1 Panel specification Romakowski Dämmpaneel Typ D TL 162 according German approval Z-10.4-549
Cross section values per [m] of module width
Outer sheet type T
Nominal thickness t_nom = 0.60 mm
Design thickness t_d = 0.54 mm
Cross sectional area A = 6.62 cm^2/m
Section modulus W = 3.4 cm^3/m
Moment of inertia I = 11.8 cm^4/m
Bending stiffness B = 24.7 kNm^2/m
Inner sheet type L
Nominal thickness t_nom = 0.50 mm
Design thickness t_d = 0.44 mm
Cross sectional area A = 4.40 cm^2/m
Sandwich panel Design values for wrinkling stress
D=16.20 cm a=12.70 cm a1= 5.07 cm a2= 7.63 cm
Outer sheet type T
Section modulus W_outside = 84.04 cm^3/m Serviceability limit state (SLS)
W_inside = 55.86 cm^3/m T <= 20°C T > 20°C
Moment of inertia I = 426.0 cm^4/m Sigma_w, field 320.0 MPa 320.0 MPa
Bending stiffness B = 894.6 kNm^2/m Sigma_w, support 320.0 MPa 320.0 MPa
Shear stiffness S = 431.6 kN/m
Ultimate limit state (ULS)
T <= 20°C T > 20°C
Sigma_w, field 320.0 MPa 320.0 MPa
Sigma_w, support 320.0 MPa 320.0 MPa
Material parameters
Steel cover sheets Inner sheet type L
Modulus of elasticity E = 210000 MPa Serviceability limit state (SLS)
Yield strength fy = 320 MPa T <= 20°C T > 20°C
Sigma_w, field 148.0 MPa 148.0 MPa
Sigma_w, support 134.0 MPa 134.0 MPa
Foam core PUR
Shear modulus Gs = 3.40 MPa Ultimate limit state (ULS)
Shear strength fcv = 0.090 MPa T <= 20°C T > 20°C
Compression strength fcc = 0.100 MPa Sigma_w, field 148.0 MPa 148.0 MPa
Creep coefficients phi-G = 7.0 Sigma_w, support 134.0 MPa 134.0 MPa
phi-Q = 1.8
2 Structural frame and loads
Loads Type 1: Trapezodial distributed load from a to a+b
Type 2: Pointload at a
Type 3: Temperature difference over full girder length
Dead load, snow, wind Load Type q1 Start q2 Length
[kN/m^2] [m] [kN/m^2] [m]
g dead load 1 0.157 0.000 0.157 4.200
1 0.157 4.200 0.157 4.200
1 0.157 8.400 0.157 4.200
s snow load 1 1.000 0.000 1.000 4.200
1 1.000 4.200 1.000 4.200
1 1.000 8.400 1.000 4.200
ws wind suction load 1 -1.750 0.000 -1.750 4.200
1 -1.750 4.200 -1.750 4.200
1 -1.750 8.400 -1.750 4.200
Temperature Ultimate limit state (ULS) dT1
[°C]
tsu,uls temperature, summer 3 55.000
twi,uls temperature, winter - with snow - 3 -20.000
twi,uls temperature, winter 3 -40.000
Temperature Service limit state (SLS) dT1
[°C]
tsu,sls temperature, summer 3 55.000
twi,sls temperature, winter - with snow - 3 -20.000
twi,sls temperature, winter 3 -40.000
3 Initial forces and deflections
3.1 Ultimate limit state (ULS), a serie of simply supported panels
3.1.1 Without creep
3.1.1.1 g, dead load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.018 2.10 0.329 2.10 0.143 2.10
2 0.018 2.10 0.329 2.10 0.143 2.10
3 0.018 2.20 0.329 2.20 0.143 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.046 0.284 0.330
2 0.000 0.000 -0.046 -0.284 0.046 0.284 0.659
3 0.000 0.000 -0.046 -0.284 0.046 0.284 0.659
4 0.000 0.000 -0.046 -0.284 0.000 0.000 0.330
3.1.1.2 s, snow load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.113 2.10 2.093 2.10 0.913 2.10
2 0.113 2.10 2.093 2.10 0.913 2.10
3 0.113 2.20 2.092 2.20 0.913 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.290 1.810 2.100
2 0.000 0.000 -0.290 -1.810 0.290 1.810 4.200
3 0.000 0.000 -0.290 -1.810 0.290 1.810 4.200
4 0.000 0.000 -0.290 -1.810 0.000 0.000 2.100
3.1.1.3 ws, wind suction load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 -0.197 2.10 -3.662 2.10 -1.597 2.10
2 -0.197 2.10 -3.662 2.10 -1.597 2.10
3 -0.197 2.20 -3.662 2.20 -1.597 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 -0.508 -3.167 -3.675
2 0.000 0.000 0.508 3.167 -0.508 -3.167 -7.350
3 0.000 0.000 0.508 3.167 -0.508 -3.167 -7.350
4 0.000 0.000 0.508 3.167 0.000 0.000 -3.675
3.1.1.4 tsu,uls temperature, summer
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 -0.125 2.10 0.125 2.10 -1.087 2.10
2 -0.125 2.10 0.125 2.10 -1.087 2.10
3 -0.125 2.20 0.125 2.20 -1.087 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 -0.434 0.434 0.000
2 0.000 0.000 0.434 -0.434 -0.434 0.434 0.000
3 0.000 0.000 0.434 -0.434 -0.438 0.438 0.000
4 0.000 0.000 0.438 -0.438 0.000 0.000 0.000
3.1.1.5 twi,uls temperature, winter - with snow -
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.045 2.10 -0.045 2.10 0.395 2.10
2 0.045 2.10 -0.045 2.10 0.395 2.10
3 0.045 2.20 -0.045 2.20 0.395 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.158 -0.158 0.000
2 0.000 0.000 -0.158 0.158 0.158 -0.158 0.000
3 0.000 0.000 -0.158 0.158 0.159 -0.159 0.000
4 0.000 0.000 -0.159 0.159 0.000 0.000 0.000
3.1.1.6 twi,uls temperature, winter
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.091 2.10 -0.091 2.10 0.791 2.10
2 0.091 2.10 -0.091 2.10 0.791 2.10
3 0.091 2.20 -0.091 2.20 0.791 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.316 -0.316 0.000
2 0.000 0.000 -0.316 0.316 0.316 -0.316 0.000
3 0.000 0.000 -0.316 0.316 0.318 -0.318 0.000
4 0.000 0.000 -0.318 0.318 0.000 0.000 0.000
3.1.2 With creep
3.1.2.1 g, dead load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.071 2.10 0.275 2.10 0.565 2.10
2 0.071 2.10 0.275 2.10 0.565 2.10
3 0.071 2.20 0.275 2.20 0.565 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.111 0.219 0.330
2 0.000 0.000 -0.111 -0.219 0.111 0.219 0.659
3 0.000 0.000 -0.111 -0.219 0.111 0.219 0.659
4 0.000 0.000 -0.111 -0.219 0.000 0.000 0.330
3.1.2.2 s, snow load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.209 2.10 1.996 2.10 1.701 2.10
2 0.209 2.10 1.996 2.10 1.701 2.10
3 0.209 2.20 1.996 2.20 1.701 2.20
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.443 1.657 2.100
2 0.000 0.000 -0.443 -1.657 0.443 1.657 4.200
3 0.000 0.000 -0.443 -1.657 0.443 1.657 4.200
4 0.000 0.000 -0.443 -1.657 0.000 0.000 2.100
3.2 Serviceability limit state (SLS), multi-span panel
3.2.1 Without creep
3.2.1.1 g, dead load - normal temperature -
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.015 1.70 0.217 1.70 0.105 2.00
2 0.011 2.10 0.083 2.10 0.066 2.10
3 0.015 2.60 0.217 2.60 0.105 2.40
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.044 0.226 0.270
2 -0.080 -0.172 -0.303 -0.087 0.301 0.028 0.720
3 -0.080 -0.172 -0.302 -0.028 0.305 0.085 0.720
4 0.000 0.000 -0.044 -0.226 0.000 0.000 0.270
3.2.1.2 s, snow load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.093 1.70 1.381 1.70 0.670 2.00
2 0.069 2.10 0.527 2.10 0.421 2.10
3 0.093 2.60 1.381 2.60 0.670 2.40
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.280 1.437 1.717
2 -0.512 -1.097 -1.930 -0.553 1.920 0.180 4.583
3 -0.512 -1.097 -1.921 -0.179 1.944 0.539 4.583
4 0.000 0.000 -0.280 -1.437 0.000 0.000 1.717
3.2.1.3 ws, wind suction load - normal temperature -
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 -0.162 1.70 -2.416 1.70 -1.173 2.00
2 -0.121 2.10 -0.921 2.10 -0.736 2.10
3 -0.163 2.60 -2.416 2.60 -1.173 2.40
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 -0.490 -2.514 -3.004
2 0.896 1.920 3.378 0.967 -3.360 -0.315 -8.021
3 0.896 1.920 3.361 0.314 -3.403 -0.943 -8.021
4 0.000 0.000 0.490 2.515 0.000 0.000 -3.004
3.2.1.4 tsu,sls temperature, summer
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 -0.097 0.70 4.767 4.20 -0.515 1.70
2 0.007 2.10 4.900 2.10 0.092 2.10
3 -0.097 3.70 4.767 0.00 -0.515 2.60
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 -0.403 1.571 1.168
2 0.140 4.767 0.494 0.674 -0.463 0.463 -1.168
3 0.140 4.767 0.463 -0.463 -0.498 -0.670 -1.168
4 0.000 0.000 0.406 -1.574 0.000 0.000 1.168
3.2.1.5 twi,sls temperature, winter - with snow -
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.035 0.70 -1.733 4.20 0.187 1.70
2 -0.003 2.10 -1.782 2.10 -0.033 2.10
3 0.035 3.70 -1.733 0.00 0.187 2.60
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.146 -0.571 -0.425
2 -0.051 -1.733 -0.180 -0.245 0.168 -0.168 0.425
3 -0.051 -1.733 -0.168 0.168 0.181 0.244 0.425
4 0.000 0.000 -0.148 0.573 0.000 0.000 -0.425
3.2.1.6 twi,sls temperature, winter
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.070 0.70 -3.467 4.20 0.374 1.70
2 -0.005 2.10 -3.564 2.10 -0.067 2.10
3 0.070 3.70 -3.467 0.00 0.374 2.60
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.293 -1.142 -0.850
2 -0.102 -3.467 -0.359 -0.490 0.337 -0.337 0.850
3 -0.102 -3.467 -0.337 0.337 0.362 0.487 0.850
4 0.000 0.000 -0.295 1.145 0.000 0.000 -0.850
3.2.2 With creep
3.2.2.1 g, dead load - normal temperature -
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.064 1.70 0.181 1.80 0.410 1.90
2 0.051 2.10 0.075 2.10 0.242 2.10
3 0.064 2.60 0.181 2.50 0.410 2.40
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.108 0.169 0.277
2 -0.169 -0.051 -0.340 -0.042 0.338 -0.008 0.712
3 -0.169 -0.051 -0.338 0.008 0.341 0.041 0.712
4 0.000 0.000 -0.108 -0.169 0.000 0.000 0.277
3.2.2.2 s, snow load
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 0.188 1.70 1.338 1.70 1.309 1.90
2 0.162 2.10 0.563 2.10 0.895 2.10
3 0.188 2.60 1.338 2.60 1.309 2.40
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 0.434 1.314 1.748
2 -0.761 -0.719 -2.071 -0.382 2.061 0.039 4.552
3 -0.761 -0.719 -2.061 -0.039 2.079 0.373 4.552
4 0.000 0.000 -0.433 -1.314 0.000 0.000 1.748
3.2.2.3 ws, wind suction load - normal temperature -
Sagging moments / Deflections
Field Mf,face Xmf,face Mf,sand Xmf,verb f Xf
[-] [kNm/m] [m] [kNm/m] [m] [cm] [m]
1 -0.329 1.70 -2.341 1.70 -2.291 1.90
2 -0.283 2.10 -0.985 2.10 -1.567 2.10
3 -0.330 2.60 -2.342 2.60 -2.291 2.40
Hogging moments / Reaction at the support
Support Mst,face Mst,sand Qle,face Qle,sand Qri,face Qri,sand V
[-] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.000 0.000 0.000 0.000 -0.759 -2.299 -3.058
2 1.332 1.259 3.624 0.668 -3.607 -0.068 -7.967
3 1.332 1.259 3.607 0.068 -3.639 -0.653 -7.967
4 0.000 0.000 0.759 2.300 0.000 0.000 -3.058
4 Design of sandwich panel
4.1 Ultimate limit state (ULS), without creep
4.1.1 Limited normal stresses in face layers: Bay
gamma_m,sigma_w(outer shell)= 1.10 gamma_m,sigma_w(inner shell)= 1.12 gamma_m,fy= 1.10
Load combination Bay Sigma,o Sigma_w,o util. Sigma,i Sigma_w,i Util.
[-] [-] [MPa] [MPa] [-] [MPa] [MPa] [-]
1.35*G+1.5*(S+TwiS) 1 -118.3 < 290.9 0.406 62.9 < 290.9 0.216
2 -118.3 < 290.9 0.406 62.9 < 290.9 0.216
3 -118.3 < 290.9 0.407 62.9 < 290.9 0.216
1.35*G+1.5*S 1 -99.1 < 290.9 0.341 64.1 < 290.9 0.220
2 -99.1 < 290.9 0.341 64.1 < 290.9 0.220
3 -99.1 < 290.9 0.341 64.1 < 290.9 0.220
1.0*G+1.5*Twi 1 -47.4 < 290.9 0.163 3.4 < 290.9 0.012
2 -47.4 < 290.9 0.163 3.4 < 290.9 0.012
3 -47.4 < 290.9 0.163 3.4 < 290.9 0.012
1.35*G+1.5*Twi 1 -50.6 < 290.9 0.174 5.5 < 290.9 0.019
2 -50.6 < 290.9 0.174 5.5 < 290.9 0.019
3 -50.6 < 290.9 0.174 5.5 < 290.9 0.019
1.0*G+1.5*Tsu 1 43.6 < 290.9 0.150 9.2 < 290.9 0.032
2 43.6 < 290.9 0.150 9.2 < 290.9 0.032
3 43.6 < 290.9 0.150 9.2 < 290.9 0.032
1.35*G+1.5*Tsu 1 40.4 < 290.9 0.139 11.3 < 290.9 0.039
2 40.4 < 290.9 0.139 11.3 < 290.9 0.039
3 40.4 < 290.9 0.139 11.3 < 290.9 0.039
1.0*G+1.5*(0.6*Ws+Twi) 1 43.8 < 290.9 0.151 -55.6 < 132.1 0.420
2 43.8 < 290.9 0.151 -55.6 < 132.1 0.420
3 43.8 < 290.9 0.151 -55.6 < 132.1 0.420
1.35*G+1.5*(0.6*Ws+Twi) 1 40.6 < 290.9 0.140 -53.5 < 132.1 0.405
2 40.6 < 290.9 0.140 -53.5 < 132.1 0.405
3 40.6 < 290.9 0.140 -53.5 < 132.1 0.405
1.0*G+1.5*(Ws+0.6*Twi) 1 119.9 < 290.9 0.412 -93.9 < 132.1 0.711
2 119.9 < 290.9 0.412 -93.9 < 132.1 0.711
3 119.9 < 290.9 0.412 -93.9 < 132.1 0.711
1.35*G+1.5*(Ws+0.6*Twi) 1 116.7 < 290.9 0.401 -91.9 < 132.1 0.695
2 116.7 < 290.9 0.401 -91.9 < 132.1 0.695
3 116.8 < 290.9 0.401 -91.9 < 132.1 0.695
1.0*G+1.5*(0.6*Ws+Tsu) 1 134.7 < 290.9 0.463 -49.8 < 132.1 0.377
2 134.7 < 290.9 0.463 -49.8 < 132.1 0.377
3 134.8 < 290.9 0.463 -49.8 < 132.1 0.377
1.35*G+1.5*(0.6*Ws+Tsu) 1 131.6 < 290.9 0.452 -47.7 < 132.1 0.361
2 131.6 < 290.9 0.452 -47.7 < 132.1 0.361
3 131.6 < 290.9 0.452 -47.7 < 132.1 0.361
1.0*G+1.5*(Ws+0.6*Tsu) 1 174.5 < 290.9 0.600 -90.4 < 132.1 0.684
2 174.5 < 290.9 0.600 -90.4 < 132.1 0.684
3 174.5 < 290.9 0.600 -90.4 < 132.1 0.684
1.35*G+1.5*(Ws+0.6*Tsu) 1 171.3 < 290.9 0.589 -88.4 < 132.1 0.669
2 171.3 < 290.9 0.589 -88.4 < 132.1 0.669
3 171.3 < 290.9 0.589 -88.4 < 132.1 0.669
4.1.2 Limited shear stress in the core material: gamma_m= 1.30
Load combination Support Tau fcv Util.
[-] [-] [MPa] [MPa] [-]
1.35*G+1.5*(S+TwiS) 1 0.023 < 0.069 0.326
2 0.023 < 0.069 0.326
3 0.023 < 0.069 0.326
4 0.023 < 0.069 0.325
1.35*G+1.5*S 1 0.024 < 0.069 0.352
2 0.024 < 0.069 0.352
3 0.024 < 0.069 0.353
4 0.024 < 0.069 0.353
1.0*G+1.5*Twi 1 0.001 < 0.069 0.022
2 0.001 < 0.069 0.022
3 0.002 < 0.069 0.022
4 0.002 < 0.069 0.022
1.35*G+1.5*Twi 1 0.001 < 0.069 0.010
2 0.001 < 0.069 0.010
3 0.001 < 0.069 0.011
4 0.001 < 0.069 0.011
1.0*G+1.5*Tsu 1 0.007 < 0.069 0.106
2 0.007 < 0.069 0.106
3 0.007 < 0.069 0.107
4 0.007 < 0.069 0.107
1.35*G+1.5*Tsu 1 0.008 < 0.069 0.118
2 0.008 < 0.069 0.118
3 0.008 < 0.069 0.118
4 0.008 < 0.069 0.118
1.0*G+1.5*(0.6*Ws+Twi) 1 0.024 < 0.069 0.346
2 0.024 < 0.069 0.346
3 0.024 < 0.069 0.346
4 0.024 < 0.069 0.346
1.35*G+1.5*(0.6*Ws+Twi) 1 0.023 < 0.069 0.335
2 0.023 < 0.069 0.335
3 0.023 < 0.069 0.335
4 0.023 < 0.069 0.335
1.0*G+1.5*(Ws+0.6*Twi) 1 0.037 < 0.069 0.541
2 0.037 < 0.069 0.541
3 0.037 < 0.069 0.541
4 0.037 < 0.069 0.541
1.35*G+1.5*(Ws+0.6*Twi) 1 0.037 < 0.069 0.529
2 0.037 < 0.069 0.529
3 0.037 < 0.069 0.530
4 0.037 < 0.069 0.530
1.0*G+1.5*(0.6*Ws+Tsu) 1 0.015 < 0.069 0.218
2 0.015 < 0.069 0.218
3 0.015 < 0.069 0.218
4 0.015 < 0.069 0.217
1.35*G+1.5*(0.6*Ws+Tsu) 1 0.014 < 0.069 0.207
2 0.014 < 0.069 0.207
3 0.014 < 0.069 0.207
4 0.014 < 0.069 0.206
1.0*G+1.5*(Ws+0.6*Tsu) 1 0.032 < 0.069 0.464
2 0.032 < 0.069 0.464
3 0.032 < 0.069 0.464
4 0.032 < 0.069 0.463
1.35*G+1.5*(Ws+0.6*Tsu) 1 0.031 < 0.069 0.452
2 0.031 < 0.069 0.452
3 0.031 < 0.069 0.452
4 0.031 < 0.069 0.452
4.1.3 Compression stresses at support, support widths: gamma_m= 1.30
Load combination Support Al Req b Exist b Util.
[-] [kN/m] [mm] [mm] [-]
1.35*G+1.5*S 1 3.595 46.7 ~ 46.7 1.001
2 7.190 93.5 < 93.5 1.000
3 7.190 93.5 < 93.5 1.000
4 3.595 46.7 ~ 46.7 1.001
4.2 Ultimate limit state (ULS), with creep
4.2.1 Limited normal stresses in face layers: Bay
gamma_m,sigma_w(outer shell)= 1.10 gamma_m,sigma_w(inner shell)= 1.12 gamma_m,fy= 1.10
Load combination Bay Sigma,o Sigma_w,o util. Sigma,i Sigma_w,i Util.
[-] [-] [MPa] [MPa] [-] [MPa] [MPa] [-]
1.35*G+1.5*(S+TwiS) 1 -160.4 < 290.9 0.551 60.2 < 290.9 0.207
2 -160.4 < 290.9 0.551 60.2 < 290.9 0.207
3 -160.4 < 290.9 0.551 60.2 < 290.9 0.207
1.35*G+1.5*S 1 -141.2 < 290.9 0.485 61.4 < 290.9 0.211
2 -141.2 < 290.9 0.485 61.4 < 290.9 0.211
3 -141.3 < 290.9 0.486 61.4 < 290.9 0.211
4.2.2 Limited shear stress in the core material: gamma_m= 1.30
Load combination Support Tau fcv Util.
[-] [-] [MPa] [MPa] [-]
1.35*G+1.5*(S+TwiS) 1 0.021 < 0.028 0.752
2 0.021 < 0.028 0.752
3 0.021 < 0.028 0.752
4 0.021 < 0.028 0.752
1.35*G+1.5*S 1 0.023 < 0.028 0.819
2 0.023 < 0.028 0.819
3 0.023 < 0.028 0.819
4 0.023 < 0.028 0.819
4.3 Serviceability limit state (SLS), without creep
4.3.1 Limited normal stresses in face layers: Bay
gamma_m,sigma_w(outer shell)= 1.00 gamma_m,sigma_w(inner shell)= 1.02 gamma_m,fy= 1.00
Load combination Bay Sigma,o Sigma_w,o util. Sigma,i Sigma_w,i Util.
[-] [-] [MPa] [MPa] [-] [MPa] [MPa] [-]
1.0*(G+S+TwiS) 1 -50.5 < 320.0 0.158 16.4 < 320.0 0.051
2 without design
3 -50.5 < 320.0 0.158 16.4 < 320.0 0.051
1.0*(G+S) 1 -50.5 < 320.0 0.158 28.6 < 320.0 0.089
2 -30.7 < 320.0 0.096 10.9 < 320.0 0.034
3 -50.5 < 320.0 0.158 28.6 < 320.0 0.089
1.0*(G+Twi) 1 without design
2 42.1 < 320.0 0.132 -65.9 < 145.1 0.454
3 without design
1.0*(G+Tsu) 1 without design
2 without design
3 without design
1.0*(G+0.6*Ws+Twi) 1 49.6 < 320.0 0.155 -56.2 < 145.1 0.387
2 67.6 < 320.0 0.211 -72.2 < 145.1 0.498
3 49.6 < 320.0 0.155 -56.2 < 145.1 0.387
1.0*(G+Ws+0.6*Twi) 1 72.8 < 320.0 0.228 -57.0 < 145.1 0.393
2 68.6 < 320.0 0.214 -53.3 < 145.1 0.367
3 72.9 < 320.0 0.228 -57.0 < 145.1 0.393
1.0*(G+0.6*Ws+Tsu) 1 without design
2 -52.7 < 320.0 0.165 103.4 < 320.0 0.323
3 without design
1.0*(G+Ws+0.6*Tsu) 1 70.0 < 320.0 0.219 -19.8 < 145.1 0.136
2 without design
3 70.1 < 320.0 0.219 -19.8 < 145.1 0.136
4.3.2 Limited normal stresses in face layers: Support
gamma_m,sigma_w(outer shell)= 1.00 gamma_m,sigma_w(inner shell)= 1.02 gamma_m,fy= 1.00
Load combination Support Sigma,o Sigma_w,o Util. Sigma,i Sigma_w,i Util.
[-] [-] [MPa] [MPa] [-] [MPa] [MPa] [-]
1.0*(G+S+TwiS) 2 224.4 < 320.0 0.701 -53.8 < 131.4 0.409
3 224.4 < 320.0 0.701 -53.8 < 131.4 0.409
1.0*(G+S) 2 188.8 < 320.0 0.590 -22.7 < 131.4 0.173
3 188.9 < 320.0 0.590 -22.7 < 131.4 0.173
1.0*(G+Twi) 2 96.7 < 320.0 0.302 -65.1 < 131.4 0.496
3 96.7 < 320.0 0.302 -65.1 < 131.4 0.496
1.0*(G+0.6*Ws+Twi) 2 -74.6 < 320.0 0.233 -44.5 < 131.4 0.339
3 -74.6 < 320.0 0.233 -44.5 < 131.4 0.339
1.0*(G+Ws+0.6*Twi) 2 -217.3 < 320.0 0.679 -5.9 < 131.4 0.045
3 -217.4 < 320.0 0.679 -5.9 < 131.4 0.045
1.0*(G+0.6*Ws+Tsu) 2 -243.5 < 320.0 0.761 102.9 < 320.0 0.321
3 -243.6 < 320.0 0.761 102.9 < 320.0 0.321
1.0*(G+Ws+0.6*Tsu) 2 -318.6 < 320.0 0.996 82.5 < 320.0 0.258
3 -318.7 < 320.0 0.996 82.5 < 320.0 0.258
1.0*(G+Tsu) 2 -72.2 < 320.0 0.225 82.3 < 320.0 0.257
3 -72.2 < 320.0 0.226 82.3 < 320.0 0.257
4.3.3 Limited shear stress in the core material: gamma_m= 1.08
Load combination Support Tau fcv Util.
[-] [-] [MPa] [MPa] [-]
1.0*(G+S+TwiS) 1 0.009 < 0.083 0.103
2 0.007 < 0.083 0.084
3 0.007 < 0.083 0.082
4 0.009 < 0.083 0.103
1.0*(G+S) 1 0.013 < 0.083 0.157
2 0.005 < 0.083 0.060
3 0.005 < 0.083 0.059
4 0.013 < 0.083 0.157
1.0*(G+Twi) 1 0.007 < 0.083 0.087
2 0.005 < 0.083 0.055
3 0.005 < 0.083 0.054
4 0.007 < 0.083 0.087
1.0*(G+0.6*Ws+Twi) 1 0.019 < 0.083 0.229
2 0.004 < 0.083 0.047
3 0.004 < 0.083 0.047
4 0.019 < 0.083 0.230
1.0*(G+Ws+0.6*Twi) 1 0.023 < 0.083 0.281
2 0.005 < 0.083 0.055
3 0.004 < 0.083 0.054
4 0.023 < 0.083 0.281
1.0*(G+0.6*Ws+Tsu) 1 0.002 < 0.083 0.027
2 0.009 < 0.083 0.110
3 0.009 < 0.083 0.109
4 0.002 < 0.083 0.027
1.0*(G+Ws+0.6*Tsu) 1 0.011 < 0.083 0.127
2 0.010 < 0.083 0.121
3 0.010 < 0.083 0.119
4 0.011 < 0.083 0.127
1.0*(G+Tsu) 1 0.014 < 0.083 0.170
2 0.005 < 0.083 0.056
3 0.005 < 0.083 0.055
4 0.014 < 0.083 0.170
4.3.4 Compression stresses at support, support widths: gamma_m= 1.08
Load combination Support Al Req b Exist b Util.
[-] [kN/m] [mm] [mm] [-]
1.0*(G+S+TwiS) 1 1.562 16.9 < 46.7 0.361
2 5.728 61.9 < 93.5 0.662
3 5.728 61.9 < 93.5 0.662
4 1.562 16.9 < 46.7 0.361
1.0*(G+S) 1 1.986 21.5 < 46.7 0.459
2 5.303 57.3 < 93.5 0.613
3 5.303 57.3 < 93.5 0.613
4 1.986 21.5 < 46.7 0.459
1.0*(G+Twi) 2 1.569 16.9 < 93.5 0.181
3 1.569 16.9 < 93.5 0.181
1.0*(G+Tsu) 1 1.438 15.5 < 46.7 0.333
4 1.438 15.5 < 46.7 0.333
4.3.5 Deflections: gamma-m= 1.0
Load combination Bay f Perm. f, L/200 Util.
[-] [-] [cm] [cm] [-]
1.0*(G+0.75*S+TwiS) 1 0.795 < 2.100 0.379
2 0.348 < 2.100 0.166
3 0.795 < 2.100 0.379
1.0*(G+0.75*(0.6*Ws+Twi)) 1 -0.142 < 2.100 0.068
2 -0.315 < 2.100 0.150
3 -0.142 < 2.100 0.068
1.0*(G+0.75*(Ws+0.6*Twi)) 1 -0.606 < 2.100 0.289
2 -0.516 < 2.100 0.246
3 -0.606 < 2.100 0.289
1.0*(G+0.75*(0.6*Ws+Tsu)) 1 -0.809 < 2.100 0.385
2 -0.196 < 2.100 0.094
3 -0.809 < 2.100 0.385
1.0*(G+0.75*(Ws+0.6*Tsu)) 1 -1.006 < 2.100 0.479
2 -0.445 < 2.100 0.212
3 -1.006 < 2.100 0.479
1.0*(G+S) 1 0.776 < 2.100 0.369
2 0.487 < 2.100 0.232
3 0.776 < 2.100 0.369
1.0*(G+Ws) 1 -1.068 < 2.100 0.509
2 -0.670 < 2.100 0.319
3 -1.068 < 2.100 0.509
1.0*(G+Twi) 1 0.480 < 2.100 0.228
2 -0.001 < 2.100 0.000
3 0.480 < 2.100 0.228
1.0*(G+Tsu) 1 -0.409 < 2.100 0.195
2 0.158 < 2.100 0.075
3 -0.410 < 2.100 0.195
4.4 Serviceability limit state (SLS), with creep
4.4.1 Limited normal stresses in face layers: Bay
gamma_m,sigma_w(outer shell)= 1.00 gamma_m,sigma_w(inner shell)= 1.02 gamma_m,fy= 1.00
Load combination Bay Sigma,o Sigma_w,o util. Sigma,i Sigma_w,i Util.
[-] [-] [MPa] [MPa] [-] [MPa] [MPa] [-]
1.0*(G+S+TwiS) 1 -91.5 < 320.0 0.286 14.8 < 320.0 0.046
2 -31.9 < 320.0 0.100 -45.1 < 145.1 0.311
3 -91.5 < 320.0 0.286 14.8 < 320.0 0.046
1.0*(G+S) 1 -92.0 < 320.0 0.287 27.2 < 320.0 0.085
2 -70.1 < 320.0 0.219 11.4 < 320.0 0.036
3 -92.0 < 320.0 0.287 27.2 < 320.0 0.085
1.0*(G+Twi) 1 without design
2 29.0 < 320.0 0.091 -64.2 < 145.1 0.442
3 without design
1.0*(G+Tsu) 1 without design
2 -76.3 < 320.0 0.239 89.1 < 320.0 0.278
3 without design
4.4.2 Limited normal stresses in face layers: Support
gamma_m,sigma_w(outer shell)= 1.00 gamma_m,sigma_w(inner shell)= 1.02 gamma_m,fy= 1.00
Load combination Support Sigma,o Sigma_w,o Util. Sigma,i Sigma_w,i Util.
[-] [-] [MPa] [MPa] [-] [MPa] [MPa] [-]
1.0*(G+S+TwiS) 2 317.5 < 320.0 0.992 -44.8 < 131.4 0.341
3 317.6 < 320.0 0.992 -44.8 < 131.4 0.341
1.0*(G+S) 2 282.0 < 320.0 0.881 -13.8 < 131.4 0.105
3 282.0 < 320.0 0.881 -13.8 < 131.4 0.105
1.0*(G+Twi) 2 121.4 < 320.0 0.379 -63.0 < 131.4 0.479
3 121.4 < 320.0 0.379 -63.0 < 131.4 0.479
4.4.3 Limited shear stress in the core material: gamma_m= 1.08
Load combination Support Tau fcv Util.
[-] [-] [MPa] [MPa] [-]
1.0*(G+S+TwiS) 1 0.007 < 0.033 0.215
2 0.005 < 0.033 0.158
3 0.005 < 0.033 0.156
4 0.007 < 0.033 0.215
1.0*(G+S) 1 0.012 < 0.033 0.350
2 0.003 < 0.033 0.100
3 0.003 < 0.033 0.098
4 0.012 < 0.033 0.350
1.0*(G+Twi) 1 0.008 < 0.033 0.230
2 0.004 < 0.033 0.126
3 0.004 < 0.033 0.125
4 0.008 < 0.033 0.231
4.4.4 Deflections: gamma-m= 1.0
Load combination Bay f Perm. f, L/100 Util.
[-] [-] [cm] [cm] [-]
1.0*(G+0.75*S+TwiS) 1 1.579 < 4.200 0.376
2 0.880 < 4.200 0.210
3 1.579 < 4.200 0.376
1.0*(G+S) 1 1.719 < 4.200 0.409
2 1.138 < 4.200 0.271
3 1.719 < 4.200 0.409
1.0*(G+Twi) 1 0.784 < 4.200 0.187
2 0.176 < 4.200 0.042
3 0.784 < 4.200 0.187
1.0*(G+Tsu) 1 -0.105 < 4.200 0.025
2 0.334 < 4.200 0.080
3 -0.105 < 4.200 0.025
5.1 Design of connection elements
Loads Type 1: Trapezodial distributed load from a to a+b
Type 2: Pointload at a
Type 3: Temperature difference over full girder length
Dead load, snow, wind Load Type q1 Start q2 Length
[kN/m^2] [m] [kN/m^2] [m]
ws wind suction load 1 -1.750 0.000 -1.750 4.200
1 -1.750 4.200 -1.750 4.200
1 -1.750 8.400 -1.750 4.200
Temperature Service limit state (SLS) dT1
[°C]
tsu,sls temperature, summer 3 55.000
twi,sls temperature, winter - with snow - 3 -20.000
twi,sls temperature, winter 3 -40.000
Tension capacity of the connection elements, gamma_m= 1.33
End support Fz,d= Fz,k/gamma_m= 2.30/1.33= 1.73 kN/connection element
Internal support Fz,d= Fz,k/gamma_m= 2.30/1.33= 1.73 kN/connection element
Reaction at the supports, single load case excluding safety factors
Support V(d,uls) V(ws,uls) V(d,sls) V(ws,sls) V(tsu,sls) V(twi,sls)
[-] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]
1 0.330 -3.675 0.270 -3.004 1.168 -0.850
2 0.659 -7.350 0.720 -8.021 -1.168 0.850
3 0.659 -7.350 0.720 -8.021 -1.168 0.850
4 0.330 -3.675 0.270 -3.004 1.168 -0.850
Reaction at the supports, load combination including safety factors - reqired connection
elements rely on the module width, module width = 1.000 m
Load combination Support Vlfk req. n_con cho. n_con
[-] [kN/m] [-] [-]
1.0*G,t+1.5*Ws,t 1 -5.183 3 3
1.0*G,g+1.50*(Ws,g+0.6*Tso) 2 -12.363 7 6 ***
1.0*G,g+1.50*(Ws,g+0.6*Tso) 3 -12.363 7 6 ***
1.0*G,t+1.5*Ws,t 4 -5.183 3 3
The proof "Introduction of the shear load of the roof into the substructure" is not part
of this design and must be done subsequently!
6 Summary of design
Ultimate limit state (ULS)
sigma_w,mf 71.1 %
sigma_w,mst -
fcv 54.1 %
fcc 100.1 %
sigma_w,mf,cr 55.1 %
sigma_w,mst,cr -
fcv,cr 81.9 %
Serviceability limit state (SLS)
sigma_w,mf 49.8 %
sigma_w,mst 99.6 %
fcv 28.1 %
fcc 66.2 %
f 50.9 %
sigma_w,mf,cr 44.2 %
sigma_w,mst,cr 99.2 %
fcv,cr 35.0 %
f,cr 40.9 %