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Design of structural barriers (column) for swing object.

Material properties

Material yield stress Fy = 355 N/mm (NV A36)

Young's modulus E = 210000 N/mm

Material factor m = 1.0

Weight input

Lift weight W = 20.0 T

= 200.0 kN

Rigging weight Wrw = 5.0 T (Assumed)

= 50.0 kN

Static hook load Wst = W + Wrw

= 250.0 kN

Loading as per ISO 19901-6

Horizontally directed force in plane of bumper Fh = 0.10 Wst (refer Table 18 of ISO 1990

= 233.0 kN

Horizontally directed force out-of-plane of bumper Fl = 0.05 Wst (refer Table 18 of ISO 1990

= 11.7 kN

Vertically directed force Fv = 0.01 Wst (refer Table 18 of ISO 1990

= 23.3 kN

Height of column Lc = 0.75 m

No. of columns in a row n = 3 Nos.

Spacing between columns (average) Lb = 4.20 m

No. of tie beams in one column = 4 Nos.

Permissible deflection Lc / 150 = 5.0 mm

Section properties for column = H 200-200

D Bf tw tf Root Rd.

200 200 10 15 10 mm

Moment of inertia of section Iy Iz

5.55E+07 2.00E+07 mm4

Elastic section modulus Zey Zez

555441.67 200141.7 mm3

Plastic section modulus Zpy Zpz

634117 304250 mm3

Plastic moment capacity Mpy Mpz

225.1 108.0 kN-m

Torsional rigidity of column Jt = 506667 mm4

Cross-section area Ax = 7700 mm2

Shear area for Fh Aw = 2000 mm2

Shear area for Fl Af = 5700 mm2

Section class

Web c/t = 15.0

< 58.6 (= 72) -----------> Web is Class 1

Flange c/t = 5.7

< 7.3 (= 9) -----------> Flange is Clas

Weight of one column = 0.45 kNWeight/ unit length of tie beams = 0.31 kN

Total weight on one column Wc = 5.6 kN

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Work done by horizontal force (Fh) WFh = Fh*

Moment at a distance x` from top My = Fh* x

Elastic Strain energy developed in the column Wse =

=

From energy balance theory WFh = Wse

Fh* =

Hence, =

= 1.40 mm

< 5.00 mm Hence OK

Moment developed at base of column My = Fh* L

= 174.75 kN-m

Mz = Fl* L /n

= 2.91 kN-m

BMD

(Assumption:Horizontal out-of-plane force being

distributed among all columns in a row equally.)

Fh

D

LcColumn

x

My

1

2

Y Y

Z

Z

Fl

Fh

dx2EI

xFdx

2EI

M L

0

22h

L

0

2y

3

L

2EI

F 32h

3

L

2EI

F 32h

3

L

2EI

F 3h

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Bending stress at base of column h = My/ Zey

= 314.6 N/mm2

l = Mz/ Zez

= 14.6 N/mm2

Axial compressive stress v = (Fv+ Wc) / Ax

= 3.76 N/mm2

Shear stress y = Fh/ Aw

= 116.50 N/mm2

z = Fl/ Af

= 2.04 N/mm2

Note: Torsion is assumed not to reach the bottom of column due to the presence of tie members.

Elastic verification at location

x,Ed = h+ v

= 318.37 N/mm2

Ed = 1.53 N/mm2

= 0.80 (UR)


x,Ed = h+ l+ v

= 332.93 N/mm2

Ed = 0.00 N/mm2

= 0.88 (UR)

Plastic check as per eqn. 6.2 of EC3-1-1

Axial Check:

Design Axial Force, NEd = 28.94 kN

Axial Capacity, NRd = 2733.5 kN

Utilization Ratio, Ura=NEd/NRd = 0.01 Safe

Shear Check:

Design Shear Force, VzEd= Fh = 233.00 kN

Shear Capacity, VzRd = 409.92 kN

Utilization Ratio, Ursz = VzED/VzRD = 0.57 Safe

Design Shear Force, VyEd = Fl = 11.65 kN

Shear Capacity, VyRd = 1168.27 kNUtilization Ratio, Ursy = VyED/VyRD = 0.01 Safe

Bending Check:

Moment Capacity is reduced if design shear force is geater than half the plastic shear resistance of section.

1

2

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(Equation 6.33 of EN 1993-1-1:2005 / NA: 2008)

NEd

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= 355.0 kN

NEd 28.9 kN 0.01 UR

Buckling check not required

Joint check

Impact force Fh = 233.00 kN

Fl = 11.7 kN

YY

Z w1

w2

w1

0

5.0

M

yww fth

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235 NV A

355 NV A36

Section D Bf tw tf r Na wt Wp We

100x100 100 100 6 8 10 50 16.5 87360 76500

125x125 125 125 6.5 9 10 62.5 23.1 153268 13600

150x150 150 150 7 10 11 75 30.7 245755 21900

200x100 200 100 5.5 8 11 100 20.5 209137 18400

194x150 194 150 6 9 13 97 29.5 308037 27700

200x200 200 200 8 12 13 100 48.7 524975 47200

250x125 250 125 6 9 12 125 28.6 365458 32400

250x250 250 250 9 14 16 125 70.6 959523 86700

300x150 300 150 6.5 9 13 150 35.6 541589 48100

300x300 300 300 10 15 18 150 91.8 1499794 136000

350x175 350 175 7 11 14 175 48.2 867262 77500

350x350 350 350 12 19 20 175 133.8 2543313 230000

400x200 400 200 8 13 16 200 64.3 1325288 119000

390x300 390 300 10 16 22 195 103.5 2185409 198000

400x400 400 400 13 21 22 200 168.4 3669932 333000

428x407 428 407 20 35 22 214 279.9 6308904 557000

488x300 488 300 11 18 26 244 123.8 3223436 291000

600x200 600 200 11 17 22 300 102.3 2976187 259000588x300 588 300 12 20 28 294 145.8 4483890 402000

0.880 (NV A36)

D Bf tw tf r Na wt Wp We

Built-up 200-200 200 200 10 15 10 100 60.4 634117 55544

Box [350-300] 350 300 20 25 10 175 164.9 3237447 291071Side plate thickness = 15 15

UR for Tie members

0.81

0.88

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Na = Neutral axis depth

b1 = 200

t1 = 15

b1 = 170 t 1 = 10N.A.

t2 = 15

b2 = 200

Plastic section modulus, Wp

Neutral axis from top of plate = 100.00 mm

Flange = 277500 mm3

Web above N.A. = 36125 mm3

Web below N.A. = 36125mm

3

Flange = 277500 mm3

Second moment of Area, I


Flange = 25725000 mm4

web = 4094167 mm4

Flange = 25725000 mm4

Total = 55544167 mm4

Elastic section modulus, W = I/(D/2) = 555441.7 mm3


b1 = 200

t1 = 15

b1 = 170 t 1 = 10

N.A.

t2 = 15

b2 = 200


Neutral axis from top of plate = 100.00 mm 100 mm

Flange = 277500 mm3

75000 75


2125 2

3

ELASTIC SECTION MODULUS

ELASTIC SECTION MODULUS OF BUILT-UP SECTION

Major axis Minor axis

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Minor axis

2* E * Iz/ Lcr

2

18436.3

737

28.9 0.04 UR

P

l Column

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(Fh2+ Fl

2)

l Mp

l-x Me

Plastic moment capacity of section Mp = 225.1 kN-m

Elastic moment capacity of section Me = #REF! kN-m

Height of column l = 0.8 m

Length of plastic hinge x =

= #REF! m

(Mp - Me) * l

Mp

=

Hinge

Me

Mp

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Top fl Bot fl Top web Bot web Top RR Bot RR c Web c Flng. Ix Iy Zx

36800 36800 5292 5292 1588 1588 64 37 3.83E+06 1.34E+06 7.65E+04 2

65250 65250 9302.3125 9302.313 2082 2082 87 49.25 8.47E+06 2.93E+06 1.36E+05 4

105000 105000 14787.5 14787.5 3090 3090 108 60.5 1.64E+07 5.63E+06 2.19E+05 7

76800 76800 23276 23276 4492 4492 162 36.25 1.84E+07 1.34E+06 1.84E+05 2

124875 124875 23232 23232 5912 5912 150 59 2.69E+07 5.07E+06 2.77E+05 6

225600 225600 30976 30976 5912 5912 150 83 4.72E+07 1.60E+07 4.72E+05 1

135562.5 135562.5 40368 40368 6799 6799 208 47.5 4.05E+07 2.94E+06 3.24E+05 4

413000 413000 55444.5 55444.5 11317 11317 190 104.5 1.08E+08 3.65E+07 8.67E+05 2

196425 196425 64613.25 64613.25 9756 9756 256 58.75 7.21E+07 5.08E+06 4.81E+05 6

641250 641250 91125 91125 17522 17522 234 127 2.04E+08 6.75E+07 1.36E+06 4

326287.5 326287.5 94136 94136 13207 13207 300 70 1.36E+08 9.84E+06 7.75E+05 1

1100575 1100575 146016 146016 25065 25065 272 149 4.03E+08 1.36E+08 2.30E+06 7

503100 503100 139876 139876 19668 19668 342 80 2.37E+08 1.74E+07 1.19E+06 1

897600 897600 160205 160205 34899 34899 314 123 3.87E+08 7.21E+07 1.98E+06 4

1591800 1591800 208266.5 208266.5 34899 34899 314 171.5 6.66E+08 2.24E+08 3.33E+06 1

2799143 2799143 320410 320410 34899 34899 314 171.5 1.19E+09 3.94E+08 5.57E+06 1

1269000 1269000 280918 280918 61800 61800 400 118.5 7.10E+08 8.11E+07 2.91E+06 5

991100 991100 440489.5 440489.5 56504 56504 522 72.5 7.76E+08 2.28E+07 2.59E+06 21704000 1704000 450456 450456 87489 87489 492 116 1.18E+09 9.02E+07 4.02E+06 6


277500 277500 36125 36125 3434 3434 150 85 55544167 20014167 555442

1218750 1218750 225000 225000 6223 6223 280 130 509375000Side plt. 168750 168750

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Na = N

plastic elastic

100 7700

19 770000

eutral Axis 100 100

X = 85.0

N.A. = X + t1 = 100.00 mm

Yc = 81.5 mm C = 3850 x syp

Yt = 81.5 mm T = 3850 x syp

Zp = 627250 mm3

P

Neutral

S

Neutral

Elastic section

plastic elastic

100 7700

19 770000

eutral Axis 100 100

X = 85.0

N.A. = X + t1 = 100.00 mm

Yc = 81.5 mm C = 3850 x syp

Yt = 81.5 mm T = 3850 x syp

Zp = 627250 mm3

(Torsion) T = Tf* r / Jt

325 2 N

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Torsion at base of column Tf = 1.17 kN-m

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b1 = 300

t1 = 25 plastic elastic

175.00 30000.0

35.00 5250000

Neutral Axis 175.00 175.0

20

t3

=

N.A. X = 150.0

t4 = 15 N.A. = X + t1 = 175.00 mm

Yc = 137.5 mm C =

Yt = 137.5 mm T =

t2 = 25

b2 = 300 Zp = 2887500 mm3

, Wp

= 175.00 mm

= 1218750 mm3

N.A. = 225000 mm3

ve N.A. = 168750 mm

3

N.A. = 225000 mm3

ow N.A. = 168750 mm3

= 1218750 mm3

, I

= 175.00 mm

= 198437500 mm4

= 45000000 mm4

= 67500000 mm4

= 198437500 mm4

= 509375000 mm4

) = 2910714.286 mm3

TION MODULUS OF BOX SECTION

300

b3

=

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Material properties

Material yield stress Fy

Young's modulus E

Material factor m

Weight input

Lift weight W

Rigging weight Wrw

Static hook load Wst


Horizontally directed force in plane of bumper Fh

Horizontally directed force out-of-plane of bumper Fl

Vertically directed force ( -ve for Tension) Fv

Nsd

Design Hydrostatic pressure Psd

Height of column Lc

No. of columns in a row n

Spacing between columns Lb

No. of tie beams in one column

Permissible deflection 2*Lc / 200

Supporting bottom girder/beam

Unsupported length of supporting girder/beam lg

Moment of inertia of supporting girder/beam Ig

Section properties for column

D

219.08

Moment of inertia of CHS Ic

Elastic section modulus of CHS Ze,c

Plastic section modulus of CHS Zp,c

(Assumption:- Horizontal members checked for 2840mm span and found to be

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Work done by horizontal force (Fh) WFh

Moment at a distance `xc` from top My,c

Elastic Strain energy developed in the column due to bending moment Wse,c

Elastic Strain energy developed in the beam due to bending moment Wse,b

From energy balance theory WFh

Fh*

Hence,

Design bending moment about member y-axis (in-plane) My,sd

Mz,sd

BMD for Column

(Assumption:Horizontal out-of-plane force being distributed among all

columns in a row equally.)

xc

My,c

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k in equation 3 & 4 relate to buckling in the y and z directions, respectively.

Reduction factors

For cantilever tubular member Cmy

For bottom fixed and top free to move for tubular member Cmz

Ic/LcIg/Lg

GB

Hence from fig. 12-4 of N-004 (pg 72) k y

Here, k z

Calculation of material factor, M

Geometric parameter =

Hence, / (D/t)and 0.825D/t

Elastic hoop buckling factor Ch

Ch = = 0.0368

Ch = =

Ch = =

L/D (2D/t)

GA=

.

0.44t/D4/30.21(D/t)0.44t/D

579.0/737.0

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Ch = 0.80 =

Elastic hoop buckling strength f he=

Hence, f he/fy

Characteristic hoop buckling strength f h

fh

= = 355 N/mm^2

fh = =

fh = =

c,Sd

Design hoop stress due to hydrostatic pressure p,Sd = pSd* D/2t

c =

h =

Shell slenderness parameter S

Material factor MM = 1.15 = 1.15

M = 0.85+0.60s =

M = 1.45 =

Calculation of design axial compressive resistance, Nc,Rd

Critical elastic buckling coefficient Ce

Characteristic elastic local buckling strength fcle = 2*Ce*E*t/D

Hence, fy/ fcle

Characteristic local buckling strength f cl

fcl = = 355 N/mm^2

Max. combined design compressive stress, design axial stress

in damaged cylinder

2Ch* E * t/D

yf

yf

4.07.0 yhey /fff

hef

cley/ff

hey/ff

Et

Dfy

E

fy120

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fcl = =

fcl = =

l = = 1.84

fc = =

fc = = 94.77753 N/mm^2

Design axial compressive resistance Nc,Rd = Afc/M

Calculation of design bending moment resistance, MRd

Characteristic bending strength fm

fm = = 490.5 N/mm^2

fm = =

fm = =

Design axial local buckling resistance Ncl,Rd= fcl* A / M

Euler buckling strengths corresponding to the member y - axis NEy

Euler buckling strengths corresponding to the member z - axis NEZ

Combined stress

Check 1

Check 2

Design bending moment resistance MRd =

y

cle

yf

f

f0.274-1.047

clef

yfW

Z

yy

fW

Z

Et

Df

58.213.1

yy

fW

Z

Et

Df

76.094.0

M

mWf

E

lf

i

k c

l

yf

228.00.1 l

yf2

9.0

l

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Shear check

Design shear resistance VRd

Applied shear force VSd

VSd

VRd

Interaction shear and bending moment

My,sd

MRd

Mz,sd

MRd

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= 355N/mm

= 210000N/mm

= 1.0

= 20.0 T

= 200.0 kN

= 5.0 T (Assumed)

= 50.0 kN

= W + Wrw

= 250.0 kN

= 0.10 Wst (refer Table 18 of ISO 1

= 25.0 kN


= 12.5 kN


= 2.5 kN

= 0.00 kN/m^2

= 5000 mm

= 2 Nos.

= 1800 mm

= 8 Nos.

= 50.0 mm (assumed cantilever???)

= PG 200x200x15x25

= 700.00 mm

= 199327500 mm4

= CHS

= 200 #80

d t

182.48 18.3 mm

= 5.86E+07 mm4

= 535417.4 mm3

= 739764 mm3

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= 71.3 mm

= 117299252 mm4

= 11543.1 mm2

= CHS 130 #80d t

122.3 9.5 mm

= 8.59E+06 mm4

= 12.0

< 33.1 (= 50^2) ----------->

= 0.91 kN

= 0.906 kN

= 14.0 kN

Lb

Column

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= Work done on col. + work done on tie beam= Fh* /2 + Fh* /2

= Fh*

= Fh* x

=

=

=

= Wse,c+ Wse,b

=

=

= 55.77 mm

> 50.00 mm Check

= Fh* L

= 125.00 kN-m

= Fl* L /n

= 31.25 kN-m

BMD for beam

xb

My,b

dx2EI

xFdx

2EI

M L

0

2c

2h

L

0

2cy,

3

L

2EI

F 3

c

c

2h

3

L

2EI

F

3

L

2EI

F 3b

b

2h

3c

c

2h

b

3b

c

3ch

I

L

I

L

6E

F

3

L

2EI

F 3

b

b

2

h

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= 1.0

= 0.85

11730

284754

= 0.04

=

= 2.0

= 1.0

= 111.7

= 9.33

= 9.88

for

for

for

1.6

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for

= 1289.43 N/mm^2

= 3.63

for

for

for

=

= 240.9 N/mm^2

= 0.00 N/mm^2

=0.18

= 0.52

=

= 0.12

for S < 0.5

for 0.5

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for 0.17< fy/ fcle 1.911

for l 1.34

= 951.3 kN

= 3563.3 kN

= 1215.6 kN

= 4862.3 kN

= 0.563 UR

for

for

for

= 228.4 kN-m

0517.0Et

Dfy

103.00517.0 Web is Class 1

Flange c/t = 6.9

< 7.3 (= 9) -----------> Flange is Clas

Weight of one column = 1.95 kNWeight/ unit length of tie beams = 0.31 kN

Total weight on one column Wc = 13.6 kN

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Work done by horizontal force (Fh) WFh = Work done on col. + work done on tie beam

= Fh* /2 + Fh* /2

= Fh*

Moment at a distance `xc` from top My,c = Fh* x

Elastic Strain energy developed in the column Wse,c =

=

Elastic Strain energy developed in the beam Wse,b =

BMD for Column BMD for beam

xc

My,c

2Lb

Horizontal member

connecting columns

Fh

D

Column

Column

Column

Horizontal member

connecting columns

Lc

Fh

2Lb

Col. location

Col. locationMy,b

Fh

dx2EI

xFdx

2EI

M L

0

2c

2h

L

0

2cy,

3

L

2EI

F 3c2h

384EI2LFb

2

h

3

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Mz = Fl* L /n

= 16.67 kN-m

Elastic verification as per eqn. 6.1 of EC3-1-1

Bending stress at base of column h = My/ Zey

= 211.9 N/mm2

l = Mz/ Zez

= 104.2 N/mm2

Axial compressive stress v = (Fv+ Wc) / Ax

= 2.54 N/mm2

Shear stress y = Fh/ Aw

= 15.63 N/mm2

z = Fl/ Af

= 2.71 N/mm2

Note: Torsion is assumed not to reach the bottom of column due to the presence of tie members.


x,Ed = h+ v

= 214.40 N/mm2

Ed = 2.03 N/mm2

= 0.36 (UR)


x,Ed = h+ l+ v

= 318.57 N/mm2

Ed = 0.00 N/mm2

= 0.81 (UR)

(Assumption:Horizontal out-of-plane force being

distributed among all columns in a row equally.)

1

2

1

2

Y Y

Z

Z

Fl

Fh

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Shear Check:

Design Shear Force, VzEd= Fh = 25.00 kN

Shear Capacity, VzRd = 327.93 kN

Utilization Ratio, Ursz = VzED/VzRD = 0.08 Safe

Design Shear Force, VyEd = Fl = 12.50 kN

Shear Capacity, VyRd = 944.45 kN

Utilization Ratio, Ursy = VyED/VyRD = 0.01 Safe

Bending Check:Moment Capacity is reduced if design shear force is geater than half the plastic shear resistance of section.

Moment Reduction Factor for MzRdis z = 0.948

Moment Reduction Factor for MyRdis y = 0.718

Moment Capacity about Z-Z is MzvRd = 86.20 kNm

Moment Capacity about Y-Y is MyvRd = 186.37 kNm

Moment Capacity is further reduced if axial force is present and does not satisfy following criteria.

Moment Capacity reduction paramerters:

n = 0.007

a = 0.252

For Z-Z axis: Criteria for Moment Capacity reduction:

(Equation 6.33 of EN 1993-1-1:2005 / NA: 2008)

NEd

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Weld type w1 = Full penetration weld

w2 = Full penetration weld

Weld thk. around flange tw1 = 12.0 mm

Fillet weld thk. around web tw2 = 8.0 mm

Shear area of weld w1 a1 = 4800 mm2

Shear area of weld w2 a2 = 1408 mm2

Shear stress in weld w1

Shear due to direct stress w1,d,ll = 2.6 N/mm2

Shear stress in weld w2 w2,ll = 17.8 N/mm2

Permissible shear stress perm = (Fy/m) / 3

= 205.0 N/mm2

= ll -----------> Safe in shea

Material tensile stress Fu = 490 N/mm

Section modulus of weld w1 W = 472000 mm3

Moment at base of swing barrier Mb = Fr x L

= 100.00 kN-m

Normal stress due to bending moment T = Mp /Z

= 211.9 N/mm2

Permissible normal stress perm = Fu/m

= 490.0 N/mm2

> T -----------> Safe in norm

Von misses stress [T2+ 3(ll

2)] = 211.9 N/mm

2UR = 0.43

< 490.0 N/mm2

-----------> Hence OK

Z

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235 NV A

355 NV A36

Section D Bf tw tf r Na wt Wp We

100x100 100 100 6 8 10 50 16.5 87360 76500

125x125 125 125 6.5 9 10 62.5 23.1 153268 13600

150x150 150 150 7 10 11 75 30.7 245755 21900

200x100 200 100 5.5 8 11 100 20.5 209137 18400

194x150 194 150 6 9 13 97 29.5 308037 27700

200x200 200 200 8 12 13 100 48.7 524975 47200

250x125 250 125 6 9 12 125 28.6 365458 32400

250x250 250 250 9 14 16 125 70.6 959523 86700

300x150 300 150 6.5 9 13 150 35.6 541589 48100

300x300 300 300 10 15 18 150 91.8 1499794 136000

350x175 350 175 7 11 14 175 48.2 867262 77500

350x350 350 350 12 19 20 175 133.8 2543313 230000

400x200 400 200 8 13 16 200 64.3 1325288 119000

390x300 390 300 10 16 22 195 103.5 2185409 198000

400x400 400 400 13 21 22 200 168.4 3669932 333000

428x407 428 407 20 35 22 214 279.9 6308904 557000

488x300 488 300 11 18 26 244 123.8 3223436 291000

600x200 600 200 11 17 22 300 102.3 2976187 259000588x300 588 300 12 20 28 294 145.8 4483890 402000

0.805 (NV A36)

D Bf tw tf r Na wt Wp We

Built-up 200-200 200 200 10 15 7.5 100 60.4 631173 55544

Box [350-300] 350 300 20 25 10 175 164.9 3237447 291071Side plate thickness = 15 15

UR for Tie members

0.81

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Col. location

My,b

My,b

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b1 = 200

t1 = 12

b1 = 176 t 1 = 8

N.A.

t2 = 12

b2 = 200



Fl 2256003

ELASTIC SECTION MODULUS

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Total = 46104917 mm4

Elastic section modulus, W = I/(D/2) = 461049.2 mm3


b1 = 200t1 = 15

b1 = 170 t 1 = 10

N.A.

t2 = 15

b2 = 200



Flange = 277500 mm3

75000 7


2125

Web below N.A. = 36125 mm3

Flange = 277500 mm3

75000 7

Total = 627250 mm3

304250 mm3



Flange = 25725000 mm4

1.000E+07 mm4

web = 4094167 mm4

14167 mm4

Flange = 25725000 mm4

1.000E+07 mm4

Total = 55544167 mm4

20014166.7 mm4


Major axis Minor axis

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Elastic section modulus, W = I/(D/2) = 555442 mm3

200142 mm3

Minor axis

2* E * Iz/ Lcr

2

518.2

21

16.1 0.78 UR

P

l Column

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(Fh2+ Fl

2)

l Mp

l-x Me

Plastic moment capacity of section Mp = 186.4 kN-m

Elastic moment capacity of section Me = #REF! kN-m

Height of column l = 4.0 m

Length of plastic hinge x =

= #REF! m

=

(Mp - Me) * l

Mp

Hinge

Me

Mp

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36800 36800 5292 5292 1588 1588 64 37 3.83E+06 1.34E+06 7.65E+04 2

65250 65250 9302.3125 9302.313 2082 2082 87 49.25 8.47E+06 2.93E+06 1.36E+05 4

105000 105000 14787.5 14787.5 3090 3090 108 60.5 1.64E+07 5.63E+06 2.19E+05 7

76800 76800 23276 23276 4492 4492 162 36.25 1.84E+07 1.34E+06 1.84E+05 2

124875 124875 23232 23232 5912 5912 150 59 2.69E+07 5.07E+06 2.77E+05 6

225600 225600 30976 30976 5912 5912 150 83 4.72E+07 1.60E+07 4.72E+05 1

135562.5 135562.5 40368 40368 6799 6799 208 47.5 4.05E+07 2.94E+06 3.24E+05 4

413000 413000 55444.5 55444.5 11317 11317 190 104.5 1.08E+08 3.65E+07 8.67E+05 2

196425 196425 64613.25 64613.25 9756 9756 256 58.75 7.21E+07 5.08E+06 4.81E+05 6

641250 641250 91125 91125 17522 17522 234 127 2.04E+08 6.75E+07 1.36E+06 4

326287.5 326287.5 94136 94136 13207 13207 300 70 1.36E+08 9.84E+06 7.75E+05 1

1100575 1100575 146016 146016 25065 25065 272 149 4.03E+08 1.36E+08 2.30E+06 7

503100 503100 139876 139876 19668 19668 342 80 2.37E+08 1.74E+07 1.19E+06 1

897600 897600 160205 160205 34899 34899 314 123 3.87E+08 7.21E+07 1.98E+06 4

1591800 1591800 208266.5 208266.5 34899 34899 314 171.5 6.66E+08 2.24E+08 3.33E+06 1

2799143 2799143 320410 320410 34899 34899 314 171.5 1.19E+09 3.94E+08 5.57E+06 1

1269000 1269000 280918 280918 61800 61800 400 118.5 7.10E+08 8.11E+07 2.91E+06 5

991100 991100 440489.5 440489.5 56504 56504 522 72.5 7.76E+08 2.28E+07 2.59E+06 21704000 1704000 450456 450456 87489 87489 492 116 1.18E+09 9.02E+07 4.02E+06 6


277500 277500 36125 36125 1962 1962 155 87.5 55544167 20014167 555442

1218750 1218750 225000 225000 6223 6223 280 130 509375000Side plt. 168750 168750

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Na = N

plastic elastic

100 6208

16 620800

eutral Axis 100 100

X = 88.0

N.A. = X + t1 = 100.00 mm

Yc = 82.7 mm C = 3104 x syp

Yt = 82.7 mm T = 3104 x syp

Zp = 513152 mm3

P

Neutral

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Elastic sectio

plastic elastic

100 7700

19 770000

eutral Axis 100 100

X = 85.0

N.A. = X + t1 = 100.00 mm

Yc = 81.5 mm C = 3850 x syp

Yt = 81.5 mm T = 3850 x syp

Zp = 627250 mm3

(Torsion) T = Tf* r / Jt

= 678.8

Torsion at base of column Tf

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Torsion at base of column Tf = 1.25 kN-m

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Left web right web left flng*2 right flng*2 Zpz Tor. Rigidity Radius of G

378 378 20000 20000 40756 40181 41.8

565 565 35156 35156 71443 70545 52.9

796 796 56250 56250 114093 114863 63.9

696 696 20000 20000 41392 44338 82.3

792 792 50625 50625 102834 85572 83.0

1408 1408 120000 120000 242816 260437 86.2

1044 1044 35156 35156 72401 77454 103.7

2248 2248 218750 218750 441996 511279 108.2

1489 1489 50625 50625 104229 98715 124.1

3375 3375 337500 337500 681750 765000 130.5

2009 2009 84219 84219 172456 192785 146.8

5616 5616 581875 581875 1174982 1780145 152.2

2992 2992 130000 130000 265984 356763 167.9

4475 4475 360000 360000 728950 938533 168.7

7563 7563 840000 840000 1695126 2731775 174.5

17900 17900 1449429 1449429 2934658 12588083 181.6

6837 6837 405000 405000 823673 1366937 208.4

8561 8561 170000 170000 357122 906182 240.39864 9864 450000 450000 919728 1915648 247.6

Left web right web left flng*2 right flng*2 Zpz Tor. Rigidity

2125 2125 150000 150000 304250 506667 84.9

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b1 = 300

t1 = 25 plastic elastic

175.00 30000.035.00 5250000

Neutral Axis 175.00 175.0

20

t3=

N.A. X = 150.0

t4 = 15 N.A. = X + t1 = 175.00 mm

Yc = 137.5 mm C =

Yt = 137.5 mm T =

t2 = 25

b2 = 300 Zp = 2887500 mm3

, Wp

= 175.00 mm

1218750 mm3

TION MODULUS OF BOX SECTION

300

b3

=

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= 45000000 mm4

= 67500000 mm4

= 198437500 mm4

= 509375000 mm4

) = 2910714.286 mm3

kN-m

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Material properties

Material yield stress Fy

Young's modulus E

Material factor m

Weight input

Lift weight W

Rigging weight Wrw

Static hook load Wst


Horizontally directed force in plane of bumper Fh

Horizontally directed force out-of-plane of bumper Fl

Vertically directed force ( -ve for Tension) Fv

Nsd

Design Hydrostatic pressure Psd

Height of column Lc

No. of columns in a row n

Spacing between columns (average) Lb

No. of tie beams in one column

Permissible deflection 2*Lc / 200

Supporting bottom girder/beam

Unsupported length of supporting girder/beam lg

Moment of inertia of supporting girder/beam Ig

Section properties for column

D

219.08

Moment of inertia of CHS Ic

Elastic section modulus of CHS Ze,c

Plastic section modulus of CHS Zp,c

(Assumption:- Horizontal members checked for 2840mm span and found to be

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Radius of gyration of CHS i

Torsional rigidity of column Jt

Cross-section area Ax

Section properties for top beamD

141.3

Moment of inertia of CHS Ib

Section class

Tubular Sextion d/t

Weight of one column

Weight/ unit length of tie beams

Total weight on one column Wc

2Lb

Horizontal m

connecting c

Fh

D

Column

Column

Horizontal member

connecting columns

Lc

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Work done by horizontal force (Fh) WFh

Moment at a distance `xc` from top My,c

Elastic Strain energy developed in the column Wse,c

Elastic Strain energy developed in the beam Wse,b

From energy balance theory WFh

Fh*

Hence,

BMD for Column

xc

My,c

Col. location

My,b

Fh

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Design bending moment about member y-axis (in-plane) My,sd

Mz,sd

k in equation 3 & 4 relate to buckling in the y and z directions, respectively.

Reduction factors

For cantilever tubular member Cmy

For bottom fixed and top free to move for tubular member Cmz

Ic/Lc

Ig/Lg

GB

Hence from fig. 12-4 of N-004 (pg 72) k y

Here, k z

Calculation of material factor, M

(Assumption:Horizontal out-of-plane force being distributed among all

columns in a row equally.)

GA=

.

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Calculation of design axial compressive resistance, Nc,Rd

Critical elastic buckling coefficient Ce

Characteristic elastic local buckling strength fcle = 2*Ce*E*t/D

Hence, fy/ fcle

Characteristic local buckling strength f cl

fcl = = 355 N/mm^2

fcl = =

fcl = =

l = = 1.44

fc = =

fc = = 154.6027 N/mm^2

Design axial compressive resistance Nc,Rd = Afc/M

Calculation of design bending moment resistance, MRd

Characteristic bending strength fm

fm = = 478.6 N/mm^2

fm = =

fm = =

Design axial local buckling resistance Ncl,Rd= fcl* A / M

Euler buckling strengths corresponding to the member y - axis NEy

Euler buckling strengths corresponding to the member z - axis NEZ

Combined stress

Check 1

Design bending moment resistance MRd =

y

cle

yf

f

f0.274-1.047

clef

yf

yfW

Z

yy

fW

Z

Et

Df

58.213.1

yy

fW

Z

Et

Df

76.094.0

M

mWf

E

lf

i

k c

l

yf

228.00.1 l

yf2

9.0

l

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Check 2

Shear check

Design shear resistance VRd

Applied shear force VSd

VSd

VRd

Interaction shear and bending moment

My,sd

MRd

Mz,sd

MRd

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= 355N/mm

= 210000N/mm

= 1.0

= 20.0 T

= 200.0 kN

= 5.0 T (Assumed)

= 50.0 kN

= W + Wrw

= 250.0 kN

= 0.10 Wst (refer Table 18 of ISO 19901-6)

= 25.0 kN


= 12.5 kN


= 2.5 kN

= 0.00 kN/m^2

= 4015 mm

= 6 Nos.

= 2100 mm

= 4 Nos.

= 40.2 mm

= PG 200x200x15x25

= 550.00 mm

= 199327500 mm4

= CHS UR = 0.79

= 200 #80 UR = 0.61

d t

193.68 12.7 mm

= 4.40E+07 mm4

= 401730.8 mm3

= 541610 mm3

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= 73.1 mm

= 88011193 mm4

= 8234.2 mm2

= CHS 130 #80d t

122.3 9.5 mm

= 8.59E+06 mm4

= 17.3

< 33.1 (= 50^2) -----------> Tube is Class 1

= 0.65 kN

= 0.646 kN

= 6.1 kN

ember

olumns

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= Work done on col. + work done on tie beam

= Fh* /2 + Fh* /2

= Fh*

= Fh* x

=

=

=

= Wse,c+ Wse,b

=

=

= 31.86 mm

< 40.15 mm Hence OK

BMD for beam

Column

Fh

2Lb

Col. locationCol. location

My,b

My,b

dx2EI

xFdx

2EI

M L

0

2c

2h

L

0

2cy,

3

L

2EI

F 3c

c

2h

b

b2h

3c

c

2h

384EI

2LF

3

L

2EI

F 3

b

b2h

384EI

2LF 3

b

3b

c

3ch

24I

L

3I

L

2E

F

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= Fh* L

= 100.38 kN-m

= Fl* L /n

= 8.36 kN-m

= 1.0

= 0.85

10960

362414

= 0.03

=

= 2.0

= 1.0

=

.......4

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= 0.3

= 7304.2 N/mm^2

= 0.049

for f y/ fcle

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= 0.605 UR

= 0.603 UR

= 733.8 kN

= 37.5 kN

< 1.00 OK 0.60 UR

< 1.00 OK 0.05 UR

= 0.60

= 0.05

= 0.05 UR

= 1.16

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CHS

Section D tw d Iy Iz We

80 #80 88.9 7.62 73.66 1620938 1620938 36467

100 #80 114.3 8.56 97.18 4000262 4000262 69996

130 #80 141.3 9.5 122.3 8585789 8585789 121526

150 #80 168.28 10.97 146.34 16851647 16851647 200281

200 #80 219.08 12.70 193.68 44005596 44005596 401731

D Bf tw tf r Na

Built-up 300x300x10x15 300 300 10 15 18 150

K2 K3

K5

K2

186.9

1.0

0.23

Deflection = 31.86 mm

Strength

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Wp Jp Ax wt.

50489 3241875 1945.8 0.153

95918 8000523 2843.6 0.223

165313 17171578 3933.6 0.309

271908 33703293 5421.4 0.426

541610 88011193 8234.2 0.646

wt Wp We Web ht. Top fl Bot fl Top web Bot web

91.8 1499794 1328850 270 641250 641250 91125 91125

E = 210000 N/mm^2

G = 80769 N/mm^2

1 2.33E-03 + 1.71E-03 + 1.30E-03

K2

= 5.35E-03

Hence, K2 = 186.9 N/mm

: K5 : K3

: 428.3 : 186.9

: 2.3 : 1.0

: 0.53 : 0.23

=

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Na =

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Neutra

Neutra

Elastic secti

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strength

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Top RR Bot RR c Web c Flng. Ix Iy Zx Zy A

17522 17522 234 127 ######## #REF! 1328850 #REF! 11700

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Neutral axis depth

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b1 = 300

t1 = 15

b1 = 270 t 1 = 10

N

N.A.

t2 = 15

b2 = 300


l axis from top of plate = 150.00 mm 150 mm

Flange = 641250 mm3

168750 168750


3375 0

Web below N.A. = 91125 mm3

Flange = 641250 mm3

168750 168750

Total = 1464750 mm3

#REF! mm3


l axis from top of plate = 150.00 mm 150 mm

Flange = 91462500 mm4

######## mm4

web = 16402500 mm4

22500 mm4

Flange = 91462500 mm4

######## mm4

Total = 1.99E+08 mm4

######## mm4

n modulus, W = I/(D/2) = 1328850 mm3 #REF! mm3

Minor axis


Major axis

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Left web right web left flng*2 ight flng*2 Zpz Tor. Rigidity

3375 3375 337500 337500 681750 765000 130.5

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plastic elastic

150 11700

20 1755000

eutral Axis 150 150

X = 135.0

N.A. = X + t1 = 150.00 mm

Yc = 125.2 mm C = 5850 x syp

Yt = 125.2 mm T = 5850 x syp

Zp = 1464750 mm3

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Dia of top bar = 101 mm

Angle for weld = 120.0o

Actual weld length = 105.8 mm

Weld length for shear stress = 52.9 mm

Weld length for normal stress = 52.9 mm

Design horz. force along length = 25 kN

Design horz. force normal to length = 25 kN

Yield strength (of weaker part joined) = 235.0 N/mm^2

Material factor for welds = 1.3

Correlation factor = 0.8

Permissible stress = 226.0 N/mm^2

Weld size = 4.5 mm

Weld area for shear stress = 336.5 mm^2

Weld area for normal stress = 336.5 mm^2

Shear stress per unit length of weld = 74.3 N/mm^2

Normal stress per unit length of weld = 74.3 N/mm^2

Combine stress at location "1" = 148.6 N/mm^2

UR = 0.66

Combine stress at location "2" = 182.0 N/mm^2

UR = 0.81

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1

2

5.15 swing barrier v.1.0

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