As-Design of Column Splice

Document Ref: SX018a-EN-EU Sheet 1 of 21

Title

Example: Column splice - non-bearing splice

Eurocode Ref EN 1993-1-8, EN1993-1-1Made by Edurne Nunez Date Mar 2005

CALCULATION SHEET

Checked by Abdul Malik Date Mar 2006


This example presents a method for verifying the adequacy of a non-bearing column splice using bolted flange and web cover plates. The design forces on the cover plates are determined from the axial load on the column, the nominal moments and shear forces. The design resistances of the cover plates and the bolt groups are then determined. The example also demonstrates the calculation of the tensile tying resistance of the splice for structural integrity.

1 Column Splice Design Resistance This example presents full details and procedures for each of the possible design checks; it also includes diagrams both for the notations and for the dimensions. In practice the presentation would normally be much shorter.

Design procedures are in accordance with guidance in SN023.

Table 1 gives the Section number in this example where the procedure for calculating the design resistance is presented. In Section 13, a summary of the values for design resistances and critical mode of failure are given.

SN023

Table 1: Design resistance of a non-bearing column splice

Mode of failure Section Design Resistance

Flange cover plate compression tension

7 NRd,fp,c

NRd,fp,t

Flange cover plate bolt group 8 VRd,fp

Web cover plate 9 NRd,wp,c

Web cover plate bolt group 10 VRd,wp

Column web bolt group 11 VRd,w

Structural integrity of the splice (under tying force)

12 NRd,u

2 Column Splice Details The details of the column splice are based on guidance for initial sizing given in SN024 and are shown in the Figures below.

The hole positions for bolts comply with minimum and maximum spacing, end and edge distance requirements of §3.5 of EN1993-1-8.

EN1993-1-8 §3.5

Example: Column splice - non-bearing spliceC

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http://www.access-steel.com/discovery/linklookup.aspx?id=SN023

http://www.access-steel.com/discovery/linklookup.aspx?id=EC203


SX018a-EN-EU Sheet 2 of 21 Document Ref:

Title

Example: Column splice - non-bearing splice CALCULATION SHEET



Column splice - Details

1,fp

1,fp

1,fp

1,fp

1,fp

1,fp

1,fp

fp

2,fp

fp

2,fp 2,fpb

p

p

p

p

p

p

p

e

pe e

h

= 8

= 8

n

n

fp

fp

jL

jL

gv 1,fp,j

1,wp

1,wp

1,wp

2,wp 2,wpwp

fp

wp

e

p

p

p

e ep

b

tt

t

h

2,wp

e 1,w

gv

n

n

wp= 4

= 4wp

f,uc

f,lc

t pae 2,w

1,wp,j


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Title




n

n

fp

fp

n

n

= 8

= 8

= 4

= 4

wp

wp

690

80

80

80

80

80

80

80

80

12.525

1050

1912

350

50

50

110

15055 55260

40

110

40

80150

35 35

85

240

240

10

HE 300 B

HE 260 A


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Title



CALCULATION SHEET


3 Main joint data Configuration Non bearing column splice

Upper column HE 260A, S355

Lower column HE 300B, S355

Type of connection Flange and web cover plates, S355

Bolts M24, class 8.8

(Category A: Bearing type, Non-preloaded)

3.1 Upper Column HE 260A, S355 Depth huc = 250 mm

Width buc = 260 mm

Thickness of the web tw,uc = 7,5 mm

Thickness of the flange tf,uc = 12,5 mm

Fillet radius ruc = 24 mm

Area Auc = 86,80 cm2

Area of web Aw,uc = 21,80 cm2

Area of flange Af,uc = 32,50 cm2

Yield strength fy,uc = 355 N/mm2

Ultimate tensile strength fu,uc = 510 N/mm2

Number of bolts between one flange cover plate and upper column nfp = 8

Number of bolts between web cover plate and upper column nwp= 4

Direction of load transfer (1)

End of upper column to first bolt row on column web el,w = 50 mm

Pitch between bolt rows on column web pl,w =p1,wp= 80 mm

Direction perpendicular to load transfer (2)

Edge of upper column to first bolt line on the column web e2,w= 85 mm

Pitch between bolt lines on column web p2,w =p2,wp= 80 mm


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Title



CALCULATION SHEET


3.2 Lower Column HE 300B, S355 Depth hlc = 300 mm

Width blc = 300 mm

Thickness of the web tw,lc = 11 mm

Thickness of the flange tf,lc = 19 mm

Fillet radius rlc = 27 mm

Area Alc = 149,10 cm2

Area of web Aw,lc = 35,10 cm2

Area of flange Af,lc = 57,00 cm2

Yield strength fy,lc = 355 N/mm2

Ultimate tensile strength fu,lc = 510 N/mm2

3.3 Flange cover plate 260 × 12 × 690, S355 Vertical gap between column ends gv = 10 mm

Height hfp = 690 mm

Width bfp = 260 mm

Thickness tfp = 12 mm

Number of bolts between one flange cover plate and upper column nfp = 8


Plate edge to first bolt row el,fp = 50 mm

Pitch between bolt rows pl,fp = 80 mm

Pitch between bolt rows (across joint) pl,fp.j = 110 mm


Plate edge to first bolt line e2,fp = 55 mm

Pitch between bolt lines p2,fp = 150 mm

Yield strength fy,p = 355 N/mm2

Ultimate tensile strength fu,p = 510 N/mm2


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CALCULATION SHEET


3.4 Flange packs 250 × 25 × 340, S355 Vertical gap between column ends gv = 10 mm

Depth hfp,pa = 340 mm

Width bfp,pa = 250 mm

Thickness tpa = 25 mm

3.5 Web cover plate 150 × 8 × 350, S355 Vertical gap between column ends gv = 10 mm

Height hwp = 350 mm

Width bwp = 150 mm

Thickness twp = 8 mm

Number of bolts between web cover plate and upper column nwp = 4


Plate edge to first bolt row el,wp = 40 mm

Pitch between bolt rows pl,wp = 80 mm

Pitch between bolt rows (across joint) pl,wp,j = 110 mm


Plate edge to first bolt line e2,wp = 35 mm

Pitch between bolt lines p2,wp = 80 mm

Yield strength fy,p = 355 N/mm2

Ultimate tensile strength fu,p = 510 N/mm2

3.6 Web packs 150 × 2 × 170, S355 Vertical gap between column ends gv = 10 mm

Height hwp,pa = 170 mm

Width bwp,pa = 150 mm

Thickness twp,pa = 2 mm


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Title



CALCULATION SHEET


3.7 Bolts M24, class 8.8 (Category A: Bearing type, Non-preloaded)

Tensile stress area As = 353 mm2

Diameter of the shank d = 24 mm

Diameter of the holes d0 = 26 mm

Yield strength fyb = 640 N/mm2

Ultimate tensile strength fub = 800 N/mm2

4 Partial safety factors γMO = 1,0

γM1 = 1,0

γM2 = 1,25 (for design resistance at ULS)

γM,u = 1,1 (for tying resistance at ULS)

5 Design forces and moments (at ULS) Compression force due to permanent load NEd,G = 825 kN

Compression force due to variable load NEd,Q = 942 kN

Total design force NEd = 1767 kN

Nominal design bending moment

(due to permanent and variable loads) MEd = 15 kNm

Shear force (due to permanent and variable loads) VEd = 8 kN

Tying force NEd,u = 400 kN


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6 Design model For maximum design compression force in the flange cover plates and maximum compression in the web cover plates (see Figure 6.1):

• Assumed that all the beams are subjected to permanent and variable actions in combination.

Ed

Ed

Ed

N

V

M

Ed,fp,cEdN

V

Ed,wpN2

NEd = NEd,G + NEd,Q

VEd = VEd,G + VEd,Q

MEd is the nominal design moment (see SN005) (due to permanent and variable actions) in the upper column, i.e. at the floor level immediately below the splice.

= MEd,G + MEd,Q

For evaluation of NEd,fp,c and NEd,wp, see Sections 7 and 9 respectively.

Figure 6.1 For maximum compression in flange and web cover plates

For maximum design tension force in the flange cover plates ( Figure 6.2):

• For nominal design moment MEd, assume that the beams causing the moment are subject to permanent and variable actions in combination

• For design axial force in the column NEd,G, assume that all the beams are subject to permanent actions only

Ed

Ed

N

V

M

N Ed,fp,t

Ed,G

NEd,G is the axial force in the column due to permanent action on all the beams

VEd = VEd,G + VEd,Q

MEd is the nominal design moment (see SN005) (due to permanent and variable actions) in the upper column, i.e. at the floor level immediately below the splice.

= MEd,G + MEd,Q

For evaluation of NEd,fp,t, see Section 7

Figure 6.2 For maximum tension in flange cover plates


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Title




7 Flange cover plate NEd,fp,c ≤ NRd,fp,c (1) (For compression in flange cover plate)

NEd,fp,t ≤ NRd,fp,t (2) (For tension in flange cover plate)

Design axial forces

The maximum compressive design force on the flange cover plate (NEd,fp,c) may be calculated from:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++=

uc

ucf,QEd,GEd,

uc

Edcfp,Ed, A

ANN

hMN

∴ ( ) kN 71980,86

32,5042982510260

153cfp,Ed, =⎟

⎠

⎞⎜⎝

⎛×++×

= −N

The maximum tensile design force on the flange cover plate (NEd,fp,t) may be calculated from:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

uc

ucf,GEd,

uc

Edtfp,Ed, A

AN

hMN

∴ kN 25180,86

32,5082510260

153tfp,Ed, −=⎟

⎠

⎞⎜⎝

⎛×−×

= −N

Note: Since NEd,fp,t is less than zero, there is no tensile force on the flange cover plate and check (2) for tension in the flange cover plate is not required.

SN023

Design resistance The design resistance of the flange cover plate in compression (NRd,fp,c) may be calculated from:

M0

py,fpcfp,Rd, γ

fAN = if p1,fp,j /tfp ≤ 9ε (see note 2 in Table 3.3 of EN1993-1-8)

M1

py,fpfpRd,b,cfp,Rd, γ

fANN

χ== if p1,fp,j /tfp > 9ε

2fpfpfp mm 312012260 =×=×= tbA

p1,fp,j /tfp = 110/12 = 9.2 which is greater than 9ε

EN1993-1-1 §6.2.4(2)

EN1993-1-1 §6.3.1.1(3)


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Title




For Lcr = 0,6 p1,fp,j and using buckling curve c, χ = 1,0

∴ kN 1108100,1

35531200,1 3cfp,Rd, =×

××= −N

EN1993-1-1 §6.3.1.2

Design check

Since NEd,fp,c < NRd,fp,c (719 kN < 1108 kN), the design axial resistance of the flange cover plate is adequate.

8 Flange cover plate bolt group

fpRd,cfp,Ed, VN ≤

Design axial force The design axial force on the flange cover plate is:

kN 719cfp,Ed, =N (see section 7)

SN023

Design resistances The design resistance of the bolt group for Category A bolts (bearing type):

∑= Rdb,fpRd, FV ( )maxRdb,Rdv,if FF ≥

minRdb,fp )(Fn= maxRdb,Rdv,minRdb, )()(if FFF <≤

Rdv,fpFn= ( ) Rdv,minRdb,if FF >

EN1993-1-8 §3.7

The design bearing resistance of a single bolt on the flange cover plate (Fb,Rd) is given by:

M2

fppu,b1Rdb, γ

α tdfkF =

where:

⎟⎟⎠

⎞⎜⎜⎝

⎛= 01;;

pu,

ubdb ,

ff

αα

⎟⎟⎠

⎞⎜⎜⎝

⎛−−= 52;71417182min

0

fp2,

0

fp2,1 ,,

dp

,;,d

e,k


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Title




where for the end bolts:

64,0263

503 0

fp1,d =

×==

de

α

and for the inner bolts:

78,041

26380

41

3 0

fp1,d =−

×=−=

dp

α

57,1

510800

pu,

ub ==ff

Hence:

( 64,00,1;57,1;64,0minb == )α for end bolts and

( ) 78,00,1;57,1;78,0minb ==α for inner bolts.

22,47,1

26558,27,1

8,2

0

fp2, =−×

=−de

38,67,126

1504,17,14,1

0

fp2, =−×

=−dp

∴ ( ) 5,25,2;38,6;22,4min1 ==k

Hence:

kN 1881025,1

122451064,05,2)( 3minRdb, =×

××××= −F for end bolts, and

kN 2291025,1

122451078,05,2)( 3maxRdb, =×

××××= −F for inner bolts.

The design shear resistance of a single bolt (Fv,Rd) is given by:

M2

subvpRdv, γ

αβ AfF =

where:

mm 25pa =t

mm 83

243

==d

EN1993-1-8 Table 3.4


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Title




Since tpa > d/3, the reduction factor should be applied.

( ) ( ) 81,0253248

24938

9

pap =

×+××

=+

=td

dβ

25,1M2 =γ for shear resistance

6,0v =α for class 8.8 bolts

EN1993-1-8 §3.6.1(12)

2s mm 353=A

∴ kN 1101025,1

3538006,081,0 3Rdv, =×

×××= −F

Since Fv,Rd < (Fb,Rd)min i.e 110 kN < 188 kN

1108Rdv,fpfpRd, ×== FnV

∴ kN 880fpRd, =V

Design check Since NEd,fp,c < VRd,fp (719 kN < 880 kN), the design resistance of the flange cover plate bolt group is adequate.

9 Web cover plate

cwp,Rd,wpEd, NN ≤

Design axial force The compressive design force on one web cover plate (NEd,wp) may be calculated from:

uc

ucw,EdwpEd, 2A

ANN =

∴ kN 22280,862

80,211767wpEd, =

××

=N

SN023


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Title




Design resistance The design resistance of one web cover plate in compression (NRd,wp,c) may be calculated from:

M0

py,wpcwp,Rd, γ

fAN = if p1,wp,j /twp ≤ 9ε (see note 2 , Table 3.3 of EN1993-1-8)

M1

py,wpwpRd,b,cwp,Rd, γ

fANN

χ== if p1,wp,j /twp > 9ε

2wpwpwp mm 12008150 =×=×= tbA

EN1993-1-1 §6.2.4(2)

EN1993-1-1 §6.3.1.1(3)

p1,wp,j /tfp = 110/8 = 13.8 which is greater than 9ε

For Lcr = 0,6 p1,wp,j and using buckling curve c, χ = 0,9

∴ kN 383100,1

35512009,0 3cwp,Rd, =×

××= −N

EN1993-1-1 §6.3.1.2

Design check Since NEd,wp < NRd,wp,c (222 kN < 383 kN), the design resistance of the web cover plate is adequate.

Web cover plates should also be checked for combined bending, shear and axial force in accordance with § 6.2.10 or § 6.2.1 (5) of EN1993-1-1. However in this case the shear force is small and the interaction is judged to be satisfactory by inspection.

10 Web cover plate bolt group

Normally (unless end, edge distances are small) column web bolt group (see section 11) will be critical, but for completeness the verification for the web cover plate bolt group is shown here:

wpRd,wpEd, VN ≤

Design axial force The design axial force on one web cover plate (NEd,wp) was calculated previously as:

NEd,wp = 222 kN

SN023


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Title




Design resistance The design resistance of the bolt group for Category A bolts (bearing type):

∑= Rdb,wpRd, FV ( )maxRdb,Rdv,if FF ≥

minRdb,wp )(Fn= maxRdb,Rdv,minRdb, )()(if FFF <≤

Rdv,wpFn= ( ) Rdv,minRdb,if FF >

EN1993-1-8 §3.7

The design bearing resistance of a single bolt on one web cover plate (Fb,Rd) is given by:

M2

wppu,b1Rdb, γ

α tdfkF =

EN1993-1-8 Table 3.4

where:

⎟⎟⎠

⎞⎜⎜⎝

⎛= 01;;min

pu,

ubdb ,

ffαα

⎟⎟⎠

⎞⎜⎜⎝

⎛−−= 5271417182min

0

wp2,

0

wp2,1 ,;,

dp

,;,d

e,k

where for the end bolts:

51,0263

403 0

wp1,d =

×==

de

α

and for the inner bolts:

78,041

26380

41

3 0

wp1,d =−

×=−=

dp

α

57,1

510800

pu,

ub ==ff

Hence:

( 51,00,1;57,1;51,0minb == )α for end bolts

( 78,00,1;57,1;78,0minb == )α for inner bolts.


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Title




07,27,1

26358,27,1

8,2

0

wp2, =−×

=−de

61,27,126

804,17,14,1

0

wp2, =−×

=−dp

∴ ( ) 07,25,2;61,2;07,2min1 ==k

Hence:

kN 831025,1

82451051,007,2)( 3minRdb, =×


kN 1261025,1

82451078,007,2)( 3maxRdb, =×


From section 8, the design shear resistance of a single bolt (Fv,Rd), with reduction factor bp =1.0 (i.e. web packing thickness < d/3) would be:

kN 136Rdv, =F

Since Fv,Rd > (Fb,Rd)max i.e 136 kN > 126 kN

∑= Rdb,wpRd, FV

kN 4181262832wpRd, =×+×=V

∴ kN 418wpRd, =V

Design check Since NEd,wp < VRd,wp (222 kN < 418 kN), the design resistance of the web cover plate bolt group is adequate.


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Title




11 Column web bolt group

wRd,wEd, VN ≤

Design axial force

The design axial force on the upper column web (NEd,w) may be calculated from:

uc

ucw,EdwEd,

AAN

N =

∴ kN 44480,86

80,211767wEd, =

×=N

SN023

Design resistance The design resistance of the bolt group for Category A bolts (bearing type):

∑= Rdb,wRd, FV ( )maxRdb,Rdv,if FF ≥

minRdb,wp )(Fn= maxRdb,Rdv,minRdb, )()(if FFF <≤

Rdv,wp2 Fn= ( ) Rdv,minRdb,if FF >

Factor 2 used, because the bolts are in double shear.

EN1993-1-8 §3.7

The design bearing resistance of a single bolt on the column web (Fb,Rd) is given by:

M2

ucw,ucu,b1Rdb, γ

α tdfkF =

where:

⎟⎟⎠

⎞⎜⎜⎝

⎛= 01;;min

ucu,

ubdb ,

ffαα

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 52;7141min

o

wp2,1 ,,

dp

,k

where:

64,0263

503 o

w1,d =

×==

de

α for the end bolts and

78,041

26380

41

3 o

wp1,d =−

×=−=

dp

α for the inner bolts


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Title




EN1993-1-8 Table 3.457,1

510800

pu,

ub ==ff

Hence:

( 64,00,1;57,1;64,0minb == )α for end bolts

( 78,00,1;57,1;78,0minb == )α for inner bolts.

61,27,1

26804,17,14,1

0

pw2, =−×

=−d

p

∴ ( ) 5,25,2;61,2min1 ==k

Hence:

kN 1181025,1

5,72451064,05,2)( 3minRdb, =×


kN 1431025,1

5,72451078,05,2)( 3maxRdb, =×

××××= −F for inner bolts

From section 8, the design shear resistance of a single bolt (Fv,Rd), with reduction factor bp =1.0 (i.e. web packing thickness < d/3) would be:

kN 136Rdv, =F

Since i.e 118 kN < 136 kN < 143 kN maxRdb,Rdv,minRdb, )()( FFF <<

wRd,V minRdb,wp )( Fn=

kN 4721184wRd, =×=V

∴ kN 472wRd, =V

Design check Since NEd,w < VRd,w (444 kN < 472 kN), the design axial resistance of the web of the upper column is adequate.


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Title




12 Structural integrity of the splice (under tying force)

uRd,uEd, NN ≤

For a non-bearing column splice, there is no need to carry out this check, because it will always be satisfied, since the tying force will always be less than the design compression force. However, for a bearing column splice (see SN019) this check will be required. But, since there is no worked example for a bearing column splice, the above check is demonstrated here.

Design tying force The design tying force on the column is:

kN 400 uEd, =N

SN023

SN019

Design resistance Conservatively it can be assumed that the tying force at the column splice is resisted by the flange cover plates only.

Therefore, the design axial resistance of the column splice (in tension) (NRd,u) is given by:

fpu,Rd,uRd, 2NN =

⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑ uRd,b,uRd,v,fp

uM,

pu,netfp,fpu,Rd, ;;

90min FFn

γfA,

N

where:

( ) 2fp0fpfpnetfp, mm 249612262122602 =××−×=−×= tdtbA

kN 1042101.1

51024969090 3

uM,

pu,netfp, =×××

= −,γ

fA,

The design shear resistance of a single bolt (Fv,Rd) is given by:

uM,

subvpRdv, γ

αβ AfF =

where:

mm 25pa =t and mm 83

243

==d

Since tpa > d/3, the reduction factor should be applied.

EN1993-1-8 Table 3.4


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Title




( ) ( ) 81,0

253248249

389

pap =

×+××

=+

=td

dβ

1,1uM, =γ for tying resistance

6,0v =α for class 8.8 bolts

2s mm 353=A

∴ kN 125101,1

3538006,081,0 3Rdv, =×

×××= −F

The design bearing resistance of a single bolt (Fb,Rd) on the flange cover plate is given by:

uM,

fppu,b1uRd,b, γ

α tdfkF =

EN1993-1-8 Table 3.4

where:

1,1uM, =γ for tying resistance

⎟⎟⎠

⎞⎜⎜⎝

⎛= 01;;min

pu,

ubdb ,

ff

αα

⎟⎟⎠

⎞⎜⎜⎝

⎛−−= 52;7141;7182min

0

fp2,

0

fp2,1 ,,

dp

,,d

e,k

For end bolts:

64,0263

503 0

fp1,d =

×==

de

α

and for inner bolts:

78,041

26380

41

3 0

fp1,d =−

×=−=

dp

α


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Title




57,1

510800

pu,

ub ==ff

Hence:

( 64,00,1;57,1;64,0minb == )α for end bolts, and

( ) 78,00,1;57,1;78,0minb ==α for inner bolts.

22,47,1

26558,27,18,2

0

fp2, =−×

=−d

e

38,67,126

1504,17,14,10

,2 =−×

=−d

p fp

∴ ( ) 5,25,2;38,6;22,4min1 ==k

Hence:

kN 214101,1

122451064,05,2 3uRd,b, =×


kN 260101,1

122451078,05,2 3uRd,b, =×


⎟⎟⎠

⎞⎜⎜⎝

⎛= uRd,b,fpuRd,v,fp

uM,

pu,netfp,fpu,Rd, ;;

90min FnFn

γfA,

N

( )26062142;1258;1042minfpu,Rd, ×+××=N

( ) kN 10001988;1000;1042minfpu,Rd, ==N

kN 2000100022 fpu,Rd,uRd, =×== NN

Design check Since NEd,u < NRd,u (400 kN < 2000 kN), the design tying resistance of the column splice is adequate.


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SX018a-EN-EUDocument Ref: Sheet 21 of 21

Title




13 SUMMARY The following table summarizes the values for all the applicable modes of failure. The critical values for normal design and tying are shown in bold type.

Mode of failure Design resistance Design force Ratio:

ResistanceForce

7. Flange cover plate compression

NRd,fp,c = 1108 kN NEd,fp,c = 719 kN 0,65

7. Flange cover plate tension

N/A NEd,fp,t= − 251 kN N/A

8. Flange cover plate bolt group

VRd,fp = 880 kN NEd,fp = 719 kN 0,82

9. Web cover plate NRd,wp,c = 383 kN NEd,wp = 222 kN 0,58

10. Web cover plate bolt group

VRd,wp = 418 kN NEd,wp = 222 kN 0,53

11. Column web bolt group

VRd,w = 472 kN NEd,w = 444 kN 0,94

12. Structural integrity of the splice (under tying force)

NRd,u = 2000 kN NEd,u = 400 kN 0,20


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Example: Column splice - non-bearing splice SX018a-EN-EU

Quality Record

RESOURCE TITLE Example: Column splice - non-bearing splice

Reference(s)

ORIGINAL DOCUMENT

Name Company Date

Created by Edurne Nunez, SCI 03/2005

Technical content checked by Abdul Malik, SCI 03/2006

Editorial content checked by

Technical content endorsed by the following STEEL Partners:

1. UK G W Owens SCI 17/3/06

2. France A Bureau CTICM 17/3/06

3. Germany A Olsson SBI 17/3/06

4. Sweden C Müller RWTH 17/3/06

5. Spain J Chica Labein 17/3/06

Resource approved by Technical Coordinator

G W Owens SCI 18/07/06

TRANSLATED DOCUMENT

This Translation made by:

Translated resource approved by:


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Documents

As-Design of Column Splice