Inter Girder 1

Design Forces for Intermidiate Girder  Design forces are taken from the STAAD analysis. Design is carried out for  maximum of the axial force/ shear force / Moments and corresponding remaining values. Sr.

Axial Forces (Fx)

Shear Forces (Hy)

Torsion

Bending moments

No.

PT (kN)

PC (kN)

Fy (k ( kN)

Fz (k ( kN)

Mx (kNm)

1

-16.208

0

0.766

0.052

0.003

-0.049

62.583

2

0

79.371

104.289

0

0

0

342.266

3

0

79.371

104.289

0

0

0

342.266

4

0

69.505

23.038

0.585

-0.011

-0.228

-169.266

5

0

77.378

101.772

-0.002

-0.011

0.001

331.878

6

0

67.795

5.942

0.474

-0.011

1.281

-210.776

7

0

79.371

104.289

0

0

0

342.266

My (kNm)

Mz (kNm)

Data : Span of beam

20 m

Unsupported length of compression flange :

1.5 m

(refer beams layout dwg )

Section properties in S.I Units Overall Depth of section ( mm) D

=

500

mm mm

Width of flange B (mm)

=

250

mm mm

=

16

mm

Flange thickness Tf  (mm) Web thickness tw (mm)

= 10 mm To account for corrosion allowance the flange thickness and web thickness are reduced by 2 mm Therefore for design purpose the thickness considered are as follows, Flange thickness Tf  (mm)

=

14

Web thickness tw (mm)

=

8

Web Depth d1 (mm)

=

468

=

10744

4

=

4.82E+08

4

IYY (mm ) RXX (mm)

=

3.65E+07

=

211.76

RYY (mm)

2

Sectional Area A (mm ) IXX (mm )

=

58.27

3

=

1.93E+06

3

=

2.92E+05

=

4000

=

5.38E+05

ZXX (mm ) ZYY (mm ) 2

Web Area Aw (mm ) 4

Torsional constant J (mm )

Check for the minimum web thickness: Cl. 6.7.3.1, IS : 800 – 1984, for unstiffened web, web thk is to be greater than 1), 2) but not< than 3) 1)

d1 * sqrt (tva cal ) / 816

=

2.9

468 * SQRT ( 26.07 ) / 816

(refer 5 : stress calculations for tvacal) 2)

d1 * sqrt ( fy ) / 1344

=

5.5

3)

d1 / 85

=

5.5

Web thickness provided 10 mm

468 * SQRT ( 250 ) / 1344 468 / 85

no stiffener reqt.

*For vertically stiffened web,  As per cl. 6.7.3.1.(b), IS : 800 – 1984, for vertically stiffened web, web thk is to be greater than 1), 2) but not less then 3) d2

468

1)

d1/180 =

2.60

2)

d2*sqrt(fy)/3200 =

2.31

3)

d2/200 =

2.34

Web thickness provided 10 mm

2.60 ok

Permissible stresses in the section : Permissible bending stress in the section ( bc ) Young's modulus (E) = 2.0E+05 MPa Slenderness ratio

= =

Leff  / Rmin ( 1.5 * 1000 ) / 58.269

= 25.743

Y

=

Y

=

3998.82

X X k1 k2 c1 c2

= = = = = =

3998.821 * ( SQRT ( 1 + ( 1/20 * ( ( 25.743 * 14 / 500 ) )^2 ) ) ) 4050.43 MPa 1 0 250 mm 250 mm

fcb fy n 1/n

= = = =

4050.43 345 1.4 0.71

sbc

=

sbc

2650000 (Leff / Ry)^2 MPa

MPa MPa [1]

0.66*4050.43*345

( (4050.43 ) ^1.4 + ( 345 ) ^1.4 ) ^ 0.714 = 222.66 MPa

Permissible stress in bending compression sbc = 222.67 For bending about minor axis, sbc = Permissible shearing stress ( t = t =

MPa

227.70

MPa

0.4 * fy 138

MPa

).

Permissible Direct Compressive stress in the section ( ac ) f cc

=

f cc

=

sac

=

3.14 ^2 * 200000 25.74 ^2 2978.62 MPa 0.6 * 2978.625 * 345 { ( 2978.625 ) ^ 1.4 + ( 345 ) ^ 1.4} ^ 0.714

sac

=

200.06 MPa

Permissible Direct Tensile stress in the section ( at) sat = 0.6 * fy sat = 207 MPa Permissible Bending Tensile stress in the section ( bt) sbt = 0.66 * fy sbt = 227.7 MPa

Stress Calculations : Sr. No.

 Axial Stresses (N/mm2)

Shear Stress (N/mm2)

Bending Stresses (N/mm2)

sat, cal

sac, cal

t Vcal

t Hcal

t Tcal

sbcY, cal

sbcX, cal

( PT / A )

( PC / A )

HY / AW

Hz / AF

T * t f /J

1

1.51

0.00

0.19

0.01

0.08

0.17

32.47

2

0.00

7.39

26.07

0.00

0.00

0.00

177.60

3

0.00

7.39

26.07

0.00

0.00

0.00

177.60

4

0.00

6.47

5.76

0.17

0.29

0.78

87.83

5

0.00

7.20

25.44

0.00

0.29

0.00

172.21

6

0.00

6.31

1.49

0.14

0.29

4.39

109.37

7

0.00

7.39

26.07

0.00

0.00

0.00

177.60

( MYY / ZYY ) ( MZZ / ZXX )

Interaction Checks : Combined axial compression and bending No.

sac,cal / sac s bcXcal / sbcx s bcYcal / sbcy Interaction ratio

Remark

1

0.000

0.146

0.001

0.15

< 1 ok

2

-0.037

0.798

0.000

0.76

< 1 ok

3

-0.037

0.798

0.000

0.76

< 1 ok

4

-0.032

0.394

0.003

0.37

< 1 ok

5

-0.036

0.773

0.000

0.74

< 1 ok

6

-0.032

0.491

0.019

0.48

< 1 ok

7

0.037

0.798

0.000

0.835

< 1 ok

Combined axial tension and bending No. at cal / 0.6 f  btYcal / 0.66 f s btXcal / 0.66 f  Interaction ratio

Remark

1

0.007

0.001

0.143

0.15

< 1 ok

2

0.000

0.000

0.780

0.78

< 1 ok

3

0.000

0.000

0.780

0.78

< 1 ok

4

0.000

0.003

0.386

0.39

< 1 ok

5

0.000

0.000

0.756

0.76

< 1 ok

6

0.000

0.019

0.480

0.50

< 1 ok

7

0.000

0.000

0.780

0.78

< 1 ok

Combined shear, torsion and bending No.

 s bcXcal + s bcYcal

(t Tcal + t Vcal + t Hcal)

qu va ent stress

Remark

1

32.642

0.284

32.6

ok

2

177.600

26.072

183.3

ok

3

177.600

26.072

183.3

ok

4

88.613

6.213

89.3

ok

5

172.213

25.730

177.9

ok

6 7

113.760 177.600

1.907 26.072

113.8 183.3

ok ok

Deflection check  Allowable deflection in beam Deflection available from staad

( 20 * 1000 / 600 ) =

33.33 mm 33.00 mm Hence OK