CT-SHS Joint Design Examples 15-02-06

8/6/2019 CT-SHS Joint Design Examples 15-02-06

1/21

Job No: Sheet: 1 of 4

Made by: CPM Date: 24/02/05

Checked by: Date:

Client:

Job Title:SHS Joints Worked Example

Subject:CHS Gap K-joint, Axial Capacity

Corus Tubes

PO Box 101, Weldon Road

Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com

Care has been taken to ensure that this information is accurate, but Corus Group plc, including its subsidiaries, does not accept responsibility or liability for errors orinformation which is found to be misleading.

References are to Corus publication Design of SHS welded joints

-500 kN 400 kN

CHS 219.1x12.5

All material EN 10210 S355J2H

CHS 139.7x5.0 CHS 114.3x3.6

4545

40

-1000 kN -1636 kN

Parameter limits

d0/t0 50 d0/t0 = 219.1/12.5 = 17.53 PASS

di/ti 50 d1/t1 = 139.7/5 = 27.94 PASSd2/t2 = 114.3/3.6 = 31.75 PASS

di/d0 0.2 d1/d0 = 139.7/219.1 = 0.64 PASS

d2/d0 = 114.3/219.1 = 0.52 PASS

g t1 + t2 40 5 + 3.6 = 8.6 mm PASS

30 i 90 1 = 45 PASS2 = 45 PASS

-0.55 d0 e +0.25 d0 e = 0 mm-0.55 x 219.1 e +0.25 x 219.1-120.5 e +54.8 PASS

5.1.1 Table 6(page 20)

3.1(page 9)


2/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Chord face deformationNote: Brace 1 usually designated compression and brace 2 tension.

Compression brace (1):

( ) ( )p0

1

1

2

00y

Rd,1 nfgfd

d2.108.1

sin

tfN

+

=

where,

Gap/lap function f(g)

Using formulae: Using graph:

( )( )

+

+=33.1t/g5.0exp1

024.01gf

0

2.12.0

Note: g is positive for a gap and negative for an overlap

764.85.122

1.219t2

d0

0 =

==

( )( )

+

+=33.15.12/405.0exp1

764.8024.01764.8gf

2.12.0

( ) 761.1gf =

from graph;

f(g) = 1.761

where;

g/to = 40/12.5 = 3.2

do/to = 219.1/12.5do/to = 17.528

5.1.3(page 21)

Formulae Graph

5.1.2(page

20)

7.1(page

43)

Graph5.1.2

Fig. 22(page

21)


3/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


CHS chord end load function f(np)


0.1butf

3.0f

3.01)n(f

2

0y

p

0y

p

p

+=

where;

CHS chord least compressive

stress p;

0,el

2

0,op

2

0,ip

0

0,p

pW

MM

A

N +=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For CHS chords use least compressivechord stress.

2p 101.81

10001000

=

2

p mm/N30.123=

2

p355

3.1233.0

355

3.1233.01)n(f

+=

0.1860.0)n(f p =

where;


stress p;

0,el

20,op

20,ip

0

0,p

pW

MM

A

N +=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For CHS chords use leastcompressive chord stress.

2p 101.81

10001000

=

2

p mm/N30.123=

CHS chord stress ratio;

347.0355

30.123

f 0y

p =

=

from graph;

f(np) = 0.860

Formulae Graph

5.1.2(page

20)

5.1.2(page

20)

5.1.2(page

20)

5.1.2(page

20)

5.1.2GraphFig. 21

(page21)


4/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


860.0761.11.219

7.1392.108.1

45sin

5.12355N

2

Rd,1

+

=

kN986N Rd,1 =

Tension brace (2):

98645sin

45sinN

sin

sinN

Rd,12

1

Rd,2

=

=

kN986N Rd,2 =

Chord punching shear

(valid when di d0 - 2t0)

i

2

ii00y

Rd,i

sin2

sin1

3

dtfN

+

=

Brace (1):

+

=

45sin2

45sin1

3

7.1395.12355N

2Rd,1

kN1919N Rd,1 =

Brace (2):

+

=

45sin2

45sin1

3

3.1145.12355N

2Rd,2

kN1570N Rd,2 =

Joint strength dictated by chord face deformation for both bracings;

Brace 1 joint capacity, kN986NRd,1

=

Brace 2 joint capacity, kN986N Rd,2 =

5.1.3(page 21)

5.1.3(page 22)


5/21



Checked by: Date:

Client:


Subject:CHS Overlap K-joint, Axial Capacity

Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com



-500 kN

-1000 kNCHS 219.1x12.5


CHS 139.7x5.0

400 kN

-1636 kN

CHS 114.3x3.6

4545

-45

e = -42.2

Parameter limits

d0/t0 50 d0/t0 = 219.1/12.5 = 17.53 PASS

di/ti 50 d1/t1 = 139.7/5 = 27.94 PASSd2/t2 = 114.3/3.6 = 31.75 PASS

di/d0 0.2 d1/d0 = 139.7/219.1 = 0.64 PASSd2/d0 = 114.3/219.1 = 0.52 PASS

25% Overlap 100% Overlap = g sin i /di x 100%Overlap = 45 sin 45 / 114.3 x 100%Overlap = 27.8%

25% 27.8% 100% PASS

30 i 90 1 = 45 PASS2 = 45 PASS

-0.55 d0 e +0.25 d0 e = -42.2 mm

-0.55 x 219.1 e +0.25 x 219.1-120.5 e +54.8 PASS


7.1 Fig. 31(page 43,44)

3.1(page 9)


6/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Chord face deformation

Note: Brace 1 usually designated compression and brace 2 tension.


( ) ( )p0

1

1

2

00y

Rd,1 nfgfd

d2.108.1

sin

tfN

+

=

5.1.3 (page 21)

where,

Gap/lap function f(g)


( )( )

+

+=33.1t/g5.0exp1

024.01gf

0

2.12.0

Note: g is positive for a gap and negative for an overlap

764.85.122

1.219t2

d0

0 ===

( )( )( )

+

+=33.15.12/455.0exp1

764.8024.01764.8gf

2.12.0

( ) 024.2gf =

from graph;

f(g) = 2.024

where;

g/to = -45/12.5 = -3.6

do/to = 219.1/12.5do/to = 17.528

Formulae Graph

5.1.2(page

20)

7.1(page

43)

Graph5.1.2

Fig. 22(page

21)


7/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


CHS chord end load function f(np)


0.1butf

3.0f

3.01)n(f

2

0y

p

0y

p

p

+=

where;


stress p;

0,el

2

0,op

2

0,ip

0

0,p

pW

MM

A

N +=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For CHS chords use least compressivechord stress.

2p 101.81

10001000

=

2

p mm/N30.123=

2

p355

3.1233.0

355

3.1233.01)n(f

+=

0.1860.0)n(f p =

where;


stress p;

0,el

20,op

20,ip

0

0,p

pW

MM

A

N +=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For CHS chords use leastcompressive chord stress.

2p 101.81

10001000

=

2

p mm/N30.123=

CHS chord stress ratio;

347.0355

30.123

f 0y

p =

=

from graph;

f(np) = 0.860

Formulae Graph

5.1.2(page

20)

5.1.2(page

20)

5.1.2(page

20)

5.1.2(page

20)

5.1.2Graph

Fig. 21(page

21)


8/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


860.0024.21.219

7.1392.108.1

45sin

5.12355N

2

Rd,1

+

=

kN1134N Rd,1 =

Tension brace (2):1134

45sin

45sinN

sin

sinN Rd,1

2

1Rd,2

=

=

kN1134N Rd,2 =

Chord punching shear check not required for overlapping bracings.Joint strength dictated by chord face deformation for both bracings;



5.1.3(page 21)


9/21



Checked by: Date:

Client:


Subject:RHS Gap K-joint, Axial Capacity

Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com



-650 kN

RHS 200 x 200 x 10


SHS 120 x 120 x 5

45

5

45

650 kN

40

-1000 kN -1920 kN

Parameter limits

b0/t0 35 b0/t0 = 200/10 = 20 PASSh0/t0 35 h0/t0 = 200/10 = 20 PASS

bi/ti ; hi/ti 35 and 34.5(275/fyi) = 30.4 compression braceb1/t1 = 120/5 = 24 PASSh1/t1 = 120/5 = 24 PASS

bi/ti ; hi/ti 35 tension braceb2/t2 = 120/5 = 24 PASSh2/t2 = 120/5 = 24 PASS

bi/b0 0.35 and 0.1+0.01 b0/t0 = 0.3b1/b0 = 120/200 = 0.6 PASSb2/b0 = 120/200 = 0.6 PASS

g t1 + t2 40 5 + 5 = 10 mm PASS

0.5(b0-(b1+b2)/2) g 1.5(b0-(b1+b2)/2) g = 40 mm0.5(200-(120+120)/2) g 1.5(200-(120+120)/2)

40 g 120 mm PASS

30 i 90 1 = 45 PASS2 = 45 PASS

-0.55 h0 e +0.25 h0 e = 5 mm-0.55 x 200 e +0.25 x 200-110 e +50 PASS


2.1(page 4)

3.1(page 9)


10/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Chord face deformation brace 1Note: Brace 1 usually designated compression and brace 2 tension.


( )nfb4

hbhb

t

b

sin

tf3.6N

0

2211

0

0

1

2

00y

Rd,1

+++

=

where,

RHS chord end load function f(n)


( ) 0.1butf

4.03.1nf

0y

0

+=

where;

6.02002120120

b2bb

0

21 =+=+=

RHS chord most compressive

stress 0;

0,op,el

0,op

0,ip,el

0,ip

0

0

0W

M

W

M

A

N++=

Note: Moment part is additive to compressive

stress which is negative, hence minus sign formoments. For RHS chords use most compressivechord stress.

20 109.74

10001920

=

2

0 mm/N34.256=

( )( )

0.1

6.0355

34.2564.03.1nf

+=

( ) 0.1819.0nf =

where;


stress 0;

0,op,el

0,op

0,ip,el

0,ip

0

0

0W

M

W

M

A

N

++=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For RHS chords use mostcompressive chord stress.

20 109.74

10001920

=

2

0 mm/N34.256=

RHS chord stress ratio;

722.0355

34.256

f 0y

0 =

=

from graph;

for 6.0200

120

b

b

0

i ==

f(n) = 0.819

5.2.3(page 28)

Formulae Graph

5.2.2(page

25)

7.1(page

43)

5.2.2(page

25)

5.2.2

(page25)

5.2.2(page

25)

5.2.2GraphFig. 23(page

26)


11/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


819.02004

120120120120

10

200

45sin

103553.6N

2

Rd,1

+++

=

kN695N Rd,1 =

Chord shear check brace 1

i

v0y

Rd,isin3

AfN

=

where

212.0

103

4041

1

t3

g41

1

5.0

2

2

5.0

2

0

2=

+

=

+

=

( ) ( ) 2000v mm442410200212.02002tbh2A =+=+=

=

45sin3

4424355N Rd,1

kN1282N Rd,1 =

5.2.3(page 28)

5.2.2(page 27)

5.2.2(page 27)


12/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Bracing Effective width brace 1

( )effiiiiyiRd,i bbt4h2tfN ++=

where iiiyi

00y

0

0eff bbutb

tf

tf

b

t10b =

mm120butmm1201205355

10355200

1010beff ==

( )1201205412025355N Rd,1 ++=

kN817N Rd,1 =

Chord punching shear brace 1

(valid when 1 - 2t0/b

0)

++

= epi

i

i

i

00y

Rd,i bbsin

h2

sin3

tfN

where ii0

0ep bbutb

b

t10b =

120but120200

1010bep

=

mm60bep =

++

= 60120

45sin

1202

45sin3

10355N Rd,i

kN1506N Rd,1 =

Summary - brace 1Joint strength for brace 1 dictated by chord face deformation.


5.2.3(page 28)

5.2.2(page 26)

5.2.3(page 28)

5.2.2(page 26)


13/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Brace 2

Repeat brace capacity formulae for brace 2.

Note: As both braces are of same geometry, brace 2 capacity will be the same:

Chord face deformation, kN695N Rd,2 =

Chord shear check, kN1282N Rd,2 =

Bracing effective width, kN817N Rd,2 =

Punching shear, kN1506N Rd,2 =



14/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Chord axial load resistance in gap

Chord: Axial load in gap (valid when V 0.5 Vp)

( )2pv00yRd,gap,0 1V/V2AAfN =

where 20 mm7490A =

2v mm4424A =

kN619.45945sin650sinNV ii ===

kN740.9063

4424355

3

AfV v0yp ===

=

2

Rd,gap,0 1

740.906

619.459244247490355N

kN2659N Rd,gap,0 =

-650 650

-1000 -1000-460-460

-1920

-1000-460

-1460

Axial load in gap (kN)

kN1460N gap,0 =

2659 > 1460 Passes axial load in gap

5.2.3(page 28)


15/21



Checked by: Date:

Client:


Subject:RHS Overlap K-joint, Axial Capacity

Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com



-600 kN

-1000 kN -1849 kNSHS 200 x 200 x 10


SHS 120 x 120 x 5 600 kN

4545

70 i

-50.1

Parameter limits


bi/ti ; hi/ti 30.4(275/fyi) = 26.8 compression braceb1/t1 = 120/5 = 24 PASSh1/t1 = 120/5 = 24 PASS

bi/ti ; hi/ti 35 tension braceb2/t2 = 120/5 = 24 PASSh2/t2 = 120/5 = 24 PASS

bi/b0 0.25 b1/b0 = 120/200 = 0.6 PASSb2/b0 = 120/200 = 0.6 PASS

bi/bj 0.75 bi/bj = 120/120 = 1.0 PASS

25% overlap 100% Overlap = g sin i /hi x 100%

Overlap = 70 sin 45 / 120 x 100%Overlap = 41.2%

25% 27.8% 100% PASS

30 i 90 1 = 45 PASS2 = 45 PASS

-0.55 h0 e +0.25 h0 e = -50.1 mm-0.55 x 200 e +0.25 x 200-110 e +50 PASS


7.1 Fig. 31(page 43,44)


2.1(page 4)

3.1(page 9)


16/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Bracing Effective widthNote: Only the overlapping brace (i) need be checked. The capacity of the overlapped brace (j) is

based on on an efficiency ratio to that of the overlapping brace.

Overlapping brace, i (2):

For 25% Ov < 50%

( )

++

= eoveffii

viyiRd,i bbt4h2

50

OtfN

where, iiiyi

00y

0

0eff bbutb

tf

tf

b

t10b =

120but1205355

10355

200

1010beff

=

mm120beff =

ii

iyi

jyj

j

j

eov bbutbtf

tf

b

t10b =

120but1205355

5355

120

510beov

=

mm50beov =

( )

++

= 5012054120250

2.415355N Rd,i

kN624N Rd,i =

5.2.3(page 28)

5.2.2(page 26)

5.2.2(page 26)


17/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Overlapped brace, j (1):

yii

yjj

Rd,iRd,jfA

fANN =

3557.22

3557.22624N Rd,j

=

kN624N Rd,j =

5.2.3(page 28)


18/21



Checked by: Date:

Client:


Subject:RHS T-joint, Moment In-Plane Capacity

Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com



RHS 150 x 150 x 10All material EN 10210 S355J2H

RHS 150 x 150 x 8

90

54 kNm-19.2 kN

35.8 kNm-136 kN

18.2 kNm-350 kN

For simplicity only the moment in plane capacity calculations are shown as otherexamples cover axial capacity. Axial and moment out of plane capacity wouldneed to be calculated and included in the interaction check.

Parameter limits


bi/ti ; hi/ti 35 and 34.5(275/fyi) = 30.4 compression braceb1/t1 = 150/8 = 24 PASSh1/t1 = 150/8 = 24 PASS

bi/b0 0.25 b1/b0 = 150/200 = 0.75 PASS

30 i 90 1 = 45 PASS

5.2.1 Table 7

(page 25)

2.1(page 4)


19/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Chord face deformation

(Valid when 0.85)

0.1150

150

b

b

0

1 === Check not required

Although this check is not required in this particular case, the calculation for chordend load function is shown for information as it includes moments;

RHS chord end load function f(n)


( ) 0.1butf

4.03.1nf

0y

0

+=

where;


stress 0;

0,op,el

0,op

0,ip,el

0,ip

0

00

W

M

W

M

A

N++=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For RHS chords use most compressivechord stress.

320

10236

100010008.35

109.54

1000136

+

=

2

0 mm/N47.176=

( )( )

0.10.1355

47.1764.03.1nf

+=

( ) 0.1)n(f0.1but101.1nf ==

where;


stress 0;

0,op,el

0,op

0,ip,el

0,ip

0

00

W

M

W

M

A

N++=

Note: Moment part is additive to compressivestress which is negative, hence minus sign formoments. For RHS chords use mostcompressive chord stress.

320 10236

100010008.35

109.54

1000136

+

=

2

0 mm/N47.176=

RHS chord stress ratio;

497.0355

47.176

f 0y

0 =

=

from graph;

for 0.1150

150

b

b

0

i ==

f(n) = 1.101

(However, not required in this case as chord deformation not critical as >0.85)

7.1(page 43)

Formulae Graph

5.2.2(page

25)

5.2.2(page

25)

5.2.2(page

25)

5.2.2(page

25)

5.2.2GraphFig. 23(page

26)


20/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com


Chord side wall crushing

(Valid when 0.85 < 1.0)

( )2010ykRd,ip t5htf5.0M +=

where, 0yyk ff = for T-joints

( )2Rd,ip 105150103555.0M +=

kNm71M Rd,ip =

Bracing Effective width

(Valid when 0.85 < 1.0)

= 111

1

eff1,pl1yRd,ip thb

bb1WfM

where, 1111y

00y

0

0eff bbutb

tf

tf

b

t10b =

mm150butmm1251508355

10355

150

1010beff =

=

= 8150150

150

125110237355M 3Rd,ip

kNm49.73M Rd,ip =

5.2.5.1(page 28)

5.2.5.1(page 28)

5.2.2(page 26)


21/21



Checked by: Date:

Client:



Corus Tubes


Corby, Northants

NN17 5UA

Tel: +44 (0) 1536 402121

Fax: +44 (0) 1536 404049

www.corusgroup.com

Summary Moment in plane

Joint moment in-plane capacity dictated by chord side wall failure.

Brace joint capacity, kNm71M Rd,ip =

Interaction formula

(When moments are present an interaction check is required)

RHS Chord, Check 0.1M

M

M

M

N

N

Rd,op

op

Rd,ip

ip

Rd

++

CHS Chord, Check 0.1M

M

M

M

N

N

Rd,op

op

2

Rd,ip

ip

Rd

+

+

Note: For CHS chords the in-plane moment term is squared

2.4(page 7)

2.4(page 7)

CT-SHS Joint Design Examples 15-02-06

Documents

Transcript of CT-SHS Joint Design Examples 15-02-06