Node no. 3 - CHS connection in lattice Node info Project data for

Node no. 3 - CHS connection in lattice Node info Project data for

Projekt nr 1 - Poz. 1.1 page no. z
Node no. 3 - CHS connection in lattice
Node info
Location: (x=7.600m, y=1.600m)
Project data for elements
Eccentricity e: 0mm
Distance g between brace members: -21.4mm
Brace members: RP 60x40x4
d: 60.0 mm
t: 4.0 mm
A: 7.2 cm²
Steel: S 235
fy: 235 MPa
fu: 360 MPa
Ix: 32.8 cm⁴
Iy: 17.0 cm⁴
Ix: 776.0 cm⁴
Iy: 314.0 cm⁴
Ix: 32.8 cm⁴
Iy: 17.0 cm⁴
Ix: 776.0 cm⁴
Iy: 314.0 cm⁴
Brace members: RP 140x80x8
d: 140.0 mm
t: 8.0 mm
A: 32.0 cm²
Steel: S 235
fy: 235 MPa
fu: 360 MPa
Brace members: RP 60x40x4
d: 60.0 mm
t: 4.0 mm
A: 7.2 cm²
Steel: S 235
fy: 235 MPa
fu: 360 MPa
Chord: RP 140x80x8
d: 140.0 mm
t: 8.0 mm
A: 32.0 cm²
Steel: S 235
fy: 235 MPa
fu: 360 MPa
Connection calculations
Most adverse load combination
Load groups: 0, 1, +2, +K5
Forces in bars
Brace members: RP 60x40x4
N: -22.48 kN
V: -0.06 kN
M: 0 kNm
Brace members: RP 140x80x8
N: 4.45 kN
V: 1.13 kN
M: 1.95 kNm
Brace members: RP 60x40x4
N: 20.43 kN
V: 0 kN
M: 0 kNm
V: 4.24 kN
M: 8.05 kNm
Chord: RP 140x80x8
N: 20.27 kN
Design conditions
Warunek mimośrodu węzła
−0.55≤ e /d 0 ≤ 0.25 , e / d 0=0 /140.0=0
−0.55≤ 0 ≤ 0.25
Chord, RP 140x80x8
0.5 ≤ h0 /b0 ≤ 2.0 , h 0 /b0=140.0 /80.0=1.75
0.5 ≤ 1.75 ≤ 2.0
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Projekt nr 1 - Poz. 1.1 page no. z
Brace member 1, RP 60x40x4
bi /b 0 ≥ 0.25 , bi /b 0=60.0 /80.0=0.75
0.75 ≥ 0.25
Brace member 1, RP 60x40x4
bi /t i ≤ 35. , bi /t i=40.0/ 4.0=10.00
10.00 ≤ 35.
Brace member 1, RP 60x40x4
hi /t i ≤ 35. , hi /t i =60.0/4.0=15.00
15.00 ≤ 35.
Brace member 1, RP 60x40x4
0.5 ≤ hi /bi ≤ 2.0 , hi / bi=60.0 /40.0=1.50
0.5 ≤ 1.50 ≤ 2.0
Brace members: 1, RP 60x40x4, 2, RP 140x80x8 !!!Range of validity requirements are not met!!!
bi /b j ≥ 0.75 , bi /b j=40.0/ 80.0=0.50
0.50<0.75
Brace members: 1, RP 60x40x4, 3, RP 60x40x4
bi /b j ≥ 0.75 , bi /b j=40.0/ 40.0=1.00
1.00 ≥ 0.75
Brace member 2, RP 140x80x8
bi /b 0 ≥ 0.25 , bi /b 0=140.0/80.0=1.75
1.75≥ 0.25
Brace member 2, RP 140x80x8
bi /t i ≤ 35. , bi /t i=80.0 /8.0=10.00
10.00 ≤ 35.
Brace member 2, RP 140x80x8
hi /t i ≤ 35. , hi /t i =140.0/8.0=17.50
17.50 ≤ 35.
Brace member 2, RP 140x80x8
0.5 ≤ hi /bi ≤ 2.0 , hi / bi=140.0 /80.0=1.75
0.5 ≤ 1.75 ≤ 2.0
Brace members: 2, RP 140x80x8, 1, RP 60x40x4
bi /b j ≥ 0.75 , bi /b j=80.0 /40.0=2.00
2.00 ≥ 0.75
Brace members: 2, RP 140x80x8, 3, RP 60x40x4
bi /b j ≥ 0.75 , bi /b j=80.0 /40.0=2.00
2.00 ≥ 0.75
Brace member 3, RP 60x40x4
bi /b 0 ≥ 0.25 , bi /b 0=60.0 /80.0=0.75
0.75 ≥ 0.25
Brace member 3, RP 60x40x4
bi /t i ≤ 35. , bi /t i=40.0/ 4.0=10.00
10.00 ≤ 35.
Brace member 3, RP 60x40x4
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hi /t i ≤ 35. , hi /t i =60.0/4.0=15.00
15.00 ≤ 35.
Brace member 3, RP 60x40x4
0.5 ≤ hi /bi ≤ 2.0 , hi / bi=60.0 /40.0=1.50
0.5 ≤ 1.50 ≤ 2.0
Brace members: 3, RP 60x40x4, 1, RP 60x40x4
bi /b j ≥ 0.75 , bi /b j=40.0/ 40.0=1.00
1.00 ≥ 0.75
Brace members: 3, RP 60x40x4, 2, RP 140x80x8 !!!Range of validity requirements are not met!!!
bi /b j ≥ 0.75 , bi /b j=40.0/ 80.0=0.50
0.50<0.75
Eccentricity of connection
−0.55b 0 ≤ e ≤ 0.25b0 , e /b0=0/80.0=0
−0.55 ≤ 0 ≤ 0.25
Effect of bending moments can be omitted.
Stresses in chord
Stresses in chord outside node
σ 0, Ed =
N 0, Ed M 0, Ed
±
=20.27 /32.00−805.41/ 110.86=−6.63 kN /cm2=−66.3 MPa
A0
W el ,0
Maximal compression stresses
σ 0, Ed =min (−66.32 ; )=−66.3 MPa
σ p , Ed =min (−66.32 ; )=−66.3 MPa
Resistance calculation parameters
β=
b1 +b2 +b 3+ h1 +h 2 +h3 40.0+80.0+ 40.0+60.0+140.0+60.0
=
=0.500
6 b0
6⋅80.0
Stresses ratio (28.2 %)
n=− ( σ 0, Ed / f y0 ) /γ M5 =− (−66.3 /235.0 ) /1.00=0.282>0
(
k n =min 1.3−
) (
)
0.4 n
0.4 ⋅0.282
; 1,0 =min 1.3 −
; 1,0 =1.000
β
0.500
Brace member failure resistance (33.2 %)
Only overlapping brace members were verified. It is taken into account, that all members have identical
efficiency.
Overlapping brace member: number 1, RP 60x40x4
beff =min
(
(
be ,ov =min
) (
) (
10 f y0 t 0
10
235.0 ⋅8.0
bi ; b i =min
40.0 ; 40.0 =40.0 mm
b0 /t 0 f yi t i
80.0 /8.0 235.0 ⋅4.0
)
)
10 f yj t j
10
235.0 ⋅8.0
b i ; bi =min
40.0 ; 40.0 =40.0 mm
b j /t j f yi t i
80.0 /8.0 235.0⋅4.0
25 % ≤ λ ov=25.16 %<50 %
(
N i , Rd = f yi t i b eff + be , ov + 2 hi
)
λov
− 4 t i / γ M5
50
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(
N i , Rd =0.235⋅4.0 40.0+40.0+ 2 60.0
)
25.16
− 4⋅4.0 /1.00=154.53 kN
50
Overlapping brace member: number 3, RP 60x40x4
beff =min
(
(
be ,ov =min
) (
) (
10 f y0 t 0
10
235.0 ⋅8.0
bi ; b i =min
40.0 ; 40.0 =40.0 mm
b0 /t 0 f yi t i
80.0 /8.0 235.0 ⋅4.0
)
)
10 f yj t j
10
235.0 ⋅8.0
b i ; bi =min
40.0 ; 40.0 =40.0 mm
b j /t j f yi t i
80.0 /8.0 235.0⋅4.0
25 % ≤ λ ov=35.58% <50 %
(
N i , Rd = f yi t i b eff + be , ov + 2 hi
)
λov
− 4 t i / γ M5
50
(
N i , Rd =0.235⋅4.0 40.0+40.0+ 2 60.0
)
35.58
− 4 ⋅4.0 /1.00=154.53 kN
50
N 1, Ed sin θ 1 + N 3, Ed sin θ 3=22.48⋅sin ( 45.0 )+(−20.43)⋅sin (90.0 )=−4.53 kN
N 1, Rd sin θ 1=154.53 ⋅sin ( 45.0 )=109.27 kN
N 2, Ed sin θ 2=4.45 ⋅sin ( 30.3 )=2.24 kN
N 1, Ed sin θ 1 + N 3, Ed sin θ 3=−4.53 kN ≤ 109.27 kN =N 1, Rd sin θ 1
N 2, Ed sin θ 2=2.24 kN ≤ 109.27 kN = N 1,Rd sin θ 1
Cranked-chord joint resistance (27.5 %)
Chord's cross-section class: 1 (required: 1)
N pl , Rd =
A0 ⋅ f y0
=3200.0 ⋅0.235/ 1.00=752.00 kN
γ M0
N Ed
∣20.27∣
=
=0.13≤ 1,0
0,2 N pl , Rd 0,2 ⋅752.00
W x , pl ⋅ f y,0 146.0 ⋅0.235
M pl , Rd =
=
=34.97 kNm
γ M0
1.00
κ 90=
3 √b 0 /h0
0,8
+
1
3 80.0 /140.0
1
= √
+
=0.826
0,8
1+ 2b0 /h 0 [ 80.0/8.0 ]
1+2 ⋅80.0 /140.0
[ b 0 /t 0 ]
κ=1 − ( √ 2 cos ( θ /2 ) ) ( 1 − κ90 )=1 − ( √ 2 cos ( 149.74/2 ) ) ( 1 −0.826 )=0.936
∣N Ed∣ ∣M Ed∣ ∣20.27∣ ∣8.05∣
+
=
+
=0.27 ≤ 0.936
N pl , Rd M pl , Rd 752.00 34.97
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