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  • 1. BASIS OF STRUCTURAL DESIGN (EN1990:2002) Ultimate limit state verification (EN1990,cl.6.4.1(1)P) The following ultimate limit states shall be verified as relevant: EQU: Loss of equilibrium of the structure, (considering for sliding, overturning or uplift) STR: Internal failure or excessive deformation of the structure of structural member (Design of structural for strength of members and frames), GEO: Failure due to excessive deformation of the ground (Design of structural members such as footing, piles, basement walls, etc.), FAT: Fatigue failure of the structure or structural member. Design working life (CYS NA EN1990,Table 2.1) Design working life category Indicative design working life (years) Examples 1 10 Temporary structures (1) 2 10 – 25 Replaceable structural parts, e.g. gantry girders, bearings 3 15 – 30 Agricultural and similar structures 4 50 Building structures and other common structures 5 100 Monumental building structures, bridges, and other civil engineering structures (1) Structures or parts of structures that can be dismantled with a view to being re-used should not be considered as temporary. In the case of replaceable structural parts the design life for the structural determination of loads should be the design life of the structure. Design Working life Ultimate Limit State (ULS) Ultimate Limit State Concern (EN1990,cl.3.3(1)P)  Safety of people,  Safety of the structure  Protection of the contents Design situations (EN1990,cl.3.2(2)P) Persistent design situation: Normal use condition Transient design situation: Temporary condition, e.g. during execution or repair Accidental design situation: Exceptional condition, e.g. fire, explosion, impact. Seismic design situation: Structure subject to seismic events.
  • 2. Ultimate Limit State (ULS) COMBINATION OF ACTIONS FOR PERSISTENT/TRANSIENT DESIGN SITUATION (EN1990,cl.6.4.3.2) Persistent and transient design situation – EQU Equation 6.10 (Set A) 6.10 Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2 Action Favourable γ Unfavourable γ Permanent (dead, earth), γG 0.9 1.1 Variable (imposed, wind), γQ 0 1.5 Note: Single source is not applicable for EQU design situation. Different γ factors can be used in favourable and unfavourable areas. Persistent and transient design situation – STR/GEO Equation 6.10, 6.10a & 6.10b (Set B) 6.10 6.10a 6.10b Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2 Ed=ΣξγG Gk +γQ ψ0,1 Qk1 + γQ ψ0,2 Qk2 Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2 Action Favourable γ Unfavourable γ Permanent (dead, earth), γG 1.0 1.35 Variable (imposed, wind), γQ 0 1.5 Note: Single source is applicable for STR/GEO design situation. Persistent and transient design situation – GEO Equation 6.10 (Set C) 6.10 Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2 Action Favourable γ Unfavourable γ Permanent (dead, earth), γG 1.0 1.0 Variable (imposed, wind), γQ 0 1.3 Note: Single source is applicable for STR/GEO design situation. Important notes (EN1990,cl.3.2(2)P)  Approach 2 (CYS NA EN1990,Table.A1.2(B)) should be used for the design of the structural members of substructure (i.e. footings, piles, basement walls, etc.) (CYS NA EN1990,cl. 2.2.3.4).  Actions that cannot exist simultaneously due to physical of functional reasons should not be considered together in combination.  The use of expression 6.10a and 6.10b lead to a more economic design in most circumstances. 
  • 3. Summary table of partial, combination and reduction factors for the STR and GEO ultimate limit states for buildings Expression Unfavourable Permanent action Unfavourable Variable actions Self-weight Imposed floor loads Wind loads Snow loads 6.10 γG=1.35 γQ,1 =1.5 γQ,iψ0,i =1.5x05=0.75 γQ,iψ0,i =1.5x05=0.75 γG=1.35 γQ,iψ0,i =1.5x07=1.05 γQ,1 =1.5 γQ,iψ0,i =1.5x05=0.75 γG=1.35 γQ,iψ0,i =1.5x07=1.05 γQ,iψ0,i =1.5x05=0.75 γQ,i =1.5 Less favourable equations 6.10a & 6.10b 6.10a γG=1.35 γQ,iψ0,i =1.5x07=1.05 γQ,iψ0,i =1.5x05=0.75 γQ,iψ0,i =1.5x05=0.75 γG=1.35 γQ,iψ0,i =1.5x07=1.05 γQ,iψ0,i =1.5x05=0.75 γQ,iψ0,i =1.5x05=0.75 γG=1.35 γQ,iψ0,i =1.5x07=1.05 γQ,iψ0,i =1.5x05=0.75 γQ,iψ0,i =1.5x05=0.75 6.10b ξγG=0.85*1.35 γQ,1 =1.5 γQ,iψ0,i =1.5x05=0.75 γQ,iψ0,i =1.5x05=0.75 ξγG=0.85*1.35 γQ,iψ0,i =1.5x07=1.05 γQ,1 =1.5 γQ,iψ0,i =1.5x05=0.75 ξγG=0.85*1.35 γQ,iψ0,i =1.5x07=1.05 γQ,iψ0,i =1.5x05=0.75 γQ,i =1.5 Note: Shaded boxes indicate the ‘leading variable action’, Combination (sensitivity) factor, ψ (CYS NA EN1990:2002, Table A1.1) Category Specific Use ψο ψ1 ψ2 A Domestic and residential 0.7 0.5 0.3 B Office 0.7 0.5 0.3 C Areas for Congregation 0.7 0.7 0.6 D Shopping 0.7 0.7 0.6 E Storage 1.0 0.9 0.8 F Traffic < 30 kN vehicle 0.7 0.7 0.6 G Traffic < 160 kN vehicle 0.7 0.5 0.3 H Roofs 0.7 0 0 Snow, altitude < 1000 m 0.5 0.2 0 Wind 0.5 0.2 0
  • 4. Serviceability Limit State (SLS) COMBINATION OF ACTIONS FOR SERVICEABILITY LIMIT STATE (EN1990,cl.6.5.3) Characteristic combination Equation 6.14b Ed=Gk +Qk,1 + ψ0 Qk,2 Frequent combination Equation 6.15b Ed=Gk + ψ1Qk,1 + ψ2 Qk,2 Quasi-permanent combination Equation 6.16b Ed=Gk + ψ2Qk,1 Characteristic value of variable actions For each variable action there are four representative values: 1.The characteristic value Qk (determine by insufficient data). 2.The combination value ψ0Qk (of an action is intended to take account of the reduced probability of the simultaneous of two or more variable actions). 3. Frequent value ψ1Qk (exceeded only for a short period of time and is used primary for the SLS and also the accidental ULS). 4. Quasi-permanent value ψ2Qk (exceeded for a considerable period of time or considered as an average loading over time and used for the long-term affects at the SLS and also accidental and seismic ULS). INDICATIVE LIMITING VALUES FOR VERTICAL DEFLECTIONS (Manual of EC0 &EC1, Table D.1) Serviceability Limit States Vertical deflections Serviceability Requirement Characteristic Combination (Expression 6.14b in EC0) wmax Function and damage to non- structural elements (e.g. partition walls claddings etc) –Brittle -Non-brittle Function and damage to structural elements ≤L/500 to L/360 ≤L/300 to L/200 ≤L/300 to L/200 Serviceability Limit State (SLS) – Vertical and Horizontal deformations
  • 5. INDICATIVE LIMITING VALUES FOR HORIZONTAL DEFLECTIONS (Manual of EC0 &EC1, Table D.2) Serviceability Limit States Vertical deflections Serviceability Requirement Characteristic Combination (Expression 6.14b in EC0) wmax Function and damage to non- structural elements –Single storey buildings top of column -Each storey in a multi-storey building -The structure as a whole for a multi-storey building u≤H/300 u≤H/500 to H/300 u≤H/500
  • 6. Category of use (EN1991-1-1:2002,Table 6.1) Category Specific Use Example A Area for domestic and residential activities Rooms in residential buildings and houses bedrooms and wards in hospitals, bedrooms in hotels and hostels kitchens and toilets B Office areas C Areas where people may congregate (with the exception of areas defined under category A, B, and D1)) C1: Areas with tables, etc. e.g. areas in schools, cafés, restaurants, dining halls, reading rooms, receptions. C2: Areas with fixed seats, e.g. areas in churches, theatres or cinemas, conference rooms, lecture halls, assembly halls, waiting rooms, railway waiting rooms. C3: Areas without obstacles for moving people, e.g. areas in museums, exhibition rooms, etc. and access areas in public and administration buildings, hotels, hospitals, railway station forecourts. C4: Areas with possible physical activities, e.g. dance halls, gymnastic rooms, stages. C5: Areas susceptible to large crowds, e.g. in buildings for public events like concert halls, sports halls including stands, terraces and access areas and railway platforms. D Shopping areas D1: Areas in general retail shops D2:Areas in departments stores Imposed loads (EN 1991-1-1:2002, Table 6.2) Category Of loaded areas qk (kN/m2 ) Qk (kN) Category A -Floors -Stairs -Balconies Category B Category C -C1 -C2 -C3 -C4 -C5 Category D -D1 -D2 1.5-2.0 2.0-4.0 2.5-4.0 2.0-3.0 2.0-3.0 3.0-4.0 3.0-5.0 4.5-5.0 5.0-7.5 4.0-5.0 4.0-5.0 2.0-3.0 2.0-4.0 2.0-3.0 1.5-4.5 3.0-4.0 2.5-7.0 4.0-7.0 3.5-7.0 3.5-4.5 3.5-7.0 3.5-7.0Imposed load on Roof (CYS NA EN1991-1-1, Table 6.10) Sub-category Actions Imposed load, qk (kN/m2 ) Q (kN) H Roof (inaccessible except for normal maintenance and repair) 0.4 1.0 STRUCTURAL LOADS (EN1991:2002) Imposed Loads
  • 7. Permanent load (EN 1991-1-1:2002, Table A.1-A.12) Materials Density, γ (kN/m3 ) Modulus of Elasticity, E kN/mm2 Reinforced Concrete Steel Glass Water Plastic PTFE Softwood timber Hardwood timber Concrete blockwork Asphalt Roof tiles Soil (Sand) Soil (Clay) Insulation board Aluminium Copper Cement mortar Νylon Epoxy resin Polystyrene Carbon fibre Fibre glass Granite 25 78 25 10 21-22 5 7 18 22 20 16-18 20-22 3 27 87-89 19-23 11.5 16-20 10-13 20 15 26 17-31 210 74 - 0.3-0.6 10 12 - - 5-30 - - - 69 96 20-31 2-3.5 20 3-3.3 415 10 40-70 Permanent Loads Typical unit floor Typical loadings Typical unit floor Typical loadings Steel floor kN/m2 Self weight of beam 0.25 Self weight of decking 0.10 Self weight of meshing 0.05 Ceiling and services 0.15 Total 0.55 Internal ConcreteFloor kN/m2 Partition (minimum) 1.00 Screed (5-70cm) 1.20-1.80 Raised floor 0.40 Concrete floor (15cm) 3.75 Celling and services 0.15 Total 6.50-7.10 External Concrete Floor kN/m2 Slabs / paving 0.95 Screed (50cm) 1.20 Asphalt waterproofing 0.45 Concrete floor (15cm) 3.75 Celling and services 0.15 Total 6.50 Metal deck roofing kN/m2 Live loading: snow/ wind uplift 0.6-1.0 Outer covering, insulation and metal deck liner 0.30 Purlins-150 deep at 1.5m c/c 0.10 Services 0.10 Total 1.1-1.5 Timber Floor kN/m2 Partition 1.00 Timber boards/plywood 0.15 Timber joist 0.20 Celling and services 0.15 Total 1.50 Timber Flat Roof kN/m2 Asphalt waterproofing 0.45 Timber joist and insulation 0.20 Celling and services 0.15 Total 0.80
  • 8. SNOW LOAD (EN1991-1-3) Snow load on roof for transient design situations s=μiCeCtsk (EN 1991-1-3Equ.5.1) Snow load shape coefficients, μ (EN1991-1-3, Table 5.2) Angle of pitch of roof, a 0ο ≤α≤30ο 30ο ≤α≤60ο α≥60ο μ1 0.8 0.8(60-α)/30 0 μ2 0.8+0.8 α/30 1.6 - For monopitch roof use only μ1 For pitched roof use μ1andμ2 THERMAL COEFFICIENTS C (ΕΝ1991-1-3¨2003, cl. 5.2(8)) Ct=1.0 Thermal transmission on the roof <1W/m2 K Exposure coefficient(ΕΝ1991-1-3, Table 5.1) Topography Ce Windswept 0.8 Normal 1.0 Sheltered 1.2 CHARACTERISTIC SNOW LOAD ON GROUND,sk (kN/m2 ) (CYS NA ΕΝ1991-1-3, cl. NA 2.7) sk = 0.289*(1+(A/452)2 ) A:is the attitude above sea level (m) Snow load shape coefficients for cylinder roofs, μ (EN1991-1-3, Eq. 5.4-5.5) μ1 0.8 μs=0 a≤15o μ2 μs+μw μw=(b1+b2)/2h ≤ γh/sk Range must:0.8≤μw≤4 γ:is the weight density of snow may taken as 2kN/m3 Angle of pitch of roof, a β>60ο β≤60 μ3 should be less than μ3≤2 0 0.2+10 h/b Monopitch roof Pitch roof Cylinder roof
  • 9. WIND LOAD (EN1991-1-4) Fundamental Basic wind velocity, vb,0 (CYS NA EN1991-1-4,Fig.1) Directional factor (CYSEN1991-1-4,NA 2.4) cdir=1.0 (Conservative value for all direction) Season factor (CYS EN1991-1-4,NA 2.4) cseason=1.0 Basic wind velocity (EN1991-1-4, Eq. 4.1) vb=cdir.cseasonvb,0 BASIC WIND VELOCITY
  • 10. STRUCTURAL FACTOR (EN1991-1-4, cl.6.0) cscd =1.0 Builiding with less than h≤15m Natural frequency f≤5Hz Walls≤100m high Chimney with circular cross-sectional area and, h≤60m h≤6.5·diameter h Determination of cscd Determine of structural factor cscd Size factor (EN1991-1-4,Eq.6.2) It is on the safe side to use B2 =1 kp=3 Calculation of R2 can be found in Annex B of EN1991-1-4:2005 Can be found Dynamic factor (EN1991-1-4,Eq.6.3) It is on the safe side to use B2 =1 kp=3 Calculation of R2 can be found in Annex B of EN1991-1-4:2005 Consider Ignore Upwind Slope≤3o NOYES TERRAIN OROGRAPHY, (EN1991-1-4, cl.4.3.3) Detail calculation of terrain orography factor can be found in Annex A of EN1991-1-4:2005
  • 11. PEAK VELOCITY PRESSURE Roughness factor, cr(z) (EN1991-1-4,Eq.4.3-4.5) cr(z)=kr . ln(z/z0) for zmin≤z≤zmax cr(z)=cr . (zmin) for z≤zmin z0: is the roughness length Maximum height, zmax (EN1991-1-4, cl. 4.3.2) zmax=200m Orography factor co(z) co(z)=1 Terrain factor, (EN1991-1-4,cl.4.4) kr=0.19(z0/z0,II)0.07 Mean wind velocity, vm(z) (EN1991-1-4 cl.4.3.1 ) vm(z)=cr(z).co(z).vb Wind turbulence, Iv(z) (EN1991-1-4,Eq.4.7) Iv(z)=σv/vm(z)=kl/co(z)ln(z/z0) for zmin≤z≤zmax Iv(z)=Iv(zmin) for z≤zmin Turbulence factor: kl=1.0 (NA CYS EN1991-1-4, cl. NA 2.10) Note: for co(z)=1 Iv(z) is not important Peak velocity pressure, qpeak(z) (EN1991-1-4 Eq.4.8 ) qpeak(z)=[1+7 Iv(z)]0.5ρ vm 2 (z)=ce(z)·0.5·ρ·vb 2 Air density:ρ=1.25kg/m3 Terrain category and terrain parameters (EN1991-1-4, Tab.:4.1) Terrain category Description z0 (m) zmin(m) 0 Sea, costal area exposed to the open sea. SEA 0.003 1 I Lakes or area with negligible vegetation and without obstacles. COUNTRY 0.01 1 II Area with low vegetation such as grass and isolated obstacles trees, buildings) with separations of at least 20 obstacle height. 0.05 2 III Area with regular cover of vegetation or buildings or woth isolatd obstacles with seperations of maximum 20 obstacle height (such as villages, suburban terrain, permanent forest). TOWN 0.3 5 IV* Area in which at least 15% of the surface is covered with building and their average height exceeds 15m. 1.0 10 * For buildings in terrain category IV, displacement height hdis should be consider and information can be found in Aneex A.5 of EN1991-1-4:2005
  • 12. Values of external pressure coefficient for vertical walls of rectangular plan buildings (EN1991-1-4, Tab.:4.1) ZONE A B C D E h/d cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 5 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.7 1 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.5 ≤0.25 -1.2 -1.4 -0.8 -1.1 -0.5 +0.7 +1.0 -0.3 Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2 or less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for loadaded area of 1m2 and 10m2 respectively. Reference height ze, depending on h and b, and corresponding velocity pressure profile (EN1991-1-4, Fig. 7.4) Key for vertical walls – Flat Roof (EN1991-1-4, Fig.7.5) Key for vertical walls –Mono&dual pitch Roof (EN1991-1-4, Fig.7.5) Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref EXTERNAL WIND PRESSURE/FORCE ON WALLS
  • 13. EXTERNAL WIND PRESSURE/FORCE ON FLAT ROOF Recommended values of external pressure coefficients for flat roofs (EN1991-1-4,Tab. 7.2) Roof type Zone F G H I cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 Sharp eaves -1.8 -2.5 -1.2 -2.0 -.07 -1.2 +0.2 With Parapets hp/h=0.025 -1.6 -2.2 -1.1 -1.8 -0.7 -1.2 -0.2 hp/h=0.05 -1.4 -2.0 -0.9 -1.6 -0.7 -1.2 +0.2 hp/h=0.10 -1.2 -1.8 -0.8 -1.4 -0.7 -1.2 -0.2 Curved Eaves r/h=0.05 -1.0 -1.5 -1.2 -1.8 -0.4 +0.2 r/h=0.10 -0.7 -1.2 -0.8 -1.4 -0.3 -0.2 r/h=0.20 -0.5 -0.8 -0.5 -0.8 -0.3 +0.2 Mansard Eaves a=30o -1.0 -1.5 -1.0 -1.5 -0.3 -0.2 a=45o -1.2 -1.8 -1.3 -1.9 -0.4 +0.2 a=60o -1.3 -1.9 -1.3 -1.9 -0.5 -0.2 Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2 or less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for loadaded area of 1m2 and 10m2 respectively. Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref
  • 14. Recommended values of external pressure coefficients for monopitch roofs (EN1991-1-4,Tab. 7.3a) Pitch Angle a Zone for wind direction θ=0o Zone for wind direction θ=180o F G H F G H cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 5o -1.7 -2.5 -1.2 -2.0 -0.6 -1.2 -2.3 -2.5 -1.3 -2.0 -0.8 -1.2 +0.0 +0.0 +0.0 15o -0.9 -2.0 -0.8 -1.5 -0.3 -2.5 -2.8 -1.3 -2.0 -0/9 -1.2 +0.2 +0.2 +0.2 30o -0.5 -1.5 -0.5 -1.5 -0.2 -1.1 -2.3 -0.8 -1.5 -0.8 +0.7 +0.7 +0.4 45o -0.0 -0.0 -0.0 -0.6 -1.3 -0.5 -0.7 +0.7 +0.7 +0.6 60o +0.7 +0.7 +0.7 -0.5 -1.0 -0.5 -0.5 75o +0.8 +0.8 +0.8 -0.5 -1.0 -0.5 -0.5 Recommended values of external pressure coefficients for monopitch roofs (EN1991-1-4,Tab. 7.3b) Pitch Angle a Zone for wind direction θ=90o Fup Flow G H I cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,1 5o -2.1 -2.6 -2.1 -2.4 -1.8 -2.0 -0.6 -1.2 -0.5 15o -2.4 -2.9 -1.6 -2.4 -1.9 -2.5 -0.8 -1.2 -0.7 -1.2 30o -2.1 -2.9 -1.3 -2.0 -1.5 -2.0 -1.0 -1.3 -0.8 -1.2 45o -1.5 -2.4 -1.3 -2.0 -1.4 -2.0 -1.0 -1.3 -0.9 -1.2 60o -1.2 -2.0 -1.2 -2.0 -1.2 -2.0 -1.0 -1.3 -0.7 -1.2 75o -1.2 -2.0 -1.2 -2.0 -1.2 -2.0 -1.0 -1.3 -0.5 Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2 or less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for loadaded area of 1m2 and 10m2 respectively. EXTERNAL WIND PRESSURE/FORCE ON MONOPITCH ROOF Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref
  • 15. Recommended values of external pressure coefficients for duopitch roofs (EN1991-1-4,Tab. 7.4a) Pitch Angle a Zone for wind direction θ=0o F G H I J cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,1 -45o -0.6 -0.6 -0.8 -0.7 -1.0 -1.5 -30o -1.1 -2.0 -0.8 -1.5 -0.8 -0.6 -0.8 -1.4 -15 o -2.5 -2.8 -1.3 -2.0 -0.8 -1.2 -0.5 -0.7 -1.2 -5 o -2.3 -2.5 -1.2 -2.0 -0.8 -1.2 +0.2 +0.2 -0.6 -0.6 5 o -1.7 -2.5 -1.2 -2.0 -0.6 -1.2 -0.6 +0.2 +0.0 +0.0 +0.0 -0.6 15 o -0.9 -2.0 -0.8 -1.5 -0.3 -0.4 -1.0 -1.5 +0.2 +0.2 +0.2 +0.0 +0.0 +0.0 30 o -0.5 -1.5 -0.5 -1.5 -0.2 -0.4 -0.5 +0.7 +0.7 +0.4 +0.0 +0.0 45 o -0.0 -0.0 -0.0 -0.2 -0.3 +0.7 +0.7 +0.6 +0.0 +0.0 60 o +0.7 +0.7 +0.7 -0.2 -0.3 75 o +0.8 +0.8 +0.8 -0.2 -0.3 Recommended values of external pressure coefficients for duopitch roofs (EN1991-1-4,Tab. 7.4b) Pitch Angle a Zone for wind direction θ=90o F G H I cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 cpe,10 cpe,10 cpe,1 -45o -1.4 -2.0 -1.2 -2.0 -1.0 -1.3 -0.9 -1.2 -30o -1.5 -2.1 -1.2 -2.0 -1.0 -1.3 -0.9 -1.2 -15o -1.9 -2.5 -1.2 -2.0 -0.8 -1.2 -0.8 -1.2 -5o -1.8 -2.5 -1.2 -2.0 -0.7 -1.2 -0.6 -1.2 5o -1.6 -2.2 -1.2 -2.0 -0.7 -1.2 -0.6 15o -1.3 -2.0 -1.2 -2.0 -0.6 -1.2 -0.5 30o -1.1 -1.5 -1.4 -2.0 -0.8 -1.2 -0.5 45o -1.1 -1.5 -1.4 -2.0 -0.9 -1.2 -0.5 60o -1.1 -1.5 -1.4 -2.0 -0.8 -1.2 -0.5 75o -1.1 -1.5 -1.4 -2.0 -0.8 -1.2 -0.5 EXTERNAL WIND PRESSURE/FORCE ON DUOPITCH ROOF Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref