Tubular Truss Design Using Steel Grades S355 and S420

Markku Heinisuo, Teemu Tiainen and Timo Jokinen

Tubular truss design using steel grades S355 andS420

Version DateComplete 1.10.2013Rev 1 8.10.2013

Tubular truss design using steel grades S355 and S420 page 1

Contents

1 Introduction 2

2 Truss resistance 3

2.1 Structural analysis model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Trusses of di�erent steel grades . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Resistance checks of members . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Joint design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Cost analysis 13

3.1 Weld design, volumes and related welding costs of trusses . . . . . . . . . . . 13

3.2 Total fabrication cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2.1 Manufacturing cost by Haapio (2012) . . . . . . . . . . . . . . . . . . 19

3.2.2 Manufacturing cost by Pavlov£i£ et al. (2004) . . . . . . . . . . . . . 22

3.2.3 Manufacturing cost by Jármai & Farkas (1999) . . . . . . . . . . . . . 24

3.2.4 Cost analysis comparison . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Fire design 26

5 Conclusions 33


1 Introduction

Welded tubular roof trusses are widely used in buildings. This kind of roof structurehas shown its large potential due to its nice appearance and e�ective load bearing andeconomical properties. In this paper a detailed analysis based on Eurocodes is shown.Special attention is devoted to the joint design (failure modes) and welding using di�erentsteel grades, especially Ruukki's double grade S355/S420. Truss manufacturing includingsawing, blasting, painting, material and especially welding costs are calculated using threemethods presented in the literature.


2 Truss resistance

Consider a typical Warren-type one span symmetric roof truss shown in Figure 2.1. Thetruss is made of cold-formed square tubular members using welded gap K-joints.

The spans considered are 24 and 36 m and trusses are located center-to-center 6 m. Itis supposed that the structural systems of roof structures above the truss are such thatthe same loads are acting on all trusses. There are eight braces at both sides of the trussand the joints are located center-to-center 3 or 4.5 m, meaning evenly located joints. Theheights of the trusses are 2.4 and 3.5 m measured from the top of the top chord to thebottom of the bottom chord at the mid span. The gap is same 50 mm at each joint. Theroof inclination is 1:20 which is suitable for one-layer roo�ng.

The characteristic loads are the dead load on the roof including the weight of the truss 1kN/m2 and the snow load on the roof 2 kN/m2. The design is done using Eurocodes withFinnish National Annexes. The relevant codes are for the design of members EN 1993-1-1CEN (2006a) and for the design of joints EN 1993-1-8 CEN (2006b). Only the ultimate limitstate is considered. The serviceability limit state (de�ection limit) is taken into account bypre-chamfer of the truss.

The uniform design load qd distributed to the horizontal plane is using Finnish load factorsand load combination factors:

qd = 6 · (1.15 · 1 + 1.5 · 2) = 24.9 kN/m (2.1)

The truss design is done using three steel grades:

• All members S355;

• All members S420;

• Chords S420 and braces S355.

Two spans and three steel grade possibilities result in six di�erent cases seen in Table 2.1

Table 2.1: Truss cases

Case 1 2 3 4 5 6

Span [m] 36 36 36 24 24 24

Chords S355 S420 S420 S355 S420 S420

Braces S355 S420 S355 S355 S420 S355

page 4

Figure 2.1: Trusses

2.1 Structural analysis model

In order to take into account all features of the joints in the structural analysis, the struc-tural analysis should be generated from the geometrical model of the truss. In this case thismeans the eccentricities at the joints. The chords are modeled for the structural analysisas continuous beams and the braces are modeled as hinged members following rules of EN1993-1-8.

The structural analysis model consists of members and joints. Local analysis models ofjoints are generated �rst and after that the joint models are connected with the members'models. Linear elastic �nite element method (FEM) using Bernoulli-Euler beam elementsare used. One beam element between is used local joint models which is enough in thisanalysis. The local joint models are shown in Figure 2.2.

The joint location (4.5 m center-to-center) is de�ned as the horizontal distance from themid-point of the gap to the next mid-point of the gap along the chords. The �rst joint atthe top chord is measured from the support. The local analysis models of joints are at theintersections of the mid-lines of braces and connected to the chords by a perpendicular sti�short element. Practically the sti�ness of this eccentricity element is the same as that forHEA600. The cross-section area and the moment of inertia of the braces and chords arethose of tubular members.

Using these rules the global structural analysis model can be created. After solving theFEM model the stress resultants are available.

page 5

Figure 2.2: Local analysis model of the truss

Table 2.2: Member sizes of the trusses

Case 1 2 3 4 5 6

Top Chord 200x10 180x10 180x10 140x8 140x8 140x8

Bottom chord 180x6 160x6 160x6 140x6 120x6 120x6

1st Brace 80x3 60x3 60x3 50x3 50x3 50x3

2nd Brace 110x4 70x3 70x3 50x3 50x3 50x3

3rd Brace 90x3 90x3 90x3 70x3 60x4 60x4

4th Brace 80x3 70x3 70x3 50x3 50x3 50x3

5th Brace 120x4 110x4 110x4 90x3 80x3 90x3

6th Brace 90x3 80x3 90x3 60x3 60x3 60x3

7th Brace 160x6 140x5 140x5 100x4 100x4 100x4

8th Brace 160x6 140x5 140x5 100x4 100x4 100x4

Mass [kg] 1896 1643 1646 758 718 720

2.2 Trusses of di�erent steel grades

When the steel grade and geometry are �xed the engineer should �nd out the correct tubesizes. These are typically the ones resulting in the lightest possible design still satisfying allrequirements of Eurocodes. After some trials and errors member sizes shown in Table 2.2were found. The numbering of braces begins from the mid span. The mass is for half ofa truss. Ruukki's cold formed square tubes are used. The top chord is chosen to belongto the cross-section class 1 of EN 1993-1-1 due to requirement of EN 1993-1-8 for the kneejoint at the top chord. Other tubes can belong to class 1 or 2 based on pure compression,following rules of EN 1993-1-8.

It can be seen - as expected - that with higher strength smaller sizes can be used whichresults in lower structural mass. The hybrid solution and S420 solutions are very close toeach other the hybrid being slightly lighter. The weight of S420 solution is 14 % lighter in

page 6

Figure 2.3: Finite element model of the S355 truss at span of 36 m

Figure 2.4: Eccentricity element

the case of 36 m span and 5 % lighter in the case of 24 m span.

The numbering of braces and chord elements as well as the �nite element analysis modelS355 truss is shown in Figure 2.3. The eccentricity elements are present but quite shortand thus almost invisible. The eccentricity element of �rst joint from the mid span on thebottom chord is seen in Figure 2.4.

The moment diagram of the S355 truss can be seen in Figure 2.5. The largest moments areat the upper chord where the distributed loading is present but eccentricity elements causealso bending moment to the bottom chord and in the element nearest to the support themoment is rather large. The eccentricities can be seen in Table 2.3. The numbering startsfrom the �rst joint from the mid span on the bottom chord. As the eccentricity of a K jointcan be calculated as (Ongelin & Valkonen 2012)

e =

(h1

2 sin β1+

h22 sin β2

+ g

)sin β1 sin β2sin (β1 + β2)

− h02

(2.2)

it can be seen that with two large members are connected to chord a large eccentricity canbe expected. This can be seen also in these example structures.

As can be seen in Table 2.4 the variations in axial forces are quite small for these threetrusses of both spans. The small di�erences are due to two factors. Firstly, structure ishyperstatic and the member sizes are di�erent. Secondly, the di�erent member sizes resultin slightly di�erent geometry and eccentricities.

The de�ection at service limit state can be seen in Table 2.5. It can be seen that smallermember sizes of higher strength result in slightly higher de�ection.

page 7

Figure 2.5: Moment diagram of the S355 truss

Table 2.3: Eccentricities at joints

Case 1 2 3 4 5 6

e1 30 13.2 13.2 11.8 22.4 22.4

e2 20 13.7 13.7 18.2 14.1 14.1

e3 13.7 20.3 20.3 15.2 21.5 21.5

e4 14.1 16.6 16.6 22.2 18.3 22.9

e5 24.1 26.9 31.2 22.9 29.4 33.7

e6 28.4 27.1 31.1 25.1 25.9 25.9

e7 61.3 56.5 56.5 37.6 48.5 48.5

page 8

Table 2.4: Axial forces at elements

Case 1 2 3 4 5 6

Axialforces

[kN]

Top chord 1 -1235.2 -1228.2 -1228.2 -803.2 -799.9 -799.9

Top chord 2 -1156.9 -1150.3 -1150.5 -751.0 -747.5 -747.5

Top chord 3 -891.6 -885.3 -884.9 -577.2 -574.5 -574.8

Top chord 4 -354.0 -351.6 -351.7 -229.4 -226.7 -226.7

Bottom chord 1 1231.0 1224.2 1224.2 801.2 798.0 797.9

Bottom chord 2 1236.0 1228.9 1228.9 803.0 799.5 799.6

Bottom chord 3 1069.6 1062.7 1062.9 692.8 689.9 689.7

Bottom chord 4 680.5 676.4 676.7 440.6 437.5 437.5

1st brace 4.8 4.6 4.5 1.9 1.9 1.9

2nd brace -4.0 -3.7 -3.7 -1.2 -0.9 -1.1

3rd brace -137.6 -137.9 -137.6 -92.8 -92.9 -92.9

4th brace 139.1 140.2 140.2 94.5 94.1 94.7

5th brace -294.2 -294.8 -295.7 -196.3 -196.1 -196.3

6th brace 323.8 322.4 322.6 214.1 216.3 216.8

7th brace -516.2 -514.4 -514.8 -339.7 -341.5 -341.5

8th brace 525.5 523.8 523.9 346.2 344.6 344.5

Table 2.5: De�ection at the mid span of the trusses

Case 1 2 3 4 5 6

Maximum de�ection w [mm] 94.0 105.9 105.3 61.6 66.9 66.7

L/w [-] 383 340 342 585 538 540

page 9

2.3 Resistance checks of members

The members are checked for the interaction of the axial force and the bending momentand for shear. For the interaction of the axial force and the moment the EN 1993-1-1,method 2 is used with the material factors γM0 = γM1 = 1.0 Following Finnish NA and theimperfection factor in buckling is α = 0.49. The factor Cmy = 1.0 is used for all members,but not for the top chord. The equation used is (EN 1993-1-3 clause 6.3.3(4)):

NEd

χyAfyγM1

+kyyMy,Ed

Wpl,yfyγM1

≤ 1 (2.3)

where

• χy is the reduction factor for the relevant buckling curve c;

• A is the cross-section area of the member;

• fy is the yield strength of the member;

• γM1 is the partial factor 1.0 in this case;

• kyy is the interaction factor;

• Wpl,y is the plastic section modulus.

The left hand side of (2.3) is the utility of the member for the interaction of the axialforce and the moment. The interaction factor kyy is in this case for the top chord (plasticcross-sectional properties):

kyy = Cmy min[1 + (λ̄y − 0.2)ny; 1 + 0.8ny] (2.4)

where factor Cmy is

Cmy = 0.1 + 0.8Mspan

Msupport

(2.5)

and

λ̄y =

√AfyNcr,y

(2.6)

and the buckling load Ncr,y is:

Ncr,y =π2EIyL2cr,y

(2.7)

where buckling lengths Lcr,y are 0.9 times the member lengths in the analysis model and E= 210000 MPa. When calculating the cross-sectional property values A, Wpl,y and Iy thecorner radius of the pro�le shall be taken into account. The radiuses are de�ned followingthe standard EN 10219-2 (2006). They are:

• If the tube wall thickness t is smaller or equal to 6 mm then the outer radius r of thecorner is 2 times the wall thickness.

page 10

Table 2.6: Utilization ratios from member resistance checks

Case 1 2 3 4 5 6

Top chord 0.85 0.93 0.93 0.99 0.86 0.86

Bottom chord 0.92 0.89 0.89 0.80 0.85 0.85

1st brace 0.01 0.02 0.02 0.01 0.01 0.01

2nd brace 0.01 0.05 0.05 0.02 0.02 0.02

3rd brace 0.96 0.92 0.96 0.72 0.81 0.85

4th brace 0.43 0.43 0.51 0.49 0.41 0.49

5th brace 0.77 0.87 0.94 0.84 0.99 0.85

6th brace 0.89 0.85 0.89 0.91 0.78 0.92

7th brace 0.54 0.72 0.80 0.90 0.82 0.91

8th brace 0.41 0.47 0.56 0.65 0.55 0.65

• If the wall thickness is larger than 10 mm then the outer radius is 3 times the wallthickness.

• In between it is 2.5 times the wall thickness.

The e�ect of shear to resistances of the members is checked using EN 1993-1-1 clauses 6.2.6and 6.2.8.

Table 2.6 presents the utilities of the members for trusses using the stress resultants acquiredin �nite element analysis and Eqs. (2.3) � (2.7). Due to symmetry only the values for thehalves of the trusses are shown.

As the �nite element analysis forces and moments are used the eccetricities are automat-ically taken into account in chord member analysis. In braces there is no bending as theconnections are pinned. This can result in unsafe design but this is taken into account withtwo factors in the buckling analysis:

• The welded joints have rotational rigidity and therefore buckling length factor ishigher than it should

• Member length used in the analysis is the element length which is always longer thanthe actual member

It can be seen, that all members are feasible ful�lling the requirements of EN 1993-1-1.

2.4 Joint design

The standard EN 1993-1-8 gives a lot of requirements for welded tubular joints. Manyrequirements deal with the geometrical properties of the joints. Using notations of EN 1993-1-8, (see also Ongelin & Valkonen 2012, where the requirements are shown with correctionsof the standard) the requirements in K-joints are:

page 11

• Angles between braces and chords

θi ≥ 30 ◦ ⇒ 30 ◦

θi≤ 1 (2.8)

• Cross-section classes of both chords and compressed braces should be 1 or 2;

• Geometrical constraints

bib0≤ 1, i = 1, 2 (2.9)

β ≤ 1 (2.10)

g ≥ t1 + t2 ⇒t1 + t2g≤ 1 (2.11)

g

b0≥ 0.5(1− β)⇒ 0.5(1− β)

g/b0≤ 1 (2.12)

g

b0≤ 1.5(1− β)⇒ g/b0

1.5(1− β)≤ 1 (2.13)

hiti≤ 35⇒ hi

35ti≤ 1 (2.14)

h0t0≤ 35⇒ h0

35t0≤ 1 (2.15)

If g/b0 ≥ 1.5(1− β) and g ≥ t1 + t2 then the K-joint is treated as two separate T-joints.

All the trusses in Table 2.2 ful�ll these requirements.

The resistances of braces at K-joints are:

• Chord face failure:

Ni,Rd =8.9knfy0t

20

√γ

sin θiβ, i = 1, 2 (2.16)

• Chord shear:

Ni,Rd =fy0Av0√3 sin θi

, i = 1, 2 (2.17)

• Chord face punching shear if β ≤ (1− 1/γ):

Ni,Rd =fy0t0√3 sin θi

(2hi

sin θi+ bi + be.p

), i = 1, 2 (2.18)

• Brace failure:Ni,Rd = fyiti(2hi − 4ti + bi + beff ), i = 1, 2 (2.19)

The resistance of the chord including the e�ect of shear in the gap area is:

N0,gap,Rd = (A0 − Av0)fy0 + Av0fy0

√1−

(VEdVpl,Rd

)2

(2.20)

page 12

Table 2.7: Joint check utilization ratios

Case 1 2 3 4 5 6

TC - TC 0.71 0.78 0.78 0.84 0.78 0.78

TC - 1st 0.48 0.50 0.50 0.57 0.53 0.53

TC - 2nd 0.48 0.51 0.51 0.57 0.53 0.53

TC - 3rd 0.48 0.51 0.51 0.57 0.53 0.53

TC - 4th 0.59 0.59 0.59 0.77 0.71 0.63

TC - 5th 0.46 0.48 0.49 0.54 0.50 0.50

TC - 6th 0.71 0.73 0.68 1.00 0.85 0.84

TC - 7th 0.87 0.92 0.87 0.88 0.84 0.89

TC - 8th 0.59 0.61 0.61 0.86 0.81 0.81

BC - 1st 0.85 0.90 0.90 0.72 0.80 0.80

BC - 2nd 0.85 0.90 0.90 0.72 0.80 0.80

BC - 3rd 0.87 0.92 0.92 0.73 0.81 0.81

BC - 4th 0.87 0.92 0.92 0.73 0.81 0.81

BC - 5th 0.91 0.89 0.85 0.76 0.74 0.74

BC - 6th 0.96 0.99 0.90 0.92 0.84 0.89

BC - 7th 0.78 0.87 0.88 0.96 0.88 0.88

BC - 8th 0.64 0.65 0.65 0.93 0.83 0.83

The values for M0,Ed are taken as maximum values at both sides of the joint. The axialforce N0,Ed is the axial force from the tension diagonal side. The value for VEd is calculatedas maximum of [cos θiNi,Ed, cos θi+1Ni+1,Ed] where θi is the angle between the brace and thechord and Ni,Ed is the axial force of the brace. All notations follow EN 1993-1-8.

At the support the only check is done for the brace joint to the top chord. It is supposedto act as a T-joint. The top joint of the truss in the mid of the span is checked as a kneejoint with a separate brace. These joints are checked using the relevant equations of EN1993-1-8. The welds at joints are considered in the next chapter.

If S420 steel grade is active in the failure mode the factor 0.9 should be used in the corre-sponding resistance equation. If the truss is totally made of S355 or S420 then in Eqs. (2.16)� (2.19) no factor is needed for S355 truss and factor 0.9 is used for S420 truss, respectively.If the chords are S420 steel and braces S355 steel the factor 0.9 is used all modes exceptbrace failure (Eq. (2.19)). In the joint failure mechanisms no interaction between chordsand braces are present. This enables this interpretation.

Using these rules the utilities of the joints for the trusses are given in Table 2.7.

It can be seen, that the joint utilities of the trusses are below 1, so they are feasible.


3 Cost analysis

Truss design aspects concerning costs have been discussed by many authors in the literature.Jármai & Farkas (1999) present a cost model suitable for optimization. Pavlov£i£ et al.(2004) show the use of their model as a part of optimization. Haapio (2012) presents a verydetailed feature-based approach in his thesis. Tizani et al. (2006) present a knowledge-based system including economic module for tubular trusses, but no cost function is given.Klan²ek & Kravanja (2006a,b) use detailed cost function for composite �oor system. A verybroad cost calculation model is given by Watson et al. (1996) including all activities fromdesign to the erection at the site. However, all features of steel structures are not present.

In this work, special attention is given to welding costs which are calculated in the nextsection using three di�erent methods presented by:

• Jármai & Farkas (1999)

• Pavlov£i£ et al. (2004)

• Haapio (2012)

In the following section an estimate of truss total manufacturing costs is given followingsame references. All the costs considered in the tables and �gures of this chapter are forhalf of the trusses if else not noted.

3.1 Weld design, volumes and related welding costs of

trusses

Applying the clause 7.3.1(6) of EN 1993-1-8 full strength welds should be used, if thedeformation and rotation capacity of the joint is not shown. In this study full strengthwelds are used. They are for three cases (Ongelin & Valkonen 2012):

• Truss made of totally S355: aw = 1.11t;

• Truss made of totally S420: aw = 1.48t

• Truss with S420 chords and S355 braces: as truss made of totally S355.

The weld sizes are given in Table 3.1. Weld length for a rectangular member i connectedin a truss at end j can be calculated as

Lw,ij = 2bi +2hi

sinαj(3.1)

page 14

Table 3.1: Weld sizes by joint for six trusses.

Case 1 2 3 4 5 6

TC - 1st 3.33 4.44 3.33 3.33 4.44 3.33

TC - 2nd 4.44 4.44 3.33 3.33 4.44 3.33

TC - 3rd 3.33 4.44 3.33 3.33 5.92 4.44

TC - 4th 3.33 4.44 3.33 3.33 4.44 3.33

TC - 5th 4.44 5.92 4.44 3.33 4.44 3.33

TC - 6th 3.33 4.44 3.33 3.33 4.44 3.33

TC - 7th 6.66 7.40 5.55 4.44 5.92 4.44

TC - 8th 6.66 7.40 5.55 4.44 5.92 4.44

BC - 1st 3.33 4.44 3.33 3.33 4.44 3.33

BC - 2nd 4.44 4.44 3.33 3.33 4.44 3.33

BC - 3rd 3.33 4.44 3.33 3.33 5.92 4.44

BC - 4th 3.33 4.44 3.33 3.33 4.44 3.33

BC - 5th 4.44 5.92 4.44 3.33 4.44 3.33

BC - 6th 3.33 4.44 3.33 3.33 4.44 3.33

BC - 7th 6.66 7.40 5.55 4.44 5.92 4.44

BC - 8th 6.66 7.40 5.55 4.44 5.92 4.44

where hi is the height of the pro�le in the plane of the truss and bi is the width of thepro�le. The weld length for the trusses are shown in Table 3.2.

Pavlov£i£ et al (2004) utilize a Slovenian handbook (Polanjar 1991) giving welding time as

Tweld = Aa2 +Ba+ C [min/m] (3.2)

where A, B and C are factors depending on the welding technology. The values of A, Band C for di�erent welding situations can be seen in Table 3.3.

Welding cost is calculated by

Cweld = kweld [fweldTweld (aw)Lw + Tweld,extra] (3.3)

where kweld is the cost factor, fweld is factor contributing to a longer time in case of shortwelds or di�cult positions, Lw is the length of the weld.

Welding material cost is calculate by

Cweld,material =[∑

km,weld,iMweld,i(aw)]Lw (3.4)

where km,weld,i is weld material cost factor and Mweld,i(aw) is the material consumption(which can be of any type: welding consumables, shielding gas, energy et cetera) which issupposed to follow a quadratic function of weld size aw:

Mweld,i(aw) = Am,w,ia2w +Bm,w,iaw + Cm,w,i (3.5)

page 15

Table 3.2: Weld length [mm] joint by joint for six trusses.

Case 1 2 3 4 5 6

TC - 1st 359 269 269 223 223 223

TC - 2nd 490 313 313 222 222 222

TC - 3rd 411 409 409 317 271 271

TC - 4th 363 317 317 226 225 225

TC - 5th 555 508 508 412 366 411

TC - 6th 416 369 415 275 275 275

TC - 7th 751 657 657 466 465 465

TC - 8th 753 658 658 467 466 466

BC - 1st 352 264 264 219 219 219

BC - 2nd 481 307 307 218 218 218

BC - 3rd 402 401 401 310 266 266

BC - 4th 356 311 311 221 221 221

BC - 5th 543 496 496 403 359 403

BC - 6th 407 361 406 269 269 269

BC - 7th 733 641 641 455 454 454

BC - 8th 735 642 642 456 455 455

Table 3.3: Welding time function factors A, B and C for di�erent welding situations

Type A B C

Automatic submerged arc welding 2.62 1.37 0.09

Sti�ener plates (MMA) 17.26 2.90 1.82

End plates (MMA) 9.03 4.68 -0.82

page 16

where parameter Am,w,i, Bm,w,i and Cm,w,i should be determined from appropriate litera-ture1.

The values used in the example trusses are

kweld = 1.40 (3.6)

Tweld,extra = 0.3 [min] (3.7)

Tweld = 17.26a2w + 2.9aw + 1.82 [min/m] (3.8)

kweld = 27.68 [e/h] (3.9)

Mweld,electrodes = 1.33a2w + 0.19aw − 0.02 [kg/m] (3.10)

Mweld,power = 6.29a2w − 1.87aw + 0.44 [kWh/m] (3.11)

km,weld,electrodes = 1.4 [e/kg] (3.12)

km,weld,power = 0.11 [e/kg] (3.13)

According to Jármai & Farkas (1999), the welding preparation, assembly and tacking timecan be calculated by

Tpat = C1Θdw

√κρV (3.14)

where C1 is a parameter depending on welding technology (usually 1), Θdw is di�cultyfactor, κ is the number of structural elements in the assembly, ρ is the material density[kg/m3], V is the material volume of the assembly [m3]. The welding time can calculatedas

Tw = 1.3∑

C2ianwiLwi (3.15)

where C2i and n are constants depending on welding technology and Lwi is the weld length.Jalkanen (2007) found C2i = 0.4 and n = 2 suitable values for tubular steel trusses. Haapio(2012) presented a very general approach to cost calculation of a steel structure in whichas also welding costs were considered. According to Haapio member welding cost is

CW = (TPTaW + TPWW )

(CLW + CEqW + CREW + CSeW ) +

kgw (CCW + TPWWCEnW ) [e] (3.16)

where

• Tacking time TPTaW = 2.86 [min];

• Welding time

TPWW =LW1000

·(0.4988 · a2 − 0.0005 · a+ 0.0021

)[min]

• Length of the weld LW [mm];

• Weld size a [mm];

• Labour cost CLW = 0.46 e/min (one welder);

1At this point Pavlov£i£ et al. (2004) refer to books Aichele (1994), Czesany (1972), Polanjar (1991)

page 17

Table 3.4: Welding costs

Author Case 1 2 3 4 5 6

Haapio

Total cost of welds [e] 111.97 126.21 84.92 54.36 77.12 55.65

Cost of weld preparation [e] 30.95 30.95 30.95 27.20 27.20 27.20

Cost of welding [e] 81.03 95.26 53.98 27.16 49.92 28.45

Farkas & Jármai



Cost of welding [e] 59.09 69.48 39.37 20.92 38.46 21.92

Pavlov£i£ Cost of welding [e] 47.04 50.50 34.36 20.86 30.21 21.25

• Equipment cost CEqW = 0.01 + e/min (price 5000 e, investment time 10 years);

• Required area AW = (Ltruss + 2)(Htruss + 2) [m2];

• Truss length Ltruss [m];

• Truss height Htruss [m];

• Real estate investment cost

CREW =pREAWaw

i · (1 + i)n

i · (1 + i)n − 1[e/min];

• Real estate maintenance cost CSeW = pSe · AW/aw [e/min];

• Cost of consumables CCW = LW · a2 · 7.85 · 106 · (1.91 + 4.44) [e];

• Cost of energy CEnW = 0.01 e/min (6 kW).

Haapio considered quite small parts resulting in total tacking time

TTa = 1.59 [min] (3.17)

estimated by Schreve et al. (1999). In this work, the parts are longer than 2000 mm and alarger value

TTa = 2.86 [min] (3.18)

suggested by Schreve et al. (1999) was adopted. Still for trusses this number is quite smallcompared to numbers given by Jármai & Farkas (1999). The cost of welding is acquiredfrom the preparation, assembly, tacking and welding times by multiplying it with suitablecost factor. Haapio presents a detailed way of acquiring the cost factor including labour, realestate, equipment, energy costs et cetera whereas Jármai & Farkas leaves the determiningcost factor to the reader. In this work cost factor applied with Jármai & Farkas formulaswas k = 0.55 e/min.

The welding times as functions of weld size proposed by di�erent authors can be seen inFigure 3.1.

The total welding costs of three trusses using three methods above are given in Table 3.4.

page 18

Figure 3.1: Welding times as function of weld size

Table 3.5: Welding cost joint by joint following Haapio (2012)

Case 1 2 3 4 5 6

TC - 1st 3.50 4.02 3.11 2.73 3.44 2.73

TC - 2nd 5.72 4.35 3.29 2.73 3.44 2.73

TC - 3rd 3.72 5.10 3.71 3.12 5.35 3.80

TC - 4th 3.51 4.39 3.31 2.74 3.46 2.74

TC - 5th 6.23 8.91 5.86 3.51 4.50 3.51

TC - 6th 3.74 4.79 3.74 2.95 3.82 2.94

TC - 7th 15.00 16.03 9.87 5.23 7.86 5.22

TC - 8th 15.03 16.06 9.88 4.32 6.96 4.31

BC - 1st 3.47 3.98 3.08 2.72 3.41 2.71

BC - 2nd 5.65 4.31 3.27 2.71 3.41 2.71

BC - 3rd 3.68 5.03 3.68 3.09 5.27 3.76

BC - 4th 3.48 4.34 3.29 2.73 3.43 2.72

BC - 5th 6.13 8.76 5.77 3.48 4.44 3.47

BC - 6th 3.70 4.73 3.70 2.92 3.78 2.92

BC - 7th 14.68 15.70 9.68 5.15 7.72 5.14

BC - 8th 14.72 15.72 9.69 4.24 6.82 4.23

page 19

Welding times according to Haapio and Farkas & Jármai are very similar whereas Pavlov£i£gives considerably faster and thus less costly welding. For tacking on the other hand theestimate given by Haapio is very small compared to that of Farkas & Jármai. Still, thelatter includes also preparation and assembly to this cost as well. As the di�erence is quiteremarkable assembly, jig and tacking cost should be further investigated in order for thecost estimation tools to be accurate. Moreover, by including or excluding cost factors aremarkable di�erences in total welding cost can be expected. Therefore, the methods shouldbe used carefully using the relevant parameters preferably measured in the workshop wherethe designed structure will be manufactured.

3.2 Total fabrication cost

In this work, total fabrication cost of truss is calculated as sum of di�erent cost proportions

CTruss = CMaterial + CWeld + CBlast + CPaint + CSaw (3.19)

where Ci refers to cost of i subscripts being self-explanatory. It is known that there areother costs related to structures such as transportation and erection costs but they arenot considered in this work. The costs related to welding are being discussed in detail inprevious section. The other costs are calculated as follows.

The material cost for a truss is

CMaterial =∑

kiρAiLi (3.20)

where ki is the material cost factor [e/kg] (in this work ki = 0.8 e/kg for both S355 andS420 since Ruukki's double grade steel is considered), ρ is the material density [kg/m3], Aiis the cross-sectional are of member i and Li is the length of member i. The sum is takenover all the members in the truss. Other costs are described in the following subsectionsordered by the used reference.

3.2.1 Manufacturing cost by Haapio (2012)

Member blasting cost is

CB =TPB(CLB + CEqB + CMB + CREB+

CSeB + CCB + CEnB) [e] (3.21)

where

• Productive time TPB = LB/3000 [min]

• Member length LB [mm]

• Labour cost CLB [e/min] (one machine worker)

• Equipment cost CEqB = 0.13 e/min (price 200 000 e, investment time 20 years,interest rate 5 %)

page 20

• Equipment maintenance cost CMB = 0.01 e/min (1000 e/a)

• Real estate investment cost CREB [e/min] (supposed 400 m2)

• Real estate maintenance cost: CSeB [e/min]

• Cost of consumables: CCB = 0.02 e/min

The values chosen were typical Finnish values:

• Machine worker wage CLB = 16.26 e/h + overheads 11.40 e/h = 27.68 e/h

• Real estate price pRE = 900 e/m2

• Interest rate i = 5 % for real estate

• Length of one work year aw = 120960 min

• Investment time for real estate n = 50 a

• Real estate investment cost

CREW =pREA

aw

i · (1 + i)n

i · (1 + i)n − 1= 0.16 [e/min];

• Real estate maintenance pSe = 72 e/m2a

• Real estate maintenance cost CSeB = 0.24 e/min

• Cost of energy CEnB = 0.07 e/min (40 kW, 0.1 e/kWh).

Member sawing cost is

CS =((TNS + TPS1 + TPS2)

(CLS + CEqS + CMS + CRES + CSeS+

TPS1(CCS1 + CEnS)+

TPS2(CCS2 + CEnS)) [e] (3.22)

where

• Non-productive time TNS = 6.5 + LS/20000 [min];

• Member length LS [mm];

• Productive time for one cut

TPSi =

h(0.0328 ·

(t

cos θi

)2− 3.1794 · t

cos θi+ 115.6

)Sm

+AhiQ

[min];

page 21

• Pro�le height h [mm];

• Pro�le wall thickness t [mm];

• Sawing angle θi [◦];

• Area of horizontal parts of the pro�le Ah [mm2];

• Labour cost CLS = 0.46 e/min (one machine worker);

• Equipment cost CEqS = 0.21 e/min (price 310 000 e, investment time 20 years);

• Equipment maintenance cost CMS = 0.01 e/min (1000 e/a);

• Real estate investment cost CRES = 0.21 e/min (525 m2);

• Real estate maintenance cost CSeS = 0.31 e/min;

• Total sawing area for one cut At [mm2];

• Material factor2 Q = 8800 [mm2/min] for S355, Q = 6900 [mm2/min] for S420;

• Material factor3 Sm = 0.9 for S355, Sm = 0.8 for S420;

• Cost of energy CEnS = 0.02 e/min (10 kW).

• Cost of consumables

CCSi =100

TPSi· Ati(−1.188 ·

(t

cos θi

)2+ 188892 · t

cos θi+ 4414608

)[e/min];

Painting cost supposing Alkyd paint system AK 160/3 - FeSa212is:

CP = TPP (CLP + CREP + CSeP ) + CCP + CDyP [e] (3.23)

where

• Painting time TPP = (0.513/900000)A [min];

• Total painted area A [mm2];

• Labour cost CLP = 0.46 e/min (one machine worker);

• Real estate investment cost CREP = 0.03 e/min (75 m2);

2When considering Ruukki's double grade steel, the material is essentially the same in both cases, thusQ = 6900 should be used

3When considering Ruukki's double grade steel, the material is essentially the same in both cases, thusSm = 0.8 should be used

page 22

Table 3.6: Manufacturing cost according to Haapio.

Case 1 2 3 4 5 6

Material cost [e] 1517 1314 1317 607 575 576


Blasting cost [e] 21.85 22.02 22.01 14.65 14.71 14.70

Painting cost [e] 162.37 143.53 144.04 79.13 74.94 75.30

Sawing cost [e] 102.20 102.15 100.72 92.45 94.05 93.09

Total cost [e] 1915 1708 1668 847 836 815

• Real estate maintenance cost CSeP = 0.04 e/min;

• Paint cost CCP = 3.87 · 10−6A [e];

• Drying cost CDyP = 0.36LtrussWtruss [e];

• Top chord width Wtruss [mm].

Using the values described above, costs seen in Table 3.6 are acquired. After the calculationit was observed that when double grade steel is used, the lower sawing costs of S355 is notrealistic. After some testing it was found that this would result in approximately 2 %relative di�erence in sawing cost. As sawing cost represents only from 5 to 11 % of totalcost, the di�erence is almost neglible.

3.2.2 Manufacturing cost by Pavlov£i£ et al. (2004)

According to Pavlov£i£ et al. (2004) surface preparation is calculated as

CSurfacepreparation = ksurfprepTsurfprep(Lpl + Lblast) (3.24)

where ksurfprep is the cost factor, Tsurfprep the surface preparation time, Lpl is the memberlength, Lblast is the length of the blasting chamber.

Cutting costs are given as

Ccut = Ccut.manuf + Ccut.material + Ccut.handling (3.25)

where manufacturing costs are calculated as

Ccut.manuf = kcut [fcutTcut(tpl)Lc + Tcut.extra] (3.26)

cutting material cost as

Ccut.material =[∑

km.cutMcut(tpl)]Lc (3.27)

and handling asCcut.handling = khandlingThandling (3.28)

page 23

Table 3.7: Manufacturing cost according to Pavlov£i£ et al. (2004)

Case 1 2 3 4 5 6

Cost of welds [e] 47.04 50.50 34.36 20.86 30.21 21.25

Blasting cost [e] 150.96 152.06 152.04 103.60 103.95 103.93

Painting cost [e] 197.86 174.63 175.31 92.78 87.23 87.70

Cutting cost [e] 46.24 44.70 44.78 42.17 41.87 41.94

Total cost [e] 1959 1736 1723 866 838 831

Painting cost is expressed as

Cpainting =[kpaintTpaint +

∑km,paint,iMpaint,i

]A (3.29)

where kpaint is labour cost factor, Tpaint time consumption, km,paint paint material cost factorand Mpaint the paint consumption.

The following values were used in this work:

Tcut = −0.0015t2pl + 0.421tpl + 1.43 [min/m] (3.30)

Mcut,propan = 0.0t2pl + 2.171tpl + 7.87 [l/m] (3.31)

Mcut,poxygen = 1.645t2pl + 56.644tpl − 6.73 [l/m] (3.32)

Thandling = −4 · 10−8m2 + 0.001m+ 3.73 [min] (3.33)

ncut = 4 (3.34)

fcut = 1.03 (3.35)

Tcut,extra = 2.0 [min] (3.36)

kcut = 0.46 [e/min] (3.37)

km,cut,propane = 0.002 [e/l] (3.38)

km,cut,propane = 0.0016 [e/l] (3.39)

khandling = 0.46 [e/min] (3.40)

Tpaint = 7.0 [min/m2] (3.41)

kpaint = 0.53 [e/min] (3.42)

Mpaint,i = [0.130.1730.15] [l/m2] (3.43)

km,paint,i = [4.53.83.8] [e/l] (3.44)

Lblast = 30 [cm] (3.45)

Tblast = 2.2 [min/m] (3.46)

ksurf.prep = 1.09 [e/min] (3.47)

The total manufacturing costs according to formulas of Pavlov£i£ et al. (2004) can be seenin Table 3.7.

page 24

Table 3.8: Manufacturing cost according to Jármai & Farkas (1999)

Case 1 2 3 4 5 6

Cost of welds [e] 249.12 246.35 216.40 141.10 155.42 139.04

Blasting cost [e] 234.32 206.80 207.61 109.88 103.31 103.87

Painting cost [e] 271.55 239.66 240.59 127.34 119.72 120.37

Cutting cost [e] 206.77 166.43 167.20 102.88 99.88 100.63

Total cost [e] 2479 2173 2148 1088 1053 1040

3.2.3 Manufacturing cost by Jármai & Farkas (1999)

The time for edge grinding and cutting is calculated as

Tcut = Θdc

∑Lc(4.5 + 0.4t2

)(3.48)

where Θdc is di�culty factor, Lc is the cut length and, t is the wall thickness.

The time of painting is calculated as

Tpaint = Θdp (agc + atc)As (3.49)

where Θdp is di�culty factor for painting, agc = 3 · 10−6 min/mm2 and atc = 4.15 · 10−6

min/mm2 and As the surface are to be painted [mm2].

The time of surface cleaning is calculated as

Tsurf = ΘdsaspAs (3.50)

where Θds is di�culty factor for surface preparation, asp = 3 · 10−6 min/mm2 and As is thesurface are to be prepared. The activity times need to be multiplied with respective costfactors ki to get the respective costs. In this work following values were used:

kpainting = 0.53 [e/min] (3.51)

ksurf = 1.09 [e/min] (3.52)

kcutting = 0.46 [e/min] (3.53)

Θdc = 2 (3.54)

Θdp = 2 (3.55)

Θds = 2 (3.56)

The resulting cost distribution can be seen in Table 3.8.

3.2.4 Cost analysis comparison

From Tables 3.6�3.8 it can be seen that the total costs as well as the cost distribution aresomewhat di�erent when calculated with di�erent methods. Also Figure 3.2 illustrates thedi�erence when considering S355 truss at span of 36 m. In this work default values proposed

page 25

Figure 3.2: The cost distribution of S355 truss at span of 36 m

in the articles or other references were used with Finnish labour cost values assuming thatwould result in a fair comparison. Still, di�erences in results were rather large.

Haapios formulas give very small blasting cost in comparison to other references. Accordingto Jármai & Farkas � on the other hand � the welding cost is very high. As discussed earlier,this is due to estimation in preparation time.

Also cutting costs vary quite substantially. Partly this is due to assumptions in cuttingtechnology. Haapio assumes sawing where as other use �ame cutting.

Other thing that results in di�erences in costs is the vast amount of parameters connectedto each model. Some of them have a dramatic impact and therefore attention should bedevoted �nding the correct values when applying the methods as design tools.


4 Fire design

The truss is checked using Eurocode formulas after 30 and 60 minutes of ISO standard �rewhere gas temperature follows equation

Tgas = T0 + 345 log10 (8t+ 1) (4.1)

The truss is protected with �re intumescent paint NULLIFIRE S607 and steel temperaturesare calculated as speci�ed in the certi�cation TRY (2008). The paint is suitable for theclimate class C1 and for R15-R60 resistances in standard ISO �re. The paint thickness canbe in the range 200 - 1500 µm and the section factor Am/V : 65 - 300 1/m. This means fortubes the wall thickness range 3.33 - 15.38 mm.

The steel temperature change ∆Ts at the time interval ∆t = 5 s is following TRY (2008):

∆Ts =λ′d

d′csρs

AmV

′(Tgas − Ts)∆t (4.2)

where

• λ′d is the modi�ed thermal conductivity of the paint;

• d′ is the modi�ed paint thickness;

• cs is the thermal capacity of steel = 600 J/kgK;

• ρs is the density of steel = 7850 kg/m3;

• AmV

′is the modi�ed section factor;

• Tgas is the gas temperature.

The modi�ed paint thickness for tubes is:

d′ =d1

0.7895 + d1331.4(4.3)

where d1 is the original paint thickness in meters. The modi�ed section factor is:

AmV

′=AmV

(1.243− 1.321 · 10−3AmV

) (4.4)

The modi�ed thermal conductivity is given in Table 4.1.

Steel speci�c heat is supposed constant, ca = 600 J/(kgK).

page 27

Table 4.1: Modi�ed thermal conductivity of NULLIFIRE S607 with tubes.

Temperatureof �re paint(Tgas−Ts)/2 [

◦C]

Modi�ed thermalconductivity ofpaint [W/m ◦C]

20 0.0276

350 0.0276

375 0.0242

400 0.02

425 0.0157

450 0.0109

475 0.00839

500 0.00748

525 0.00752

550 0.00807

575 0.00891

600 0.00961

625 0.0102

650 0.0108

675 0.0118

700 0.013

725 0.014

750 0.0166

775 0.0188

800 0.0187

825 0.0109

850 0.00615

page 28

Figure 4.1: Reduction factors for yield strength and Young's modulus for carbon steel at elevatedtemperatures

In �re the material properties deteriorate as the temperature rises according to Figure 4.1.

In �re member resistance is checked by

Nfi,Ed

χfiAky,θfyγM,fi

+kyMy,fi,Ed

Wpl,yky,θfyγM,fi

≤ 1 (4.5)

where Nfi,Ed is the design axial force in �re, χfi buckling reduction factor in �re, ky is theinteraction factor, My,fi,Ed is the design moment in �re and γM,fi is the partial factor formaterial in �re.

Reduction factor χfi is calculated as

χfi =1

φθ +√φ2θ − λ̄2θ

(4.6)

φθ =1

2

[1 + αλ̄θ + λ̄2θ

](4.7)

α = 0.65

√235

fy(4.8)

λ̄θ = λ̄

√ky,θkE,θ

(4.9)

Interaction factor ky is calculated as

ky = 1− µyNfi,Ed

Ny,b,fi,t,Rd

(4.10)

µy = (2βM,y − 5) λ̄y,θ + 0.44βM,y ≤ 0.8 (4.11)

page 29

Figure 4.2: Equivalent uniform moment factors

page 30

Table 4.2: Truss member sizes when subjected to 30 minute �re

Case 1 2 3 4 5 6

Top chord 200x10 180x10 180x10 140x8 120x10 120x10


1st brace 60x4 60x4 60x5 50x3 40x4 40x3

2nd brace 110x4 70x4 80x5 50x3 80x4 80x3

3rd brace 90x4 90x4 80x5 70x3 60x4 60x4

4th brace 70x4 70x4 70x5 50x3 70x4 70x3

5th brace 140x5 110x5 110x4 80x4 90x4 80x4

6th brace 90x4 80x4 110x4 70x3 90x4 50x4

7th brace 120x8 150x6 140x6 100x6 80x6 90x6

8th brace 150x8 150x5 150x6 120x6 100x6 80x6

Intumescent paint [µm] 500 600 500 600 500 600

where βM,y is acquired from table in Figure 4.2.

In �re the cross section classi�cation is similar to ambient temperature but ε is updated asthe material properties deteriorate:

εfi =

√kE,θky,θ

ε =

√kE,θky,θ

√235

fy(4.12)

The minimal required intumescent paint thickness was calculated for all the six trussesand it was found that in some trusses cross section class constraint was violated aftervery short time of �re. Therefore, a short optimization run was performed to �nd out themost a�ordable trusses safe also in 30 or 60 minutes of �re. Fire intumescent paintingcost can be estimated by for example the method proposed by Haapio. The problem isthat rather detailed data about the painting procedure would be needed. The researchersdid not know of references including the data and therefore a rather coarse unit cost ofkint.paint = 20e/mm/m2 was supposed. The total cost of intumescent painting can then becalculated simply by

Cfire.paint = dint.paintkint.paintAs (4.13)

where dint.paint is the thickness of applied �re intumescent paint coating [mm] and As thesurface are to be painted [m2].

The member sizes of the trusses where also �re design was performed are shown in Ta-bles 4.2�4.3. The respective structural mass and costs can be seen in Tables 4.4�4.5.

It can be seen that weight of the trusses is higher than with only ambient temperatureanalysis. This is due to cross-section class requirement rule out some pro�les in whichthe ratio of h/t is high. Moreover, the section factor Am/V is now with tubular pro�lesapproximately 1/t which means that the thinner the wall of a pro�le, the faster it heats,thus the most thin-walled options cannot be used. At 30 minutes �re the weight gain isquite small but at 60 minutes �re it is over 10 %. The intumescent paint cost represents13 to 17 % of the total cost in R30 cases and 29 to 31 % in R60 cases. The total cost was

page 31

Table 4.3: Truss member sizes when subjected to 60 minute �re

Case 1 2 3 4 5 6

Top chord 200x10 180x10 180x10 150x8 120x10 120x10


1st brace 60x5 80x6 80x6 50x5 90x4 90x4

2nd brace 120x5 80x6 80x6 60x5 50x4 50x4

3rd brace 80x5 80x6 80x6 90x5 60x4 60x4

4th brace 110x5 150x6 150x6 60x5 90x4 90x4

5th brace 100x5 100x6 100x6 80x5 90x4 90x4

6th brace 80x6 80x6 80x6 90x5 70x5 70x5

7th brace 150x8 120x8 120x8 140x8 120x8 120x8

8th brace 160x8 150x8 150x8 140x8 120x8 120x8

Intumescent paint [µm] 1500 1400 1400 1400 1500 1500

Table 4.4: Truss cost when subjected to 30 minute �re

Case 1 2 3 4 5 6

Weight [kg] 1980.0 1707.9 1741.7 812.6 785.4 756.8

Material cost [e] 1584.0 1366.3 1393.4 650.1 628.3 605.5



Cost of welding [e] 122.06 140.03 93.56 49.23 98.08 45.06

Blasting cost [e] 21.94 22.01 22.01 14.70 14.83 14.84

Painting cost [e] 150.18 144.12 144.99 75.62 67.37 65.40

Sawing cost [e] 101.97 103.47 102.45 92.70 94.62 92.29

Intumescent painting cost [e] 329.07 381.17 319.73 191.51 142.92 165.84

Total cost [e] 2340.13 2188.10 2107.05 1101.05 1075.15 1017.93

Table 4.5: Truss cost when subjected to 60 minute �re

Case 1 2 3 4 5 6

Weight [kg] 2213.3 1962.3 1962.3 998.7 951.7 951.7

Material cost [e] 1770.7 1569.8 1569.8 799.0 761.4 761.4



Cost of welding [e] 152.55 295.81 166.39 119.23 171.01 96.19

Blasting cost [e] 21.91 22.03 22.03 14.58 14.76 14.76

Painting cost [e] 153.34 143.30 143.30 85.01 73.01 73.01

Sawing cost [e] 103.69 106.10 103.94 97.17 97.64 96.03

Intumescent painting cost [e] 1009.90 883.90 883.90 505.56 469.34 469.3

Total cost [e] 3242.99 3051.92 2920.34 1645.90 1614.32 1537.90

page 32

from 22 to 30 % higher than in ambient tempereture when designed for R30 and from 69to 94 % higher for R60.

In elevated temperature the weld material loses its properties faster than the steel in themembers it connects. This results in situation that larger welds are required. This extracost was not considered in this work.


5 Conclusions

As seen in the examples the welding and other costs of a warren type truss can be approx-imated with many methods available in the literature. All of the methods include certainassumptions and need typically many parameters related to manufacturing technologiesused. In this work default values proposed in the articles or other work were used withFinnish labour cost values. Still, di�erences in results were rather large. This implies thatthe cost approximation tools should be used with care.

The use of S420 instead of S355 resulted in 5 to 15 % material savings in the examplesshown in this work. In hybrid designs material saving are close to S420. When consideringmanufacturing costs 4 to 13 % savings were found. When including �re design 6 to 10 %savings were found. Adding �re constraints resulted in 22 to 30 % higher total costs thanin ambient tempereture when designed for R30 and from 69 to 94 % higher when designingfor R60. The hybrid designs seem a little less costly than trusses made of only S420 eventhough the latter weighs a little less. By looking at the tables the cost di�erence comesmostly from the welds.


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Documents

Tubular Truss Design Using Steel Grades S355 and S420