Built-up steel column

7/28/2019 Built-up steel column

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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

6.0 Column



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

=

+

.

6.0 Column



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 =

,

6.0 Column



Ky = Kz = 1.1

KLT = 0.99


= 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:


Thickness = 4.5 mm

Inner diameter of pipe = 156.1 mm

A = 2270 mm2

-c/s area


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


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

6.0 Column



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 > Pmax OK

ii ) Secondary Lacings:

Loads-

P = 47.6 kN -2.5% of (P + M/d)


Properties:


Thickness = 3.2 mm


A = 307 mm2

-c/s area


Ixx = Iyy = 0.04 x106

mm4

-second moment of area

It = 0.07 x106

mm4

-torsional const.

zp = (do3


= 2.99 x103

mm3

ze = 2 x103 mm3 -elastic section modulus



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

6.0 Column



P = 32.6 kN

θ = 43◌

ks/r1 ≤ 50


0.7 (kL/rmin)comp. = 73.24 mm (kL/rmin)comp. -for the composite sectionr1 = 112.31 mm

ks/r1 = 6.7 mm OK


L = 548 mm

kL/rmin = 50.57 mm

Buckling class = a

f c = 247.06 MPa



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]


[As per Cl. 7.6.5.1, IS 800- 2007]





10, IS 800- 2007]

3×

×

6.0 Column



ii ) Secondary Lacing-

-Using fillet weld for the joint

Weld thickness = 3 mm

tt = 2.12 mm


Weld capacity = 440.9 N/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


f u = 540 MPa

f y = 410 MPa

-Using fillet weld for the joint

Weld thickness = 6 mm

tt = 4.24 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



3×

×

6.0 Column



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


For load case 1.2 [DL+OL+LL+WL_135DEG], for member no. 401 in STAAD fileCase 2: Fx = 245 kN -maxm. axial compression


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-


Thickness = 6 mm

Inner diameter of pipe = 207.1 mm 1500

A = 4017 mm2


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


-radius of gyration

z

y

6.0 Column



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 > 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]

=

+

.

6.0 Column



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


= 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 =

,

6.0 Column



Ky = Kz = 1.0

KLT = 0.99


= 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


Properties:


Thickness = 4 mm


A = 1067 mm2

-c/s area


Ixx = Iyy = 0.96 x10

6

mm

4

-second moment of areaIt = 1.93 x10

6mm

4-torsional const.

zp = (do3


= 28.85 x103

mm3

ze = 22 x103

mm3




f u = 450 MPa

P = 2.5% of axial

force

+

+

+0.6

+

θ θ

6.0 Column



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. = 78.60 mm (kL/rmin)comp. -for the composite section

r1 = 75.37 mm

ks/r1 = 39.8 mm OK


L = 2121 mm

kL/rmin = 70.59 mm

Buckling class = a

f c = 209.58 MPa



Pd > Pmax OK

ii ) Secondary Lacings:

Loads-

P = 14.6 kN -2.5% of (P + M/d)


Properties:


Thickness = 3.2 mm


A = 307 mm2

-c/s area


Ixx = Iyy = 0.04 x106

mm4

-second moment of area

It = 0.07 x106

mm4

-torsional const.

zp = (do3


= 2.99 x103

mm3

ze = 2 x103 mm3 -elastic section modulus



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


[As per Cl. 7.6.5.1, IS 800- 2007]





10, IS 800- 2007]

[Table 9(a) of IS 800- 2007]

6.0 Column



P = 10.0 kN

θ = 43◌

ks/r1 ≤ 50


0.7 (kL/rmin)comp. = 78.60 mm (kL/rmin)comp. -for the composite sectionr1 = 75.37 mm

ks/r1 = 10.0 mm OK


L = 548 mm

kL/rmin = 50.57 mm

Buckling class = a

f c = 247.06 MPa



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


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



= 831.4 N/mm



ii ) Secondary Lacing-

Weld thickness = 3 mm -fillet weld

tt = 2.12 mm


Weld capacity = 440.9






10, IS 800- 2007]

[Table 9(a) of IS 800- 2007]

-providing weld around the whole

circumference of the tube





[As per Cl. 7.6.5.1, IS 800- 2007]

3×

×

6.0 Column

Built-up steel column

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