A UNIFIED APPROACH FOR FIRE RESISTANCE PREDICTION OF STEEL COLUMNS AND FRAMES

Transcription

1 A UNIFIED APPROACH FOR FIRE RESISTANCE PREDICTION OF STEEL COLUMNS AND FRAMES Chu Yang TANG Nanang Tchnological Univrsit, School of Civil and Environmntal Enginring,N-B4-04, Singaor Kang Hai TAN Nanang Tchnological Univrsit, School of Civil and Environmntal Enginring,N-c-97, Singaor ABSTRACT For a long tim, th Rankin mthod has bn alid succssfull to stl columns and frams subjctd to incrasing loads but maintaind at constant ambint tmratur. This ar xtnds th Rankin formula to stl columns and frams undr fir conditions. Th authors rsnt a siml xrssion for buckling cofficint that can b usd for both columns and frams undr fir conditions, taking th dtrioration of stl rortis at lvatd tmratur into considration. Th Rankin rdictions ar comard to tst rsults of 34 axiall-loadd columns, 2 swa-frams and 6 non-swa frams. It is found that th rdictions agr vr wll with th tst rsults. For th 34 stl columns, th man of agrmnt of ratios of collas tmraturs T tst /T Rankin is 0.98 with a cofficint of variation (COV) of 5.4%. As for th 8 stl frams, th man is qual to 0.99 with a COV of 9.2%. KEYWORDS: fir rsistanc, fram, column, stl, fir tst 35

2 INTRODUCTION Th Rankin formula was originatd b Prof Rankin [] of Glassgow Univrsit in th lattr art of th 9 th cntur. It was latr modifid in th mid 20 th cntur [2] and was adotd in various dsign cods sinc thn. Th formula basicall involvd a linar intraction btwn two trms, th lastic buckling load factor λ and th lastic collas load factor λ as follows: = + () P P P R with P R Rankin load P lastic collas load P lastic critical load Th formula, whn usd for frams loadd to failur at ambint tmratur, ilds vr good agrmnt with tst rsults. Th ratio of th actual failur load factor λ c to th Rankin load factor λ R is around.00 to.20 [3]. In thir rcnt ar, Tang t al. [4] rovidd th thortical drivation of th Rankin formula and th furthr alid th Rankin formula to stl columns and frams undr fir conditions [4, 5]. Th currnt ar is to show that th Rankin formula is a unifid aroach for stl columns, swa and non-swa stl frams. RANKINE FORMULA IN FIRE CONDITIONS In fir conditions, th Rankin formula taks th following form: = + (2) R with T stl mmbr tmratur; T = 20 for ambint conditions. B adoting th matrial rduction factors for th rsctiv ild strngth (k ) and lastic modulus (k ) at lvatd tmraturs, th Rankin formula can xrssd as: P R (20) = + (3) k ( T) P (20) k ( T) P (20) Clarl, th Rankin formula rovids a linar intraction rlationshi btwn th lastic squashing load P and th lastic buckling load factor P. Th actual bhaviour of a column or a fram is dndnt on its normalizd slndrnss ratio [4, 5, 6]: Λ(20) = P 20) / P (20) (4) ( 36

3 For stl columns, th normalizd slndrnss ratio Λ(20) dnds on th mmbr slndrnss and nd conditions b th following rlationshi [4]: Λ(20 ) λ = (5) λ (20 ) E with λ slndrnss ratio; λ E transition slndrnss ratio. Hr, λ 20) = π E(20) / f (20) (6) E ( with E lastic modulus of stl; f ild strngth of stl. For frams, th trm Λ not onl dnds on th mmbr slndrnss and boundar conditions, but also on th loading attrns. Gnrall, non-swa frams hav smallr normalizd slndrnss ratio than swa frams; swa frams without latral loading hav smallr normalizd slndrnss ratio than thos with latral loading. Th normalizd slndrnss ratio is a vr imortant aramtr for both stl columns and frams. It dtrmins th rlativ imortanc of th lastic collas load and lastic critical load. From Equation (2), it can b sn that, for Λ << (vr stock columns or frams), th load caacit is dtrmind b th lastic collas load. On th othr hand, for Λ >> (vr slndr columns or frams), th load caacit is dtrmind b th lastic critical load. For Λ in th intrmdiat rang, both th lastic collas load and th lastic critical load ar imortant for dtrmining th failur load of th structur. B substituting Equation (4) into Equation (3), on obtains P 20) [ Λ(20)] = + k ( T) k ( T) R ( 2 At failur, P R (T) is qual to th alid load P. Thus, k ( T) N(20) = k ( T) + [ Λ(20)] k ( T) 2 (7) whr N is th buckling cofficint, givn b: P N (20) = (8) (20) P 37

4 Firgur shows th buckling curvs for both stl columns and frams at lvatd tmraturs basd on Equation (7). Hr, Eurocod 3 [7] is adotd for th matrial rduction factors k (T) and k E (T). Buckling Cofficint N(20) T = 20 C Normalizd Slndrnss Ratio Λ(20) FIGURE : Buckling cofficint for stl columns and frams at lvatd tmraturs Figur rovids a siml and unifid wa to dtrmin th fir rsistanc of both stl columns and frams. B rforming th ncssar analsis at ambint tmratur in ordr to dtrmin th normalizd slndrnss ratio for th structurs undr concrn, on can thn rad from Figur to dtrmin th structural fir rsistanc. CASE STUDIES Cas studis comrising axiall loadd columns, swa-frams, and non-swa frams, tstd undr standard fir ISO 834 [8] ar analsd to vrif th Rankin formula. Th first cas stud comriss 34 axiall loadd stl column, which ar summarizd in Tabl. Th comarisons of th Rankin rdictions with tst rsults for th 34 stl columns ar shown in Figur 2. For comarison uros, th N(T) - Λ(T) curv is lottd, whr P N( T) = (9) Λ(T) = / P ( T) (0) 38

5 Itms () Laboratoris Dscritions (2) Borhamhood, Braunschwig, CTICM, Gnt, LABEIN, Rnns, & Stuttgart. [9, 0, ] Stl grad S 235 & S 355. End conditions Pinnd-innd, inndfixd & fixd-fixd. Slndrnss ratios λ Var from 4 to 230. Man Tmraturs Var from 60 to 863 C. Load factors Var from % to 72 % with rsct to ild load at ambint tmratur. Loading ccntricitis Var from 0 to 650 mm. Tabl : tst conditions of th four cas studis Thus, from Equation (2), th Rankin formula can b xrssd b N( T) = () 2 + [ Λ( T)] Th normalizd squashing load N r (T) = and normalizd Eulr buckling load N r (T) = /Λ r (T) 2 ar also shown in th figur for comarison uros. Buckling Cofficint N(T) Plastic squashing curv N(T) = Eulr buckling curv N r (T) = / Λ(T) 2 Rankin curv (Eq. 27) N r (T) = / ( + Λ(T) 2 ) Normalizd Slndrnss Ratio Λ(Τ) FIGURE 2 : Comarison of rdictions and tst rsults for axiall-loadd stl columns 39

6 Th tst rsults agr wll with th Rankin rdictions for th 34 columns, with a man of agrmnt of T tst /T Rankin of 0.98 and a COV of 5.4%. Th scond cas stud comriss 6 non-swa frams (including th two EHR frams), and 2 swa-frams (including th singl-stor on-ba EGR frams and singl-stor two-ba ZSR frams) [6], as shown in Figur 3. F F 2 F F F2 h h l/2 l/2 EHR l EGR F F F F2 All cross-sctions: IPE 80, St 37 h l h l X: Stiffnr against tnsional dislacmnt rndicular to th fram lan ZSR FIGURE 3 : Ts of frams [2] Figur 4 shows th tst rsults of th 8 stl frams. Th man valu of T c Rankin /T c tst is.0 with a cofficint of variation of 9.2%. This accurac of rdictions for stl frams undr fir conditions is almost as good as th finit lmnt rsults [4]. Buckling Cofficint N(T) Plastic collas curv N(T) = EHR Frams EGR Frams ZSR Frams Elastic buckling curv N(T) = / Λ(T) 2 Rankin curv (Eq. 20) N(T) = / ( + Λ(T) 2 ) Normalizd Slndrnss Ratio Λ(T ) FIGURE 4 : Comarison of rdictions and tst rsults for swa and non-swa frams 40

7 CONCLUSIONS Th Rankin formula rovids a siml and unifid aroach to fir rsistanc calculation of stl columns and frams undr fir conditions. Th authors rsnts a siml xrssion for buckling cofficint that can b usd for both columns and frams undr fir conditions, taking th dtrioration of stl rortis at lvatd tmratur into considration. Good agrmnt with tst rsults is obtaind for th Rankin rdictions. REFERENCES [] Rankin, W. J. M., Usful Ruls and Tabls, London: C. Griffin & Co., Limitd, 908. [2] Mrchant, W., Th Failur Loads of Rigid Jointd Framworks as Influncd b Stabilit, Th Structural Enginr, 32, 85-90, 954. [3] Horn, M. R. & Mrchant, W, Th Stabilit of Frams, Oxford: Prgamon Prss Ltd, 965. [4] Tang, C. Y., Tan, K. H. and Ting, S. K., Basis and Alication of a Siml Intraction Formula for Stl Columns undr Fir Conditions, J. Struct. Engrg., ASCE, Octobr, Vol. 27, No. 0, , 200. [5] Tang, C. Y. and Tan, K. H., Basis and Alication of a Siml Intraction Formula for Stl Frams undr Fir Conditions, J. Struct. Engrg., ASCE, Octobr, Vol. 27, No. 0, , 200. [6] Rubrt, A., and Schaumann, P., Structural Stl and Plan Fram Assmblis undr Fir Action, Fir Saft J., 0, 73-84, 986. [7] CEN, Eurocod 3: Dsign of Stl Structurs. Part.2: Gnral Ruls Structural Fir Dsign, ENV 993--, Euroan Committ for Standardization, 995. [8] ISO 834, Fir Rsistanc Tats-Elmnts of Building Construction, Intrnational Standards Organisation, 975. [9] Janss, J., Statistical Analsis of Fir Tsts on Stl Bams and Columns to Eurocod 3, Part.2, J. Constr. Stl Rs., 33, 39 50, 995. [0] Talamona, D., Buckling Curvs in Cas of Fir ECSC 720 SA 36/55/93/68: Fir Rsistanc of Stl Columns with Eccntric Load, CTICM, Rort No. INC- 96/450-DT/VG Part, Saint-Rm-ls-Chvrus, Paris, 995. [] Schlich, J. B. & Cajot, L. G., Buckling Curvs in Cas of Fir: Draft Final Rort, Part I (Main Txt), CEC Agrmnt 720-SA 36/55/68/93, ProfilARBED- Rchrchs, Luxmbourg,

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