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DESIGN OF BEAM

Span of Beam ( L ) 10 m

Loads per m length

Live Load 0.750 kN/m

Self Weight of Section (ISMB @ 500) 0.869 kN/m

1.619 kN/m

Say 1.700 kN/m

Concentrated Load on beam ( W ) 120.000 KN

Totl UDL Including load factor = (1.5 x 1.7) = 2.55 Kn

Total Concen. load Including load factor = (1.5 x 120) = 180.00 Kn

BM due to UDL = 2.55 x 10^2 / 8 31.88 kN-m

BM due to Concentrated Load 450.00 KN-M

Max.Bending Moment 481.88 KN.M

= 2.55 x 10 / 2 12.75 kN

90.00 KN

Total SF at Support (V) 102.75 KN

Assume A Plate girder of the following Properties

820 mm

200 mm

10 mm

8 mm

810 mm

800 mm

Width of outstanding flange (b) 96 mm

Radius at Fillet or Root (R1) 0 mm

10 m

9.6 <13.6ε (Semi Compact)

100 <105ε (Compact)

As per Table 2 of IS 800-2007, the section is classified as Semi Compact

Section Properties:

997466667

13367466.7

2432845.53

Shear Force ( Vudl ) due to UDL

Shear Force ( Vpoint ) due to Concentrated load

Overall depth (D)

Width of flange (B)

Thickness of flange tf =

Thickness of web tw =

Centre to centre distance between flanges (hf)

Depth of web (dw)

Effective length of the Plate Girder (leff)

b/tf =

d/tw =

Moment of Inertia about z axis (Izz) mm4

Moment of Inertia about z axis (Iyy) mm4

Elastic Section Modulus (Ze) = Izz/y mm3

2900000

Shear Modulus (G) 76900 Mpa

Youngs Modulus (E) 200000 Mpa

250 Mpa

810 mm

0.5

2.193E+012

269866.667

130072042

2.16239632

0.490

0.451

1.109

251.9653295707

612992725.37172

35.2 mm

13700000

Elastic Section Modulus (Zec) = 1808700

Plastic section modulus (Zp) 2074670

Length of Span 10 m

Effective Length of Span l 10.00 m

800.00 mm

Slenderness Ration (KL/r) 284.09

81.00

250.00 N/mm2

-61.70 N/mm2

Plastic Section Modulus (Zp) = 2*bf*tf(D-tf)/2+tw*d2/4 mm3

Yield Stress of steel (fy)

hy = (D-tf)

βf (for symmetrical sections, the value is 0.5) =If/If+Iw

Wraping Constant (Iw) = (1-βf)*βf*Iy*hy2 mm6

Torsion Constant (It) = bt3/3 mm4

Elastic Critical Moment =Mcr

Slenderness Ratio (λLT) = SQRT (βp*Zp*fy/Mcr)

Imperfection factor αLT for welded section

ØLT

Strength reduction factor to account for lateral torsional buckling of beams (XLT)

Design bending compressive stress (fbd) as per Eqn. under Cl. 8.2.1 of IS 800, p.54

Design bending compressive strength (Md) = βbZp*fbd

Radius of gyration (ryy)

Moment of Inertia about y axis (Iyy) mm4

mm3

mm3

Depth of web ( d)

Ration of height to thickness (hf/tf ) =

Yield Stress (fy)

Critical stress fcr,b (As per table 14 of IS 800:2007)

for rolled steel section

From Table 13(a) in IS 800:2007

34.19

-128.01 KN.M

-8.79

Design Bending Compressive stress as per Cl. 8.2.2 of IS 800-2007, P.54

#VALUE!

0.21 for rolled steel section

#VALUE!

#VALUE!

#VALUE!

Section Classification

#VALUE!

From Table 2 in IS 800:2007; Limiting width to Thickness ratio

< 9.4ε

d/tw = < 84ε

So, The section is of Class 1 Plastic

For Plastic & Compact sections

Shear capaciy of the section 1.1

839.78 kN

> 102.75

0.6Vd > V

= #VALUE! kNm > 481.88

Md > M

#VALUE!

Check for Deflection :

Permissible Deflection 66.7 mm

Actual Deflection 82.2 mm

Imperfection factor αLT =

Critical stress fcr,b (As per formula) fcr,b= N/mm2

Yield stress (fy = ) N/mm2

Lateral Torsional Buckling (Mcr)

Design bending compressive stress (fbd) as per Eqn. under Cl. 8.2.1 of IS 800, p.54

N/mm2

Slenderness Ratio (λLT)


ØLT


Design bending compressive stress (fbd) N/mm2

ε = (250/fy)1/2

For rolled section b/tf =

βb=

where γmo =

0.6Vd =

Design Bending Capacity of the section (Md)

DESIGN OF CANTILEVER BEAM


Loads per m length


Self Weight of Purlin (ISMB @ 350) 0.524 kN/m

1.274 kN/m

Say 1.300 kN/m


w = 120.00

Including load factor = (1.5 x 1.3) = 1.95 Kn

Including load factor = (1.5 x 120) = 180.00 Kn

BM due to UDL = 1.95 x 5^2 / 8 6.09 kN-m

BM due to Concentrated Load 225.00 KN-M


= 1.95 x 5 / 2 4.88 kN

90.00 KN


Assume ISMB 200:

350 mm

140 mm

14.2 mm

8.1 mm


ryy 28.4 mm

Ixx 13600000

Zec = 779000

Plastic section modulus 889570

Length of Span 5 m

Effective Length of Span l 5 4.25 m

1.3 mm

0……….. mm

KL/r 149.65

24.65

163.46

for rolled steel section


163.46

145.41 KN.M

114.15

#VALUE!


#VALUE!

#VALUE!

#VALUE!


#VALUE!

=



Overall depth h

Width of flange b

Thickness of flange tf =

Thickness of web tw =

mm4

mm3

mm3

R1

Depth of web ( d)

h/ tf =

Critical stress fcr, b=


fy = fcr,b= N/mm2

Lateral Torsional Buckling (Mcr)

fbd = design bending compressive stress = N/mm2

Slenderness Ratio (λLT)


ØLT


Design bending compressive stress (fbd) N/mm2

ε = (250/fy)1/2

λLT = 1.2 Ze fy / Mcr


< 9.4ε

d/tw = < 84ε

Plastic 2

0.88 For self compact section

=

For Plastic & Compact sections


372.00 kN

> 94.88

0.6Vd > V

= #VALUE! kNm > 231.09

Md > M

#VALUE!

Check for Deflection :

Permissible Deflection 33.3 mm



So, The section is of Class 1

βb=

βb=

where γmo =

0.6Vd =

Design Bending Capacity of the section (Md)

DESIGN OF BEAM (As per Design Manual)


Loads per m length


Self Weight of Section (ISMB @ 300) 0.869 kN/m

Total Load 1.619 kN/m

Say 1.700 kN/m


Totl UDL Including load factor = (1.5 x 1.7) = 2.55 Kn

Total Concen. load Including load factor = (1.5 x 120) = 180.00 Kn

BM due to UDL = 2.55 x 5^2 / 8 7.97 kN-m

BM due to Concentrated Load wl/4 225.00 KN-M


WL/2 = = 2.55 x 5 / 2 6.38 kN

W/2 90.00 KN


Assume ISMB 500:

300 mm

140 mm

12.4 mm

7.5 mm

287.6 mm


28.4 mm

45390000

Youngs Modulus (E) 200000 Mpa

Elastic Section Modulus (Zec) = 1808700

Plastic section modulus (Zp) 2074670

Length of Span 5 m

Effective Length of Span l 5.00 m

1.3 mm

247.20 mm

Slenderness Ration (KL/r) 176.06

23.19

250.00 N/mm2


5.65 < 9.4ε

d/tw = 32.96 < 84ε

So, The section is of Class 1 Plastic

1.0 For Plastic & Compact sections

130.88 N/mm2

W =1.5w1

W =1.5w2

WL2/8 =



Overall depth (D)

Width of flange (bf)

Thickness of flange (tf)=

Thickness of web (tw)=

Centre to centre distance between flanges (hf)

Radius of gyration (ryy)

Moment of Inertia about y axis (Iyy) mm4

mm3

Zp = mm3

R1h - 2(tf + R1)

Depth of web ( d)

Ration of height to thickness (hf/tf ) =

Yield Stress (fy)


βb=

Critical stress fcr,b (As per table 14 of IS 800:2007)



138.01

250.00

271.53 KN.M

96.36

Design Bending Compressive stress as per Cl. 8.2.2 of IS 800-2007, P.54

1.382


1.579

0.427

96.99


1.00

=


243274.408881 243.27 kN

145.96 > 96.38

0.6Vd > V Safe

= 199915201.2 199.92 kNm > 232.97

Md > M

Unsafe

Check for Deflection : As per Table 6 of IS 800:2007

Permissible Deflection L/150 33.3 mm


Safe


Critical stress fcr,b (As per formula) fcr,b= N/mm2

Yield stress (fy = ) N/mm2

Lateral Torsional Buckling (Mcr) =βb*Zp*fcr,b

Design bending compressive stress (fbd) as per Eqn. under Cl. 8.2.1 of IS 800, p.54 N/mm2

Slenderness Ratio (λLT) =(fy/fcr,b)0.5


ØLT


Design bending compressive stress (fbd) =XLT*fy/γm0 N/mm2

ε = (250/fy)1/2

λLT = βb Zp fy / Mcr ≤ 1.2 Ze fy / Mcr

fy /fcr,b

Vd = fy* h * tw/ 3 */γmo = where γmo =

0.6Vd =

Design Bending Capacity of the section (Md) βbZp fbd =

(5/384) * ( WL^4/ EIxx ) +WL^3/48EI

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