Tubular Truss Design Using Steel Grades S355 and S420

Markku Heinisuo, Teemu Tiainen and Timo Jokinen

Tubular truss design using steel grades S355 and S420

Version Complete Rev 1

Date 1.10.2013 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 dierent 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

Tubular truss design using steel grades S355 and S420

page 2

1 Introduction Welded tubular roof trusses are widely used in buildings. This kind of roof structure has shown its large potential due to its nice appearance and eective load bearing and economical 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 dierent steel grades, especially Ruukki's double grade S355/S420. Truss manufacturing including sawing, blasting, painting, material and especially welding costs are calculated using three methods presented in the literature.

Tubular truss design using steel grades S355 and S420

page 3

2 Truss resistance Consider a typical Warren-type one span symmetric roof truss shown in Figure 2.1. The truss 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. It is supposed that the structural systems of roof structures above the truss are such that the same loads are acting on all trusses. There are eight braces at both sides of the truss and the joints are located center-to-center 3 or 4.5 m, meaning evenly located joints. The heights of the trusses are 2.4 and 3.5 m measured from the top of the top chord to the bottom of the bottom chord at the mid span. The gap is same 50 mm at each joint. The roof inclination is 1:20 which is suitable for one-layer roong. The characteristic loads are the dead load on the roof including the weight of the truss 1 kN/m2 and the snow load on the roof 2 kN/m2 . The design is done using Eurocodes with Finnish National Annexes. The relevant codes are for the design of members EN 1993-1-1 CEN (2006a) and for the design of joints EN 1993-1-8 CEN (2006b). Only the ultimate limit state is considered. The serviceability limit state (deection limit) is taken into account by pre-chamfer of the truss. The uniform design load qd distributed to the horizontal plane is using Finnish load factors and 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 dierent cases seen in Table 2.1 Table 2.1:

Case Span [m] Chords Braces

1 36 S355 S355

2 36 S420 S420

Truss cases

3 36 S420 S355

4 24 S355 S355

5 24 S420 S420

6 24 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 structural analysis should be generated from the geometrical model of the truss. In this case this means the eccentricities at the joints. The chords are modeled for the structural analysis as continuous beams and the braces are modeled as hinged members following rules of EN 1993-1-8. The structural analysis model consists of members and joints. Local analysis models of joints 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 elements are used. One beam element between is used local joint models which is enough in this analysis. The local joint models are shown in Figure 2.2. The joint location (4.5 m center-to-center) is dened as the horizontal distance from the mid-point of the gap to the next mid-point of the gap along the chords. The rst joint at the top chord is measured from the support. The local analysis models of joints are at the intersections of the mid-lines of braces and connected to the chords by a perpendicular sti short element. Practically the stiness of this eccentricity element is the same as that for HEA600. The cross-section area and the moment of inertia of the braces and chords are those of tubular members. Using these rules the global structural analysis model can be created. After solving the FEM model the stress resultants are available.

page 5

Figure 2.2:

Local analysis model of the truss

Table 2.2:

Case Top Chord Bottom chord 1st Brace 2nd Brace 3rd Brace 4th Brace 5th Brace 6th Brace 7th Brace 8th Brace Mass [kg]

Member sizes of the trusses

1 200x10 180x6 80x3 110x4 90x3 80x3 120x4 90x3 160x6 160x6 1896

2 180x10 160x6 60x3 70x3 90x3 70x3 110x4 80x3 140x5 140x5 1643

3 180x10 160x6 60x3 70x3 90x3 70x3 110x4 90x3 140x5 140x5 1646

4 140x8 140x6 50x3 50x3 70x3 50x3 90x3 60x3 100x4 100x4 758

5 140x8 120x6 50x3 50x3 60x4 50x3 80x3 60x3 100x4 100x4 718

6 140x8 120x6 50x3 50x3 60x4 50x3 90x3 60x3 100x4 100x4 720

2.2 Trusses of dierent steel grades When the steel grade and geometry are xed the engineer should nd out the correct tube sizes. These are typically the ones resulting in the lightest possible design still satisfying all requirements of Eurocodes. After some trials and errors member sizes shown in Table 2.2 were found. The numbering of braces begins from the mid span. The mass is for half of a truss. Ruukki's cold formed square tubes are used. The top chord is chosen to belong to the cross-section class 1 of EN 1993-1-1 due to requirement of EN 1993-1-8 for the knee joint 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 which results in lower structural mass. The hybrid solution and S420 solutions are very close to each 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 model S355 truss is shown in Figure 2.3. The eccentricity elements are present but quite short and thus almost invisible. The eccentricity element of rst joint from the mid span on the bottom chord is seen in Figure 2.4. The moment diagram of the S355 truss can be seen in Figure 2.5. The largest moments are at the upper chord where the distributed loading is present but eccentricity elements cause also bending moment to the bottom chord and in the element nearest to the support the moment is rather large. The eccentricities can be seen in Table 2.3. The numbering starts from the rst joint from the mid span on the bottom chord. As the eccentricity of a K joint can be calculated as (Ongelin & Valkonen 2012)   h1 h2 sin β1 sin β2 h0 + +g − (2.2) e= 2 sin β1 2 sin β2 sin (β1 + β2 ) 2 it can be seen that with two large members are connected to chord a large eccentricity can be 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 three trusses of both spans. The small dierences are due to two factors. Firstly, structure is hyperstatic and the member sizes are dierent. Secondly, the dierent member sizes result in slightly dierent geometry and eccentricities. The deection at service limit state can be seen in Table 2.5. It can be seen that smaller member sizes of higher strength result in slightly higher deection.

page 7

Figure 2.5:

Moment diagram of the S355 truss

Table 2.3:

Case e1 e2 e3 e4 e5 e6 e7

1 30 20 13.7 14.1 24.1 28.4 61.3

Eccentricities at joints

2 13.2 13.7 20.3 16.6 26.9 27.1 56.5

3 13.2 13.7 20.3 16.6 31.2 31.1 56.5

4 11.8 18.2 15.2 22.2 22.9 25.1 37.6

5 22.4 14.1 21.5 18.3 29.4 25.9 48.5

6 22.4 14.1 21.5 22.9 33.7 25.9 48.5

page 8

Axial forces [kN]

Table 2.4:

Case Top chord 1 Top chord 2 Top chord 3 Top chord 4 Bottom chord Bottom chord Bottom chord Bottom chord 1st brace 2nd brace 3rd brace 4th brace 5th brace 6th brace 7th brace 8th brace

1 2 3 4

Table 2.5:

Axial forces at elements

1 2 3 4 5 6 -1235.2 -1228.2 -1228.2 -803.2 -799.9 -799.9 -1156.9 -1150.3 -1150.5 -751.0 -747.5 -747.5 -891.6 -885.3 -884.9 -577.2 -574.5 -574.8 -354.0 -351.6 -351.7 -229.4 -226.7 -226.7 1231.0 1224.2 1224.2 801.2 798.0 797.9 1236.0 1228.9 1228.9 803.0 799.5 799.6 1069.6 1062.7 1062.9 692.8 689.9 689.7 680.5 676.4 676.7 440.6 437.5 437.5 4.8 4.6 4.5 1.9 1.9 1.9 -4.0 -3.7 -3.7 -1.2 -0.9 -1.1 -137.6 -137.9 -137.6 -92.8 -92.9 -92.9 139.1 140.2 140.2 94.5 94.1 94.7 -294.2 -294.8 -295.7 -196.3 -196.1 -196.3 323.8 322.4 322.6 214.1 216.3 216.8 -516.2 -514.4 -514.8 -339.7 -341.5 -341.5 525.5 523.8 523.9 346.2 344.6 344.5

Deection at the mid span of the trusses

Case 1 2 3 4 5 6 Maximum deection 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 moment and 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 γM 0 = γM 1 = 1.0 Following Finnish NA and the imperfection factor in buckling is α = 0.49. The factor Cm y = 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 χy Afy γM 1

+

kyy My,Ed Wpl,y fy γM 1

≤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; • γM 1 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 axial force and the moment. The interaction factor kyy is in this case for the top chord (plastic cross-sectional properties):

kyy = Cmy min[1 + (λ¯y − 0.2)ny ; 1 + 0.8ny ]

(2.4)

where factor Cmy is

Cmy = 0.1 + 0.8 and

s

Mspan Msupport

(2.5)

λ¯y =

Afy Ncr,y

(2.6)

Ncr,y =

π 2 EIy L2cr,y

(2.7)

and the buckling load Ncr,y is:

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 the corner radius of the prole shall be taken into account. The radiuses are dened following the 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 the corner is 2 times the wall thickness.

page 10 Table 2.6:

Utilization ratios from member resistance checks

Case Top chord Bottom chord 1st brace 2nd brace 3rd brace 4th brace 5th brace 6th brace 7th brace 8th brace

1 0.85 0.92 0.01 0.01 0.96 0.43 0.77 0.89 0.54 0.41

2 0.93 0.89 0.02 0.05 0.92 0.43 0.87 0.85 0.72 0.47

3 0.93 0.89 0.02 0.05 0.96 0.51 0.94 0.89 0.80 0.56

4 0.99 0.80 0.01 0.02 0.72 0.49 0.84 0.91 0.90 0.65

5 0.86 0.85 0.01 0.02 0.81 0.41 0.99 0.78 0.82 0.55

6 0.86 0.85 0.01 0.02 0.85 0.49 0.85 0.92 0.91 0.65

• If the wall thickness is larger than 10 mm then the outer radius is 3 times the wall thickness. • In between it is 2.5 times the wall thickness. The eect of shear to resistances of the members is checked using EN 1993-1-1 clauses 6.2.6 and 6.2.8. Table 2.6 presents the utilities of the members for trusses using the stress resultants acquired in nite element analysis and Eqs. (2.3)  (2.7). Due to symmetry only the values for the halves of the trusses are shown. As the nite element analysis forces and moments are used the eccetricities are automatically taken into account in chord member analysis. In braces there is no bending as the connections are pinned. This can result in unsafe design but this is taken into account with two factors in the buckling analysis:

• The welded joints have rotational rigidity and therefore buckling length factor is higher than it should • Member length used in the analysis is the element length which is always longer than the actual member It can be seen, that all members are feasible fullling 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. Many requirements deal with the geometrical properties of the joints. Using notations of EN 19931-8, (see also Ongelin & Valkonen 2012, where the requirements are shown with corrections of the standard) the requirements in K-joints are:

page 11

• Angles between braces and chords θi ≥ 30 ◦ ⇒

30 ◦ ≤1 θi

(2.8)

• Cross-section classes of both chords and compressed braces should be 1 or 2; • Geometrical constraints bi ≤ 1, i = 1, 2 b0 β≤1 t1 + t2 g ≥ t1 + t2 ⇒ ≤1 g g 0.5(1 − β) ≥ 0.5(1 − β) ⇒ ≤1 b0 g/b0 g g/b0 ≤ 1.5(1 − β) ⇒ ≤1 b0 1.5(1 − β) hi hi ≤ 35 ⇒ ≤1 ti 35ti h0 h0 ≤ 35 ⇒ ≤1 t0 35t0

(2.9) (2.10) (2.11) (2.12) (2.13) (2.14) (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 fulll these requirements. The resistances of braces at K-joints are:

• Chord face failure: Ni,Rd • Chord shear:

√ 8.9kn fy0 t20 γ β, i = 1, 2 = sin θi

fy0 Av0 Ni,Rd = √ , i = 1, 2 3 sin θi

• Chord face punching shear if β ≤ (1 − 1/γ):   fy0 t0 2hi Ni,Rd = √ + bi + be.p , i = 1, 2 3 sin θi sin θi • Brace failure: Ni,Rd = fyi ti (2hi − 4ti + bi + bef f ), i = 1, 2 The resistance of the chord including the eect of shear in the gap area is: s  2 VEd N0,gap,Rd = (A0 − Av0 )fy0 + Av0 fy0 1 − Vpl,Rd

(2.16)

(2.17)

(2.18)

(2.19)

(2.20)

page 12 Table 2.7:

Case TC - TC TC - 1st TC - 2nd TC - 3rd TC - 4th TC - 5th TC - 6th TC - 7th TC - 8th BC - 1st BC - 2nd BC - 3rd BC - 4th BC - 5th BC - 6th BC - 7th BC - 8th

1 0.71 0.48 0.48 0.48 0.59 0.46 0.71 0.87 0.59 0.85 0.85 0.87 0.87 0.91 0.96 0.78 0.64

Joint check utilization ratios

2 0.78 0.50 0.51 0.51 0.59 0.48 0.73 0.92 0.61 0.90 0.90 0.92 0.92 0.89 0.99 0.87 0.65

3 0.78 0.50 0.51 0.51 0.59 0.49 0.68 0.87 0.61 0.90 0.90 0.92 0.92 0.85 0.90 0.88 0.65

4 0.84 0.57 0.57 0.57 0.77 0.54 1.00 0.88 0.86 0.72 0.72 0.73 0.73 0.76 0.92 0.96 0.93

5 0.78 0.53 0.53 0.53 0.71 0.50 0.85 0.84 0.81 0.80 0.80 0.81 0.81 0.74 0.84 0.88 0.83

6 0.78 0.53 0.53 0.53 0.63 0.50 0.84 0.89 0.81 0.80 0.80 0.81 0.81 0.74 0.89 0.88 0.83

The values for M0,Ed are taken as maximum values at both sides of the joint. The axial force N0,Ed is the axial force from the tension diagonal side. The value for VEd is calculated as maximum of [cos θi Ni,Ed , cos θi+1 Ni+1,Ed ] where θi is the angle between the brace and the chord 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 supposed to act as a T-joint. The top joint of the truss in the mid of the span is checked as a knee joint with a separate brace. These joints are checked using the relevant equations of EN 1993-1-8. 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 corresponding 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 except brace failure (Eq. (2.19)). In the joint failure mechanisms no interaction between chords and 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.

Tubular truss design using steel grades S355 and S420

page 13

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 very detailed feature-based approach in his thesis. Tizani et al. (2006) present a knowledgebased 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 very broad cost calculation model is given by Watson et al. (1996) including all activities from design 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 next section using three dierent 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 following same references. All the costs considered in the tables and gures of this chapter are for half 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 the deformation and rotation capacity of the joint is not shown. In this study full strength welds 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 connected in a truss at end j can be calculated as

Lw,ij = 2bi +

2hi sin αj

(3.1)

page 14 Table 3.1:

Case TC - 1st TC - 2nd TC - 3rd TC - 4th TC - 5th TC - 6th TC - 7th TC - 8th BC - 1st BC - 2nd BC - 3rd BC - 4th BC - 5th BC - 6th BC - 7th BC - 8th

Weld sizes by joint for six trusses.

1 3.33 4.44 3.33 3.33 4.44 3.33 6.66 6.66 3.33 4.44 3.33 3.33 4.44 3.33 6.66 6.66

2 4.44 4.44 4.44 4.44 5.92 4.44 7.40 7.40 4.44 4.44 4.44 4.44 5.92 4.44 7.40 7.40

3 3.33 3.33 3.33 3.33 4.44 3.33 5.55 5.55 3.33 3.33 3.33 3.33 4.44 3.33 5.55 5.55

4 3.33 3.33 3.33 3.33 3.33 3.33 4.44 4.44 3.33 3.33 3.33 3.33 3.33 3.33 4.44 4.44

5 4.44 4.44 5.92 4.44 4.44 4.44 5.92 5.92 4.44 4.44 5.92 4.44 4.44 4.44 5.92 5.92

6 3.33 3.33 4.44 3.33 3.33 3.33 4.44 4.44 3.33 3.33 4.44 3.33 3.33 3.33 4.44 4.44

where hi is the height of the prole in the plane of the truss and bi is the width of the prole. 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, B and C for dierent welding situations can be seen in Table 3.3. Welding cost is calculated by

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

(3.3)

where kweld is the cost factor, fweld is factor contributing to a longer time in case of short welds or dicult positions, Lw is the length of the weld. Welding material cost is calculate by

Cweld,material =

hX

i km,weld,i Mweld,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 is supposed to follow a quadratic function of weld size aw :

Mweld,i (aw ) = Am,w,i a2w + Bm,w,i aw + Cm,w,i

(3.5)

page 15

Table 3.2:

Weld length [mm] joint by joint for six trusses.

Case TC - 1st TC - 2nd TC - 3rd TC - 4th TC - 5th TC - 6th TC - 7th TC - 8th BC - 1st BC - 2nd BC - 3rd BC - 4th BC - 5th BC - 6th BC - 7th BC - 8th

Table 3.3:

1 359 490 411 363 555 416 751 753 352 481 402 356 543 407 733 735

2 269 313 409 317 508 369 657 658 264 307 401 311 496 361 641 642

3 269 313 409 317 508 415 657 658 264 307 401 311 496 406 641 642

4 223 222 317 226 412 275 466 467 219 218 310 221 403 269 455 456

5 223 222 271 225 366 275 465 466 219 218 266 221 359 269 454 455

6 223 222 271 225 411 275 465 466 219 218 266 221 403 269 454 455

Welding time function factors A, B and C for dierent welding situations

Type A B C Automatic submerged arc welding 2.62 1.37 0.09 Stiener 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 literature1 . The values used in the example trusses are

kweld = 1.40 Tweld,extra = 0.3 [min] Tweld = 17.26a2w + 2.9aw + 1.82 [min/m] kweld = 27.68 [e/h] Mweld,electrodes = 1.33a2w + 0.19aw − 0.02 [kg/m] Mweld,power = 6.29a2w − 1.87aw + 0.44 [kWh/m] km,weld,electrodes = 1.4 [e/kg] km,weld,power = 0.11 [e/kg]

(3.6) (3.7) (3.8) (3.9) (3.10) (3.11) (3.12) (3.13)

According to Jármai & Farkas (1999), the welding preparation, assembly and tacking time can be calculated by p Tpat = C1 Θdw κρV (3.14) where C1 is a parameter depending on welding technology (usually 1), Θdw is diculty factor, 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 calculated as X Tw = 1.3 C2i anwi Lwi (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 which as also welding costs were considered. According to Haapio member welding cost is

CW = (TP T aW + TP W W ) (CLW + CEqW + CREW + CSeW ) + kgw (CCW + TP W W CEnW ) [e]

(3.16)

where

• Tacking time TP T aW = 2.86 [min]; • Welding time TP W W =


LW · 0.4988 · a2 − 0.0005 · a + 0.0021 [min] 1000

• Length of the weld LW [mm]; • Weld size a [mm]; • Labour cost CLW = 0.46 e/min (one welder); 1

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

page 17 Table 3.4:

Author

Case Total cost of welds [e] Haapio Cost of weld preparation [e] Cost of welding [e] Total cost of welds [e] Farkas & Jármai Cost of weld preparation [e] Cost of welding [e] Pavlov£i£ Cost of welding [e]

Welding costs

1 111.97 30.95 81.03 249.12 190.03 59.09 47.04

2 126.21 30.95 95.26 246.35 176.88 69.48 50.50

3 84.92 30.95 53.98 216.40 177.03 39.37 34.36

4 54.36 27.20 27.16 141.10 120.18 20.92 20.86

5 77.12 27.20 49.92 155.42 116.97 38.46 30.21

6 55.65 27.20 28.45 139.04 117.13 21.92 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 =

pRE AW i · (1 + i)n [e/min]; aw i · (1 + i)n − 1

• 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

TT a = 1.59 [min]

(3.17)

estimated by Schreve et al. (1999). In this work, the parts are longer than 2000 mm and a larger value TT a = 2.86 [min] (3.18) suggested by Schreve et al. (1999) was adopted. Still for trusses this number is quite small compared to numbers given by Jármai & Farkas (1999). The cost of welding is acquired from the preparation, assembly, tacking and welding times by multiplying it with suitable cost factor. Haapio presents a detailed way of acquiring the cost factor including labour, real estate, equipment, energy costs et cetera whereas Jármai & Farkas leaves the determining cost factor to the reader. In this work cost factor applied with Jármai & Farkas formulas was k = 0.55 e/min. The welding times as functions of weld size proposed by dierent authors can be seen in Figure 3.1. The total welding costs of three trusses using three methods above are given in Table 3.4.

page 18

Figure 3.1:

Table 3.5:

Welding times as function of weld size

Welding cost joint by joint following Haapio (2012)

Case TC - 1st TC - 2nd TC - 3rd TC - 4th TC - 5th TC - 6th TC - 7th TC - 8th BC - 1st BC - 2nd BC - 3rd BC - 4th BC - 5th BC - 6th BC - 7th BC - 8th

1 3.50 5.72 3.72 3.51 6.23 3.74 15.00 15.03 3.47 5.65 3.68 3.48 6.13 3.70 14.68 14.72

2 4.02 4.35 5.10 4.39 8.91 4.79 16.03 16.06 3.98 4.31 5.03 4.34 8.76 4.73 15.70 15.72

3 3.11 3.29 3.71 3.31 5.86 3.74 9.87 9.88 3.08 3.27 3.68 3.29 5.77 3.70 9.68 9.69

4 2.73 2.73 3.12 2.74 3.51 2.95 5.23 4.32 2.72 2.71 3.09 2.73 3.48 2.92 5.15 4.24

5 3.44 3.44 5.35 3.46 4.50 3.82 7.86 6.96 3.41 3.41 5.27 3.43 4.44 3.78 7.72 6.82

6 2.73 2.73 3.80 2.74 3.51 2.94 5.22 4.31 2.71 2.71 3.76 2.72 3.47 2.92 5.14 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 the estimate given by Haapio is very small compared to that of Farkas & Jármai. Still, the latter includes also preparation and assembly to this cost as well. As the dierence is quite remarkable assembly, jig and tacking cost should be further investigated in order for the cost estimation tools to be accurate. Moreover, by including or excluding cost factors a remarkable dierences in total welding cost can be expected. Therefore, the methods should be used carefully using the relevant parameters preferably measured in the workshop where the designed structure will be manufactured.

3.2 Total fabrication cost In this work, total fabrication cost of truss is calculated as sum of dierent cost proportions

CT russ = CM aterial + CW eld + CBlast + CP aint + CSaw

(3.19)

where Ci refers to cost of i subscripts being self-explanatory. It is known that there are other costs related to structures such as transportation and erection costs but they are not considered in this work. The costs related to welding are being discussed in detail in previous section. The other costs are calculated as follows. The material cost for a truss is

CM aterial =

X

ki ρAi Li

(3.20)

where ki is the material cost factor [e/kg] (in this work ki = 0.8 e/kg for both S355 and S420 since Ruukki's double grade steel is considered), ρ is the material density [kg/m3 ], Ai is the cross-sectional are of member i and Li is the length of member i. The sum is taken over all the members in the truss. Other costs are described in the following subsections ordered by the used reference.

3.2.1 Manufacturing cost by Haapio (2012) Member blasting cost is

CB =TP B (CLB + CEqB + CM B + CREB + CSeB + CCB + CEnB ) [e]

(3.21)

where

• Productive time TP B = 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 CM B = 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 =

pRE A i · (1 + i)n = 0.16 [e/min]; aw i · (1 + i)n − 1

• Real estate maintenance pSe = 72 e/m2 a • 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 =((TN S + TP S1 + TP S2 ) (CLS + CEqS + CM S + CRES + CSeS + TP S1 (CCS1 + CEnS )+ TP S2 (CCS2 + CEnS )) [e] where

• Non-productive time TN S = 6.5 + LS /20000 [min]; • Member length LS [mm]; • Productive time for one cut TP Si = h   2 0.0328 · cost θi − 3.1794 ·

t cos θi

Ahi  + [min]; Q + 115.6 Sm

(3.22)

page 21

• Prole height h [mm]; • Prole wall thickness t [mm]; • Sawing angle θi [◦ ]; • Area of horizontal parts of the prole 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 CM S = 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 · TP Si

Ati −1.188 ·



t cos θi

2

+ 188892 ·

t cos θi

 + 4414608

[e/min]; Painting cost supposing Alkyd paint system AK 160/3 - FeSa2 21 is:

CP = TP P (CLP + CREP + CSeP ) + CCP + CDyP [e]

(3.23)

where

• Painting time TP P = (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 );

When considering Ruukki's double grade steel, the material is essentially the same in both cases, thus should be used 3 When considering Ruukki's double grade steel, the material is essentially the same in both cases, thus Sm = 0.8 should be used 2

Q = 6900

page 22 Table 3.6:

Manufacturing cost according to Haapio.

Case 1 2 3 Material cost [e] 1517 1314 1317 Total cost of welds [e] 111.97 126.21 84.92 Blasting cost [e] 21.85 22.02 22.01 Painting cost [e] 162.37 143.53 144.04 Sawing cost [e] 102.20 102.15 100.72 Total cost [e] 1915 1708 1668

4 607 54.36 14.65 79.13 92.45 847

5 575 77.12 14.71 74.94 94.05 836

6 576 55.65 14.70 75.30 93.09 815

• Real estate maintenance cost CSeP = 0.04 e/min; • Paint cost CCP = 3.87 · 10−6 A [e]; • Drying cost CDyP = 0.36Ltruss Wtruss [e]; • Top chord width Wtruss [mm]. Using the values described above, costs seen in Table 3.6 are acquired. After the calculation it was observed that when double grade steel is used, the lower sawing costs of S355 is not realistic. After some testing it was found that this would result in approximately 2 % relative dierence in sawing cost. As sawing cost represents only from 5 to 11 % of total cost, the dierence 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

CSurf acepreparation = ksurf prep Tsurf prep (Lpl + Lblast )

(3.24)

where ksurf prep is the cost factor, Tsurf prep the surface preparation time, Lpl is the member length, 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 [fcut Tcut (tpl )Lc + Tcut.extra ]

(3.26)

cutting material cost as

Ccut.material =

hX

i

km.cut Mcut (tpl ) Lc

and handling as

Ccut.handling = khandling Thandling

(3.27) (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

h i X Cpainting = kpaint Tpaint + km,paint,i Mpaint,i A

(3.29)

where kpaint is labour cost factor, Tpaint time consumption, km,paint paint material cost factor and Mpaint the paint consumption. The following values were used in this work:

Tcut = −0.0015t2pl + 0.421tpl + 1.43 [min/m] Mcut,propan =

0.0t2pl

+ 2.171tpl + 7.87 [l/m]

(3.30) (3.31)

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

(3.32)

Thandling = −4 · 10 m + 0.001m + 3.73 [min] ncut = 4 fcut = 1.03 Tcut,extra = 2.0 [min] kcut = 0.46 [e/min] km,cut,propane = 0.002 [e/l] km,cut,propane = 0.0016 [e/l] khandling = 0.46 [e/min] Tpaint = 7.0 [min/m2 ] kpaint = 0.53 [e/min] Mpaint,i = [0.130.1730.15] [l/m2 ] km,paint,i = [4.53.83.8] [e/l] Lblast = 30 [cm] Tblast = 2.2 [min/m] ksurf.prep = 1.09 [e/min]

(3.33) (3.34) (3.35) (3.36) (3.37) (3.38) (3.39) (3.40) (3.41) (3.42) (3.43) (3.44) (3.45) (3.46) (3.47)

−8

2

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

page 24 Table 3.8:

Manufacturing cost according to Jármai & Farkas (1999)

Case Cost of welds [e] Blasting cost [e] Painting cost [e] Cutting cost [e] Total cost [e]

1 249.12 234.32 271.55 206.77 2479

2 246.35 206.80 239.66 166.43 2173

3 216.40 207.61 240.59 167.20 2148

4 5 6 141.10 155.42 139.04 109.88 103.31 103.87 127.34 119.72 120.37 102.88 99.88 100.63 1088 1053 1040

3.2.3 Manufacturing cost by Jármai & Farkas (1999) The time for edge grinding and cutting is calculated as X
Tcut = Θdc Lc 4.5 + 0.4t2

(3.48)

where Θdc is diculty 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 diculty 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 = Θds asp As

(3.50)

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

kpainting = 0.53 [e/min] ksurf = 1.09 [e/min] kcutting = 0.46 [e/min] Θdc = 2 Θdp = 2 Θds = 2

(3.51) (3.52) (3.53) (3.54) (3.55) (3.56)

The resulting cost distribution can be seen in Table 3.8.

3.2.4 Cost analysis comparison From Tables 3.63.8 it can be seen that the total costs as well as the cost distribution are somewhat dierent when calculated with dierent methods. Also Figure 3.2 illustrates the dierence 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 that would result in a fair comparison. Still, dierences in results were rather large. Haapios formulas give very small blasting cost in comparison to other references. According to 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 cutting technology. Haapio assumes sawing where as other use ame cutting. Other thing that results in dierences in costs is the vast amount of parameters connected to each model. Some of them have a dramatic impact and therefore attention should be devoted nding the correct values when applying the methods as design tools.

Tubular truss design using steel grades S355 and S420

page 26

4 Fire design The truss is checked using Eurocode formulas after 30 and 60 minutes of ISO standard re where gas temperature follows equation

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

(4.1)

The truss is protected with re intumescent paint NULLIFIRE S607 and steel temperatures are calculated as specied in the certication TRY (2008). The paint is suitable for the climate class C1 and for R15-R60 resistances in standard ISO re. The paint thickness can be in the range 200 - 1500 µm and the section factor Am /V : 65 - 300 1/m. This means for tubes 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 =

λ0d Am 0 (Tgas − Ts )∆t d0 cs ρs V

(4.2)

where

• λ0d is the modied thermal conductivity of the paint; • d0 is the modied paint thickness; • cs is the thermal capacity of steel = 600 J/kgK; • ρs is the density of steel = 7850 kg/m3 ; •

Am 0 V

is the modied section factor;

• Tgas is the gas temperature. The modied paint thickness for tubes is:

d0 =

d1 0.7895 + d1 331.4

(4.3)

where d1 is the original paint thickness in meters. The modied section factor is:

Am 0 Am Am = (1.243 − 1.321 · 10−3 ) V V V The modied thermal conductivity is given in Table 4.1. Steel specic heat is supposed constant, ca = 600 J/(kgK).

(4.4)

page 27

Table 4.1:

Modied thermal conductivity of NULLIFIRE S607 with tubes. Temperature of re paint (Tgas − Ts )/2 [ ◦ C] 20 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800 825 850

Modied thermal conductivity of paint [W/m ◦ C] 0.0276 0.0276 0.0242 0.02 0.0157 0.0109 0.00839 0.00748 0.00752 0.00807 0.00891 0.00961 0.0102 0.0108 0.0118 0.013 0.014 0.0166 0.0188 0.0187 0.0109 0.00615

page 28

Figure 4.1:

Reduction factors for yield strength and Young's modulus for carbon steel at elevated temperatures

In re the material properties deteriorate as the temperature rises according to Figure 4.1. In re member resistance is checked by

Nf i,Ed χf i Aky,θ fy γM,f i

+

ky My,f i,Ed Wpl,y ky,θ fy γM,f i

≤1

(4.5)

where Nf i,Ed is the design axial force in re, χf i buckling reduction factor in re, ky is the interaction factor, My,f i,Ed is the design moment in re and γM,f i is the partial factor for material in re. Reduction factor χf i is calculated as

1 p ¯2 φθ + φ2θ − λ θ  1 ¯θ + λ ¯2 φθ = 1 + αλ θ 2 s 235 α = 0.65 fy s ¯θ = λ ¯ ky,θ λ kE,θ

χf i =

(4.6) (4.7) (4.8) (4.9)

Interaction factor ky is calculated as

µy Nf i,Ed Ny,b,f i,t,Rd ¯ y,θ + 0.44βM,y ≤ 0.8 µy = (2βM,y − 5) λ ky = 1 −

(4.10) (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 Bottom chord 150x8 160x6 160x6 120x8 100x8 100x8 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 classication is similar to ambient temperature but  is updated as the material properties deteriorate: s s s kE,θ kE,θ 235 f i = = (4.12) ky,θ ky,θ fy The minimal required intumescent paint thickness was calculated for all the six trusses and it was found that in some trusses cross section class constraint was violated after very short time of re. Therefore, a short optimization run was performed to nd out the most aordable trusses safe also in 30 or 60 minutes of re. Fire intumescent painting cost can be estimated by for example the method proposed by Haapio. The problem is that rather detailed data about the painting procedure would be needed. The researchers did not know of references including the data and therefore a rather coarse unit cost of kint.paint = 20e/mm/m2 was supposed. The total cost of intumescent painting can then be calculated simply by Cf ire.paint = dint.paint kint.paint As (4.13) where dint.paint is the thickness of applied re intumescent paint coating [mm] and As the surface are to be painted [m2 ]. The member sizes of the trusses where also re design was performed are shown in Tables 4.24.3. The respective structural mass and costs can be seen in Tables 4.44.5. It can be seen that weight of the trusses is higher than with only ambient temperature analysis. This is due to cross-section class requirement rule out some proles in which the ratio of h/t is high. Moreover, the section factor Am /V is now with tubular proles approximately 1/t which means that the thinner the wall of a prole, the faster it heats, thus the most thin-walled options cannot be used. At 30 minutes re the weight gain is quite small but at 60 minutes re it is over 10 %. The intumescent paint cost represents 13 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 Bottom chord 160x10 150x8 150x8 140x8 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 Total cost of welds [e] 153.00 170.98 124.51 76.43 127.11 74.09 Cost of weld preparation [e] 30.95 30.95 30.95 27.20 29.03 29.03 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 Total cost of welds [e] 183.49 326.76 197.34 144.61 198.21 123.39 Cost of weld preparation [e] 30.95 30.95 30.95 25.37 27.20 27.20 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 69 to 94 % higher for R60. In elevated temperature the weld material loses its properties faster than the steel in the members it connects. This results in situation that larger welds are required. This extra cost was not considered in this work.

Tubular truss design using steel grades S355 and S420

page 33

5 Conclusions As seen in the examples the welding and other costs of a warren type truss can be approximated with many methods available in the literature. All of the methods include certain assumptions and need typically many parameters related to manufacturing technologies used. In this work default values proposed in the articles or other work were used with Finnish labour cost values. Still, dierences in results were rather large. This implies that the cost approximation tools should be used with care. The use of S420 instead of S355 resulted in 5 to 15 % material savings in the examples shown in this work. In hybrid designs material saving are close to S420. When considering manufacturing 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 than in ambient tempereture when designed for R30 and from 69 to 94 % higher when designing for R60. The hybrid designs seem a little less costly than trusses made of only S420 even though the latter weighs a little less. By looking at the tables the cost dierence comes mostly from the welds.

Tubular truss design using steel grades S355 and S420

page 34

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rules for buildings.

CEN (2006b), EN-1993-1-8. Eurocode 3: Design of steel structures. Part 1-8: Design of joints. Czesany, G. (1972), Kostenrechnung beim Schweiÿen, Vulkan Verlag Dr. W. Classen. EN 10219-2 (2006), Cold formed welded structural hollow sections of non-alloy and ne grain steels. Part 2: Tolerances, dimensions and sectional properties, CEN. Haapio, J. (2012), Feature-Based Costing Method for Skeletal Steel Structures based on the Process Approach, Phd thesis, Tampere University of Technology. Jalkanen, J. (2007), Tubular Truss Optimization Using Heuristic Algorithms, Phd thesis, Tampere University of Technology. Jármai, K. & Farkas, J. (1999), `Cost calculation and optimisation of welded steel structures', Journal of Constructional Steel Research 50, 115135. Klan²ek, U. & Kravanja, S. (2006a), `Cost estimation, optimization and competitiveness of dierent composite oor systems - part 1: Self-manufacturing cost estimation of composite and steel structures', Journal of Constructional Steel Research 62, 434448. Klan²ek, U. & Kravanja, S. (2006b), `Cost estimation, optimization and competitiveness of dierent composite oor systems - part 2: Optimization based competitiveness between the composite i beams, channel-section and hollow-section trusses', Journal of Constructional Steel Research 62, 449462. Ongelin, P. & Valkonen, I. (2012), Rakenneputket, Rautaruukki Oyj. in Finnish. Pavlov£i£, L., Krajnc, A. & Beg, D. (2004), `Cost function analysis in the structural optimization of steel frames', Structural and Multidisciplinary Optimization 28, 286295. Polanjar, A. (1991), Handbook for planning and managing the manufacturing processes (in Slovenian), Faculty of mechanical engineering, University of Maribor. Schreve, K., Schuster, H. R. & Basson, A. H. (1999), Manufacturing cost estimation during design of fabricated parts, in `Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering manufacture'. Tizani, W. M. K., Nethercot, D., Davies, G., Smith, N. & McCarthy, T. (2006), `Object-oriented fabrication cost model for the economic appraisal of tubular truss design', Advances in Engineering Software 27, 1120. TRY (2008), NULLIFIRE S607-palosuojamaali putki- ja I-proilien, sekä WQ-palkin alalaipan palosuojaukseen. Varmennettu käyttöseloste. in Finnish. Watson, K. B., Dallas, S., Van der Kreek, N. & Main, T. (1996), `Costing of steelwork from feasibility through to completion', Journal of Australian Steel Construction 30, 29.