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:
Shear strength = N/mm2
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)
Height of signboard = mm
Spacing of post = mm= kN/m2
Width of post = mm
Size of proposed project signboard Type E
= 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
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
= kN (37% wind load for temporary works)
Design vertical loads:
Dead load
4.25 3.003.28
Concrete
15.45
Front View
1000
0.37
3000
Footing
12
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
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 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
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
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 : = = =
= = =
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
= 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. = 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
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
VR
15.45
22.82
F
144.0
1.5
71.48
=85.0
15.45= 5.50 >
30
0.9
27
Factor of safety against sliding
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
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/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
=
Factor of safety against overturning
=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)
Height of signboard = mm
Spacing of post = mm= kN/m2
Width of post = mm
Size of proposed project signboard Type G
= 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
UB Post= (for signboard)
Design Wind Load
= q x Cp xζ = kN/m2
Wind load on proposed signboard
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
= kN (37% wind load for temporary works)
Design vertical loads:
Dead load
Front View
1300
0.37
3000
Footing
30.29
Concrete
3.28 4.205.95
19
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
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 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
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
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 : = = =
= = =φ0.0077
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
= 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. = 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
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
2.40
349.37
34.88
2400 4200 1300
4.20 1.30 24.0
30
0.9
27
Factor of safety against sliding
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
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/m211.16 > 0
58.16 < 125
=349.4
-165.8
10.08 7.06
FootingConcrete
205.2
419.22.04 >
Factor of safety against overturning
=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
Shear 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
x x kg/m Grade S275 steel
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
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
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
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 : = = =
= = = 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
= 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. = 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