1 Section properties of the trapezoidal sheet in compliance with

baustatische Typenprüfung Bescheid Nr. T18-056

Hacierco 135/310

broad flange in compression

Nominal thickness = 0.88 mm Design thickness = 0.84 mm

Dead load g = 0.106 kN/m^2 Yield strength fy,k = 350 N/mm^2

Effective Properties of section

Properties of section for bending: Ief+ = 317.2 cm^4/m Ief- = 314.2 cm^4/m

Properties of section for axial force: Ag = 13.26 cm^2/m ig = 4.91 cm zg = 8.23 cm

Aef = 5.50 cm^2/m ief = 5.78 cm zef = 8.04 cm

Characteristic capacity of the trapezoidal sheet for UDL downwards

Width of the end support bA = 40 mm Width of the internal support bB = 60 mm eps = 2

Mc,Rk,F = 13.83 kNm/m Rw,Rk,A = 11.56 kN/m Vw,Rk = 45.75 kN/m

M0,Rk,B = 15.10 kNm/m R0,Rk,B = 30.43 kN/m Mc,Rk,B = 10.95 kNm/m Rw,Rk,B = 25.99 kN/m

minL = 5.07 m maxL = 5.80 m maxMR,Rk = 2.66 kNm/m

Width of the end support bA = 40 mm Width of the internal support bB = 160 mm eps = 2

Mc,Rk,F = 13.83 kNm/m Rw,Rk,A = 11.56 kN/m Vw,Rk = 45.75 kN/m

M0,Rk,B = 14.81 kNm/m R0,Rk,B = 43.41 kN/m Mc,Rk,B = 12.65 kNm/m Rw,Rk,B = 36.00 kN/m

minL = 5.88 m maxL = 6.39 m maxMR,Rk = 2.78 kNm/m

Characteristic capacity of the trapezoidal sheet for UDL upwards

Connection to every flange eps = 1

Mc,Rk,F = 11.59 kNm/m Rw,Rk,A = 45.75 kN/m Vw,Rk = 45.75 kN/m

M0,Rk,B = 17.29 kNm/m R0,Rk,B = 0.00 kN/m Mc,Rk,B = 13.83 kNm/m Rw,Rk,B = 0.00 kN/m

Connection to every second flange eps = 1

Mc,Rk,F = 11.59 kNm/m Rw,Rk,A = 22.88 kN/m Vw,Rk = 22.88 kN/m

M0,Rk,B = 8.64 kNm/m R0,Rk,B = 0.00 kN/m Mc,Rk,B = 6.92 kNm/m Rw,Rk,B = 0.00 kN/m

Symbols (elements of capacity)

Mc,Rk,F Sagging moment capacity maxMR,Rk residual moment capacity

Rw,Rk,A External support capacity Vw,Rk Shear force

M0,Rk,B Hogging moment capacity under the assumption of no shear force

R0,Rk,B Internal support capacity under the assumption of no moment

Mc,Rk,B Hogging moment capacity Rw,Rk,B Internal support capacity

eps 1: linear interaction for M and R 2: quadratic interaction for M and R

2 Structural system and loads

Loads Type 1: Trapezodial distributed load from a to a+b

Type 2: Pointload at a

Load Type q1 Start q2 Length

[kN/m^2] [m] [kN/m^2] [m]

g Dead load 1 0.350 0.000 0.350 1.000

1 0.350 1.000 0.350 5.000

1 0.350 6.000 0.350 4.000

1 0.350 10.000 0.350 4.000

1 0.350 14.000 0.350 5.000

s Snow load 1 0.750 0.000 0.750 1.000

1 0.750 1.000 0.750 5.000

1 0.750 6.000 0.750 4.000

1 0.750 10.000 0.750 4.000

1 0.750 14.000 0.750 5.000

ws Wind suction load 1 -0.480 0.000 -0.480 1.000

1 -0.600 0.000 -0.600 1.000

1 -0.480 1.000 -0.480 5.000

1 -0.480 6.000 -0.480 4.000

1 -0.480 10.000 -0.480 4.000

1 -0.480 14.000 -0.480 5.000

3 Design of trapezoidal sheets in compliance with German Standard "DIN EN 1993-1-3 (EC3)"

3.1 Ultimate limit state (ULS) elastic-elastic

3.1.1 Sagging moment gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Bay MEd Mc,Rd,F Utilization

[-] [-] [kNm/m] [kNm/m] [-]

1.35*G+1.50*S 1 2.855 < 12.573 0.227

2 0.815 < 12.573 0.065

3 0.726 < 12.573 0.058

4 3.231 < 12.573 0.257

1.00*G+1.50*Ws 1 -0.479 < 10.536 0.045

2 -0.224 < 10.536 0.021

3 -0.150 < 10.536 0.014

4 -0.751 < 10.536 0.071

3.1.2 Reaction at end support gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Support FEd Rw,Rd,A Utilization

[-] [kN/m] [kN/m] [-]

1.35*G+1.50*S 5 3.213 < 10.509 0.306

1.00*G+1.50*Ws 5 -0.746 < 20.795 0.036

3.1.3 Shear force at internal support gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Support VEd Vw,Rd bv Utiliz.

[-] [kN/m] [kN/m] [-] [-]

1.35*G+1.50*S 1 3.417 < 41.591 0.363 0.082

1.35*G+1.50*S 2 -4.571 < 41.591 0.093 0.110

1.35*G+1.50*S 3 -2.599 < 41.591 0.011 0.062

1.35*G+1.50*S 4 4.775 < 41.591 0.108 0.115

1.00*G+1.50*Ws 1 1.270 < 20.795 0.166 0.061

1.00*G+1.50*Ws 2 0.942 < 20.795 0.060 0.045

1.00*G+1.50*Ws 3 0.644 < 20.795 0.035 0.031

1.00*G+1.50*Ws 4 -1.104 < 20.795 0.113 0.053

bv > 0.20, it will be calculated with reduced support widths (DIN EN 1993-1-3, 6.1.7.3).

3.1.4 Reaction at internal support gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Support FEd Rw,Rd,B Utilization

[-] [kN/m] [kN/m] [-]

1.35*G+1.50*S 1 5.014 < 13.770 0.364

1.35*G+1.50*S 2 8.362 < 32.727 0.256

1.35*G+1.50*S 3 5.142 < 32.727 0.157

1.35*G+1.50*S 4 8.622 < 32.727 0.263

1.00*G+1.50*Ws Design not necessary!

3.1.5 Hogging moment gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Support MEd Mc,Rd,B Utilization

[-] [kNm/m] [kNm/m] [-]

1.35*G+1.50*S 1 -0.799 < 5.801 0.138

2 -3.683 < 11.500 0.320

3 -1.298 < 11.500 0.113

4 -3.905 < 11.500 0.340

1.00*G+1.50*Ws 1 0.635 < 6.286 0.101

2 0.720 < 6.286 0.115

3 0.336 < 6.286 0.053

4 0.897 < 6.286 0.143

3.1.6 Combined check for bending and reaction gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Support MEd/M0,Rd,B + (FEd/R0,Rd,B)^eps Utiliz.

[-] [-] [-] [-]

1.35*G+1.50*S 1 0.100 + 0.097 0.197

2 0.274 + 0.045 0.318

3 0.096 + 0.017 0.113

4 0.290 + 0.048 0.338

1.00*G+1.50*Ws Design not necessary!

3.1.7 Combined check for bending and shear gamma-F,G= 1.35 gamma-F,Q= 1.50 gamma-M= 1.10

Load combination Support MEd/Mc,Rd,B + (2*VEd/V,Rd,B-1)^2

[-] [-] [-] [-]

1.35*G+1.50*S Design not necessary!

1.00*G+1.50*Ws Design not necessary!

3.2 Serviceability limit state (SLS) elastic - elastic

3.2.1 Deflection gamma-F,G= 1.00 gamma-F,Q= 1.00 gamma-M= 1.00

Load combination Bay f Perm. f, L/300 Utilization

[-] [-] [cm] [cm] [-]

1.00*G+1.00*S 1 0.627 < 1.667 0.376

2 0.046 < 1.333 0.035

3 -0.053 < 1.333 0.040

4 0.724 < 1.667 0.434

Cant-le -0.385 < 0.667

1.00*G+1.00*Ws 1 -0.026 < 1.667 0.016

2 -0.014 < 1.333 0.011

3 0.008 < 1.333 0.006

4 -0.090 < 1.667 0.054

Cant-le -0.029 < 0.667

3.3 Maximum span during construction

Bay Span Maximum span Utilization

[-] [m] [m] [-]

1 5.000 < 12.500 0.400

2 4.000 < 12.500 0.320

3 4.000 < 12.500 0.320

4 5.000 < 12.500 0.400

The design of the trapezoidal sheet is ok. The load capacities of trapezoidal profiles can

have large differences from manufacturer to manufacturer. Therefore, it is important that

the trapezoidal profile listed herein is actually installed on-site during construction.

4 Design of connection elements

4.1 Connection to the construction below

Loads Type 1: Trapezodial distributed load from a to a+b

Type 2: Pointload at a

Load Type q1 Start q2 Length

[kN/m^2] [m] [kN/m^2] [m]

Ws, wind suction load 1 -0.480 0.000 -0.480 1.000

1 -0.600 0.000 -0.600 1.000

1 -0.480 1.000 -0.480 5.000

1 -0.480 6.000 -0.480 4.000

1 -0.480 10.000 -0.480 4.000

1 -0.480 14.000 -0.480 5.000

Characteristic forces of connection elements:

End support Fz,k= 3.600 kN VR,k= 3.600 kN

Internal support Fz,k= 3.600 kN VR,k= 3.600 kN

Shear and tension capacity of the connection elements, gamma= 1.33:

End support Fz,d= 2.707 kN Fq,d= 2.707 kN

Internal support Fz,d= 2.707 kN Fq,d= 2.707 kN

Reaction at the support, load case excluding safety factors:

Support Rv,k(g) Rv,k(s) Rv,k(wd) Rv,k(ws) Rv,k(opt.) Descript. Rh,k(opt.) Descript.

[-] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m] [-] [kN/m] [-]

1 1.099 2.354 0.000 -2.184 0.000 0.000

2 1.832 3.926 0.000 -2.407 0.000 0.000

3 1.127 2.414 0.000 -1.580 0.000 0.000

4 1.889 4.048 0.000 -2.582 0.000 0.000

5 0.704 1.508 0.000 -0.966 0.000 0.000

Reaction at support for load combinations:

Load combination Support Vertical Horizontal

[-] [kN/m] [kN/m]

0.9*G+1.5*Ws 1 -2.288 0.000

0.9*G+1.5*Ws 2 -1.961 0.000

0.9*G+1.5*Ws 3 -1.356 0.000

0.9*G+1.5*Ws 4 -2.173 0.000

0.9*G+1.5*Ws 5 -0.816 0.000

Design check for connecting elements

Support nVerb nbR NE,d NR,d VE,d VR,d Utilization

[-] [-] [-] [kN] [kN] [kN] [kN] [-]

1 1 1 0.709 < 2.707 0.000 < 2.707 0.262

2 1 2 1.216 < 2.707 0.000 < 2.707 0.449

3 1 2 0.841 < 2.707 0.000 < 2.707 0.311

4 1 2 1.348 < 2.707 0.000 < 2.707 0.498

5 1 1 0.253 < 2.707 0.000 < 2.707 0.093

Rv, Rh : Reaction at support caused by load combinations

nVerb : Number of connecting elements

nbR : 1 = Connection element at every trough

2 = Connection element at every second trough

bR : Module width

NE,d : Applied tension force in the connecting element = Rv·1/nVerb·bR·(-1)

NR,d : Tension capacity in the connecting element

VE,d : Applied shear force in the connecting element = Rh·1/nVerb·bR

VR,d : Shear capacity in the connecting element

5 Summary of design

Ultimate limit state (ULS) elastic-elastic

Mc,Rk,f 25.7 %

Rw,Rk,A 30.6 %

Rw,Rk,B 36.4 %

Vw,Rk 11.5 %

Mc,Rk,B 34.0 %

M-R 33.8 %

Ultimate limit state (ULS) plastic-plastic

Mc,Rk,f -

Rw,Rk,A -

Serviceability limit state (SLS) elastic - elastic

Rw,Rk,B -

Mc,Rk,B -

M-R -

f 43.4 %

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The last change was made on 14.9.2023