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 or information which is found to be misleading.
References are to Corus publication ‘Design of SHS welded joints’
-500 kN 400 kN
CHS 219.1x12.5All material EN 10210 S355J2H
CHS 139.7x5.0 CHS 114.3x3.6
45º45º 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 ∴PASS d2/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° ≤ θi ≤ 90° θ1 = 45° ∴PASS θ2 = 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)
Job No: Sheet: 2 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 or information which is found to be misleading.
Chord face deformation Note: Brace 1 usually designated compression and brace 2 tension.
Compression brace (1):
( ) ( )p0
1
1
200y
Rd,1 nfgfdd2.108.1
sintf
N
+
θ=
where, Gap/lap function f(g) Using formulae: Using graph:
( ) ( )
−+
γ+γ=
33.1t/g5.0exp1024.01gf
0
2.12.0
Note: g is positive for a gap and negative for an overlap
764.85.122
1.219t2
d
0
0 =×
==γ
( ) ( )
−×+
×+=
33.15.12/405.0exp1764.8024.01764.8gf
2.12.0
( ) 761.1gf =
from graph; f(g) = 1.761 where; g/to = 40/12.5 = 3.2 do/to = 219.1/12.5 do/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)
Job No: Sheet: 3 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 or information which is found to be misleading.
CHS chord end load function f(np) Using formulae: Using graph:
0.1 butf
3.0f
3.01)n(f2
0y
p
0y
pp ≤
σ−
σ+=
where; CHS chord least compressive stress σp;
0,el
20,op
20,ip
0
0,pp W
MMAN +
−=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For CHS chords use least compressive chord stress.
2p 101.8110001000
××−
=σ
2
p mm/N30.123−=σ
2
p 3553.1233.0
3553.1233.01)n(f
−−
−+=
0.1860.0)n(f p ≤=
where; CHS chord least compressive stress σp;
0,el
20,op
20,ip
0
0,pp W
MMAN +
−=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For CHS chords use least compressive chord stress.
2p 101.8110001000
××−
=σ
2
p mm/N30.123−=σ CHS chord stress ratio;
347.0355
30.123f 0y
p −=−
=σ
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)
5.1.2 Graph
Fig. 21 (page
21)
Job No: Sheet: 4 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 or information which is found to be misleading.
860.0761.11.2197.1392.108.1
45sin5.12355N
2
Rd,1 ×
+
°×
=
kN986N Rd,1 =
Tension brace (2):
98645sin45sinN
sinsinN Rd,1
2
1Rd,2 ×
°°
=θθ
=
kN986N Rd,2 =
Chord punching shear (valid when di ≤ d0 - 2t0)
i2
ii00yRd,i sin2
sin13
dtfN
θθ+
×π
=
Brace (1):
°°+
××π××
=45sin245sin1
37.1395.12355N 2Rd,1
kN1919N Rd,1 =
Brace (2):
°°+
××π××
=45sin245sin1
33.1145.12355N 2Rd,2
kN1570N Rd,2 =
Joint strength dictated by chord face deformation for both bracings; Brace 1 joint capacity, kN986N Rd,1 = Brace 2 joint capacity, kN986N Rd,2 =
5.1.3 (page 21)
5.1.3 (page 22)
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 Overlap 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 or information which is found to be misleading.
References are to Corus publication ‘Design of SHS welded joints’
-500 kN
-1000 kN CHS 219.1x12.5All material EN 10210 S355J2H
CHS 139.7x5.0 400 kN
-1636 kN
CHS 114.3x3.6
45º45º -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 ∴PASS d2/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 25% ≤ Overlap ≤ 100% Overlap = g sin θi /di x 100% Overlap = 45 sin 45° / 114.3 x 100% Overlap = 27.8% 25% ≤ 27.8% ≤ 100% ∴PASS 30° ≤ θi ≤ 90° θ1 = 45° ∴PASS θ2 = 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
5.1.1 Table 6 (page 20)
7.1 Fig. 31 (page 43,44)
3.1 (page 9)
Job No: Sheet: 2 of 4 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: CHS Overlap 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 or information which is found to be misleading.
Chord face deformation Note: Brace 1 usually designated compression and brace 2 tension.
Compression brace (1):
( ) ( )p0
1
1
200y
Rd,1 nfgfdd2.108.1
sintf
N
+
θ=
5.1.3 (page 21) where, Gap/lap function f(g) Using formulae: Using graph:
( ) ( )
−+
γ+γ=
33.1t/g5.0exp1024.01gf
0
2.12.0
Note: g is positive for a gap and negative for an overlap
764.85.122
1.219t2
d
0
0 =×
==γ
( ) ( )( )
−−×+
×+=
33.15.12/455.0exp1764.8024.01764.8gf
2.12.0
( ) 024.2gf =
from graph; f(g) = 2.024 where; g/to = -45/12.5 = -3.6 do/to = 219.1/12.5 do/to = 17.528
Formulae Graph
5.1.2(page
20)
7.1(page
43)
Graph5.1.2
Fig. 22(page
21)
Job No: Sheet: 3 of 4 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: CHS Overlap 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 or information which is found to be misleading.
CHS chord end load function f(np) Using formulae: Using graph:
0.1 butf
3.0f
3.01)n(f2
0y
p
0y
pp ≤
σ−
σ+=
where; CHS chord least compressive stress σp;
0,el
20,op
20,ip
0
0,pp W
MMAN +
−=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For CHS chords use least compressive chord stress.
2p 101.8110001000
××−
=σ
2
p mm/N30.123−=σ
2
p 3553.1233.0
3553.1233.01)n(f
−−
−+=
0.1860.0)n(f p ≤=
where; CHS chord least compressive stress σp;
0,el
20,op
20,ip
0
0,pp W
MMAN +
−=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For CHS chords use least compressive chord stress.
2p 101.8110001000
××−
=σ
2
p mm/N30.123−=σ CHS chord stress ratio;
347.0355
30.123f 0y
p −=−
=σ
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)
5.1.2 Graph
Fig. 21 (page
21)
Job No: Sheet: 4 of 4 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: CHS Overlap 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 or information which is found to be misleading.
860.0024.21.2197.1392.108.1
45sin5.12355N
2
Rd,1 ×
+
°×
=
kN1134N Rd,1 =
Tension brace (2):
113445sin45sinN
sinsinN Rd,1
2
1Rd,2 ×
°°
=θθ
=
kN1134N Rd,2 =
Chord punching shear check not required for overlapping bracings. Joint strength dictated by chord face deformation for both bracings; Brace 1 joint capacity, kN1134N Rd,1 = Brace 2 joint capacity, kN1134N Rd,2 =
5.1.3 (page 21)
Job No: Sheet: 1 of 6 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS 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 or information which is found to be misleading.
References are to Corus publication ‘Design of SHS welded joints’
-650 kN
RHS 200 x 200 x 10All material EN 10210 S355J2H
SHS 120 x 120 x 5
45º
5
45º
650 kN
40
-1000 kN -1920 kN
Parameter limits
b0/t0 ≤ 35 b0/t0 = 200/10 = 20 ∴PASS h0/t0 ≤ 35 h0/t0 = 200/10 = 20 ∴PASS bi/ti ; hi/ti ≤ 35 and ≤ 34.5√(275/fyi) = 30.4 compression brace b1/t1 = 120/5 = 24 ∴PASS h1/t1 = 120/5 = 24 ∴PASS bi/ti ; hi/ti ≤ 35 tension brace b2/t2 = 120/5 = 24 ∴PASS h2/t2 = 120/5 = 24 ∴PASS bi/b0 ≥ 0.35 and ≥ 0.1+0.01 b0/t0 = 0.3 b1/b0 = 120/200 = 0.6 ∴PASS b2/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 mm 0.5(200-(120+120)/2) ≤ g ≤ 1.5(200-(120+120)/2) 40 ≤ g ≤ 120 mm ∴PASS 30° ≤ θi ≤ 90° θ1 = 45° ∴PASS θ2 = 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
5.2.1 Table 7 (page 25)
2.1 (page 4)
3.1 (page 9)
Job No: Sheet: 2 of 6 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS 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 or information which is found to be misleading.
Chord face deformation – brace 1 Note: Brace 1 usually designated compression and brace 2 tension.
Compression brace (1):
( )nfb4
hbhbtb
sintf3.6
N0
2211
0
0
1
200y
Rd,1
+++θ
=
where, RHS chord end load function f(n) Using formulae: Using graph:
( ) 0.1butf4.03.1nf0y
0 ≤βσ
+=
where;
6.02002120120
b2bb
0
21 =×
+=
+=β
RHS chord most compressive stress σ0;
0,op,el
0,op
0,ip,el
0,ip
0
00 W
M
W
M
AN
++=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For RHS chords use most compressive chord stress.
20 109.7410001920
××−
=σ
2
0 mm/N34.256−=σ
( ) ( ) 0.16.035534.2564.03.1nf ≤
×−×
+=
( ) 0.1819.0nf ≤=
where; RHS chord most compressive stress σ0;
0,op,el
0,op
0,ip,el
0,ip
0
00 W
M
W
M
AN
++=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For RHS chords use most compressive chord stress.
20 109.7410001920
××−
=σ
2
0 mm/N34.256−=σ RHS chord stress ratio;
722.0355
34.256f 0y
0 −=−
=σ
from graph;
for 6.0200120
bb
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 (page
25)
5.2.2 (page
25)
5.2.2 Graph
Fig. 23 (page
26)
Job No: Sheet: 3 of 6 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS 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 or information which is found to be misleading.
819.02004
12012012012010200
45sin103553.6N
2
Rd,1
×+++
×°××
=
kN695N Rd,1 =
Chord shear check – brace 1
i
v0yRd,i sin3
AfN
θ=
where
212.0
1034041
1
t3g41
1
5.0
2
2
5.0
20
2 =
××
+=
+=α
( ) ( ) 2
000v mm442410200212.02002tbh2A =×+×=α+=
°×
=45sin3
4424355N Rd,1
kN1282N Rd,1 =
5.2.3 (page 28)
5.2.2 (page 27)
5.2.2 (page 27)
Job No: Sheet: 4 of 6 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS 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 or information which is found to be misleading.
Bracing Effective width – brace 1
( )effiiiiyiRd,i bbt4h2tfN ++−=
where iiiyi
00y
0
0eff bbutb
tftf
bt10b ≤××=
mm120butmm1201205355
10355200
1010beff ≤=×××
××
=
( )1201205412025355N Rd,1 ++×−××=
kN817N Rd,1 =
Chord punching shear – brace 1 (valid when β ≤ 1 - 2t0/b0)
++
θθ= epi
i
i
i
00yRd,i bb
sinh2
sin3
tfN
where ii0
0ep bbutb
bt10b ≤×=
120but120200
1010bep ≤××
=
mm60bep =
++
°×
°×
= 6012045sin1202
45sin310355N Rd,i
kN1506N Rd,1 =
Summary - brace 1 Joint strength for brace 1 dictated by chord face deformation. ∴ Brace 1 joint capacity, kN695N Rd,1 =
5.2.3 (page 28)
5.2.2 (page 26)
5.2.3 (page 28)
5.2.2 (page 26)
Job No: Sheet: 5 of 6 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS 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 or information which is found to be misleading.
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 = ∴ Brace 2 joint capacity, kN695N Rd,2 =
Job No: Sheet: 6 of 6 Made by: CPM Date: 24/02/05 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS 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 or information which is found to be misleading.
Chord axial load resistance in gap Chord: Axial load in gap (valid when V ≥ 0.5 Vp)
( )[ ]2
pv00yRd,gap,0 1V/V2AAfN −−= where 2
0 mm7490A = 2
v mm4424A = kN619.45945sin650sinNV ii =°=θ=
kN740.9063
44243553
AfV v0yp =×==
−×−=
2
Rd,gap,0 1740.906619.459244247490355N
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)
Job No: Sheet: 1 of 3 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS Overlap 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 or information which is found to be misleading.
References are to Corus publication ‘Design of SHS welded joints’
-600 kN
-1000 kN -1849 kNSHS 200 x 200 x 10All material EN 10210 S355J2H
SHS 120 x 120 x 5 600 kN
45º45º 70 i j
-50.1
Parameter limits
b0/t0 ≤ 40 b0/t0 = 200/10 = 20 ∴PASS h0/t0 ≤ 40 h0/t0 = 200/10 = 20 ∴PASS bi/ti ; hi/ti ≤ 30.4√(275/fyi) = 26.8 compression brace b1/t1 = 120/5 = 24 ∴PASS h1/t1 = 120/5 = 24 ∴PASS bi/ti ; hi/ti ≤ 35 tension brace b2/t2 = 120/5 = 24 ∴PASS h2/t2 = 120/5 = 24 ∴PASS bi/b0 ≥ 0.25 b1/b0 = 120/200 = 0.6 ∴PASS b2/b0 = 120/200 = 0.6 ∴PASS bi/bj ≥ 0.75 bi/bj = 120/120 = 1.0 ∴PASS 25% ≤ overlap ≤ 100% Overlap = g sin θi /hi x 100% Overlap = 70 sin 45° / 120 x 100% Overlap = 41.2% 25% ≤ 27.8% ≤ 100% ∴PASS 30° ≤ θi ≤ 90° θ1 = 45° ∴PASS θ2 = 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
5.2.1 Table 7 (page 25)
7.1 Fig. 31 (page 43,44)
5.2.1 Table 7
(page 25)
2.1 (page 4)
3.1
(page 9)
Job No: Sheet: 2 of 3 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS Overlap 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 or information which is found to be misleading.
Bracing Effective width Note: 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%
( )
++−
= eoveffiiv
iyiRd,i bbt4h250OtfN
where, iiiyi
00y
0
0eff bbutb
tftf
bt10b ≤××=
120but1205355
10355200
1010beff ≤×××
××
=
mm120beff =
iiiyi
jyj
j
jeov bbutb
tftf
bt10
b ≤××=
120but12053555355
120510beov ≤×
××
××
=
mm50beov =
( )
++×−×
×= 50120541202
502.415355N Rd,i
kN624N Rd,i =
5.2.3 (page 28)
5.2.2 (page 26)
5.2.2 (page 26)
Job No: Sheet: 3 of 3 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS Overlap 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 or information which is found to be misleading.
Overlapped brace, j (1):
yii
yjjRd,iRd,j fA
fANN =
3557.223557.22624N Rd,j ×
××=
kN624N Rd,j =
5.2.3 (page 28)
Job No: Sheet: 1 of 4 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS T-joint, Moment In-Plane 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 or information which is found to be misleading.
References are to Corus publication ‘Design of SHS welded joints’
RHS 150 x 150 x 10All material EN 10210 S355J2H
RHS 150 x 150 x 8
90º
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 other examples cover axial capacity. Axial and moment out of plane capacity would need to be calculated and included in the interaction check.
Parameter limits b0/t0 ≤ 35 b0/t0 = 150/10 = 15 ∴PASS h0/t0 ≤ 35 h0/t0 = 150/10 = 15 ∴PASS bi/ti ; hi/ti ≤ 35 and ≤ 34.5√(275/fyi) = 30.4 compression brace b1/t1 = 150/8 = 24 ∴PASS h1/t1 = 150/8 = 24 ∴PASS bi/b0 ≥ 0.25 b1/b0 = 150/200 = 0.75 ∴PASS 30° ≤ θi ≤ 90° θ1 = 45° ∴PASS
5.2.1 Table 7 (page 25)
2.1 (page 4)
Job No: Sheet: 2 of 4 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS T-joint, Moment In-Plane 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 or information which is found to be misleading.
Chord face deformation (Valid when β ≤ 0.85)
0.1150150
bb
0
1 ===β ∴Check not required
Although this check is not required in this particular case, the calculation for chord end load function is shown for information as it includes moments;
RHS chord end load function f(n) Using formulae: Using graph:
( ) 0.1butf4.03.1nf0y
0 ≤βσ
+=
where; RHS chord most compressive stress σ0;
0,op,el
0,op
0,ip,el
0,ip
0
00 W
MWM
AN
++=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For RHS chords use most compressive chord stress.
320 10236100010008.35
109.541000136
×××−
+××−
=σ
2
0 mm/N47.176−=σ
( ) ( ) 0.10.135547.1764.03.1nf ≤
×−×
+=
( ) 0.1)n(f0.1but101.1nf =∴≤=
where; RHS chord most compressive stress σ0;
0,op,el
0,op
0,ip,el
0,ip
0
00 W
MWM
AN
++=σ
Note: Moment part is additive to compressive stress which is negative, hence minus sign for moments. For RHS chords use most compressive chord stress.
320 10236100010008.35
109.541000136
×××−
+××−
=σ
2
0 mm/N47.176−=σ RHS chord stress ratio;
497.0355
47.176f 0y
0 −=−
=σ
from graph;
for 0.1150150
bb
0
i ==
f(n) = 1.101
(However, not required in this case as chord deformation not critical as β>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)
5.2.2 Graph
Fig. 23 (page
26)
Job No: Sheet: 3 of 4 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS T-joint, Moment In-Plane 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 or information which is found to be misleading.
Chord side wall crushing (Valid when 0.85 < β ≤ 1.0)
( )2
010ykRd,ip t5htf5.0M += where, 0yyk ff = for T-joints
( )2Rd,ip 105150103555.0M ×+××=
kNm71M Rd,ip =
Bracing Effective width (Valid when 0.85 < β ≤ 1.0)
−−= 111
1
eff1,pl1yRd,ip thb
bb1WfM
where, 1111y
00y
0
0eff bbutb
tftf
bt10b ≤××=
mm150butmm1251508355
10355150
1010beff ≤=×××
××
=
××
−−×= 8150150
150125110237355M 3
Rd,ip
kNm49.73M Rd,ip =
5.2.5.1 (page 28)
5.2.5.1 (page 28)
5.2.2 (page 26)
Job No: Sheet: 4 of 4 Made by: CPM Date: 01/11/04 Checked by: Date: Client: Job Title: SHS Joints Worked Example Subject: RHS T-joint, Moment In-Plane 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 or information which is found to be misleading.
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 0.1MM
MM
NN
Rd,op
op
Rd,ip
ip
Rd
≤++
CHS Chord, Check 0.1M
M
MM
NN
Rd,op
op2
Rd,ip
ip
Rd
≤+
+
Note: For CHS chords the in-plane moment term is squared
2.4 (page 7)
2.4 (page 7)