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8/3/2019 Tall Building Data Sheet
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Structures & Tall Buildings Data Page 1
A. REINFORCED CONCRETE DESIGN FORMULAE (For fcu 40 MPa)(Based on Hong Kong Code of Practice for the Structural Use of Concrete 2004, and moment
redistribution < 10%)
A1. Lever Arm (Singly reinforced section)
9.025.05.0 kdz
A2. Bending Reinforcement
,2
cufbd
MK
zf
MA
y
s87.0
For d/x < 0.43, compressive stress in steel = 0.87fy
ForK 0.156, compression steel required.
,'87.0
156.0'
2
ddf
fbdKA
y
cus
dzA
zf
bdfA s
y
cus
775.0and'87.0
156.0 2
Min. 18.0100
bh
As for bw / b < 0.4
Min. 13.0100 bhAs for bw / b 0.4
Max. 0.4100
bh
As
Min. 2.0'100
bh
As , Max. 0.4'100
bh
As
A3.1 Bending Moments for Two-way Spanning Simply Supported Slabs
22 and, xsysyxsxsx lnmlnm
A3.2 Bending Moments for Restrained Two-way Spanning Solid Slabs
and2
xsxsxlnm 2
xsysy lnm
A3.3 Loads on Supporting Beams of Restrained Two-way Slabs
andxvxsxlnV
xvysy lnV
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A4. Deflection
bprovs
reqsy
ss
tA
Aff
bd
M
fm
1
3
2,2
9.0120
47755.0
,
,
2
5.1'100
3
'100
1,
,
bd
A
bd
A
mprovs
provs
c
A5.1 Shear Reinforcement for Beam & Slab
yvv
sv
yv
c
v
sv
f
b
s
A
f
vvb
s
A
87.0
4.0,
87.0
,
A5.2 Punching Shear Reinforcement for Slab
cyv
csv vv
f
udvvA 6.1ewher
87.0sin
or cc
yv
csv vvv
f
udvvA 21.6ewher
87.0
7.05sin
in either case 87.0
4.0sin
yv
svf
udA
m
s
c
dbd
A
v
4/13/1400100
79.0
, m = 1.25;
bd
As100 should not be taken as greater than 3;
d
400should not be less than 0.67 for members without shear reinforcement,
d
400should not be less than 1 for members with shear reinforcement providing minimum links.
For characteristic concrete strengths greater than 25 N/mm2, the values ofvc may be multiplied by (fcu/
25)1/3. The value offcu should not be taken as greater than 80.
Note: All the terms and symbols bear their usual meanings.
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Structures & Tall Buildings Data Page 3
Table 1: Lever Arm Factor (b 0.9)
K= M/bd2fcu
0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.043 0.156
0.950 0.7750.941 0.928 0.915 0.901 0.887 0.873 0.857 0.842 0.825 0.807 0.789la = z/d
Table 2 Area of Steel Reinforcement
Steel Reinforcement
Bar Size Area of one Bar (mm2)
8 50.3
10 78.512 113
16 201
20 314
25 491
32 804
40 1257
Table 3 Area of Steel Reinforcement Per Meter
Table 4 Asv / sv Ratio for Shear Link
Steel Reinforcement - Area per one meter (mm2/m)
Bar Spacing
in mm
Bar
Size
100 125 150 175 200 225 250 275 300 350
8 503 402 335 287 251 223 201 183 168 144
10 785 628 524 449 393 349 314 286 262 224
12 1131 905 754 646 565 503 452 411 377 323
16 2011 1608 1340 1149 1005 894 804 731 670 574
20 3142 2513 2094 1795 1571 1396 1257 1142 1047 898
25 4909 3927 3273 2805 2454 2182 1964 1785 1636 1403
32 8042 6434 5362 4596 4021 3574 3217 2925 2681 2298
40 12566 10053 8378 7181 6283 5585 5027 4570 4189 3590
Asv/sv Ratio for Shear Link (2 legs)
Spacing of Links in (mm)
Link Size (mm)80 100 125 150 175 200 225 250 275 300 325 350
8 1.257 1.005 0.804 0.670 0.574 0.503 0.447 0.402 0.366 0.335 0.309 0.287
10 1.964 1.571 1.257 1.047 0.898 0.785 0.698 0.628 0.571 0.524 0.483 0.449
12 2.827 2.262 1.810 1.508 1.293 1.131 1.005 0.905 0.823 0.754 0.696 0.646
16 5.027 4.021 3.217 2.681 2.298 2.011 1.787 1.608 1.462 1.340 1.237 1.149
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Shear
Reproduced from Hong Kong Code of Practice for Structural Use of Concrete (2004)
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Deflection:
Reproduced from Hong Kong Code of Practice for Structural Use of Concrete (2004)
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Deflection:
Effective Flange Width
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Force Coefficients:
Table 6.5 Bending moment coefficients for slabs spanning in two directions at right
angles, simply supported on four sides
ly / lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0
sx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118
sy 0.062 0.061 0.059 0.055 0.051 0.046 0.037 0.029
Reproduced from Hong Kong Code of Practice for Structural Use of Concrete (2004)
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Structures & Tall Buildings Data Page 8
Two-Way Spanning Slabs:
Reproduced from Hong Kong Code of Practice for Structural Use of Concrete (2004)
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Two-Way Spanning Slabs:
Reproduced from Hong Kong Code of Practice for Structural Use of Concrete (2004)
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B. Design Formulae for Prestressed Concrete Structures
B1.1 Concrete Stresses at transfer:
'min
ftZ
iM
tZ
ei
P
cA
iP and '
maxf
bZ
iM
bZ
ei
P
cA
iP
B1.2 Concrete stresses at service:
maxf
tZ
sM
tZ
ei
P
cA
iP and
minf
bZ
sM
bZ
eiP
cA
iP
B2. Section modulus:
min'max ff
iMsM
tZ
and
minmax' ff
iMsM
bZ
B3. Prestressing force based on allowable stresses:
)min'max'
(
tZbZ
ftZfbZcA
iP or )min
max(
tZbZ
fbZftZcA
iP
The greater value of Pi obtained from the above equations should be used.
B4. Prestressing force and eccentricity:
)/(
min'
ec
At
Z
iMf
tZ
iP
iP
iMfZ
iP
cA
tZ
e
t
)
min'(
)/(
max'
e
c
A
b
Z
iMf
bZ
iP
i
P
iMfZ
iP
cA
bZ
e
b
)max'(
)/(
max
ec
At
Z
sMftZ
iP
i
P
sMfZiP
cA
tZ
e
t
)max(
)/(
min
ec
Ab
Z
sMfbZ
iP
i
P
sMfZiP
cA
bZ
e
b
)
min(
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Structures & Tall Buildings Data Page 11
B5. Prestress Loss:
B5.1 Relaxation:
Loss of prestress =1000 hr
relaxationx
relaxation
factorx
initial prestress
in steel
Table 1 Relaxation Factor
Wires and strands
Class 1 Class 2 Bars
Normal Relaxation Low Relaxation
Pre-tensioning 1.5 1.2 -
Post-tensioning 2.0 1.5 2.0
B5.2 Elastic Deformation:
I
eM
r
eA
Am
ff i
ps
c
pi
co
)1(2
2
at mid-span
Loss = m fco for pre-tensioned member
Loss = m fco for post-tensioned member with sequential tensioning
B5.3 Shrinkage:
CS = Cs kL kC ke kj in microstrains
Loss of prestress = CS Es
B5.4 Creep:
28E
fccc
= kL km kc ke kjLoss of prestress = cc Es
B5.5 Anchorage Draw-in:
p
pssad
A
AEx
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B5.6 Friction due to Curvature and 'Wobble' effect:
)(
0
KxR
x
x ePP or )](1[0 Kx
R
xPPx
R = L2
/ 8 dr
where dr
is the drape
B6. Moment Capacity:
Neutral axis depth trial: ' = (1 + 2c
s
F
F) /3
Strain in steel: 0.0035/x = p/(d-x)
B7. For unbonded tendons in rectangular section or flanged section in which stress block lies within
the flange.
bdf
Af
dl
ffcu
pspupepb 7.11
7000
df
f
bdf
Afx
pu
pb
cu
pspu47.2
B8. Shear Resistance
Uncracked Shear resistance:
tcp2tvco f0.8ffh0.67bV where ft = 0.24 fcu
Cracked Shear resistance:
cuv
0
vcpu
pe
cr fd0.1bthanlessnotbutVM
M
db)vf
f
0.55(1V
Mo =0.8 [fptI/y]
d)(0.87f
V-V
s
A
yv
c
v
sv if V - Vc > 0.4 b d
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B9. Deflection
Deflection due to uniformly distributed load :
EI
wLy
4
384
5 Deflection due to prestress force from straight tendon :
EI
PeLy
8
2
Deflection due to prestress force from symmetrical parabolic tendon profile: EI
LPey c
2
48
5
Table 2 Short Term Elastic Modulus of Concrete (Hong Kong)
Characteristic Strength Modulus of
at Age Considered (N/mm2) Elasticity (N/mm
2)
20 18900
25 20200
30 21700
40 24000
45 26000
50 2740055 28800
60 30200
Note: All the terms and symbols bear their usual meanings.
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C. Design Formulae for Water Retaining Structures
C1. Allowable steel stresses in direct or flexural tension for SLS (Table 3.1 of BS 8007)
Design crack width Allowable stress (N/mm2)
(mm) Plain bars Deformed bars
0.1 85 100
0.2 115 130
C2 Elastic design
Depth of neutral axis:
dxe
e
121
Level Arm3
xdz
Moment of resistance zfbxzfAM cbssr 5.0
C3.1 Crack width calculations (direct tension)
Steel: yss
ys ff
E
f8.0or
8.0
Average strain 21 m andssEA
T1 For a limiting design surface crack width of 0.2 mm:
ss
t
AE
hb
3
22
For a limiting design surface crack width of 0.1 mm:
2ss
t
AE
hb
The design surface crack width mcraw 3
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C3.2 Crack width calculations (flexure)
Concrete: cucb ff 45.0
Steel: yss
ys ff
E
f8.0or
8.0
Average strain 21 m and ss
E
f
xd
xh 1
For a limiting design surface crack width of 0.2 mm:
xdAE
xaxhb
ss
t
3
'2
For a limiting design surface crack width of 0.1 mm:
xdAE
xaxhb
xdAE
xaxhb
ss
t
ss
t
2
'or
3
'5.122
The design surface crack width
xh
ca
aw
cr
mcr
min21
3
Where222
22
csacr
C3.3 Crack width calculations (Temperature and moisture effects)
Crack width max21 sTTRw
C4. Critical Steel:y
ctcrit
crit
s
f
f
bh
A
C5. Maximum crack spacing:
cb
ct
f
fss
22max
For Type 2 deformed bar,b
ctf
f= 3
2
Note: All the terms and symbols bear their usual meanings.
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Typical value of T1 ( C ) for Hong Kong condition
Cement content
(kg/m3)
Steel Formwork 18 mm Plywood
Formwork
Winter Summer Winter Summer
300 12 18 20 28350 15 23 27 35
400 17 27 32 43
T2 = 20C in summer and 10C in winter
Restraint Factor R
Restraint condition Restraint Factor
R
External : Base cast onto blinding 0.2
Edge restraint in box typedeck cast in stages
0.5
Wall cast onto base 0.6
Edge element cast onto slab 0.8
Infill bays 1.0
Internal : 0.5