sherman[9.] (shape factor) 1.5 9.3 ( ) (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 ( 0.658 ) F y F c = (9.3-) 0.877 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 -
A 0 = 0.037 A DF y te + 0. 667 A D/t 0.441 (E/F y ) (9.3-7) ( ) /( ) A = (F e ) (A e ) (9.3-5) 9.4 9-3
10.1 (1)C I ()C Z (3) 10. 10..1 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
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/ [10.1 10.] I (10.-1) C r I. I (10.-) [10.] C C-10.-1 Q (Qm) (T s (T s g) 10 -
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-10.-1 C C-10.- C L/3 L/6 (10.-) 10.. 10-3
( ) 1.. 1.16t(E/f c ) 0.5 t f c 3. 1.11t(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 ) 1 1.7 mm (0.5 in) C-10.-3 (W) 1.67f c C-10.-3 f c, [10.1 10.] σ = cr π E ( KL / r) σ cr = 1.67f c K = 0.6 L = s r = t/(1) 0.5 K 0.6 0.5( ) [10.1 10.] C-10.-3 10.3 10-4
10.3.1 ( ) Winter [10.3] Haussler [10.4] Haussler Pabers [10.5] Lutz Fisher [10.6] Salmon Johnson [10.7] Yura [10.8] SSRC [10.9] 10.3. C Z C Z (1) () C Z 1 10.3..1 6..1 C Z /360 1. C C 0.05W W ( ) 0.05W/. Z 4 0 Z 10-5
(1) P L 1.50 0.0b = 0.5 sinθ W 0.7 0.90 0.60 n p d t () 1/3 P L 1. 0.474b = 0.5 sinθ W 0.57 0.89 0.33 n p d t (3) P L 1.3 0.4b = sinθ W 0.65 0.83 0.50 n p d t (4) P L 1.88 0.13 0.053b L = Ctr sinθ W 0.95 1.07 0.94 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 1.15 0.5 0.181b L = Cth sinθ W 0.54 1.11 0.9 n p d t (10.3-5) C th = 0.57 C th = 0.48 (6) P L 1.3 0.18 0.116b L = Cms sinθ W 0.70 0.50 n p d t (10.3-6) C ms = 1.05 C ms = 0.90 b = d = t = L = 10-6
θ = Z ( ) n p = W = P L 4 1.1 (10.3-1 10.3-6) 0 (10.3-1 10.3-6) n p 0 W Z Murray Elhouar [10.10] (10.3-1) (10.3-6) Murray Elhouar 1/4 10.3.. ( ) (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 = 10..1 d = Z K =I xy / I x (10.3-8) I xy = I x = 10-7
C I C C-10.3-1 C-10.3- C C-10.- I I C (1) ( ) () C-10.3-1 C C-10.3- C C [10.1] C 10-8
C-10.3-3 (Qm) P = Qm/d C Winter Lansing McCalley[10.11] C-10.3-4 C (P L ) C-10.3-3 C C-10.3-4 10.3.3 0.086 E/F y 10-9
10.4 10.4.1 10.4.3 1. 4.3. F n (A e ) A e (1) 610mm () 0.5 d 63.5mm (3) 114mm (4) (d/t) 0 (5) 54mm. 10.4.1 10.4.3 (A e ) 10.4-1 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
( ) Green Winter Cuykendall [10.1] 10 4 1970 ( ) C Z Yu [10.] Simaan [10.13] Simaan Pekoz [10.14] Simaan [10.13] Simaan Pekoz [10.14] Davis Yu [10.15] 16 10.4.1 M nxo M nyo φ b = 0.95 φ b = 0.90 M nxo M nyo 6. 6.. 10.4. P n = A e F n (10.4-1) φ c = 0.85 A e = F n F n = 1. F n 10-11
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) (10.4-10) σ t = 1 Ar 0 GJ π EC + L w (10.4-11) σ tq = Q = σ + Q (10.4-1) t t Q o (-s/s ) (10.4-13) s = (mm) 15mm s 305mm s =305mm 10-1
Q o = 10.4-1 Q a = Q / A (10.4-14) A = L = t ( Qd ) ( 4Ar ) Q = (10.4-15) / o d = I xy = 3. F n γ = (π/l)[c 1 +(E 1 d/)] (10.4-16) C 1 E 1 C 1 E 1 (1) C C 1 = (F n C o )/( σ ey -F n + Q ) (10.4-17) 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 )] (10.4-18) ()Z Fn [ Co( σ ex Fn ) Doσ exy ] C 1 = ( σ F + Q )( σ F ) σ ey n a ex n exy (10.4.19) 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
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 ( ) 10.4-1 10.4-1 Q o γ kn / 107.0 53.4 3.0 9.5mm 15.9mm ( ) ( ) 64.1 0.008 0.009 0.007 0.010 10.4-1 6 S-1 1.7mm Q o γ C-10.4-1 ( C-10.4-) Simaan[10.13] Simaan Pekoz[10.14] 10.4 ( ) Pekoz [10.17] Miller Pekoz [10.18 10.19] 10-14
C-10.4-1 C-10.4-10.4.3 P n = 10.4. (8.3-1) (8.3-) (8.3-3) M nx M ny M nxo M nyo 10-15
11.1 [11.1] 1. ( ) ). (1) ( ) () 11. 4.57 mm 4.57 4.57 mm (AWS) AWS D1.3 AWS D1.3 11.-1 AWS C1.1 AWS C1.3 11-1
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-11.-1 C-11.-6 3.81 mm (0.15 in) 11..1 11..6 4.57 mm (0.18 in) ( 11.-3) 3.81 mm 11..1 P n 1. P n = L t e F y (11.-1) φ = 0.90. (11.-) (11.-3) 11 -
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 = 11.. 11.-1 11.- 0.711 mm 1.7 mm.03 mm 9.53 mm d e 9.5mm C-11.-1 11-3
C-11.- ( ) ( ) 11...1 P n πd e 1. P n = 0.75Fxx 4 φ =0.60. (d a /t) 0.815 E / F ) ( u (11.-4) P n =.0 t d a F u (11.-5) φ =0.60 0.815 E / F ) < (d a /t) <1.397 E / F ) ( u ( u E / F P n =0.80 + u 1 5.59 t d a F u (11.-6) d a / t φ =0.50 (d a /t) 1.397 E / F ) ( u P n =1.40 t d a F u (11.-7) φ =0.50 P n = 11-4
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-11.-3 C-11.-4 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-11.-5 C-11.-6 1.5 d 1.0 [11.] (1) () (3) (4) C-11.-7 ( C-11.-4 ) 0.711 mm 11-5
C-11.-3 - C-11.-4 C-11.-5-11 - 6
C-11.-6 C-11.-7 11... P n πd 1. P n = e Fxx 4 φ =0.60. F u /E < 0.00187 (11.-10) Pn = [6.59-3150(F u /E)]td a F u 1.46td a F u (11.-11) F u /E 0.00187 Pn = 0.70 td a F u (11.-1) φ = 0.60 e min d 11-7
F xx 414 Mpa F u 565 Mpa F xx F u 11...1 50% 11.-11 11.-1 70% - [11.5 11.6] (1) () [11.5 11.6] 11.-11 11.-1 50% [11.5 11.6] C-11.-8 C-11.-8 ( C-11.-8 ) [11.7] 70% 11..3 ( C-11.-9) 11-8
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 11...1 11...1 ( C-11.-10) 11.-1 [11.4] 11.-13 C-11.-9-11 - 9
C-11.-10 11..4 1.. 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 = 0.55. P n =tlf u (11.-16) φ =0.60 t C-11.-11 C-11.-1 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 1 0.707w 11-10
w 1 w = ( C-11.-11 C-11.-1) L w 1 t 1 F u F xx 11...1 [11.] L w 1 w w 1 ( C-11.-11) C-11.-13 C-11.-11 L C-11.-1 T [11.] 3.81mm 11-11
3.81mm C-11.-13 11..5 1. V. 3. P n 1. ( C-11.-14) P n =0.833tLF u (11.-18) φ =0.55. ( C-11.-15 ~ C-11.-17d) (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
t w = 90 ( C-11.-17a C-11.-17b) = 5/16R V =1/R( R>1.7mm 3/8R = 90 = 0.707w 1 0.707w ( C-11.-17c C-11.-17d) = R = w 1 w = ( C-11.-17c C-11.-17d) F u F xx 11...1 ( C-11.-18) 11.-1 11.-1 11.-17a 11.-17b 90 AWS D1.1-96[11.8] 11.-17c 11.-17d 90 W 1 ( 11.-17c) ( 11.-17d) C-11.-14 11-13
C-11.-15 C-11.-16 V C-11.-17a (W 1 =R) 11-14
C-11.-17b (W 1 =R) C-11.-17c (W 1 >R) C-11.-17d (W 1 <R) 11-15
C-11.-18 11..6 P n P n = 11.. φ = 0.65 11.. (mm) (mm) (kn) (kn) 0.5 0.58.03 14.81 0.51.14.9 17.79 0.76 4.45.54.0 1.0 6.3.79 7.00 1.7 7.34 3.17 3.43 1.5 10.14 4.83 45.19 1.78 1.59 6.35 66.7 3. mm Recommended Practice for Resistance Welding Coated Low-Carbon Steel AWS C1.3-70 (.1- ) 3. mm Recommended Practice for Resistance Welding Coated Low-Carbon Steel AWS C1.1-66( 1.3- ).7 N/m AWS C1.3-70.1 AWS C1.1-66 1.3 11-16
AWS C1.3-70 AWS C1.1-66[11.9 11.10] 11..7 11..3 11..3 CNS 6183 SSC41 CNS 115 CNS 3506 11.3 4.76 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
11.3-1 11.3-1 ( ) d <1.7 1.7 d h d + 0.8 d + 1.6 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 + 1.6 d + 3. 1. 4.76 mm 4.76 mm [11.11] ( 4.76 mm). A35 A490 1.7 mm A449 A354 Grade BD 1.7 mm 3. 11-18
4. 11.3-1 1.7 mm ( ) [11.1 11.13] 1.7 mm 0.794 mm 11.3-1 11.3.4 11.3.1 (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 11.3-1 11-19
(d) (d) e min (F u ) F u /F sy P e = (C-11.3-1) Fu t e = P = t = (C-11.3-1) Winter [11.14 11.15] Yu [11.16-11.18] 11.3. P n 1. P n = (1.0-0.9r+3rd/s)F u A n F u A n (11.3-) φ = 0.65 φ = 0.55. 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
1. 4.76 mm 4.76. (P n ) (F u ) r d/s 3. [11.19] 4. ( ) (P n ) 11.3.3 F u /F sy 11.3-11.3-3 (P n ) φ 11.3-11.3-3 φ P n d F u t 11.3- t (mm) F u /F sy φ P n 0.61 t<4.76 t 4.76 1.08 0.55 3.33F u dt <1.08 0.65 3.00F u dt 0.60 3.00F udt 11.3-3 t (mm) F u /F sy φ P n 0.61 t<4.76 1.08 0.65 3.00F u dt 1.08 0.70.F u dt t 4.76 11-1
F u /F sy (Winter[11.14 11.15] Yu[11.16 11.18] Chong Matlock[11.19]) 11.3-11.3-3 11.3.4 P n P n = A b F (11.3-5) A b = F 11.3-4 F nv F nt φ 11.3-4 F 11.3-5 F nt φ 11.3-5 11 -
11.3-4 F φ nt F φ nv (MPa) (MPa) A307 Grade A 0.75 79 0.65 165 6.4 mm d<1.7 mm A307 Grade A 310 186 d 1.7 mm A35 61 37 A35 61 496 A354 Grade BD 6.4 mm d<1.7 mm 696 407 A354 Grade BD 6.4 mm d<1.7 mm 696 61 A449 6.4 mm d<1.7 mm 558 34 A449 6.4 mm d<1.7 mm 558 496 A490 6.4 mm d<1.7 mm 776 465 A490 6.4 mm d<1.7 mm 776 61 11-3
11.3-5 F nt (MPa) φ A35 779-17f v 61 779-13f v 61 A354 Grade BD 876-17f v 696 876-13f v 696 A449 0.75 696-17f v 558 696-13f v 558 A490 97-17f v 776 97-13f v 776 A307 Grade A 6.4 mm d<1.7 mm d 1.7 mm 34-5f v 79 359-5f v 310 0.75 1.7 mm (1/ in.) A307 A449 A354 1.7 mm 10% 6.35 mm (1/4 in.) 9.63 mm (3/8 in.) (tensile-stress area / gross-area) 0.68 1.7 mm(1/ in) 5.4 mm(1 in.) 0.75 10% 11.3-4 LRFD ( ) (pull-out failure) ( ) C Z 11.4 d = ( C-11.4-1) φ = 0.5 P ns = P nt = P not = P nov = t 1 = t = F u1 = F u = 11-4
11.4.03 mm(0.08 in.) 6.35 mm(0.5 in.) 10.5 11..3 3500 [11.0] [11.1 11.] [11.3] C-11.4-1 C-11.4-1 C-11.4-1 d mm (in.) 0 1.5 (0.060) 1 1.85 (0.073).18 (0.086) 3.51 (0.099) 4.84 (0.11) 5 3.18 (0.15) 6 3.51 (0.138) 7 3.84 (0.151) 8 4.17 (0.164) 10 4.83 (0.190) 1 5.49 (0.16) 1/4 6.35 (0.50) 11-5
C-11.4-1 11.4.1 (3d) 11.4. (3d) 1.5 (1.5d) 3 11.4.3 11.4.3.1 (P ns ) t /t 1 1.0 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-11.4-11 - 6
P ns Eq. 11.4-3 Eq. 11.4-1 C-11.4- t ( C-11.4-3 ) ( C-11.4-4) N/A t 1.7 t 1 df u1 t.7 t df u C-11.4-3 4.(t 3 d) 1/ F u t 1.7 t 1 df u1 t.7 t df u C-11.4-4 11.4.3. 1.5 P ns φ 11.4.3. 11.4.3.1 1.5 11-7
11.4.4 ( ) d w 7.94 mm 1.7 (1) (pull-out failure) () (pull-over failure) (3) 1.7 mm 11.4.4.1 (P not ) P not =0.85 t c d F u (11.4-6) t c t 11.4-6 [11.1] Pekoz [11.3] 11.4.4. (P nov ) P nov =1.5t 1 d w F u1 (11.4-7) d w 1.7 mm 11.4-7 [11.] Pekoz [11.3] 11.4.4.3 (P nt ) 1.5 P not P nov φ 1.5 11.5 (V n ) V n = 0.6 F u A wn (11.5-1) φ = 0.75 11-8
A wn = (d wc n d h ) t d wc = n = d h = F u = t = Birkernoe Gilmor [11.4] C-11.5-1 [11.11] [11.11] P C-11.5-1 11.6 11.6.1 P p = 0.85f c A 1 (11.6-1) P p = 0.85f c A 1 A / A (11.6-) 1 φ c = 0.60 11-9
f c = A 1 = A = A / A 1.0 11.6. ( ) ( ) / 11.6.3 11-30
1.1 1.1.1 1. -. - 3. - 4. - 5. - 6. - 7.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. 10. - 1. ( ) (Shop drawing) (Approve) (Detail Dimension) 1.3 1-1
1. 1. 3..1 3.1.3 1.3.1 1.3. 1.3.3 1.3.4 CNS AWS JIS 1.. 3. 4. 5. 6. 7. 1 -
1.3.5 1.3.5.1 1.. 3. 4. 5. 1.3.5. 1. (1) () (3). (1) () CNS ASTM (3) (White Rust) 1-3
1.3.6 1.3.7 1.4 1.4.1 1. (studs) (top and bottom track) (anchors) 10 ( ) 60 1.5. 30 3. 4. (axially loaded studs) 5. (lintels) 6. (horizontal strap bracing) 1.4. 1. (joist bridging) (metal deck or plywood). (end clips) 3. (joist) (wall studs) (lintels) 4. 4 9 1-4
1.5 1.. 3. 4. 1.. 3. CNS147. ASTM 4. 1.5.1 1.5.1.1 1. (studs) (gage) (depth and width) (spacing). 3. 4. 5. 6. 1.5.1. 1. (joists) (gage) (depth and width) (spacing). 3. 4. 1-5
5. 6. 1-6
1-7
13.1 UBC-97 AISC-97 UBC-97 13. 1.4D + 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 + 1.6 (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 ( ) 13.3 1. (l/r) 00. 3. (Ω 0 ) 4. (braced bay) 5. 13-1
6. 13.4 1. 1.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 0 3.0 R 1.6~.4 0.4 C.5 Fu 1.6~1.7 1.4 y Fu 1.764~.38 UBC-97 Ω 0.~.8 C/Fu<=1 Ω 0 3.0 13 -
1.1 1998 1. 1.3 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 1973. 1.5 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 1974. 1.6 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, 1986. 1.7 Yu, W. W., Cold Formed Steel Design, nd Edition, Wiley-Interscience, New York, NY, 1991. 1.8 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 1978. 1.9 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 1998. 1.10 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 1990. 1.11 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 1980. 1.1 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
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 1997. 1.14 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 1979. 1.15 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 1979. 1.16 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 1979. 1.17 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 1979. 1.18 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 198..1 American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE Standard 7-95, 1995.. 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 1980..3 Ellingwood, B., J. G. MacGregor, T. V. Galambos, and C. A. Cornell, R -
Probability Based Load Criteria: Load Factors and Load Combinations, Journal of the Structural Division, ASCE, Vo1. 108, No. ST5, May 198..4 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 1988. 3.1 American Iron and Steel Institute, Cold-Formed Steel Design Manual, 1996 Edition. 3. 3.3 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 1967. 3.4 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 1963. 3.5 American Society for Testing and Materials, Standard Methods and Definitions for Mechanical Testing of Steel Products, ASTM 370, 1994. 4.1 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, 1970. 4.3 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 1978. 4.4 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 1978. 4.5 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 198. 4.6 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
June 1978. 4.7 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, 1980. 4.8 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 1978. 4.9 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 1978. 4.10 Yu, W. W., Cold-Formed Steel Design, nd Edition, Wiley-Interscience, New York, NY, 1991. 4.11 Bleich, F., Buckling strength of Metal Structures, McGraw-Hill Book Co., New York, NY, 195. 4.1 Weng, C. C. and T. B. Pekoz, Subultimate Behavior of Uniformly Compressed Stiffened Plate Elements, Research Report, Cornell University, Ithaca, NY, 1986. 4.13 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, 1981. 4.14 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, 1986. 4.15 Cohen, J. M. and T. B. Pekoz, Local Buckling Behavior of Plate Elements, Research Report, Cornell University, Ithaca, NY, 1987. 4.16 Bulson, P. S., The Stability of Flat Plates, American Elsevier Publishing Company, New York, NY, 1969. 4.17 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 1986. 4.18 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. 1981. 4.19 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 1978. 4.0 Hsiao, L. E., W. W. Yu, and T. V. Galambos, Loads and Resistance Factor R - 4
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. 1988. 6.1 American Iron and Steel Institute, LRFD Cold-Formed Steel Design Manual, Washington, D. C., 1991. 6. 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 1988. 6.3 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 1975. 6.4 Yener, M. and T. B. Pekoz, Partial Stress Redistribution in Cold-Formed Steel, Journal of Structural Engineering, ASCE, Vol. 111, No. 6, June 1985. 6.5 Yener, M. and T. B. Pekoz, Partial Moment Redistribution in Cold-Formed Steel, Journal of Structural Engineering, ASCE, Vol. 111, No. 6, June 1985. 6.6 American Iron and Steel Institute, Cold-Formed Steel Design Manual, Washington, D. C., 1996. 6.7 Yu, W. W., Cold-Formed Steel Design, nd edition, Wiley-Interscience, NY, 1991. 6.8 Winter, G., Discussion of Strength of Beams as Determined by Lateral Buckling, by Karl de Vries, Transactions, ASCE, Vol. 11, 1947. 6.9 Winter, G., Lateral Stability of Unsymmetrical I-beams and Trusses, Transactions, ASCE, Vol. 198, 1943. 6.10 Kirby, P. A. and D. A. Nethercot, Design for Structural Stability, John Wiley and Sons, Inc., NY, 1979. 6.11 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 1969. 6.1 Pekoz, T. B. and N. Celebi, Torsional-Flexural Buckling of Thin-Walled Sections Under Eccentric Load, Engineering Research Bulletin 69-1, Cornell University, 1969. 6.13 Galambos, T. V., Inelastic Buckling of Beams, Journal of Structural Division, ASCE, Vol. 89, No. ST5, October 1963. 6.14 Pekoz, T. B. and P. Soroushian, Behavior of C- and Z- Purlins Under Uplift, Report, No. 81-, Cornell University, 1981. R - 5
6.15 Pekoz, T. B. and P. Soroushian, Behavior of C- and Z- Purlins Under Wind Uplift, Proceedings of the Sixth International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, November 198. 6.16 Laboube, R. A., Roof Panel to Purlin Connection: Rotational Restraint Factor, Proceedings of the IABSE Colloquium on Thin-Walled Metal Structures in Buildings, Stockholm, Sweden, 1986. 6.17 Laboube, R. A., M. Golovin, D. J. Montague, D. C. Perry, and L. L. Wilson, Behavior of Continuous Span Purlin System, Proceedings of the Ninth International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, November 1988. 6.18 Haussler, R. W. and R. F. Pahers, Connection Strength in Thin Metal Roof Structures, Proceedings of the Second International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, October 1973. 6.19 Haussler, R. W., Theory of Cold-Formed Steel Purlin/Girt Flexure, Proceedings of the Ninth International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, November 1988. 6.0 Bleich, F., Buckling Strength of Metal Structures, Mcgraw-Hill, NY, 195. 6.1 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 1978. 6. Winter, G. and R. H. J. Pian, Crushing Strength of Thin Steel Webs, Cornell Bulletin 35, pt. 1, April 1946. 6.3 Zetlin, L., Elastic Instability of Flat Plates Subjected to Partial Edge Loads, Journal of Structural Division, ASCE, Vol. 81, September 1955. 6.4 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, June 1978. 6.5 Winter, G., Commentary on the 1968 Edition of the Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, NY, 1970. 6.6 Bhaka, B. H., R. A. Laboube, and W. W. Yu, The Effect of Flange Restraint on Web Crippling Strength, Final Report, Civil Engineering Study 9-1, University of Missouri-Rolla, Rolla, MO, March 199. 6.7 Cain, D. E., R. A. Laboube, and W. W. Yu, The Effect of Flange Restraint on Web Crippling Strength of Cold-Formed Steel Z- and I-Sections, Final Report, R - 6
Civil Engineering Study 95-, University of Missouri-Rolla, Rolla, MO, May 1995. 6.8 Laboube, R. A., J. N. Nunney, and R. E. Hodge, Web Crippling Behavior of Nested Z-Purlins, Engineering Structures, Hancock, G. J., Editor, Vol. 16, No. 5, Butterworth-Heinemann Ltd., London, July, 1994. 7.1 American Iron and Steel Institute, Cold-Formed Steel Design Manual, Washington, D. C., 1996. 7. 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, 1986. 7.3 American Institute of Steel Construction, Load and Resistance Factor Design Specification for Structural Steel Buildings, Chicago, IL., December 1993. 7.4 Galambos, T. V. (Editor), Guide to Stability Design Criteria for Metal Structures, Fourth Edition, John Wilen and Sons, New York, N.Y., 1988. 7.5 Harper, M. M., R. A. La Boube and W. W. Yu, Behavior of Cold-Formed Steel Roof Trusses, Summary Report, Civil Engineering study 95-3, University of Missouri-Rolla, Rolla, MO, May 1995. 7.6 Winter, G., Commentary on the 1968 Edition of the Specification for the Design of Cold-Formed Steel Structural Members, American Iron Steel Institute, New York, NY, 1970. 7.7 American Institute of Steel Construction, Specification for Structural Steel Building-Allowable Stress Design and Plastic Design, Chicago, IL, 1989. 7.8 Chajes, A. and G. Winter, Torsional-Flexural Buckling of Thin-Walled Members, Journal of the Structural Division, ASCE, V01. 91, No. ST4, August 1965. 7.9 Chajes, A., P. J. Fang, and G. Winter, Torsional-Flexural Buckling, Elastic and Inelastic and Inelastic of Cold-Formed Thin-Walled Columns, Engineering Research Bulletin, No. 66-1, Cornell University, 1966. 7.10 Yu, W. W., Cold-Formed Steel Design, nd Edition, Wiley-Interscience, New York, N. Y. 1991. 7.11 Pekoz, T. B. and G. Winter, Torsional-Flexural Buckling of Thin-Walled Section Under Eccentric Load, Journal of the Structural Division, ASCE, V01. 95, No. ST5, May 1969. 8.1 Pekoz, T. B., Combined Axial Load and Bending in Cold-Formed Steel R - 7
Members, Thin-Walled Metal Structures in Buildings, IABSE Colloquium, Stockholm, Sweden, 1986. 8. Pekoz, T. B. and O. Sumer, Design Provisions for Cold-Formed Steel Columns and Beam-Column, Final Report, submitted to American Iron and Steel Institute, Cornell University, September 199. 8.3 American Institute of Steel Construction, Load and Resistance Factor Design Specification for Structural Steel Buildings, Chicago, IL, December 1993. 8.4 9.1 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, 1970. 9. Sherman, D. R., Bending Equations for Circular Tubes, Annual Technical Session Proceedings, Structural Stability Research Council, 1985. 10.1 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, 1970. 10. Yu, W. W., Cold Formed Steel Design, nd Edition, wiley-intersciance, New York, NY, 1991. 10.3 Winter, G., Lateral Bracing of Columns and Beams, Transactions, ASCE, Vo1. 15, 1960. 10.4 Haussler, R. W., Strength of Elastically Stabilized Beams, Journal of Structural Division, ASCE, Vo1.90, No. ST3, June 1964; also ASCE Transaction, Vo1. 130, 1965. 10.5 Haussler, R. W. and R. F. Pahers, Connection Strength in Thin Metal Roof Structures, Proceeding of the Second Specialty Conference on Cold Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, October 1973. 10.6 Lutz, L. A. and J. M. Fisher, A Unified Approach for Stability Bracing Requirements, Engineering Journal, AISC, 4 th Quarter, Vo1., No. 4,1985. 10.7 Salmon, C. G., and J. E. Johnson, Steel Structures: Design and Behavior, Third Edition, Harper Row, New York, NY, 1990. 10.8 Yura, J. A., Fundamentals of Beam Bracing, Is Your Structure Suitably Braced? Structural Stability Research Council, April 1993. 10.9 10-9 Structural Stability Research Council, Is Your Structure Suitably Braced?, Lehigh University, Bethlehem, PA, April 1993. R - 8
10.10 Murray, T. M. and S. Elhouar, Stability Requirements of Z-Purlin Supported Conventional Metal Building Roof Systems, Annual Technical Session Proceedings, Structural Stability Research Council, 1985. 10.11 Winter, G., W. Lansing, and R. B. McCalley, Jr., Performance of Laterally Loaded Channel Beams, Research, Engineering Structures Supplement. (Colton Papers, Vo1. ), 1949. 10.1 Green, G. G., G. Winter and T. R. Cuykendall, Light Gage Steel Columns in Wall-Braced Panels, Bulletin, No. 35/, Cornell University Engineering Experimental Station, 1947. 10.13 Simaan, A., Bucking of Diaphragm-Braced Columns of Unsymmetrical Sections and Applications to Wall Studs Design, Report No. 353, Cornell University, Ithaca, NY, 1973. 10.14 Simaan, A.and T. Pekoz, Diaphragm-Braced Members and Design of Wall Studs, Journal of the Structural Division, ASCE, Vo1 10, ST1, January 1976. 10.15 Davis, C. S. and W. W. Yu, The Structural Performance of Cold Formed Steel Members with Perforated Elements, Final Report, University of Missouri-Rolla, Rolla, MO, May 197. 10.16 Rack Manufacturers Institute, Specification for the Design, Testing, and Utilization of Industrial Steel Storage Racks, Charlotte, NC, 1990. 10.17 Pekoz, T. B., Design of Cold Formed Steel Columns, Proceedings of the Ninth International Specialty Conference on Cold Formed Steel Structural University of Missouri-Rolla, Rolla, MO, November 1988. 10.18 Miller, T. H. and T. Pekoz, Studies on the Behavior of Cold Formed Steel Wall Stud Assemblies, Final Report, Cornell University, Ithaca, NY, 1989. 10.19 Miller, T. H. and T. Pekoz, Unstiffened Strip Approach for Perforated Wall Studs, Journal of the Structural Engineering, ASCE, Vo1.10, No., February 1994. 11.1 Brokenbrough, Rl L., Fastening of Cold-Formed Steel Framing, American Iron and Steel Institute, Washington, DC, September 1995. 11. Pekoz, T. B. and W. McGuire, Welding of Sheet Steel, Report SG-79-, American Iron and Steel Institute, January 1979. 11.3 Yu, W. W., Cold Formed Steel Design, nd Edition, Wiley-Interscience, New York, NY, 1991. 11.4 American Welding Society, Structural Welding Code Sheet Steel, ANSI/AWS D1.3-89, Miami, FL, 1989. 11.5 LaBoube, R. A. and W. W. Yu, Tensile Strength of Welded Connections, Final R - 9
Report, Civil Engineering Study 91-3, University of Missouri-Rolla, Rolla, MO, June 1991. 11.6 LaBoube, R. A. and W. W. Yu, Behavior of Arc Spot Weld Connections in Tension, Journal of Structural Engineering, ASCE, Vol. 119, No. 7, July 1993. 11.7 LaBoube, R. A. and W. W. Yu, Tensile Strength of Welded Connections, Final Report, Civil Engineering Study 91-3, University of Missouri-Rolla, Rolla, MO, June 1991. 11.8 American Welding Society, Structural Welding Code Steel, ANSI/AWS D1.1-96, Miami, FL, 1996. 11.9 American Welding Society, Recommended Practice for Resistance Welding, AWS C1.1-66, Miami, FL,1966. 11.10 AWS, Recommended Practice for Resistance Welding Coated Low Carbon Steels, AWS C1.3-70, Miami, FL, 1970. 11.11 11.1 Research Council and Structural Connections, Allowable Stress Design Specification for Structural Joints Using ASTM A35 or A490 Bolts, 1985. 11.13 Research Council and Structural Connections, Load and Resistance Factor Design Specification for Structural Joints Using ASTM A35 or A490 Bolts, 1988 11.14 Winter, G, Light Gage Steel Connections with High-Strength, High-Torqued Bolts, Publications, IABSE, Vol. 16, 1956. 11.15 Winter, G., Tests on Bolted Connections in Light Gage Steel, Journal of the Structural Division, ASCE, Vol. 8, No. ST, February 1956. 11.16 Yu, W. W., AISI Design Criteria for Bolted Connections, Proceedings of the Sixth International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, November 198. 11.17 Yu, W. W., Cold-Formed Steel Design, Wiley-Interscience, New York, NY, 1985. 11.18 Yu, W. W., Cold-Formed Steel Design, nd Edition, Wiley-Interscience, New York, NY, 1991. 11.19 Chong, K. P. and R. B. Matlock, Light Gage Steel Bolted Connections without Washers, Journal of the Structural Division, ASCE, Vol. 101, No. ST7, July 1974. 11.0 Pekoz, T.B., Design of Cold-Formed Steel Screw Connections, Proceedings of the Tenth International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, MO, October 1990. 11.1 European Convention for Construction Steelwork, European Recommendations for the Design of Light Gage Steel Members, First Edition, R - 10
Brussels, Belgium, 1987. 11. British Standards Institution, British Standard: Structural Use of Steelwork in Building, Part 5 Code of Practice for Design of Cold-Formed Sections, BS 5950: Part 5: CF9-, 199. 11.3 American Iron and Steel Institute, Test Methods for Mechanically Fastened Cold-Formed Steel Connections, Research Report CF9-, Washington, D. C., 199. 11.4 Birkernoe, P. C. and M. I. Gilmor, Behavior of Bearing Critical Double-Angle Beam Connections, Engineering Journal, AISC, Fourth Quarter, 1978. R - 11
Anneal Amplification factor Arc seam weld Arc spot weld Aspect ratio Batten plate Beam Beam-column Biaxial bending Braced frame Buckling Coefficient Buckling fracture Buckling load Built-up member Butt joint Cladding Closed-form solution Coefficient of variation Cold-formed steel member Cold-work effect Cold rivet Column Column Curve Combined mechanism Compact section Composite beam Composite column Connection Critical load Critical moment Curvature Design documents Design strength Diagonal bracing Diagonal tension field action Diaphragm Diaphragm action Double curvature Drift A - 1
Ductility factor Effective length k Effective length factor k Effective moment of inertia Effective stiffness Effective width Elastic analysis - Elastic-perfectly plastic Element Elongation Embedment Euler formula Euler load Factor load Fastener Fatigue Fillet weld First-order analysis Flat width Flange Curling Flexible connection Flexural strength Floor system Force Fracture toughness Fracture buckling Fracture instability Fully composite beam Fusion weld Gradual-yielding type Groove weld Hot rivet Hot-rolling Hybrid-beam Hysteresis loop Inclusions Inelastic action Inside bend radius Instability Joint Lateral bracing member ( - ) Lateral (or lateral-torsional) buckling A -
Limit state Lip Load factor Loads LRFD Load and Resistance Factor Design Local buckling Lower-bound load Moment redistribution Nominal load Nominal length Noncompact section P- P-delta effect Panel-zone Partial plastification Partially composite beam Plane frame Plastic analysis Plastic design section Plastic hinge Plastic modulus Plastic moment Plastic strain Plastic zone Plastic Plug weld Post-buckling strength Pull-out failure Pull-over failure Purlin Radius of gyration Required strength Residual stress Resistance Resistance factor Resistance weld Ridge frame Roof deck Root of the flange Rotation capacity Rotational stiffness St. Venant torsion A - 3
Second-order analysis Section modulus Service load Serviceability limit state Shape factor Sharp-yielding type Shear-friction Shear lag Shear wall Sidesway Sidesway buckling Single curvature Slenderness ratio Slenderness section Slip-critical joint Space frame Splice Stability-limit load Steel deck Steel panel for roof Steel panel for floor Steel panel for wall Steel roof deck Stiffened element Stiffer Stiffness Strain aging Strain hardening Strength design Strength limit state Stress Stress concentration Strength axial Structural system Stub column Successive approximation Supported frame Tangent modulus Temporary structure Tensile strength Tensile field action Toe of the fillet A - 4
- Torque-tensile relationship Unbraced length Undercut Uneven cooling Universal-mill plate Unstiffened element Upper bound load Vertical bracing ( ) Wall panel Wall stub Warping torsion Weak axial Web buckling Web crippling Weld Width-to-thickness ratio Working load Yield moment Yield plateau Yield point Yield strength Yield stress A - 5
A A 1 A A b A g A n A s A se A w b e c C C mx C my C w C y d D d a d e d h d s D s d se d wc - = d s B - 1
e E e y = F y /E f c f 1 f f av f b f cr F cr F m F sy F u F u1 F u F wy F xx F y F yc F yf F yu F yv g H I a I s I sf I x I y I yc J k ( ) / (F y or F ys ) X Y ( ) St. Venant B -
K K v K x K y L L r L s L st L x L y m M A M B M c M e M m M max M n M no X Y X Y C 1/4 3/4 ( / ) Z M nx M ny M nxo M u X P u M ux M uy M y n n p N P P DL P E P LL P m / B - 3
P n P no P not P nov P ns P nt P u R r r cy r I r 0 R n R r R u s S S c S e S f S ft t C I ( ) s M c /S f B - 4
t 1 t t e T n T s T u t w V R V Q V n w W 90 w 1 w w f Y o β ( )/( ) µ 0.3 λ φ φ b φ v φ w φr n θ ρ τ τ cr (45 o θ<90 o ) Z ( ) B - 5
B - 6