EUROCODES Spreadsheets Structural Design
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(2) - evaluation copy -. Copyright© 2013 http://www.sigmundcarlo.net All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission from the publisher. -----------------------------------------------First Edition: January 2013 Sigmund, Carlo <1971-> Eurocodes - Structural Design. --------------------------------. The sponsoring editor for this document and the production supervisor was Carlo Sigmund. Electronic mail: [email protected]. ________________________________________________________ Cover Art from: F. A. Clignett Photography Delft - Copyright© 2006. The Cover Art (optimized electronically) is a mirror image of the original picture.. Have not been able to contact the owner of the photograph to give full consent to the publication. The author is at the disposal of the beneficiaries. Bridge: Erasmus Bridge Location: Rotterdam, Netherlands Length/ main span: 802 m/284 m Pylon: 139 m Designer: Architects Ben van Berkel, Freek Loos, UN Studio.. ________________________________________________________. Note: The pages of this document were created electronically using Inkscape 0.48 Copyright© 1989, 1991 Free Software Foundation, Inc. 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. www.inkscape.org.
(3) - evaluation copy -. Contents Eurocode 1 EN 1991-1-2...........................................................................................................5 1.1 General .................................................................................................................................................... 5 1.2 Terms relating to thermal actions............................................................................................................. 5 1.3 Structural Fire design procedure.............................................................................................................. 7 1.4 Design fire scenario, design fire............................................................................................................... 7 1.5 Temperature Analysis .............................................................................................................................. 7 1.6 Thermal actions for temperature analysis (Section 3).............................................................................. 8 1.7 Nominal temperature-time curves ............................................................................................................ 9 1.8 Verification tests....................................................................................................................................... 10 1.9 References [Section 1]............................................................................................................................. 18. Eurocode 1 EN 1991-1-2 Annex B ................................................................................................................19 2.1 Thermal actions for external members - Simplified calculation method................................................... 19 2.2 Verification tests....................................................................................................................................... 25 2.3 References [Section 2]............................................................................................................................. 33. Eurocode 1 EN 1991-1-2 Annex C, Annex E ................................................................................................35 3.1 ANNEX C: Localised fires ........................................................................................................................ 35.
(4) - evaluation copy -. EN 1991-1-2 - Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on structures exposed to fire CONTENTS - page iv. 3.2 ANNEX E: fire load densities ....................................................................................................................38 3.3 Verification tests .......................................................................................................................................41 3.4 References [Section 3] .............................................................................................................................47. Eurocode 1 EN 1991-1-2 Annex F, Annex G, Sec. B.5 Annex B................................................................................................. 49 4.1 ANNEX F: Equivalent time of fire exposure..............................................................................................49 4.2 ANNEX G: configuration factor .................................................................................................................51 4.3 ANNEX B, Section B.5: Overall configuration factors...............................................................................53 4.4 Verification tests .......................................................................................................................................53 4.5 Reference [Section 4] ...............................................................................................................................60.
(5) - evaluation copy -. Section 1. Eurocode 1 EN 1991-1-2. 1.1 General. T. he methods given in this Part 1-2 of EN 1991 are applicable to buildings, with a fire load related to the building and its occupancy. This Part 1-2 of EN 1991 deals with thermal and mechanical actions on structures exposed to fire. It is intended to be used in conjunction with the fire design Parts of prEN 1992 to prEN 1996 and prEN 1999 which give rules for designing structures for fire resistance. This Part 1-2 of EN 1991 contains thermal actions related to nominal and physically based thermal actions. More data and models for physically based thermal actions are given in annexes. In addition to the general assumptions of EN 1990 the following assumptions apply: —. any active and passive fire protection systems taken into account in the design will be adequately maintained. —. the choice of the relevant design fire scenario is made by appropriate qualified and experienced personnel, or is given by the relevant national regulation.. The rules given in EN 1990:2002, 1.4 apply. For the purposes of this European Standard, the terms and definitions given in EN 1990:2002, 1.5 and the following apply.. 1.2 Terms relating to thermal actions FIRE COMPARTMENT. Space within a building, extending over one or several floors,. which is enclosed by separating elements such that fire spread beyond the compartment is prevented during the relevant fire exposure.. FIRE RESISTANCE. Ability of a structure, a part of a structure or a member to fulfil its. required functions (load bearing function and/or fire separating function) for a specified load level, for a specified fire exposure and for a specified period of time.. EQUIVALENT TIME OF FIRE EXPOSURE. time of exposure to the standard temperature-time curve supposed to have the same heating effect as a real fire in the compartment.. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 5.
(6) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. EXTERNAL MEMBER. Structural member located outside the building that may be. exposed to fire through openings in the building enclosure.. GLOBAL STRUCTURAL ANALYSIS (FOR FIRE). Structural analysis of the entire structure,. when either the entire structure, or only a part of it, are exposed to fire. Indirect fire actions are considered throughout the structure.. MEMBER. Basic part of a structure (such as beam, column, but also assembly such. as stud wall, truss,...) considered as isolated with appropriate boundary and support conditions.. DESIGN FIRE SCENARIO. Specific fire scenario on which an analysis will be conducted. EXTERNAL FIRE CURVE. Nominal temperature-time curve intended for the outside of. separating external walls which can be exposed to fire from different parts of the facade, i.e. directly from the inside of the respective fire compartment or from a compartment situated below or adjacent to the respective external wall.. FIRE LOAD DENSITY. Fire load per unit area related to the floor area q f , or related to. the surface area of the total enclosure, including openings, q t .. FIRE LOAD. Sum of thermal energies which are released by combustion of all. combustible materials in a space (building contents and construction elements).. HYDROCARBON FIRE CURVE. Nominal temperature-time curve for representing effects of an hydrocarbon type fire. OPENING FACTOR. Factor representing the amount of ventilation depending on the area of openings in the compartment walls, on the height of these openings and on the total area of the enclosure surfaces. STANDARD TEMPERATURE‐TIME CURVE. Nominal curve defined in prEN 13501-2 for. representing a model of a fully developed fire in a compartment.. TEMPERATURE‐TIME CURVES. Gas temperature in the environment of member surfaces. as a function of time. They may be: —. nominal: conventional curves, adopted for classification or verification of fire resistance, e.g. the standard temperature-time curve, external fire curve, hydrocarbon fire curve. —. parametric: determined on the basis of fire models and the specific physical parameters defining the conditions in the fire compartment.. CONVECTIVE HEAT TRANSFER COEFFICIENT. Convective heat flux to the member related to. the difference between the bulk temperature of gas bordering the relevant surface of the member and the temperature of that surface.. EMISSIVITY. Equal to absorptivity of a surface, i.e. the ratio between the radiative heat absorbed by a given surface and that of a black body surface. FLASH‐OVER. Simultaneous ignition of all the fire loads in a compartment.. page 6. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(7) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. 1.3 Structural Fire design procedure A structural fire design analysis should take into account the following steps as relevant: —. selection of the relevant design fire scenarios. —. determination of the corresponding design fires. —. calculation of temperature evolution within the structural members. —. calculation of the mechanical behaviour of the structure exposed to fire.. Mechanical behaviour of a structure is depending on thermal actions and their thermal effect on material properties and indirect mechanical actions, as well as on the direct effect of mechanical actions. Structural fire design involves applying actions for temperature analysis and actions for mechanical analysis according to this Part and other Parts of EN 1991. Actions on structures from fire exposure are classified as accidental actions, see EN 1990:2002, 6.4.3.3(4).. 1.4 Design fire scenario, design fire To identify the accidental design situation, the relevant design fire scenarios and the associated design fires should be determined on the basis of a fire risk assessment. (2) For structures where particular risks of fire arise as a consequence of other accidental actions, this risk should be considered when determining the overall safety concept. Time- and load-dependent structural behaviour prior to the accidental situation needs not be considered, unless (2) applies. For each design fire scenario, a design fire, in a fire compartment, should be estimated according to section 3 of this Part. The design fire should be applied only to one fire compartment of the building at a time, unless otherwise specified in the design fire scenario. (3) For structures, where the national authorities specify structural fire resistance requirements, it may be assumed that the relevant design fire is given by the standard fire, unless specified otherwise.. 1.5 Temperature Analysis When performing temperature analysis of a member, the position of the design fire in relation to the member shall be taken into account. For external members, fire exposure through openings in facades and roofs should be considered. (3) For separating external walls fire exposure from inside (from the respective fire compartment) and alternatively from outside (from other fire compartments) should be considered when required.. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 7.
(8) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. Depending on the design fire chosen in section 3, the following procedures should be used: —. Note. with a nominal temperature-time curve, the temperature analysis of the structural members is made for a specified period of time, without any cooling phase; The specified period of time may be given in the national regulations or obtained from annex F following the specifications of the national annex.. — Note. with a fire model, the temperature analysis of the structural members is made for the full duration of the fire, including the cooling phase. Limited periods of fire resistance may be set in the national annex.. 1.6 Thermal actions for temperature analysis (Section 3) Thermal actions are given by the net heat flux h· net W m 2 to the surface of the member. On the fire exposed surfaces the net heat flux h· net should be determined by considering heat transfer by convection and radiation as: · · · h net = h net c + h net r. (Eq. 1‐1). where h· net c is the net convective heat flux component and h· net r is the net radiative heat flux component. The net convective heat flux component should be determined by: · h net c W m 2 = c g – m . (Eq. 1‐2). where: •. c is the coefficient of heat transfer by convection W m 2 K . •. g is the gas temperature in the vicinity of the fire exposed member [°C]. •. m is the surface temperature of the member [°C].. On the unexposed side of separating members, the net heat flux h· net should be determined by using equation 1-1, with c = 4 W m 2 K . The coefficient of heat transfer by convection should be taken as c = 9 W m 2 K , when assuming it contains the effects of heat transfer by radiation. The net radiative heat flux component per unit surface area is determined by: · h net r W m 2 = m f r + 273 4 – m + 273 4 . (Eq. 1‐3). where:. page 8. •. is the configuration factor. •. m is the surface emissivity of the member. •. f is the emissivity of the fire. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(9) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. –8. •. is the Stephan Boltzmann constant 5 67 10. •. r is the effective radiation temperature of the fire environment [°C]. •. m is the surface temperature of the member [°C].. Note. W m2K4 . Unless given in the material related fire design Parts of prEN 1992 to prEN 1996 and prEN 1999, m = 0 8 may be used. The emissivity of the fire is taken in general as f = 1 0 .. Where this Part or the fire design Parts of prEN 1992 to prEN 1996 and prEN 1999 give no specific data, the configuration factor should be taken as = 1 . A lower value may be chosen to take account of so called position and shadow effects. For the calculation of the configuration factor a method is given in annex G.. Note. In case of fully fire engulfed members, the radiation temperature r may be represented by the gas temperature g around that member. The surface temperature m results from the temperature analysis of the member according to the fire design Parts 1-2 of prEN 1992 to prEN 1996 and prEN 1999, as relevant. Gas temperatures g may be adopted as nominal temperature-time curves according to 3.2, or adopted according to the fire models given in 3.3. Note. The use of the nominal temperature‐time curves according to 3.2 or, as an alternative, the use of the natural fire models according to 3.3 may be specified in the national annex.. 1.7 Nominal temperature-time curves STANDARD TEMPERATURE‐TIME CURVE. The standard temperature-time curve is given by:. g = 20 + 345 log 10 8t + 1 . (Eq. 1‐4). where: •. g is the gas temperature in the fire compartment [°C]. •. t is the time [min].. The coefficient of heat transfer by convection is c = 25 W m 2 K . EXTERNAL FIRE CURVE. The external fire curve is given by:. g = 20 + 660 1 – 0 687 e –0 32t – 0 313e –3 8t . (Eq. 1‐5). where: •. g is the gas temperature near the member [°C]. •. t is the time [min].. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 9.
(10) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. The coefficient of heat transfer by convection is c = 25 W m 2 K . HYDROCARBON CURVE. The hydrocarbon temperature-time curve is given by:. g = 20 + 1080 1 – 0 325 e –0 167t – 0 675e –2 5t . (Eq. 1‐6). where: •. g is the gas temperature in the fire compartment [°C]. •. t is the time [min].. The coefficient of heat transfer by convection is c = 50 W m 2 K .. 1.8 Verification tests EN1991‐1‐2_(A).XLS. 6.4 MB. Created: 3 February 2013. Last/Rel.-date: 3 May 2013.. Sheets: —. Splash. —. CodeSec3. —. Annex A.. EXAMPLE 1-A‐ Section 3.1 ‐ Thermal actions for temperature analysis ‐ test 1 Given:. Determine the net heat flux on a fire exposed surface, in case of fully fire engulfed members ( r g around the member). Suppose: c = 4 00 W m 2 K (coefficient of heat transfer by convection); g = 700C (gas temperature in the vicinity of the fire exposed member); m = 70C (surface temperature of the member); = 1 (configuration factor); m = 0 8 (surface emissivity of the member); f = 1 0 (emissivity of the fire); r = 700C (effective radiation temperature of the fire environment). [Reference sheet: CodeSec3]‐[Cell‐Range: A1:O1‐A64:O64].. Solution:. The net convective heat flux component is given by: · h net c = c g – m = 4 00 700 – 70 = 2520 W m 2 = 2 52 kW m 2 . The net radiative heat flux component is determined by: 5 67 · - 700 + 273 4 – 70 + 273 4 h net r = m f r + 273 4 – m + 273 4 = 1 0 8 1 ----------10 8 5 6710 11 · h net r = 1 0 8 1 ---------- 8 963 10 11 – 0 138 10 11 = 40 ---------8- = 40000 W m 2 = 40 kW m 2 8 10 10. Therefore, the net heat flux (considering heat transfer by convection and radiation) is given by: · · · h = h +h = 2 52 + 40 = 42 52 kW m 2 . net. net c. net r. Now, considering r g with (say) m = 500C , g = 720C , we get:. page 10. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(11) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. · h net c = c g – m = 4 00 720 – 500 = 880 W m 2 = 0 88 kW m 2 5 67 · - 720 + 273 4 – 500 + 273 4 h net r = m f r + 273 4 – m + 273 4 = 1 0 8 1 ----------10 8 11 5 67 · 11 – 3 570 10 11 = 27 91 10 --------- = 27910 W m 2 = 27 91 kW m 2 h net r = 1 0 8 1 ---------- 9 723 10 10 8 10 8. Figure 1.1. View Plot (from input). See cells Range H63:J65 - Sheet: CodeSec3.. Hence, we find: h· net = h· net c + h· net r = 0 88 + 27 91 = 28 79 kW m 2 (see plot above). example-end. EXAMPLE 1-B‐ Section 3.2 ‐ Nominal temperature‐time curves ‐ test 2 Given:. Determine the standard temperature‐time curve at t = 120 min (time of the exposure), the external fire curve and the hydrocarbon temperature‐time curve at t = 15 min . [Reference sheet: CodeSec3]‐[Cell‐Range: A68:O68‐A190:O190].. Solution:. The standard temperature‐time curve is given by (gas temperature in the fire compartment): g = 20 + 345 log 10 8t + 1 . Sobstituting t = 120 min , we get:. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 11.
(12) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. g = 20 + 345 log 10 8t + 1 = 20 + 345 log 10 8 120 + 1 = 20 + 345 2 983 = 1049C .. Figure 1.2. Standard temperature-time curve.. Figure 1.3. External fire curve.. The external fire curve is given by (gas temperature near the member):. page 12. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(13) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. g = 20 + 660 1 – 0 687 e –0 32t – 0 313e –3 8t . Sobstituting t = 15 min , we get: g = 20 + 660 1 – 0 687 e –0 32 15 – 0 313e –3 8 15 = 20 + 660 1 – 0 687 e – 4 8 – 0 313e –57 g 20 + 660 1 – 0 687 0 00823 – 0 = 676 3C .. We find that: g = 680C = cost for t 40 min approximately. The hydrocarbon temperature‐time curve is given by (gas temperature in the fire compartment): g = 20 + 1080 1 – 0 325 e –0 167t – 0 675e –2 5t . Sobstituting t = 15 min , we get: g = 20 + 1080 1 – 0 325 e –0 167 15 – 0 675e –2 5 15 = 20 + 1080 1 – 0 325 e –2 505 – 0 675e – 37 5 g 20 + 1080 1 – 0 325 e –2 505 – 0 = 20 + 1080 1 – 0 325 0 0817 – 0 = 1071 3C .. Figure 1.4. Hydrocarbon curve.. We find that: g = 1100C = cost for t 65 min approximately. example-end. EXAMPLE 1-C‐ Annex A ‐ Parametric temperature‐time curves ‐ test 3 Given:. For internal members of fire compartments, calculate the gas temperature in the compartment using the method given in informative Annex A of EC1 Part 1‐2. The theory assumes that temperature rise is independent of fire load.. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 13.
(14) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. The temperature within the compartment is assumed to vary as a simple exponential function of modified time dependent on the variation in the ventilation area and the properties of the compartment linings from this “standard” compartment.. Figure 1.5. Plan of fire compartment (height = 3,60 m).. [Reference sheet: Annex A]‐[Cell‐Range: A1:O1‐A152:O152]. Solution:. Dimension of the compartment: width = 6,50 m; lenght = 15,00 m; heigth = 3,60 m. Dimension of windows: number of windows = 4; width = 2,30 m (mean value); heigth = h eq = 1,70 m (weighted average of window heights on all walls).. [kg/m3]. . c. . [J/kgK]. [W/mK]. CEILING. 2400. 1506. 1,50. 2400 1506 1 50 = 2328 (a). WALLS. 900. 1250. 0,24. 900 1250 0 24 = 519 6. FLOOR. 900. 1250. 0,24. Table 1.1. b =. c. [J/m2s0,5K]. 519 6. Thermal properties of enclosure surfaces.. (a). b (thermal absorptivity) with the following limits 100 b 2200 .. We assume: ceiling b = 2200 J m 2 s 0 5 K ; walls and floor b = 520 J m 2 s 0 5 K . . page 14. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(15) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. Total area of vertical openings on all walls: A v = 4 2 30 m 1 70 m = 15 64 m 2 .. Total area of enclosure (walls, ceiling and floor, including openings): A t = 2 6 50 15 00 + 6 50 + 15 00 3 60 = 349 8 m 2 .. Opening factor: h eq 1 70 - - = 15 64 -------------------O = A v ---------= 0 0583 m 1 / 2 At 349 8 . with the following limits: 0,02 < O = 0,0583 < 0,20. We find: ceiling A j = 6 50 15 00 = 97 50 m 2 and floor A j = 97 50 m 2 , wall A j = 2 6 50 + 15 00 3 60 – 15 64 = 139 2 m 2 . Hence, we get:. . bj Aj 97 50 + 520 139 2 + 520 97 5- = 1010 J m 2 s 0 5 K . ------------------------------------------------------------------------------------------------b = ----------------------- = 2200 At – Av 349 8 – 15 64 . with the following limits: 100 < b = 1010 < 2200. Time factor function: O b 2 0 0583 1010 2 = ----------------------------------2- = --------------------------------------------- = 2 802 . 0 04 1160 0 04 1160 2. Design value of the fire load density related to the surface area A f of the floor: q f d = 700 MJ m 2 .. Floor area of the fire compartment: A f = 97 5 m 2 . Design value of the fire load density related to the total surface area A t of the enclosure: A 97 5 q t d = q f d -----f = 700 --------------- = 195 11 MJ m 2 . At 349 8. Fire growth rate: say t lim = 20 min 0 333 h (medium fire growth rate). 0 2 10 –3 q t d O = 0 2 10 –3 195 11 0 0583 = 0 67 h . t max = max 0 2 10 –3 q t d O ; 0 333 h = max 0 67 ; 0 333 = 0 67 h . t max t lim the fire is ventilation controlled.. The maximum temperature max in the heating phase happens for t * = t *max : t *max = t max = 0 67 2 802 = 1 88 h .. Maximum temperature (heating phase): – 0 2t * – 0 204e – 1 7t * – 0 472e – 19t * max = 20 + 1325 1 – 0 324e t *max = 1 88 h max = 20 + 1325 1 – 0 324e – 0 2 1 88 – 0 204e – 1 7 1 88 – 0 472e – 19 1 88 max 20 + 1325 1 – 0 324 0 687 – 0 204 0 041 – 0 = 1039C .. Cooling phase t t *max : with t max = 0 67 h t lim = 0 33 h , we get: x = 1 (see eq. A.12). Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 15.
(16) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. – 3 q t d – 3 195 11 - 2 802 = 0 669 2 802 = 1 88 h With t ** max = 0 2 10 -------- = 0 2 10 ----------------O 0 0583 – 3 q t d - = 1 88 h 2 h , we get: 0 5 h 0 2 10 ------ O * ** g = max – 250 3 – t ** max t – t max x ,. g = max – 250 3 – 1 88 t * – 1 88 = 1039 – 250 3 – 1 88 t * – 1 88 .. For (say) t = 1 10 h t * = t = 1 10 2 802 = 3 08 h , we find:. Figure 1.6. Parametric curve: heating, cooling.. g = 1039 – 250 3 – 1 88 t * – 1 88 = 1039 – 250 3 – 1 88 3 08 – 1 88 = 703C .. Rounding error: 100 x (703 – 699,7)/699,7 = 0,5%. example-end. EXAMPLE 1-D‐‐ Annex A ‐ Parametric temperature‐time curves ‐ test 4 Given:. Maintaining the same assumptions in the previous example and assuming q f d = 200 MJ m 2 , calculate the cooling phase. [Reference sheet: Annex A]‐[Cell‐Range: A107:O107‐A152:O152].. page 16. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(17) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. Solution:. We find: A 97 5 q t d = q f d -----f = 200 --------------- = 55 75 MJ m 2 At 349 8 t max = max 0 2 10 –3 q t d O ; 0 333 h = max 0 19 ; 0 333 = 0 333 h. Time factor function (A.2b): O lim b 2 0 0167 1010 2 -2 --------------------------------------------- = 0 23 , with lim = --------------------------------- 0 04 1160 0 04 1160 2 0 1 55 75 0 1 q t d - = --------3- ------------------- = 0 0167 . O lim = --------3- ------10 0 333 10 t lim. If (O > 0,04 and qt,d < 75 and b < 1160), lim in (A.8) has to be multiplied by k given by: q t d – 75 1160 – b 0583 – 0 04- 55 75 – 75 1160 – 1010 O – 0 04 - --------------------- = 1 + 0---------------------------------- --------------------------- ------------------------------ k = 1 + ---------------------- ------------------ 0 04 75 1160 0 04 75 1160 k = 1 + 0 4575 – 0 2567 0 1293 = 0 98 .. We get: t *max = t max k lim = 0 333 0 98 0 231 0 08 h .. Maximum temperature (heating phase): – 0 2t * – 0 204e – 1 7t * – 0 472e – 19t * max = 20 + 1325 1 – 0 324e t *max 0 757 h max = 20 + 1325 1 – 0 324e – 0 2 0 076 – 0 204e – 1 7 0 076 – 0 472e – 19 0 076 max 20 + 1325 1 – 0 324 0 985 – 0 204 0 879 – 0 472 0 236 = 537C ,. Rounding error: 100 x (537 – 536,1)/536,1 < 0,2%. 0 2- ---------------------0 2- q------ 55 75 t d - = ------- 2 802 = 0 536 h . t ** max = -------10 3 0 0583 10 3 O t max t lim = 0 333 h (the fire is fuel controlled): t lim 0 333 2 802 --------------------------------------- = 1 74 . x = --------------0 536 t ** max. For 0 5 t ** max 2 : * ** * g = max – 250 3 – t ** max t – t max x = max – 250 3 – 0 536 t – 0 536 1 74 .. For (say) t = 0 50 h t * = t = 0 50 2 802 = 1 40 h , we find: g 537 – 250 3 – 0 536 1 40 – 0 536 1 74 = 249C ,. Rounding error: 100 x (249 – 248,4)/248,4 < 0,25%. example-end. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls. page 17.
(18) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 1 E UROCODE 1 EN 1991-1-2. 1.9 References [Section 1] BS EN 1991-1-2. Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on structures exposed to fire. 26 November 2002 EN 1991-1-2:2002/AC:2013. Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on structures exposed to fire. CEN Brussels, February 2013. Manual for the design of building structures to Eurocode 1 and Basis of Structural Design - April 2010. © 2010 The Institution of Structural Engineers.. page 18. Topic: User’s Manual/Verification tests - EN1991-1-2_(a).xls.
(19) - evaluation copy -. Section 2. Eurocode 1 EN 1991-1-2 Annex B. 2.1 Thermal actions for external members - Simplified calculation method. T. his method considers steady-state conditions for the various parameters. The method is valid only for fire loads q f d 200 MJ m 2 . This method allows the determination of: —. the maximum temperatures of a compartment fire. —. the size and temperatures of the flame from openings. —. radiation and convection parameters.. CONDITIONS OF USE. When there is more than one window in the relevant fire compartment, the weighted average height of windows h eq , the total area of vertical openings A v and the sum of windows widths are used.. When there are windows in only wall 1, the ratio D/W is given by: D W = W2 W1 .. (Eq. 2‐7). When there are windows on more than one wall, the ratio D/W has to be obtained as follows: W A v1 , D W = -------2 -------W1 Av. (Eq. 2‐8). where: •. W 1 is the width of the wall 1, assumed to contain the greatest window area. •. A v1 is the sum of window areas on wall 1. •. W 2 is the width of the wall perpendicular to wall 1 in the fire compartment.. When there is a core in the fire compartment, the ratio D/W has to be obtained as follows:. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 19.
(20) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. W 2 – L c A v1 D W = --------------------------------, W 1 – W c A v. (Eq. 2‐9). where: •. L c and W c are the length and width of the core. •. W 1 and W 2 are the length and width of the 'fire compartment. •. the size of the fire compartment should not exceed 70 m in length, 18 m in width and 5 m in height.. (5) All parts of an external wall that do not have the fire resistance (REI) required for the stability of the building should be classified as window areas. The total area of windows in an external wall is: —. the total area, according to (5), if it is less than 50% of the area of the relevant external wall of the compartment. —. firstly the total area and secondly 50% of the area of the relevant external wall of the compartment if, according to (5), the area is more than 50%. These two situations should be considered for calculation. When using 50% of the area of the external wall, the location and geometry of the open surfaces should be chosen so that the most severe case is considered.. The flame temperature should be taken as uniform across the width and the thickness of the flame. EFFECT OF WIND ‐ MODE OF VENTILATION, DEFLECTION BY WIND. If there are windows on opposite sides of the fire compartment or if additional air is being fed to the fire from another source (other than windows), the calculation shall be done with forced draught conditions. Otherwise, the calculation is done with no forced draught conditions.. Figure 2.7. Deflection of flame by wind (from fig. B.1).. Flames from an opening should be assumed to be leaving the fire compartment (see figure below):. page 20. —. perpendicular to the facade. —. with a deflection of 45° due to wind effects.. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(21) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Figure 2.8. Flame dimensions, no through draught (from fig. B.2).. CHARACTERISTIC OF FIRE AND FLAMES: NO FORCED DRAUGHT. The rate of burning or the rate. of heat release is given by [MW]:. 0 036. 1/2. – --------------h eq A f q f d O Q = min -----------------; 3 15 1 – e A v ------------ F DW . . . (Eq. 2‐10). The temperature of the fire compartment is given by [°K]: T f = 6000 1 – e. – 0 1 O. – 0 00286. O 1 – e. + T0 .. (Eq. 2‐11). The flame height (see Figure B.2) is given by: 2/3 Q L L = max 0 ; h eq 2 37 --------------------------- – 1 A h g v g eq. (Eq. 2‐12). where: • • •. . A v is the total area of vertical openings on all walls A v = A v i i h eq = A v i h i A v is the weighted average of windows on all walls i A t is the total area of enclosure (walls, ceiling and floor, including openings). . •. q f d is the design fire load density MJ m 2 related to the floor area A f. •. A f is the floor area of the fire compartment. •. O = A v h eq A t is the “opening factor” of the fire compartment. •. F = 1200 s is the free burning duration (in seconds). Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 21.
(22) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. •. D W i the “ratio” (see section B.2 “Conditions of use”). •. = A f q f d A v A t. •. T 0 = 273 K = 20C is the “initial temperature”. •. g is the internal gas density kg m 3 . •. g = 9 81 m s 2 .. The flame width is the window width (see Figure B.2). The flame depth is 2/3 of the window height: 2/3 heq (see Figure B.2). (6) The horizontal projection of flames: —. in case of a wall existing above the window, is given by: L H = h eq 3 if h eq 1 25w t ; L H = 0 3 h eq h eq w t 0 54 if h eq 1 25w t and distance to any other window > 4w t ; L H = 0 454 h eq h eq 2w t 0 54 in other cases, (with w t = sum of window widths on all walls). —. in case of a wall not existing above the window, is given by: L H = 0 6 h eq L L h eq 1 / 3 .. The flame length along axis is given by: —. when L L 0 , L f = L L + h eq 2 if wall exists above window or if h eq 1 25w t ; Lf =. L2L + L H – h eq 3 2 + h eq 2 if no wall exists above window or if. h eq 1 25w t. —. when L L = 0 , then L f = 0 .. The flame temperature at the window is given by [°K]: 520 - + T0 T w = --------------------------------------------------------L f w t -------------1 – 0 4725 Q . (Eq. 2‐13). with L f w t Q 1 . The emissivity of flames at the window may be taken as f = 1 0 . The flame temperature along the axis is given by [°K]: L x w t T z = T w – T 0 1 – 0 4725 --------------+ T0 Q . (Eq. 2‐14). with L x w t Q 1 and L x is the axis length from the window to the point where the calculation is made. The emissivity of flames may be taken as: f = 1 – e – 0 3df. (Eq. 2‐15). where d f is the flame thickness [m]. The convective heat transfer coefficient is given by [W/m2K]: c = 4 67 1 d eq 0 4 Q A v 0 6 .. page 22. (Eq. 2‐16). Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(23) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. (13) If an awning or balcony is located at the level of the top of the window on its whole width for the wall above the window and h eq 1 25w t , the height and horizontal projection of the flame should be modified as follows: —. the flame height L L given in eq. 2-12 is decreased by W a 1 + 2 . —. the horizontal projection of the flame given in (6), is increased by W a .. Figure 2.9. Deflection of flame by balcony (from fig. B.3).. With the same conditions for awning or balcony as mentioned in (13), in the case of no wall above the window or h eq 1 25w t , the height and horizontal projection of the flame should be modified as follows: —. the flame height L L given in eq. 2-12 is decreased by W a. —. the horizontal projection of the flame L H , obtained in (6) with the above mentioned value of L L , is increased by W a .. FORCED DRAUGHT. The rate of burning or the rate of heat release is given by [MW]:. A f q f d Q = -----------------. F . (Eq. 2‐17). The temperature of the fire compartment is given by [°K]:(1) T f = 1200 1 – e – 0 00288 + T 0 .. (Eq. 2‐18). (1) There were errors in the equation B.19 of Annex B of the English version of the standard. These have been corrected in the BS EN 1991-1-2:2002.. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 23.
(24) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Figure 2.10 Flame dimensions, through or forced draught (from fig. B.4).. The flame height (see Figure B.4) is given by: Q L L = 1 366 1 u 0 43 ---------- – h eq A . (Eq. 2‐19). v. where u m s is the wind speed, moisture content. The horizontal projection of flames is given by: L H = 0 605 u 2 h eq 0 22 L L + h eq .. (Eq. 2‐20). The flame width is given by w f = w t + 0 4L H . The flame length along axis is given by L f = L2L + L2H 0 5 . The flame temperature at the window is given by [°K]: 520 T w = --------------------------------------------------------------- + T 0 Lf Av 1 – 0 3325 ------------------ Q . (Eq. 2‐21). with L f A v Q 1 . The emissivity of flames at the window may be taken as f = 1 0 . The flame temperature along the axis is given by [°K]: Lx Av T z = T w – T 0 1 – 0 3325 -------------------+ T0 Q . (Eq. 2‐22). where L x is the axis length from the window to the point where the calculation is made. The emissivity of flames may be taken as: f = 1 – e – 0 3df. page 24. (Eq. 2‐23). Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(25) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Figure 2.11 Deflection of flame by awning (from fig. B.5).. where d f is the flame thickness [m]. The convective heat transfer coefficient is given by [W/m2K]: u 0 6 Q c = 9 8 1 d eq 0 4 ------------------ + --------- . 17 5 A v 1 6 . (Eq. 2‐24). Regarding the effects of balconies or awnings, see Figure B.5 (below), the flame trajectory, after being deflected horizontally by a balcony or awning, is the same as before, i.e. displaced outwards by the depth of the balcony, but with a flame length L f unchanged.. 2.2 Verification tests EN1991‐1‐2_(B).XLS. 6.85 MB. Created: 6 February 2013. Last/Rel.-date: 3 June. 2013. Sheets: —. Splash. —. Annex B.. EXAMPLE 2-E‐Section B.2 ‐ Conditions of use ‐ test 1 Given:. Find the ratio D/W when: Case 1) there are windows in only one wall Case 2) there are windows on more than one wall Case 3) there is a core in the fire compartment. . Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 25.
(26) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. When Case 1) or 2) applies, assume that: – the width W 1 of the wall 1 (assumed to contain the greatest window area) is equal to 0,40 m – the width W 2 of the wall perpendicular to wall 1 in the fire compartment is equal to 0,25 m – the sum A v1 of windows areas on wall 1 is equal to 4,20 m2 – the total area A v of vertical openings on all walls is equal to 6,80 m2. When Case 3) applies, assume that: – the length L c and width W c of the core are equal to 5,00 m and 3,50 m respectively – the length W 1 and the width W 2 of the fire compartment are equal to 6,00 m and 6,50 m respectively. [Reference sheet: Annex B]‐[Cell‐Range: A75:Q75‐CommandButton]. Solution:. Case 1). From eq. (B.1): W 25- = 0 625 . D W = -------2 = 0----------W1 0 40. Figure 2.12 PreCalculus Excel® form: procedure for a quick pre-calculation: Case 1).. Case 2). From eq. (B.2): W A v1 0 25 4 20 = ------------ ---------------- = 0 386 . D W = -------2 -------W1 Av 0 40 6 80 . Case 3). From eq. (B.3): W 2 – L c A v1 6 50 – 5 00 4 20 - = 0 371 . D W = -------------------------------- = -------------------------------------------------- W 1 – W c A v 6 00 – 3 50 6 80 Note. page 26. All parts of an external wall that do not have the fire resistance (REI) required for the stability of the building should be classified as window areas.. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(27) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Using the PreCalculus Excel form, for the Case 2) we find:. Figure 2.13 PreCalculus Excel form: procedure for a quick pre-calculation: Case 2).. Finally, for the case 3), we find:. Figure 2.14 PreCalculus Excel form: procedure for a quick pre-calculation: Case 3).. Note. The size of the fire compartment should not exceed 70 m in length, 18 m in width and 5 m in height. The flame temperature should be taken as uniform across the width and the thickness of the flame.. example-end. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 27.
(28) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. EXAMPLE 2-F‐ Sec. B.4.1, Characteristic of fire and flames: no awning or balcony ‐ test2 Given:. Assume that: A f = 30 00 m 2 ; q f d = 500 MJ m 2 (taken from Annex E); h eq = 1 70 m ; A t = 112 00 m 2 ; A v = 6 80 m 2 and D/W = 0,625. Assuming no awning or balcony is located at the level of the top of the windows, find: – the rate of burning – the temperature of the fire compartment – the flame height, width and depth – the horizontal projection of flames – the flame temperature at the window – the flame temperature along the axis – the emissivity of flames – the convective heat transfer coefficient. [Reference sheet: Annex B]‐[Cell‐Range: A59:O59‐A264:O264 and A343:O343‐A502:O502].. Solution:. No forced draught. “Opening factor” of the fire compartment: O = A v h eq A t = 6 80 1 70 112 = 0 0792 m 1 / 2 .. Rate of burning or rate of heat release (eq. 2‐10): 0 036. 1/2. – --------------h eq A f q f d O Q = min -----------------; 3 15 1 – e A v ------------ DW F 0 036. 1/2. – ----------------- 30 500 1 70 0 0791 min ------------------- ; 3 15 1 – e 6 80 --------------- 1200 0 625 . . = min 12 5 ; 12 9 = 12 5 MW . . Factor : = A f q f d A v A t = 30 500 6 80 112 543 5 MJ m 2 . Temperature of the fire compartment (eq. 2‐11): T f = 6000 1 – e. – 0 1 O. T f = 6000 1 – e. – 0 1 0 0792 . – 0 00286. O 1 – e. + T0 – 0 00286 543 5 . 0 0791 1 – e. + 293K. T f = 6000 0 7171 0 2812 0 7887 + 273 955K + 293K = 1248K T f = 1248 – 273 = 975C .. Internal gas density, say = 0 50 kg m 3 . Flame height (eq. 2‐12): 2/3 Q L L = max 0 ; h eq 2 37 --------------------------- – 1 A h g v g eq 2/3 12 5 L L = max 0 ; 1 70 2 37 ------------------------------------------------------------------------ – 1 = 2 056 m . 6 80 0 50 1 70 9 81 . The flame width is the window width: say w t = 1 00 m . Flame depth: 2h eq 3 = 2 1 70 3 = 1 13 m .. page 28. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(29) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Horizontal projection of flames: Case a) ‐ Wall above the window and h eq 1 25w t : if h eq 1 25w t , L H = h eq 3 = 1 70 3 = 0 57 m . If h eq 1 25w t and distance to any other window > 4w t , L H = 0 3h eq h eq w t 0 54 = 0 3 1 70 1 70 1 00 0 54 = 0 68 m .. In other cases: L H = 0 454h eq h eq 2w t 0 54 = 0 454 1 70 1 70 2 1 00 0 54 = 0 71 m . Flame length along axis (when L L 0 ): L f L L + 0 5h eq = 2 056 + 0 5 1 70 = 2 91 m . Check: 1 70 2 2 056 + 0 57 2 + ----------------- 9 2 86 m 2 h eq 2 2 1 70 2 L f = L L + L 1 = L L + L H + ------- = 2 056 + 0 68 + ------------------- = 2 94 m 9 9 2 96 m 2 1 70 2 056 + 0 71 2 + -----------------9 . Mean value: L f = 2 86 + 2 94 + 2 96 3 = 2 92 m L L + 0 5h eq = 2 91 m (satisfactory). The flame temperature at the window is given by (eq. 2‐13): 520 - + T0 T w = --------------------------------------------------------L f w t -------------1 – 0 4725 Q 520 - + 293K = 877K = 877 – 273 = 604C . T w = ---------------------------------------------------------------------2-------------------------- 91 1 00- 1 – 0 4725 12 5 . with L f w t Q = 2 91 1 00 12 5 = 0 23 1 (case applicable). Case b) ‐ No wall above the window or h eq 1 25w t : L H = 0 6h eq L L h eq 1 / 3 = 0 6 1 70 2 056 1 70 1 / 3 = 1 09 m . L 1 0 5h eq = 0 5 1 70 = 0 85 m . Lf =. L2L + L H – h eq 3 2 + 0 5h eq =. 2 056 2 + 1 09 – 1 70 3 2 + 0 5 1 70 = 2 97 m .. The flame temperature at the window is given by (eq. 2‐13): 520 - + T0 T w = --------------------------------------------------------L f w t 1 – 0 4725 -------------- Q 520 - + 293K = 879K = 879 – 273 = 606C . T w = ---------------------------------------------------------------------2-------------------------- 97 1 00- 1 – 0 4725 12 5 . with L f w t Q = 2 91 1 00 12 5 = 0 23 1 (case applicable). The emissivity of flames at the window may be taken as f = 1 0 .. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 29.
(30) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Figure 2.15 Plots eq. (B.15).. The flame temperature along the axis is given by (eq. 2‐14): L x w t T z = T w – T 0 1 – 0 4725 --------------+ T0 . Q L x 1 00 + 293 . For case a: T z = 877 – 293 1 – 0 4725 --------------------12 5 . page 30. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(31) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. For (say) L x = 1 45 m , we get (case a): 1 45 1 00 T z = 877 – 293 1 – 0 4725 ---------------------------- + 293 = 845K = 845 – 273 = 572C . 12 5 L x 1 00 + 293 . For case b: T z = 877 – 293 1 – 0 4725 --------------------12 5 For (say) L x = 1 49 m , we get (case b): 1 49 1 00 T z = 879 – 293 1 – 0 4725 ---------------------------- + 293 = 846K = 846 – 273 = 573C . 12 5 . Flame thickness (say): d f = 1 00 m , geometrical characteristic of an external structural element (diameter or side): d eq = 0 70 m . Emissivity of flames (eq. 2‐15): f = 1 – e –0 3df = 1 – e –0 3 1 00 = 0 26 . Convective heat transfer coefficient (eq. 2‐16): c = 4 67 1 d eq 0 4 Q A v 0 6 = 4 67 1 0 70 0 4 12 5 6 80 0 6 = 7 8 W m 2 K .. Forced draught. Rate of burning or rate of heat release (eq. 2‐17): A f q f d 30 00 500 = ---------------------------- = 12 50 MW . Q = ----------------- F 1200 . Temperature of the fire compartment (eq. 2‐18): T f = 1200 1 – e – 0 00288 + T 0 = 1200 1 – e – 0 00288 543 5 + 293 = 1242K T f = 1242 – 273 = 969C .. Flame height (eq. 2‐19), with wind speed equal to (say) u = 6 00 m s : Q 12 5 L L = 1 366 1 u 0 43 ---------- – h eq = 1 366 1 6 00 0 43 ---------------- – 1 70 = 1 33 m . A 6 80 v. The horizontal projection of flames is given by (eq. 2‐20): L H = 0 605 u 2 h eq 0 22 L L + h eq = 0 605 6 00 2 1 70 0 22 1 33 + 1 70 = 3 59 m .. The flame width is given by: w f = w t + 0 4L H = 1 00 + 0 4 3 59 = 2 44 m . The flame length along axis is given by: L f =. L L2 + L H2 =. 1 33 2 + 3 59 2 = 3 83 m .. The flame temperature at the window is given by (eq. 2‐21): 520 520 - + T 0 = -------------------------------------------------------------------------T w = -------------------------------------------------------------- + 293 = 1001K A L 3 83 6 80 f v 1 – 0 3325 -------------------------------1 – 0 3325 ------------------- Q 12 5 T w = 1001 – 273 = 728C , with L f A v Q = 3 83 6 80 12 5 = 0 8 1 (case applicable). The emissivity of flames at the window may be taken as f = 1 00 . The flame temperature along the axis is given by (eq. 2‐22): Lx Av T z = T w – T 0 1 – 0 3325 -------------------+ T0 Q . Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 31.
(32) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. Figure 2.16 Plots eq. (B.25).. 2 50 6 80 T z = 1001 – 293 1 – 0 3325 -------------------------------- + 293 = 878K = 878 – 273 = 605C , 12 5 . with (say) L x = 2 50 m . The convective heat transfer coefficient is given by (eq. 2‐24): u - 0 6 Q + ------- c = 9 8 1 d eq 0 4 ----------------- 17 5 A v 1 6 12 5 - + 6---------- 00- 0 6 = 25 4 W m 2 K . c = 9 8 1 0 70 0 4 ------------------------------- 17 5 6 80 1 6 example-end. EXAMPLE 2-G‐ Sec. B.4.1, Characteristic of fire and flames: with awning or balcony ‐ test3 Given:. Consider the same assumptions in the example above. Find the flame height L L and the horizontal projection L H of the flame if an awning or balcony (with horizontal projection: W a = 0 50 m ) is located at the level of the top of the window on its whole width. [Reference sheet: Annex B]‐[Cell‐Range: A267:O267‐A340:O340].. Solution:. Case a), wall above and h eq 1 25w t . The flame height L L given in eq. 2‐12 is decreased by W a 1 + 2 : L*L = L L – W a 1 + 2 = 2 06 – 0 50 1 + 2 = 0 85 m .. The horizontal projection of the flame L H given in (6), is increased by W a : page 32. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls.
(33) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 2 E UROCODE 1 EN 1991-1-2 A NNEX B. L*H = L H + W a = 0 57 + 0 50 = 1 07 m * L H = L H + W a = 0 68 + 0 50 = 1 18 m * L H = L H + W a = 0 71 + 0 50 = 1 21 m. Case b), no wall above or h eq 1 25w t . The flame height L L given in (3) is decreased by W a : L*L = L L – W a = 2 06 – 0 50 = 1 56 m .. The horizontal projection of the flame L H given in (6), with the above mentioned value of L*L , is increased by W a : L H = 0 6h eq L L* h eq 1 / 3 * L L = 1 56 m L H = 0 6h eq L*L h eq 1 / 3 = 0 6 1 70 1 56 1 70 1 / 3 = 0 99 m . L*H = W a + L H = 0 50 + 0 99 = 1 49 m . example-end. 2.3 References [Section 2] BS EN 1991-1-2. Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on structures exposed to fire. 26 November 2002. EN 1991-1-2:2002/AC:2013. Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on structures exposed to fire. CEN Brussels, February 2013. EN 1991-1-2 (2002) (English): Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on structures exposed to fire [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]. European Committee for Standardisation.. Topic: User’s Manual/Verification tests - EN1991-1-2_(b).xls. page 33.
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(35) - evaluation copy -. Section 3. Eurocode 1 EN 1991-1-2 Annex C, Annex E. 3.1 ANNEX C: Localised fires. T. he thermal action of a localised fire can be assessed by using the expression given in this annex. Differences have to be made regarding the relative height of the flame to the ceiling. The heat flux from a localised fire to a structural element should be calculated with expression (3.1): · · · h net = h net c + h net r = c g – m + m f r + 273 4 – m + 273 4 . (Eq. 3‐25). and based on a configuration factor established according to annex G. The flame lengths L f of a localised fire (see Figure C.1) is given by: L f = – 1 02D + 0 0148Q 2 / 5 .. (Eq. 3‐26). Figure 3.17 From figure C.1.. Topic: User’s Manual/Verification tests - EN1991-1-2_(c).xls. page 35.
(36) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 3 E UROCODE 1 EN 1991-1-2 A NNEX C, A NNEX E. When the flame is not impacting the ceiling of a compartment ( L f H ; see Figure C.1) or in case of fire in open air, the temperature z in the plume along the symmetrical vertical flame axis is given by: z = 20 + 0 25Q c2 / 3 z – z 0 – 5 / 3 900C. (Eq. 3‐27). where: •. D is the diameter of the fire [m], see Figure C.1. •. Q is the rate of heat release [W] of the fire according to E.4. •. Q c is the convective part of the rate of heat release [W], with Q c = 0 8Q. •. z is the height [m] along the flame axis, see Figure C.1. •. H is the distance [m] between the fire source and the ceiling, see Figure C.1.. The virtual origin z 0 of the axis is given by: z 0 = – 1 02D + 0 00524Q 2 / 5 .. (Eq. 3‐28). When the flame is impacting the ceiling ( L f H ; see Figure C.2) the heat flux · h W m 2 received by the fire exposed unit surface area at the level of the ceiling is given by: · h = 100000 if y 0 30 · h = 136300 to 121000y if 0 30 y 1 0 · h = 15000y – 3 7 if y 1 0. (Eq. 3‐29). where:. Figure 3.18 From figure C.2.. page 36. Topic: User’s Manual/Verification tests - EN1991-1-2_(c).xls.
(37) - evaluation copy S ECTION 3. • •. •. E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN E UROCODE 1 EN 1991-1-2 A NNEX C, A NNEX E. r + H + zy is a parameter given by: y = -------------------------L h + H + z r is horizontal distance [m] between the vertical axis of the fire and the point along the ceiling where the thermal flux is calculated, see Figure C.2 H is the distance [m] between the fire source and the ceiling, see Figure C.2.. L h is the horizontal flame length (see Figure C.2) given by the following relation: L h = 2 9H Q*H 0 33 – H. (Eq. 3‐30). Q*H is a non-dimensional rate of heat release given by: Q Q*H = -------------------------------------. 6 1 11 10 H 2 5. (Eq. 3‐31). z is the vertical position of the virtual heat source [m] and is given by: z = 2 4D Q*D 2 / 5 – Q *D 2 / 3 when Q*D 1 0 z = 2 4D 1 0 – Q*D 2 / 3 when Q*D 1 0 .. (Eq. 3‐32). where: Q Q *D = -------------------------------------. 6 1 11 10 D 2 5. The net heat flux h· net received by the fire exposed unit surface area at the level of the ceiling, is given by: · · h net = h – c m – 20 – m f m + 273 4 – 293 4 . (Eq. 3‐33). (see expressions 3.2, 3.3).. The rules set up to this point are valid if the following conditions are met: the diameter of the fire is limited by D < 10 m; the rate of heat release of the fire is limited by Q < 50 MW.. In case of several separate localised fires, expression (C.4, see eq. 3-29) may be used in order to get the different individual heat fluxes h· 1 , h· 2 ,... received by the fire exposed unit surface area at the level of the ceiling. The total heat flux may be taken as: · · · h tot = h 1 + h 2 + 10 5 W m 2 .. Topic: User’s Manual/Verification tests - EN1991-1-2_(c).xls. (Eq. 3‐34). page 37.
(38) - evaluation copy E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN S ECTION 3 E UROCODE 1 EN 1991-1-2 A NNEX C, A NNEX E. 3.2 ANNEX E: fire load densities The fire load density used in calculations should be a design value, either based on measurements or in special cases based on fire resistance requirements given in national regulations. The design value may be determined: —. from a national fire load classification of occupancies; and/or. —. specific for an individual project by performing a fire load survey.. The design value of the fire load q f d is defined as: q f d MJ m 2 = q f k m q1 q2 n. (Eq. 3‐35). where: •. q f k is the characteristic fire load density per unit floor area [MJ/m²] (see f.i. Table E.4). •. m is the combustion factor equal to 0,8. •. q1 is a factor taking into account the fire activation risk due to the size of the compartment (see Table E.1). •. q2 is a factor taking into account the fire activation risk due to the type of occupancy (see Table E.1). Compartment floor area Af [m2]. Danger of Fire Activation q1. Danger of Fire Activation q2. 25. 1,10. 0,78. Art gallery, museum, swimming pool. 250. 1,50. 1,00. Offices, residence, hotel, paper industry. 2500. 1,90. 1,22. Manufactory for machinery & engines. 5000. 2,00. 1,44. Chemical laboratory, painting workshop. 10000. 2,13. 1,66. Manufactory of fireworks or paints. Table 3.2. •. Examples of Occupancies. From table E.1 - Factors q1 , q2 .. n is a factor taking into account the different active fire fighting measures i (sprinkler, detection, automatic alarm transmission, firemen,…). These active measures are generally imposed for life safety reason (see Table E.2 and clauses (4) and (5)): n =. 10. . ni .. i=1. For the normal fire fighting measures, which should almost always be present, such as the safe access routes, fire fighting devices, and smoke exhaust systems in staircases, the ni values of Table E.2 should be taken as 1,0. However, if. page 38. Topic: User’s Manual/Verification tests - EN1991-1-2_(c).xls.
(39) - evaluation copy S ECTION 3. E UROCODES S PREADSHEETS S TRUCTURAL D ESIGN E UROCODE 1 EN 1991-1-2 A NNEX C, A NNEX E. these fire fighting measures have not been foreseen, the corresponding ni value should be taken as 1,5. If staircases are put under overpressure in case of fire alarm, the factor n8 of Table E.2 may be taken as 0,9. CHARACTERISTIC FIRE LOAD. It is defined as:. Q fi k =. M. k j. H ui i =. Q. (Eq. 3‐36). fi k j. where: •. M k j is the amount of combustible material [kg], according to (3) and (4). •. H ui is the net calorific value [MJ/kg], see (E.2.4). •. i is the optional factor for assessing protected fire loads, see (E.2.3).. CHARACTERISTIC FIRE LOAD DENSITY. It is defined as:. Q fi k q f k = ---------Af. (Eq. 3‐37). where A f is the floor area of the fire compartment or reference space. NET CALORIFIC VALUES. Net calorific values should be determined according to EN. ISO 1716:2002. The moisture content of materials may be taken into account as follows: H u = H u0 1 – 0 01u – 0 025u. (Eq. 3‐38). where:. Material. wood. •. u is the moisture content expressed as percentage of dry weight. •. H u0 is the net calorific value of dry materials.. Hu. Material. Hu. Material. Hu. 17,5. Alcohols. 30. Polyvinylchloride, PVC (plastic). 20. cellulosic materials. 20. Fuels. 45. Bitumen, asphalt. 40. carbon. 30. Pure hydrocarbons plastics. 40. Leather. 20. Paraffin series. 50. ABS (plastic). 35. Linoleum. 20. Olefin series. 45. Polyester (plastic). 30. Rubber tyre. 30. Aromatic series. 40. Polyisocyanerat and polyurethane (plastics). 25. Table 3.3. Net calorific values H u [MJ/kg] of combustible materials for calculation of fire loads.. Topic: User’s Manual/Verification tests - EN1991-1-2_(c).xls. page 39.
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