Faculty Wing Building Design: Roof Truss

Truss Roof Loading

*Developed based on EN 1991-1-1-2002 loading recommendations

Dead Load: Steel Sheeting = 0.075 KN/m2

Insulation = 0.020 KN/m2

Fixings = 0.025 KN/m2

Services = 0.1 KN/m2

Self-wt. of purlin = (auto-generated by STAAD Pro V8i)

Self-wt. of truss = (auto-generated by STAAD Pro V8i)

Avg. Solar Panel self-wt. = 0.2 KN/m2

Acoustic Ceiling Panels = 0.05 KN/m2

Live Load: Maintenance/Miscellaneous = 0.75KN/m2

Total Loads: Dead Load = 0.47KN/m2 + Self Weight of Members

Live Load = 0.75KN/m2

Figure 1 The critical section of Faculty Wing Truss (highlighted) for member design
Modelled by Jonathan Hohenkirk 26/06/2017 using STAAD Pro V8i
Figure 2 The member lengths of critical section of Faculty Wing Truss for member design
Modelled by Jonathan Hohenkirk 26/06/2017 using STAAD Pro V8i

Figure 3 The member lengths of critical section of Faculty Wing Truss for member design
Modelled by Jonathan Hohenkirk 26/06/2017 using STAAD Pro V8i
 Figure 4 Showing the loadings applied to the critical section of the truss as well as deflection, compression and tension
occurrences.

Modelled by Jonathan Hohenkirk 27/06/2017, STAAD Pro V8i

*Pink lines are the resultant deflected shape which is exaggerated by a factor of 984%

*Red lines at joints designate the occurrence of a member primarily in compression

*Blue lines at joints designate the occurrence of a member primarily in tension

MEMBERS LOCATION MAX AXIAL MEMBERS LOCATION MAX AXIAL

FORCE (KN) FORCE (KN)
37 Top Chord 0.622 (T) 46 Diagonal 45.466 (T)
38 Top Chord 35.816 (C) 47 Diagonal 38.746 (T)
39 Top Chord 71.411 (C) 48 Diagonal 32.153 (T)
40 Top Chord 106.819 (C) 49 Diagonal 25.697 (T)
41 Top Chord 141.909 (C) 50 Diagonal 19.237 (T)
42 Top Chord 176.278 (C) 51 Diagonal 11.237 (T)
43 Top Chord 207.901 (C) 52 Diagonal 49.093 (C)
44 Top Chord 232.922 (C) 53 Diagonal 45.707 (C)
30 Bottom Chord 105.285 (C) 54 Diagonal 39.425 (C)
31 Bottom Chord 70.093 (C) 55 Diagonal 33.566 (C)
32 Bottom Chord 34.995 (C) 56 Diagonal 28.472 (C)
33 Bottom Chord 0.13 (T) 57 Diagonal 24.954 (C)
34 Bottom Chord 35.164 (T) 58 Diagonal 25.647 (C)
35 Bottom Chord 70.135 (T) 45 Vertical 3.933 (C)
Table 1 showing member label designation and the critical axial forces in members. (See Appendix 1 for additional analysis
output files regarding the axial forces
Member Design to EN 1993:1:1:2005
Load combinations for ultimate design force in the members by ULS method

Using Case 1 from table A.12 (B) of EN 1990: 2002

When only DL + LL are acting

The Ultimate design load Fu = gk Gk + Qk Qk = 1.35 Gk + 1.5 Qk

Top Chord Member Design

Design Data
Using member 44 (max loading)

Design Loading Combination: 1.35 PA + 1.5 VA

The ultimate design force in the member (Ned) = 232.922 KN (C)

To design the member as a compression member

Assume section of S275-Square Hollow Section (SHS) 60mm x 60mm x 5mm (hot finished)

A = 10.7 cm2, ry = 2.23 cm

The classification of the cross section

Fy = 275 N/mm2

2 = (235/fy) = (235 / 275) = 0.85

From table 5.2 of Eurocode 3 for class 1 classification of Tubular Sections:

d/t 50 2

So: d = 60mm; t = 5mm

d/t = 60/5 mm = 12 and 50 2 = 50 x 0.85 = 42.5

Therefore 12 < 42.5

Therefore OK, section is Class 1: Plastic

Buckling Resistance
The buckling resistance to compression referring to clause 6.3.1 EN.1993.1.1 a compressive member
should be verified against buckling by the following equation:

Ned / Nb rd 1.0

Where:

Ned - ultimate design compressive force

Nb rd design buckling resistance of the compressive member

So:

Nb rd = X A fy / m1

Where:

X The reduction factor for the relevant buckling mode.

A Area of the section

Fy 275 N/mm2

m1 partial factor = 1.0 (Clause 6.1 EN.1993.1.1)

X = 1/ [ + (2 2)0.5

Where: = 0.5 [1 + ( 0.2) + 2]

And

2
, =
2
Where:

= non-dimensional slenderness

= is the elastic critical force for the relevant buckling mode

= Design Strength of Steel

A Gross cross sectional Area

Therefore

= 205 /2

= 533000 4
= 777
= 1786.236

10702 275 /2
= = = 0.406
1786236

From table 6.1 & 6.2 EN.1993.1.1, = 0.21 (Buckling Curve = a for S275 Grade Steel)

= 0.5 [1 + ( 0.2) + 2] X = 1/ [ + (2 2)0.5]

= 0.5[1 + 0.21 (0.406 0.2) + 0.406 2] = 1/ [0.61 + (0.612 0.4062) 0.5]

= 0.5 x 1.21 = 1/ 1.065

= 0.61 = 0.94

There fore

Nb rd = X A fy / m1

= 0.94 x 1070 mm2 x 275 N/mm2 / 1

= 276.6 KN

Ned / Nb rd = 232.922 KN / 276.6 KN = 0.84

So: 0.84 1

Therefore section assumed is adequate in buckling resistance.

Provide S275-SHS-60mm x 60mm x 5mm

Figure 5 The Steel SHS section designed for member 44 in the top chord of the truss (max compressively loaded member).
Created by Jonathan Hohenkirk using STAAD Pro V8i
Bottom chord Design
From Clause 6.2.3 of EN.1993.1.1: Tension Members, the design value of the tension force NED at each
cross section shall satisfy:

1.0
.
Where . = Design Tension Resistance (lesser of Npl,Rd and Nu.Rd)

Design Data
Using member 36 (max loading)

The ultimate design force in the member (Ned) = 104.93 KN (Tension)

Design of Section
Maximum ultimate tension = 104.93 KN

Assume section of S275-Square Hollow Section (SHS) 60mm x 60mm x 5mm (hot finished)

Agross = 10.7 cm2

Using 2-M16 bolts: Dh = Diameter + 2mm = 18mm

Anet = Agross (2 x 1.8 x 0.5) = 8.9 cm 2

The design plastic resistance is given by

Npl,Rd = Agross fy / m

= (10.7 x 100) mm2 x 275 N/mm2 / 1

= 294.25 KN
And the ultimate resistance:

From Table 3.1 EN.1993.1.1, = 430 /2

From EN.1993.1.1 Clause 6.1 m2 = 1.25

Nu Rd = 0.9 Anet fu / m2

= (0.9 x (8.9 x 100) mm2 x 430 N/mm2 ) / 1.25

= 275.54 KN

The smaller value should be taken as the design tension resistance = 275.54 KN
104.93
= = 0.38 < 1
. 275.54
Therefore assumed section is adequate in tension resistance.

Provide S275-SHS-60mm x 60mm x 5mm

Figure 6 The Steel SHS section designed for member 36 in the bottom chord of the truss (member in maximum tension). Created
by Jonathan Hohenkirk using STAAD Pro V8i

Diagonal & Vertical Member Design

Design Data
Using member 52 (max loading)

The ultimate design force in the member (Ned) = 49.093 KN (C)

Assume section of S275-Square Hollow Section (SHS) 50mm x 50mm x 3mm (hot finished)

A=5.54 cm2
The classification of the cross section
Fy = 275 N/mm2

2 = (235/fy) = (235 / 275) = 0.85

From table 5.2 of Eurocode 3 for class 1 classification of Tubular Sections:

d/t 50 2

So: d = 50mm; t = 3mm

d/t = 50/3 = 16.67 and 50 2 = 50 x 0.85 = 42.5

Therefore 16.67 < 42.5 (Therefore OK, section is Class 1: Plastic)

Design of Section
From Clause 6.2.4: Compression Members, the design value of the compression force NED at each cross
section shall satisfy:

1.0
.

. =

For class 1,2 or 3 cross sections

Where . = Design Compression Resistance

(5.54 100)2 (275 /2 )

. = = = 152.35
1
49.093
= = 0.32 < 1
. 152.35
Therefore assumed section is adequate in compression resistance.

Provide S275-SHS-50mm x 50mm x 5mm

Figure 7 The Steel SHS section designed for member 52 in the diagonal member of the truss (member in maximum compression).
Created by Jonathan Hohenkirk using STAAD Pro V8i
Purlin Member Design

Assuming S275-UPN-80 (C-channel profile purlin: Zx = 32.1 cm3)

Span of truss = 4.5732m

Spacing of purlins = 1.55m

Total Dead Load acting on design purlin: Steel Sheeting = 0.075 KN/m2

Insulation = 0.020 KN/m2

Fixings = 0.025 KN/m2
Services = 0.1 KN/m2
Self wt. of purlin = 0.1 KN/m2
Self wt. of truss = 0.2 KN/m2
Avg. Solar Panel self wt. = 0.2 KN/m2
Acoustic Ceiling Panel = 0.05 KN/m2
Total DL = 0.77 KN/m2
Total Live Load acting on Design purlin: 0.75 KN/m2

Design Load acting purlin = (0.77 + 0.75) KN/m2 x 4.5732m x 1.55m

= (1.52) x 7.09
= 10.8 KN
From BS5950, Table 27: Empirical values for purlins
Wp L (10.8KN)(4573.2mm)
Required Zx for angled sections: = = 27.44 3
1800 1800
= 32.1 3
Therefore Section is adequate. Provide S275-UPN-80 (C-channel profile purlin)

Figure 8 The steel C-channel section designed for member 133 (longest purlin member).
Created by Jonathan Hohenkirk using STAAD Pro V8i
Final Design Sections for critical truss

Table 2 showing final member sections..

MEMBERS LOCATION MEMBER CODE MEMBER

SIZE (mm)
37 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
38 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
39 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
40 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
41 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
42 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
43 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
44 Top Chord TUB60605 Square Hollow Section 60 x 60 x 5
30 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
31 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
32 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
33 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
34 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
35 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
36 Bottom Chord TUB60605 Square Hollow Section 60 x 60 x 5
46 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
47 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
48 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
49 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
50 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
51 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
52 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
53 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
54 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
55 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
56 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
57 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
58 Diagonal TUB50503 Square Hollow Section 50 x 50 x 3
45 Vertical TUB50503 Square Hollow Section 50 x 50 x 3