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A. Intermediate frame
6.A.1 Loads:
-Checking the member for the following combination of loads:
For load case 1.5 [DL+OL+WL_0DEG], for member no. 401 in STAAD file
Case 1: Fx = -750 kN -maxm. axial tension
Mz = 1730 kN-m -momentFor load case 1.2 [DL+OL+LL+WL_135DEG], for member no. 401 in STAAD file
Case 2: Fx = 710 kN -maxm. axial compression
Mz = 1650 kN-m -moment
Vmax = Fy,max = 780 kN -maxm. shear force
-the beam is connected at the face of column. Forces to be tranferred at the centroid of column:
Offset, o = 750 mm -offset of column in major axis directn.
6.A.2 Sectional properties & end conditions:
Section: 4 x 300 NB 6 THK. TATA STRUCTURAProperties:
Individual member-
Outer diameter of pipe = 323.9 mm
Thickness = 6.3 mm
Inner diameter of pipe = 311.3 mm 1500
A = 6286 mm2
Self-wt. = 49.34 kg/m
Izz = Iyy = 79288969 mm4
It = 158.58 x106
mm4
Composite section-
Acomp. = 25143.8 mm2 400
Self-wt.comp = 197.4 kg/m
Izz,comp. = 14.46 x109
mm4
Iyy,comp. = 1.32 x109
mm4
Iw,comp = 5.80 x1012
mm6
-warping const.
It,comp = 15.78 x109
mm4
-torsional constant
zpz,comp = 18.86 x106
mm3
zpy,comp = 5.03 x106
mm3
zez,comp = 15.86 x10
6
mm
3
zey,comp = 3.65 x106
mm3
rz = 758.36 mm
ry = 229.38 mm
f y = 310 MPa
f u = 450 MPa
6. COLUMN
-plastic section modulus
-elastic section modulus
-radius of gyration
Fig. 4.a Column c/s
z
y
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Structural restrain:
L = 12000 mm -unrestrained length
LLT = 0.8 L
= 12000 mm
k = 2
.'. kL = 24000 mm
6.A.3 Moment capacity: [As per 8.2.2, IS 800- 2007]
-elastic critical moment
[Annex. E-1.1, IS 800- 2007]
E = 200000 MPa -Young's modulus
G = 79300 MPa -modulus of rigidity
Mcr = 150655.8 kN-m
f cr,b = Mcr / Zpx
= 7989.0 MPa
.'. f bd = 281.8 MPa
Section Classification:
D/t = 51.4
ε = 0.90
D/t < 146ε2
.'. βb = 0.84 As section is semi-compact
Mdz = βbzpf bd
= 4468.4 kN-m
Mz,max = Mz + (F x o) F- axial force, o-offset
= 2292.5 kN-m for case I
= 2182.5 kN-m for case IIMdz > Mz,max OK
6.A.4 Tensile strength:
-considering yeilding of gross section
Td = Agf y/γmo
= 7086.0 kN -design tensile strength
Tmax = 750 kN -maxm. axial tension
Td > Tmax OK
6.A.5 Compressive strength:
1.05 x (kL/rmin) = 109.86 mm -for laced column
[As per Cl. 7.6.1.5, IS 800- 2007]
Buckling class = c
f c = 101.19 MPa
Pd = 2544.3 kN -design compressive strength
Pmax = 710.0 kN -maxm. axial compression
Pd > Pmax OK
[For built-up sections as per Table
10, IS 800- 2007]
[Table 9(c) of IS 800- 2007]
[As per Cl. 6.2 of IS 800- 2007]
[Table 15, IS 800- 2007], (full torsional
restrain, partial warping restrain)
-for effective length of compression member
(one end fixed, other free)
-extreme fibre bending
compressive stress
-moment capacity @ major axis
=
+
.
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COMBINED CHECKS:
6.A.6 Section strength: [As per Sec. 9.3.1 of IS 800- 2007]
N = 750 kN -axial tension
= 710 kN -axial compression
My = 0 kN-m -no moment acting @ minor axis
= 0.62 -for Case I
= 0.59 -for Case II
6.A.7 Overall member strength:
A) Bending + Axial tension [As per Sec. 9.3.2.1, IS 800- 2007]
Meff = [M-ΨTZec/A] ≤ Md
Ψ = 1 -T & M cannot vary independently
Meff = 2292.50 kN-m
Md > Meff OK
B) Bending + Axial compression [As per Sec. 9.3.2.2, IS 800- 2007]
Ky = 1+(λ y-0.2)ny ≤ 1 + 0.8ny
Kz = 1+(λ z-0.2)nz ≤ 1 + 0.8nz
KLT =
f cc,z = 1970.9 MPa
.'. λz = 0.40
nz = P/Pd
= 0.279
f cr,b = 7989.0 MPa
λLT = 0.20
CmLT = 0.7
Cmy = Cmz = 0.7
[Table 18, IS 800- 2007]
(M2/M1 = 0.2)
OK
+
+
≤ 1.0
+
+
+
+
≤ 1.0
+0.6
+
≤ 1.0
1− 0.1λ
− 0.25≥ 1− 0.1
− 0.25
λ = λ =
=
λ =
,
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Ky = Kz = 1.1
KLT = 0.99
My = 0 kN-m -no moment acting @ minor axis
= 0.76 OK
= 0.64 OK
6.A.8 Design of Lacings:
-Lacings are designed to take the shear force on the column section
Lacings would be of two types:
i) Primary: these take shear force obtained by analysis acting along the y directn. (Fig. 4.a)
ii) Secondary: these take shear = 2.5% of axial load along the z directn. (Fig. 4.a)
Fy s P
(shear)
1500 400
i) Primary Lacings: Loads-
Fy,max = 780 kN -maxm. SF in the column
Section: 150 NB 4.5 THK. TATA STRUCTURA
Properties:
Outer diameter of pipe = 165.1 mm
Thickness = 4.5 mm
Inner diameter of pipe = 156.1 mm
A = 2270 mm2
-c/s area
Self-wt. = 17.82 kg/m
Ixx = Iyy = 7.33 x10
6
mm
4
-second moment of areaIt = 14.65 x10
6mm
4-torsional const.
zp = (do3
- di3)/6 -plastic section modulus
= 116.10 x103
mm3
ze = 89 x103
mm3
-elastic section modulus
rmin = 56.8 mm -radius of gyration
f y = 310 MPa -grade of steel
f u = 450 MPa
P = 2.5% of axial
force
Fig. 4.b- Lacing arrangement
+
+
+0.6
+
θ θ
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Structural restrain- k = 1
Other Parameters-
s = 3000 mm -spacing of lacing system
P = 551.5 kN
θ = 45◌
ks/r1 ≤ 50
≤ 0.7 (kL/rmin)comp.
0.7 (kL/rmin)comp. = 73.24 mm (kL/rmin)comp. -for the composite section
r1 = 112.31 mm
ks/r1 = 26.7 mm OK
Compression capacity-
L = 2121 mm
kL/rmin = 37.35 mm
Buckling class = a
f c = 263.15 MPa
Pd = 597.5 kN -design compressive strength
Pmax = 551.5 kN -maxm. axial compression
Pd > Pmax OK
ii ) Secondary Lacings:
Loads-
P = 47.6 kN -2.5% of (P + M/d)
Section: 32 NB 3.2 THK. TATA STRUCTURA
Properties:
Outer diameter of pipe = 33.7 mm
Thickness = 3.2 mm
Inner diameter of pipe = 27.3 mm
A = 307 mm2
-c/s area
Self-wt. = 2.41 kg/m
Ixx = Iyy = 0.04 x106
mm4
-second moment of area
It = 0.07 x106
mm4
-torsional const.
zp = (do3
- di3)/6 -plastic section modulus
= 2.99 x103
mm3
ze = 2 x103 mm3 -elastic section modulus
rmin = 10.8 mm -radius of gyration
f y = 310 MPa -grade of steel
f u = 450 MPa
Structural restrain- k = 1 -considering both ends pinned
Other Parameters-
s = 750 mm -spacing of lacing system @ z-axis
[For hollow sections as per Table-
10, IS 800- 2007]
[Table 9(a) of IS 800- 2007]
-c/c length of each lacing member
-both ends pinned, as lacings take only axial loads
-axial compression on each lacing element
[As per Cl. 7.6.5.1, IS 800- 2007]
r1 - radius of gyration of individual member
being laced together
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P = 32.6 kN
θ = 43◌
ks/r1 ≤ 50
≤ 0.7 (kL/rmin)comp.
0.7 (kL/rmin)comp. = 73.24 mm (kL/rmin)comp. -for the composite sectionr1 = 112.31 mm
ks/r1 = 6.7 mm OK
Compression capacity-
L = 548 mm
kL/rmin = 50.57 mm
Buckling class = a
f c = 247.06 MPa
Pd = 75.8 kN -design compressive strength
Pmax = 32.6 kN -maxm. axial compression
Pd > Pmax OK
6.A.9 Welded connection between lacing & column:
Force to be transmitted, Fmax = 551.5 kN -for primary lacing
= 32.6 kN -for secondary lacing
Grade of weld = Fe 540
f u = 540 MPa
f y = 410 MPa
i) Primary Lacing-
-Using fillet weld for the jointWeld thickness = 4 mm
tt = 2.83 mm
γmw = 1.25 -for shop fabrications
Weld capacity = N/mm
= 587.9 N/mm
Weld length reqd. = 938.2 mm
-using welded gusset plated connection for the member:
l = 275.0 mm.'. Weld length = 1100.0 mm
OK
-effective throat thickness of weld
Fig. 4.c- Typical welded gusset plated connection
[Table 9(a) of IS 800- 2007]
-axial compression on each lacing element
[As per Cl. 7.6.5.1, IS 800- 2007]
r1 - radius of gyration of individual member
being laced together
-c/c length of each lacing member
[For hollow sections as per Table-
10, IS 800- 2007]
3×
×
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ii ) Secondary Lacing-
-Using fillet weld for the joint
Weld thickness = 3 mm
tt = 2.12 mm
γmw = 1.25 -for shop fabrications
Weld capacity = 440.9 N/mm
Weld length reqd. = 74.0 mm
Provided weld length = 105.9 mm OK
6.A.10 Welded connection between gusset plate & column CHS:
-Gusset plate is provided for primary lacings
-Gusset plate transfers force from lacings to column members
Force transferred, F = 551.5 kN
Grade of plate = Fe 540
f u = 540 MPa
f y = 410 MPa
t = 6 mm -thickness of gusset plate
Grade of weld = Fe 540
f u = 540 MPa
f y = 410 MPa
-Using fillet weld for the joint
Weld thickness = 6 mm
tt = 4.24 mm
γmw = 1.25 -for shop fabrications
Weld capacity = N/mm
= 1058.2 N/mm
Weld length reqd. = 521.2
l = 350.0 mm -length of plate
Provided weld length = 700 mm -providing weld on both sides
-effective throat thickness of weld
-effective throat thickness of weld
3×
×
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B. End frame
6.B.1 Loads:
-Checking the member for the following combination of loads:
For load case 1.5 [DL+OL+WL_0DEG], for member no. 401 in STAAD file
Case 1: Fx = -230 kN -maxm. axial tension
Mz = 475 kN-m -moment
For load case 1.2 [DL+OL+LL+WL_135DEG], for member no. 401 in STAAD fileCase 2: Fx = 245 kN -maxm. axial compression
Mz = 510 kN-m -moment
Vmax = Fy,max = 240 kN -maxm. shear force
-the beam is connected at the face of column. Forces to be tranferred at the centroid of column:
Offset, o = 750 mm -offset of column in major axis directn.
6.B.2 Sectional properties & end conditions:
Section: 4 x 200 NB 6 THK. TATA STRUCTURA
Properties:Individual member-
Outer diameter of pipe = 219.1 mm
Thickness = 6 mm
Inner diameter of pipe = 207.1 mm 1500
A = 4017 mm2
Self-wt. = 31.53 kg/m
Izz = Iyy = 22819474 mm4
It = 45.64 x106
mm4
Composite section-
Acomp. = 16067.36 mm2
400
Self-wt.comp = 126.1 kg/m
Izz,comp. = 9.13 x109
mm4
Iyy,comp. = 0.73 x109
mm4
Iw,comp = 1.70 x1012
mm6
-warping const.
It,comp = 9.86 x109
mm4
-torsional constant
zpz,comp = 12.05 x106
mm3
zpy,comp = 3.21 x106
mm3
zez,comp = 10.62 x106
mm3
zey,comp = 2.37 x10
6
mm
3
rz = 753.78 mm
ry = 213.73 mm
f y = 310 MPa
f u = 450 MPa
Fig. 4.a Column c/s
-plastic section modulus
-elastic section modulus
-radius of gyration
z
y
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Structural restrain:
L = 12000 mm -unrestrained length
LLT = 0.8 L
= 12000 mm
k = 2
.'. kL = 24000 mm
6.B.3 Moment capacity: [As per 8.2.2, IS 800- 2007]
-elastic critical moment
[Annex. E-1.1, IS 800- 2007]
E = 200000 MPa -Young's modulus
G = 79300 MPa -modulus of rigidity
Mcr = 88710.3 kN-m
f cr,b = Mcr / Zpx
= 7361.5 MPa
.'. f bd = 281.8 MPa
Section Classification: [Table 2, IS 800- 2007]
D/t = 36.5
ε = 0.90
D/t < 52ε2 Section is compact
.'. βb = 1.00 As section is compact
Mdz = βbzpf bd
= 3395.8 kN-m
Mz,max = Mz + (F x o) F- axial force, o-offset
= 647.5 kN-m for case I
= 693.8 kN-m for case IIMdz > Mz,max OK
6.B.4 Tensile strength:
-considering yeilding of gross section
Td = Agf y/γmo
= 4528.1 kN -design tensile strength
Tmax = 230 kN -maxm. axial tension
Td > Tmax OK
6.B.5 Compressive strength:
1.05 x (kL/rmin) = 117.91 mm -for laced column
[As per Cl. 7.6.1.5, IS 800- 2007]
Buckling class = c
f c = 90.92 MPa
Pd = 1460.9 kN -design compressive strength
Pmax = 245.0 kN -maxm. axial compression
Pd > Pmax OK
[Table 9(c) of IS 800- 2007]
[Table 15, IS 800- 2007], (full torsional
restrain, partial warping restrain)
-for effective length of compression member
(one end fixed, other free)
-extreme fibre bending
compressive stress
-moment capacity @ major axis
[As per Cl. 6.2 of IS 800- 2007]
[For built-up sections as per Table
10, IS 800- 2007]
=
+
.
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COMBINED CHECKS:
6.B.6 Section strength: [As per Sec. 9.3.1 of IS 800- 2007]
N = 230 kN -axial tension
= 245 kN -axial compression
My = 0 kN-m -no moment acting @ minor axis
= 0.24 -for Case I
= 0.26 -for Case II
6.B.7 Overall member strength:
A) Bending + Axial tension [As per Sec. 9.3.2.1, IS 800- 2007]
Meff = [M-ΨTZec/A] ≤ Md
Ψ = 1 -T & M cannot vary independently
Meff = 647.50 kN-m
Md > Meff OK
B) Bending + Axial compression [As per Sec. 9.3.2.2, IS 800- 2007]
Ky = 1+(λ y-0.2)ny ≤ 1 + 0.8ny
Kz = 1+(λ z-0.2)nz ≤ 1 + 0.8nz
KLT =
f cc,z = 1947.1 MPa
.'. λz = 0.40
nz = P/Pd
= 0.168
f cr,b = 7361.5 MPa
λLT = 0.21
CmLT = 0.7
Cmy = Cmz = 0.7
OK
[Table 18, IS 800- 2007]
(M2/M1 = 0.2)
+
+
≤ 1.0
+
+
+
+
≤ 1.0
+0.6
+
≤ 1.0
1− 0.1λ
− 0.25≥ 1− 0.1
− 0.25
λ = λ =
=
λ =
,
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Ky = Kz = 1.0
KLT = 0.99
My = 0 kN-m -no moment acting @ minor axis
= 0.37 OK
= 0.32 OK
6.B.8 Design of Lacings:
-Lacings are designed to take the shear force on the column section
Lacings would be of two types:
i) Primary: these take shear force obtained by analysis acting along the y directn. (Fig. 4.a)
ii) Secondary: these take shear = 2.5% of axial load along the z directn. (Fig. 4.a)
Fy s P
(shear)
1500 400
i) Primary Lacings: Loads-
Fy,max = 240 kN -maxm. SF in the column
Section: 80 NB 3.2 THK. TATA STRUCTURA
Properties:
Outer diameter of pipe = 88.9 mm
Thickness = 4 mm
Inner diameter of pipe = 80.9 mm
A = 1067 mm2
-c/s area
Self-wt. = 8.38 kg/m
Ixx = Iyy = 0.96 x10
6
mm
4
-second moment of areaIt = 1.93 x10
6mm
4-torsional const.
zp = (do3
- di3)/6 -plastic section modulus
= 28.85 x103
mm3
ze = 22 x103
mm3
-elastic section modulus
rmin = 30.0 mm -radius of gyration
f y = 310 MPa -grade of steel
f u = 450 MPa
P = 2.5% of axial
force
+
+
+0.6
+
θ θ
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Structural restrain- k = 1
Other Parameters-
s = 3000 mm -spacing of lacing system
P = 169.7 kN
θ = 45◌
ks/r1 ≤ 50
≤ 0.7 (kL/rmin)comp.
0.7 (kL/rmin)comp. = 78.60 mm (kL/rmin)comp. -for the composite section
r1 = 75.37 mm
ks/r1 = 39.8 mm OK
Compression capacity-
L = 2121 mm
kL/rmin = 70.59 mm
Buckling class = a
f c = 209.58 MPa
Pd = 223.6 kN -design compressive strength
Pmax = 169.7 kN -maxm. axial compression
Pd > Pmax OK
ii ) Secondary Lacings:
Loads-
P = 14.6 kN -2.5% of (P + M/d)
Section: 32 NB 2.6 THK. TATA STRUCTURA
Properties:
Outer diameter of pipe = 33.7 mm
Thickness = 3.2 mm
Inner diameter of pipe = 27.3 mm
A = 307 mm2
-c/s area
Self-wt. = 2.41 kg/m
Ixx = Iyy = 0.04 x106
mm4
-second moment of area
It = 0.07 x106
mm4
-torsional const.
zp = (do3
- di3)/6 -plastic section modulus
= 2.99 x103
mm3
ze = 2 x103 mm3 -elastic section modulus
rmin = 10.8 mm -radius of gyration
f y = 310 MPa -grade of steel
f u = 450 MPa
Structural restrain- k = 1 -considering both ends pinned
Other Parameters-
s = 750 mm -spacing of lacing system @ z-axis
-both ends pinned, as lacings take only axial loads
-axial compression on each lacing element
[As per Cl. 7.6.5.1, IS 800- 2007]
r1 - radius of gyration of individual member
being laced together
-c/c length of each lacing member
[For hollow sections as per Table-
10, IS 800- 2007]
[Table 9(a) of IS 800- 2007]
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P = 10.0 kN
θ = 43◌
ks/r1 ≤ 50
≤ 0.7 (kL/rmin)comp.
0.7 (kL/rmin)comp. = 78.60 mm (kL/rmin)comp. -for the composite sectionr1 = 75.37 mm
ks/r1 = 10.0 mm OK
Compression capacity-
L = 548 mm
kL/rmin = 50.57 mm
Buckling class = a
f c = 247.06 MPa
Pd = 75.8 kN -design compressive strength
Pmax = 10.0 kN -maxm. axial compression
Pd > Pmax OK
6.B.9 Welded connection between lacing & column:
Force to be transmitted, Fmax = 169.7 kN -for primary lacing
= 10.0 kN -for secondary lacing
Grade of weld = Fe 540
f u = 540 MPa
f y = 410 MPa
i) Primary Lacing-
-Using full penetration groove weld for the jointWeld thickness = 4 mm
tt = 4 mm
γmw = 1.25 -for shop fabrications
Weld capacity = N/mm
= 831.4 N/mm
Weld length reqd. = 204.1 mm
Provided weld length = 279.3 mm OK
ii ) Secondary Lacing-
Weld thickness = 3 mm -fillet weld
tt = 2.12 mm
γmw = 1.25 -for shop fabrications
Weld capacity = 440.9
Weld length reqd. = 22.7 mm
Provided weld length = 105.9 mm OK
-effective throat thickness of weld
-c/c length of each lacing member
[For hollow sections as per Table-
10, IS 800- 2007]
[Table 9(a) of IS 800- 2007]
-providing weld around the whole
circumference of the tube
-effective throat thickness of weld
r1 - radius of gyration of individual member
being laced together
-axial compression on each lacing element
[As per Cl. 7.6.5.1, IS 800- 2007]
3×
×
6.0 Column