DESIGN CALCULATION OF PROJECT SIGN BOARDS … · BETWEEN ISLAND HOUSE INTERCHANGE AND FANLING ... - BS 6399: 1995, Loading for Building : Part 2 - Code of Practice for Wind Loads

OF

BETWEEN ISLAND HOUSE INTERCHANGE AND FANLING

(STAGE 1 - BETWEEN MA WO AND TAI HANG)

MARCH 2010

WIDENING OF TOLO HIGHWAY / FANLING HIGHWAY

CONTRACT NO.HY/2009/08

DESIGN CALCULATION

PROJECT SIGN BOARDS(TYPE C, TYPE E AND TYPE G)

Design Codes and References

- BS 5400: 2000, Steel, Concrete and Composite Bridge : Part 3 - Code of Practicefor Design of Steel Brdiges

- BS 5400: 1978, Steel, Concrete and Composite Bridge : Part 2 - Specificationfor Loads

- BS 6399: 1995, Loading for Building : Part 2 - Code of Practice for Wind Loads

- Structures Design Manual for Highways and Railways - Highways Department

- Code of Practice on Wind Effects, HK 2004

1.0

1

Design Notes and Data

- All structural steelworks shall be designed and constructed in accordance with BS5400 Part 3: Code of Practice for Design of Steel Bridges and General Specification forCivil Engineering Works (2006 Edition) and all Corrigenda and amendment publishedby Hong Kong Special Administrative Region.

- All structural steel shall be Grade S275 complying with BS EN 10025

- All electrodes used for welding to match Grade S275 steel shall be 42 electrodeto BS EN ISO 2560: 2005.

- Weldings shall be carried out in accordance with BS EN 1011 and welding consumableshall be complied with BS EN ISO 2560: 2005.

- All weldings to be continous fillet welds. Unless otherwise stated, size of weld tobe 5mm or equal to the thickness of the steel elements whichever is smaller.

- All cast-in bolts shall be Grade 8.8 to BS 3692 : 2001.

Structural Steel

All structural steel to be Grade S275 in accordance with BS EN 10025

Design strength of Grade S275 structural steel members and plates to BS EN 10025 shall have maximum Py of 275MPa for member thickness ofless than or equal to 16mm in conformance to BS 5400.

Density = kg/m3

Design strength = N/mm2

Shear strength = N/mm2

Poisson's ratio =

Modulus of elasticity = N/mm2E 2.05x105

2.0

γ 7850

Py 275

Pv 165

υ 0.3

2

Cast-in Bolts

Design strength of cast-in steel bolts and nuts of Grade 8.8 to BS3692 in conformance to BS 5950 are as follows:


Bearing strength = N/mm2

Tensile strength = N/mm2

Welds

For 42 electrode to BS EN ISO 2560: 2005

Design strength of weld = N/mm2

Pbb 1035

Pt 450

Ps 375

Pw 215

3

Design Loads

- Wind Load

Design Basic Wind Pressure = kN/m2

Solidity Ratio =

Refer to Cl. 2.7.6, BS6399: 1995 Part 2, for signboardDesign Net Pressure Coefficients =

The wind load should be taken as 37% of the design wind load (PNAP 224)

Design Wind Load:

Wind load = q x = x x = kN/m2

- Partial Factors of Safety for Loadings γfL

Wind load γfL =

=

=

Cp 1.8

0.37

1.05

1.1

Cp 1.8

3.0

q 1.82

ζ 1.0

1.211.82

1.4

mγ

3fγ

4

4.0 Design for Project Signboard

4.1 Design for Project Signboard Type C (1800 x 2550)

Height of signboard = mm

Spacing of post = mm= kN/m2

Width of post = mm

Size of proposed project signboard Type C

= mm (H) x mm (W)

Max eccentricity of sign plate N M

V

= mm (max)

Design lateral load:

Lateral wind load

Basic wind pressure

= kN/m2

Solidity ratio of the sign plate

=

Net Pressure Coefficients x x

Channel Post= (for signboard)

Design Wind Load

= q x Cp xζ = kN/m2

Wind load on proposed signboard

1800

1500

Proj

ect

sign

boar

d

Side View2550

Footing

1000Concrete

230 75

1000

1200

1.82

kg/m

3.28

2550 1800

e 0

q

3.28

e

Concrete

Cp 1.8

Wlateral

5050

1200

ζ 1.0 2550

75

Design wind load

25.7

Project

signboard

2500

2500

4775

WL = x x x

= kN (37% wind load for temporary works)

Design vertical loads: Front View

1000

0.37

1800

Footing

5.56

Concrete

3.28 1.802.55

5

Dead load

Weight of post = x x x

= kN/m

Weight of signage = x x + x

= kN

Design forces on vertical steel post (SLS)

Design axial load on each vertical post

= x + /

= kN

Design bending moment on each vertical post

= x ( -

= kNm

Design shear force on each vertical post

= /

= kN

V

5.05

4.78

2

2.550.50

2

1.80

0.50

25.7 9.81

N

M

4.97

5.56

0.50

10.50

2.78

5.56

1.00

4.84

10-3

4.84 2

) / 2

5.050.50

6

4.1.1 Check Section of Main Post for Signboard Type C

x x kg/m Grade S275 steel

Maximum bending moment x = kNm

Maximum shear force x = kN

x x kg/m

cm3 cm3 Ix = cm4

cm2 mm T = mm

mm

mm mm ry = cm

Grade S275 steel mm t

Nominal yield stress

σy = N/mm2

Classification of Trial Section

(Ref: BS5400 : Part 3, Cl.9.3.7)

Web

The depth between the elastic neutral axis of the beam and the compressive edgeof the web

= < =

Comprssive flange

The projection of the compression flange outstand

bfo = < =

The section is classified as

10.50 1.40

2.78 1.40

Compact

16

275

For

75

2750

For

Try 230

32.7

6.5

3.89Fvx =

D =

230 75

>=

278

151

12.5A = 230

x =u =tw = 17.3

2.35b = 37.5 d =

Zx = 239 Sx =

0.945

RSC

RSC

25.7

25.7

14.70Mx =

75.5 207

31.0 99

∴

2d

yww

355t28

σ

yffo

355t7

σ

7

Checking section at critical locations

Bending resistance(Ref: BS5400 : Part 3, Cl.9.9.1)

Bending resistance for a section is given by :

MD = where = the limiting compresive stress

= N/mm2

xx = =

= kNm = plastic modulus of the effective section

= cm3

Maximum design bending moment

kNm

kNm O.K.

Shear resistance(Ref: BS5400 : Part 3, Cl.9.9.2)

Shear resistance of a web panel under pure shear should be

VD = where tw = thickness of the web = mm

dw = D for rolled section = mm

hh = the height of the largest hole or cut-out if any. = mm

= limiting shear strength of the web panel determined from figures 11 to17 of BS5400 Part 3

Determination of : = = =

= = =φ0.0749

Mx = 14.7

275

1.05

Compact

66.2

MD

1.1

6.5

230

0

278

278 275

1.05 1.1= x 10-3

66.19

<

=

mfw 142.0bfe

50

∴

3fm

tcpeZ

γγ

σtcσ

mγ 3fγ

peZ

l3fm

hww )hd(tτ

γγ−

lτ

lτw

2weyw

2ffeyf

td2

tb

σ

σ

yff

355t10

σ

weda

8

= d for rolled sections=

= clear length of panel between= transverse stiffeners

= = =

VD = kN

Maximum design shear force

kN

kN O.K.

Combined bending and shear(Ref: BS5400 : Part 3, Cl.9.9.3)

For rolled sections

= = kNm

but not > MD

= kNm

= the distance between= the centroids of the two

flanges< O.K. = mm217.5

66.19

3.89 <

df

)

Fvx =

148.88

205.5- 1

MR

dwe

)(7.8

66.2+( 1 -

66.2

66.2

0.22

1.0

205.51

=14.7

205.51

VD

=

158.8

λ

20.446

= 1.0τy 158.8

a355td yw

w

weσ

y

l

ττ

3ywσ

lτ

∴

3fm

ffef dAγγ

σ

−

−+ 1

VV2

MM

1MM

DD

R

D

∴

9

4.1.2 Check Stability of Signboard Type C

Design lateral load on concrete footing V = kN

Design vertical load on concrete footing N = kN

Design moment on concrete footing M = kNm

Size of concrete footing = (B) x (L) x (H)

Weight of concrete block W = x x x = kN

Design vertical force N = kN

Total vertical force at base of concrete footing NT = kN

Check sliding

Assumed fill material under the concrete block

φ' = o γ = kN/m3

Angle of skin friction between soil and construction material: Rough Concrete

δs = φ' ( Geoguide 1 - Table 13 )

Angle of base shearing resistance

δb = o

Shear force between mass concrete block and soil

VR = x tanδb

= x

= kN

1.50

74.73

9.93

1500 1800 1000

1.80 1.00 24.0

30

0.9

27

Factor of safety against sliding

19

=

NT

74.73 0.510

38.08

=38.1

5.56= 6.84 >

VR

5.56

9.93

F

64.80

1.5

21.00

K.O∴

10

Check overturning

Take moment about back toe (Point A ) of the concrete blockM

Total overturning moment F

Mo = x + M

= kNm A

Total restoring moment

Mr = x / 2

= kNm

Check bearing pressure

Base area of footing A = x = m2

Modulus of footing Z = = m3

Maximum bearing pressure

Pmax =

= kN/m2 Allowable bearing pressure = kN/m2

Minimum bearing pressure

Pmin =

= kN/m2 kN/m21.75 > 0

53.61 < 125

=74.7

-21.0

2.70 0.81

FootingConcrete

26.6

56.12.11 >

Factor of safety against overturning

=74.7

+21.0

2.70 0.81

1.50 1.80 2.7

=

56.05

NT

=MrMo

NT 1.50

1500

10

00F 1.00

26.57

0.81

= 1.5

6LB2

ZM

+ANT

ZM

ANT -

K.O∴

K.O∴

11

4.2 Design for Project Signboard Type E (3000 x 4250)



Width of post = mm

Size of proposed project signboard Type E

= mm (H) x mm (W)


V

= mm (max)


Lateral wind load

Basic wind pressure

= kN/m2


=


Channel Post= (for signboard)

Design Wind Load



41.4

Project

signboard

2500

2500

5625

6750

2000

ζ 1.0 4250

90

Design wind load

Cp 1.8

Wlateral

3.28

e

Concrete

4250 3000

e 0

q 1.82

kg/m

3.28

300 90

1000

2000

3000

2000

Proj

ect

sign

boar

d

Side View4250

Footing

1000Concrete

WL = x x x


Design vertical loads:

Dead load

4.25 3.003.28

Concrete

15.45

Front View

1000

0.37

3000

Footing

12


= kN/m


= kN



= x + /

= kN


= x ( -

= kNm


= /

= kN

6.750.81

10-3

11.86 2

) / 21.00

11.86

7.73

15.45

N

M

11.41

15.45

0.81

35.74

4.250.50

2

3.00

0.81

41.4 9.81

V

6.75

5.63

2

13

4.2.1 Check Section of Main Post for Signboard Type E




x x kg/m

cm3 cm3 Ix = cm4

cm2 mm T = mm

mm

mm mm ry = cm



σy = N/mm2


(Ref: BS5400 : Part 3, Cl.9.3.7)

Web


= < =

Comprssive flange


bfo = < =


50.03Mx =

122.5 286

36.0 123

RSC

RSC

41.4

41.4

0.934

Zx = 481 Sx =

18.4

2.77b = 45 d =

A = 300

x =u =tw =

>=

568

245

10.82Fvx =

D =

300 90

15.5

90

7220

For

Try 300

52.7

9

16

275

For

Compact

35.74 1.40

7.73 1.40

∴

2d

yww

355t28

σ

yffo

355t7

σ

14





= N/mm2

xx = =


= cm3


kNm

kNm O.K.








= = =

176.1bfe

50

568 275

1.05x 10-3

mfw

568

275

1.05

Compact

135.2

MD

1.1

9.0

300

0

Mx = 50.0

1.1=

135.24

<

=

φ0.0392

∴

3fm

tcpeZ

γγ

σtcσ

mγ 3fγ

peZ

l3fm

hww )hd(tτ

γγ−

lτ

lτw

2weyw

2ffeyf

td2

tb

σ

σ

yff

355t10

σ

weda

15



= = =

VD = kN


kN

kN O.K.


For rolled sections

= = kNm

but not > MD

= kNm


flanges< O.K. = mm

1.0τy 158.8

a

158.8

371.15

VD

= 371.15

=50.0

135.2+( 1 -

135.2

135.2

0.37

1.0

)(21.6

371.2- 1

MR

dwe

23.959

314.98

)

Fvx =

284.5

135.24

10.82 <

df

λ

=

355td yw

w

weσ

y

l

ττ

3ywσ

lτ

∴

3fm

ffef dAγγ

σ

−

−+ 1

VV2

MM

1MM

DD

R

D

∴

16

4.2.2 Check Stability of Signboard Type E








Check sliding


φ' = o γ = kN/m3




δb = o


VR = x tanδb

= x

= kN

VR

15.45

22.82

F

144.0

1.5

71.48

=85.0

15.45= 5.50 >

30

0.9

27


19

=

NT

166.82 0.510

85.00

2000 3000 1000

3.00 1.00 24.02.00

166.82

22.82

K.O∴

17

Check overturning



Mo = x + M

= kNm A


Mr = x / 2

= kNm





Pmax =



Pmin =

= kN/m2 kN/m2

3.00

= 1.5

10

00F 1.00

86.93

166.82

NT

=MrMo

NT 2.00

2000

2.00 3.00 6.0

=


=166.8

+71.5

6.00 3.00

FootingConcrete

86.9

166.81.92 >

125

=166.8

-71.5

6.00 3.00

3.98 > 0

51.63 <

6LB2

ZM

+ANT

ZM

ANT -

K.O∴

K.O∴

18

4.3 Design for Project Signboard Type G (4200 x 5950)



Width of post = mm

Size of proposed project signboard Type G

= mm (H) x mm (W)


V

= mm (max)


Lateral wind load

Basic wind pressure

= kN/m2


=


UB Post= (for signboard)

Design Wind Load



4200

2400

Proj

ect

sign

boar

d

Side View5950

Footing

1300Concrete

356 171

1300

2800

1.82

kg/m

3.28

5950 4200

e 0

q

3.28

e

Concrete

Cp 1.8

Wlateral

8450

2800

ζ 1.0 5950

171

Design wind load

45

Project

signboard

2500

2500

6775

WL = x x x


Design vertical loads:

Dead load

Front View

1300

0.37

3000

Footing

30.29

Concrete

3.28 4.205.95

19


= kN/m


= kN



= x + /

= kN


= x ( -

= kNm


= /

= kN

V

8.45

6.78

2

5.950.50

2

4.20

0.88

45.0 9.81

N

M

17.44

30.29

0.88

82.92

15.15

30.29

1.30

19.96

10-3

19.96 2

) / 2

8.450.88

20

4.3.1 Check Section of Main Post for Signboard Type G




x x kg/m

cm3 cm3 Ix = cm4

cm2 mm T = mm

mm

mm mm ry = cm



σy = N/mm2


(Ref: BS5400 : Part 3, Cl.9.3.7)

Web


= < =

Comprssive flange


bfo = < =


82.92 1.40

15.15 1.40

Compact

16

275

For

171

12100

For

Try 356

57

6.9

21.20Fvx =

D =

356 171

9.7

>=

773

312.2

A = 352

x =u =tw = 37

3.77b = 85.5 d =

Zx = 686 Sx =

0.875

UB

UB

45

45

116.09Mx =

156.1 220

78.6 77

∴

2d

yww

355t28

σ

yffo

355t7

σ

21





= N/mm2

xx = =


= cm3


kNm

kNm O.K.








= = =φ0.0077

Mx = 116.1

1.1=

184.05

<

=

275

1.05

Compact

184.0

MD

1.1

6.9

352

0

773

x 10-3

mfw

773 275

1.05

110.2bfe

50

∴

3fm

tcpeZ

γγ

σtcσ

mγ 3fγ

peZ

l3fm

hww )hd(tτ

γγ−

lτ

lτw

2weyw

2ffeyf

td2

tb

σ

σ

yff

355t10

σ

weda

22



= = =

VD = kN


kN

kN O.K.


For rolled sections

= = kNm

but not > MD

= kNm


flanges< O.K. = mm342.3

184.05

21.20 <

df

λ

=

Fvx =

278.27

333.9- 1

MR

dwe

39.823

))(42.4

184.0+( 1 -

184.0

184.0

0.63

1.0

333.87

=116.1

333.87

VD

=

158.81.0

τy 158.8

a355td yw

w

weσ

y

l

ττ

3ywσ

lτ

∴

3fm

ffef dAγγ

σ

−

−+ 1

VV2

MM

1MM

DD

R

D

∴

23

4.3.2 Check Stability of Signboard Type G








Check sliding


φ' = o γ = kN/m3




δb = o


VR = x tanδb

= x

= kN

2.40

349.37

34.88

2400 4200 1300

4.20 1.30 24.0

30

0.9

27


19

=

NT

349.37 0.510

178.01

5.88 >=178.0

30.29=

VR

30.29

34.88

F

314.5

1.5

165.84

K.O∴

24

Check overturning



Mo = x + M

= kNm A


Mr = x / 2

= kNm





Pmax =



Pmin =

= kN/m2 kN/m211.16 > 0

58.16 < 125

=349.4

-165.8

10.08 7.06

FootingConcrete

205.2

419.22.04 >


=349.4

+165.8

10.08 7.06

2.40 4.20 10.1

=

419.25

NT

=MrMo

NT 2.40

2400

13

00F 1.30

205.22

= 1.5

7.066LB2

ZM

+ANT

ZM

ANT -

K.O∴

K.O∴

25

4.4 Fixing Design for Main Beam of Type G Project Signboard

4.4.1 Welding between members x x UBand steel base plate

Maximum bending moment at connection M = kNm (ULS)

Maximum vertical load at connection N = kN (ULS)

Maximum shear force at connection V = kN (ULS)

For x x kg/m thickness of web t = mmthickness of flange T = mm

Weld length L = 2 x + 2 x ( - ) + x

= mm

Inertia of weld Ix = (2 x x 2 ) + (2 x ( - )x( - )2 )

(2 x 3 ) /

x x

= x mm3 mm thick base plate

Load on weld due to shear 8 mm fillet weld all round

V x x

L 8 Nos. Grade

Holding down

= N/mm bolts

Load on weld due to moment & vertical load

M y NL

= x xx

= N/mm

Resultant load on weld

mm fillet weld, strength = x x

= N/mm > = N/mm

8.8

18.86

171

171 171 6.9

31

2.2

60

0

360

= 838.9 N/mm

+

171 45 UB 6.9

838.7

25.2 106

Ix

116.1 106 178

178 9.7

1232

1295

kg/m UBx

6.9

356 x

FR 838.9

0.7 8

45171

356 kg/m

Provide 8 220

FR =

171

356

45

21.20

116.1

24.4

178

312

9.7

2

12

312.2

+

16.4

171

600 360

FT =

FS =

25.2 106

M20

20

2T

2S FF +

K.O∴

26

4.4.2 Base Plate and Holding Down Bolt Design

Maximum axial compression at column base (factored) = kN (ULS)

Co-existing moment at column base (factored) = kNm (ULS)

Member size : x x

The cube strength of concrete under the base plate = N/mm2

Bearing strength of concrete

= x fcu = N/mm2

Provide x x andNos. holding down bolts

Assume that the maximum design strengths Moccur simultaneously in the concrete and steel. C

From the elastic theory of reinforced concretedesign, the depth to the neutral axis is given by

d1

d =

= modular ratio = tensile strength of holding down bolt

= = N/mm2

= mm = bearing strength of concrete

= N/mm2

xx +

= mm

The lever arm la = d1-dn/3 = - / 3

= mm

e

dn

60

122 N

a

d1 540

15 450

3606008

m

Grade

dn =15

M20

24.4

356 171 kg/m UB

116.1

N

45

dn/3

540

488.6

450

12.0

x 54012.0

Pcc

20 mm thick M.S. base plate

Pt

12.015

154.3

154.3

8.8

fcu 30

M

la

T

600

Pcc 0.4 12.0

Pmax

∴

1tcc

ccn d

PmPmP

d

+

=

27

Take moments about the centreline of bolts in tension:

C la = M + N a M = kNm N = kN

la = mm a = mm

= kN

The maximum compressive stress in concrete

Pmax = 2C/bdn = 2 x x 103 / ( x )

= N/mm2 < = N/mm2

The tensile force in holding down bolts is

T = C - N

= -

= kN

Tensile force per bolt = / = kN

Thickness of base plate

The moment in the base slab due to compressive force Consider a cantilever strip 1 x mm

Base pressure at section X-X

Px = ( - ) / x

= N/mm2

Mx = ( x x ) / 2 +( x x ) / 2

= kNm/mm = kNm/mN/mm2

The moment in the base slab due to bolt tension= N/mm2

Bolt load = 4 x = kN

C =

225.2

249.6

la

249.6

Pcc

249.6 360 154.3

488.6 240

8.99

M + N a

116.1

225.2

12.00

4

24.41

40.67

122.0

154.3

1.88 122.0

154.3 122.0

1.88

56.3 225.2

x

122.0

24.41

49.26

8.99 122.0 81.33

0.0493

Px 1.88

81.33

40.67

8.99

8.99

x

56.30

1.0 mmthickcantileverstrip

K.O∴

∴

28

M = x /

= kNm/mm = kNm/m

Thereforce, densign bending moment on base plate = kNm/m

The section of plate is 1mm wide x t mm thick

Z = t2 / 6

Assume that the thickness is not greater than 40mm

Py = N/mm2

Required thickness of base plate

t = ( 6 x / x )

= mm

Provided base plate thickness = mm

225.2 62.0 360

49.26

38.780.0388

19.5

20

275

49256.9 1.2 275

29

4.4.3 Holding Down Bolt Design

Use mm dia. steel bolts as holding downbolts for fixing the base plate

Tensile strength = N/mm2


Bearing strength = N/mm2

Design tensile force per bolt Ft = kN

Design shear force per bolt Fs = / 8

= kN

For steel bolts to BS 3692:2001

Tensile strength Ptb = N/mm2

Design tensile stress on bolt ft = (At = mm2 )

= N/mm2

< N/mm2

Shear strength Psb = N/mm2

Design shear stress on bolt fs =

π 2

= N/mm2

< N/mm2

Combined tensile and shear

<

Ptb

Psb

245

56.30

21.20

2.65

Grade

8.8

450

375

1035

8.8

20 Grade

M20

Pbb

450

Ft

229.8

450

245

= 0.53

1.4

375

4Fs

20

8.44

375

tb

t

sb

s

Pf

Pf

+

30

4.4.4 Check Minimum Anchorage Length of the Cast-in Anchor Bolt

The minimum bond length

where Ft = total factored tension in bolt

= kN

d = diameter (nominal) of bolt= mm

fbu = design ultimate anchorage bond stress

=

β = coefficient dependent on bar type and= for plain bar in tension

fcu = concrete cube strength on 28 days

= N/mm2

xx x

= mm

Provided anchorage length for cast-in bolt = mm

> I = mm

584.2

900

584.2

30

I = 56.30 103

3.1416 20 1.534

0.28

56.30

20

bu

t

dfF

Iπ

=

cufβ

∴

K.O∴

31

4.5 Design of Secondary Steel Beam( 102 x 51 x 10.42kg/m RSC ) w = kN/m

L = (max)

Loadwidth of beam = mm (max) S S

(R1) (R2)Design loads (ULS): L =

x

= x x x = kN/m

= x x x = kN/m

= x x x = kN/m

= x x x = kN/m

w = kN/m (ULS)

Bending moment (ULS)

Max. bending moment due to UDL ( w ):

= kNm

Shear force (ULS)

Max. shear force due to UDL ( w ):

= kN

1.4

-

-

-

Span 2800 mm

810

-

- - -

-

Uniform distributed loads (UDL):

10-3

--

W.L

--

-

1.92

8101.21

-

M =

1.35

-

V =

1.37

-

1.37

1.37

-

-

2800

102x51x10.42kg/m RSC

Bending Moment

-1.5

-1.0

-0.5

0.0

0 0.2 0.4 0.6 0.8 1

( x /L)

B.M

(kNm

)

Shear Force

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0.0 0.2 0.4 0.6 0.8 1.0

( x /L)

S.F

(kN)

wL21

⋅

2wL81

⋅

32

Reactions at supports

Reactions due to UDL ( w ):

= kN

=

Deflection (SLS)

Maximum deflection due to unfactored load

E = 2.05 x 105 N/mm2

I = cm4

5 x x 4

x x 105 x x 104

= mm

δ / span = /

= < 1 / =

=

0.00068 200 0.00500

207

207.0

1.90

1.90 2800

0.98 2800

384 2.0

RL = x

RL =

1.92

1.92 kN

1.37

1.37 2.80

2.80

RR = x

RR =wL21

wL21

×21

×21

EI384wL5

δ4

=

33

4.5.1 Check Section of Secondary Beam


Maximum bending moment kNm

Maximum shear force kN

x x kg/m

cm3 cm3 Ix = cm4

cm2 mm T = mm

mm

mm mm ry = cm



σy = N/mm2

Classification of Trial Section(Ref: BS5400 : Part 3, Cl.9.3.7)

Web


= < =

Comprssive flange


bfo = < =


32.9 194

19.4 60

RSC

RSC

10.42

10.42

1.35Mx =

0.9

Zx = 40.8 Sx =

1.48b = 25.5 d =

7.6A = 102

x =u =tw = 10.8

>=

48.7

65.8

1.92Fvx =

D =

102 51

51

207

For

Try 102

13.3

6.1

16

275

For

Compact∴

2d

yww

355t28

σ

yffo

355t7

σ

34





= N/mm2

xx = =


= cm3


kNm

kNm O.K.








= = = 50

11.6

<

=

mfw

48.7

x 10-3

bfe

275

1.05

Compact

11.6

MD

1.1

6.1

102

0

Mx = 1.35

48.7 275

1.05 1.1=

φ0.0944

86.3

∴

3fm

tcpeZ

γγ

σtcσ

mγ 3fγ

peZ

l3fm

hww )hd(tτ

γγ−

lτ

lτw

2weyw

2ffeyf

td2

tb

σ

σ

yff

355t10

σ

weda

35



= = =

VD = kN


kN

kN O.K.


For rolled sections

= = kNm

but not > MD

= kNm


flanges< O.K. = mm

a

158.8

λ

9.494

= 1.0

85.53

VD

= 85.5

=1.3

11.6+( 1 -

11.6

11.6

0.12

1.0

)(3.8

85.5- 1

MR

dwe

τy

17.42

)

Fvx =

94.4

11.60

1.9 <

df

158.8

355td yw

w

weσ

y

l

ττ

3ywσ

lτ

∴

3fm

ffef dAγγ

σ

−

−+ 1

VV2

MM

1MM

DD

R

D

∴

36

Documents

DESIGN CALCULATION OF PROJECT SIGN BOARDS … · BETWEEN ISLAND HOUSE INTERCHANGE AND FANLING ... - BS 6399: 1995, Loading for Building : Part 2 - Code of Practice for Wind Loads