Module 9.1 Software toepassing 4 (SAFIR) Toelichten van de mogelijkheden met SAFIR

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1 TETRA Module 9.1 Software toepassng 4 (SAFIR) Toelchten van de mogeljheden met SAFIR Jean-Marc Franssen [email protected] Sept. 15, 009 Queston: what s an advanced calculaton model? Accordng to EN (Eurocode 3 - Fre part): Advanced calculaton models are desgn methods n whch engneerng prncples are appled n a realstc manner to specfc applcatons. Smple calculaton models are smplfed desgn methods for ndvdual members, whch are based on conservatve assumptons. Advanced calculaton methods shall provde a realstc analyss of structures exposed to fre. They shall be based on fundamental physcal behavour n such a way as to lead to a relable approxmaton of the expected behavour of the relevant structural component under fre condtons. Queston: what s an advanced calculaton model? Any potental falure modes not covered by the advanced calculaton method (ncludng local buclng and falure n shear) shall be elmnated by approprate means. The decson on use of advanced calculaton models n a Country may be found n ts Natonal Annex. In Belgum: ether the desgner s certfed, or hs desgn s revewed by a certfed body. Should nclude separate models, thermal and mechancal. Thermal model based on the acnowledged prncples and assumptons of the theory of heat transfer. Mechancal model based on the acnowledged prncples and assumptons of the theory of structural mechancs Any heatng curve (f materal propertes are nown). Any type of cross-secton. Mosture n fre protecton materal may be neglected. 3 4 Should be consdered: The change of mechancal propertes wth temperatures. The effects of thermal strans. The effects of geometrcal mperfectons (h/1000 for solated columns). Geometrcal non lnear effects. (large dsplacements) Non lnear materal propertes, ncludng the unfavourable effects of loadng and unloadng on the structural stffness (plastcty) The deformaton at ultmate lmt state should be lmted (for, e.g., compatblty between parts of the structure, loss of support) The effects of creep need not explct consderaton. 5 Valdaton by tests and senstvty analyses on, e.g., buclng length, sze of the elements, load level. 6 1

2 Numercal modelng of buldng structures under fre. «Structures n Fre» modelng. Step. Thermal response: dscretsaton of the structure 1 Temperatures n the compartment Desgn fre, zone model (e.g. OZone from ULg), Temperatures n the structure 3 Mechancal behavour } = SF (SAFIR n Ulg) True secton Matchng Dscretsed secton Thermal conductvty [W/mK] Enthalpy [J/cm³K] Specfc heat [J/gK] Temperature [ C] ==> Temperature [ C] ==> Thermal conductvty of steel steel 9 steel 10 Specfc heat of steel Thermal conductvty [W/mK] Heatng Coolng Temperature [ C] Thermal conductvty of concrete (non reversble durng coolng). 11 The local equlbrum equaton for conducton s T T Q = x y It s transformed n an element equlbrum equaton. [ K ]{ T } = { q} 1,1 Sym 1,, 1,3,3 3,3 1,4,4 3,4 4,4 T1 T T3 T 4 = q1 q q3 q 4

3 Noeuds Elements Step. Mechancal analyss Dscretsaton of the D beam Y X σ a 100 C f 1.0, y 00 C 0.9, 300 C 0.8, 400 C 0.7, 500 C 0.6, 0.5, , C 0.3, , C 0.1, 800 C 900 C 1000 C 1100 C 0.0, 0.000, 0.005, 0.010, 0.015, 0.00, Déformaton εa Thermal expanson [mm/m] Temperature [ C] ==> Stress-stran stran relatonshp n steel 17 Thermal expanson n steel 18 3

4 Stress / Pea Stress at 0 C C 100 C 00 C 300 C 400 C 500 C 600 C Stress Related Stran [%] Stress-Stran Stran relatonshp n concrete Thermal stran Tmax = Tmax = 600 Tmax = Tmax = Température [ C] EC Thermal expanson of concrete Non reversble durng coolng Tmax = 1000 concrete 19 0 The local equlbrum equaton s : σ σ x y +... y x The element equlbrum equaton s : [ K ]{} u = { P} 1,1 Sym 1,, 1,3 3,3 4,4 5,5 6,6 1,7 6,7 7,7 u1 u u 6 u 7 p1 p = p6 p7 SF modelng determnaton of the temperatures n the structure; of the mechancal response; Ts(t) = f 1 (x, y, z, Tg(t)) u = f (x, y, z, loads,, Ts(t)) SAFIR : general presentaton Ln between thermal and mechancal analyses Temperature feld Mechancal model Temperature feld Mechancal model 3D F.E. => Smple calculaton model 3D F.E. => Smple calculaton model D F.E. => Beam F.E. (D or 3D) D F.E. => Beam F.E. (D or 3D) 1D F.E. or user s feld => Shell F.E. (3D) 1D F.E. or user s feld => Shell F.E. (3D) Smple calculaton model => Truss F.E. (D or 3D) 3 Smple calculaton model => Truss F.E. (D or 3D) 4 4

5 3D temperature dstrbuton - Examples Renforced concrete beam wth a crcular hole n the web (Courtesy: Halfann & Krchner) Smple calculaton models (struts and tes model) 5 6 Ln between thermal and mechancal analyses Integraton on the secton of the beam element Temperature feld Mechancal model Y 3D F.E. D F.E. 1D F.E. or user s feld => Smple calculaton model => => Smple calculaton model => Beam F.E. (D or 3D) Shell F.E. (3D) Truss F.E. (D or 3D) 7 Z EA ES EI N M * y * y * * * y = = = = = = 1 = 1 = 1 n n ( T ) A ( = E b h) ( T ) y A ( 0) ( T ) σ ( T ) = 1 n n n σ ( T ) = 1 E E E A y A y A E b h

6 Ln between thermal and mechancal analyses Temperature feld Mechancal model 3D F.E. D F.E. => => Smple calculaton model Beam F.E. (D or 3D) 1D F.E. or user s feld => Shell F.E. (3D) Smple calculaton model => Truss F.E. (D or 3D) 31 3 The shell fnte element Y, v d 1 4 a y c α α 3 b x θ X, u The temperature vares on the thcness of the shell Deflecton = l x / 5 (no amplfcaton n the drawng) Ln between thermal and mechancal analyses Temperature feld Mechancal model 3D F.E. D F.E. => => Smple calculaton model Beam F.E. (D or 3D) 1D F.E. or user s feld => Shell F.E. (3D) Smple calculaton model => Truss F.E. (D or 3D)

7 q' Am t = cs ρs V T => T = f(t) Ln between thermal and mechancal analyses Capabltes of thermal analyses 1. Versatlty n the geometry Load, P [N] A Deflecton, w [mm] D temperature dstrbuton - Examples ¼ of a concrete column 39 Steel secton 40 Composte steel-concrete beam 41 4 A steel tube. 7

8 A steel tube, flled wth concrete secton 44 A steel tube, flled wth concrete,, and a hot rolled steel secton Natural fre 45 SAFIR calculatons 46 Wndow frame (courtesy: Permasteelsa) 47 A box steel secton flled wth concrete (dscretsaton) 48 8

9 49 50 A box steel secton flled wth concrete (sotherms after 10 mn.) A box steel secton flled wth concrete (sotherms after 10 mn.) Ln between thermal and mechancal analyses Capabltes of thermal analyses 1. Versatlty n the geometry. 3D analyses Composte steel-concrete columns (1/) Courtesy: Technum 51 5 Beam-to to-column wth cleats - dscretsaton Unprotected,, 5 mnutes dscretsaton

10 Beam-to to-column wth end plates and stffeners 55 Protected,, 90 mnutes 56 Steel column passng through a concrete slab Ln between thermal and mechancal analyses Capabltes of thermal analyses 1. Versatlty n the geometry. 3D analyses 3. Radatons n nternal cavtes 58 Radaton n the cavtes s taen nto account 59 Concrete hollow core slab 60 Ancent prefabrcated floorng system (radaton n the cavtes) Courtesy Halfann & Krchner, Erelenz, Germany 10

11 Ln between thermal and mechancal analyses Capabltes of thermal analyses 1. Versatlty n the geometry. 3D analyses 3. Radatons n nternal cavtes 4. Evaporaton of free mosture (pro memory) Man steel box grder of the TGV ralway staton n Lege (CALATRAVA arch.) 61 6 Ln between thermal and mechancal analyses Capabltes of thermal analyses 1. Versatlty n the geometry. 3D analyses 3. Radatons n nternal cavtes 4. Evaporaton of free mosture 5. Quantty and qualty of the results 63 Composte steel-concrete connecton Test by Prof. Junbluth, German Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses 1. Thermal propertes of (nsulatng( nsulatng) materals

12 Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses 1. Thermal propertes. Fxed geometry (.e. no spallng) Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses 1. Thermal propertes. Fxed geometry 3. Perfect contact Composte floor based on a corrugated steel sheet Composte floor based on a corrugated steel sheet Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses 1. Thermal propertes. Fxed geometry 3. Perfect contact 4. Local fres 71 Example of result from a feld model (SOFIE) How to transfer the results to the structure? 7 1

13 Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses 1. Dmensons of the structure DIAMOND 009 for SAFIR FILE: Modelo_Def_3 NODES: 64 BEAMS: 940 TRUSSES: 0 SHELLS: 0 SOILS: 0 DISPLACEM ENT PLOT ( x 1) TIME: sec sec Z X Y 1.0 E+01 m Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses 1. Dmensons of the structure. Statcally ndetermnate structures (ncl. load redstrbuton) Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses 1. Dmensons of the structure. Statcally ndetermnate structures (ncl. load redstrbuton) 3. Second order effects Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses 1. Dmensons of the structure. Statcally ndetermnate structures (ncl. load redstrbuton) 3. Second order effects 4. Quantty and qualty of the results

14 Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses 1. Dmensons of the structure. Statcally ndetermnate structures (ncl. load redstrbuton) 3. Second order effects 4. Quantty and qualty of the results 5. Parametrc studes Rf (mn) Wth concrete Wthout concrete Nsd,f (N) Vert. Dspl [m] nfn =EA/L =EA/3L =EA/6L =EA/1L =EA/4L =EA/48L =EA/96L =EA/19L = 0 Restraned concrete beam Analyss of the response for dfferent restrant levels Tme [sec] Restrant concrete beam Evoluton of the vert. dspl.. for dfferent restrant levels 8 Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses 1. Dmensons of the structure. Statcally ndetermnate structures (ncl. load redstrbuton) 3. Second order effects 4. Quantty and qualty of the results 5. Parametrc studes 6. 3D structures 83 Steel starcase submtted to the fre 84 14

15 Steel beams Steel beams supportng a concrete slab. Test made at Branz, N.Z. Courtezy L. Lm, Unv. of Canterbury Test made at Branz, N.Z. Courtezy L. Lm, Unv. of Canterbury Dsplacements at room temperature. 87 Dsplacements (x1) under fre. 88 Membrane forces at room temperature. 89 Membrane forces n fre condtons

16 Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses Lmtatons of mechancal analyses 1. Very large structures 91 9 Ths structure s huge, numercaly speang RACK STORAGE SYSTEM SUPPORTS THE ENVELOP OF THE BUILDING TRAVHYDRO Amens - France Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses Lmtatons of mechancal analyses 1. Very large structures. Boundary condtons Industral buldng: one frame + purlns represented95 Elongaton of the purlns: free or fxed? 96 16

17 Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses Lmtatons of mechancal analyses 1. Very large structures. Boundary condtons 3. Spallng Ln between thermal and mechancal analyses Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses Lmtatons of mechancal analyses 1. Very large structures. Boundary condtons 3. Spallng 4. Local (and temporary) falures BIG QUESTION How s falure defned/consdered n the general calculaton model? ANSWER Falure s not consdered n the general calculaton model (because the noton of falure s totally arbtrary and can only be defned by a human beeng, wth dfferent crtera for dfferent structures, dfferent So, what do I do, practally? Buld your model and run SAFIR. Two possbltes: 1) SAFIR does not run => chec the model for Materal propertes (f y or E too small or = 0 Boundary condtons Mechansm n structures (axal rotaton n dagonals) Isolated nodes (nodes not lned to any element) Load level (load s too bg) Tme step (too bg) Etc ) SAFIR runs (and t wll run as far as possble). => examne the results stuatons, )

18 Examne the results 1) The dsplacements are too bg (for me). => I decde that fre resstance s lost when the dsplacements reach my lmt. Horzontal dsplacement at a support leads to loss of support of the beam. Beam of a frame deflects nto the ground. Cantlver beam s transformed nto a cable hangng on the support. etc. 103 Smply supported beam (dsplacements x 1) 104 Is ths falure or not? Is ths falure or not? Smply supported beam (dsplacements x 1) 105 Smply supported beam (dsplacements x 1) 106 Is ths falure or not? Is ths falure or not? Smply supported beam (dsplacements x 1) 107 Smply supported beam (dsplacements x 1)

19 Is ths falure or not? Is ths falure or not? Smply supported beam (dsplacements x 1) 109 Smply supported beam (dsplacements x 1) 110 Examne the results 1) The dsplacements are too bg (for me ) The dsplacements are not too bg. => Loo for a vertcal asymptote n the dsplacement curve of (at least) one degree of freedom. Ths s good ndcaton of (run away) falure. Note: there are some exceptons f the load bearng mode s changng, e.g. snap through, concrete slab gong from bendng nto membrane acon, etc. For these case, there s a post-crtcal behavour after the vertcal asymptote. 111 Examne the results 1) The dspl. are too bg (for me). ) The dspl. are not too bg, wth a vertcal asymptote. 3) The dspl. are not too bg, No vertcal asymptote. Ths s a good ndcaton of numercal falure (prematurely lac of convergence) Note: there s one excepton f the falure mode s really fragle (STEEL IN DESCENDING BRANCH) => Do a dynamc calculaton => Increase the mass => Reduce the tme step => Try wth another materal (just to now) => Try wthout thermal expanson (just to now) 11 => Etc Capabltes of thermal analyses Lmtatons of thermal analyses Capabltes of mechancal analyses Lmtatons of mechancal analyses 1. Very large structures. Boundary condtons 3. Spallng 4. Local falures 5. Bernoull hypothess Consequences of Bernoull hypotheses n the beam F.E. 1. Local buclng (All sectons are seen by a Bernoull beam F.E. as compact sectons). Shear falure 3. Debondng

20 U secton n bendng elastc at 0 C Dsplacements x Imposed shortenng and heatng : 1 C/sec1 No amplfcaton of the dsplacements n the drawng 116 Order a free demonstraton verson of SAFIR Courses "Fre Eurocodes", ULg SF'10, Unv. of Mchgan Lvres J-M Franssen 119 0