Project A Pg.
1. ROOF -009
Monopitch roof
1.1. General description, assumptions, materials, loads
1.1.1. Construction type
Timber roof, from beams with timber C24. The roof type as sketch above.
Span 2.500 m, height 0.717 m, roof pitch 16.00°, beam spacing 0.850m
Purlins from timber C24, with dimensions 50x50 mm, in spacing 0.300 m
Elements , cross section 100x150 [mm]
Beam volume =0.039 m³, beam weight =0.134 kN
1.1.2. Design codes
EN1990-1-1:2002, Eurocode 0 Part 1-1, Basis of structural design
EN1991-1-1:2002, Eurocode 1 Part 1-1, Actions on structures
EN1991-1-3:2003, Eurocode 1 Part 1-3, Snow loads
EN1991-1-4:2005, Eurocode 1 Part 1-4, Wind actions
EN1995-1-1:2009, Eurocode 5 Part 1-1, Design of timber structures
1.1.3. Design methodology
All the load combinations according to Eurocode 1 and Eurocode 5 are taken into account,
and the checks are performed in the most unfavourable loading conditions, for combined action,
in ultimate limit state, according to EC5 EN1995-1-1:2009, §6. The connections are designed
as bolted connections with metal plates according to EC5 EN1995-1-1:2009, §8.
The deflections are checked in serviceability limit condition,
according to EC5 EN1995-1-1:2009, §7.
1.1.4. Material properties (beam, purlins) (EC5 EN1995-1-1:2009, §3)
Timber class : C24
Service classes : Class 1, moisture content<=12% (EC5 §2.3.1.3)
Characteristic material properties for timber
fmk = 24.0 MPa, ft0k = 14.0 MPa, ft90k= 0.4 MPa
fc0k= 21.0 MPa, fc90k= 5.3 MPa, fvk = 2.5 MPa
E0m =11000 MPa, E005 = 7400 MPa, E90m = 370 MPa
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Project A Pg. 2
1.1.5. Distributed roof loads
Permanent load of roof covering Ge= 0.650 kN/m² (Tiles from clay)
Purlins, finishing, insulation Gt= 0.500 kN/m² Ge+Gt= 1.150 kN/m²
Load of ceiling under the roof Gc= 0.400 kN/m²
Snow load on the ground Sk= 1.500 kN/m²
Wind pressure on vertical surface Qw= 0.500 kN/m²
Imposed load (category H) Qi= 0.400 kN/m²
1.2. Snow load (EC1 EN1991-1-3:2003, §5)
Characteristic value of snow load on the ground: sk=1.500 kN/m²
Snow load on the roof (EC1 EN1991-1-3:2003, §5)
Exposure coefficient : Ce=1.000 (EC1-1-3 §5.2(7))
Thermal coefficient : Ct=1.000 (EC1-1-3 §5.2(8))
Snow load (EC1 EN1991-1-3:2003, §5.2(5.1), §5.3.2)
1.3. Wind loading (EC1 EN1991-1-4:2005 §5)
Pick velocity pressure Q(z)=Qref·Ce(z), Qref=Vref²/1.6 (EC1 EN1991-1-4:2005 §4.5)
Wind pressure on vertical surface Qref.Ce(z)= 0.500 kN/m²
Wind pressure on roof we=Qref·Ce(z).Cpe (EC1 EN1991-1-4:2005, §5.2)
External pressure coefficients (EC1 EN1991-1-4:2005 Table 7.4)
Wind pressure we=0.107 kN/m²
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Project A Pg. 3
1.4. Design of purlins
Structural system for purlins
The purlins are designed as simply supported beams with span length L=0.850m the distance
between the beams. They are loaded with a surface load of width L1=0.300m (purlin spacing).
Dimensions of purlins
Timber of purlins: C24, Class 1, moisture content<=12%, cross section of purlins BxH:50x50mm
Uniform loading of purlins kN/m²
Roof covering Ge= 0.650 kN/m²
Finishing+self weight G1= 0.500 kN/m²
Snow load Qs= 1.200 kN/m²
Wind load Qw= 0.107 kN/m²
Concentrated load Qp= 1.000 kN
Line loading of purlins (kN/m) in z-z and y-y
Roof covering+self weight Gk = 0.345 kN/m, Gkz = 0.332 kN/m, Gkez= 0.095 kN/m
Snow load Qks= 0.360 kN/m, Qksz= 0.346 kN/m, Qksz= 0.099 kN/m
Wind load Qkw= 0.032 kN/m, Qkwz= 0.032 kN/m, Qkwy= 0.000 kN/m
Concentrated load Qkp= 1.000 kN, Qkpz= 0.961 kN, Qkpz= 0.276 kN
Internal forces of purlins (span L=0.850 m, BxH: 50x50 mm)
(Gk) Permanent Gk =0.345[kN/m] Permanent 1.35 0.00 1.00 0.141 0.040 0.030 0.009
(Qk1) Snow Qks=0.360[kN/m] Short-term 0.00 1.50 0.70 0.147 0.042 0.031 0.009
(Qk2) Wind Qkw=0.032[kN/m] Short-term 0.00 1.50 0.60 0.014 0.000 0.003 0.000
(Qk3) Concentr. Qkp=1.000[kN] Instantaneous 0.00 1.00 0.00 0.481 0.138 0.204 0.059
1.4.1. Serviceability limit state (EC5 EN1995-1-1:2009, §2.2.3, §7)
Control of deflection (EC5 §7.2)
(Gk) Permanent Gk =0.332[kN/m] 0.163 Permanent 1.00 1.00 1.00 0.60
(Qk1) Snow Qks=0.346[kN/m] 0.170 Short-term 0.70 0.50 0.20 0.60
(Qk2) Wind Qkw=0.032[kN/m] 0.016 Short-term 0.60 0.20 0.00 0.60
Load combination w.inst w.fin [mm]
Maximum deflection values
w.inst = 0.343 mm, w.fin = 0.462 mm
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Project A Pg. 4
Check according to EC5 EN1995-1-1:2009 §7.2, Tab.7.2
Final deflections
w.inst = 0.343 mm < L/300=850/300= 2.833 mm
w.net,fin = 0.462 mm < L/250=850/250= 3.400 mm
w.fin = 0.462 mm < L/150=850/150= 5.667 mm
The check is satisfied
1.4.2. Check of purlins, Ultimate limit state of design (EC5 EN1995-1-1:2009, §6)
L.C. Load combination duration class kmod Qz/Kmod Qy/Kmod My/Kmod Mz/Kmod
Maximum values 0.610 0.175 0.222 0.064
Purlin, load combination No 4
Shear, Fv=0.671 kN (EC5 §6.1.7)
Rectangular cross section, bef=0.67x50=34 mm, h=50 mm, A= 1 700 mm²
The check is satisfied
Purlin, load combination No 4
Shear, Fv=0.192 kN (EC5 §6.1.7)
Rectangular cross section, bef=0.67x50=34 mm, h=50 mm, A= 1 700 mm²
The check is satisfied
Purlin, load combination No 4
Bending, Myd=0.245 kNm, Mzd=0.070 kNm (EC5 §6.1.6)
Rectangular cross section, b=50mm, h=50mm, A=2.500E+003mm², Wy=2.083E+004mm³, Wz=2.083E+004mm³
Rectangular cross section Km=0.70 (EC5 §6.1.6.(2))
The check is satisfied
Purlin, load combination No 4
Lateral torsional stability of beams, Myd=0.245 kNm, Mzd=0.070 kNm (EC5 §6.3.3)
Rectangular cross section, b=50mm, h=50mm, A=2.500E+003mm², Wy=2.083E+004mm³, Wz=2.083E+004mm³
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Project A Pg. 5
Rectangular cross section Km=0.70 (EC5 §6.1.6.(2))
Buckling length Sk
Sky= 1.00x0.850=0.850 m= 850 mm
Skz= 1.00x0.850=0.850 m= 850 mm
Slenderness
Ö
Ö
Critical stresses
Ö
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The check is satisfied
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Project A Pg. 6
1.5. Beam design
Beam geometric characteristics
Length L=2.500 m, height H=0.717 m, beam spacing d=0.850 m
Number of nodes = 3, number of elements =2, supports 2
Nodal coordinates Beam element properties
Node x[m] y[m] Sup. Element K1 K2 bxh[mm] L[m] A[mm²] Iy[mm4] Wy[mm³]
1 0.000 0.000 11 1 1 3 100x150 1.301 1.500E+004 2.813E+007 3.750E+005
2 2.500 0.717 01 2 3 2 100x150 1.300 1.500E+004 2.813E+007 3.750E+005
3 1.250 0.359
Line loads per beam
Timber density =350.00 kg/m³, beam self weight =0.134 kN
beam spacing d=0.85 m, weight of beam connections =0.013 kN
Permanent line loads (kN/m) on beam
Roof covering+self weight Gk1= 1.036 kN/m
Ceiling under roof Gk2= 0.340 kN/m
Variable line loads of short term action (kN/m) on beam
Imposed Qki= 0.40x0.850= 0.340 kN/m
Snow load Qk1= 1.020 kN/m
Wind load Qk2= 0.091 kN/m
Design load combinations
L.C. Actions Permanent-Variable Duration classes
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Project A Pg. 7
1.6. Beam static analysis
The roof structure is a continuous beam.
The internal forces are computed for separate loadings conditions
(permanent-live-snow-wind) and then from their combinations the
internal forces for the unfavourable load combinations are computed.
Number of nodes = 3, number of elements =2, supports 2
1.6.1. Internal forces for applied loads
Internal forces, Loading: ( Gk) Dead Gk1 = 1.036, Gk2 = 0.340 [kN/m]
elem. node-1 node-2 N1[kN] V1[kN] M1[kNm] N2[kN] V2[kN] M2[kNm] Nm[kN] Vm[kN] Mm[kNm]
1 1 3 -0.49 1.72 0.00 0.00 0.00 1.12 0.00 0.00 1.12
2 3 2 0.00 0.00 1.12 0.49 -1.72 0.00 0.00 0.00 1.12
(m point of maximum span moment for permanent load, or element middle point)
Internal forces, Loading: (Qk1) Snow Qks = 1.020 [kN/m]
elem. node-1 node-2 N1[kN] V1[kN] M1[kNm] N2[kN] V2[kN] M2[kNm] Nm[kN] Vm[kN] Mm[kNm]
1 1 3 -0.35 1.23 0.00 0.00 0.00 0.80 0.00 0.00 0.80
2 3 2 0.00 0.00 0.80 0.35 -1.23 0.00 0.00 0.00 0.80
(m point of maximum span moment for permanent load, or element middle point)
Internal forces, Loading: (Qk2) Wind Qkw = 0.091 [kN/m]
elem. node-1 node-2 N1[kN] V1[kN] M1[kNm] N2[kN] V2[kN] M2[kNm] Nm[kN] Vm[kN] Mm[kNm]
1 1 3 0.03 0.12 0.00 0.03 0.00 0.08 0.03 0.00 0.08
2 3 2 0.03 0.00 0.08 0.03 -0.12 0.00 0.03 0.00 0.08
(m point of maximum span moment for permanent load, or element middle point)
Internal forces, Loading: (Qki) Imposed (H) Qi = 0.340 [kN/m]
elem. node-1 node-2 N1[kN] V1[kN] M1[kNm] N2[kN] V2[kN] M2[kNm] Nm[kN] Vm[kN] Mm[kNm]
1 1 3 -0.12 0.42 0.00 0.00 0.00 0.28 0.00 0.00 0.28
2 3 2 0.00 0.00 0.28 0.12 -0.43 0.00 0.00 0.00 0.28
(m point of maximum span moment for permanent load, or element middle point)
1.6.2. Vertical nodal displacements (in mm)
node Gk Qk1 Qk2 Qki
1 0.00 0.00 0.00 0.00
2 0.00 0.00 0.00 0.00
3 -2.45 -1.74 -0.17 -0.61
1.6.3. Support reactions (kN)
node react. Gk Qk1 Qk2 Qki
1 Fx 0.00 0.00 -0.07 0.00
1 Fy 1.79 1.28 0.10 0.44
2 Fx 0.00 0.00 0.00 0.00
2 Fy 1.79 1.27 0.12 0.44
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Project A Pg. 8
1.7. Serviceability limit state
1.7.1. Serviceability limit state (EC5 EN1995-1-1:2009, §2.2.3, §7)
Control of deflection at node 3 (EC5 §7.2)
( Gk) Dead Gk1 = 1.036, Gk2 = 0.340 -2.548 Permanent 1.00 1.00 1.00 0.60
(Qk1) Snow Qks = 1.020 -1.815 Short-term 0.70 0.50 0.20 0.00
(Qk2) Wind Qkw = 0.091 -0.175 Short-term 0.60 0.20 0.00 0.00
Load combination w.inst w.fin [mm]
Maximum deflection values at node 3
w.inst = 4.468 mm, w.fin = 6.215 mm
Check according to EC5 EN1995-1-1:2009 §7.2, Tab.7.2
Final deflections at node 3
w.inst = 4.468 mm < L/300=2601/300= 8.669 mm
w.net,fin = 6.215 mm < L/250=2601/250= 10.403 mm
w.fin = 6.215 mm < L/150=2601/150= 17.339 mm
The check is satisfied
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Project A Pg. 9
1.8. Characteristic structural natural frequencies (self weight + permanent loads)
After a dynamic analysis the basic natural frequencies of the structure are computed.
For the computation of natural frequencies, we consider mass corresponding
No. Frequency[Hz] Period[sec]
1 13.70014 0.07299
2 47.46535 0.02107
3 90.64781 0.01103
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Project A Pg. 10
1.8.1. Ultimate limit state (EC5 EN1995-1-1:2009, §6)
Rafter, elements: 1, 2
( Gk) Dead Gk1 = 1.036, Gk2 = 0.340 Permanent 1.35 0.00 1.00
(Qk1) Snow Qks = 1.020 Short-term 0.00 1.50 0.70
(Qk2) Wind Qkw = 0.091 Short-term 0.00 1.50 0.60
(Qki) Imposed (H) Qi = 0.340 Short-term 0.00 1.50 0.00
L.C. Load combination duration class kmod -N/Kmod +N/Kmod V/Kmod M/Kmod
Maximum values -1.328 1.385 4.837 3.145
1.8.2. Check of cross section Rafter, elements: 1, 2
Rafter, elements: 1, 2 , load combination No 7
Tension parallel to the grain, Ft0d=1.247 kN (EC5 §6.1.2)
Rectangular cross section, b=100 mm, h=150 mm, A= 15 000 mm²
The check is satisfied
Rafter, elements: 1, 2 , load combination No 2
Compression parallel to the grain, Fc0d=-1.195 kN (EC5 §6.1.4)
Rectangular cross section, b=100 mm, h=150 mm, A= 15 000 mm²
The check is satisfied
Rafter, elements: 1, 2 , load combination No 7
Shear, Fv=4.353 kN (EC5 §6.1.7)
Rectangular cross section, bef=0.67x100=67 mm, h=150 mm, A= 10 050 mm²
The check is satisfied
Rafter, elements: 1, 2 , load combination No 7
Bending, Myd=2.830 kNm, Mzd=0.000 kNm (EC5 §6.1.6)
Rectangular cross section, b=100mm, h=150mm, A=1.500E+004mm², Wy=3.750E+005mm³, Wz=2.500E+005mm³
Rectangular cross section Km=0.70 (EC5 §6.1.6.(2))
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Project A Pg. 11
The check is satisfied
Negligible compressive stress, combined bending-compression check is omitted (EC5 §6.2.4)
Rafter, elements: 1, 2 , load combination No 2
Column stability with bending, Fc0d=-1.195kN, Myd=2.706kNm, Mzd=0.000kNm (EC5 §6.3.2)
Rectangular cross section, b=100mm, h=150mm, A=1.500E+004mm², Wy=3.750E+005mm³, Wz=2.500E+005mm³
Rectangular cross section Km=0.70 (EC5 §6.1.6.(2))
Buckling length Sk
Sky= 1.00x2.601=2.601 m= 2601 mm (most unfavourable)
Skz= 0.12x2.601=0.300 m= 300 mm (effective length/total length=0.30/2.60=0.12)
Slenderness
Ö
Ö
Critical stresses
Ö
Ö
Ö
Ö
The check is satisfied
Rafter, elements: 1, 2 , load combination No 7
Lateral torsional stability of beams, Myd=2.830 kNm, Mzd=0.000 kNm (EC5 §6.3.3)
Rectangular cross section, b=100mm, h=150mm, A=1.500E+004mm², Wy=3.750E+005mm³, Wz=2.500E+005mm³
Rectangular cross section Km=0.70 (EC5 §6.1.6.(2))
Buckling length Sk
Sky= 1.00x2.601=2.601 m= 2601 mm (most unfavourable)
Skz= 0.12x2.601=0.300 m= 300 mm (effective length/total length=0.30/2.60=0.12)
Slenderness
Ö
Ö
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Project A Pg. 12
Critical stresses
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The check is satisfied
Negligible tensile stress, combined bending-tension check is omitted (EC5 §6.2.3)
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