Analyses of Composite Beams and Frames at Elevated Temperature

Transcription

1 Analyses f Cmpsite Beams and Frames at Elevated Temperature T. MORTA Cnstructin Engineering Research Department, nstitute f Technlgy Shimizu Crpratin , Etchujima Kt-ku, Tky 135, Japan T. WAKAMATSU Department f Architecture, Faculty f Science and Technlgy Science University f Tky 2641, Yamazaki Nda-shi, Chiba 278, Japan H. UESUG and H. SATO Department f Architectural Engineering, Faculty f Engineering Chiba University 1-33, Yayich Chiba-shi. Chiba 260, Japan ABSTRACT This paper presents analyses f cmpsite beam which is cmpsed f H-sectin steel and reinfrced cncrete slab. Analyzed mdels were simply supprted beams and H-shaped structural frames which were cmpsed f 2-stry clumns and l-span beam. n analyzing simply supprted beams, sme ther factrs (fr example, thickness f fire prtectin, width f slab etc...) were cnsidered. n analyzing H-shaped structural frames, tw mdels were cnsidered. One mdel has cmpsite beam, and the ther mdel has H-sectin steel beam nly. Frm the results f these analyses, it is cncluded that the fire resistance f the structural frame with H-sectin steel beam and the structural frame with cmpsite beam is almst the same. KEYWORDS: fire behavir, thermal stress, thermal defrmatin, steel structure, reinfrced cncrete slab, cmpsite beam, inside temperature NTRODUCTON During the last tw decades, analyses f steel frame structures expsed t fire have been advanced. Thugh, in general, a frame f an actual steel structure building is cnnected with reinfrced cncrete slab, its effect is nt taken int accunt in mst analyses f structural behavir in fire. Steel frame members, beam and clumn, are cvered with fire prtectin s that the steel shuld nt reach a high temperature, at which the mechanical prperties (elastic mdules, yield stress and strength), decrease. Hwever, reinfrced cncrete slab is nt cvered with fire prtectin, if the thickness frm surface t reinfrcement is cnsidered adequate [,2J. n these cnditins, when expsed t fire, the temperature f the slab near the sffit is higher than that f steel members. Especially in regard t the beam, it can be assumed that the behavir f steel frame structure is influenced by the difference f temperature between slab sffit and steel beam [3,4J. FRE SAFETY SCENCE-PROCEEDNGS OF THE THRD NTERNATONAL SYMPOSUM. pp Cpyright nternatinal Assciatin fr Fire Safety Science

2 n this investigatin f the influence f reinfrced cncrete slab in steel frame structure, the cmpsite beam cmpsed f l-l-sectin steel and reinfrced cncrete slab is cnsidered. Analyses cnsist f (a)calculatin f inside temperature f structural member depending n fire temperature-time curve and (b)analysis f structural behavir in elast-plastic range at the temperatures btained frm step(a). Analyzed mdels are simply supprted beams and H shaped structural frames which are cmpsed f 2-stry cl umns and l-span beam. n analyzing simply supprted beams, sme factrs (fr example, thickness f fire prtectin, width f slab etc...) are cnsidered. And, in analyzing H-shaped structural frames, tw mdels, ne f cmpsite beam and ne f H-sectin steel beam, are cnsidered. CALCULATON Calculatin Methds Calculatin f nside Temperature f Structural Member. The fire severity as heat lad t a structure is generally btained fr each fire cmpartments. n this paper, hwever, the standard temperature-time curve prescribed in SO 834 is applied as the fire temperature-time curve. nside temperature f a structural member as a functin f time is calculated by "a finite difference methd" [5,6,7]. The inside temperature is calculated fr a tw dimensinal crss sectin f each member. The crss sectin f member is divided int subslices, and temperature f each subslice is cnstant during a time increase. Generally, thermal prperties, thermal cnductivity and specific heat, f the member's cmpsite materials are dependent n temperature. Useful thermal prperty data are shwn in reference[8]. n the reference these thermal prperties are assumed t be secnd degree functins f temperature. n this paper, thermal prperties f materials are quted frm this reference. Latent heat f misture evapratin in cmpsite materials must be cnsidered. Sme assumptins are intrduced in calculating latent heat. n the actual case f expsure t fire, misture mves in the material, and because f inside pressure f the material, misture evapratin des nt start at precisely 100 degrees centigrade. But, in the calculatin f temperature, the fllwing tw main premises are assumed. One is that misture des nt mve in material. The ther is that misture evapratin ccurs at precisely 100 degrees centigrade. By the latter assumptin, misture in subslices decreases at every time step, after its temperature reaches 100 degrees centigrade. And when quantity f misture decreases t 0%, the temperature f subslices starts rising again. Calculatin f Structural Behavir. Thermal stress and defrmatin analyses f structural members and frames in fire are carried ut by using the cmputer prgram "Fires-Frame 1"[9]. This prgram applies "a nn-linear direct stiffness frmulatin cupled with a time step integratin" [10]. T apply this methd, a structural member is divided lngitudinally int segments, and the crss sectin f each segment is divided int subslices. t is cnvenient t use the same subslices fr temperature calculatin and structural calculatin. The analysis f structural behavir is carried ut by using thermal cnditins btained frm the calculatin f temperature. Calculated Mdels Simply Supprted Beams. 10 mdels are discussed in this paper. All mdels cnsisting f simply supprted beams whse spans are 2,000mm are shwn in TABLE l. Each beam is expsed t fire n its bttm and sides. Fr example, the crss sectin f Mdel-A is shwn in FGURE 1. The beams are lngitudinally divided int 8 segments f equal length. The crss sectins f the slabs are divided int 16 meshes (directin f thickness) and 3 meshes (directin f width). n the crss sectin f H-sectin steel, flange is divided int 3 subslices, and web int 8 subslices. Mdel-L and Mdel-N are l-l-sectin steel beams nly. Mdel-F and 762

3 TABLE 1. Mdels f Simply Supprted Beams t.. Thickness Width Upper Thickness f f Reinfrce- Lad f Slab Slab ment *1 Fire Prtectin Mdel (mm) (mm) (mm) (mm) A ll,o B 1000 N/A Sprayed C 150 N/A Rck Wl *5 D E 2000 DlO-@lOO F 120 *3 G H N/A 70 L N/A *2 50 N (Nt Applicable) *4 * 1 Cver (cncrete surface t reinfrcement) S 30mm. All mdels have lwer reinfrcement (DlO-@100). *2 Mdel-L and Mdel-N are beam withut reinfrced cncrete slab. *3 Vertical lad kN*2, *6 *4 Vertical lad kN*2, *6 *5 Sprayed Rck Wl is cmpsed f rck wl and cement. Spraying t steel, water is added t these materials. The distributin rati f this material is as fllws, rck wl: 60-75%, cement 25-40%. *6 Lcatin f lads is an each side at a distance f L/4 frm the middle f span (where L is span f beam). 1,000 H-SectinSteel> (H-300X1 50x6.5x9mm)= (Steel Grade: SS4l). (Length Unit: mm) FGURE 1. Crss Sectin Mdel f Cmpsite Beam (Mdel-A) Mdel-N are laded t prduce 80% f yielding stress in the middle span f the H-sectin beam. H-Shaped Structural Frames. FGURE 2 shws a H-shaped structural frame cut ut frm an actual steel structure building. Bending defrmatin f upper edges f clumns in upper stry is restricted, and all defrmatin f lwer edges f clumns in lwer stry is restricted cmpletely. 2 frame mdels are calculated. TABLE 2 shws specificatin f the mdels. Mdel-O is the structural frame with H-sectin steel beam. Mdel-P is the structural frame with cmpsite beam. The beams are lngitudinally divided int 12 segments and clumns int 7 segments. n the calculatins, clumns in lwer stry and beam were assumed t be expsed t fire. The lwer clumn is heated frm surrundings, and the beam is heated n its bttm and sides by fire. Equal lads is cnsidered fr bth mdels. 763

4 22,000 5,375 5,375 l (kn) (kn) 134lkNJ t t FRE (. '... : Unlabeled arrws represent Heat Flw) -_ ,000 -_1..-- (Length Unit: mm) '"" '"" H-900x300x9x19mm (Steel grade: SS41) / Fire Prtectin "- )f (Thickness: 45mm) " D-500x400x32mm (Steel grade: SM50) <BEAM> <COLUMN> FGURE 2. H-Shaped Structural Frame TABLE 2. Mdels f H-Shaped Structural Frames ::>: Thicckness Width Reinfrce- Thickness f f ment Lad f Slab Slab *1 Fire Prtectin Mdel (mm) (mm) (mm) (mm) 0 NjA (Nt Applicable) Sprayed Actual Rck-Wl P DlO-@OO Live Lad 45 (duble) * 1 Cver (cncrete surface t reinfrcement) S 30mm. Assumptins. The assumptins f the analysis in this paper are as fllws. Member is unifrmly expsed t fire s that lngitudinal temperature distributin is unifrm. The percentages f misture cntent in cncrete and fire prtectin are 5%. Mechanical prperties f steel are quted frm reference[9]. Grade f H-sectin steel is SS41. The Stress-Strain relatins are shwn in FGURE 3. Cmpressive strength f cncrete is 20.6N/mm 2 at rm temperature. Creep and shrinkage f cncrete are ignred. Cefficient f thermal expansin f cncrete is quted frm reference[10]. Stress-Strain relatins f cncrete are assumed as FGURE 4. Effective structural slab width expsed t fire is nt sure presently. n this paper, 1,000mm is used as basic slab width. (Effects f slab width are investigated in the analyses f simply supprted beams.) 764

5 /'" '" E -E 200 (S </} 150 </} g </} "' 10 ;, : ; 20'C 100,c! _..., lr::::>--=,,,,,.l. _L200'C[,:,---;.._ 300 r:...4()ot: ' cwe" 700'C -, "c sdc strain (%) FGURE 3. Stress-Strain Curve f Steel (SS41) [9] strain (%) FGURE 4. Stress-Strain Curve f Cncrete RESULTS AND CONSDERATONS Results f Simply Supprted Beams Temperature Distributin in Crss Sectin f Beams. FGURE 5 and FGURE 6 shw the inside temperature-time curve fr Mdel-A as an example. The highest temperatures in H sectin steel ccurred in the lwer flange, fllwed by the web and then the upper flange. The temperature in the upper flange is influenced by misture evapratin in the reinfrced cncrete slab. Temperature distributin in the crss sectin f the slab prtected frm direct expsure t fire by H-sectin steel beam is lwer than that f slab whse sffit is directly expsed t fire. While these tw tendencies appeared in the ther mdels, they were less appearance fr mdels that prvided less prtectin. General Structural Behavir f Unladed SimplY Supprted Beams. FGURE 7 shws deflectin at the middle f span f unladed simply supprted beams. When expsed t fire, the middle f span f the cmpsite beams initially mves upward. This behavir is caused by the temperature distributin in the crss sectin f the cmpsite beam. Frm the beginning f expsure t fire, the temperature f slab sffit rises, the slab elngates lngitudinally, and the temperature f H-sectin steel cvered with fire prtectin des nt rise as quickly. On the ther hand, the middle f span f the beam withut slab, Mdel-L, mves dwnward frm the beginning f fire expsure, because thermal elngatin appears directly crrespnding t temperature distributin in the H-sectin steel. Cmparisn f Mdel-A,B and COnfluence f upper reinfrcement). Upward deflectin f Mdel-B appears larger than that f Mdel-A and C. Cncerning dwnward deflectin, it can be said that mre effective upper reinfrcement makes mre dwnward deflectin. Cmparisn f Mdel-A, D and E (nfluence f slab width), The wider the slab is, the larger the upward deflectin. The wider slab shws the larger rate f increase in dwnward deflectin. Because the reinfrcement per unit crss sectin is the same in all three mdels, upward deflectin will be influenced by the rati f slab width t crss sectinal area f H sectin steel, and the rate f increase f dwnward deflectin will be influenced by the rati f strength f upper reinfrcement t crss sectinal area f H-sectin steel. 765

6 400 - j..., c,-". 30 FGURE 5. Temperature-Time Curve f H-Sectin Steel (Mdel-A) : The part f slab whse sffit is directly expsed. - : The part f slab n upper flange. 5,35,85,115 : Distance frm the sffit (unit: mm) ,..,..,-,-;-r-.--r-r-,...,...,..,..,..., S-rRiE j'1000 5h 5 'J:! ::: <ll '" <ll 3)_ 600 :s " 400 '" '" <ll - & '" '" '" FGURE 6. Temperature-Time Curve f Cncrete Slab (Mdel-A) ;> :::. () <ll t;:::l <ll '" 4 --B-- Mdel-A ----B-- Mdel-B 2 -'7-Mdel-C Mdel-D Mdel-E 0 ---tr--- Mdel-G Mdel-H Mdel-L FGURE 7. Deflectin at the Middle f Span fr Unladed Beams 766

7 Cmparisn f Mdel-A, G and H (nfluence f thickness f fire prtectin). Regarding deflectin at the middle f span, the thicker the fire prtectin is, the larger the upward deflectin. And the thinner the fire prtectin is, the larger the dwnward deflectin and rate f increase f dwnward deflectin. Laded Simply Supprted Beam. FGURE 8 shws deflectin at the middle f span and elngatin f beam fr Mdel-F and Mdel-N. Thugh the dwnward deflectin at the middle f span f the H-sectin steel beam is larger than that f the cmpsite beam, rates f increase f dwnward deflectin are almst the same. n this case, 80% f the yielding stress is prduced in the middle f span f beams by the vertical lad, and the vertical lad fr cmpsite beam (Mdel-F) is greater than that fr H-sectin steel beam (Mdel-N), n case f a simply supprted beam, if the vertical lad is the same, it is fund that a cmpsite beam is mre advantageus than H-sectin steel beam even in fire. But, in the case f cmpsite beam, the calculatin shws that cmpressive stress prduced by vertical lad cncentrates in the crss sectinal area in the lwer part f slab whse sffit is directly expsed t fire. t can be seen that the strength f H-sectin steel f the cmpsite beam decreases, structural behavir fr the cmpsite beam wuld be much the same as fr the H-sectin steel beam nly. The elngatin f the cmpsite beam is greater than that f the H-sectin steel beam as shwn in FGURE 8. Results f H.Shaped Structural Frames Defrmatin. FGURE 9 and FGURE 10 shw the inside temperature-time curve fr the beams f H-shaped structural frame. FGURE 11 shws structural defrmatin f H-shaped structural frames. Prgressive defrmatin f Mdel-O and P are much the same. But Hrizntal defrmatin "U" f Mdel-P is greater than that f Mdel-O, O 40 r--, '-' :> 0 :: 0 :: gjl.s g 0) FGURE 8. Deflectin at the Middle f Span and Elngatin fr Laded Beams 767

8 SO-FRE 'j:) k (l) OOO c<:l 5h ''is 800 : (l) ,,,,/ :3 al 400 tr, ;, /:v : The part f slab whse sffit is directly expsed, -- : The part f slab n upper flange, 5,35,85, 115 : Distance frm the sffit (unit: mm) 1200 ', ', '''-'',...,-,,...,...,...,.-, () Ch (l) (l) 5h :3 600 :::: 400 ;:j / (;j... (l) 0.. E 2:l 200 / / / " " SO 180 FGURE 9. Temperature-Time Curve f H Sectin Steel and Clumn(H-shaped frame) FGURE 10. Temperature-Time Curve f Cncrete Slab (H-shaped frame) E 0 g > :l 0 'g -400 J2-600.g -800 P(u)! ;::J :l ' -30 <B (l) 'Cl SO FGURE. Defrmatin f H-Shaped Structural Frames Bending Mment in Heated Clumn. FGURE 12 shws develpment f bending mment in the heated clumns. t must be nted that yielding mment and plastic mment in FGURE 12 were btained frm the average temperature f heated clumn at each time step. The bending mment fr the l-l-sectin steel beam f Mdel-O is less than that f the cmpsite beam f Mdel-P, and nly in the case f Mdel-P des the bending mment in the heated clumn reach yield mment. Bending mment in the clumns increases t 90 minutes in the case f Mdel-O and ls minutes in the case f Mdel-P. 768

9 E :: 1500 <l.l S 0 S FGURE 12. Develpmentf Bending Mment in Heated Clumns Bending Mment in Beam at End f Span. FGURE 13 shws develpment f bending mment in the beams. t must be nted that yielding mment and plastic mment in FGURE 13 was btained frm the average temperature f H-scctin steel beam at each time step and slab effect was nt included. The bending mment at the end f the H-sectin steel beam span is greater than that f the cmpsite beam, because flexural rigidity f the cmpsite beam is greater than that fr H sectin steel beam. n the case f Mdel-P, the bending mment decreases at the beginning f fire expsure, because cmpsite beams will bend upwards due t inside temperature distributin. At 45 minutes, it seems that yielding ccurs in the lwer edge f each beam in an end f span, and after that, cmpressive yield area in the crss sectin increases t the upper flange f each beam, and cmpressive strength f steel decreases with rising temperature. By this prgress, plastic hinges are prduced at the ends f span, and the beams act as a simply supprted beam. Behavir at the ends f span f the mdels is much the same, because cncrete almst des nt bear tensin stress. But, if the amunt f upper reinfrcement is greater than that f this case, the difference between steel beam and cmpsite beam wuld appear mre clearly than this case E 1000 t: S 500 i!.. _ L' plastic mment 2..YietdiJ:tg?menr :--- t-... """-.j FGURE 13. Develpment f Bending Mment in Heated Beams 769

10 .Bending Mment in Beam at Middle f Spa!}. Bending mment at the middle f span decreases at the beginning f expsure t fire, althugh the bending mment in Mdel-P increases fr the initial 15 minutes due t elngatin f the slab. After 45 minutes, bending mment at the middle f span increases with decreasing flexural rigidity at the end f span. After 165 minutes, cmpressin failure f cncrete ccurs in slab in the case f Mdel-P, and plastic hinges are created at the middle f span in bth mdels. Due t the develpment f plastic hinges in the end and middle f span in bth mdels, H-shaped structural frames cllapse. n such cases, the cllapse time f each mdel is almst the same. CONCLUSONS Frm the analyses, the fllwing cnclusins can be btained. Temperature distributin in the crss sectin f cmpsite beams is generally that the highest temperature ccurred in slab sffit, fllwed by the lwer flange.then the web and then the upper flange. This temperature distributin causes the difference f structural behavir between steel beam and cmpsite beam. The defrmatin f steel beam appears directly crrespndent t temperature distributin in the crss sectin. On the ther hand, at the beginning f fire expsure, the cmpsite beam mves upward. And als, at the beginning f fire expsure, thermal expansin f slab sffit causes greater elngatin f the cmpsite beam than in the steel beam. The influence f these behavirs can be seen in the analyses f H-shaped structural frames. At the beginning f fire expsure, the bending mments at the end f the span f cmpsite beam decrease, and the bending mment at the middle f span increases. And the bending mments at the restraint clumns f cmpsite beam are greater than that f steel beam. n spite f these differences between steel beam and cmpsite beam, analyses f structural frames in this paper shw that the fire resistance f structural frame with H-sectin steel beam and the structural frame with cmpsite beam is almst the same. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] Article 107 in The Building Standard Law f Japan Enfrcement Order Ntificatin N.1675 f Ministry f Cnstructin in Japan. Jding,R.H and Bresler,B,Effect f Fire Expsure n Steel Frame Buildings (Cmputer Mdel FASBUS ), Final Reprt wje Wiss, Janney,Elstner and Assciates, Jnc., September CEC Research F21O-SA/502-REFAO/CAFR, Cmputer Assisted Analysis f the Fire Resistance f Steel and Cmpsite Steel-Cncrete structures (Cmputer Prgram CEFCOSS), Te.chnical Reprts RT 1-6, 1982/85. Wakamatsu,T, "Heat Flw Analysis f Building Members during Fire Expsure", First and Secnd Reprts, Translatin f the Architectural nstitute f Japan. N.109 and ll, (in Japanese) Wakamatsu,T, "Heat Transfer during Fire Test", Bull. f the Fire Preventin Sciety f Japan, Vl.l7 N.1, September (in Japanese) Wakamatsu,T, "Estimatin f Fire Damage f Reinfrced Cncrete Beams", Fire Science and Technlgy, Vl.7, N.2, pp.1-l6, Ministry f Cnstructin in Japan, Develpment f Design System fr Building Fire Safety, March (in Japanese) H.Sait, H.Uesugi, M.Yamaguchi and A.Kdaira, "Thermal Stress and Defrmatin f Steel Structures f High Rise Buildings in Fire", Fire Safety Science - Prceedings f the Secnd nternatinal Sympsium, pp , Becker.J and Bresler,B, "Fires-RC A Cmputer Prgram fr the Respnse f Structures Reinfrced Cncrete Frames", Reprt N.UCB FRO 74-3, University f Califrnia, Berkeley, July