Eurocode 4: Design of composite steel and concrete structures– EN : Part 1–2: General rules – Structural fire design Annex F [informative]: Calculation of moment resistances of partially encased steel beams connected to concrete slabs

Content Design Procedures Annex A Stress-strain relationships for structural steel Basis of Design Basic requirements Actions Material design values Verification methods Simple Models General aspects Thermal response Mechanical response Validation Tabulated data Partially encased beams Composite columns Material Properties Mechanical & thermal properties Structural steel Concrete Reinforcing steel General Advanced Models Constructional Details Composite beams Composite columns Connections Annex B Stress-strain relationships for siliceous concrete Annex C Stress-strain relationships for concrete adapted to natural fires Unprotected / protected composite slabs Composite beams Composite columns Annex E Moment resistance of unprotected beams Annex D Fire resistance of unprotected slabs Annex F Moment resistance of partially encased beams Annex G Simple models for partially encased columns Annex H Simple models for concrete filled columns Annex I Planning & evaluation of experimental models

F.1(1) Flat slab system h hchc ewew bcbc b efef b eff + - x Compressive stress in concrete Tensile stress in steel h c,h h c,fi f c / γ M,fi,c f ay / γ M,fi,a f ay,x / γ M,fi,a k r f ry / γ M,fi,s k a f ay / γ M,fi,a The section of concrete slab is reduced as follows: regardless fire classes Standard fire resistanceR30R60R90R120R180 Slab reduction h c,fi (mm) Table F.1

F.1(2-3) Other slab systems applies Joint between precast elements which is unable to transmit compression stress trapezoidal profiles transverse to beam Table F.1 re-entrant profiles transverse to beam h c,fi h c,fi,min h c,fi ≥ h c,fi,min prefabricated concrete planks h c,fi h c,fi,min h c,fi ≥ h c,fi,min h c,fi trapezoidal profiles parallel to beam h eff Annex D For calculation refer to

F.1(4) Active width of upper flange (b - 2b fi ) ewew bcbc b efef f ay / γ M,fi,a (b – 2b fi ) varies with fire classes. Yield strength of steel is taken equal to f ay / γ M,fi,a. Standard fire resistance Width reduction b fi of upper flange R30(e f / 2) + (b – b c ) / 2 R60(e f / 2) + (b – b c ) / R90(e f / 2) + (b – b c ) / R120(e f / 2) + (b – b c ) / R180(e f / 2) + (b – b c ) / Table F.2 b fi

F.1(5) Web division ewew bcbc b Web is divided into two parts: h x Top part Bottom part hlhl h h l are given for different fire classes: For h/b c ≤ 1 or h/b c ≥ 2 For 1< h/b c < 2 h l is given directly in Table F.3 Parameters a 1 & a 2 are given in Table F.3  Next

Table F.3 Bottom part of web: h l Standard fire resistance h/b c ≤ 1h/b c ≥ 2 a 1 [mm 2 ] a 2 [mm 2 ] h l,min [mm] a 1 [mm 2 ] a 2 [mm 2 ] h l,min [mm] R R R R R = h – 2e f h l,min ≤ h l ≤ h l,max ewew bcbc b h x hlhl h efef

Table F.3 Bottom part of web: h l Standard fire resistance 1< h/b c < 2 h l,min [mm] R3020 R6030 R9040 R12045 R18055 = h – 2e f h l,min ≤ h l ≤ h l,max

F.1(7-8) Section yield strength ewew bcbc h x hlhl h The reduced yield strength depends on distance x: Bottom web Top web f ay / γ M,fi,a Standard fire resistance Reduction factor k a k a,min k a,max R30[1.12 – 84 / b c + h / 22b c ] a R60[0.21 – 26 / b c + h / 24b c ] a R90[0.12 – 17 / b c + h / 38b c ] a R120[0.1 – 15 / b c + h / 40b c ] a R180[0.03 – 3 / b c + h / 50b c ] a a 0 = e f efef k a f ay / γ M,fi,a Bottom flange

F.1(9) Yield strength of rebars ewew bcbc h Standard fire resistance a3a3 a4a4 a5a5 k r,min k r,max R R R R R u 1,3 Yield strength decreases with temperature. Reduction factor k r depends on fire class & position of rebar: h b c 2h + b c 12 u2u2 3 usus

F.1(11) Shear resistance of web May be verified using the distribution of the design yield strength according to (7) Resistance of reinforced concrete may be considered If V fi,d ≥ 0.5V fi,pl,Rd

Fire classes Position of rebars F.2 Yield strength of rebars Reduction factor k s depends on: h bcbc b efef 3 b + Stress in concrete Stress in steel h fi uhuh ulul hchc Standard fire resistance Reduction factor k s k s,min k s,max R R u R u – 0.1 R u – 0.2 R u – 0.26 u = u i Bottom bars Top bars u = h c - u h Table F.6

F.2(2) Upper flange f ay / γ M,fi,a Active width of upper flange: (b – 2b fi ) varies with fire classes. Yield strength of steel is taken equal to f ay / γ M,fi,a. Standard fire resistance Width reduction b fi of upper flange R30(e f / 2) + (b – b c ) / 2 R60(e f / 2) + (b – b c ) / R90(e f / 2) + (b – b c ) / R120(e f / 2) + (b – b c ) / R180(e f / 2) + (b – b c ) / F.1(4) applies as follows: h bcbc b efef h fi

F.2(3) Reduced concrete section f c / γ M,fi,c Section is reduced as shown. Compressive strength: Standard fire resistance h fi [mm] b c,fi [mm] R30≥ 25 R60165 – 0.4b c – 8(h / b c ) ≥ 2560 – 0.15b c ≥ 30 R90220 – 0.5b c – 8(h / b c ) ≥ 4570 – 0.1b c ≥ 35 R – 0.6b c – 10(h / b c ) ≥ 5575 – 0.1b c ≥ 45 R – 0.7b c – 10(h / b c ) ≥ 6585 – 0.1b c ≥ 55 h bcbc b h fi 3 b b c,fi not varying with fire classes Table F.7

F.2(4-5) Yield strength of rebars Standard fire resistance a3a3 a4a4 a5a5 k r,min k r,max R R R R R Reduction factor k r depends on fire class & position of rebar: h b c 2h + b c F.1(9) applies as follows: h bcbc b 3 b u 1,3 1 u2u2 3 usus 2 ewew

F.2(6-7) Shear resistance Assumptions: Shear force is transmitted by steel web, which is neglected when calculating the hogging bending moment resistance. Resistance of reinforced concrete may be considered If V fi,d ≥ 0.5V fi,pl,Rd