AISC (1999) Load and Resistance Factor Design Specification for Structural Steel Buildings AISC, Inc., Chicago.
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1 REFERENCE ST ASC (999 oad and Resistance Factor Design Specification for Structural Steel Buildings ASC, nc., Chicago. Boer J.P. (96. Castellated Beams Ne Developments ASC Engineering Journal, nd qtr, pp Chen, W.F. and ui, E.M. (987. Structural Stailit: Theor and mplementation Ne York : Elsevier. Clark, J.W.,and Hill, H.N. (960. ateral Buckling of Beams ASC Engineering Journal Structural Division, Jul, No. ST7, pp Galamos, T. (99. Bracing of Trussed Beams s Your Structure Suital Braced?, Structural Stailit Research Council Conference, April, pp 9-9. Galamos, T. (998. Guide to Stailit Design Criteria for Metal Structures John Wile and Sons nc., Fifth Edition, Ne York, pp 9-. Halleux, P. (967. imit Analsis of Castellated Beams Acier-Stahl-Steel, No., pp -. Hosain, M.U. and Speirs, W.G. (97. Experiments on Castellated Steel Beams Journal of the American Welding Societ, Vol. 5, pp 9-. Jackson, R. (00. Viration and Flexural Strength Characteristics of Composite Castellated Beams. M.S. Thesis, Virginia Tech, Blacksurg, Virginia. Knoles, P.R. (99. Castellated Beams Proceeding of the nstitution of Civil Engineers, Part, No. 90, pp Kerdal, D. and Nethercot, D.A. (98. ateral-torsional Buckling of Castellated Beams The Structural Engineer, Part B, No. pp 5-6. Kerdal, D. and Nethercot, D.A. (98. Buckling of aterall Unsupported Castellated Beams Structural Stailit Research Council Proceedings, rd nternational Colloquium, Stailit of Metal Structures, Conference Code:05, pp 5-7. Kerdal, D. and Nethercot, D.A. (98. Failure Modes for Castellated Beams Journal of Constructional Steel Research, th qtr., pp
2 Murra, T.M. Allen, D.E. and Ungar, E.E. (997. ASC Steel Design Guide Series : Floor Virations Due to Human Activit. American nstitute of Steel Construction, Chicago. Pattanaak, U. and Chesson, E. (97. ateral nstailit of Castellated Beams ASC Engineering Journal, rd qtr, pp Salmon, C. and Johnson, E. (996. Steel Structures Design and Behavior Prentice Hall, th Edition, pp , SM Steel Products. (00. SM Steel Products; Smart Beam, The ntelligent Alternative. Steel Joist nstitute. (99. Fortieth Edition Standard Specifications oad Tales and Weight Tales For Steel Joist and Joist Girders Toprac, A., Altfillisch, M. and Cooke, B. (957. An nvestigation of Open-We Expanded Beams Journal of the American Welding Societ, Vol. 9, pp
3 Appendix A CBx6 Calculations 58
4 A. Measured Dimensions of CBx6 Specimen f.60" e 6.5".5".5" e 6.5" e 6.5" dt.5" t 0.5" dg.75" ho 5.88" dt.5" tf 0." A. Tee Section Properties A C [( f ( tf (( dt tf ( t ]( 5.75 Total 6 f tf h t J 6 ( 0.5 ( f tf ht ( 0.9 ( tf ( f ( dt tf ( t 0.09 x x S c x 58.5 r. in A 59
5 A.. Classical ateral-torsional Buckling Solution X X Sx C EGJA 7.5 Sx GJ M cr 8 P Mcr CSxX X X k kφ k r r When k.0 and k φ.0: 5. 0 ft When k.0 and k φ 0.5: 5. 0 ft When k 0.8 and k φ 0.5: 7. 0 ft ( kφ A.. Addition of oad ocation Term 8 P Mcr M cr C EGJ k C ( kφ EC ( C GJ 9.89 k C kφ EC GJ 9.87 ( kφ (.57.5 kφ 60
6 When k.0 and k φ.0:. 9 ft When k.0 and k φ 0.5:. 9 ft When k 0.8 and k φ 0.5: 6. 8 ft A.. Galamos Formula ~ Aottom chord ( de Atop chord β x o x ~ Aottom chord de 0.8 Atotal 0 o ottom chord d e 0 ( ( P P 6 9 ( E ( E ( EC ( 7.99 E ( o βx GJ βx a ( ( ( 6.0 [] 0 [] ( ( 6
7 When K.0: 0. ft When K 0.8:. ft When K 0.5:. ft A. Full Section Properties A ( f ( tf ( ( dg ( * tf ( t 9.55 Total C h.8 6 J ( f tf ht ( tf ( f ( h tf ( t 0. x x S c x 6.6 r A.0 6
8 A.. Classical ateral-torsional Buckling Solution X X Sx C EGJA Sx GJ 0. M cr 8 P Mcr CSxX X X k k ( φ k kφ r r When k.0 and k φ.0: 9. 8 ft When k.0 and k φ 0.5:. 6 ft When k 0.8 and k φ 0.5: 5. 7 ft When k.0 and 7.5ft: k φ 0.0 When k 0.8 and 7.5ft: k φ 0.0 A.. Addition of oad ocation Term 8 P Mcr
9 C M cr C EGJ k ( kφ EC ( C C kφ k When k.0 and k φ.0: GJ EC GJ 9.87 ( kφ ( kφ 6. 8 ft When k.0 and k φ 0.5: 0. 0 ft When k 0.8 and k φ 0.5:. 9 ft When k.0 and 7.5ft: k φ 0.8 When k 0.8 and 7.5ft: k φ 0. A.. Galamos Formula ~ Aottom chord ( de Atop chord β x o x ~ Aottom chord de 8.0 Atotal 0 o ottom chord d e 0 6
10 ( ( P P 6 9 ( E ( E ( EC ( 7.99 E ( o βx GJ βx a ( ( ( 6.0 [] 0 [] ( ( When K.0:. 8 ft When K 0.8: 9. ft When K 0.5:. ft A. Weighted Average Section Properties % e Tee 00 9% e % e Solid 00 9% e % Transition 00 % e 65
11 ATotal 7.65 C J x 79.8 Sx 6.5 r.8 A.. Classical ateral-torsional Buckling Solution X X Sx C EGJA Sx GJ 0.69 M cr 8 P Mcr CSxX X X k k ( φ k kφ r r When k.0 and k φ.0: 8. ft When k.0 and k φ 0.5:. 6 ft 66
12 When k 0.8 and k φ 0.5:. 6 ft A.. Addition of oad ocation Term 8 P Mcr C 0.50 M cr C EGJ k ( kφ EC ( C C kφ k When k.0 and k φ.0: GJ EC GJ 9.87 ( kφ ( kφ 5. 8 ft When k.0 and k φ 0.5: 7. 9 ft When k 0.8 and k φ 0.5: 9. 7 ft A.. Galamos Formula ~ Aottom chord ( de Atop chord β x o x ~ Aottom chord de 9. Atotal 0 67
13 0 e ottom chord o d 0 ( ( ( ( 6 ( 9 ( ( 6 o x x GJ EC E E a E P P β β [] ( [] ( ( ( ( When K.0: ft. When K 0.8: ft 7. When K 0.5: ft 8. 68
14 Appendix B CBx6 Specimen Test Data 69
15 CASTEATED BEAM TEST SUMMARY TEST DENTFCATON: CBx6 TEST DESCRPTON oading Gravit Point of oad Application Mid-span Span 7'-6" Bracing Points None Numer of eams End Condition We-to-column flange doule angle connection FAURE MODE: ateral-torsional Buckling THEORETCA CRTCA UNBRACED ENGTH: (a Classical ateral-torsional Buckling Solution ( Addition of oad ocation Term (c Galamos Formula EXPERMENTA CRTCA UNBRACED ENGTH: Total Applied oad Unraced ength 5.7 ft.9 ft 9. ft 00 l 7.5 ft R-VAUE: DSCUSSON: R(a Experimental ength/theoretical ength.05 R( Experimental ength/theoretical ength.8 R(c Experimental ength/theoretical ength.8 0 l eights ere loaded on a loading plate clamped to the top flange of the castellated eam at midspan. Catch racing as installed to stop excessive deflections and help characterize failure. Concentrated oad (l Test ength Eccentricit 8.ft.8ft.ft 7.5ft e e /" e "
16 Photos of CBx6 Testing Support Column Quarter Point Catch Bracing Midspan Catch Bracing Quarter Point Catch Bracing Photo of CBx6 Entire Test Set-up 7
17 ocation of Failure Photo of CBx6 Specimen at failure 7
18 Appendix C CB7x0 Calculations 7
19 C. Measured Dimensions of CB7x0 Specimen f 6.06" e 7.5" 6.0" 6.0" e 7.5" e 7.5" dt.88" t 0.0" dg 6.875" ho 8.5" dt.88" tf 0.5" C. Tee Section Properties A C [( f ( tf (( dt tf ( t ]( 8.70 Total 6 f tf h t J 6 ( ( f tf ht ( ( tf ( f ( dt tf ( t ( 9.8 x 9.66 x S c x 0.7 r A.50 7
20 C.. Classical ateral-torsional Buckling Solution X X Sx C EGJA Sx GJ M cr 8 P Mcr CSxX X X k kφ k r r When k.0 and k φ.0: 0. 0 ft When k.0 and k φ 0.5: 0. 0 ft When k 0.8 and k φ 0.5:. ft ( kφ C.. Addition of oad ocation Term 8 P Mcr M cr C EGJ k C ( kφ EC ( C GJ k C kφ EC GJ 9.87 ( kφ (.69. kφ 75
21 When k.0 and k φ.0: 9. 9 ft When k.0 and k φ 0.5: 9. 9 ft When k 0.8 and k φ 0.5:. ft C.. Galamos Formula ~ Aottom chord ( de Atop chord β x o x ~ Aottom chord de.6 Atotal 0 o ottom chord d e 0 ( P P 6 ( E ( ( 9 E ( EC ( E ( o βx GJ βx a ( ( [] 0 ( 0.0 [] ( ( 76
22 When K.0:. ft When K 0.8: 7. 9 ft When K 0.5: 8. ft C. Full Section Properties A ( f ( tf ( ( dg ( * tf ( t.6 Total C h J ( f tf ht ( tf ( f ( h tf ( t 9.5 x 56.7 x S c x 6.8 r A.6 77
23 C.. Classical ateral-torsional Buckling Solution X X Sx C EGJA 7.0 Sx GJ 0.0 M cr 8 P Mcr CSxX X X k k ( φ k kφ r r When k.0 and k φ.0:. 0 ft When k.0 and k φ 0.5: 7. 7 ft When k 0.8 and k φ 0.5: 0. ft When k.0 and.5ft: k φ 0.8 When k 0.8 and.5ft: k φ 0.7 C.. Addition of oad ocation Term 8 P Mcr
24 M cr C EGJ k C ( kφ EC When k.0 and k φ.0: 0. 9 ft When k.0 and k φ 0.5:. 7 ft When k 0.8 and k φ 0.5: 5. 9 ft When k.0 and.5ft: k φ 0.6 When k 0.8 and.5ft: k φ 0. ( C GJ k C kφ EC GJ 9.87 ( kφ ( kφ C.. Galamos Formula ~ Aottom chord ( de Atop chord β x o x ~ Aottom chord de 9.8 Atotal 0 o ottom chord d e 0 79
25 ( P P 6 ( E ( ( 9 E ( EC ( E ( o βx GJ βx a ( ( [] 0 ( 0.0 [] ( ( When K.0: 8. 0 ft When K 0.8:. 8 ft When K 0.5: 6. 0 ft C. Weighted Average Section Properties % e Tee 00 8% e % e Solid 00 8% e % Transition 00 % e 80
26 ATotal.66 C 695. J x Sx 0.00 r. C.. Classical ateral-torsional Buckling Solution X X Sx C EGJA 089. Sx GJ M cr 8 P Mcr CSxX X X k k ( φ k kφ r r When k.0 and k φ.0:. 7 ft When k.0 and k φ 0.5: 5. 7 ft When k 0.8 and k φ 0.5: 8. 0 ft 8
27 C.. Addition of oad ocation Term 8 P Mcr M cr C EGJ k C ( kφ When k.0 and k φ.0: 9. 8 ft EC When k.0 and k φ 0.5:. 7 ft When k 0.8 and k φ 0.5:. 8 ft ( C GJ k C kφ EC GJ 9.87 ( kφ ( kφ C.. Galamos Formula ~ Aottom chord ( de Atop chord β x o x ~ Aottom chord de 0.99 Atotal 0 o ottom chord d e 0 8
28 0 ( ( ( ( 6 ( 9 ( ( 6 o x x GJ EC E E a E P P β β [] ( [] ( ( ( ( When K.0: 5 ft 6. When K 0.8: 0 ft. When K 0.5: ft. 8
29 Appendix D CBx6 Specimen Test Data 8
30 CASTEATED BEAM TEST SUMMARY TEST DENTFCATON: CB7x0 TEST DESCRPTON oading Gravit Point of oad Application Mid-span Span.5" Bracing Points None Numer of eams End Condition We to column flange doule angle connection FAURE MODE: ateral Torsional Buckling THEORETCA CRTCA UNBRACED ENGTH: (a Classical ateral-torsional Buckling Solution ( Addition of oad ocation Term (c Galamos Formula EXPERMENTA CRTCA UNBRACED ENGTH: Total Applied oad Unraced ength 0. ft 5.9 ft.8 ft 00 l.5 ft R-VAUE: DSCUSSON: R(a Experimental ength/theoretical ength.06 R( Experimental ength/theoretical ength.8 R(c Experimental ength/theoretical ength.0 0 l eights ere loaded on a loading plate clamped to the top flange of the castellated eam at midspan. Catch racing as installed to stop excessive deflections and help characterize failure. Concentrated oad (l Test ength Eccentricit 5.8ft 7.ft.5ft.5ft e 0 self t e /" self t e " self t
31 Photos of CB7x0 Testing Support Column Quarter Point Catch Bracing Midspan Catch Bracing Quarter Point Catch Bracing Photo of CB7x0 Entire Test Set-up 86
32 ocation of Failure Photo of CB7x0 Specimen at failure 87
33 VTA T. Patrick Bradle as orn on Jul, 977 in Clemmons, North Carolina. He graduated from West Forsth high school in eisville, North Carolina. He received his Associate in Applied Science in Architectural Technolog from Guilford Technical Communit College in Ma 998. He received his Bachelor of Science in Civil Engineering from North Carolina Agricultural and Technical State Universit in Greensoro, North Carolina in Ma of 00. He enrolled in the graduate program at Virginia Tech in the fall of 00 and plans to ork for a metal uilding manufacturer in North Carolina after completion. T. Patrick Bradle 88
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