Beam Design IS800 2007

STEEL DESIGN AS PER IS 800 : 2007 Section

UC254X254X89

T

Forces in member (kN-m) bf  =

17.3 mm

t d1 D lx ly lz ky kz ry rz

10.3 200.3 260.3 4000 4000 8000 1 1 6.6 11

Perm. Slenderness

mm mm mm mm mm mm

 A  g  . f   y

P(Comp) I-Section

cm cm

0

F(tension) My Mz Vz Vy A Sy Sz Iy Iz

0 0 165 110 0 113 379 1096 4856.885 14270

D/W ky*ly/ry kz*lz/rz

1.01561 60.6 72.7

T/ T/t d1/t D/T It or J

1.67961 19.4466 15.0462 973210

Iw

7.2E+11

Roll ed ed or W el elded Section -(R/W ) ?

R

78846.1

Is beam laterally supported - (Y/N) ?

Y

Cantilever or Simply supported - (C/S) ?

S

fy

2.05E+05

Tdg =

mm Section

250

E (Mpa)

256.3

G (Mpa) 2568.182 kN

250

cm2 cm3 cm3 cm4 cm4

 mo

Pd =

 

1846.485339  kN 1846.485339 kN

RATIO 0.290909  Slenderness 0  Tension

1163.6206 kN

Compression Shear major

0  Compression 0.312676  Shear major 

 

278.1818182 kN.m

Shear minor

 

103.3636364 kN.m

Bending major

0.593137  Bending major 

Bending minor Comb Combin ined ed sect sectio ion n stre streng ngth th Comb. Bend. & Tension Tension - Major Major

0  Bending minor  0.59 0.5931 3137 37 Combined  Combined section strength 0.593137 0.593137 Comb.  Comb. Bend. & Tension - Major 

 Av

Vdz =

 

 mo

Vdy = Mdz = Mdy =

Item Slenderness Tension

 

f   yw



351.80 kN

3



Governing Condition : Ratio

Bending major  0.593137

0  Shear minor 

Comb. Bend. & Tension - Minor Comb. Comb. Bend. Bend. & Compre Compressi ssion on

0  Comb. Bend. & Tension - Minor  0.5931 0.593137 37 Comb.  Comb. Bend. & Compression

Properties - I Sections Desig-nation

hw bf tf tw (mm) (mm) (mm) (mm) R

MB 100

68

50

7

4.7

9

MB 125

91

70

8

5

9

MB 150

116

75

8

5

9

MB 175

137

85

9

5.8 10

MB 200

158

100

10

5.7 11

MB 225

177.4

110

11.8

6.5 12

MB 250

199

125

12.5

6.9 13

MB 300

245.8

140

13.1

7.7 14

MB 350

293.6

140

14.2

8.1 14

MB 400

340

140

16

8.9 14

MB 450

385.2

150

17.4

9.4 15

MB 500

431.6

180

17.2

10.2 17

MB 550

475.4

190

19.3

11.2 18

MB 600 UC254X254X89 WW F  

519.4

210

20.3

12 20

200.3 256.3

17.3

10.3 13

559.4

20.3

210

12

 

Iz h (cm4) (mm)

Sz (cm3)

Sy (cm3)

Zpz (mm3)

41680 183 100 36.6   5.16 445 125 71.2 11 81850 718 150 95.733 12.5 110480 1260 175 144 18 166080 2120 200 212 27.4 253860 3440 225 305.78 39.7 348270   5130 250 410.4 53.5 465710 8990 300 599.33 69.5 651740   13600 350 777.14 76.8 889570 20500 400 1025 88.9 1176180   30400 450 1351.1 111 1350700 45200 500 1808 152 2074670 193 2711680 64900 550 2360 252 3510630 91800 600 3060 379 1224000   14270 260.3 1096 89164 600   2972.1   299.2 3410046.2

Zpy (mm3)

Iy wt A (kg/m) (cm2) (cm4)

Ry

yt,b

yl,r

Iy

(cm) (mm) (mm) (cm4)

It or J (mm4)

Iw (mm4) Rz (cm)

9524.0

8.949

11.40

12.9

1.05 37.35 8.354

12.9 14651.85 315328125

4

20707.6

13.345

17.00

38.5

1.51 48.27 12.18

38.5 28768.33 1. 565E+09

5.16

23836.7 14.9935

19.10

46.8

1.57 57.56 12.48 46.875 31516.67 2.836E+09

6.13

34656.3

19.625

25.00

76.7

1.76 66.68 13.86

76.5

52106.2 6. 346E+09

7.13

52380.4

24.178

30.80

137.0

2.11

137 78395.56 1.504E+10

8.29

78.05

17.01

74739.1 31.1645

39.70

218.0

2.34 87.74 18.83 218.35 140005.7 2.975E+10

9.31

101889.5 37.2875

47.50

335.0

2.65 98.01 21.45 334.38 188767.4 5.738E+10

10.4

134358.4

46.001

58.60

486.0

2.86 116.1 22.93

486.5 253481.6 1.233E+11

12.4

146389.2 52.3595

66.70

538.0

2.84 133.3 21.95

537.6 326726.2 1.831E+11

14.3

165881.5

61.544

78.40

622.0

2.82 149.8 21.16

622.3 472529.4 2.697E+11

16.2

207103.3

72.377

92.20

834.0

3.01 168.2 22.46

832.5 646572.6 4.579E+11

18.2

294972.3

87.135 111.00 1370.0

3.52 187.1 26.57

1368 781397.5 9.742E+11

20.2

368261.4

103.62 132.00 1830.0

3.73 205.1

478840.4

122.46 156.00 2650.0

4.12 223.8 30.69

575000.0

88.705 113.00 4857.0

467753.4 119.625 152.39 3141.4

6.60

108

27.9 1833.5

1159146 1.553E+12

22.2

1505067 2.632E+12

24.2

51.3 4856.9 973210.1 7.166E+11

11

2646

4.54 223.8 30.69 3141.4

1505067 2.632E+12 24.189

Properties - Channel Sections Desig-nation

hw bf tf tw (mm) (mm) (mm) (mm)

ISMC75 ISMC100 ISMC125 ISMC150 ISMC175 ISMC200 ISMC225 ISMC250 ISMC300 ISMC350 ISMC400

43 66.6 89.6 112 133.6 155.2 176.2 197.8 246.8 295 339.4

40 50 65 75 75 75 80 80 90 100 100

7.5 7.7 8.2 9 10.2 11.4 12.4 14.1 13.6 13.5 15.3

4.8 5 5.3 5.7 6 6.2 6.5 7.2 7.8 8.3 8.8

Iz h R (cm4) (mm) 9 9 10 10 11 11 12 12 13 14 15

78.5 192 425 788 1240 1830 2710 3880 6420 10000 15200

75 100 125 150 175 200 225 250 300 350 400

Sz (cm3) 20.9 33.5 68.1 105 141 181 241 307 428 576 760

Sy (cm3) 4.81 7.71 13.4 19.5 23 26.4 33 38.5 47.1 57.3 67

Zpz (mm3)

Zpy (mm3)

24170 9686.0 43830 16240.0 77150 29450.0 119820 43520.0 161650 50150.0 211250 56620.0 277930 70430.0 356720 80640.0 496770 101000.0 672190 125400.0 891030 142400.0

Iy wt A (kg/m) (cm2) (cm4) 7.14 9.56 13.1 16.8 19.6 22.3 26.1 30.6 36.3 42.7 50.1

9.1 12.2 16.7 21.3 24.9 28.5 33.3 39 46.3 54.4 63.8

12.9 26.7 61.1 103 122 141 188 211 313 434 508

Ry

yt,b

(cm) (mm) 1.19 1.48 1.91 2.2 2.21 2.22 2.37 2.37 2.6 2.82 2.82

27.67 37.29 47.44 57.08 65.89 74.74 84.02 92.05 108.3 124.7 140.8

α

0.42 0.413 0.416 0.414 0.408 0.404 0.403 0.396 0.379 0.368 0.361

Iy

It or J

(cm4)

(mm4)

12.9 26.7 61.1 103 122 141 188 211 313 434 508

13063.32 18302.71 28714.81 43768.97 62803.58 85998.23 117017.4 172127.1 189691.1 221353.4 315653.3

Iw (mm4) Rz (cm) 311255411 1.291E+09 5.109E+09 1.376E+10 2.448E+10 4.031E+10 7.338E+10 1.181E+11 2.564E+11 5.098E+11 8.617E+11

2.94 3.97 5.05 6.08 7.04 8.02 9.02 9.92 11.8 13.6 15.4

Properties - I Sections Desig-nation

hw bf tf tw (mm) (mm) (mm) (mm) R

MB 100

68

50

7

4.7

9

MB 125

91

70

8

5

9

MB 150

116

75

8

5

9

MB 175

137

85

9

5.8 10

MB 200

158

100

10

5.7 11

MB 225

177.4

110

11.8

6.5 12

MB 250

199

125

12.5

6.9 13

MB 300

245.8

140

13.1

7.7 14

MB 350

293.6

140

14.2

8.1 14

MB 400

340

140

16

8.9 14

MB 450

385.2

150

17.4

9.4 15

MB 500

431.6

180

17.2

10.2 17

MB 550

475.4

190

19.3

11.2 18

MB 600 UC254X254X89 WW F  

519.4

210

20.3

12 20

200.3 256.3

17.3

10.3 13

559.4

20.3

210

12

 

Iz h (cm4) (mm)

Sz (cm3)

Sy (cm3)

Zpz (mm3)

41680 183 100 36.6   5.16 445 125 71.2 11 81850 718 150 95.733 12.5 110480 1260 175 144 18 166080 2120 200 212 27.4 253860 3440 225 305.78 39.7 348270   5130 250 410.4 53.5 465710 8990 300 599.33 69.5 651740   13600 350 777.14 76.8 889570 20500 400 1025 88.9 1176180   30400 450 1351.1 111 1350700 45200 500 1808 152 2074670 193 2711680 64900 550 2360 252 3510630 91800 600 3060 379 1224000   14270 260.3 1096 89164 600   2972.1   299.2 3410046.2

Zpy (mm3)

Iy wt A (kg/m) (cm2) (cm4)

Ry

yt,b

yl,r

Iy

(cm) (mm) (mm) (cm4)

It or J (mm4)

Iw (mm4) Rz (cm)

9524.0

8.949

11.40

12.9

1.05 37.35 8.354

12.9 14651.85 315328125

4

20707.6

13.345

17.00

38.5

1.51 48.27 12.18

38.5 28768.33 1. 565E+09

5.16

23836.7 14.9935

19.10

46.8

1.57 57.56 12.48 46.875 31516.67 2.836E+09

6.13

34656.3

19.625

25.00

76.7

1.76 66.68 13.86

76.5

52106.2 6. 346E+09

7.13

52380.4

24.178

30.80

137.0

2.11

137 78395.56 1.504E+10

8.29

78.05

17.01

74739.1 31.1645

39.70

218.0

2.34 87.74 18.83 218.35 140005.7 2.975E+10

9.31

101889.5 37.2875

47.50

335.0

2.65 98.01 21.45 334.38 188767.4 5.738E+10

10.4

134358.4

46.001

58.60

486.0

2.86 116.1 22.93

486.5 253481.6 1.233E+11

12.4

146389.2 52.3595

66.70

538.0

2.84 133.3 21.95

537.6 326726.2 1.831E+11

14.3

165881.5

61.544

78.40

622.0

2.82 149.8 21.16

622.3 472529.4 2.697E+11

16.2

207103.3

72.377

92.20

834.0

3.01 168.2 22.46

832.5 646572.6 4.579E+11

18.2

294972.3

87.135 111.00 1370.0

3.52 187.1 26.57

1368 781397.5 9.742E+11

20.2

368261.4

103.62 132.00 1830.0

3.73 205.1

478840.4

122.46 156.00 2650.0

4.12 223.8 30.69

575000.0

88.705 113.00 4857.0

467753.4 119.625 152.39 3141.4

6.60

108

27.9 1833.5

1159146 1.553E+12

22.2

1505067 2.632E+12

24.2

51.3 4856.9 973210.1 7.166E+11

11

2646

4.54 223.8 30.69 3141.4

1505067 2.632E+12 24.189

Properties - Channel Sections hw

Desig-nation

bf tf tw (mm) (mm) (mm) (mm)

ISMC75 ISMC100 ISMC125 ISMC150 ISMC175 ISMC200 ISMC225 ISMC250 ISMC300 ISMC350 ISMC400

43 66.6 89.6 112 133.6 155.2 176.2 197.8 246.8 295 339.4

40 50 65 75 75 75 80 80 90 100 100

7.5 7.7 8.2 9 10.2 11.4 12.4 14.1 13.6 13.5 15.3

4.8 5 5.3 5.7 6 6.2 6.5 7.2 7.8 8.3 8.8

Iz

h R (cm4) (mm) 9 9 10 10 11 11 12 12 13 14 15

78.5 192 425 788 1240 1830 2710 3880 6420 10000 15200

75 100 125 150 175 200 225 250 300 350 400

Sz (cm3) 20.9 33.5 68.1 105 141 181 241 307 428 576 760

Sy (cm3) 4.81 7.71 13.4 19.5 23 26.4 33 38.5 47.1 57.3 67

Zpz (mm3)

Zpy (mm3)

24170 9686.0 43830 16240.0 77150 29450.0 119820 43520.0 161650 50150.0 211250 56620.0 277930 70430.0 356720 80640.0 496770 101000.0 672190 125400.0 891030 142400.0

Iy wt A (kg/m) (cm2) (cm4) 7.14 9.56 13.1 16.8 19.6 22.3 26.1 30.6 36.3 42.7 50.1

9.1 12.2 16.7 21.3 24.9 28.5 33.3 39 46.3 54.4 63.8

12.9 26.7 61.1 103 122 141 188 211 313 434 508

Ry

yt,b

(cm) (mm) 1.19 1.48 1.91 2.2 2.21 2.22 2.37 2.37 2.6 2.82 2.82

27.67 37.29 47.44 57.08 65.89 74.74 84.02 92.05 108.3 124.7 140.8

α

0.42 0.413 0.416 0.414 0.408 0.404 0.403 0.396 0.379 0.368 0.361

Iy

It or J

(cm4)

(mm4)

12.9 26.7 61.1 103 122 141 188 211 313 434 508

13063.32 18302.71 28714.81 43768.97 62803.58 85998.23 117017.4 172127.1 189691.1 221353.4 315653.3

Iw (mm4) Rz (cm) 311255411 1.291E+09 5.109E+09 1.376E+10 2.448E+10 4.031E+10 7.338E+10 1.181E+11 2.564E+11 5.098E+11 8.617E+11

2.94 3.97 5.05 6.08 7.04 8.02 9.02 9.92 11.8 13.6 15.4

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

Prep. By

Date

Chkd. By

Date

:

Project : Subject :

1.0

Calculation of required plastic section modulus

Zp,req =

 M      mo

3

726000

=

mm

  f   y 2.0

Selection of suitable Section

Zpz

= 

1224000

mm

Zpy

= 

575000

mm

3

Section OK

3

Section Classification

ε =

250

b / tf / ε < 9.4 Plastic 10.5 Semi-Compact 15.7 Compact

1

=

 f   y b =

7 4075

;

d 

=

19 447

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

Prep. By

Date

Chkd. By

Date

:

Project : Subject :

1.0

Calculation of required plastic section modulus

Zp,req =

 M      mo

3

726000

=

mm

  f   y 2.0

Selection of suitable Section

Zpz

= 

1224000

mm

Zpy

= 

575000

mm

3

Section OK

3

Section Classification

250

ε =

1

=

 f   y b = t   f  

7.4075

d 

;

t 

b / tf / ε d / tw / ε

w

84 105 126

b / tw / ε < Plastic Semi-Compact Compact

Plastic

Thus, the section is 3.0

b / tf / ε < Plastic Semi-Compact Compact

19.447

=

7.4075 19.447

= =

9.4 10.5 15.7

Design Compression Strength of section

f cd

  f   y

=

  mo  

λ



(  2





Buckling Class

-

=

b c



0 . 5 (1    (  

f cdz =

163.40578

Similarly, for minor axis:

f cdy =

168.34007

(Refer Table 10; IS 800 : 2007)

(about major axis) (about minor axis) 

0 .2 )



 2 =)

0.9306

Mpa

λ =

(..major axis) 0.6740304

;

 lt  =

Mpa

Thus, design axial compressive stress

G-ENGG-008.006-F-00

Buckling Class a b c d

0.808836475

(major axis) (minor axis)

α = 0.34 α = 0.49

 lt 

Imperfection factor 

 mo

 2 ) 0 .5

2   f   y ( KL ) r  2    E 

=

 f   y

0.8432959

(..minor axis) =

163.40578

Mpa

α 0.21 0.34 0.49 0.76

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

Prep. By

Date

Chkd. By

Date

:

Project : Subject :

Design Strength

4.0

1846.4853

=

kN

Design Shear Strength of section Web is not susceptible to Shear Buckling;cl.8.4.1 is applicable

Vd

 Av  f   yw

=

351.80

kN

 Actual Shear force

=

110

kN

0.6*Vd

=

211.08

kN

=

 mo

5.0

3



Design capacity of the section Is V < 0.6Vd Md

=

Mdv

=

Mdv

=

?

  b  Z  p

Yes



  f   y

 M d    .( M d   Z  e





M   fd  )

  f   y

{Cl.8.2.1.2}

for plastic and compact section

{Cl.9.2.2.a}

for semi-compact section

{Cl.9.2.2.b}

  mo

=

Md

=

  b   Z  p  f bd 

f bd

=

  lt  . f   y  mo

1

  b . Z  p .  f   y



(laterally supported beams)

 mo

βb

 lt 

Thus,Cl.8.2.1.2 is applicable

(laterally unsupported beams)

Mcr 

;

 M cr 

Mcr 

=

 

0.549387235 = ≤ 0.5694869 Thus,   = 0.5493872

lt 

1013828038

=

(

  2 . E . I  y

N.mm

lt 

αlt

 lt 

= 

G-ENGG-008.006-F-00

0.21 2

0.5(1   lt  ( lt   0.2)   lt =)

0.687598827

2

 Llt 

)(G. I t  

{Cl.8.2.2}

  2 . E . I w 2

 Llt 

)

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

Prep. By

Date

Chkd. By

Date

:

Project : Subject :

  lt 



0.908200089

  lt 



0.908200089

f bd

206.409111

=

Mpa

Md

=

252.6447519

Md

=

278.1818182

Mdlaterally supp

=

6.0

Md - β (Md - Mfd)   kN.m 272.6161211 (for laterally supported)

278.1818182

kN.m

..(if V>0.6Vd)

(..major axis)

Section OK

?

130.6818182

Thus, Mdy

=

Is M < Mdy

?

kN.m

..(if V<0.6Vd)

103.3636364 kN.m

should be less than

103.3636364 kN.m

(..minor axis)

Section OK

Overall Section Strength

 N   N d  7.0

..(if V<0.6Vd)

298.9090909 kN.m

Mdv

Mdz =

Mdy = Mdy

(for laterally supported)

= = 278.1818182 kN.m

Therefore, Is M < Mdz

(for laterally unsupported)

kN.m

should be less than

For high shear condition; Thus, Md

kN.m



 M  y  M dy



 M  z  M dz 

=

 1.0

0.5931

Hence OK

Overall Member Strength (i) Bending and Axial Tension

Meff  = [ M   .T . Z ec A] Meff  =

0

  M d 

=

165

kN.m

kN.m

(..major axis) (..minor axis)

(ii) Bending and Axial Compression

 P   P dy

 P   P dz   K  y

G-ENGG-008.006-F-00

  K  y .

C my . M  y  M dy

 0.6. K  y .

  K lt 

C my. M  y  M dy

 M  z  M dz 

 K  z 

 1.0

C mz  M  z  M dz 

 1  (  y  0.2).n y  1  0.8.n y

 1.0

=

0.5931373

HENCE OK

=

0.5931373

HENCE OK

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

Prep. By

Date

Chkd. By

Date

:

Project : Subject :

 K  z 



1  (   z 

λz

=

nz

=

0

Kz

=

1

(1+nz) Kz

 K lt  λlt

0 . 2 ). n z  1  0 . 8 . n  z  λy

=

0.6740304

;

ny

=

0

;

Ky

=

1

0.8088365 ;

1  

= 1

=  1

=



(1+ny) Ky

;

0.1. lt .n y (C mlt   0.25)

=

 1

1

= 1

0.1.n y (C mlt   0.25)

0.5493872

Cmy =

1

(assuming that moments at both ends of member is equal)

Cmz =

1

(assuming that moments at both ends of member is equal)

Cmlt =

0.9

Klt

=

1

Klt

=

1

G-ENGG-008.006-F-00



1

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

:

Project : Subject :

G-ENGG-008.006-F-00

Prep. By

Date

Chkd. By

Date

Project No :

Calculation Number :

Aker Powergas Pvt. Ltd. Rev. Client

:

Project : Subject :

G-ENGG-008.006-F-00

Prep. By

Date

Chkd. By

Date