Built-up Steel Beam 1k3hf

1 DESIGN OF MAIN BEAM Design wind load 0.16 kN/m^2 [As per IS 800- 2007] Analysis: DL = WL thr =

2

0.05 kN/m 2 0.16 kN/m

Purlin spacing = Main beam spacing= Loading on main beam: DL = 0.05 x 4 = WLthr = 0.16 x 4 =

-Thrust pressure (downwards)

1.2 m 4m 0.2 kN/m 0.64 kN/m

-UDL on main beam due to DL -UDL on main beam due to Thrust pressure

*Considering the loads acting on main beam as UDL instead of point loads that are transferred from purlin to main beam. Load Combinations for design: (As per IS 800-2007) 1.5 (DL+WLthr) = 1.40601 kN/m

-Acting downwards

UDL 1.2 m 8m Rf

Re Loading on the main beam and condition Spacing of purlins = No. of purlins =

1.2 m 7

-From the symmetry of the loading, the reaction force from beam are; Re = R f = -For the load case 1.5 (DL+WLthr), downwards 5.62404 kN

Bending Moment: Mmax = 11.248 kN-m

-For the load case 1.5 (DL+WLthr), downwards (Maxm. BM at section of the beam)

1

bf = 80

Trial Section:

tf = 4 BUILT UP SECTION (refer fig.) Grade: E 350 fu= 490 MPa fy=

dw = 150

350 MPa

tw = 4

tf, tw- thickness of flange & web respectively dw- clear depth of the web bf- width of the flange *All dimensions are in mm Sectional properties: A= H= rz=

1240 mm 158 63.0 mm

Zze=

2

3

3

3

3

Zzp=

9.73 kg/m

ry=

16.6 mm 8.6 x103 mm3 0.3421 x106 mm4

Zye=

62.3 x10 mm 4.92 x106 mm4

Iz=

m=

Iy=

Zyp= 71.780 x10 mm Y_ver= 57.887 X_hori= mm Zze,Zye- Elastic section modulus @ major & minor axes respectively

13.40 x103 mm3 10.8065 mm

Zzp,Zyp- Plastic section modulus @ major & minor axes respectively Iz,Iy- Second moment of area @ major & minor axes respectively rz,ry- Radius of gyration @ major & minor axes respectively D,t- Depth & thickness of the section respectively m- mass per unit length of the section Classification of section =√(250/ _ )

For I-sections: Plastic Compact 9.4ε 10.5ε 7.944 8.874 b/tf= 9.500

=

0.8452

Semi-compact 15.7ε 13.269

[ As per Table 2 of IS 800- 2007] b- outstand element of compression flange tf- thickness of the flange

.'. Section is

Semi-compact

2

βb =

0.868

Moment carrying capacity of the section Md- moment carrying capacity of the section

_ = _

_

_

zp- plastic section modulus for the given c/s fbd- design bending compressive stress

Calculation of fbd: _

/

_

=

72.243

h= tf =

154.0 mm 4 mm

h/tf =

h- c/c distace betwn. the flanges

38.50

fcr,b interpolation h/t LLT/r

35 38.5 70 485.5 478.85 72.243 455.4736 80 381.2 374.62 .'. fcr,b = 455.4736004

40 476 371.8 -Table 14 of IS 800- 2007

αLT= 0.49

-For Builtup steel sections

fbd interpolation fy .'. fcr,b 500 455.4736 450 .'. fbd =

350 203.55 195.0455 191.6 194 195.045 MPa

.'. Md =

340 200.9

360 206.2 196.4 -Table 13 (b) of IS 800- 2007

12.148 kN-m

-Moment carrying capacity of the section

Md >

SAFE

Mmax.

Stress Ratio=

0.926

where, M max. is maxm. bending moment in the main beam for the all possible load cases. Shear capacity of the section: Vu,max = 5.62404 kN

-For the load case 1.5 (DL+WL thr), downwards -Maxm. SF at section of the beam

_ =( _ × _ )/(ϒ_ ×√3)

Vd - shear capacity of the section fyw - yield strength of web of the section ϒmo - partial safety factor= 1.1 3

Av -Shear area of the section i.e web area for I-sectn. 2

Av =

600 mm

fyw=

350 MPa .'. Vd=

110.221 kN

0.6 Vd=

66.13 kN

.'. 0.6 Vd >

Vu,max

Hence SAFE

[As per Cl. 8.2.1.2 of IS 800- 2007]

Deflection: Load Combinations for serviceability: 1.0 (DL+WLthr) = 0.937 kN/m Δ_ =(5 _ ^4)/384 Δ_ = Δ_ =

-Acting downwards

-Maxm. deflection at any point in the beam for any possible load case (occuring at the mid-point of the beam)

50.800 mm span/150 =

-So, no reduction in moment carrying capacity is to be made

53.33 mm

Hence OK

4