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design built up column of eff length 5.9m It is sub to factored axial comp load of 2000 kN provide 2 channel back to back with battens by site welding used steel grade fe 410
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Given

L=5.9m = 5900 mm

Pu=2000×103N

required two channel back to back with battern & site welding γ mw=1.5

  1. Pu=Aea× fcd

2000×103=Area× 150

Area=13333.33mm2

Area of each section=13333.332=6666.67mm2

provide fcd=190mpa

Pu=Area× fcd

2000×103=Area×190

Area=1056.31mm2

Area of each section=10526.312=5263.15mm2

2) Provide ISMC 350

Aprov=5366mm2

γ xx=136.6mm         Ixx=10008×104mm4

γyy=28.3mm            Iyy=430.6×104mm4

Cyy=24.4

kLγ=5900136.6=43.19

λe=1.1×43.19

λe=47.51

40          198

47.51      fcd

50         183

fcd=186.74mpa

Pd=Ae× fcd

=2×5366)×186.74

Pd=2004.09kN> 2000 KN s safe

Step II

Ixx=Iyy

2[Ixx1+Ab2]=2[Ixx+Ah2]

[10008×104+0]=[430.6×104+5366(52+cyy)2]

S=218.99mm

S=220mm

Step III Sapcing between batten

cγyy<50 & cγyy<0.7λe

c<50×γyy

c<50×28.33

c<1415mm

c<0.7×λ×γyy

<0.7×97.81×28.3

<941.17

c=940mm

Step IV Size of batten

end batten

over all depth=eff depth d

d=s+2cyy

=220+2(24.4)

=268.8

D=270mm

thickness=150×s

=150×220

=4.4mm

provide 8mm

overlao=4× 8 =32mm

length provide 60mm

length=s+2 overlap

=220+2 60

=340mm

Intermedient

d=34d

=34×270

D=d=205mm

t=8mm

Step V check for shear stress

Vdt<fy3γmo

Vb=Vt×c2N

Vt=2.5 P4

2.5100×2000×103

Vt=5000NVt=50kN

shear stress=Vbd×t

69.12×103250×8

=42.15×131.26

safe

Vb=50×103×9402×(s+2overlap)=50×103×9402(5+260)

Vb=69.12×103N

Shera Stress=69.12×103270×8=32KN<fy3.γm=131.26

Step VI Check for bending stress=6mtd2

end batten

m==vt×c2N=50×103×9402(2)

m=11.75×106 N.mm

bending stress=6×11.75×1068×2702

=120.88mpa

<fyγmo=227.27

Intermedient

b. stress=6×11.75×1068×2052

=209.70mpa

< 227.27

Step VII

Connection

enter image description here

(rn)2=302+(2052)2

direct shera stress=(f1)=VbLw×t

=69.12×103530×1

f1=130.41N/mm

Torrtn stress(F2)=m.γnIP

IP=IXX+IYY

Ixx=2[60×t312+Ah2]+2[t×205312+0]

Ixx=2.69×106mm4

Iyy=2[1×60312+0]+2[25×t312+(205×)×302]

Iyy=405×103mm4

Ip=Ixx+Iyy

=2.69×106+405×103        rn2=(30)2+(2052)2

=3.0595×106mm4       γn=106.800

bending stress=m.rn2D

=11.75×106×106.83.095×106

cosθ=30106.8

f2=405.46N/mm

θ=0.28

Resultant stress=F21+F22+2F1F2cosθ

=130.472+405.462+2×130.42×405.46×γcosθ

R=459.37N/m--------eq A

force in p=Lw×FT.T×fu3γmw

459.37=1×(0.7×sw)4103×1.5

459.37=1×(0.7sw)4103×1.5

sw=4.16mm

sw=5mm

enter image description here

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