Design of wall panel according to EN 160 Example 3: Wall panel with wind load 1.1 Issue Design of a wall panel at an industrial building Materials with a compressive strength 3,5, density class 500, welded steel reinforcement with tensile yield strength 500 MPa and ultimate tensile strength 550 MPa. EN 160, table 1 and EN 10080 1. Material properties Dry Density Table 1: Density classes, dry densities in kg/m³ Density 400 450 500 550 600 650 700 class Mean dry density ρ m > 350 400 > 400 450 > 450 500 > 500 550 > 550 600 > 600 650 > 650 700 Compressive strength Table : Compressive strength classes for in MPa Strength class,5 3 3,5 4 4,5 5 f ck,0,5 3,0 3,5 4,0 4,5 5,0 EN 160, 4...3 EN 160, 4..4 1.3 Type of element
System and dimensions.1 System Longitudinal section 00 5883 Minimum value for support length component beams floor elements roof elements minimum requirement 60 mm 40 mm 35 mm EN 160, A.11 Recommended values component support material minimum requirement beams masonry 100 mm floor elements roof elements wall elements masonry steel concrete masonry steel concrete wood steel concrete 70 mm 70 mm
L eff l w + 3 1 a1,min + 3 1 a,min 5,85 + 3 0,05 5,883 m The component has to be designed for all load cases also for impacts resulting from transport. The relevant load case for that is the transport with a fork lifter and for the weak axis. Figure 1: Transport situation fork lift truck Assumption for distance forks: b s 1,00 m ( L bs ) (6,00 1,00) L eff,cantilever,50 m. Cross section h 00 mm b 65 mm.3 Concrete cover and effective depth c 1 5 mm c 5 mm Assumption for fire resistance class: REI 60 With a granted diameter of 6 mm the effective depth is: d 00 mm 5 6 17 mm 3
3 Loads Self-weight of element: with 35 kg / m³ steel and 6 M-% % moisture content of, g 5,7 KN/m³ EN 160, 4...4 (1) wind load, w e 0,5 kn/m² (assumption) EN 1991-1-4 Transport weight of element: g t 7,05 kn/m³ EN 160, 4...4 (3) 4 Internal forces Internal forces are determined 65 mm. for a single component with a width of 4.1 Internal forces for characteristic combinations Q d1 Q b q k 1,50 0,655 0,50 0,47 kn/m Load combinations acc. to EN 1990 Qd 1 l V Sd1 eff 0,47 5,883 1,38 kn Qd 1 leff M Sd1 0,47 5,883,03 knm 8 8 4. Internal forces for frequent combinations G d 0 kn/m Q d ψ 1 b q k 0, 0,65 0,50 0,06 kn/m V Sd Q M Sd Q d leff d eff l 8 0,06 5,883 0,18 kn 0,06 5,883 8 0,6 knm ψ 1 0, (see EN 1990, Table A.1.1) 4.3 Internal forces for quasi-permanent combinations G d3 0 kn/m Q d3 ψ b q k 0 0,65,00 0 kn/m ψ 0 (see EN 1990, Table A.1.1) 4
V Sd3 0 kn M Sd3 0 knm 4.4 Internal forces for transport situations G T G b g T 1,35 0,65 7,05 0,0 1,19 kn/m V T T G T L 1,3 1,19,50 3,87 kn cantilever γt GT L 1,3 1,19,50 M T 4,83 knm where T 1,3 (assumption for dynamic coefficient due to manipulationn of components, when indicatedd consideration of national regulations) 5
5 Design 5.1 Material properties Characteristic compressive strength, f ck 3,5 MPa 3500 kn/m² Basic Shear Strength, 0,5 0,063 f τ Rd ck 0,063 3,5 0,5 / 1,73 0,0681 MPa γ c Mean Modulus of Elasticity of slab, E cm 5 (ρ m 150) 1750 N/mm² Characteristic strength of steel, f yk 500 MPa 500 N/mm² EN 160, 4..4 EN160, A.4.1. (A.6) EN 160, 4..7 EN 160, 4.3.1 5. Design for bending Finding equilibrium of stress / strain: 1000 MT γ c 1000 m d α f A d ck c 4,83 1,44 16,4 0,85 3,5 0,65 0,17 0,17 Reading from design table (see Annex A): ε c,74 ε s 10,00 k x 0,16 1000 ϖ 136,8 A s α f γ Ac ϖ ck S γ f c yk 0,65 0,17 136,8 0,85 3,5 1,15 0,699 cm² 1000 1,44 500 chosen: layers with 4 Ø 6,0 mm each (A sl 1,13 cm²) 5.3 Minimum reinforcement f cflm 0,7 3,5 0,945 MPa h A ct b 6,5 10,0 65 cm² EN 160 A.3.4 (A.3) A s,min k A ct f cflm / f yk 0,4 65 0,945 / 500 0,47 cm² A s,min 0,47 cm² < 1,13 cm² 6
5.4 Design for shear force Determination of reinforcement ratio: A ρ l s, exis 1,13 0,0011 < 0,005 ( b d) 6,5 17, Minimum design value of shear force ctk;0,05 V Rd1 0,5 f b w d 0,5 0,10 3500 / 1,73 0,65 0,17 γ c 10,87 kn EN 160, A.4 EN 160, (A.6) Design value of shear force: V Rd1 τ Rd (1 0,83 d) (1 + 40 ρ l ) b w d 68,1 (1 0,83 0,17) (1 + 40 0,0011) 0,65 0,17 7,93 kn Higher value is determinant (critical) : V Rd1 13,05 kn V Rd1 10,87 kn > 3,87 V T Therefore, no shear reinforcement is required. 5.5 Spacing of Longitudinal Bars Centre distance between bars : 50 Ø s l1 700 EN 160, 5..7.. Therefore, we consider the longitudinal bars at a distance of 15 mm centre to centre as per the limits. And the distance of longitudinal bars from the panel surface is supposed to be 15 mm. 7
6 Anchoring of longitudinal reinforcement EN 160, A.10.3 Cross-Sectional View Description reinforcement layout: diameter cross bars: Ø t 5,0 mm distance between longitudinal bars: s t 15 mm distance to bottom side of panel: e c + Ø sl + Ø t / 5 + 6,0 + 5,0 / 33,5 mm Effective length of transverse anchorage bars t t 3 s t / 15 mm > 14 Ø t 70 mm > t t 3 70 mm t 1 t 4 15 mm < 8 Ø t 40 mm > t 1 t 4 15 mm t 1 t 4 s t / 6,5 mm > 8 Ø t 40 mm > t 1 t 4 40 mm t 1 t 4 40 + 15 mm 55 mm > 8 Ø t 40 mm > t 1 t 4 40 mm t t t 1 + t + t 3 + t 4 180 mm Maximum tensile force: F ld,max M T,max / z 4,83 / (0,9 0,17) 31,0 kn F ld,support M T,support / z 0,96 / (0,9 0,17) 6,58 kn 8
Assume 8 transverse cross bars with diameter 5,0 mm for half of the panel and the arrangement is shown below: Figure 1: Reinforcement layout Design value for bearing strength at support (m 1,3; n p 1, transverse compression at support): 1,35 m (e / Øt) α fck f ld,support 1/3 f, ck γ γ c 1,35 1,3 (33,5 / 5,0) 1,44 1/3 0,85 3,5 c, 3,5 1,44 Bond Class B1 6,84 MPa > 5,35 MPa therefore, f ld,support 5,35 MPa Design value for bearing strength at middle of span (m 1,04; n p 1, transverse compression at support): 1,35 m (e / Øt) α fck f ld,field 1/3 f, ck γ γ c 1,35 1,04 (33,5 / 5,0) 1,73 4,55 MPa > 4,45 MPa therefore, f ld,field 4,45 MPa 1/3 0,85 3,5 c, 3,5 1,73 where, α is a reduction coefficient for long term effect on compressive strength of (α 0,85) 9 EN 160, A.3.
Anchorage force capacity (F RA ) per cross bar: F RA,support 0,83 n t Ø t t t f ld,support 0,6 n l F wg / γ s 0,83 1 5,0 180 5,35 0,6 4 0,5 A sl f yk / γ s 4,00 kn < 7,38 kn Welding Strength Class S1 0,60 nl nt F F RA,max min 0,83 φtot tt fld ( nt ); γ S 43,93 kn < 59,01 kn wg As, F RA,support F ld,support and F RA,max F ld,max Figure : Anchorage of tensile forces As we can see from fig. that the anchorage capacity force does exceed the design tensile force at each section of the panel. Therefore, the assumption is satisfied for the required conditions. So, we can use 16 cross bars with Ø 5,0 mm (for whole panel). 10
7 Serviceability Limit States EN 160, A.9.4 Cracking moment, M cr (b h / 6) f cflm (0,65 0,0 / 6) (0,7 0,8 3,5) 3,15 knm EN 160, A.9.4.3 and 4..5 where, f cflm is the flexural strength of ( 0,7 0,8 f ck ) As, M Sd < M cr, therefore, the slab is considered to be uncracked condition. 7.1 Short-term deflection Ratio of the modulus of elasticity of reinforcing steel and : Es 00000 N / mm n 114,3 E 1750 N / mm cm EN 160, (A.4) Moment of area of and reinforcement: 3 b h l c, brutto + n (4 π (ø 1 /) 4 / 4 + 4 π (ø /) 4 / 4) 4167,48 cm 4 1 Both layers of the longitudinal reinforcement can be fully taken into account to determine the moment of inertia. Parts of moment of inertia from consideration of the reinforcement: A s1 A s 1,13 cm As the reinforcement layout is symmetrical the centre of gravity is y s 10,00 cm h I ST b h ( ys ) + n ( As1 ( ys1 ys ) + As ( ys ys ) ) 150 (10,0 10,0) + 114,3 (1,13 (,8 10,0) + 1,13 (17, 10,0) ) 4 13391,1 cm E I E I + I ) 1750 (4167,5 + 13391,) 10 cm ci cm 0,964MNm ( C; BRUTTO st Deflection due to load combination (frequent action combinations): 5 MSd Leff 5 0,0006 5,883 yel 0, 0010m 48 Ecm Ici 48 0,964 Leff y el 0,0010 m 0,10 cm <,35 cm 50 11 8
General note: The limit value for the maximum deflection may be found in a national application document. 7. Long-term deflection No long term effects! 1
Annex A 1000 M 1000 m d Sd1 γ c α fck Ac d α f γ A s Ac ϖ ck S γ c fyk M sd1 d A c A s f ck f yk γ c,ductile γ S bending moment under characteristic combination of loading (respecting transport load situations) effective depth of component cross section of, A c b d cross sectional area of reinforcement characteristic compressive strength of characteristic yield strength of reinforcing steel partial safety factor of for ductile failure partial safety factor for reinforcing steel stainless steel, f yk 35 MPa steel, f yk 500 MPa 13